Part 1 Seminar on Possible Responses of Weather Phenomena to Variable

NCAR LIBRARY

03422

. Proceedings of the Seminar on Possible Responses of Weather Phenomena to Variable Extra-Terrestrial Influences

Workshop, June 16 to July 28, Open Meeting, July 29 and 30, 1965 Boulder, Colorado

Ni,' .S 7

NCAR Technical Note, TN-8 NATIONAL CENTER FOR ATMOSPHERIC RESEARCH BOULDER, COLORADO 1965

NCARLibrary - V

5 0583 01011903 4 ERRATA

Page 23 -- Under the text figure the following is missing:

Time

Page 37 -- The second figure caption is missing:

Fig. 7 -- Sketch of a wind profile from Wallops Island that was obtained after a strong magnetic storm

The National Center for Atmospheric Research (NCAR) is dedicated to the advancement of the atmospheric sciences for the benefit of mankind. It is operated by the University Corpora- tion for Atmospheric Research (UCAR), a private, university-controlled, non-profit organization, and is sponsored and principally,funded by the National Science Foundation.

NCAR shares with other atmospheric research groups four interrelated, long-range objectives that provide justification for major expenditures of public and private funds: * To ascertain the feasibility of controlling weather and climate, to develop the techniques for control, and to bring about the beneficial application of this knowledge; * To bring about improved description and prediction of astrophysical influences on the atmosphere and the space environment of our planet; * To bring about improved description and prediction of atmospheric processes and the forecasting of weather and climate; * To improve our understanding of the sources of air contamination and to bring about the application of better practices of air conservation.

The research and facilities operations of NCAR are conducted in four organizational entities: The Laboratory of Atmospheric Sciences The High Altitude Observatory The Facilities Division The Advanced Study Program

All visiting scientist programs and joint-use facilities of NCAR are available to scientists from UCAR-member and non-member institutions (including private and government laboratories in the U.S. and abroad) on an equal basis. The member universities of UCAR are: University of Alaska Florida State University Pennsylvania State University University of Arizona University of Hawaii Saint Louis University University of California The Johns Hopkins University Texas A and M University University of Chicago Massachusetts Institute of Technology University of Texas Colorado State University University of Michigan University of Utah University of Colorado University of Minnesota University of Washington Cornell University New York University University of Wisconsin Proceedings of the Seminar on Possible Responses of Weather Phenomena to Variable Extra-Terrestrial Influences

Workshop, June 16 to July 28, Open Meeting, July 29 and 30, 1965 Boulder, Colorado

John E. Kutzbach, Editor Emmy H. Shakeshaft, Assistant

NCAR Technical Note, TN-8 NATIONAL CENTER FOR ATMOSPHERIC RESEARCH BOULDER, COLORADO 1965 Conference Sponsors:

Workshop, June 16 to July 28, 1965 - Sponsored by the Office of Naval Research and the National Center for Atmospheric Research.

Open Meeting, July 29 and 30, 1965 - Sponsored by the American Meteorological Society, the Office of Naval Research, and the National Center for Atmospheric Research. iii

FOREWORD

Every morning at nine, a small group of regular participants in our seminar climbed the hill to the same blackboard-walled classroom, underneath the telescope dome at the High Altitude Observatory, where many of us had similarly met nine years before to discuss closely related questions. There at HAO, for an hour and a half or more each morning, spirited discussions centered around an introductory and sometimes very informal paper aimed at some selected topic of the seminar. After this, each of us devoted the rest of the day to individual research projects, informal discussions, and other tasks.

This document was put together principally to remind those of us who participated, in months to come, of clues and ideas that emerged in the morning sessions. The collection was assembled from notes and tape recordings -- by John Kutzbach, who, with the help of Emmy Shakeshaft, worked diligently as seminar recorder. Each "kickoff" talk is covered, sometimes in detail, sometimes more sketchily.

The papers are not to be taken as formal or original publications. Much of the material is derived, and not new. Much is not yet ready for publication, but reveals us, instead, thinking out loud before a blackboard. In these instances the summary is nothing more than a transcript of an informal debate -- and thus there are gaps in coverage of important contributions from the literature, and there is sometimes no definitive thread of logic pervading the arguments. In spite of these shortcomings in the document, we have felt that many who could not attend our sessions would like to know something of what went on. We are glad, in this way, to share our sometimes all-too-random thoughts.

In the call to the seminar I quoted some brilliant and hortatory remarks of John R. Platt ("Strong Inference," Science, 146, No. 3642, 347-353, October 16, 1964). Platt urged people interested in things like the possible effects of anomalous solar radiation on weather to structure their thinking toward the development of chains of logical inference -- a process he called "strong inference." He urged, for complex systems like atmospheric science, that working hypotheses be developed, however speculative they might prove, so that systematic searches might be made, at each step, for alternatives and for critical tests to eliminate false elements of the tree of logic.

We did not really meet this goal -- though some of us now feel more prepared to try. But we did focus on constructing plausible mechanisms to explain assumed relationships, rather than on delineating empirical-statistical findings or conducting iv

arguments about whether or not such extra-terrestrial effects were "proven beyond reasonable doubt" instead of simply "strongly suggested," etc. The pages reflect, I think, some of this character. At least one "regular," whose contributions were of great value, remains convinced that the evidence is slender for a lunar influence on heavy rainfall occurrences -- even though to explain this was a prime target of our deliberations.

We divided up into three topic groups, with topic chairmen, as follows:

Topic A. Chairman: C. Rooth -- Interactions between different types of motions in a deep, stratified atmosphere

Topic B. Chairman: G. Brier -- Mechanisms involving the apparent influences of solar and lunar tidal forces on peak rainfall and other meteorological phenomena

Topic C. Chairman: W. O. Roberts -- Miscellaneous selected background or summary topics

This document is arranged to reflect the topic areas.

The long title of our seminar -- which went through several variants -- was quickly abbreviated to "extra-terrestrial influences." Thus, the sign on the top floor of Hallett Hall, where many of us had our offices, bore simply that legend, under which some anonymous wit, early in our sessions, boldly marked in "Like God?" But, of course, our discussions were not quite that inter- disciplinary.

The workshop was jointly sponsored, with NCAR, by the Office of Naval Research; the "wrap-up" meeting at the conclusion of the seminar was sponsored by the American Meteorological Society as well. We are grateful to these organizations. I want also to express deep appreciation to Glenn W. Brier, Claes Rooth, Paul Twitchell, Emmy Shakeshaft, and John Kutzbach, whose hard work went far toward making things a success. And, of course, many others -- full-term and occasional participants -- generously entered the spirit of our deliberations, and contributed magnificently.

Walter Orr Roberts v

PREFACE

The presentations and discussions at the workshop moved from one topic to another depending on such things as the availability of speakers, the time required for preparing material and the pre- ferences of the participants. The material has been reorganized for presentation here to obtain a more logical grouping. The three general topics of this seminar are strongly interrelated and in some cases the inclusion of a presentation or discussion in a particular section of these proceedings is rather arbitrary. The Table of Contents provides an additional brief outline of the subject matter. I vii

CONTENTS

Foreword ...... iii

Preface ...... v

Participants List ...... xi

Topic A

Interactions between Different Types of Motions in a Deep Stratified Atmosphere

Summary paper presented at open meeting, C. Rooth . . . . . 3

* Certain aspects of stratospheric-mesospheric circulations and dynamics

Global Circulations of the Stratosphere and Mesosphere, W. L. Webb ...... 13

Thermal Tidal Effects in the Upper Stratosphere and Lower Mesosphere, W. L. Webb ...... 21

Motions in the 80 to 100 Kilometer Region, A. Kochanski. . . 27

Photochemical Interactions near the Mesopause, C. Leovy. . . 39

* Suggested models for studying possible dynamic interactions between various levels in the atmosphere

Models for Studying Interactions between Various Layers of the Atmosphere, C. Rooth...... 41

Dynamic Interactions, P. D. Thompson ...... 43

* Results of experiments with numerical models of the atmosphere

Responses to Heating, E. N. Lorenz ...... 47

Models of Atmospheric Circulation, E. B. Kraus . . . . . 59

Effects of High Level Heating on the Large-Scale Circulation of the Lower Atmosphere, R. Shapiro...... 67 viii

Topic B

Mechanisms Involving the Apparent Influences of Solar and Lunar Tidal Forces on Peak Rainfall and Other Meteorolog- ical Phenomena

Summary paper presented at open meeting, G. Brier. . . . . 79

• Empirical evidence for the apparent influences of solar and lunar tides on meteorological phenomena; physical mechanisms are suggested

Apparent Influences of the Moon on Peak Rainfall and other Meteorological Phenomena, G. Brier ...... 87

Continued Discussions, Lunar Influences, G. Brier. . . . . 95

Possible Influences of the Horizontal Component of the Lunar Tidal Force on Large-Scale Circulation Features, J. Kutzbach...... 103

• Observed atmospheric tidal oscillations; specifications of the spatial and temporal variability of the gravitational component of the tidal forces

Atmospheric Tides, B. Haurwitz ...... 107

Variability in Gravitational Tidal Forces, T. R. Visvanathan...... 115

* Certain aspects of cloud physics, precipitation processes, and tropical convection

Physics of Clouds and Precipitation Processes; in Particular, Ways in which These Processes could be Modified by Tidal or Electrical Effects, P. Squires. . . .. 129

Tropical Convection, D. Lilly ...... 135

· Mathematical models for studying the occurrence of extreme events

Physical Mechanisms, Mathematical Models and Time Series, G. Brier and J. M. Mitchell ...... 141

Interaction between Tidal Forces and Atmospheric Processes, T. R. Visvanathan ...... 149 ix

Topic C

Miscellaneous Selected Background or Summary Topics

The Solar Inconstant, summary paper presented at open meeting, J. M. Mitchell...... 155

• Long-term solar/weather relationships

Climatic Evidence on Probable Physical Nature of Solar Disturbance of Climatic Patterns, H. C. Willett...... 175

· Short-term solar/weather relationships

Stratospheric Circulation and Auroral Activity, W. 0. Roberts ...... 189

Further Discussions on Noctilucent Clouds...... 199

Solar Corpuscular Emission Effects on the Terrestrial Atmosphere, K. D. Cole ...... 201

• Solar activity and radio noise; influences of the satellite lo on Jupiter's radio emissions

Solar Activity and Radio Noise, J. W. Warwick...... 215

Influences of the Satellite Io on Jupiter's Atmosphere, J. W. Warwick ...... 223

Participants in the Workshop on Possible Responses of Weather Phenomena to Extra-Terrestrial Influences

Dr. Louis Berkofsky Meteorology Laboratory (CRHD) Air Force Cambridge Research Laboratories Laurence G. Hanscom Field Bedford, Massachusetts

Dr. D. E. Billings Department of Astro-Geophysics University of Colorado Boulder, Colorado

Mr. Glenn W. Brier Meteorological Research Projects Branch U. S. Weather Bureau Washington, D. C.

Dr. K. D. Cole High Altitude Observatory Boulder, Colorado

Dr. John C. Freeman, Jr. National Engineering Science Company Houston, Texas

Dr. Michael Gadsden Central Radio Propagation Laboratory National Bureau of Standards Boulder, Colorado

Dr. Bernhard Haurwitz National Center for Atmospheric Research Boulder, Colorado

Dr. Paul R. Julian National Center for Atmospheric Research Boulder, Colorado

Dr. W. W. Kellogg National Center for Atmospheric Research Boulder, Colorado xii

Participants ......

Dr. R. W. Knecht National Bureau of Standards Boulder, Colorado

Dr. Adam Kochanski U. S. Weather Bureau Washington, D. C.

Dr. E. B. Kraus Woods Hole Oceanographic Institution Woods Hole, Massachusetts

Mr. John E. Kutzbach Center for Climatic Research University of Wisconsin Madison, Wisconsin

Dr. Conway Leovy The RAND Corporation Santa Monica, California

Dr. Julius London Department of Astro-Geophysics University of Colorado Boulder, Colorado

Dr. E. N. Lorenz Massachusetts Institute of Technology Cambridge, Massachusetts

Dr. J. Murray Mitchell, Jr. Laboratory of Climatology U. S. Weather Bureau Washington, D. C.

Mr. Jack NordO Meteorology Department Massachusetts Institute of Technology Cambridge, Massachusetts

Dr. Claes Rooth Woods Hole Oceanographic Institution Woods Hole, Massachusetts

Mr. Stanley Ruttenberg National Center for Atmospheric Research Boulder, Colorado xiii

...... Participants

Dr. Gerhard F. Schilling The RAND Corporation Santa Monica, California

Dr. Ralph Shapiro Meteorology Laboratory (CRHD) Air Force Cambridge Research Laboratories Laurence G. Hanscom Field Bedford, Massachusetts

Mr. John W. Sparkman, Jr. National Center for Atmospheric Research Boulder, Colorado

Dr. Philip D. Thompson National Center for Atmospheric Research Boulder, Colorado

Mr. Paul F. Twitchell Office of Naval Research Boston, Massachusetts

Mr. T. R. Visvanathan Northern Hemisphere Analysis Center Office of the Director General of Observatories New Delhi, India

Dr. James W. Warwick Department of Astro-Geophysics University of Colorado Boulder, Colorado

Dr. Guenter Warnecke Institut fur Meteorologie und Geophysik der Freien Universitat Berlin Germany

Mr. Willis L. Webb Environmental Sciences Directorate U. S. Army R&D Activity White Sands Missile Range, New Mexico

Dr. Hurd C. Willett Department of Meteorology Massachusetts Institute of Technology Cambridge, Massachusetts I TOPIC A

Interactions between Different Types of Motions in a Deep Stratified Atmosphere m 3

Summary Paper, Topic A

INTERACTIONS BETWEEN DIFFERENT TYPES OF MOTIONS IN A DEEP STRATIFIED ATMOSPHERE

Claes Rooth Woods Hole Oceanographic Institution

Introduction

The primary goal stated in the call to this conference was an ambitious one. It called upon us to build up chains of causal inference -- chains of working hypotheses and alternative series -- which could be beautifully documented, critically tested, and sorted out, one by one. I am afraid that in my topic particularly we have fallen short of this goal. Perhaps judging from some of the papers being presented in this special AMS Meeting, we should have held the six- weeks seminar at the close of the "Summary Meeting" instead of at the beginning. Perhaps in two years we will be able to make better progress than we have now. But we shall see.

The questions facing us during the recent weeks have brought to my mind something I read in a book on the foundations of mathematics. In an introductory chapter, devoted to the structure of sentences, the author defined the concept of a logically misleading sentence. He gave us, as an example, the proposition "Lions are real." The problem with this sentence is that it invites interpretation of the word "real" as a value judgment analogous to the word "fierce" in the proposition "Lions are fierce."

If we substitute the phrase, "anomalous extra-terrestrial influences on the weather" for the word "lion" in these two propositions, the same consideration pinpoints one of our major semantic difficulties in this conference.

Once a single lion has been spotted, no amount of weak statistics can make its existence any less real. But while a single unequivocal observation may have settled the question of existence of the effect, the ecological significance of lions could still be an unsolved problem approachable by a combination of theory and statistical inference, based on circumstantial evidence. 4

Summary Paper, Topic A ......

a process explains In terms of the problem at hand, the fact that in a body of data says only a fraction of 1 per cent of the variance provides an ampli- nothing about whether it occurs or not; it only the a priori condition tude estimate relative to other processes under never prove correctness of that it occurs. Statistical arguments can of the inferences can be the a priori assumption. But the strength process through physical enhanced by sharpening the definition of the to do in my section arguments. This is what we have at least attempted of the Seminar. Influences" On the Character of "Anomalous Extra-Terrestrial for extra- If we want to begin to talk about physical models to do is to define terrestrial influence, the first thing we have atmosphere is after all the relevant input forces to our system. The more or less closely a very complex thermodynamic machine with several that there are essen- interrelated energy processes, but we recognize two direct inputs to tially two primary inputs that you can have -- in one single statement, the dynamics. And they can really be combined relation to the gravity namely, the distribution of the mass field in field. in- This state of affairs can be perturbed by extra-terrestrial the gravity field, fluences by two means. Either we can perturb tomorrow that is, the tidal problem which will be the topic of can perturb the distri- morning's discussion by Glenn Brier, or we and cooling. I wish bution by thermodynamic processes of heating only to underline to speak here of the tidal-gravitational forcing, extra-terrestrial that it enjoys the unique position, among anomalous necessary accuracy. influences, of being known with more than the By these, Now let's speak about the thermal forcing effects. for the particular we understand departures from the mean value be rather appreciable calendar date, and these have been found to to satellite observa- in the thermosphere. We know by now, thanks in this terminology, tions, that very strong anomalous influences, and intensive di- exist up in the thermosphere. There is a strong that at times -- and urnal temperature fluctuation, and over-riding are the fluctuations certainly of a similar order of magnitude -- have been tied in quite in mean state over various time periods which example, well with fluctuations in solar activity. These show, for 120 km. The total in variations in the temperature distribution above is still, however, small amount of energy involved in these processes the troposphere. in relation to the mean heat flux passing through 5

...... Interactions in a Stratified Atmosphere

But whatever we do, it seems that we have no direct mechanisms available for applying a thermal forcing at low levels or for making it likely that any extensive thermal forcing at low levels occurs by direct external anomalous means. To the extent that low-level effects are occurring, they would either have to be dynamically coupled to thermal forcing at high levels, or be thermal effects which are caused indirectly by what goes on due to extra-terrestrial influence. Thus, it is conceivable that an important effect might occur, from the point of view of influencing lower-level circulation from above, if we were to invent a mechanism that would give us a modification of the transmission properties of the atmosphere, either by chemical changes, formation of haze layers, or by nucleation of cloud formation in particle-depleted humid air masses around the tropospheric level. Still another example of an indirect effect which has been suggested, but not given any detailed consideration by us, is the modulation of the transformation of latent heat to sensible heat by rainfall-triggering due to freezing nuclei of extra-terrestrial origin.

Even though we gave some consideration to the possibility that upper-level effects might be the result, rather than the cause, of phenomena in the lower atmosphere, we still have not put together any really solid models linking variations of the high atmosphere, where extra-terrestrial influences are known on some occasions to be significant, to the low atmosphere, where extra-terrestrial influences would be of great theoretical interest if they can be shown to exist.

The Forging of a Causal Chain

We had originally thought of planning the seminar in terms of building up trees of inference which might serve as a basis for sort- ing out these various inferences. We did not really attempt this until the last few days of the conference because of the bewildering variety of possibilities. If you want to forge a chain, and you find yourself sitting in a room with an assortment of possible links and not quite knowing how to put them together, it's very hard. Moreover, if the chain is to be useful, and to be plausible, it must not be too long, or at least it must not contain too many enigmatic links.

However, let me put up at least the skeleton of a "tree of inference," as a departure point for the balance of this discussion. I have done this in Fig. 1.

The significance of the symbols in Fig. 1 is as follows: The little arrows suggest possible, more or less direct, influences from the outside; the "6(T) ionosphere", below arrow C, suggests a change in temperature in ionospheric layers caused directly by some kind of 6

Summary Paper, Topic A ......

radiative influence from the outside. Now, how would that couple downward? It would depend on the scale of the heating. We know that in a rotating system, if we apply heating to a fluid in a limited region, what happens is to some extent dependent on the scale of the heating. If the scale is very large, then the primary adjustment will be the development of a geostrophic motion field. The smaller we make the heating scale, the larger is the influence of the mass flows in distorting the pressure fields caused by the primary influence, and finally we end up with the convection situation where a local element is just moving vertically upward without inducing any direct large- scale effects.

So this diagram is built, at the moment, on the notion that we are dealing with a reasonably large-scale effect.

In that case, the primary effects of the heating in the ionosphere would be a change in the stability, or vertical temperature structure of the mesopause region. This is the upper boundary for the mesospheric-stratospheric circulation. So we might look to whatever theories exist for the behavior of fluids bounded above by a stably stratified layer, and inquire to what extent the flows in the lower layer are likely to be modified by such a change in stability of the upper boundary layer. Some effects are bound to occur; we leave it open at the moment how large they are going to be. ' That brings us to the symbol "6(\V) mesosphere-stratosphere," meaning some kind of changes occurring in the circulation in the mesosphere-stratosphere region. The reason why I'm developing the chain in this particular manner is that the indications are (both from thermodynamic and dynamic observations) that we can split the dynamic problem into a three-layer cake with one division probably somewhere just above the mesopause and another division down at what Willis Webb likes to call the stratonull, at 25 km. The upper division may be at 85 or 90 km, I don't know exactly where the dynamic crossover from dynamic control from below to major dynamic control from above would be.

There are analogies between the 85 km interface and the 25 km interface. Perturbations here (mesosphere-stratosphere) might exert an influence in the geographic distribution of ozone which could have a similar effect on the tropopause structure, as the changes in the ionospheric radiation absorption could have on the mesopause structure. Thus we see that the problems associated with the behavior of fluids bounded above by stably stratified layers appear twice. 7

...... Interactions in a Stratified Atmosphere

The kind of reasoning described to this point might be relevant for seasonal or climatic type influences.

Now looking to the left of Fig. 1, let us consider an anomalous input at point A -- leading to an alternative route of influence to the atmosphere below.

Although I find it very difficult to consider that a small anomalous extra-terrestrial input could have the effect postulated here, at least it is one that we discussed in the closing days of the seminar. And even though it is improbable, it has some features that are subject to experimental checks. In this chain, some mysterious and admittedly completely unknown event, such as auroral secondary X-rays, penetrates down to a level shown by "6 nuclei concentration," where through some process yet to be understood, the number of nucleating particles is altered in such a way that a change in cirrus cover occurs, shown by "6 cirrus". In this speculative mechanism, cirrus level heating then occurs from the steady infrared radiative source from the surface of the earth, below. This changed blanketing reduces the heat supply to higher levels, resulting in a 6T in the ozonosphere.

One might say that it might be possible to show a downward influence from the cirrus blanket itself to the lower interface, resulting in a "6(\V) -- troposphere change, though I have not drawn the line for this possible link.

A more attractive alternative mechanism might involve the in- jection of anomalous extra-terrestrial energy, presumably solar near-ultraviolet, at Point B in the ozonosphere. This would produce a direct temperature change in the ozonosphere, which would feed into a change in the mesospheric velocity field, as shown by the line extending to "6(\V) mesosphere-stratosphere". This would start again this cycle, if the region heated were large. However, alternatively, one might think of this process produced by a rather localized heating also, and a different scale of process might result, as follows:

On an intermediate scale, we could have appreciable mass field readjustment, in addition to the dynamic reactions, and hence a creation of a pressure perturbation which would allow dynamic coupling downward, through essentially gravitational-inertial effects. In this way one can go on, building more and more linkages. Of course, one could turn many of these processes around, and consider dynamical linkages upward. In some ways it may be more plausible to think that parts of the variability at high atmospheric levels may 8

Summary Paper, Topic A ......

result from tropospheric velocity field anomalies, and have nothing to do with anomalous solar radiation -- but may simply be superimposed on the well-known anomalous solar radiation influences in the ionospheric levels.

The problem with this kind of reasoning at the moment, as I indicated, is that we have very little information with which to pin down various assertions. In order for this type of reasoning to be meaningful, we should be able to fill in all kinds of possible linkages here, then go either to existing dynamic models or to existing observations and decide, "proposition A ruled out because of such-and-such," etc. We cannot do that at the moment, but I feel that we are not too far away from being able to check and to provide checks on many of these links. Some of these are closer than others, for instance, the question of the influence of changes in stability in a stably stratified layer on the motion field below is something which has been put into numerical forecasting models. But to my knowledge, systematic investigation of the effects of variations in temperature in the topping layer which would allow us to quantify that effect and make definite statements about what a 100 temperature change would do to the circulation below, are not immediately available. One might see something in experiments that people have done, but to my knowledge nothing systematic has been done to provide direct quantitative relations in terms, say, of statistics of the motions below to be expected with various conditions of the state above.

It seems particularly worthwhile to commend continuation of approaches like that of Shapiro and Berkofsky, in which various models of heating are introduced into the atmosphere, and then numerical forecasts are made, with and without the heat source, for comparison with each other and also for comparison with real meteorological situations. Numerical experiments of this sort can be very fruitful in filling out an inferential chain like the one schematically suggested here.

The model experiments of Lorenz and Kraus, a couple of years ago, also have promise in this regard, and should be extended. They were concerned with internal stability in a two-layer model, and the calculations would have substantial relevance to what goes on at the two interfaces shown here in our diagram.

One should further note that a great deal of work is going on in the process of ozone formation, distribution, and heating. This is clearly of high importance, and merits attention from several 9

.•...... •.•.•.•.•..Interactions in a Stratified Atmosphere

regards, as suggested by our schematic diagram. We particularly need to know what the direct forcing in the ozone level is -- radiational, chemical, etc.

Then there is the question of the internal dynamics of the mesospheric and ozonospheric layers. We wonder whether present numerical models for prediction are suitable. Recent rocket observations, and other soundings at high levels, have indicated that there are large diurnal and semi-diurnal variations, so that the diurnal and semi- diurnal oscillations of the wind are of such magnitude that we probably have to consider direct interactions between motions on the time scale of 12 and 24 hr with the meteorological flows. This could possibly be handled with primitive equation models of the type that have been used in the past by Schumann at the Weather Bureau. This might be an extremely profitable way to look at some of these mechanisms. Moreover, it might be interesting for Schumann to put into his present models some tidal forcing terms, and see what influence these have.

Concluding Comments

I can only say that there is much still to be done in attempt- ing to make more specific and quantitative the mechanisms at individual steps in the chain. There is much to be done in the way of collecting information, developing techniques for observing critical steps, and in applying more sophisticated or more relevant model calculations. But it seems clear, at the very least, that we know now that savoring the cake involves tasting all three layers of it.

There are many useful things to be done for one who is too impatient to wait until the whole cause-effect chain of events from the top to the bottom can be completed. Individual steps to get us from point one to point two can be speculated about, and experiments can be done to check them.

To be specific, one of the mechanisms suggested in our seminar involves an effect of the aurora to produce changes in the ability of supercooled water vapor near the lower stratosphere to freeze and thus produce cirrus clouds and, from that, infrared blanketing. It is clear that a direct test could be made to find out, from existing cloud observational data, whether there is any tendency for cirrus cover, in appropriate geographical regions, to be more abundant following strong displays of auroral activity. Such a step, even though it is only the connection of a pair of links in a chain, still could be of great interest, and give confidence that this particular link is a significant part of the whole scheme 10

Summary Paper, Topic A ......

examples of this kind of things. And there are any number of other of link-pairing that could be done.

a list of In the section headed by Glenn Brier, we prepared out would be relevant topics meriting further study, which if worked to connect the to the construction of an over-all tree of inference significant meteoro- seemingly infinitesimal gravitational forces to logical tropospheric events. a com- Though we have failed in our objective to put together emerging at least prehensive scheme for research, I think we can see -- though some plausible, possible, avenues of physical connection -- between the we may not know whether the flow is upward or downward and the levels levels of the atmosphere belonging to the aeronomers belonging to the meteorologists. 11

. t .. I..s .. . Interactions in a Stratified Atmosphere

LARGE SCALE E FF ECTS (SEASOJAL... Oi. CUM\ATIC) C

SMAL/ SCALE () (TI I oODSPH

sY.O OPTI C)rF=E - !

I (T)OtOOSPHe|. 0

/// VS(03) LOW STRA7OSPEpe g NkUCLe C~r)CoJ7^ATIOcTz T-ROPO~f A E 5 TR UCTU R e S (C URRU) TROP O'PA SES

O (RADTIAl-r0t o uD6T) (\V) TRoPOSPHLE E TRoPSOP5PH6E1

IRE.CT b/JAMIC Ll UK. DOWJ )\AvPO FO, SMALL SCALES

Fig. 1 -- Diagram of speculative claims for interaction between the upper and lower atmosphere. Alternative extra-terrestrial inputs are labeled A, B, and C. I 13

GLOBAL CIRCULATIONS OF THE STRATOSPHERE AND MESOSPHERE

Willis L. Webb White Sands Missile Range

Climatology of Zonal and Meridional Circulations

I will briefly describe the climatology of global circulations of the stratosphere and mesosphere based on data obtained by the Meteorological Rocket Network (MRN, Fig. 1) over the past six years [1]. Much of the material presented can be found in Refs. [2] and [3].

Based on the character of the annual variations in zonal and meridional flow (Figs. 2 and 3) in the vicinity of the stratopause (about 50 km, for climatological purposes) the year can be divided into six periods:

1. Summer -- 15 June to 15 August -- easterlies (v50 mps)

2. Fall reversal -- 15 August to 15 October -- easterlies to westerlies

3. Early winter -- 15 October to 15 December strong (100 mps) 4. Winter storm period -- 15 December to 15 variable February westerlies

5. Late winter -- 15 February to 1 April -- moderate westerlies

6. Spring reversal -- 1 April to 15 June -- westerlies to easterlies

In most of these periods the gross features can be explained in terms of the geometry of solar heating. However, certain lag effects must be considered. For example, the fall reversal from easterlies to westerlies in midlatitudes occurs within a day or two of the autumnal equinox, while the spring reversal from westerlies to easterlies occurs about 40 days after the vernal equinox. Because of this lag, there is a period of about 40 days when winds are westerly over the entire globe. The winter storm period from 14

Willis L. Webb .. ..

During mid-December to mid-February is of particular interest. inter- this period the zonal flow is disrupted as a result of the action of the hemispheric flows as summer easterlies cross equator into the winter hemisphere to the 15 to 20 latitude band (giving rise to a semi-annual oscillation at the tropical "shear stratopause). Disturbances (cyclonic) forming along this from zone" between easterlies and westerlies appear to propagate pole, subtropical stratopause levels downward toward the winter producing gross reductions in speed of the zonal circulation warming" (Fig. 2) and large meridional flows (Fig. 3). "Sudden these phenomena appear related to the size and intensity of large disturbances, representing the special case of a very and intense eddy in this shear zone. These inter-hemispheric in the dynamic interactions give rise to a semi-annual variation for tropical stratospheric flow, as illustrated by the data Ascension Island in Figs. 2 and 3.

There is some indication that two distinct circulation easter- regimes are involved in the establishment of the summer in the lies. The easterlies appear first in the polar region to merge ionosphere and gradually work downward and equatorward with the dominant low-latitude easterlies in the stratosphere (see Fig. 4 derived from data contained in Fig. 2).

Evidence for a Meridional Cell

Analysis of MRN data shows a net mid-latitude convergence dur- of stratospheric mass toward the poles at the stratopause implied ing summer. Vertical motions at high latitudes are that the (on the order of 1 mps) and Coriolis effects dictate at maximum of such an ascending current would not be located symmet- the pole, but that the belt of ascending air would be for an rical about the poles. There is additional evidence of inter-hemispheric meridional circulation since return and equatorial flow (at levels of 100 km in polar regions by above 65 km in the sub-tropics) has also been reported Kochanski [4].

The vertical motion implied by these data over summer cloud high latitudes appears sufficient to support noctilucent noctilucent particles at the mesopause. The observed maximum in such a cloud observations in late July [5] is in agreement with meridional circulation model. 15

...... Global Circulations of the Stratosphere and Mesosphere

Diurnal Effects

Diurnal temperature variations of 15 to 20 C at levels around 50 km have been observed. These are significantly larger than most theoretical estimates. The magnitude of this variation decreases at lower altitudes and is very small below 35 km. Diurnal wind oscillations have been observed in the upper stratosphere with amplitudes of 10 to 20 mps (Figs. 5 and 6). Above the stratopause the meridional flow is toward the pole during the daytime and toward the equator at night. The phase of this oscillation is shifted 1800 below the stratopause. A detailed study of the amplitude and phase variations will appear soon.

Final Remarks

We are happy to make all of the MRN data available to any- one wanting to use it.

Based on what we know now, we are rapidly adding tropical stations, since it appears that extremely interesting things are happening there.

The MRN data have pointed to certain interesting aspects of the general atmospheric circulation. First, the "stratonull" surface at an approximate altitude of 24 km represents the most definite separation of the tropospheric and stratospheric circulation systems. It slopes upward in polar regions. In winter it is characterized by a minimum in the distribution of meridional temperature gradient with height, while in summer it is an inflec- tion point at the base of the stronger upper stratospheric gradient. The stratonull is variable in time and space, rising when the stratospheric circulation intensifies.

It is on the equatorial portion of the stratonull surface that the biennial wind oscillation has its maximum intensity, while in polar regions the stratonull surface is the scene of the maximum effects of the biennial sudden warming events. The stratonull surface thus appears to represent the separation of the tropospheric ant stratospheric circulations, and also to serve as the site of the dynamic interactions between these major circulation systems.

Development of summer easterlies across the equator into the winter hemisphere has been shown to produce a semi-annual oscillation in the wind field at 50 km with a maximum in the tropics. This semi-annual variation dominates the annual wind field at 16

Willis L. Webb ......

50 km and decreases rapidly with decreasing altitude to become essentially negligible at the stratonull level. The biennial variation, on the other hand, decreases with increasing altitude and it is very small at the stratopause (50 km).

Discussion

Questions were raised concerning the reality of the summertime maximum in noctilucent clouds. Observational probabilities must be taken into account.

Questions were raised concerning the long-term reliability of averages based on six years' data or less.

The need for more observations was stressed. Most of the data have been obtained over North America. Observations are lacking at very high and very low latitudes.

References

1. Webb, W. L., W. I. Christensen, E. P. Varner and J. F. Spurling: "Inter-Range Instrumentation Group Partic- ipation in the Meteorological Rocket Network," Bulletin of the American Meteorological Society, 43, 640-649, 1962.

2. Webb, W. L.: "Stratospheric Solar Response," Journal of the Atmospheric Sciences, 21, No. 6, 582-591, 1964.

3. Webb, W. L.: "A Dynamic Climatology of the Stratosphere," Chapter 5 of World Survey of Climatology, Vol. III, Elseveir Publishing Company, Amsterdam, 1965.

4. Kochanski, A.: "Circulation and Temperatures at 70-100 Kilometers Height," Journal of Geophysical Research, 68, 213-221, 1963.

5. Fogle, B.: Results of the Study of Noctilucent Clouds over North America during 1963, University of Alaska, Geophys- ical Institute, Cloud Report 2 (NSF Grant GP 1759), 1963. 17

.GlobalCirculations of the Stratosphere and Mesosphere

j~~~~

fill~~~~~~~~~~~~~~~~~~~~~~~~~4

/::: ati~j-~-~··:· 2l

'OKWAMLN (

/,M ,E Il ;i7~~L DNi ~

i~~~~~~~~~~~~

: ·i u ~~~~~~~~~~

Fig 1 -- Mtoooia oktnewr n1Jnay16 18

Willis L. Webb . o . o o o o o o o o o o o o o. AS - Ascension Island BKH - Barking Sands, Hawaii 0oo- FG - Fort Greeley WI - Wallops Island WSMR - White Sands Missile Range W/

,So I -'i /

0-n |\\\ ^ \,

J F M A M J J A S O N D

Fig. 2 -- Mean zonal stratospheric circulation index (SCI) for selected MRN stations which provide a latitudinal sample. The SCI is the mean wind over a station in the 10-km- thick layer from 45 to 55 km.

II0

10 ,A\ B \ F J \ I

ao .. 1' I \

J A O OJ A 'S O 'N D

Fig. 3 ---- Mean meridional SCI components for selected MRN stations which provide a latitudinal sample 19

...... Global Circulations in the Stratosphere and Mesosphere

46-

o -

640 ) - ( 0 620

...-.. , I

Fig. 4 -- Latitudinal distribution of mean zonal SCI values for comparison of the hemispheric circulations. The curves are from the first semimonthly data points for the indicated months as plotted in Fig. 2, the upper left for 8 April, upper right 8 May, lower left 8 June, and lower right 8 July. 20

Willis L. Webb ...... 1oo

80-

0 60 E so

0 K40

0 6 2. 24

Fig. 5 -- Analysis of diurnal distribution of zonal wind speeds in the stratosphere over White Sands Missile Range as observed on 7-9 February 1964

\0 58 kr

D .3 K

-30 -

o_ 12 t8 Z4 TIKE (hr) Fig. 6 -- Analysis of diurnal distribution of meridional wind speeds in the stratosphere over White Sands Missile Range as observed on 7-9 February 1964 21

THERMAL TIDAL EFFECTS IN THE UPPER STRATOSPHERE AND LOWER MESOSPHERE

Willis L. Webb, Discussion Leader White Sands Missile Range

Considerations of the Global Geometry of Input Heating into a Uniform Exponential Absorbing Atmosphere

1. The level of heat input will rise as the sun's rays become more oblique (Fig. 1).

2. At equinox times the meridional temperature gradient will, in general, be negative.

3. A small region of continuous illumination will produce a hot region over the pole at high altitudes, resulting in a reversal in the meridional temperature gradient in that region, and thus an easterly circulation in that region.

4. As the summer season progresses this pool of hot air will expand and descend, as indicated by the dashed lines in Fig. 1. In the summer case easterlies should begin in the upper mesosphere and lower ionosphere and descend as the heated zone rotates into the solstice position.

5. The heated zone will lift and recede from the pole in the winter case, so westerlies will begin near the stratonull at the pole and expand upward and toward lower latitudes.

6. A most important item to be noted is that the maximum zonal winds of the summer stratospheric circulation are found directly under the sun. This feature of the maximum meridional temperature gradient being found at that point can only be as- cribed to a latitudinal variation in the absorbing parameter or in the heat deposition mechanism.

Model of Stratospheric Tidal Motions

1. A projection of the stratospheric thermal and wind field on the equatorial plane for a time just after the spring equinox is illustrated in Fig. 2. 22

Willis L. Webb, Discussion Leader ......

lines (dashed) 2. The diurnal maximum and minimum temperature following local are different by 15 to 200 C, with the maximum occurring just before noon by approximately 2 hr and the minimum change is approximately sunrise. Since this diurnal temperature difference, the maxi- the same magnitude as the equator-to-pole to be found at mum meridional temperature gradient is clearly peak in thermal driv- high latitudes in the nighttimeOsky. This latitude at a local time ing energy should be between 60 and 80 the pole with a 24-hr of 0100-0400. It will, of course, circle period. of equal 3. The thin lines of Fig. 2 represent contours relation then re- temperature (or thickness). The thermal wind toward the pole, quires that the wind veer away from the equator again in the region ahead of the temperature maximum, and back occur over approx- of falling temperatures. Rising temperatures while the return flow imately 1200 of latitude (8 hr duration), is of some 16 hr duration. meridional at 4. These tidal-type oscillations are largely with increasing lat- low latitudes, but become increasingly zonal and will result in the itude. This zonal motion is non-linear, is uniquely related to development of a circulation system which the diurnal heat input.

the summer season 5. The pool of warm air at the pole, as tidal circulation to progresses, will force this stratospheric zone of the late night- circle the pole. It will converge in the tidal jet" time upper mesosphere, and develop the "stratospheric acceleration on the which should represent a periodic (24 hr) support of noctilucent easterly wind field. Vertical motions for strong enough, the cur- cloud particles should be present and, if stable region provide rent could cross the mesopause and in that to the winter pole. a divergent meridional flow from the summer provide an effi- 6. This tidal circulation system should cient mixing system for the stratosphere.

Discussion of maximum heating London: Murgatroyd [1] has put the level Also, it is hard to at 50 km over the summer pole, not 70 km. 20 C (5 changes are explain diurnal temperature variations of expected theoretically). 23

...... Thermal Tidal Effects

Webb: The temperature surfaces do slope upward at high latitudes. Leovy's work shows this clearly. There are diurnal zonal wind variations of 20 to 30 m/sec. This raises the possibility that energy conversions may explain the temperature rise, and not just photochemical effects.

Webb: There is evidence from Jodrell Bank and Adelaide [2] that winds at lower ionospheric levels always blow from the summer pole. These tidal motions at lower levels may drive this meridional circulation.

Each spring and each fall a special event takes place -- a meshing of the polar and mid-latitude circulations. This meshing is postulated to be a result of the tidal interactions.

London: Up to 35 to 40 km, the general picture of the atmosphere -- as obtained from balloon data -- agrees with Webb's picture. However, the magnitudes of the diurnal oscillations don't agree at all. Webb indicated that the amplitude and phase of these oscillations change rapidly at levels below 50 km.

Webb: I'd like to make an observation: The semi-annual oscillation caused by the seasonal monsoon and the winter storm period dominates at 50 km, while the biennial oscillation dominates at 25 km. The former decreases downward from the stratopause -- the latter decreases slowly above and below the 25 km stratonull level.

Webb: I'm supervising a thesis at Texas Western College on the relationship between tropospheric and stratospheric circulations. Time sections are being drawn showing the zonal flow from the surface to 60 km (data for the stratosphere is from WSMR and Point Mugu) for the spring season. Results show approximate 3-day displacement from the breakdown of strong westerlies at 50 km to development of a cut-off low over the southwestern United States in the troposphere.

8° 0 "sec I/-

30 i ^ \ I

a 10- V 5 DAYS 24

Willis L. Webb, Discussion Leader ......

lines may slope the These events are cyclic so the change downward, however, and other way. The events appear to move levels. continuity is noted at intermediate

References

Temperatures between 20 km and 1. Murgatroyd, R. J.: "Wind and of the Royal Meteor- 100 km - a Review," Quarterly Journal October 1957. ological Society, 83, No. 358, 417-458, at 70-100 A.: "Circulation and Temperatures 2. Kochanski, Research, 68, Kilometers Height," Journal of Geophysical 213-221, 1963. 25

5oK.M• •• •.... i .Thermal Tidal Effects

Fig. 1 -

Global geometry of input heating into a uniform exponential absorbing atmosphere. Solid lines ROTATIONAL ~~~~AXIS 7~ \ \refer to the equinox, dashed lines refer to the summer solstice.

\ \ $UN'S RAYS EQUATOR

IINO"TH_ I SUN'S ^ \\ POLE ^EARTH^ 'RAYS

A projection of the stratospheric thermal and wind \ fields on the equatorial plane for a time just after \/ the spring equinox. Thin lines are isotherms, arrows 1 indicate wind field. ^^i^ ^^ ^ I 27

MOTIONS IN THE 80 TO 180 KM HEIGHT REGION

Adam Kochanski U.S. Weather Bureau

Introduction

It has been known for about 15 years [C, 2] that in the region from about 80 to 130 km there are rather regular variations of velocity, with a vertical scale of about 6 km, measured from a velocity maximum to the adjoining velocity minimum. (Strictly, as in the concept of internal gravity waves, this is X/2, i.e. one-half of the vertical wave length.) More recent data from sodium cloud drifts have added a great amount of new and important information about gross-scale motions, turbulence, and energy exchanges in this region. At present a total of 54 wind profiles are available for study. These profiles are determined from photographs of sodium vapor trails (or aluminum com- pounds trails) and extend from about 80 km to 180 km. On the average, the photographs are taken over periods of 4 minutes and the profiles obtained can be considered instantaneous.

The available profiles are tabulated here:

Station Number of Approximate Profiles Coordinates

Wallops Island 23 380 N, 75°W Sardinia 5 390 N, 90 E Eglin 23 300 N, 86°W Ft. Churchill 3 59 N, 920 W

Analysis of Wind Profiles

A typical example of these wind profiles is shown in Fig. 1. There are more or less regular variations in speed with a vertical scale of about 6 km from 80 to 130 km. Maxima of 100 to 150 m/sec are usually observed near 105 km. Above 135 or 140 km there is a change of regime. The profiles become remarkably steady both with respect to speed and direction. Within latitudes 300 to 40°N 28

Adam Kochanski ......

the winds in summer are almost always from the northeast, and in winter from the northwest. Sometimes vertical variations of a much larger scale are observed in this region.

There are several ways of looking at these motions and the subject is quite controversial. The author has assumed earlier [3] that the fairly regular velocity oscillations observed in the 80 to 160 km region are due to the internal gravity waves postulated by Hines [4]. By plotting the magnitude and direction of the wind at adjacent levels A and B in Fig. 1 on a hodograph, as illustrated in Fig. 2, it is possible to resolve the wind into two components, one of which, W, represents the amplitude of the wave motion while the other, R, represents a sum of slowly varying drift and tidal components.

At high levels some of the hodographs look like Fig. 2b. This in a sense forces the amplitude of the periodic motion, W, to become smaller with increasing height. This vectorial reso- lution method becomes increasingly difficult above 150 km where the vertical depth of these oscillations becomes much larger and where often one cannot see a complete half-wavelength. There is some help from Hines' theoretical expectations of permitted half-wavelengths as a function of height, shown in Fig. 3.

Note that at heights of 170 km one has to identify half- wavelengths on the order of 35 km or greater. Thus the smooth profiles observed at these levels don't necessarily indicate an absence of gravity waves.

In the discussed material of 54 soundings there are four exceptional cases from Ft. Churchill -- three from May 1963, and one from October 1958. One of these cases is sketched in Fig. 4. Up to 120 km they show velocity oscillations very similar to those from stations in 300 to 400 N latitude, but above 120 km the magnitude of the motion steadily increases to a maximum of 240 m/sec near 160 km. Either there are tremendous tidal components, or drift velocities, or tremendous gravity waves in this region. There were no magnetic disturbances in any of these cases.

A summary of my analysis of these profiles (excluding Ft. Churchill data) is shown in Fig. 5. These may be considered annual averages, valid for 300 to 400 N latitudes. 29

...... a. Motions in the 80 to 180 km Height Region

Note in Fig. 5 that the magnitudes of W and of W x F decrease with increasing height. Thus energy is being taken from the stratosphere and lower mesosphere and dissipated in these regions. Figure 6 illustrates the exponential decrease of kinetic energy of internal gravity waves with height. Assuming viscous dissipation, Hines [5] has translated these values into the following heating rates:

100 C/day at 95 km

30° C/day at 130 km

1000 C/day at 140 km

Using closely spaced observations (two series of four soundings each) Rosenberg and Justus [6] treated the observed velocity variations as a semi-diurnal tide and made independent estimates of these heating rates. They obtained the same value at 130 km, but a value of 4000 C/day at 150 km. It is apparent that tremendous amounts of heat are being deposited at these levels.

Diurnal Oscillations

Hines [7j has estimated components of the diurnal tide at heights from 90 to 130 km. His results for dawn hours indicate that the average magnitude in the 100 to 120 km layer is about 20 m/sec.

The same value for the layer 100 to 115 km can be inferred from a study b.y Rao and Rao [8 which compared observations of apparent motion of ionospheric irregularities in the E-region over several stations in the northern hemisphere. It is certainly true that they may not be observing the motion of the neutral atmosphere -- but we can at least compare their results with the radio meteor wind data on prevailing winds and tides. The results are shown in the first three rows of Table 1. The agreement suggests that their motions in the E-region are reflecting tidal motions of the neutral atmosphere.

Rao and Rao [9] also have some data from higher levels we can transpose these data (F2 -region) and, as a first guess, to 160-km height to obtain estimates of resultant drift (Dr) and the amplitudes of the diurnal and semi-diurnal tides (A24 and A12). These are shown in the bottom row of Table 1. 30

Adam Kochanski ......

Table 1

COMPONENTS OF ATMOSPHERIC MOTION (m/sec)

(Values implied from ionospheric drifts are circled.) Data for Adelaide and Jodrell Bank are from radio meteor winds, for Wallops Island from sodium trails.)

Station Height Scalar Term R: Drift Amplitudes (km) speed V result- of tides ant D 2 Speed, R Result- r A24 A12 ant Rr

Wallops 110-115 69 59 26 (1) (1

Adelaide 95 21 18 9

Jodrell 92 12 5 10

Wallops 160 83 81 60 (37) 9) )

In summary we can compile tentative estimates of the magnitude of various types of motion that enter into the total observed drift. These estimates are shown in Table 2.

TABLE 2 N ESTIMATES OF VARIOUS TYPES OF MOTION FOR LATITUDES 30°-40 (all values in m/sec)

Motion Speed, m/sec

110-115 km 160 km

V, total motion (scalar speed) 67 90

D, prevailing drift (scalar speed) 50 60

W, wave motion (amplitude) 50 40

24-hr tide (amplitude) 21 20

12-hr tide (amplitude) 18 30 31

...... Motions in the 80 to 180 km Height Region

This may not be a fair comparison, but it suggests that the amplitude of the 24-hr oscillation remains constant or decreases with height, while the amplitude of the 12-hr oscillation increases with height.

Summary

It is encouraging that we have good agreement in the lower levels (70 to 100 km) between sodium vapor trail estimates of motion and estimates based on geostrophic assumptions. The fact that these methods work at lower levels lends confidence to the estimates we have above.

Rosenberg and Justus [6] have been trying to explain some of these oscillations in terms of 12-hr tides rather than gravity waves. They have two series of four soundings each that indicate much larger vertical and horizontal scales of motion. The horizontal scale estimates are on the order of 10,000 km.

With the limited number of profiles, collected at irregular intervals from only a few stations, there is still much room for speculation.

Discussion

Mitchell asked why the layer around 105 km (which corresponds to the lowest boundary of the diffusive separation layer) shows up so sharply as the boundary between turbulent diffusion and molecular diffusion processes. The level of this transition is 105 km + 5 km. No reason is known for the abrupt nature of the transition. The transition layer may be as thin as 100 m. More typically, it is 1 to 2 km.

Kochanski made a further comment regarding heating in the 100 to 160 km region. This layer may be heated from above (ultraviolet or corpuscular radiation) as well as from below (dissipation of energy by gravity-waves and tides) and it is difficult to separate these effects.

Kochanski mentioned that there is some polarization in the W statistics. That is, the preferred direction of motion of the gravity waves is E-W. He inquired if this might be connected with the preferred direction of movement of Sporadic E. Cole didn't agree that there is a preferred direction for movement of Sporadic E but did believe that there might be an association between the preferred direction of the wind and the occurrence of Sporadic E, 32

Adam Kochanski ......

the since there is a relationship between negative H (change in horizontal component of the geomagnetic field) and the occurrence of Sporadic E, and the negative H may be interpreted in terms of a westward wind.

The work of King and Kohl [10] was mentioned. They suggest vice that the atmospheric wind field may affect F2 variation, or versa.

Rooth asked if there might not be large semi-permanent waves just at these levels -- the steady northeasterly wind would then wave. be an indication of the station's position with respect to the

Kochanski showed one profile from Wallops Island that followed from a fairly strong magnetic storm (Fig. 7). Of the 23 soundings the Wallops Island, this one is strikingly different with regard to depth of the layer from velocity maximum at 120 km to the velocity minimum at 160 km.

REFERENCES

1. Liller, W. and F. L. Whipple: "High-altitudeWinds by Meteor- train Photography," Special Supplement to Journal of Atmospheric and Terrestrial Physics, 1, 112-130, 1954.

2. Greenhow, J. S. and E. L. Neufeld: "Large Scale Irregularities in High Altitude Winds," Proceedings Physical Society, London, 75, 228-234, 1960.

3. Kochanski, A.: "Atmospheric Motions from Sodium Cloud Drifts," Journal of Geophysical Research, 69, No. 17, 3651-3662, September 1964.

4. Hines, C. 0.: "Internal Gravity Waves at Ionospheric Heights," Canadian Journal of Physics, 38, 1441-1481, 1960.

5. Hines, C. 0.: "Dynamical Heating of the Upper Atmosphere," Journal of Geophysical Research, 70, No. 1, 177-183, January 1965. 33

...... Motions in the 80 to 180 km Height Region

6. Rosenberg, N. W. and C. G. Justus: "Space and Times Correlations of Ionospheric Winds," to be published, Journal of Research of the National Bureau of Standards, Section D, Radio Sciences.

7. Hines, C. 0.: "Diurnal Tide in the Upper Atmosphere," to be published, Journal of Research of the National Bureau of Standards, Section D, Radio Science.

8. Rao, G. L. N. and B. R. Rao: "The Latitude Variation of Apparent Horizontal Movements in the E Region of the Ionosphere," Journal of Geophysical Research, 70, No. 3, 667-677, February 1965

9. Rao, G. L. N. and B. R. Rao: 'World-Wide Studies on Apparent Hori- zontal Movements in the F2 Region of the Ionosphere," Journal of Atmospheric and Terrestrial Physics, 26, 213-229, February 1964.

10. King, J. W. and H. Kohl: "Movements in the Atmosphere and the Ionosphere," Internal Memorandum No. 207, Radio and Space Research Station, Slough, Bucks., England, April 1965. 34

Adam Kochanski ......

l&O - - i_/ \

o so / I\

Vo 12a n n n119 f-k _ A4nlTT-rl 4 i% W N t Io A J OB._R-IM 01 0 /-o spDo, m/s25^ECT^oN

Fig. 1 -- Sketch of typical mid-latitude wind profile obtained from sodium or aluminum compound trails

o.^ vJ/ W

(ca) MAJORrTY or CA >ES b) She' CASES

Fig. 2 -- Wind hodographs used to resolve the wind into two components, the wave motion component (W) and the slowly varying drift and tidal components (R) 35

...... Motions in the 80 to 100 km Height Region

I QO .. FOneB G-EO

14 ALLOWEC

- 1o ,/ I =: / /

100 .f < — 1 — i — \ — 1 — 1 — \ — 0 10 20 30

PLk F- iAfCL C G)tH H: (N

Fig. 3 -- Sketch of permitted half-wavelengths as a function of height (From theoretical work of Hines.)

.0- l~~~~boa I·~~~~~~ /I 140rt0~~~~~ /

" 120

t0 zO go 4 2ootoo 302 SPE oD, r/sec.

Fig. 4 -- Sketch of wind profile from Fort Churchill, May 1963 36

Adam Kochanski . I ...... * * * -

ISOo ,\,.X - "O 'X,O , / ,o%

140=

W x F driftmeasure and of tidal total components influence of internal gravity waves

100 7

1O 40 40 s1000 sPED? rn/sEc

Fig. 5 -- Summary of analysis of all available wind profiles (excluding Fort Churchill data)

V = observed wind speed, regardless of direction

W = amplitude of wave-like oscillations attributed to gravity waves postulated by Hines

R = magnitude of residual motion which presumably contains drift and tidal components

F = visually established frequency of occurrence of gravity- wave oscillations

W x F = measure of total influence of internal gravity waves 37

...... MotionsN.I in the 80 to 100 km Height Region

160 \

X '40I i1MPLI G1 \\ 35 SE VED

\ A oc P,[6. 0 i I

(tOO-0

n seC'-ki' - Fig. 6 -- Vertical distribution of the kinetic energy of internal gravity waves / /

140

I LO

LOI too0 1

0 SO I00 t~ 0 A00

PHOTOCHEMICAL INTERACTIONS NEAR THE MESOPAUSE

C. Leovy The RAND Corporation

An understanding of the dynamics of the mesosphere appears to be an essential prerequisite for investigating the influence of variable solar radiation on the atmosphere. One of the most interesting aspects of mesosphere dynamics is the possibility of interactions between motion systems and photochemical processes. Lindzen [1] has studied these effects in the region below 70 km. Above 70 km, however, large amounts of chemical energy are available in the form of atomic oxygen, so that significant interactions may be expected.

The interaction of internal gravity waves with four photochemical processes occurring in the region of 80 to 120 km has been examined. These are: (1) absorption of solar radiation by ozone, (2) absorption of solar radiation by molecular oxygen, (3) fluctuations of optical depth for molecular oxygen absorption, and (4) heat released by oxygen recombination. It is found that the latter is the dominant effect and leads to destabilization of the gravity waves. The waves grow as over- stable oscillations. Growth rates give a doubling time of the order of three days for maximum atomic oxygen concentrations of 1.6 x 1012 per 3 cm . This rate is probably not significant for gravity waves and may be dominated by damping due to eddy viscosity effects. However, the growth rate increases rapidly as the atomic oxygen concentration increases. Calculations by Young and Epstein [2] indicate that steady descending motion of less than 1 cm/sec, which might be associated with very large-scale circulations, would produce a threefold increase in atomic oxygen concentration near 95 km. Such an increase in atomic oxygen concentration would lead to wave amplitude doubling times of about one-third of a day, a very significant rate.

It is suggested that the mechanism studied here may be the link between large-scale descending motion and highly disturbed conditions in the upper mesosphere, both of which seem to occur during the mid- winter in middle and high latitudes. 40

C. Leovy ......

References

and 1. Lindzen, R.: Radiative and Photochemical Processes in Strato Mesosphere Dynamics. Ph. D. Thesis, Harvard Univ., 228 pp., 1964.

2. Young, C. and E. S. Epstein: "Atomic Oxygen in the Polar Winter Mesosphere," Journal of the Atmospheric Sciences, 19, 435-443, 1962. 41

MODELS FOR STUDYING INTERACTIONS BETWEEN VARIOUS LAYERS OF THE ATMOSPHERE

Claes Rooth Woods Hole Oceanographic Institute

There is virtually no limit to the variety of atmospheric interactions that can be investigated with tools presently available. As an example, if we are concerned with the propagation of disturbances resulting from the heating of a certain layer in the atmosphere, we must anticipate different effects depending on the time scale of the heating and the spatial distribution of the heating. Time scales may range from hours (solar, geomagnetic disturbances; diurnal, semi-diurnal tides) to months or even years (as, for example, the much discussed 26-month oscillation). Similarly, spatial scales may vary over several orders of magnitude from localized auroral heating to tidal forcing on the hemispheric scale.

By making assumptions regarding the vertical form of the heating (or tidal) forcing function, the temporal and spatial form of the forcing function, and the initial state of the atmosphere, it is possible to construct numerical models to study the response of the atmosphere.

Numerical models open many interesting possibilities. For example, with respect to diurnal tidal forcing, certain models pre- dict strong amplification at 300 latitude -- where the period of the forcing equals the local inertial period. Such an effect has been found in the oceans. Or, to take an example where the forcing is thermal, one can show that for an atmosphere in radiative-conductive equilibrium (for example, the thermosphere), the temperature response is proportional to the square of the thermal forcing; this results because heating of a layer expands the layer from which heat must be conducted away.

We may find it convenient to make use of certain similarities between the upper and lower portions of the atmosphere. We have three layers with identifiable driving forces, the lower troposphere, the ozone layer, and the thermosphere. These three layers are separated by two stable boundary layers as illustrated below. 42

Claes Rooth ......

THERMOSPHERE

Boundary Layer Boundary Layer -- Mesopause - 85 km

OZONE LAYER

Boundary Layer -Boundary< -Stratonull - 24 km TROPOSPHERE -- Surface Boundary Layer

For many purposes, the troposphere and its boundary layer, ozone layer and its boundary and the layer, may be treated as single layers. There are also important differences between certain portions of the atmosphere. For example, we can't dissipate top of the atmosphere momentum at the the way we can at the base of the It has seemed possible atmosphere. that magnetic coupling between the hemispheres could play a role in balancing the momentum budget; calculation, there appears but on to be a difference of ten orders of magnitude between the amount of magnetic coupling we can expect and the amount required for this to work. 43

DYNAMIC INTERACTIONS

Philip D. Thompson National Center for Atmospheric Research

Introduction

We can consider two major types of interaction: those due to perturbations of the gravitational field and those due to variable emission from the sun. With regard to the latter, one can consider:

1. Local heating by direct absorption.

2. Cases in which the principal effect of the emission is to produce ionization or photochemical reaction which leads to a change in physical or chemical composition, thus changing the absorption properties of the higher atmosphere (a way of producing fairly large and long-term effects). This would have the power-multiplying effect of a valve or radio tube.

Effects of Heating

I have looked into the problem of short-term effects (on the order of a few days). I assumed impulsive heating and the production of a local disturbance at some high level, and then studied the effects at lower levels using a quasi-geostrophic model. From the vorticity equation and the thermodynamic energy equation for quasi-geostrophic motion, one obtains, upon eliminating the vertical vorticity, an elliptic-type equation for the pressure tendency. It is possible to express the pressure tendency at a given point in the lower atmosphere in terms of conditions throughout the atmosphere. The question is then: How big is the influence from some point tens of km high? The influence function dies off something like [e-kz/z ] where z = altitude, and k = constant depending on the static stability. The magnitude of the effect will depend upon the pressure depth of the region in which the disturbance has been produced and the altitude of that region. My magnitude estimate of the possible effects on the lower atmosphere was extremely small. 44

Philip D. Thompson ......

Shapiro and Berkofsky [1] have carried out some actual calculations with conventional numerical prediction models in which they assumed certain heating distributions. They made more detailed studies of the kinds of effects that could be expected, but concluded that their magnitude would not be appreciable over short periods.

Perturbations in the Gravitational Field due to Lunar Tides

The amplitude of the gravitational perturbation is small and the spectrum of atmospheric motion is very broad; therefore resonance effects don't appear likely. If there is an effect, it may just be that the perturbation increases the probability of getting over the threshold of some kind of instability. One must then ask, where is the atmosphere from day to day with respect to this threshold of instability?

With respect to large-scale atmospheric perturbations, there are fairly long periods of time when the atmosphere is well below any threshold. There is not much evidence that the atmosphere hovers on the threshold of baroclinic instability for any length of time. When this level is reached, fairly rapid adjustment usually takes place.

One should look for a mechanism of instability that is mar- ginally operative and dependent on persistent and small differences (for example) of temperature or vapor pressure such as are prevalent in the equatorial and subtropical regions.

Discussion

Visitor: One could consider a model in which heating at high levels would result in potential flow outward from the heat source. This would change the pressure distribution at the surface, particularly if the heating persisted for several days. This might have the effect of introducing small ageostrophic components in the motion field at low levels and triggering baroclinic instability.

London: Haurwitz [2] has considered just such a model in which very large heating in the ozone layer led to ageostrophic motions which could then result in detectable pressure changes in the upper troposphere. Spar [3], considering a heat source in the mesosphere, found no concomitant changes in the tropospheric circulation. 45

...... Dynamic Interactions

Lorenz: One can consider two kinds of long-period effects:

1. The long-period effect of a single impulse: If one assumes a fairly quick response to this impulse then one has essentially just changed the initial conditions. One can then carry out computations for an arbitrary length of time and observe how the final state of the system that received the impulse differs from that of a system that wasn't pulsed.

2. The long-period effect of a succession of impulses: For example, what would happen if you could control the timing of solar events without affecting the overall number? What effect might this have?

Mitchell: It is worth stressing that the lunar rainfall effect seems to involve non-linear interactions. The increase in rainfall observed when lunar tides are in phase with solar thermal tides is more than one would expect from a linear addition of these effects. Brier commented that the Batavia pressure data showed the non-linearity of the response even more clearly.

References

1. Berkofsky, L. and R. Shapiro: "Some Numerical Results of a Model Investigation of the Atmospheric Response to Upper-level Heating," Planetary and Space Science, 12, 219, 1964.

2. Haurwitz, B.: "Relations between Solar Activity and the Lower Atmosphere," Transactions of the American Geo- physical Union, 27, 161-163, 1946.

3. Spar, J.: "Meteorological Models for the Study of Atmospheric Responses to Anomalous Solar Emissions," Technical Report No. 5, Institute for Solar-Terrestrial Research, High Alti- tude Observatory of the University of Colorado, October 1958. I 47

RESPONSES TO HEATING

E. N. Lorenz Massachusetts Institute of Technology

The material I should like to present today is somewhat like the things we have been discussing. However, it is different in that it doesn't primarily concern tidal motions or regular periodic motions, but involves response to heating of any sort. Originally this work was prompted by my interest in responses to heating at very high levels (the ozone layer or higher, but below the ionosphere). However, the methods are applicable to any heating, whether anomalous or normal, at low as well as high levels.

First I will describe briefly some material which I presented about five years ago at a conference on solar/weather relationships at Lake Arrowhead, and then go on to further discussion. This particular study was concerned with the effect of anomalous heating at some unspecified high level. The aim was first to establish a multilayer numerical forecasting model which would contain high levels together with lower levels. The model would then be integrated twice with the same initial conditions, in one case with anomalous heating at a high level and in the other with no anomalous heating. The object of the experiment was to see how rapidly the two solutions tended to diverge if, indeed, they diverged at all.

Extending a model up to the 1-mb level or higher frequently leads to a good deal of difficulty in the differencing processes, as it certainly isn't practical then to space the layers equally according to pressure. If instead there are very thick layers below and thin layers above, there is a question as to whether the difference between the stream functions in a thick lower layer and a thin upper layer can be identified with temperature.

The model which I am about to discuss is a geostrophic model, which automatically eliminates it for tidal studies, although I think that the vertical differencing method which it uses could be used in a primitive equation model, which might be suitable for tidal studies. This means in effect that we are assuming not only that adjustment to hydrostatic equilibrium is essentially instantaneous, but also that adjustment to geostrophic equilibrium is essentially instantaneous. 48

E. N. Lorenz ......

So let me begin by writing down the equations for a geostrophic system. Then we shall take a look at the construction of the model. I'll use pressure coordinates, and let w= dp/dt.

We have for the continuity equation

7V' + /a p =- o (1)

As Claes Rooth pointed out in his recent talk, the continuity equation is simplified by using pressure coordinates; however, I have used p instead of In p as he did. The hydrostatic equation, after substituting the ideal gas law, becomes

i^ai-^L =(2) aP a P and the geostrophic equation can be expressed as

SF - 9 (3)

This simplification is permissible when f is treated as constant; certainly in any realistic tidal problem the geostrophic equation would have to be considerably more complicated.

From Eqs. (2) and (3) we get the thermal wind equation

(4)

This will be one of our working equations. Another will be the vorticity equation

B . f=-J(q, v' i) ) + a + (viscous ter-s)(5)

If we wish the model to generate its own statistics (that is, come to a statistical equilibrium) the viscous terms would be required. Finally we have the thermodynamic equation 49

...... Responses to Heating

g RT__S-t T-- -- )k) 4- C, (6) + (LoC-n/ucI ve ers) (6

Equations (4), (5), and (6) are the working equations of the model, and would actually be just as suitable for a system which is continuous in the vertical.

In order to introduce this multilayer model, let me first briefly review at least one way to build a two-layer model. In this model

0 — 0 =0—

1 1

2 ______T ______static stability - 2 prespecified

3 P3 = 4 — 4- 0- it is convenient to label the boundaries and layers 0 through 4, as shown, where boundary 2 separates layer 1 from layer 3. For the lower boundary it would be better to have a level surface with zero vertical motion, but for simplicity we shall use a constant pressure surface, with w = 0.

In the figure we have indicated w2, '1, 3 , and T2. These four quantities will be the four dependent variables. Gov- erning these four quantities are one diagnostic equation -- the thermal wind equation (4), which relates the difference of the stream functions to temperature -- and three prognostic equations. The vorticity equation (5) applied to the upper and lower layers separately accounts for two prognostic equations. The thermodynamic equation (6) is applied to the boundary between the layers, and is the third prognostic equation. As usual we can eliminate 50

E. N. Lorenz ......

one of the prognostic equations by differentiating the diagnostic equation with respect to time. This will allow us to eliminate some of the variables. In the final formulation of the two-layer model, we end up with two diagnostic equations and two prognostic equations. The two variables could be taken as the stream functions in the two layers. More commonly they are taken as the sum and difference which we identify with the mean flow (at the 500 mb level) and the temperature. This, in brief, is how we develop a two-layer model. It is desirable that the two layers be of approximately the same thickness.

Now the model which I should like to propose for studying the effects of heating at rather high levels, and which I actually used in the numerical integrations I carried through several years ago, is something I have called a stack of two-layer models. In- stead of having all the layers of equal thickness, there are two layers of equal thickness, on top of which are two more layers of equal thickness, but thinner than the lower pair, etc. I shall illustrate this with a stack of three two-layer models on top of each other.

1b1mb I 0 = 0 °— 2 T2 w o2 prespecified 10 mb 5 4 - d w4 5 W5

6 T6 _ 6 6 prespecified 7 I7 100 mb 8 —8- 9 '9

10 . T10o —10 ------prespecified 11 "11 1000 mb 12 —12 "

We can think of this as three two-layer models, but they are not completely independent. They are associated with one another through the boundaries separating them, i.e., levels 4 and 8. For each individual two-layer model we shall have a static stability C preassigned; for all practical purposes we can regard C as

-T7/a "' - T 51

...... Responses to Heating

W's In the above, Wo and W 1 2 are zero, but the intermediate are not zero.

Now let us take a look at the available equations. Letting n be the number of two-layer models, or in this case n = 3, we would have n diagnostic (thermal wind) equations. We also have n - 1 additional diagnostic equations which are necessary to give us continuity of the stream function in the vertical. In other words the stream function extrapolated linearly to the top of one two-layer model must equal the stream function extrapolated linearly to the bottom of the two-layer model just above. This gives us 2n - 1 diagnostic equations altogether. For prognostic equations we have two vorticity equations plus a thermodynamic equation for each of the two-layer models, which gives us 3n prognostic equations. Now if we count the variables, we note that we have as many variables as equations, and thus a closed system. As in the simple two-layer model, we can differentiate each diagnostic equation with respect to time, and use it to convert another prognostic equation to a diagnostic equation. This leads to 4n - 2 diagnostic equations and 3n - (2n - 1) = n + 1 prognostic equations. Thus, ultimately, by eliminating variables we can express the whole system in terms of n + 1 variables, which can be chosen in a number of ways. A convenient procedure is to take the stream functions 0o, #4, #8 and #12 or, in general, at levels separating pairs of layers. Given the values of these, we can interpolate linearly between any two adjacent ones to get values of the other stream functions. Then we can take differences to get the temperatures. Thus we shall have all the necessary initial quantities.

This, then, was the model which I used. An additional feature of the model was the expansion of the horizontal fields in terms of orthogonal functions, in order to reduce the number of variables enough so that the problem could be placed on a small computer, and run fairly quickly. This is not necessary, of course, but it was convenient at the time.

The lowest level was taken as 1000 mb, as shown in the diagram. I essentially put a 1-mb lid on the atmosphere, but the top could just as well have been set at zero, since there is nothing in the final equations which makes use of the pressure at the very highest surface, except in combination with the pressure at some other surface.

I should make a few remarks about the results of the study. First of all, the integrations were run both with and without heating in the highest levels (10 to 1 mb). What happened was 52

E. N. Lorenz ......

that the two solutions tended to diverge from two to four weeks afterward. There were considerable differences in the final fields of motion, so that there was some real effect from the heating. As for the magnitude of this effect, some additional runs were made when anomalous heating was put in the lowest layer. The same total amount of heat was put in; that is, a very small heating per unit thickness, since the mass of the low layers is so much greater. With the same total amount of heating at lower layers, the solutions diverged at roughly the same rate. However, they didn't diverge to the same solutions; in other words, the three solutions, one with no anomalous heating, one with heating at the top, and the third with the same amount of heating in the lowest layer, all diverged from each other at roughly the same rate, so that the three of them eventually went their own ways.

I might mention that 02 was made small to correspond with the troposphere, 6 was quite large to correspond with the stratosphere, and 10 was again quite small. Heating was a function of latitude, and lasted for the order of a day. The time steps were at 4-hr intervals.

If the results of some more recent studies had been available, I think that we could have anticipated some of the results of this study before performing the computations. One result, which I hadn't obtained at the time of this study, is that if a system varies in a non-periodic manner, and if two separate solutions start off with slightly different initial conditions, the solutions will eventually diverge from one another. Even if the initial differences are so small that they affect only the last decimal place of one of the variables, the solutions will still diverge if you wait long enough. Thus, we could have anticipated that no matter how small the anomalous heating which we introduced into one solution, the solutions would have diverged.

However, the rate at which the solutions ought to diverge is somewhat uncertain. Recent numerical studies have suggested that small errors may double in something like five days. This means a factor of only 64 in about a month. Initial differences appearing only in the last decimal place should require several months to become appreciable.

Thus there are some questions left to be answered. How does heating introduced only at high levels in one solution lead to 53

...... Responses to Heating

divergence of the solutions at low levels? Does the high-level heating have some appreciable immediate effect at low levels, so that effectively the low-level initial conditions are noticeably different? Or is the immediate effect at low levels only in the last decimal place, and does the divergence of the solutions occurring at high levels somehow work its way down to low levels?

This suggests that at least two separate features of the problem of high-level heating should be looked into. First, if there is anomalous heating at some high level, what is the immediate effect at some lower level, as opposed to the effect after a good many days? Or, more generally, what is the effect when geostrophic equilibrium is reestablished, which in the present model is equivalent to the immediate effect, since adjustment to geostrophic equilibrium is regarded as instantaneous? Is it significantly large, or just an alteration of the last decimal place?

Second, if two solutions are initially identical in the lower layers, but slightly different in the highest layers, and if heating is the same in the two solutions, will the solutions eventually diverge in the low layers, and, if so, how rapidly?

The thing I have been looking into during the course of this seminar is the former problem. That is, if you heat one portion of the atmosphere, what will be the immediate change in the temperature and wind fields, if everything is maintained in geostrophic and hydrostatic equilibrium? For this purpose I propose to use the same system of equations, but instead of a layered model I plan to use one which is continuous in the vertical. I have not solved the problem, so I want to go over briefly what we can easily do, and also indicate some of the difficulties which come up when we try to solve the complete problem.

Essentially we are asking how aT/ at and aV 2 A/ 3t will be altered if the value of Q is modified at some location. This suggests a perturbation method; we linearize about the present state and ask what sort of perturbation we would have in aT/!t or V 2 J/ at if we put in a perturbation in Q. We can easily write down a system of perturbation equations to be solved for perturbation temperature and wind tendency.

We find first of all that the effect of heating depends not only upon the location and intensity of the heating, but upon the entire state of the circulation at that time. So in this sense 54

...... E. N. Lorenz ......

consider the problem resembles the tidal problem, where we must to consider only the entire circulation. What I have done so far is and horizontal the simplest case, with an initial field of no motion lapse rate of stratification, but with vertical variations of the of temperature taken into account, that is, with cr a function top and pressure alone. Also, I have again let W 0 at the this assump- bottom of the atmosphere, regardless of how realistic tion may be. vor- With these assumptions we obtain for the perturbation ticity equation

v'-_ = + ha) (7)

and for the perturbation thermodynamic equation

o1T d_c i Q (8)

Cr Here 4, T and W are perturbation quantities, and and is a prespecified function of p. Note that conductivity the viscosity have been disregarded; this of course affects solution. The thermal wind equation

_^~ ^ ^^ ~~~~~(9)J:

still applies to the perturbation quantities.

Next we eliminate W by differentiating Eq. (8) with respect to p, and obtain

o slv+ t- -i *e f r)n]= ( pt )(lo bt ' F p 60 p 5o6P ( ) variable To solve this equation, we can introduce a new dependent

(11I) 11' \ 2I 0 55

...... Responses to Heating

whence

L 2 J +4. ___-T-i _ · _ a $(12) (2) ^L^ 'b:]J '^ps ~ Q where S2 R o f 2 (13) or, in terms of the lapse rate y and the dry-adiabatic lapse rate yd,

s2 - R2T (d - y) (14)

Solving Eq. (12) involves inverting an operator which is somewhat like the Laplacian operator but differs because of the variable factor 1/S2. The operator could easily be inverted in the special case where S2 is constant, but this case has no physical meaning, since 1/S2 must approach zero about as rapidly as p2 , as p-O, according to Eq. (14).

So we shall make several more changes of variable, and let

Z = -IIr / ) (15)

C ( pOOP )y^ (16)

A 2 ' 5 T2 j-Y (17) 56

E. N. Lorenz ......

To a first approximation, Z is the elevation in scale heights. The temperature perturbation is then

CrT =_ -e o A 4 i) - (-

in terms of , and Eq. (12) becomes

a[vt [v( AZ (Az - )] = e Q (9)

equation can also be solved in the special case that This 2 A2 is constant, but here a constant value of A , although not meteorologically realistic, is at least physically meaningful. A more realistic situation would be to have a different constant value of A2 in each of several layers. An interesting case would be three layers -- a troposphere, a stratosphere, and a mesosphere.

For the case where A2 is constant, Eq. (19) may be solved in terms of irfluence functions:

at 1(x)^ ( "e_ex (x-)X'4'4z' (20) at (xsI)J POO

where

^ (A-2x') A2 (y-y) 2 + (z-z) 2 (21)

and

_= A ,(- ,(. A"-5Az (y. ^ (22) + A + Z +Z~~~~~~~~~./ 57

...... Responses to Heating

From Eq. (18) it follows that

-T_i H (x, p,' y, r ')Q (x', y P' dx 'd y'd

where -ie, A4A2pip ' ' 4. (u,y,- ,x, Yz-Z,) "

e-2e^ 'J12 e + + ( _ e 2 _ -) - 3 (Z+Z) 1) (24) -e l I+ + 2^^^ — ^^UL^^^ 3 0^- I) -- pJ

Note that we have changed the variable of integration from Z' back to p', since dx' dy' dp' is proportional to an element of mass. If the heating is concentrated near one point, the field of 8 T/ at becomes essentially proportional to the influence function H itself. In particular, at points directly below or above the point of heating, H reduces to H (xy, p,, y, p')

+ ) >f 4Tr A'D'(2eirA" [ ( - e3>__ o_ (,ir Q' +

Even from the solution for such a simple case, two interesting features emerge. First, the function H(x,y,p,x,y,p') is symmetric in p and p'. The influence of a given amount of heating at a given high level upon the temperature at a given low level is the same as would be the influence of a similar amount of heating at the low level upon the temperature at the high level. 58

E. N. Lorenz ......

2 Second, as long as A is constant, even though the value of 2 the influence depends upon A , the rate at which the influence 2 the vertical direction is independent of A . Only the decays in 2 rate of decay in the horizontal direction depends upon A i.e., upon the lapse rate of temperature; the decay is least rapid under stable conditions. For high-level heating the terms in (24) and (25) involving P* are negligible, and the following table of 47rA2 H as a function of Z'-Z, or lnp/p', shows the rate of vertical decay.

2 Z' - Z 47rA H(x,y,p,x,y,p')

O 0o 1 0.55 2 0.034 3 0.0046 4 0.00086 5 0.00019

If the heating occurs as high as 50 km, the temperature change even as high as 18 km, or about four scale heights below the heating, would seem to be very small indeed.

The solution in the general case is much more complicated. I have not obtained any answer, but perhaps the two features just noted, the symmetry of H and the rapid downward decay of H, are typical. 59

MODELS OF ATMOSPHERIC CIRCULATION

Eric B. Kraus Woods Hole Oceanographic Institution

Introduction numerical model of the Lorenz and I experimented with a simple with different forcing func- general circulation, which was integrated model is of the type developed tions for long periods of time. The by both of us [2] in monsoon by Lorenz [1]. It also was used can be found in the origi- circulation studies. Mathematical details present study will be published nal paper. The complete result of the within a year. Present Experiment Basic Properties of Models used in the difference between a "thermal 1. Heating is proportional to the and the actual potential temperature. equilibrium" potential temperature temperature can vary 2. In space, the "equilibrium" potential -- between schematized oceans from S to N and along parallel circles themselves vary seasonally and continents. These horizontal variations with time. also varies vertically 3. The "equilibrium" potential temperature time in the present series of but this variation is invariant with the actual potential temperature experiments. The vertical gradient of is allowed to vary with time. two equal layers. Vertical 4. The atmosphere is divided into by the difference of Beir gradients of variables are approximated in potential temperature between values in each layer. The difference c and the corresponding difference the upper and lower is denoted by by o0. in "equilibrium" potential temperature

model are: N-S distance 5800 5. The simulated dimensions of the of the circumference of the earth km; E-W distance 11,600 km (one-third at 300 N).

the E and W boundaries. There 6. Cyclic continuity is required at and no mass flux across, the N and is no temperature difference along, friction between two layers is assumed S boundaries. Ground friction and to the lower layer and to the shear proportional to the stream function of the stream function between the two layers. 60

Eric B. Kraus ......

7. Stream functions and temperature distributions are expanded 0 through as a truncated series of orthogonal functions. Wave numbers 4 in 2 are permitted in the N-S direction and wave numbers 0 through the E-W direction.

Summary of Experiments para- 1. Integration was carried out for six different sets of these was meters. Three different values of 'c were used. Each of potential combined first with a zonally uniform field of equilibrium potential temperature, and second with a field in which the equilibrium circles. temperature varied differentially along different parallel 100 2. The integration was carried out for a simulated period of five years years real time for one of the six configurations, and for for all the others. the 3. Comparison shows that the temperature differences between no forcing N and S boundaries of the model were larger when there was The along parallel circles. The same applied to the mean westerlies. the difference is pronounced during the "summer" of the model when heating gradient is weak. It is due to the meridional heat meridional on a conti- transport by standing, monsoon-type circulations which form temperature nental scale as a result of zonal forcing. The meridional when there is difference and the associated zonal thermal wind is larger is not no such heat transport by standing circulations. The difference hemisphere unlike that which is actually observed between the northern more sym- where zonal heating differences are more pronounced, and the metric Southern Hemisphere

4. Temperature, pressure, kinetic energy and other physical variations characteristics of the actual atmosphere exhibit seasonal solar which characteristically lag several months behind the seasonal lesser extent -- cycle. The thermal capacity of the sea and -- to a and may be that of the soil and the air, must contribute to this lag the dynamics its virtual cause. It can be considered, however, that from the of the system itself will necessarily involve phase shifts in winter forcing function. The meridional heating gradient is larger thermal than in summer. As it increases during fall the mean zonal of wind becomes stronger. This, in turn, leads to the development perturbations, which can add to the strength of the mean baroclinic so check westerlies, and which can transport heat toward the poles and tempera- or reverse temporarily the seasonal increase of the meridional ture difference and of the associated thermal wind. The development contribute to of baroclinic perturbations to the state where they can the meri- the meridional temperature difference cannot be in phase with dional heating gradient. 61

...... Models of Atmospheric Circulation

5. In electrical terms, the heating difference between the equator and the poles corresponds to an applied (seasonally variable) potential; the zonal thermal wind becomes then the charge on a capacitor; a baroclinic perturbation may be simulated by some device, a neon bulb for example, which requires a critical voltage before it begins to operate, but which will then conduct current rather effi- ciently. The meridional temperature contrast of the mean strength of the westerlies may then be compared with the output voltage from a simple network made of these elements (Fig. i). An oscilloscope photo- graph of this output is shown as Fig. 2. In this case, we simply used 60-cycle alternating current to simulate the "seasonally" variable input potential.

6. The oscillograph trace is suggestively similar to the plot of the output from our model or to the plotted values of actual observed mean zonal available potential energy (Fig. 3) which were published by Krueger, Winston and Haines [3].

7. The analogy could be taken further by comparing the effect of the standing, monsoon-type circulation to a variable leakage across our capacitor, which would be most effective when the input voltage is closed to its highest or lowest value (solstices) and which would be zero at some intermediate time (equinox). This would result in a lowering of the output voltage (westerlies) at the time when the input wave is close to its vertices (solstices). At the intermediate time, the output potential will build up rapidly and fluctuate rather vigorously (equinoctial storms). All these features are observed in fact in our model, though it would be misleading to take the analogies too far. There are essential differences between the action of a neon bulb and that of a baroclinic disturbance. Our numerical model is considerably more complex than the network in Fig. 1; the real atmosphere, in turn, is far more complex than the simple model which forms the topic of this paper (Fig. 4).

8. For the 100-year model, autocorrelations were computed of the 10-day means of the N-S potential temperature gradient. Lag times are multiples of 10 days. There was no significant autocorrelation in fall when the system tends to fluctuate more vigorously. A relation may exist in late winter and spring, though the evidence is ambiguous. In summer we do find systematic persistence between subsequent 10-day periods. This flips over to prevailingly negative autocorrelations which are discernible over fully three months. To explain this pattern, it may be considered that a weak temperature gradient, for example, will cause the travelling perturbations to die out. This permits the meridional gradient to build up considerably in autumn until this buildup is checked by the renewed development of wave perturbations. The opposite 62

Eric B. Kraus ......

happens if the N-S potential temperature gradient is large in spring or early summer. It will then tend to be small in late summer or fall. A negative autocorrelation of this type could cause a two-year cycle in our data, though we have not explored this matter.

Possible Relations to Extra-Terrestrial Influences

1. The timing of the breakdown of zonal motion in fall and similar real atmospheric events, closely related to calendar dates, may be influenced considerably by weak external effects.

2. During late fall and winter when our system fluctuates most vigrorously and exhibits the greatest amount of variety, it not only shows least evidence of autocorrelation, but it also "forgets" any initial conditions most rapidly. By the same token it can be concluded that any spikes or other short-period random fluctuation in the forcing function would probably not be discernible in winter. In summer, the actual potential temperature follows much closer the equilibrium potential temperature. Irregular variations in the forcing during the season would probably have a more obvious influence on the statistical state of the actual atmosphere.

Discussion

Shapiro: Smaller perturbations might be able to produce a breakdown more easily in winter, since the atmosphere may be closer to some threshold of baroclinic instability. Thus, it may even be easier to find effects of pulsing in winter.

Lorenz: With regard to the ability of pulses to affect the timing of events, I would like to suggest that impluses may have more effect at point A than at point B.

i/-5L A J

If the system is already approaching point B, its subsequent behavior is pretty well determined. This is not true in the region around point A. 63

Circulation .. .. . Models of Atmospheric

to be: How often is the atmos- Rooth: The question still seems respond to small perturbations? phere in the proper state to the electrical circuit analogy, Freeman: With respect to are the "constants" of this circuit work [4] would imply that question is, recent threshold is variable. So the really variable so that the at which can impluses change the time where are these thresholds and the threshold is reached? an effect. a small perturbation does produce Shapiro: Let's say that If you with a correlation function. We can treat this statistically perturbations of atmospheric parameters with take day-to-day correlations year, the persistence for that time of and compare them with the normal in persistence can be removed. effect of seasonal variation

References

Equations," Simplification of the Dynamic 1. Lorenz, E.N.: "Maximum August 1960. Tellus, 12, No. 3, 243-254, Study of the Effect E.B. and E.N. Lorenz: "A Numerical 2. Kraus, and Zonal Circulations," Vertical Stability on Monsoonal of of the Rome Symposium in Changes of Climate, proceedings Meteorological Organi- organized by Unesco and the World zation, 361-372, 1963. "Computations J.S. Winston and D.A. Haines: 3. Krueger, A.F., for the Northern Atmospheric Energy and Its Transformation of Period," Monthly Weather Hemisphere for a Recent Five-Year 1965. Review, 93, No. 4, 227, April Components in Hurricane Development," 4. Bradley, D.A.: "Tidal October 10, 1964. Nature, 204, No. 4954, 136, 64

Eric B. Kraus ...... C . • •.• •

z 3 4 5

I, Smnus5ocal power )rnput Z Capacltator 3. Resistor 4, Neon bulb S. Oscl Lloscope

Fig. 1 -- Electronic analog of model

Fig. 2 -- Output of oscilloscope 65

0 O ...... Models of Atmospheric Circulation

LU 2r o

2 50 J

O a . .. .I. I .. . . . I . . I, , . . .. I , ...... :

Fig. 3 -- Ten-day means of zonal available potential energy, after Kreuger, Winston, and Haines

r0.0 -O5 CASE OF LOWEST IMPOSEPD 5TAGILITY cx*0.050 0.075 - CASE OF GREATEST lMPO5ED ATA6\LtTr

,08e- ,"''.- ,

.07 : '.

*,'',', 6

I /\V /

.I05

|JIJ IA SA N / I M A I - J

Fig. 4 -- Ten-day means of mean zonal flow generated by model I 67

EFFECTS OF HIGH-LEVEL HEATING ON THE LARGE-SCALE CIRCULATION OF THE LOWER ATMOSPHERE

Ralph Shapiro Air Force Cambridge Research Laboratories

Introduction

I will describe some model investigations of the response of the lower atmosphere to high-level heating [1, 2]. I will not discuss the mathematical details of the model -- these are treated in the references given above. Using a vertically integrated model, numerical integrations have been carried out for periods of ten days. In one case (referred to as the no heating case, NH) the integrations are carried out from actual data starting with an initial situation coincident with a moderate geomagnetic disturbance. In the other case (referred to as the heating case, H) the initial conditions are identical except that the temperature distribution at the top of the atmosphere has been modified to simulate the effect of anomalous heating.

Our principal purpose was not to produce an accurate forecast but to show a difference in the flow fields between the heating and no heating cases.

Remarks About the Model

Functions have been developed to describe the temperature at a level in terms of the temperature at p = po = 1000 mb and p = = 0.1 mb, i.e.,

T(x,y,p,t) = G(p)Tpo (x,y,t) + H(p) T,(x,y,t)

The functions G(p) and H(p) have been determined from the properties of the standard atmosphere. The stream function at any level can then be described as:

i(x,y,p,t) = *(x,y,t) + I(p) Tpo(x,y,t) + J(p) Te(x,y,t)

where the bar means an average with respect to pressure, and I(p) and J(p) depend on G(p) and H(p). 68

Ralph Shapiro ......

to pressure and The vorticity equation averaged with respect p = Po and p = then the first law of thermodynamics applied_at Tp , and T . The model represent three forecast equations for 4, o 6 there is no bottom topography. atmosphere is assumed frictionless and be anomalous solar corpus- The source of energy is assumed to auroral activity and geo- cular radiation which produces increased = = 0.1 mb is applied magnetic disturbance. The heating at p In the case I'm describing statically to the model for 24 hr. ° temperature increase of 17 C today, this resulted in a maximum 2640 K) at 0.1 mb (64-65 km). The horizontal (from 2470 K to (Fig. 1) agrees distribution of the heating function, Qe(x,y) (map was rotated 900 by with maps of observed auroral frequency be in much narrower bands. error). Actual auroral heating would heated bands during the 24-hr We've assumed a broadening of these heating period.

Results of Numerical Integration the 500 mb heights, and The initial data were obtained from 1200Z. The top tem- the 1000 mb temperatures on January 2, 1964, K = constant in the no-heating perature was taken to be TE = 2470 for the heating case is shown case. The initial Te distribution in Fig. 1. out for ten days Numerical integrations were then carried 2 shows the total (240 hr) using 0.5 hr time steps. Figure internal energy, both kinetic energy and total potential plus as a function of time to in the heating and no-heating cases, t = 240 hr. somewhat greater in the The initial total kinetic energy is of the top temperature heating case because of the existence internal energy is consider- gradients. The total potential plus to the higher average top tem- ably larger in the heating case due energy is maintained through- perature. This difference in potential cases the total kinetic energy out the integration period. In both a maximum at about 2 days. How- reaches a minimum in 7 to 8 hr, and is considerably higher, and ever, the maximum in the no-heating case energy in the no-heating case occurs a few hours later. The kinetic at about 19 hr and remains greater surpasses that in the heating case However, the greatest difference throughout the integration period. 4 days. By the end of the 10-day occurs during the period from 2 to each other in an oscillatory period, the energies are approaching fashion. 69

Effects of High-Level Heating

The smaller kinetic energy in the heating case can probably be explained by the increased static stability due to the heating at high levels.

The gradual increase in potential energy in both cases, even when the kinetic energy has levelled off (between t = 220 and t = 248) is due to the nature of the smoothing operator in con- junction with the boundary conditions.

We can compare the predicted mean stream function (which is a good approximation to the flow pattern in the upper troposphere) for the heating and no-heating cases:

1. Up to 24 hr the charts are almost identical.

2. At 48 hr the positions of centers are almost identical, but amplitudes are slightly greater in the no-heating case. (See Figs. 3 and 4.)

3. Beginning at about 72 hr, the forecasts begin to diverge. and The amplitudes are considerably different as well as the shapes locations of the highs and lows. For example, there is a broad trough in the Central Atlantic in the heating case which is sharper and farther east in the no-heating case.

It was not the intention of this experiment to produce a forecast of the actual flow field, but rather to assess the effects of a heat function of the type postulated here on an actual flow field. Nevertheless, it is of some interest to compare the results of both the heating and the no-heating forecasts of the mean stream field with actual maps, which show the geopotential at 500 mb.

The agreement between forecast and actual maps is good through both 48 hr (both heating and no-heating cases). Beginning at 72 hr, forecast charts begin to diverge from the real map. It is our impression that the divergence is somewhat less in the heating case.

We plan to carry out a number of experiments with the same heating function, but with different initial conditions at times of geomagnetic disturbances. In addition, we plan to repeat the experiments with different heating functions. We may try repeated heating impulses. Finally, we may try working with a multilevel model rather than the vertically integrated model. 70

Ralph Shapiro ......

Discussion

Lorenz: Because of the distribution of the H(p) function, isn't it correct that you are really initially increasing the temperature at much lower levels than 0.1 mb?

Shapiro: Yes - H(p) - 0.5 at 50 mb, for example, so that a temperature increase of 170 C at 0.1 mb means a temperature increase of 8 or 90 C at 50 mb.

Kraus: What are the real physical processes that bring heat down from 0.1 mb?

Shapiro: These processes must be dynamical.

Kraus: Assuming they are dynamical -- where do you get the heat capacity at these levels?

Shapiro: That is one of the reasons H(p) has such a sharp variation with pressure. This is one of the basic difficulties with a vertically integrated model.

Rooth: Did you identify the energy input with the temperature change at 0.1 mb, or with the temperature change throughout the atmosphere implied by your H(p) function?

Shapiro: We took a heat input believed to represent the energy input from a moderate corpuscular storm -- and distributed this heat in the layer O to 0.2 mb to arrive at the initial temperature distribution at p = e = 0.1 mb.

Rooth: Then actually much more energy (2 to 3 orders of magnitude) would be required to produce the initial vertical distribution of temperature specified by your H(p) function. Thus I feel that your experiment is valid as a demonstration of the results that can be expected from an increase in the static stability of the magnitude you have assumed, but that it is not fair to say that a typical auroral storm would supply that much energy over the height range you've really implied.

Freeman: There is 100 times more energy impinging on the magnetosphere in the solar wind than Shapiro has used in this model. The problem is to show how this energy is propagated downward.

Lorenz: Have you checked your forecasts with standard barotropic forecasts for the same day? 71

...... - SaI . Effects of High-Level Heating

Shapiro: The no-heating case is essentially a barotropic model.

Shapiro: We've taken the same energy input and concentrated it in a more narrow auroral region. The total kinetic energy and the total potential energy distributions were almost identical to the results I showed here, but the details of the forecasts were different. Thus in this case, the details of the heating seemed to affect the details of the forecast.

We will try using repeated impulses to see if the atmosphere is more sensitive sometimes to this type of forcing. Perhaps we could provide a heating impulse at, say, the point at which the total kinetic energy reached its maximum (48 hr) in the figure I showed you.

Schilling: Is this 48-hr maximum in your total kinetic energy a property of your system or might something else be happening then?

Shapiro: It's not implicit in the system -- it must be associated with the initial conditions.

Rooth: Maybe the dip in total kinetic energy at the start of integration results from not fitting Tpo to represent the mean temperature of the atmosphere. Internal balancing may be taking place. It might be better to run the model for 24 hr before applying the heat. Then, in terms of the model at least, you would be starting with a balanced state.

Schilling: The point is that there may be other types of heat arriving, say, 48 hr after a solar flare so that the idea of repeated impulses is good.

Shapiro: The type of heating makes a big difference as to whether it will have an auroral-type horizontal distribution or be a maximum at the sub-solar point.

Freeman: It might be worthwhile to make your second impulse a cooling -- if heating gets to these levels by dynamic processes, there is some reason to expect that your heating would be followed by cooling.

Nordo: Could you try the no-heating case with a change of just d which corresponds to that of the heating case? In other words, does such a small correction of the flow at 500 mb give similar diverse flow patterns even in the barotropic case?

Shapiro: This could be done. 72

Ralph Shapiro ......

References

1. Berkofsky, L. and R. Shapiro: "A Dynamic Model for Investi- gation of the Downward Transfer of Energy Introduced by Upper-atmospheric Heating," Planetary and Space Science, 7, 434, 1961.

2. Berkofsky, L. and R. Shapiro: "Some Numerical Results of a Model Investigation of the Atmospheric Response to Upper- level Heating," Planetary and Space Science, 12, 219, 1964. 73

Heating · .· Effects of High-Level

IT'a ' rl~~~~~~~~~~~~~~~~~~~~~~~~~~~a180 -86 I Is ID I* t oilis r " rr ~__~_,,, , .:.d,...... · ·· s' ';';,;7-;;;..L:.'...... I .0 ......

. 4.-4 . ,1':,.* .44* 4* .. . .,.... -~...... -·· -·· ·'··~··~'. ' -4, ... ;;ŽLL.I'..j.. -" M~~~~~~~~i~i~oi .~~·~~'.~'"-...... c '.4.4.4'-T. . 4 4.4 4.... ., 4. -41.4. 4. 4.~ "...... *...... :' : : ?ii: :~..:~.* ~: :::.i4. ... 4.4.4.4.4...... : ' .. ...,. .. ':""...... J'...... D'.-'~ O ·- · · , ~.~~'Ot:, . ~~~~~~~~~~~~~~~·~n;F;o~~oi;;~~ ~ ...... ;,..,..."~~..~4UH~r·~. . ·~ulll~f~fffftfll. ~r~rr~r~···~...... · ...... : ...

...... ·.. =":....::'""...... = -- ...... rl.?.O ,,,,,,,.,,.%i7;i-;,;,O... ,:O _00 0 ~ ~ 0.0~ ··~·~~~~·~HI· III~~~

·...... ,;i...... ,.;.... -. ::i ...- ii: i ...... o. : : ! 1. ). I, -r ·~..··r.·~ "'O.1...1.0 1.0.1.0 .I I "Ir.p rW.I ...... _OI· ItrOa ).~~~~~~~~~~~~~~,. l...... rr l. O ).o ' · I'I ." ..... '~'...... 7.0 .1.0 . .7.2 I .1. "~~~~~~'.4 ...... ~··~rir~~ur··~~urur· -e6.. - IIla 6 -. 1.0 .. .?.O.,.C,

...... ~~~~~ ~~ ~ ~ ...... 0.. .Q.W..4 ....

ka .'A~~···~·~~.LI.1.0 ..... 4 .. .. ~,,..... :l.O: .'.O ..4...... rur~~~~~~~~~~~~~g

11 1.0 .ttt(.tt t .t1t .;..1;:· ... :.,.O1:;:.0 .... .,.;-;;~,;Ta-n;;~;;;;~,.,,,.... o .1·o.tl:O..... ::: fI:::.. I:: :::: o. '~. . of,.....,------...... WSM ...... I .:...... ·N1 ,.:,-~:: ::...... r.r1 '--- .....rtt b··I .1.. .1.. .. Ilt .... ,~~.I-2 b2·2 )M $1. 1.1 S..L r01o~·~llb·V~~l·~d cn\(l -O ? I I I : . so.~~ .....~~~~~ ...... ! :.:.:e::.-.; .:.g:..... ::: ...... 9 0 ...... o .1...... e. i·ri~ .p.IE.- 0 sob !"" 4_.4, ,...... :...... ~~~~~~~.....::.:...... 6...... S'L., I S I A .0 ...... 0 L.I2 )· S? _41. -0. .7 .1. O 1 0 .7~I . .3 O.. .. tL· L·lD · IIII·~~~~~~~~LC·L4~~~~1·~~...... ~.0 ...... tt tLUL ~ ~ ~ ~ ~ ~ ~ ~ ~~H ~~ ·I...... ,r.·...... · .1.1 1.0 -0.I·L rr~o·r~oI~or,.o rr. 11.1 Z.5 II., I... S.). IS..~~.·~~·· I.., ~~(I -0. -0. -0. -0. -0. .1. 0 2 1..2~)r~.o 1. i g dintialte.1--Smothe m r p eratuefieldatthe~tttt.u p p eu ...... ~~~L·-0. -0. -0...... p=. -=OI.lmb2.....I SO.1VU.. I St..11 S2.S Ss I- io n~~ I· ·1 )IL·ll) )·DI· 0. ' '; . ( · III LU ~DII...... ~. -0 ~ ~~~IIII~(1 .. 2 ~ ~11.1 ~ ~ ~~ ~ ~ ~ 01 44, -e.-. -.-0.I -0. -0 0 .1 II I .1..O.. -Z

.1 ? 5 C,O.. .1.. ?.O.. I O I O..S . '-It~~~~~~~~~~~~~~~~~~~~~~~~~~~ItII·rr· · 4·0 -0. r)~-0. )· -~I0-0. ~·1. -0.1~·~)· 41A .1 .0 .1.0 .,.L ~· -0. -0. -0. -0. -0. 0. . .?.O I··I··· 0 -0 -0 .1..0·. r·0 -.0.· ·~~·~~~~~·~~~~·~·tIII1LL· I~~~~~~~ttttI

0. -0. -0. -0. -0 0. -0.-0. -0.-0. -0.-0. -0.-0. -0.-4,. S'--°, .1./-/$ 17.0.1.0 .?.O ...... 1.0 1.0 1.. 1.1W 1.2:,?""Z",O H UL·~I l~·III Fig...,...o~.1 Smoothed initial temperature field·· ·;;~' At ·~"· thery~-~ upperI)· I· · ·~·10 pressure~··~~·~;~-I -· '·-e ,...3s = E = 0 .1 mb"~~Z!"'··U.~· "-~'Xit::;.=.:::;::' "'.'""'' ''"'"·"'"' '~ '~' ~ ' 74

Ralph Shapiro . . . .. , ......

2450

2350 -

2250 -

2150- N t 2050/

1950 -

1850 -

1750 -- H

--- 165000 -

40600 __ , -,,,______- 1250 - 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250

Q3 407000 - (sz 406000-

405000-

-- 404000

403000-

0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 HOURS

Fig. 2 -- Total kinetic energy and total potential plus internal energy in the heating and no-heating cases as a function of time 75

0 1lI Effects of High-Level Heating

00"~~~~~~~~~~~: O. ,I -L 0. 0. 0. 0. 0.D. 0I. 0.5S1 Mt. to.I IIS.S S. 10,I lo'I LO S . 0. S. SS.. .. D.S... S... ..I ...5 S.5.5 .. 5 ,8...... o tl,.I5 .5s 5. 5.i 5.5 5 5., 5 5. ·IS.· I · .S· e5.5to s.II III 5.55.5'&. . . 0. O5 0. 0. IS 1155. 5.55.5 5.55.5 5 15.5 ISS 11. 1S.SS, S..L55. ? 10.! O~t:. o. . o. Lo.oO.II 0. ..o.I o.. Io. oI.I o.I. o. S. o.o . . S S., 5.5 5I.IS.O.o5. o .O.I o.SI0o. a IO 00 o LO.Io... o. S. e. S.e.o. I 0 o5 DSo .SS SI eIISeS. . eI o e..S . .eS.SreoIS . o.. S ...... 5.1 ..S ..I 5.1 .. S.S.· 5.5 .)5.o. .)S. ..SIII.o. ' O. ' .'·II~ . . g.. . . . 50L.5.0 1M.6 9o 0. . . Oo5.1 ...... 5.1 IS .· ~ IS. IS.S S SII SGS.5. 0 5 .to. ~~~~~~~~~~~~~~~~~~~~~~~~.0000000 0000 I.LL. 0.00 ggO212122 II 000000I+IIIII ~~

o.1 SSS . 0. 0. 0. . 0. 0. 6"6 -64" ". 0. e.5. ,&0S 1211222222 1.1II00000io.0 0 886"88699.q 0.i o.5 I. D.S0.IS. i. Lo.5.i 4. .15. 2to .z 1o.1 t,, .,.1 to.029 .

*1 ,,,-, Z0H 0ooo5· 0 55221 &6e2III 152? III0 I IS S S22 .. .. . LotoI.. . 0 . 0.0. o.0 . 90 E. ,., : .!:;!'.o.r.. . . 55III2":O:I6w46 SS II OI H Y '" ' 222222229 S0.IS I S S1H11.1 SII0000SIIsee:55 . 5 15IS IIS 5 S 51 5 1151 SSSSS 1 000.S SS SS '--- .III to. 0 6 .... 22222 22252. S .O: ...... 222222222 ;6 I· IL 0.6 t0e0 00tM 22?222222Z22Z 0; SSI ll SS 5I 5 50 0. kO.110.1LI ;L 10.000 II I 1511 , S S S S S I 1 1.1 5.S S0.SS ,S0 I SS .5 I5 0I 2 12 2 05 S I I IS I. I . 150.ISIDe ot S 0000"00000QOQSi 1.1 0 LI1 10 221 0000 x ~....., " ISIS S·.·IO .IS.0 S. S. I.5. ~ ,a ISI ·IS .... ISI ISS .. IS , , .·S· I· SI .·SISS ISS IS. SI ISS11.11 S·'..SL S 5 5· .551 11.D. S 1 1· 11..5.5° °M. I::""· · 1.· ·6 r 9 ....S 0. SSS. I II SI IS115.1 IS.. 11.5 11.5 S SSSSS S SSIS .0.-.000o "I.! !!!!~:..I'll ...11 ...SlS 2!i!!!I~- SS00I SSSSS ISSI o : .- " :;!.0.0.. ° 00 0 0 0 0I SI SS I SS ' .:S $5 0 0 05 . II22zS2 I I.II I0. I 0S00 00 0 aSsIllto". 000000 O 2222222222,. 6& Pill IS SI S Io . SI 5S6 00 00S . 00 II 6 l · . 41 0 0mm el · - · .·~ · 1·2·1·· . - · - ~ IS 11.115211.1.·1 5.51 S.S 1 S··I S I· S. · · · · Il tt. 1.1 ISS.1L t SI L SI II 10 .1 SI]0.1 0.1 IS g000000000000Q00ooooo 2i ...... -1q...6. 0... . ",-, o~ ' 2Z2,22222ZZ22Z2 oo 6~r ;ZZ222 .·W~l~aO~O~O,o,,,zz zz zzaw MO.2;'"°oooT:.· . II...000 M...... A.,2";::' , ... .. 000 225222 221 11. ISS 5555555.55.5555,. . ...::.O . .111 ::::15.S 11.111.5 IIIII II 2215.1lz : 5. IS : .ISS IS Ill .1as . S 5. 005.5.5 SI SI 13~0 .,I ,,, 1 5 50 SIasISISSISSSI1.: I,., SSSS..5 IS.. 15III.9IIoS S S. I 0o0l ISZ 51e2 225 I S . 5. ISS M&16L Q0000000.9 O I 9.7 O22222. 0S ..S ... .1S,. 0 ..... 2t.1 .1 IS.0 S.S SS SI S Ill 5.1 5ItI ,. . 5 .5 5 I S S .5·. .IS. IIS9 .. 1I '5 . 1.1 ISS .1 SI 11. ISSI .. s IS. I III ,,WIois 5.o .5.1t 4 1 50.151 5.;2·· J. 1 S.2222222 S 0L O:, ."lo.66616 .)668 00000 iII a IN o. IS ~S to 1010.1 3 tla 10.1 2 Io.,10.2 tola 2L ~ it I I ..II.1. I .Stoi.1I222 I. to.I .SI . 1SS12222O I"I'l ° o ...... o .000...... I o0000000oo 21 MIIM 10.1LO.1...0.11 Vf"VIO'.) 10"oo .. ... -I* ?o-oooO .. ,,,~s~, oo lo S o .SXII o ,1(111~11 11~~~2o000. SS51 5 II SSSS ss CIIIaooIaIIIISI55SSSS O I 000 .0 I 0Z I...... 900E · · .0 1.1 9.2 1.3 re1O.L MD 1o. A. C. Lo..222 to...... to... ..rV0zj_T·0 0;00-0 ...... Ii ,CD 000 UTZ222222222 o00~V(I~o.iir.i o.. OQO 211 I SIL 000 .....)b . .. SI I S55 0 5 SS *rWI WL.Z 1~12...... IIIII 2221 Y, .II~~~~~~~~~~~~~~~~Da22 o.1LO.O II," .110.1 tO.L Ml10.t t0-O .0S.~~~~~~",., .. :lo. .. S0I.I o., . S. S ,oz e.t. 0o.z1o0 O.1o.IiO.t S00~~~~0 S.a.,SS. i,22 o.eo . ,o,. ,o ~oz o, ,O.0ooIooo 1 3I- I- 10 1 or . o. . 1O~~t10.2 kQ t5Co5 10. o.t55 1II H·II I------5 5 5 S 5 SSLIS =.6. zzr OR 'M0.3 II I

I!, o."-- 0.. III~~~~:10"t 11III· ILIIILIIII 211III 000IL L1I· IO.... I.....to...... th n ei ...... at 2 t = 48. hr in 2a. Fig.O...... 3O reicted 22 meano strea funtio ·CLC ·IIb1 10.1 ....21 00000. . I s I" ~~~~~~~o...O.... ,..,,..0~.... :2222 cas222 ...eile : ... :: ,,:: ....I...... 2222... . id

5. .00 S5 5 S,:..01..SSlos 11.115. O" ,S toI .2 50.25. Ot1 . 1.1W 10.1 to1Ito.%~~~~~~~~~~~~~00000000 0000. 111. 1 SS 5 11.1 1 .5 S.5511. SS S .. 5IS5. 00 '1z ...... 2.5.25 5. 5. 5 5. . 0 200.~~~~~~~~~~~~~~~~~~· O 5. ;8.8 ~ 000000 $o.z0z~. M oz . t~ eo. O. O. 10.1~~~~~I.o ,. e . o.O II ·· to.. I... l...... o.r o., o.· o. .46.00 · .0. t~~~1hto".- ...... :I. ~ ~~~9. 1...... , ~ . ~ 116,6 ::::?::,:~:~(~ 1.0,:o~~~ke"O"100000.1 ...... 12,...... 66.. ~ ~ ~~ ~~~I·II a. ~ ~ ~ ~ ~ ~ "%I"" lizz~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~O~ ~ ~ ~ ~ ~ , o;0oO.1'', 9.S1.31.2S.,..?II...... ""t :.:g"OO." Goz.-...... Il.to...... S10p 2~~ ~ ~0 ~ o...... ~~7ooo...... I1, 5L...... 0 . 2200"Z'I I ~ ~ ...... ~ O0....I ...... 76

RalphSh ~ p ~r.S. S . . S, . . SS S, . SS .SI . . .

II~~~~~~~~~~~itl9~ ~II? 2 isttII I So.o . S., .l . e 18 S. llll,.llll 1. @11. @1 @11. |^l.1 n1X1I S, X X 940,0"SX11.

10.1 I1. 01z. 011. 011. oiw. ele 91 1.to.1 1 10.0I 1.1 e O- O' 46~ ~ oooooooooooooooooooooooooooooo L1- ~ ~ ~~ ~~~~1 1G-Soso ooooovooooo.ovooooooo J 10.0I 1 0.010.0100.0 0-0t 0. lll °l -° °°t °°l o~~~~~~~~.1 10.1 10.1Io.,10.

10.010.010- 10. 10. 0.;0u ooe .1. . . 10 10 Gt1.1 10- 1.1

0"0;'""|iIe ; OOUu__,' " " ; ;014.10 to.. lo. * " * s** ;* t**t*l6. .*00;0z*; a8.84.~~~~~I--1000-l- .00.4.4

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~...... aO

" ' " " * * ' " "' : : : ' ' O. O 0. .. I I0 00 ... 0tZ o ... .2 S 4" ISS *. i '~i=~ t@ to.* 10.

0. 0.9o*222i ; .5 b.v *.1lo. *-O. 0 = 0 " a so 66

0.|22ss 0 222 112M Zf*tM2 2@ °..2111lose22 2°° - a2-- 0* 22 * ) 222 0222222222222222°° olq *" f ,

...... ' ','fi ';:, ';: ':: '.-

2 §.^ .2 2z.i2 -1 -t ."' g't **. 2210.10. 10-t O.oo.10.1 10.1I 10.0 I^.,222.1°°2°.o' ',_ IC B

Mechanisms Involving the Apparent Influences of Solar and Lunar Tidal Forces on Peak Rainfall and Other Meteorological Phenomena

Summary Paper, Topic B

MECHANISMS INVOLVING THE APPARENT INFLUENCES OF SOLAR AND LUNAR TIDAL FORCES ON PEAK RAINFALL AND OTHER METEOROLOGICAL PHENOMENA

Glenn W. Brier U.S. Weather Bureau

Topic B took as an assumption the empirical-statistical finding that peak rainfall occurrences are significantly more frequent a few days after maximum solar-lunar gravitational forces. We have observed in the seminar discussions that other weather parameters seem also to be appreciably influenced by gravitational tidal factors, and in a fashion plausibly con- cordant with the above result. Among these are hurricane formation, the position of the eastern Pacific anticyclone, periods of sunny weather, etc.

A number of papers within the last three or four years have delineated the empirical basis for our assumption that such effects merit a serious effort to find physical mechanisms to explain them. However, one can trace the origins of these notions to many earlier works. For example, Reid Bryson published a paper on this subject in 1948. And in 1956, at the predecessor conference to this one, John W. Mauchly made some observations about a suggested relation between lunar tidal effects and precipitation. This led to more recent work by Woodbury, Bradley, and myself.

At the outset, let me reiterate that the amounts of total rainfall variance accounted for by the gravitational tidal effects are very small. On the other hand, it is of great scientific importance in our efforts to understand the physics of rainfall distribution, to understand how so very nearly infinitesimal tidal forces can produce effects in seemingly very indirectly related rainfall mechanisms.

One helpful fact is that the tidal forces, as Chapman pointed out years ago, are very thoroughly predictable from astronomical geometry -- so that the nature of the forcing function, however complex, is precisely known. 80

Summary Paper, Topic B ...... •.•.••

A Mepchanism-Oriented Framework for Looking at the Empirical Evidence

Let me refer to the "black box" diagram, Fig. 1. The atmosphere, a highly complex system, may be thought of as an analog of the electronic engineer's black box. It has many inputs, such as the annual and diurnally varying solar energy inputs. One input is the small gravitational tidal forcing function, variable on several time scales.

One can learn much about the characteristics of the system represented by the black box if one applies a precisely known input signal and studies its presence in the output. The tidal forcing function is such a precisely known input.

The gravitational tidal force functions vary in many ways. Figure 2 shows three recognizable extremes. The actual semi- diurnal tidal functions of different periods of time can be grouped into two classes by the nearness of their approach to the three prototypes: A = large variance; B = small variance; furthermore, one can think of letting the system operate in an ideal third state, C, where C = zero variance. Of course, all meteorological model studies to date have tacitly operated under the assumption of C. Whether a given period of time falls into A or B depends on such things as the distance of moon from earth, the distance of the moon from the ecliptic plane, the season, the latitude of the station, etc. (The zero variance case, of course, does not occur in nature.)

Examples of tidal forcing functions classed as A and B, for real dates, have been discussed in detail during the seminar. I presented evidence indicating that a tidal influence on rainfall in the U.S. appears to occur in periods of type A tidal change. The type B cases give no significant correlation with lunar phase at all. These facts lend plausibility to the lunar hypothesis. They also show how empirical studies can be designed not simply to "fish" for relations blindly, but to test specific hypotheses more precisely.

Similarly, the Bowen rainfall peaks attributed to January "singular dates" (now sometimes called "calendaricities") have been shown by Visvanathan and independently by me to derive plausibly from the fact that "favorable tidal conditions" occurred preferentially, over the last 50 years, on the Bowen dates. 81

Solar and Lunar Influences

The dates on which these favorable tidal conditions occurred during the period 1900-1949 are given in Table 1. Of course, these dates will shift with time and, over periods of several hundred years, favorable tidal conditions would appear to be more randomly distributed with respect to calendar date.

It is even possible that the 26-month tropical stratosphere wind reversal is related to the favorable tidal conditions. There is a 26-month periodic term in the tidal forcing. And my analysis of work by Mauchly, Woodbury, and Holloway shows that the 26-month variation of Batavia pressures indeed peaks on the favorable tidal condition months.

All of these studies contain clues to mechanisms at work. We made little headway in our seminar toward precisely defining a comprehensive cause-effect linkage, chain, or inferential tree -- even speculatively -- to explain how lunar and solar gravitational tides can produce a variation in a subtle parameter like rainfall. But future statistical studies should be sharply focussed toward tests of mechanisms, if indeed they can be suggested.

Suggested General Guiding Principles for Future Analyses

We did reach a few general conclusions about desirable directions to proceed. Plans for future work might profitably take account of these, we felt. Our suggestions included the following:

1. Are physical models, numerical or otherwise, available into which tidal forcing functions can profitably be incorporated?

(a) Can one model sea-air interactions in which tidal (oceanic or air) terms have a plausible effect?

(b) Can one think of a theoretical basis for wave effects that might reflect a tidal influence at a discontinuous atmospheric level such as the mesopause, the tropopause, dust layers, etc?

(d) Are there possible non-linear interactions of thermal and gravitational tides, due to the lag times between them, that might be studied? 82

Summary Paper, Topic B......

(e) Can variable solar activity plausibly interact with gravitational tides to produce any predictable effects -- using model studies like the Shapiro-Berkofsky approach, or otherwise?

(f) Can tides modulate the abundance, or effective temperature, of freezing nuclei? Or of condensation nuclei?

(g) Can tides affect cloud height enough to make a radiational heat source (or sink) modulation model plausible?

(h) Can a physical model based on changing of the timing or the amplitude of triggering at a critical state (such as temperature for rainfall) be made plausible?

2. Are the tidal -influences predominant on a particular scale of interaction -- i.e., local, synoptic or global scale? Time response studies, lag analyses and spatial studies are possible. For example, already it seems that winter-continental rainfall may be most significantly affected. But the approach to such questions can be sharpened.

3. Are the tidal effects instantaneously operative or are they integrated over some appreciable time period?

Specific Analyses Suggested

Several things were suggested as worthwhile specific further steps of analysis. We listed the following, though undoubtedly added or different items and priorities may be postulated:

1. A complete ephemeris of key dates, months, and tidal classi- fications should be published, based on solar-lunar gravitational tides, for representative locations, over the period of available reliable weather records. This is no small task!

2. The semi-diurnal solar pressure tidal wave, S2, in the tropics should be analyzed in detail.

3. Tidal forces should be put in an appropriate numerical model and integrations run with and without the tidal forcing.

4. It should be determined whether tidal variations occur in convective precipitation regimes, in over-running systems, or in both, 83

Solar and Lunar Influences

5. We should consider whether the gradual build-up of the horizontal tidal forces has an effect on the mass distribution of the atmosphere. This would follow up on the idea that displacements of the Pacific high are associated with changes of the N-S horizontal component of the lunar tidal force.

6. Cloudiness in tropics and differences in sea-air temperatures might be related to tidal forces -- can statistical tests of these hypotheses be devised?

Other Priority Items Suggested

1. Look at the sensitivity of thermal solar tides to heating in the ozone layer.

2. Extend radiosonde and ozone measurement to the tropics and to as great heights as possible, to permit tidal variation analyses in the tropical stratosphere.

3. Compare tidal parameters with ozone and with various circulation indices.

4. Stratify tidal-rainfall or tidal-weather analyses by local topography and by large-scale circulation indices.

5. Look for modulation of errors of USWB Numerical Weather Prediction forecasts by tidal regimes. 84

Summary Paper, Topic B...... •......

Table 1. Dates that certain "favorable tidal conditions" occurred during the period 1900-1949. The range of dates is shown for each group and the mean date is underlined. The number of events is shown in parentheses ( ) after the dates.

January 1-3-5 (8); 11-12-14 (9); 20-21-22 (5); 30-1-3 (8).

February 9-11-12 (6); 18-20-22 (8); 28-1-4- (11).

March 10-11-12 (6); 19-20-21 (8); 28-30-1 (5).

April 8-9-11 (2); 17-18-19 (4); 28-29-30 (3).

May 6-8-10 (6); 16-17 (2); 27-28-29 (5).

June 4-5-7 (3); 14-15-16 (3); 23-25-27 (4).

July 4-5-6 (3); 13-14-16 (4); 22-24-26 (6).

August 1-2 (2); 11-12-14 (4); 19-21-23 (4); 30-31-1 (3).

September 7-9-12 (5); 19 (2); 29 (2).

October 4-8-11 (7); 17-18 (2); 27-28-29 (4).

November 4-6-8 (5); 15-16-17 (3); 23-25-27 (6).

December 3-4-5 (4); 13-14 (2); 21-23-26 (5). 85

*0'O.•«.<,,.•.•••..,. Solar and Lunar Influences

INPUTS OUTPUTS

—1 ^^AS^~~~~i~FALL SOL.AR ZE~ERGY -^t e fJF AL —^t>LA^O CLOU I WC-SS

(-THE ATMOSPHERF) OSuLLiTv. SQL.AP / LUMAK -ETC GRAVITATIOOAL

ETC,

Fig. I -- Simple model for studies of atmospheric response to known inputs

IMPUT Fu KJICOT i VAIAi^Ce CLASS

V'(ZIAMCE ^^AA f I^VWA A - A - LA(GC

-______- B^S('~M LL VARI A OC6

____—__ ___—___ - C HZERO ^^P^ECX NEW FULL FJEu Mcc M iOO'J mooo)

Fig. 2 -- Classes of gravitational tidal inputs

THE APPARENT INFLUENCE OF THE MOON ON PEAK RAINFALL AND OTHER METEOROLOGICAL PHENOMENA

Glenn W. Brier U.S. Weather Bureau

Introduction

My brief summary will hit some high spots only, and will not give the deserved attention to work by Adderley and Bowen [13, Wulf [2], Bigg [3], Bryson [4], Visvanathan [5] and others. Most of the work I shall summarize here has been published [6,7,8] or will soon be 09,101 The Monthly Weather Review paper [8] is the principal source from which I will speak today.

My interest in this field began when Max Woodbury of New York University and I examined some preliminary work by Donald A. Bradley, indicating an apparent lunar influence on the occurrence of extreme precipitation in the United States.

Lunar/Rainfall Effects, with Emphasis on Work of Brier, Bradley and Woodbury

In our statistical tests of lunar/rainfall relationships we have relied mainly on valid non-parametric tests that avoid the problems of non-normality and autocorrelation in precipitation data. The major emphasis has been on testing for phase consistency in independent data samples, thus avoiding the more difficult and controversial problem of the significance of the amplitude of a cyclical wave, which is very much affected by the normal meteorological persistence in the data and in smoothing procedures.

The results of the work I published with Bradley and Woodbury [6] show an apparently significant tendency for heaviest 24-hr rainfalls to occur about two or three days after full moon and new moon at North American stations in time series of the order of 50 years' length.

Iver Lund [11] independently analyzed sunshine data over the U.S. and found a curve almost exactly opposite. This might be expected of course, since less sunshine would tend to occur during periods of heavy rain. A number of other data sets appear also to show such effects. For example, Berson and Deacon [12] at Djakharta 88

Glenn W. Brier ......

and Mangalore, detected evidence of a lunar effect but found an indication that years of low solar activity tend to show the effect more clearly than years of high solar activity. We have found the same result in our data for the U. S. [7] .

There is even some evidence that large-scale circulation phenomena show the effects of lunar association. For example, many years ago Bryson [4] looked at the position of the eastern Pacific anticyclone in the subtropical high pressure zone, and found what appeared to be significant effect. Bradley [13] has found that hurricane starting dates listed by the USWB also seem to be related to the time of full moon and new moon.

Visvanathan [14] found, for tropical atmospheric depressions over the Indian Ocean, a similar lunar period relationship peaking near new and full moon. Other data-apparent relationships to lunar phase, real or accidental include:

1. Pressure jumps (same phase relation as peak rainfall).

2. 1936-1956 data by Korshover [15] on the number of stagnant highs over the eastern U. S. that are potential air pollution hazard periods. (Mirror curve to peak rainfall.)

If these lunar effects are real and are produced by tidal forces, they should be related not only to the lunar phase but to the other cycles which reflect the tidal variations. The most important tidal periods are:

1. The Synodic period -- the one described above, from new moon to new moon: 29.53 days.

2. The Anomalistic cycle-- variation of the moon-earth distance; the period from one perigee to the next: 27.55 days.

3. Nodical cycle (or Draconitic cycle) -- declination of moon's orbit from the ecliptic plane: 27.21 days.

Moreover, the periods resulting from the coincidences of these periods (i.e., moon at new or full moon, at perigee, in the ecliptic plane) would be much longer. However, these occasions would be times of the highest lunar and solar gravitational tidal forces. Evidence for all these periods as well as for the lunar semi-diurnal tide can be found in rainfall, suggesting that very small lunar and solar gravitational forces can produce effects on maximum rainfall large enough to be discovered. They may be too small to be practical predictors, 89

...... Lunar Influence on Peak Rainfall

but the effects are of theoretical importance to our understanding of rainfall and atmospheric dynamical processes.

Bowen's "Singularity Dates" and Lunar Effect

Visvanathan [16] , moreover, made an interesting suggestion regarding Bowen's conclusions that the rainfall data for Sydney, Australia exhibited greater than expected rainfall on some dates in January as compared with others. This had been interpreted by Bowen as a result of meteoric-shower-producedfreezing nuclei. Examining Bowen's data, Visvanathan found that rain on the "singularity dates" showed a definite lunar phase effect, suggesting that not only did Bowen's dust have to be involved, but for such dates the probability of rain increased when the lunar phase was right.

These results encouraged me to examine the same Sydney data in relation to the other tidal cycles to see whether the most extreme rainfalls fell at favorable times in the synodic month, and also to see if they were associated with the time of perigee of the moon and with its position with respect to the plane of the ecliptic. This was found to be the case, and furthermore these concurrences, which I call "favorable tidal conditions" (FTC), are not randomly distributed with respect to calendar dates, but occur much more often on four January dates, and in particular on Bowen's published singularity dates. This is because of the relationship of the annual calendar to the "beat periods" of the three lunar tidal cycles. In a longer data sample, because these lunar and solar calendars slip about nine days per century, the preference for the "Bowen dates" would progress through all January dates (and similarly for other months, of course). Thus, over a very long period, the FTC events would occur equally frequently on each day of the year.

Thus, it may be unnecessary to postulate an annually recurring meteor shower singularity to explain, in a 50-year data sample, an effect peaking in frequency on certain calendar dates.

26-Month Tropical Stratospheric Circulation Reversal

There is also a beat phenomenon involving a 27-month tidal period and the solar 3-monthly peak thermal heating at approximately 10ON or S of the equator. Holloway, Woodbury and Mauchly [17] had noticed an effect in Batavia S2 (solar semi-diurnal wave) of about 26 months. Since Batavia is 60S of the equator, I took their data to test for evidence of a lunar/solar tidal effect. One would expect the lunar and solar pressure waves to be in phase twice a synodic month and, when the favorable tidal conditions 90

Glenn W. Brier......

occur, one might expect the S2 wave to show extremes related to these favorable tidal conditions. This is how it turned out. A real effect seems to be present! Thus the 26-month or 27-month effect may be tidal. The driving force might be the increased cloudiness and rainfall produced by small mean vertical motions associated with tidal forces. This is consistent with the earlier suggestion by Gold [18] and the recent conclusion by Malkus [19] that overall cloudiness variations in the tropics can be sensitive to small changes in the mean vertical motion comparable to those which would be induced by the divergence-convergence field of the S2 tidal wind.

A Suggested Model of the Lunar Tidal Rainfall Effect

I suggest a very simple model of what may be happening to show that a very small force may be able to produce the kind of observed distributions we find for peak rainfall or extreme weather occurrences. In Fig. 1, I illustrate a simple model in which the superposition of a small periodic forcing function f on the basic linear forcing function F can affect the time at which some critical level Fc is reached. An event E occurs when the critical level is reached. The timing of the events will depend upon the slope of the basic linear forcing function and the amplitude (or phase) of the small periodic forcing function. Variations in the ratio between these parameters have a marked effect on the timing of events. This is illustrated in Fig. 2. Experiments of this sort are discussed in greater detail in my Monthly Weather Review paper [8]. This type of model may, if operative in peak rainfall, explain the kind of statistics we observed. The phase analysis may show the small force sensitively. When the main force is far from the critical level nothing happens regardless of the phase of the small perturbation. But near Fc things become sensitive to the phase of the small force.

This mechanism, of course, is not limited to the effect of tides -- but includes any event that might be triggered earlier or later as a result of a small superposed force.

Discussion

Visvanathan pointed out the astronomical fact that about every 26 months the new moon (or full moon) and maximum perigee values coincide.

Brier suggested we should now try to go to actual computation of vertical and other motions associated with tidal forces, and attempt an explanation of how these motions might generate the meteorological phenomena observed. Also he urged that correlation searches be done 91

••....•. . • •...... Lunar Influence on Peak Rainfall

with a view to testing a specific idea or hypothesis rather than simply fishing for associations —-which can always be found if you search awhile. For example, a latitude effect in lunar tides can be predicted from tidal theory -- and a meteorological consequence of this latitude effect might be sought in the data.

Lorenz warned that "aliasing" can be dangerous. For example, once-a-solar day observations can give an aliasing of a lunar semi- diurnal effect with a lunar fortnightly effect. These dangers need be thought about and to be guarded against. Brier indicated that he had given much thought and consideration to this type of aliasing problem as well as other aliasing phenomena which seemed to be even more subtle or complex.

References

1. Adderley, E. E. and E. G. Bowen: "Lunar Component in Precipita- tion Data," Science, 137, 749-750, September 7, 1962.

2. Wulf, 0. R., and S. B. Nicholson: "Terrestrial Influences in the Lunar and' Solar Motions of the Air," Terrestrial Magnetism and Atmospheric Electricity, 52, 175-182, 1947.

3. Bigg, K., and G. Miles: "The Results of Large-Scale Measurements of Natural Ice Nuclei," Journal of the Atmospheric Sciences 21, 396, 1964.

4. Bryson, R. A.: "A Lunar Bi-fortnightly Tide in the Atmosphere," Transactions of the American Geophysical Union, 29, 473-475, 1948.

5. Visvanathan, T. R.: "Heavy Rainfall Distributions in Relation to the Phase of the Moon," Indian Journal of Meteorology and Geophysics, Symposium issue on Hydrometeorology of India with special reference to flood forecasting and warnings, 1965.

6. Bradley, D. A., M. A. Woodbury, and G. W. Brier: "Lunar Synodical Period and Widespread Precipitation," Science, 137, 748-749, September 7, 1962.— — 92

Glenn W. Brier ......

7. Brier, G. W., and D. A. Bradley: "The Lunar Synodical Period and Precipitation in the United States," Journal of the Atmospheric Sciences, 21, 386- 395, July 1964.

8. Brier, G. W.: "Diurnal and Semi-diurnal Atmospheric Tides in Relation to Precipitation Variations," Monthly Weather Review, 93, 93, 1965.

9. Brier, G. W.: "Remarks on Paper by T. R. Visvanathan, 'On Bowen's Hypothesis'," Australian Journal of Physics, 18, 1965.

10. Brier, G. W.: "Comment on the 26-Month Oscillation in Tropical Latitudes," submitted to the Quarterly Journal of the Royal Meteorological Society.

11. Lund, I. A.: "Indications of a Lunar Synodical Period in United States Observations of Sunshine," Journal of the Atmospheric Sciences, 22, 24, 1965.

12. Berson, F. A., and E. L. Deacon: "Heavy Rainfall and the Lunar Cycle," submitted to Nature.

13. Bradley, D. A.: "Tidal Components in Hurricane Development," Nature, 204, 138, 1964.

14. Visvanathan, T. R.: "Formation of Depressions in the Indian Seas and Lunar Phase," submitted to Nature.

15. Korshover, J.: "Synoptic Climatology of Stagnating Anticyclones East of the Rocky Mountains in the United States for the Period 1936-1956," U. S. Weather Bureau, 1959.

16. Visvanathan, T. R.: "On Bowen's Hypothesis," to be published in Australian Journal of Physics.

17. Holloway, L., A. Holt, J. Mauchly, and M. Woodbury: Topics in Statistical Meteorology, Final Report, Meteorological Statistics Project of the Institute for Cooperative Research of the Univer- sity of Pennsylvania, 1955.

18. Gold, E.: Quarterly Journal of the Royal Meteorological Society, 39, 293, 1913.

19. Malkus, J. S.: "Tropical Convection: Progress and Outlook," Proceedings of the Symposium on Tropical Meteorology, World Meteorological Organization, Rotorua, New Zealand, 247-277, 1963. 93

..... «,,«..<,...••• Lunar Influence on Peak Rainfall

Fig. 1 -- How the time reaching a critical level Fc can be changed by the superposition of a periodic force f on a force F which is changing slowly with time.

Jo OL (CP-creP>CCT_^E .10

2, ,0 l l l l l l l l l l l0l

'..) .00 I I I I I I~~~o %4I I .0 --ASo-A^

2L 0 ' r(ExpecTeD) 0.0 Or .40040 Or.40 o./' —

^z) *OC - I JJ.W.L.L.LJ -LLI o ~~(Exp~creo) ____ _

0c0o *O *j ^3 .0 .40 *(0 .70 .S0 .00 .0 T-r1M OF CYCLE (t~eC.MAL CL^SS)

Fig. 2 -- Distribution showing relative frequency of occurrence of E (change in state) according to the decimal class of period T. Curves (a) to (e) are for various ratios 8=Af/AF where ^F is the total change during the period T of the linearly increasing function F.

CONTINUED DISCUSSIONS, LUNAR INFLUENCES

Glenn W. Brier U. S. Weather Bureau

In this session, I will continue my discussion of several topics and present facts and some speculations concerning possible physical mechanisms that might explain the influences of solar and lunar tidal forces on peak rainfall and on other meteorological phenomena. My position today can be-expressed by a quotation from Fielding's Tom Jones -- "It is our province to relate facts and leave causes to persons of much higher genius." It is up to you gentlemen to criticize and evaluate physical mechanisms that have been suggested, and to propose new ones.

Modulation of the Semi-Diurnal Pressure Wave in the Tropics by Lunar Tides

Please refer to Ref. [11 for a more complete discussion of the analysis of the lunar influence on the magnitude of the semi- diurnal pressure oscillation at Batavia. Briefly, the facts are:

1. There are great variations in the amplitude of the tidal forces from month to month.

2. There is an approximately 27-month period in the tidal forces, due to the beating of the three most important tidal cycles.

3. Holloway's [2] data show a fairly regular 26- to 27-month oscillation in the monthly averages of the amplitude of the semi- diurnal pressure wave. (Daily values might show the lunar effects even better.)

4. The amplitude of the semi-diurnal pressure wave is largest during months in which the variations in the lunar tidal force are greatest. The semi-diurnal pressure wave is smaller during months in which there is little variation in the lunar tidal force.

I have interpreted this as a modulation of the solar semi-diurnal pressure wave by the lunar tidal wave which is in phase with the solar wave twice per synodic month. There are more data available at Batavia and this idea should be pursued in greater detail. 96

Glenn W. Brier ......

The suggestion, which is consistent with previous findings and conclusions of others, is that small changes in the mean vertical motion induced by the divergence-convergence field of the solar semi-diurnal tidal wind can affect the cloudiness and perhaps the precipitation in tropical regions. This may in turn cause interaction with larger-scale phenomena of the general circulation. I have been told that Richard Lindzen [3] has been exploring the 26-month oscillation in the tropical stratosphere in terms of variations in tropical cloudiness, but I have not seen his paper.

Seasonal and Geographic Variations in the Amplitude and Phase of the Lunar Rainfall Relationship

If we hope to understand the way in which lunar tidal forces modulate the normal diurnal variations of meteorological phenomena, we must be aware of these normal diurnal variations.

Figure I shows the distribution of frequency of rainfall as a function of time of day for a network of U.S. stations over a ten-year period. Note that the wintertime maxima seem to occur about 3:00 A.M., whereas the summertime maxima occur about 4:00 to 5:00 P.M. I don't want to take the time today to attempt to describe or to explain the variations present in these curves; I do want to point out that we must take into account these normal diurnal variations in the processes that produce rainfall before we can begin to understand the effect of small lunar tidal interactions.

Normal spatial climatology must also be considered. Refer to Fig. 2, where marked geographical differences are apparent. Areas that show afternoon maxima may be triggered or modulated by lunar tidal forces about three days after syzygy, whereas other areas may be more susceptible to lunar influences during other portions of the lunar cycle. The presence of geographically preferred regions for precipitation during the various phases of the lunar cycle and their possible effects on the general circulation might also be considered. Our results indicated broad- scale increases in precipitation of the order of 20% being associated with the lunar effect, and this might result in increased heating of the atmosphere in those areas due to release of latent heat. 97

...... Lunar Influences

The Lunar Influence on Circulation Indices or Patterns such as Depressions, Anticyclones, etc.

I would like to show you the results of an unpublished experiment that we did along these lines. In an earlier paper [4] daily averages of precipitation over the U.S. were grouped with respect to favorable and unfavorable tidal conditions. I found sizable increases in precipitation several days after syzygy (period (1) in Fig. 3) and sizable decreases about 11 days later (period (2) in Fig. 3) during periods of favorable tidal conditions. It was therefore interesting to inquire whether there were more cyclones over the U.S. during those periods of increased precipitation, and whether there were any geographically preferred regions for the occurrence of these cyclones. We counted the number of cyclones in 10 -squares over most of North America for the periods of increased and decreased rainfall and subtracted the latter from the former. The results showed that on the average over the U.S. there were 15% more lows during the period of increased rainfall than during the period of decreased rainfall -- with favorable tidal conditions. As a check, I drew a similar map for the period of less favorable tidal conditions. That is, even though the rainfall effect did not appear in these cases, I compared the number of lows over the U.S. several days after syzygy with the number appearing about 11 days later. The result was similar, though not as pronounced. There were 77o more lows during the period several days after syzygy.

The geographical distribution of increased frequency of cyclones was interesting. One maximum was over the East Coast and the other was over southern California and western Nevada. There was a pronounced minimum (fewer cyclones) east of the Rocky Moun- tains. There was tendency for these centers or bands to be oriented N-S and for the centers of regions of increased lows to be located in regions characterized by afternoon maxima in rainfall. These features were suggestive, but much more work needs to be done along these lines.

Summary

I think that the facts I have presented today must be considered as we attempt to formulate hypotheses and experiments to explain the effects that have been observed. Finally, I would like to make a plea for suggestions regarding physical mechanisms and the establishment of multiple hypotheses that we can either accept or reject on the basis of the outcome of certain crucial tests. 98

Glenn W. Brier., ......

Discussion

Roberts stated that the "27-day solar rotation period" is only an average. The actual sidereal rotation rate (i.e., with respect to the stars) varies from about 25.0 days at the solar equator to about 31 days near solar latitude 60 . 0~~~~~The 25.0-day sidereal rotation period corresponds (because of the earth's 30 progress in its orbit in this time) to a period of 26.8 days for one rotation as viewed from earth (synodic period). There is no evidence of variation in the rotation rate at any specific latitude. The average synodic rotation rate in the band of greatest sunspot activity is about 27.3 days averaged over the entire sunspot cycle.

NordO agreed with the importance of classifying stations with respect to their local precipitation regimes before we can hope to understand the nature of the lunar influence.

Mitchell asked if increased shower activity was the primary factor influencing the apparent lunar effect, or if larger-scale systems were involved. It was generally felt that both small- and large-scale processes were involved, but that proper stratification of the data might help to answer this question.

Rooth made a general comment that the group should give some thought to our present data collection system and how it might be changed or broadened to permit others (in future years) to answer questions that cannot be answered now because of insufficient data or lack of the right kind of data.

Mitchell referred to work at the University of Arizona suggesting that the total amount of rainfall from convective clouds in the Southwest is ultimately controlled by the large-scale circulation patterns, and that micro-physical processes within the clouds do not seem to have much bearing on the total rainfall from the convective clouds. 99

...... Lunar Influences

References

1. Brier, G.W.: "Comment on the 26-month Oscillation in Tropical Latitudes," submitted to the Quarterly Journal of the Royal Meteorological Society.

2. Holloway, L., A. Holt, J. Mauchly, and M. Woodbury: Topics in Statistical Meteorology, Final Report, Meteorological Statistics Project of the Institute for Cooperative Research of the Univer- sity of Pennsylvania, 1955.

3. Lindzen, R.: Radiative and Photochemical Processes in Strato and Mesosphere Dynamics, Ph.D. Thesis, Harvard University, 1964.

4. Brier, G.W.: "Diurnal and Semi-diurnal Atmospheric Tides in Relation to Precipitation Variations," Monthly Weather Review, 93, 93-100, 1965. 100

Glenn W. Brier ......

1951 - 1960 1951 - 1960

110 J-AUARY 130

FEBRUARY I 110 110 100 90 B 8I 100 90

z 120 0 i MARCH ~ o Au AGUS/r i,—oo _ _ ,_ —A /

'&J 90 x l 1 1 0 —I V I I 0110W110 ——C BR 100 W 90 U. 100 0U

· "g ' D b w o o i o 100io aa—c

0 CEr 90 110 OCTDEMBER '110 DECEMBER

100 ANNUAL

110

10 49608 10 12 1416 18 20 22 24 2 4 6 8 10 12 14 16 18 20 22 24 HOUR HOUR

Fig. 1 -- Distribution of frequency of rainfall as a function of time of day for a network of U. S. stations, 1951-1960 101

I...... 0 0 * 0 * e * . Lunar Inf luences

cal~Lo~-._"~ Tme_,,. Lc/

"~~ ISF~m b(~I UOve~r50

Fig. 2 -- Geographical distribution of percentages of excessive rain 102

Glenn W. Brier ......

14.0

13.0

15.0 I i

1DNY5 MFTER $YZEYGY

Fig. 3 -- Sixty-three years of daily total precipitation data for 150 stations in the U. S., summarized according to the 15 days following new or full moon. A2 is the amplitude of the fitted 14.765-day wave. This curve is for 122 synodic months in which syzygy occurred with maximum tidal force. 103

POSSIBLE INFLUENCE OF THE HORIZONTAL COMPONENT OF THE LUNAR TIDAL FORCE ON LARGE-SCALE CIRCULATION FEATURES

J. E. Kutzbach University of Wisconsin

Introduction

Some work done by Bryson [1] in 1948 is pertinent to our present search for physical mechanisms to explain the apparent lunar influence on precipitation and other meteorological parameters. The hypothesis is that at the latitude of the subtropical anticyclones, the horizontal forces at the high centers are small. Thus, the small equatorward component of the lunar tidal force, acting over a number of days, may give rise to measurable displacements of the anticyclone. Typical horizontal accelerations at, say 30 N, are only about one order of magnitude larger than the horizontal tidal accelerations (take, for example, f = 7 x 10'4 sec-l, v = 102 cm/sec).

The Experiment

To check this hypothesis, the latitude of the eastern Pacific anticyclones was tabulated for each day of the period May-August, 1919- 1939, on which the high was clearly defined and on which there were no fronts within 10 latitude radius from the center. The latitude of the high was expressed in terms of anomaly from the 20-year daily mean.

The data were then stratified according to the day of the declination cycle., Day 1 being the day of maximum northerly declination and therefore minimum southward component of the horizontal tidal force. Figure 1 shows the observed latitude anomaly of the high. The meridional component ot the tidal force has been plotted with a six-day lag.

When the data of Fig. 1 are divided into latitude classes, the phase lag of the high behind the tidal force varies with latitude:

Latitude Days Lag

43 3 40 4 37.5 7 35 5 32.5 8 30 9.5 104

J. E. Kutzbach ...... • • • • . •

On the average, the horizontal component of the tidal force is a maximum at 450 latitude and diminishes toward the equator; therefore one might expect a faster response at mid-latitudes.

As a check on these results, the latitude of maximum pressure on the five-day mean N-S sea-level pressure profile averaged over 180 of longitude was treated in the same fashion. The results were similar.

Further Tests

I feel that the results of this experiment are sufficiently encouraging to warrant more detailed testing of this hypothesis. The same analysis could be repeated with more recent data. A more complete form of the tidal equation taking into account the anomalistic cycle (from perigee to perigee) should be used.

I am making a similar analysis of 20 years of zonal indices (pressure difference between 35 N and 55 N -- averaged from 0 to 18O W). This parameter doesn't appear to be as sensitive to lunar tides as is the latitude of the high. If the major effect of the lunar tide is a slight meridional shift of the mass distribution, then the gradient may not be changed very much.

Discussion

Rooth pointed out that these results would indicate an integrated response; that is, the high responds to the lower frequencies of the declination cycle rather than to the high frequency semi-diurnal cycle.

Brier suggested that one could compare the latitude anomalies of the high with values of the tidal force integrated over periods of five to ten days.

Mitchell suggested an alternative explanation for the latitudinal variation in the response of the high. The region around 450 latitude might be the origin of some response to lunar declination, and the greater the distance to the high, the longer the lag. In addition, the vertical component of the tidal force reaches a maximum about seven days after the horizontal components -- perhaps this might explain some of the lag.

Kutzbach referred to Brier's study (see p. 97 of the present volume) showing an increased number of lows over the U. S. with favorable tidal conditions. One would expect that meridional shifts in the positions of the sub-tropical anticyclones would be associated with changes in cyclone frequencies over the U. S. This possible connection could be checked. 105

...... Lunar Tidal Force

Visvanathan stated that only the N-S component of the lunar tidal force has net acceleration over long periods of time. It can build up, depending on the declination of the moon -- whereas the E-W component has no long period variations.

Nord6 felt that one shouldn't use geostrophic models in studying possible tidal effects on the large-scale motion field, since the tidal oscillations are too rapid to allow geostrophic balance to be achieved.

Reference

1. Bryson, R. A.: "A Lunar Bi-fortnightly Tide in the Atmosphere," Transactions of the American Geophysical Union, 29, 473-475, 1948. 106

J. E. Kutzbach . . •...... ,......

me r d;loroad co rpore rD' of +i cIcI( force /I vIk X dCAy L (4rrbibr'yCcj 5CCAie)

C Y

- ~~~// \. -^ ,/'/ \*,*^

-' ^ KT/ -\ NJ A, /

4psr 'J Cov 1^ ^^(^^^ )/4

-J 0 i 3 5 7 9 13 15 17 ^9 21 Zl ISZ V 3 5 7 9 Thoy o0 Lu n rG CycLe

Fig. 1 -- Comparison of observed latitude anomaly of .eastern Pacific anticyclone with meridional component of lunar tidal force (component depending on declination only), May-August 1919- 1939 107

ATMOSPHERIC TIDES

Bernhard Haurwitz National Center for Atmospheric Research

Introduction

Let me first give a short survey of the empirical evidence of tidal oscillations, and make a few historical comments. I shall use the term atmospheric tides to refer to the oscillations produced by the gravitational forces of the sun and moon and also by the sun's daily heating of the earth's atmosphere.

For brevity, one speaks of the lunar and solar tides, Ln and Sn, where the subscript n indicates that the tidal period referred to is the n-th part of the lunar or solar day. Where necessary, the parameter under discussion is inserted in parentheses, i.e., S2(Po) will denote the solar semi-diurnal oscillation of sea-level barometric pressure (p0 ).

Those who wish may refer for added details to a recent summary article in Science [1].

Empirical Data on Tides

1. The solar semi-diurnal pressure oscillation, S2 (po), has an amplitude of about I mb in the tropics. The amplitude decreases toward the poles with the cube of the cosine of the latitude. The pressure maxima occur at about 10:00 A.M. and 10:00 P.M., local time. A small standing pressure oscillation has also been detected. It is strongest in polar regions, but even there it is only about 0.1 mb in amplitude. Its maxima occur at about 11:30 A.M. and 11:30 P.M., U.T.

2. The solar diurnal pressure oscillation, Sl(Po), has an amplitude of about 0.5 mb in the tropics with a maximum at 6:30 to 7:00 A.M., local time, and decreases toward the poles with the cube of the cosine of the latitude.

3. Shorter-term solar tides, S3 (po) and S4 (po), have also been detected, with periods of 8 hr and 6 hr respectively. 108

Bernhard Haurwitz .•......

4. The lunar semi-diurnal pressure oscillation, L2 (po), has an amplitude of only about 0.07 mb in the tropics (at Batavia). Its amplitude, like those of the solar diurnal and semi-diurnal waves, decreases toward the poles approximately with the cube of the cosine of the latitude. The pressure maxima occur about ½ hr after upper or lower transit of the moon, but there are locally some deviations, presumably due to retarding effects of mountains and other irregularities, which we don't yet understand.

5. With regard to other parameters it may be mentioned that a lunar semi-diurnal temperature effect, L2 (T0 ), can also be detected. This effect is about what would be expected if the temperature variations are due entirely to the adiabatic law of compression and expansion. In addition, there are tidal winds. The solar semi-diurnal tidal wind components at the ground have amplitudes of about 0.5 m/sec. The lunar semi- diurnal tidal wind amplitudes are about I to 2 cm/sec in the tropics.

6. At levels of 80 to 100 km, the solar tidal winds reach amplitudes of 20 to 30 m/sec, while the lunar tidal winds have not yet been successfully determined. Their amplitudes at these levels seem to be less than 2 m/sec. Both are much greater than the corresponding surface winds.

Historical Development and Current Status of Tidal Theory

The gravitational tidal force of the moon is 2.2 times that of the sun. Therefore it is surmised that the solar semi-diurnal tides are largely attributable to thermal effects. This explanation was first proposed by Laplace. If this hypothesis is correct it becomes necessary to explain why the 12-hr oscillation is greater than the 24-hr oscillation. Kelvin, at the end of the 19th century, was the first to suggest that the atmosphere has a free period of about 12 hr, so the solar 12-hourly oscillation is magnified byresonance. This suggestion has become known as the "resonance theory" of atmospheric tides.

Much theoretical work has been done to determine the free oscillations of the atmosphere and its response to both gravitational and thermal excitation. Briefly, use is made of a linearized form of the equations of motion, the equation of continuity, and a physical equation which contains the adiabatic assumption 109

...... Atmospheric Tides

in the case of lunar tides and a periodic heating function in the case of solar tides. With suitable transformations, one can express the divergence of the motion as a function of time, longitude, latitude, and height. Assuming a periodic solution with respect to time and longitude, one can express the amplitude of the divergence term as a function of latitude and height. Then, using separation- of-variable techniques, one obtains two equations, where the separation constant hks the physical dimensions of height and is known as the equivalent depth h. The differential equation for the latitude dependence is exactly Laplace's equation for the tides of a homogeneous, incompressible ocean surrounding the earth and having uniform depth. The theory shows that in order to have a free oscillation of a certain period (and of a certain latitude dependence) the ocean has to have a certain depth, the equivalent depth h. For example, an equivalent depth h = 7.8 km is required for a free oscillation with a period of 12 hr and h = 0.7 km is required for a free oscillation with a period of 24 hr.

On the other hand, working with the height-dependent equation one finds that h can assume only discrete values since one has to satisfy two boundary conditions -- one at the surface and one at great altitudes. With reasonable assumptions about the vertical structure of the atmosphere, a value of h = 10.4 km is obtained for the semi-diurnal oscillation. Since one obtains two different values of h from the two different equations, there can only be a weak resonance magnification because the magnification is roughly inversely proportional to the difference of the two h.

However, G. I. Taylor [2] showed that more than one eigenvalue may exist in a stratified fluid and Pekeris [3] found that with high temperatures at high altitudes (350 K at 60 km) an eigenvalue h - 8 km is possible. Unfortunately, later observations, based on rocket ascents, have shown that actual temperatures at 60 km are only on the order of 2700 K, for which h equals about 10 km; i.e., we don't have an eigenvalue close enough to 7.8 km to produce for the semi-diurnal oscillation strong resonance and magnifications of the order 60-fold or more.

Sen and White [4] and Siebert [5] have suggested that maybe not so much resonance magnification is required. They explained the semi-diurnal oscillations in terms of direct absorption of incoming solar radiation by water vapor and ozone instead of the usual assumption of upward propagation of the heat by turbulent transfer from the ground. 110

Bernhard Haurwitz ......

The latter process is effective only through the first few hundred meters, and thus affects only a small part of the total mass of the atmosphere so that a large resonance magnification would be required. On the other hand, the incoming solar radiation directly absorbed in the atmosphere makes a very significant contribution to S2 since it affects the whole atmosphere, and its effect may be particularly enhanced by the strong daily absorption of incoming solar radiation in the ozone layer, as suggested by Butler and Small [6].

In summary, it appears that there is only a weak resonance magnification of the 12-hr oscillation (a magnification of 3 times, perhaps), while the 24-hr period is in fact suppressed, partly because of the small equivalent depth (0.7 km) of this oscillation, and partly because of the great difference between the appropriate Hough functions and the actual geographical distribution of the 24-hr temperature wave ("magnification"of 1/2 or 1/3 times). Thus, although (1 Z (To 1 IS, (To) /

we find

5 (POo) Z IS (Po)

The theory predicts that the tidal oscillations will increase with height. Since the kinetic energy of these tidal waves remains constant with height, the velocities increase with height as the air density decreases. For a level where the density is 0.0001 of its surface value (at around 70 km) the amplitude of the wind oscillation should be about 100 times larger than at the ground or about 20 to 30 m/sec -- in agreement with recent observations. Also, the ratio of the amplitude of the pressure oscillation to the ambient pressure varies at the same rate, 0.0005 at the surface in middle latitudes to about 0.05 at mesospheric levels.

Data regarding tidal oscillations at mesospheric levels have been mainly obtained from observations of radiometeors at two stations -- Jodrell Bank near Manchester, England, and Adelaide, Australia. At the former station, S2 >S 1 , at the latter, S1i>S 2 . Thus, at present, it is impossible to draw general conclusions as to the relative magnitude of S2 and Si aloft. I1

• •. •. • • • .• .• ...• ...... Atmospheric Tides

It has been suggested by Butler and Small [6] that much of the S2(po) oscillation is due to heating in the ozone layer. If this is so, there should be a nodal surface below the ozone layer (at about 30 km) where the amplitude of the pressure and wind oscillations should go to zero. No data are yet available to check this hypothesis. Harris, Finger, and-Teweles [71 have published data on the SI and S2 pressure and wind variations for Lajes Field in the Azores, surface to 30 km. There appears to be a decrease in the amplitude of the oscillations at 30 km, but the probable error at this level is as large as the amplitude itself so that no definite conclusions can be drawn.

Concluding Remarks

All present tidal theories involve use of a linearized equation of motion. The strong tidal winds found at high levels indicate that non-linear terms should no longer be neglected at these levels.

The possibility of tidal energy cascading downward toward higher frequencies should be considered.

Most theories assume a non-viscous atmosphere. This is probably a good assumption only up to about 80 to 90 km.

Hydromagnetic effects should be considered at high levels. Almost no work has been done on this problem.

Discussion

Mitchell made the observation that semi-diurnal pressure oscillations on microbarograph traces appear much more pronounced (up to 3 to 4 mb) during periods when the east coast of the U. S. is dominated by stagnant anticyclones and clear skies. No completely satisfactory explanation was reached, although Bartels' "curvature" effect might enter.

Gadsden suggested that Hines had explained the discrepancy between the Adelaide and Jodrell Bank observations, on the basis of the latitude-dependent factor in the expression for tidal winds. The importance of inertial oscillations, particularly when the local inertial period corresponds to the diurnal period (at 30 N or S) was mentioned by Rooth.

Lunar effects have been detected in the magnetic field but these effects are small. 112

Bernhard Haurwitz ...... •.•...•.....

Haurwitz made the following additional comments: The observed lunar tidal pressure oscillation at the equator is about 2.5 times larger than the lunar equilibrium tide, showing a slight resonance magnification predicted by the theory. There is an unexplained large amplitude of the L2 (pO) oscillation in the Indian Ocean region and adjoining regions of Africa and Indonesia. Also, L2 (PO) shows a seasonal variation which has the same phase in both hemispheres. The pressure maximum (high tide) occurs later and the amplitude is somewhat smaller during the months November through February than during the other months. Sawada [8] attempted to explain this seasonal variation in terms of the atmospheric zonal wind field. Also, Sawada and others have questioned the assumption that the vertical velocity equals zero at the surface (in the height-dependent equation) since the ocean is also rising and falling in response to gravitational effects. This may eventually explain some of the irregularities. The solar semi-diurnal gravitational pressure oscillation might be of the order of 0.03 mb at the equator.

Lorenz asked how the ratio of the amplitude of the L2 (p) oscillation to the ambient pressure would change with height.,/2 H Haurwitz suggested that it would increase as a function of e

References

1. Haurwitz, B.: "Atmospheric Tides," Science, 144, 1415, 1964.

2. Taylor, G. I.: Proceedings of the Royal Society of London, A156, 318, 1936.

3. Pekeris, C. L.: Proceedings of the Royal Society of London, A158, 650, 1937.

4. Sen, H. K. and M. L. White: Journal of Geophysical Research, 60, 483, 1955.

5. Siebert, M.: Ph.D. Thesis, Go'ttingen, 1955; also in Advances in Geophysics, 7, 105, 1961. 113

...... Atmospheric Tides

6. Butler, S. T. and K. A. Small: Proceedings of the Ro Society of London, A274, 91, 1963.

7. Harris, M. F., F. G. Finger and S. Teweles: Journal of the Atmospheric Sciences, 19, 136, 1962.

8 Sawada, R.: Submitted to Archiv fuer eteorologie, Geophysik und Bioklimatologie, Serie A. I 115

VARIABILITY IN GRAVITATIONAL TIDAL FORCES

T. R. Visvanathan New Delhi Northern Hemisphere Analysis Centre

Introduction

My talk will not be concerned with the effects of lunar and solar gravitational tidal forces, but rather with their temporal and spatial variability. When one begins to compute, say, the horizontal and vertical components of the combined lunar/solar gravitational tidal forces, one is impressed with the extreme variability of the forces. This results from the complex interactions of the various cycles involved. They are:

1. 29.53 days, the synodic cycle (phase).

2. 27.55 days, lunar anomalistic (distance of the moon from the earth).

3. 27.21 days, lunar nodical cycle (altitude of the moon above ecliptic).

4. Solar and lunar diurnal effects (rotation of the earth on its axis).

5. Solar seasonal effects (variation in distance of the sun from the earth and in its apparent declination).

6. About 8 years 290 days (cycle of moon's apsides).

7. Saros cycle, 18 years 11 days (cycle of coincidence of line of centers of earth, sun and moon).

8. About 18 years 222 days (cycle due to regression or revolution of moon's nodes).

9. Other, long term effects.

Illustrations of the Variability of Tidal Forces

I have prepared some graphs to illustrate the temporal and spatial variability of the combined lunar and solar gravitational tidal forces. Considering only the term involving the cube of parallax, the basic equation for the vertical component, Fv, and 116

T. R. Visvanathan ......

horizontal component, Fh, of the gravitational tidal force on earth due to a disturbing body [1], is

-(1) (V 3 os2-

Fh- = ) (j)3 sin 2Z g

where

M = mass of the disturbing body (sun or moon) E = mass of the earth a = mean radius of the earth d = distance between centers of the earth and the disturbing body Z = zenith distance of the disturbing body g = mean acceleration of gravity on the earth's surface.

The numbers in the graphs are to be multiplied by approximately IO'9 g to obtain actual forces.

The diurnal variation in the lunar and solar tidal force is greater at new moon than at first quarter; at higher latitudes it is also greater during solstice than at equinox. Figures 1 and 2 show the spatial and temporal variations of the vertical component of the tidal force during these four typical configurations.

Figures 1 and 2 carry two scales. The vertical scale is latitude. The horizontal scale can be interpreted as time (bottom) or longitude (top). While adjusting the time scale to the longitude scale, the movement of the moon during the 24-hr period has been ignored. Thus, while the figure gives the spatial variation rather accurately, the diurnal variation is less accurately indicated.

In the upper portion of Fig. 1, I have assumed new moon conditions, i.e., the sun and moon are in phase, and the apparent declination of sun is 23 N (summer solstice). In the lower portion I have assumed first quarter conditions, i.e., the sun and moon are 90 out of phase. Note that the resulting tidal force patterns are completely different for the two cases. Not only are the maxima and minima displaced, but the gradients are considerably different 117

. . .• ...... Variability in Gravitational Tidal Forces

and reversed. For example, in Fig. 1 assuming a new moon, the maximum range at 30ON is 141 units, whereas with the moon at first quarter, the range is only 24 and in the opposite direction. On the new moon day the double maxima at lower latitudes is replaced by a single maximum at the higher latitudes.

Figure 2 presents the same sort of information except that we now assume that the sun is over the equator (March 23). Note that there are double maxima at all latitudes on new moon day, but a single maximum in middle and higher latitudes at first quarter.

Figures 3 and 4 likewise show the southward component of the tidal force. Note the great variability and the stronger gradients in Fig. 3, observed around new moon, when the gravitational tidal forces of the moon and sun are acting together. There is a northward component near the equator and near the poles. In Fig. 4, which shows the conditions when the apparent declination of. the sun is zero, note the great asymmetry and lack of northward components in the new moon case as compared with Fig. 3.

Figures 5 and 6 show the westward component of the tidal forces. In the lower latitudes the direction reverses twice a day but nearer the poles it occurs once.

In the figures discussed to this point I haven't included the effects due to the varying distance of the moon, and its altitude above the ecliptic. Figure 7 illustrates the effects that the timing of perigee can have on the tidal forces. This shows the vertical components of the lunar/solar gravitational tidal force at the meridian of the moon or 1800 away (whichever is higher) at 40 N for two months. The upper portion of the figure shows the results for January 1965. During that month, perigee coincided with new moon (January.17) giving rise to great variations in the tidal force over the month. In April 1965 (lower portion of Fig. 7), perigee coincided with first quarter, resulting in a "damping" out of the lunar/solar tidal effect. The contrast in the amplitude of the two curves is partly due to seasonal effect.

Figure 8 brings out more clearly the information contained in Figs. 1 and 2, at 400N.

Summary

I have illustrated the great variability of the tidal forces which results from purely astronomical considerations. I hope 118

T. R. Visvanathan ......

that detailed maps of the temporal and spatial distributions of these forces (such as the ones I have shown you today) will aid us in discussing and studying the physical mechanisms that might be responsible for the lunar effect on meteorological parameters. If we are to relate variations in meteorological parameters, such as rainfall or cloudiness, to variations in tidal forces, we must have an accurate knowledge of these variations.

As the lunar tidal force is itself only small, the extreme conditions (for example, new moon at perigee) are the ones most likely to have an effect on some meteorological phenomena. Av- eraging meteorological data over many years may have the adverse effect of smoothing out these extreme cases, and lose for us the possibility of discovering them even if they are pronounced.

Discussion

Haurwitz mentioned that Bartels [2] had found evidence of a perigee effect on pressure variations at Hamburg and Potsdam. Chapman [3] did the same thing with some data from Japan.

Rooth commented that in considering the response of the atmosphere to tidal variations it is the total force that is important and that one doesn't have to worry about splitting it into lunar and solar components.

Brier pointed out that the amplitude of the 14.765-day lunar cycle in rainfall amount was about three times larger during favorable tidal conditions (perigee coinciding with new moon).

Brier, Haurwitz, and Cole discussed possible atmospheric interactions with ocean tides. A one-half meter tide, which is typical in the middle of the Pacific, produces a perturbation Ag in the local gravitational attraction g of the order of 10 g. The vertical motions of the sea surface should also affect pressure oscillations near the surface.

Haurwitz asked whether the importance of horizontal tidal forces had been considered. In the dynamic theory of ocean tides the horizontal components are the most important with respect to the motion field. Visvanathan agreed that these components should be considered.

Kochanski asked if grouping rainfall data into heavy and 119

...... Variability in Gravitational Tidal Forces

mechanism involved. Visvanathan reported that there does seem to be a difference in the phase relationship if this subclassification is made.

References

1. Schureman, Paul: Manual of Harmonic Analysis and Prediction of Tides, Coast and Geodetic Survey, U. S. Department of Commerce, Special Publication, No. 98, 1958.

2. Bartels, J.: "Uber die Atmospharischen Gezeitzen," Ver'offentlichungen des Preussischen Meteorologischen Institut, Abhandlungen Bd. VIII, No. 9, 1-51, Berlin, 1927. ("On the Atmospheric Tides," Publications of the Prussian Meteorological Institute)

3. Chapman, S.: "The Lunar Atmospheric Tide at Five Japanese Stations," Quarterly Journal of the Royal Meteorological Society, 63, 457-469, October 1937. VERTICAL COMPOJ-k) JT I,.C-lJ.1&PAP.REJ.T OF SU 2-!,T2J3- M ' . - 045 E 90 5 'Aj- j^0\ W " 0 _ 4

3 90 -33 --3 -33-3-33 -33 -33 --3 -33 -33 - 3-3 -3 - - -33 -3 -33 -3 -33 -3 -33 -33 -3 -33 -3 3

: F -7 -i - -Isg - -S --32. -'. 3 -h -14 -1-2.-4- -O -8 -3 -2. -9-j- -23 -Ig -I-L -10 - -g -'o -i4 1 — — ,10I -9 -2-0 -3 -3 -46 -48 -4S .-4q 4 . S -3373 - -lo jolc i ,2 t to I

(o- b3 %,\5- I4 -2. -t'- 4L --1 4S-4 7 -47 -4l7 -4 l. "- I - -33 -1T -. I1b q : 1/4 S

65 60C A 2 2"-20 -3^ -- 7 -3'.2 - 7-7 -33 -. -47 -t -4 -3 -2o 1o o 4 '3^ S 32 ''-~ - . 4" ° -"8 -4S --" 0 - 30 -l ' -2-3 -4--^ W - - 13. 32 | Si 1b-2 S | . ,

95 -4S -^ --2.7.\4 32. 5( s i 414 34j " F^3Or Bo^ - 93^ 28a2 ^3;C 243 ^ / 2.-2- 24x..44- --4 -i4 5- y32 '3 14- 9-½&- ^ 64k414-2..-- 2 31 • 13

c| S8 X333fi-3 -3;4°-S bH 6 22 22S 2. \34-14-34-Lg .4i\-3i 3- 3i63 \tG 8A 31 I 4- _

L 1L 73 b 4 . V 4-1-41 -Hji - ^1 43 • 73 6' 43 12 0 _5 '^ 1 1 31 2ii~ 14f9 1' ./3 65

z F - a-4S -4A -bz -42 -42 -Li 41 -42L -42- -42 -4L - -4--4L -42 -4L-42 -1 -4- - 4L -4 4 -42 -4L |

-3 372 3 .-31 -3B. -37 1 -37 - 4 -43 -4 -43 -47 -246-4 -44 -42-113 - -337 -37- -34 -3 3 -3b-3

-7 -24 -2_f -2f -U -Ii -2l -2 _ -~28-l -2 8 .- -. .-3 i -3 -. -44 -49 -4 i -4L -42 -3 --9

,o -2 -2 -' -,-IY 7 -'1 -tj -2.4 -36 -30 -43 -47 -4 -47 -43 3 -3o -14 -1 -I4 -lb -J7 -1 -10 -21 -20 -9 17 |

-14 -13 -10 -4 -3 - -- - -IIo -Sr 3 -3 -4 f3 -- 2.- -Ig- - 4o- - - ^ 3 -3 -lo -4 C '-^ - -151%35 - X7?--I -9 -t - X f L/ 5- 7 -42 I .

30p -'3^-24 s -2..813 2 - f- -30 -5 -33 -2 -531 -9g - 2'\ 13 141 4 -3- -341 - 1 j - 2 -7 (I 31 39 4o0 z.21 5\- -2.i -. 5 -2 -lo2-l . 3i 4 9 3/3 1 2 -5 2 17.

5 47 6L 1 4- 35 Loh 141 -1 ° oQ. -'- L^- 2\0 3 5 14A 5 J 7\3 . L4 -2. f Uff 3PQ0k GP I J 3, AM 6AAV, 'D 001O 3 t'

Fig. 1 -- Spatial and temporal variations of the vertical component of the lunar/solar gravitational force at summer solstice VERTICAL COMP5OJE.JT A.PPARP_,T D)ECLf'PTVOMJ Of SUM O"N U~I 1.6746 X 1o- QO ____ 4 5 ______^Q, I3 '0SC)~OE i . co '[ " 45E iI/ I I I I I I I

^o -. L^7 9 -49 -49 -0 -49 -J49 - -h -49 -'IY - -4 -? ^ -5_ 5 9 - _9 - - :

-2-^ - 457- 7 -14-'-9 -[ ' -r-1~'-- - 4 -L.77 '--1S A9 -47 17 ^ .4 ^ - 4 7-L/ -'-4 -47

-32. -33 -3 -'ho -45 -i, - ' -4 -ifo 3 -33- -? -3^ 4c ' 4 -9 ^ -" ^ & -33 41 -33 -3.3

ô0 --- ^ ^ _,4^ ^^ 123-1 L# "41 'Ly2.2 -^ â^^'f' o -3i --2^ -4 -12- 'i z^^ ^ 7^ / ~~-/7 -31^-P--J,5 4^T -- h -7.Î- -^ 3 -Mf7 it-jr

37 3; -2k -43 -4 -3 -2- 4 3, 37 3i - -L3 '131-Ii -r S$ 3; 431 3 ' 4

50- 66 3\3 r\-22. -/ c -4 ^ 33 3 5V3 \ ½^ 4l/-./{ 33 63 (0 333 3.

e 771 47 5 '7 -l -Lj -4 -17 /:/- 1) 't 7e '7j L-9 J7 ~71

VI e 7 g

^ so-^^ "^ '^ '^ ^ ^y ~-3 -1-1^ -4 60 - 'I 7 -^ 2. -3~^_ 2 1 I-4 "9 '^3, -0^ -3^"^7 ^ H- 0 H 3 F 0 - -33 -^ ^^ -^ ^' -3 -16 - s -3* . 3 -. -33 1 -3* -y -3Th-33 -- -3 - -^3 -3>, -k3 -33 -3 -24 -24 -at 20 - 2-7 --I -24 i -33 736. -- . -' ' -3 ,- N~~~~

-3o --I 4 4r 2. 7 - -2 4 2. -7L1 -4 1 -3c-3 4i 1 -44 IL~~4T

60. -- -s/ i 13 IS 13 ^ 4 -17 -33- --- 3 4 -47 A- - b 13 1 3 - LI\ < ,, -^ _ a I 1 T2_12 ^it 2. I - 35,- -2 -3 -3' 23-2-2 - 3 0-

- 1 12. '.2.-336 4 12. - -1i -2L -3•-31 2 -1 - -^ q - 3-,2 -2.3 5-3§ -43 - -' 30- 12 :L0 3iS J,-1,^7 4-7 6 n0 -7 ^- ^^3 ^ - ^ -17 -4l .-<7 -17_6H - / 2.. 32 .1 '3j3 1 5 --7 -l. 3 -- -/` ^ H-

-7 12 332. J33 t i3-f 3 4. \ 0-I - 33 36 33^ -i q -r3-11337 H

4 . 3KA -PA" I12.-'L3 -5- 1E ;O 3 9 NC L T3 Fig. 2 -- Spatial and temporal variations of the vertical component of the lunar/solar gravitational force at vernal equinox 0° 9 SOUTH CO-POMfEJT APPA:REKJT DEC.LJATIOJ OF SUM Z3 k UJIT ).6746 XIO-.q 0°E 45 D 0 135 I 1V 135 J 0 45 0 LO JG

90 53 62 1B13 0 I -263 ' 3 g. -4 -- 1`3 0(3 34 L i 3 Sl 4- 3'

75 7 0 / 4 b 1o b-4 -16 -20 -o 0^( 7- K: 9 62 - 5. "

- Go. 64g S1 5 13 0 -lo0 43 o- 3 lo ~3 66 Z t

45 5 3 i -1 -oiq3p 3I 1S.3 3'2-3ii , 3 -I33 1 3 C

IZ, I . _2I2, 1 2 -7-o 1 - -%-%D -a°_ L -1 91135 _4 - 2 5—-t h/ Q50_ 7 1. _24 ._2t5_76_7 j1 22 -2D167 -i4 L7 -412S \g5 2< 15 i4 -2

3S~ 75 I v IZ-N \ 3 xi 3 Z 1 6M -' -L S 4 3 |_

° .3 F 3 - Sl-tepoa an 5 6 rt 4 of the suhar c of the2$

o75 -^ 14t 1 1 3X o2-4 _ 6 - 1-?G ^'_ |

-i•t133 -3% 't 30 2\ 3

s-11 Il \f -( -uasl-gitio for4 atIsumme slt - )8' °1_: 3 39-Z 6° " 2 -"93 '3i 45- S 31 -'4' 31 f) t cI

Fig. 3 --and Spatial temporal variations of the southward component of the

lunar/solar gravitational force at summer solstice ' SO-FTH COM:OKAEKJT AAP'emNT ' "DCL.J" 'oJ oF Uk.) 0 UtJIT 1.)746 X 0 0 ^.S"604 :o I*J ?0 454jG. 0 L-O

0 0 0 0 0 00 0 0 0 0 6 0C)0 0 00 0 0 000 0~~~~~~

7S- 3f 3$.30o l ] c^ 3 0 3 c9 30 35 38 3S 3 . T L~ .. k^ Ho 0 1 32ft^7o 3u a1 3.0 3 c 32-4 3 4 I

30- 0 ~~~~94 3'1-~~~~~g36'O

4& -73 1 S71-7 C 037 3 I351 -1~~~~~~~~~~~~~~~~~~~~~i

30- ^(it Zs3. 4( 0 0 lz32- oO Cf o L 3^ t Qo i it 32. L - I\)~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~I

~o45'- -38' 3 30"' 19 9i_ 3 C)03 T3 51 3•7 .o3^ 393 o) ;7-71 3. -i,,

\ -•3 ^ 0 ( 0 0 O0 0 )0 0 0000 CO 0o 0 0 O 0 0 0 0 O 0 < 4' 17 i9 ~~018 ~~ 4- 4'{5 7--%3 ~ ~ 1 ~ 0 ~ ~ 7 ~.~ 9 I3'~

Cj~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~H

90 - 0 9 o 1 3i '3 3 3 ) \5g -Z• -31 -3; -3.3 -2-- - I

375 17 I3 2-i L4^ L17 .44 . A743.i[-213-. -13 --1^3 . I C 7 2 3<

601'7i/ - 13^ 3^^\ ^ i ^^ in^ 3^n ^^ 13^ S 8 9 13 ii 7 '3 V 1 0) 1 C. 4$ql0-q o% t i 3 3 33 24 -Lo i t i vZ 33 304 33 -4 20 i 102 -Lo o~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

31 13^ ~o~~~~~~~~~~~~~~~~~~~~t^ u J co 1^ ^ 0 8 ^ 9 13 8 2-4 Z LP H-

/5 c1 14 L 'a 48 L i 3 17 11 9 41 ^ ^

o . q -33i31-9 3 -31 .--33 -4{_-i -11-91 13 Z-123 3 • 3 It- 1^ 9 - . -. (D /^.hJ 3 ^•PM 3 <^.^^ ~~13 AM LOCA L TI..ME

Fig. 4 -- Spatial and temporal variations of the southward component of the lunar/solar gravitational force at vernal equinox 1

'A/&ST Cor-iPOt\J-rT APPA^CJT OCLWJAT/o'J OF -Suk -2.y I)NJ IT I. 674 I/0 3 0o /J 5 __ l 4 50 -45

0 ~ 0 3 ^ S i^ 5 3 l 5~b 5 I4 2Io i~~~~~~~~~~ I i I

75 - 6 ~o~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~-0 -2.2 53 61 57 5l 4l 2.9lo 14 Li(-12. - aV0 - 51- 5,^-5 Go. 0 3\, -I o ^ ^ 13 2. 53"0 53 75^22/2 39 9 30 '0 H A 1 27 11- 6 -L. -I2- 0-130-J-2 -3\ -2 53 -5-58 -I53 -2 34- 23.5 .37 0 3 59 C 1 45 - 0 31 5770 10 5833 15 -2 -I7 -20 -13 0 13 '20 17 2 ^- -5 -- - - 57- -3o o36 37 7 0

3 0 32 53 72.69 5 24 -23, -3 -32.- 02.0 32. -5 - - 03,

0 34 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~0-1 6-S-9- - 51 -2t 4I-h 0 I 2L 45 S3 1 9 6- 3 - -- 34i - .z c- Lr C)^~~~ ~ ~ /. ~ ,3 I a, .0 -f -i7-20-,2.- <: o-^^ ^0 51/^1 0 -3 ^ ^ 0310 1 1!6 5L1-19~31 -,4o,,,7,,ix -31\ -54^ ^-5431 6 3 511 ^) rr p.

775 - 0 1 4 7 8 G1 3 17 16 2 . 7 0 -l - i g-16-1 ^ 9 - 1G - 7 -L -l 0 1 I7 - *

G0- 0-2-2 03 0 45- 04 t2. Z9'7-2-22.I(-Z-2 10 0 g-3 02.2 0/-2<2 0 A. 0 7o '10 5 % 19 Zs-n -~.o I -O7 '--- -§ 4 'o \ I / 1 I i

3 0 (0 - 14i-43 - 10 1% 28' 2 5' 2.2. 12. 0 -12- -12. -2. $- l -1-18 ^ 10 13 o -2 -1^ - 13 ^ - 0 ^ ~- (6- 19- 44 I6. 4 II 721 2 .0ZO12. 0 - 12- I 'lo-2 4-22- - IS I S 0 . -10 -^) -/ 6 IG 1 18 16 9 -23 - -^0-to 0 0Jo 0 ^ 1-16 - 1 -'-I 19 Io 0 -I - 13) - II-10 0 10 1~3 «0 0 0- I~~~~~ I ~~~~~~~~~~~~~~~~1o-I I \iJ00^3P^ 6P>M 9I'>M V-LNJ ^,AHAM -ANAM ^ oOQ 'P tA Fig. 5 — Spatial and temporal variations of the westward component of the lunar/solar gravitational force at summer solstice ° V,;T COMPOJEJT APPAREMT :EC.,LI.JAT1O. OF SUN 0o ULI T 1.6746 X "". o05E 90 /5 1t8O 35 W0 o O4-5 L0OJ G.

60t-! 0-2 3n 1 7-3 3- nl3 i3 1 o' 3-. -3i -2- 66,3-

45 lYo q ^ I lo 0 _lo -_9_^ - tq -l p io 9 3-o 1 to 0 -t -1. Ll - p) O

- -I " 1 0 I_--L-l -• _- 3 o 5 I " t - - .- 4-5 - 0 I 3 -33 0 - .- -°3 350 Zo 1 L 1 -IS -2 -ti _'( .- [ - . - 4 1 -3 - -31 -Z5 -C .i r ) q I\ 1 4 -l -H -3i .- -I 0 • 2• Z 2-11 3 |

00g 6-3 I.G -3 333 - 9 - J 0 -1^16 33^-• 339 K 29 2 V o -1t o0.... b- . - \l-. :1 -3.)< l.-: "

-1 -31 .Fig. 6 - Spatial and temporal variations of the westward component- of the- 126

T. R. Visvanathan .a.•.•....•••.•.....•.••.•..

J#WUA1RY 1965 FEB f 3 5 *77S ^ \ «3IS is '71I Z 2 7 2.9 31 23

I00~~~~~~~~~ too ^

AIPRILU io5 A mAY * 4) 0 0, 0 1 3 5 '7 \\ lS is »7 11 U Zs IS7 2.-) I 60~~~~~~

600 - —

0 • 3J MoON) LAT 40tJ VE.RTICAL COMpOWCWT OF THr o WULL MoOtj LUJI -SOLAR T7DAL FOIC^i AT e 'PIPST (40AKTCf2,. 'THE MERIDiANJ OF THH Moc* @ LASr QOA)TER (a R 0 ) P PER I GEE U t ) IT: I 74( x /o09a A hP0oG1E

Fig. 7 -- Daily variations of the maximum vertical component of the lunar/ solar gravitational force at 40 N (upper - perigee coincides with new moon; lower - perigee coincides with first quarter) 127

•.I.Variability in Gravitational Tidal Forces

— KJE\A MOOIQ ---- FIFRST QU WTER

100 (

0 wotJo0~ ' $t% NoovlJ

P00M 1) AM K)00o (

0~~~~~

MOO^ PM ^K) A^ ^oo^~~~~~~~~~~~~~~~~~~~~~~~~~loo

N00 ,j MM MIA91 NOON ^^~~ \ — N--

^~~~~~~~ —L -~~'N.—^_""—^

Fi.8--Hulyvratoso th vetia copnn oftelna/oa

gravitational force: (a^ at 400 N, summer solstice ^b) at 40 N, vernal equinox (c) at 0 , summer solstice (d) at 0 , vernal equinox I 129

PHYSICS OF CLOUDS AND PRECIPITATION PROCESSES; IN PARTICULAR, WAYS IN WHICH THESE PROCESSES COULD BE MODIFIED BY TIDAL OR ELECTRICAL EFFECTS

Patrick Squires, Discussion Leader National Center for Atmospheric Research

Warm Rain Mechanisms

There are always, everywhere in the warm regions of the world, sufficient condensation nuclei present for the formation of cloud droplets.

If there are too many condensation nuclei present, the droplets will be small. The formation of rain eventually depends on the coagulation of drops of various sizes, and this process is highly sensitive to the size of the drops originally formed by condensation. That is, the efficiency of the coagulation process is a strong function of mean droplet radius in the cloud [1]. This is the basic reason that maritime clouds are much more effi- cient in producing rain than, for example, Colorado-type clouds. Over the oceanic regions you have much smaller counts of condensation nuclei than over continental areas, and thus much larger droplets.

Rain Mechanisms Iniving Ice

In Colorado-type clouds where there are numerous cloud droplets of small and approximately equal size, a selective mechanism for droplet growth is necessary. Ice crystals in the cloud are rare and provide the selective mechanism. They grow, first by diffusion of water vapor and later by coagulation.

Braham [2], working with summertime cummulus clouds in Missouri, has found that ice appears in the cloud only after large drops have formed by coagulation.

Discussion

If we accept the hypothesis that convective storms are involved in the observed lunar influence on precipitation then we must look for mechanisms that either influence convection or influence concentrations of condensation nuclei. 130

Patrick Squires, Discussion Leader ......

Squires: No mechanism has been suggested for bringing freezing nuclei down from the high atmosphere (where lunar tidal effects are larger) to the low atmosphere in the short times needed to be consistent with the observed sharp rainfall peaks a few days after peak tidal conditions. You are faced with the problem of explaining vertical transports of 50 to 70 km in about three days.

Brier: There is a suggestion in the rainfall data that the lunar influence is more pronounced during periods of low sunspot numbers. (Nobody knew of any long-term solar effects on condensation or freezing nuclei concentration, nor of any reasons to spec- ulate about such.)

Squires: The paper by Bigg [3] showed strong variation in freezing nuclei concentrations at the surface with respect to lunar phase. This effect appears quite strongly, even over short periods (on the order of three months), suggesting that it is a primary effect. This type of study should certainly be pursued in other areas and in greater detail.

Squires: If one accepts the possibility of lunar modulation of freezing nuclei concentrations, it would be worthwhile to look to oceanic tides for a possible explanation. This would be in view of the following: (1) there is no general agreement regarding the origin of the freezing or condensation nuclei that we find in the atmosphere; (2) no satisfactory mechanism has been advanced to explain how atmospheric tides could play a role; and (3) the peak ocean tides advance over relatively dry soil, so that perhaps effective nuclei could be formed, though the idea may seem far-fetched.

If an oceanic tidal effect is modulating freezing nuclei concentrations, one would expect to find a varying phase lag in the lunar/precipitation effect between coastal and continental areas. This hasn't really been studied in detail. However, some of Bigg's data [31 for Wellington (a windy coastal station in New Zealand) show the same phase relationship between condensation nuclei concentrations and Brier's rainfall curves. That is, the highest nuclei concentrations still lag several days behind favorable tidal conditions. You might expect such lags at an in- land station but not at a windy coastal station. 131

...... Physics of Clouds and Precipitation Processes

Telford (electrical effects on coalescence): It is certainly true that strong electrical charges and strong electrical fields have a considerable effect on the coalescence process. For example, if two droplets have opposite charges on the order of 10" e.s.u., coalescence will occur from distances of 100 times the diameter of the droplets. However, charges of this magnitude have not been found in nature. Three or four observations indicate that typical charges are about three orders of magnitude smaller than this.

Similarly, if one considers initially uncharged droplets in close proximity (say, separations on the order of 1% of the droplet's radius) electric fields have to be on the order of 800 v/m to have significant effects on coalescence. Again, such field strengths have not been observed -- except, of course, in thunder- storms.

Squires: Gravitational coalescence moderately well agrees with observations and, at best, electrical effects might represent very small modulations -- thus making them difficult to detect.

Roberts: What would happen if a few highly ionized particles were introduced into a cloud of otherwise unionized drops? Telford felt that this would have no measurable effect.

Telford: I can't think of any possible connection between lunar tides and the electrical mechanisms we've been talking about.

Brier: The present difficulty with regard to further studies of lunar influence on freezing nuclei concentration is the lack of anything even approaching a worldwide network for collection of the data.

Roberts: An alternative hypothesis would be that variations in freezing nuclei concentrations in the stratosphere affect the occurrence of stratospheric cirrus. This in turn might be postulated to affect the radiative heat balance of the stratosphere and/or troposphere. It-would be interesting to know if there is any connection between lunar phase and the occurrence of stratospheric cirrus. On a still different tack, one might look for an association between ozone and freezing nuclei concentrations at high tropospheric levels -- this would suggest rapid downward transport of air from high levels where ozone and freezing nuclei were together abundant. 132

Patrick Squires, Discussion Leader ......

At somewhat lower levels, there are suggestions in the literature [4] of a reservoir of condensation nuclei above about 30 km -- above the Junge ammonium-sulfate-forming layer. If particles can be rapidly transported through this layer (say, in 24 hr or less) they might perhaps not lose their effectiveness as freezing nuclei. This would get around the difficulty of explaining vertical transports of 50 to 70 km in about three days.

Rooth pointed out that this idea calls for a tidal modulation of exchange processes between stratosphere and troposphere. Squires questioned the reality of large freezing nuclei reservoirs above 30 km. Recent observations indicate [41 that sometimes concentrations at these levels are comparable to tropospheric concentrations but that frequently they are smaller.

Roberts: The remarkable "phase-locking" of extreme rainfalls with respect to lunar phase is difficult to understand. A larger number of the extreme cases should occur at random with respect to lunar phase, it seems to me, in the light of Brier's forcing function idea. There is no upper limit to the amplitude of chance "meteorological" factors that is comparable to the limit of the tidal factors.

It seems to me that phase-locking requires this type of process:

F CvrrTC A L >^ ^ ^

U1 ~P^^5— SMOOTH FOrCIt^JG F WCTIOk)

£F>

TIME —

If the basic forcing function is irregular with amplitudes comparable to the tidal, then there should be "accidental" occurrences of the event. It seems improbable that the basic atmospheric forcing function would be "smooth" when compared to lunar modulations with amplitudes on the order of 0.07 mb. Perhaps the lunar effect would explain, for example, one out of ten cases, not six out of ten. Looking at it another way, the degree of 133

...... Physics of Clouds and Precipitation Processes

"phase-locking" should enable you to estimate the structure of the basic forcing function.

Rooth gave, as an example, the problem of the phase of tropospheric troughs with respect to the station for which you are analyzing rainfall data.

References

1. Hocking, L. M.: "The Collision Efficiency of Small Droplets," Quarterly Journal of the Royal Meteorological Society, 85, 44-50, January 1959.

2. Braham, R,. R.: "What is the Role of Ice in Summer Rain- showers?" Journal of the Atmospheric Sciences, 21, 640-645, November 1964.

3. Bigg, E. K.: "A Lunar Influence on Ice Nucleus Concentrations," Nature, 197, 172-173, January 12, 1963.

4. Telford, J. W.: "Freezing Nuclei Above the Tropopause," Journal of Meteorology, 17, 86-88, February 1960.

135

TROPICAL CONVECTION

Douglas K. Lilly National Center for Atmospheric Research

I will review some of the recent observations of diurnal and semi- diurnal oscillations in the tropics and then suggest what mechanisms seem to be consistent with these observations.

Observational Evidence (based on [1]).

At Barbados, an island station of the Windward Islands, there is a marked diurnal oscillation of precipitation and cloudiness. Strong semi-diurnal oscillations are also found if the days of general, synoptic-scale rainfall are removed from the data.

The data were separated into five classes (very weak, weak, moderate, moderately strong, and strong convective activity). Diurnal and semi- diurnal oscillations were particularly noticable on days of very weak, weak, and moderate convective activity with peaks coming around 4:00 A.M. and 6:00 P.M.

An analysis of cloudiness at Sewell Airport (Barbados) gave similar results.

Results from cruises off the Windward Islands (150 N) show the semi-diurnal oscillation much more clearly. Every single kind of observation (rainfall, cloudiness, radar echoes) for all classes (weak through strong synoptic disturbances) shows this semi-diurnal oscillation, with maxima around dawn and dusk and minima around noon and midnight. The sharp decrease of cloudiness around noon is very pronounced.

Suggested Mechanisms

I've looked at different mechanisms of response to a semi-diurnal variation in pressure.

1. Change in air temperature due to adiabatic compressional heating and cooling:

e^ = const Cp p 136

Douglas K. Lilly ......

For variations in pressure of 4 mb, temperature variations of 0.30 C can be expected. This is of the same order of magnitude as the air-sea temperature difference. Also, if you consider that this heating or cooling would take place in about 6 hr, the cooling rate is of the same order of magnitude as the radiative cooling term.

2. Direct variation of relative humidity:

(Ah) - L hhp 8,w = const CpT p

Changes of about 1.5% in the relative humidity can be expected. In terms of response of clouds to changes in relative humidity, you might expect 3 to 4% changes in cloud cover. This is only about one- fifth of what Garstang observed [l].

Importance of Variations in Air-Sea Temperature Differences

Garstang's empirical observation is that air-sea temperature differences show a strong association with cloud regimes and with disturbed, increased rain conditions. I feel that the entire cloud regime is linked strongly and rapidly to the air-sea temperature difference.

Consider the model shown in Fig. 1. I think of the "critical layer" as a valve or communication line between the dry and wet convective layer regions. Communication occurs only in response to strong forcing. The layer itself is unfavorable for convection, but warm parcels can penetrate upward and cool evaporating downdrafts can penetrate downward.

The response of the total convective regime to impulses seems to be stable except for sufficiently large impulses that lead to the formation of tropical cyclones. In general, a balance is maintained between radiative cooling throughout the whole column, subsidence and entrainment of the dry air above, rainfall, and evaporation. Horizontal transports are often very small.

A sudden rise in sea-surface temperature of 10C should produce increased dry convection below the cloud base, increased heat and vapor fluxes, and a much better chance for bubbles to penetrate into the cloud region -- for about 1 hr. There should be increased cloudiness because of increased penetration of the sub-cloud air into the cloud layer. The initial increase will then be wiped out by dry entrainment from above, due to the increased turbulent energy in the cloud layer, or by 137

...... Tropical Convection

rainfall. Both processes lead to new equilibrium in which the cloud and sub-cloud layers are adjusted to the surface temperature. An adiabatic decrease in free air temperature, due to tidal effects, would give essentially the same response.

A sudden decrease in sea-surface temperature of 10C, or an adiabatic increase in air temperature, will tend to damp out convective activity and eliminate communication across the critical layer. Con- vection will slow down until radiative cooling in the whole regime brings about a new equilibrium.

In general, the response time should be on the order of a few hours. I'm interested in developing a numerical model of a convective regime that would allow the study of the effect of various impulses.

Discussion

Rooth, using Garstang's data, demonstrated that the semi-diurnal oscillation in radar echoes is much less pronounced if the data are plotted noon to noon (Fig. 2) ratiuer than midnight to midnight. In the former case, the only obvious feature is the diurnal variation (probably due to the diurnal radiation cycle).

Brier added that with regard to the lunar hypothesis it will be important to establish whether variations in cloudiness affect the amplitude of the solar semi-diurnal pressure oscillation and/or whether variations in the amplitude of the solar semi-diurnal pressure oscillation affect cloudiness.

Rooth inquired about methods for forecasting cloudiness in numerical models. Lilly felt that most studies up to this point rely on empirically determined relationships between humidity and cloud cover.

Lilly felt that it would be worthwhile to look at tropical cyclogenesis with respect to lunar phase. There appears to be a rather delicate balance . Up to this point tropical cyclogenesis has been largely unforecastable. Brier described some work done by Bradley [2] along these lines. Bradley stratified the days on which tropical disturbances were first called hurricanes (according to the USWB definition) with respect to lunar phase. The results are shown in Fig. 3.

There are two clearly defined peaks, one at new moon and one at full moon. Lilly thought that there now ought to be several hundred cases of tropical cyclones in the Satellite Lab files and that a more refined study of the possible relationship between tropical cyclogenesis and lunar phase could be made. 138

Douglas K. Lilly ......

References

1. Garstang, M.: Tropical Convection and Synoptic Scale Weather Systems and their Statistical Contributions to Tropical Meteor- ology, Florida State University contract final report, 1964.

2. Bradley, D. A.: "Tidal Components in Hurricane Development," Nature, 204, No. 4954, 136, October 10, 1964. 139

• .•I•.•••• •• * Tropical Convection

(VIR-TUJL ?OTWETIAL. \ — "\—7/~—.""^<— CLOUD ToP

// V L TIVE/ C.LOI J

^~ ~ (k<- \ ^ - - - - ^ p

^5UL-CLOUO ^

—^^^•^- ^—^ ^—~~~~AI-SE^sURFACE ARB1TRIR'Y SCALE

Fig. I -- Horizontally averaged conditions for typical (^j50%) coverage of tropical cumulus clouds.

90 -A gCmo VI5TiZjIBUT1OJ'o)

o / \ /\, cDuCA MAMlJWe RADAR 5 'yco- / \^ \

70 TO

Vzo ~~~~~.~ ~ ~10^. ^ fe 0

Fig. 2 -- Sketch of Fig. 6a from Garstang's report (113? replotted noon- to-noon rather than midnight -to-midnight 140

Douglas K. Lilly ......

S"(ZYGY QUANZATURE. SYGY

50I

V8 0 I

N75I

V ~~~~~~I II 40

Fig. 3 —Distribution of the 269 dates during 1899-1958 when north Atlantic tropical storms attained hurricane intensity. Thirteen-unit moving totals of the frequencies are plotted. 141

PHYSICAL MECHANISMS., MATHEMATICAL MODELS AND TIME SERIES

Glenn W. Brier U. S. Weather Bureau

and

J. Murray Mitchell, Jr. U. S. Weather Bureau

Remarks by Brier

We can frequently learn something about possible physical processes or mechanisms by studying simple mathematical or statistical models. In this seminar, we are concerned with the effect of perturbations or impulses on the atmosphere. One could list some possible examples:

1. UV heating associated with solar disturbances,

2. Increased particle fluxes in auroral zones, associated with solar disturbances,

3. Solar lunar tides,

4. Meteoritic dust,

5. Weather modification experiments, for example, seeding clouds.

It is nearly certain that weather modification experiments will receive more and more attention during the coming years. Studies of the response of the atmosphere to extra-terrestrial influences may provide information for weather modification studies. The reverse is also true.

Let's consider a simple model of the response of a system to impulses. The system can be thought of as a block of wood that can be knocked over by a certain impulse. The impulses are provided by a number of boys shooting BBs at the block. I will assume that there are ten boys, firing at random, and that all ten BBs must hit the block simultaneously to knock it over (i.e., to produce an "event"). 142

Brier, Mitchell ......

If we then examine the correlation between the occurrences of the "event" and the impulses provided by a particular boy (let's denote him by xi) we find that, on the average, the impulses provided by xi account for no more than one-tenth of the variance in the time series of the "events." Yet, the impulses provided by xi are essential to the occurrence of the event (i.e., whenever the event occurs, xi is firing). Thus, we should not be misled by the small amount of variance explained by x1 . The fact that we may not have information on the firing times of the other boys (x2 through x10 ) does not pre- vent us from discovering the influence of x1 .

Suppose that one boy (xl) is firing on a periodic basis and that all we know is the length of the period. We have no a priori information concerning the timing of the events or phase lag. A statistical analysis might provide us with valuable clues about the mechanics of the system. Information on the other sources of variation (x2 through x10 ) might be useful but is not absolutely essential for some purposes. For example, this concept might be used in designing weather modification experiments where seeding or some other impulse is introduced on a periodic basis, with the hope that conditions will eventually become favorable enough for the impulse to act as a trigger.

Remarks by Mitchell

We have been discussing the effect of tides on the timing of meteorological events. Brier [1] has described a simple model in which a forcing function (representing a meteorological variable or combination of variables) increases linearly with time and eventually reaches a critical value, or threshold, that is necessary for the occurrence of extreme or rare events. A periodic function of some prespecified (small) amplitude is then superimposed on the basic linear forcing function, and the timing of rare events is studied as a function of the phase of the periodic variation and the slope of the linear forcing function.

I will describe a somewhat more general model in which the basic forcing function (representing a harmonic component of the meteorological variations) is sinusoidal. Let Y be a function, high values of which are necessary (but perhaps not sufficient) for the occurrence of events.

Y = sin t + A sin 27r (t - At), 0

••.•...... Mechanisms, Models and Series

The symbol K denotes the length of the basic meteorological period as a multiple of the period of the smaller modulating function (the tidal term), while A defines the relative amplitude of the smaller modulating function. An additional parameter in the model is the magnitude of the critical level (Yc)' which it is assumed must be exceeded if the event is to occur. The symbol At represents the phase relationship of the modulating function to the basic forcing function. The model is illustrated in Fig. 1 for the case K = 4, A =0.1, Yc= 0 .5 (At = 0). The timing of rare events (i.e., the time at which Yc is exceeded) can now be studied with respect to the phase of the modulating function by pooling the results for all appropriate values of At. Nu- merical solutions of this model were obtained for each of various combinations of values of K, A, and Yc. (K = 2, 3, 4, 6, or 10; A = 0.02, 0.05, 0.1, 0.2, or 0.5; Yc = 0, 0.5, or 1.) Taking Yc equal to zero implies that events occur about half the time. Yc = 1 ,- implies that events occur about one-third of the time. Yc = 1 implies the occurrence of rare or infrequent events (the tidal term in this case being necessary to produce the event).

I found that the results are almost completely independent of K (where KŽ2),

As an example, the results for A = 0.02 and 0.05 (perhaps typical for tidal modulations), all values of K, and Yc = 0 are shown in Fig. 2. There is a 67o greater chance of the event during the favorable half of the modulating cycle than during the unfavorable half. For A = 0.1, there is a 10% greater chance of the event during the favorable part of the cycle than during the unfavorable part. Setting Yc = 0.5 produces similar results. However, there are important differences when we set Yc = 1. In this case, the frequency distribution of (extreme) events is very nearly independent of the amplitude of A as well as the size of K. This distribution is shown in Fig. 3. That is, in this model, the timing of extreme events is independent of the amplitude of the modulating function, and the relative frequency of events ranges up to 2.7 times the average during the favorable part of the cycle, while it remains zero during the unfavorable part. Because this result is independent of both A and K, it is valid whether the meteorological variations are red or white noise.

Discussion

NordA: If you include a time-varying random error term, statistical considerations show that the value of A will become important. 144

Brier, Mitchell ......

Rooth: Perhaps we should consider a zone of increasing probability of the occurrence of an event rather than a critical level -- then the occurrence of rare events would no longer be independent of the amplitude of the perturbation.

Lorenz: A more general model could be obtained by letting

Y _ ^ Bk sin 2 t + A sin 2Ir (t -At) K K

This would be more realistic for studying extreme events since those events which are caused by the basic meteorological variations would have a more realistic statistical distribution, rather than a bimodal one.

Brier: Since we are on the subject, I'd like to point out some statistical aspects of extreme events.

In some types of investigation, it is common to use extremes for correlation or regression studies. This can have important effects on the interpretation of the results, especially when it is not recognized that extremes are being used, or when the investigator is not aware of some of the subtleties or pitfalls in using extreme or rare events. For example, in weather forecasting, we might wish to study how the frequency of extremely large daily rainfalls is related to surface dewpoint. For a medical or health studgy, we might wish to study how the frequency of patients with blood pressure over 200 is related to the amount of salt in the diet, for example. The relationship between a dependent variable y and a possible causal or independent variable x can be represented by a scatter diagram like that shown in Fig. 4. In this figure, all the data are shown for x and y, not just the extremes. If only the highest values of y are considered, however, such as those above the line y = k, it can be seen that the relative frequency of these events can change very rapidly as x changes from negative to positive values. If we assume that x and y are distributed in a normal bivariate distribution with means x = = 0 and standard deviations Gyx = (y = 1, it is easy to construct a table to show quantitatively how the relative frequency of an extreme event y changes or x varies: 145

...... Mechanisms, Models and Series

r = 0.01 r = 0.10 y > 1.83c y 3 y >3 3> y 4 - x (Py = 0.033333) (Py = 0.001350) (Py - 0.001350) (Py = 0.000032) -3 100 100 100 100 -2 102 103 104 141 -1 105 107 109 200 0 107 110 113 278 1 109 114 119 374 2 112 118 123 527 3 114 122 129 714

This depends upon the average frequency (Py) of the event y and upon the correlation r between x and y. Even with a correlation as low as r = 0.01, there is considerable change in the relative frequency of an event according to the value of x. For example, if we take the case where an event happens only 13 times out of 10,000 (y = 35, Py = 0.00135), we find that it is 100 times (118-103) 14.6% more likely, when x is 2 above the mean than when x is 2 below the mean. For a correlation as high as r = 0.10, the percentage variations are tremendous, even though a correlation of r = 0.10 means that 1% of the variance of y is accounted for by the regression of y on x. Thus, extreme cau- tion must be used in interpreting the results of investigations where the frequency of unusual or extreme events (the pathological conditions) are related to some asserted causal variable. The use of extremes appears to sharpen the relationship or to amplify an effect. It is important that the investigator know what he is doing and understand the consequences that result from a particular treatment of the data.

Reference

1. Brier, Glenn W.: " Diurnal and Semi-diurnal Atmospheric Tides in Relation to Precipitation Variations," Monthly Weather Review, 93, 93-100, February 1965. 146

• . . .. Mechanisms, Models and Series

^^^^^^^ M~b0L.ATI,^J hUJCTeco4

'AASIC.O F09LCIKJc^ JttJCTtOI

// p\r^MODLA1trJrG 1v"C-r#i4J

YC.O ~ ~ O.C)f~ RANGE. 0r TiME ^\/ Yc 0os ^.S-- (A ^1CMW EVE"-r A O.A-I

0 c kT4 Z1T ^'AS^ 0^ ^A$ C FOR?~CIN\JG FUNCTIOtJ

Fig. I -- Illustration of the model used to investigate occurrence of extreme events

1.0Io V 0 .O ALL VALUES OF K

I 1,~~~~~~~~~~~~~~~~~~~~~~~~~~~

0 IOSo U)

1-- C~~

-J 0 V TT

Fig. 2 -- Approximate distribution of extreme events with respect to the phase of the modulating function 147

Brier, Mitchell ......

Y ' ,LOJPLLVALUe5 I /0 F\oK Ab0 ^ ~~/ \ —~.J ^ ~~~/\

0 . / U /\

1, - _ ^^_____ -______

I I I I

'PHASE OF t1OtULiLAfTIWJ FV%(,TIO^t- Fig. 3 — Approximate distribution of extreme events with respect to the phase of the modulating function

3d..

Y-=~~~~~~~~K

' p x

Fig. 4 Sc p * xandy

—6—\0302c — — \ — 3o- I 149

INTERACTION BETWEEN TIDAL FORCES AND ATMOSPHERIC PROCESSES

T. R. Visvanathan New Delhi Northern Hemisphere Analysis Centre

In other discussions in this series I dwelt on the nature of the variations in the gravitational tidal forces in time and space. On the assumption that these tidal forces, extremely small though they are, still have an effect on the atmospheric processes, I will attempt to explain,with the help of a mathematical model,the probable mode of interaction between the two. The model is essentially the one proposed by Brier [1]. It is assumed that the role of the tidal forces is as a modulator, to influence the timing or occurrence of the event only when the other meteorological forces nearly meet the requirement for the event.

Let F represent the total magnitude of the various meteorological processes favorable for the event. The zone bounded by Fci - Fc2 is the zone of probability of the event, which is considered unlikely if F has a value below the lower value, and certain if it lies above the zone. The probability of the event is governed by some probability relationship when F has a value in the zone. Ftc is the resultant curve due to the non-linear cumulative effect of the tidal force on F during the period. It is reasonable to assume that the period under consideration is of the order of a few days to a week, which is comparable to the time scale of development of synoptic situations.

Figure I shows the case when the Ftc curve is to the left of the F curve, which does not appreciably alter the probability of the event but does affect its timing. The timing of the event may be earlier, as shown in the diagram, or it may be later if the Ftc curve lies to the right of the F curve. It is also likely that shifting the timing may alter the character of the event.

Figure 2 shows the case when the Ftc is in phase with the F curve, but with a large amplitude. The timing of the event is not appreciably altered but its probability is increased.

The non-linear effects, if any, are likely to be greater during the months when the variability of the tidal force has a large amplitude, in contrast to the month when the amplitude is small. In the months when the new moon or full moon is near perigee the amplitude of the tidal force is larger than in the months when perigee is near first quarter or last quarter. Brier [1] found that the amplitude of percentage variation from the mean rainfall during the former situation is about three times the latter. 150

T. R. Visvanathan ......

Reference

1. Brier, G. W.: "Diurnal and Semi-diurnal Atmospheric Tides in Relation to Precipitation Variations," Monthly Weather Review, 93, No. 2, 93-100, February 1965. 151

.. •...•. .. •...•• .••• .•• • .a•.• Interactions

ZONK)F C11= tMCRZAStJG T' m3-BILTy OF OQCu(?AR^C6 OF Ce/ETcS

FC.~~~~~~~~~~a a a \gAB ? ROI I L TY OF Eve?'T

C)~~~~~~~~~~~

0 7-/ ME T

Fig. 1 -- Illustration of the influence of tidal forces on the timing of events.

ZOK£ OF INCREA5IJG PR%0I3AB1LT1 OF OCCURejC,_ OF EV/EtJTS

0 0 M O MA SI LI T OF EVE*J7

t c 0~ ~~^\ TIME eeT

Fig2 2^ -Ilsrto fte nlec ftdlfrcso h rbblt o "~ ~ o ocurec ofeents_ _ _ - -H-- I TOPIC C

Miscellaneous Selected Background or Summary Topics

155 Summary Paper, Topic C

THE SOLAR INCONSTANT

J. Murray Mitchell, Jr. U. S. Weather Bureau

This is a "review paper" in a manner of speaking, but I must confess that it is not intended to be (and will not be) a review of any aspect of the six-week conference we have just terminated here at NCAR; instead it will be primarily a review of certain thoughts that have been crossing my mind from time to time, and which have come back to me with some force during the course of this seminar. These thoughts are on the general problem of solar-tropospheric relationships: primarily relationships involving relatively long periods of time. Since this will concern the troposphere instead of the high atmosphere those of you who are not so interested in the troposphere may like to go for your coffee break a bit early!

We have been devoting our attention in the seminar quite largely to short-term solar/weather relationships (in addition to lunar/weather relationships, which I will not be mentioning at all), and, in particular, to the relations between what I choose to call "exotic" fluxes of solar radiation into the atmosphere and what turn out to be primarily high-level atmospheric effects of these radiations.

In speaking of short-term tropospheric effects of solar variability I think there are some problems that it would be well to identify and say just a word or two about. I am sure that these are obvious to nearly everybody here, but let's recite them anyway.

In view of the many forms of solar emission that contain significant amounts of energy, some of which can be shunted around by the earth's magnetic field, there are numerous possible arrange- ments in the atmosphere as to the altitudes, latitudes, and longitudes where this energy is ultimately transformed into heat and thereby becomes available to drive the circulation of the atmosphere or some component of it. Especially in view of the fact that variations of a number of different forms of emission are likely to be statistically correlated, this circumstance greatly complicates the problem of establishing cause-and-effect relationships with meteorological events. 156

Summary Paper, Topic C ......

All of these "exotic" forms of energy, however, have one attribute in common: in terms of total energy involved, these emissions are either (1) comparable, or nearly comparable, to the energy of the entire solar constant, but they affect the atmosphere only for very brief periods of time and in local areas; or (2) these energies are much smaller, in fact many orders of magnitude smaller, than the total solar 'constant, but they are impinging on the atmosphere at that rate more or less constantly. In either case, the effects of these radiations on the high atmosphere may very well be so large as to be downright spectacular, but by the time these effects work down to the lower atmosphere -- the troposphere -- they have become washed out almost completely, or so it seems. There are good reasons for expecting them to be washed out and I don't think these reasons have been considered as fully as they might be in some of the approaches that we have taken to the problem of solar/weather relationships.

I would like to make a specific exception in what I am about to say, and this exception relates to possible ozone-tropospheric relationships. I think the calculations of Rasool that Dr. Heath presented yesterday are one illustration of why we cannot afford to neglect ozone as having a potentially important influence on tropospheric circulation. Willett may perhaps have something more to say about this when he steps up here a little bit later.

First, from dynamic considerations we must recognize that the atmosphere is layered in such a way that in the stratosphere, and again above the mesopause, we have regions of extremely high static stability. This makes it quite likely that the perturbation energy between these layers of high static stability is to a greater or lesser extent trapped there. This in turn means that the mechanisms for dynamic linking with the troposphere are limited primarily to a weak hydrostatic form of coupling which has a far smaller potentiality for producing vertical transport of energy in the atmosphere than a direct dynamic coupling would have (were the static stability uniformly rather low at all levels).

Second, the radiative flux divergence in the troposphere appears to be quite insensitive to enormous temperature changes that are taking place in the upper atmosphere. If this were not so we should expect to find an important influence on the troposphere by changes 157

••.. ••. •••...... The Solar Inconstant

of composition or other conditions in the high atmosphere. Therefore I believe it fair to say that, in constructing numerical models of high-level heating effects, one should take account of the realistic stability structuring of the atmosphere and in addition one should also treat vertical radiative heat transfer independently of vertical dynamic heat transfer. Until we do that I fear that we are going to get results in our models all right, but not very realistic ones.

A third point to consider is this. There are quite clearly dangers involved in using geomagnetic indices as a go-between in studies of the connection between solar activity and tropospheric circulation. I think the remarks of Dr. Gregory yesterday would indicate that he subscribes to this view. This means, of course, that we must realize that the atmosphere may set itself up by influences from the bottom to the top in such a way that at certain times (that is, under certain conditions of circulation) the geomagnetic field is more responsive to solar effects than it is under other conditions of circulation. This may lead to a statistical correlation between tropospheric circulation and geomagnetic activity that means nothing whatsoever in terms of a cause-effect relationship between the sun and the earth.

A fourth point which I believe is well worth mentioning, and which I am sure is obvious to you, brings me to the main theme of what I want to say this afternoon. A change of black body radiation of the total solar luminosity of as little as 1/10th of 1% would produce anomalous heating of the atmosphere comparable in magnitude to the anomalous heating we have been postulating in connection with these high-level effects. Of course, the distribution of heating in the atmosphere would be altogether different, and this is the point. If there really are changes of the solar constant, even very small ones, these are going to enter the atmospheric dynamics through the base of the atmosphere and their effects on the troposphere would therefore be direct and positive, rather than indirect and highly conditional.

I think it is a rather curious thing -- I am tempted to use the word shocking, but I don't think I need to say that -- that in the year of our Lord 1965 and the year of our Satellite 7, going on 8, we have yet to put an instrument into space above the atmosphere to find out once and for all whether the solar constant is changing along with all the other features on the sun that we know are changing. Obviously this is a very crucial question. 158

Summary Paper, Topic C ......

The situation is rather like a mother who takes her son to the doctor for an examination. The doctor wants to know what is the trouble, and she says, "Well, I can't really put my finger on it, doctor, but I am a bit worried about the boy, that's all. He just doesn't seem to be quite himself. Would you please take a look at him?" "Hum," the doctor says, as the boy kicks him in the shins, "he does seem to be a bit impulsive doesn't he, but that's normal for a boy his age, isn't it? His eyes are a bit dilated I see, and he is breathing rather hard." The doctor holds his hand to the boy's forehead and he says, "He feels a little warm too, but maybe that's just my imagination. Oh well, if he isn't better by next week bring him back again and we will take another look at him."

Well, I'm sure that doesn't sound like your doctor; at least I hope it doesn't. One of the very first things either he or his nurse is going to do is to stick a thermometer in that boy's mouth! If he has a fever, that will change the picture a good deal. And, if he doesn't have a fever, that is something well worth knowing too. Clearly we should be giving highest priority in our space program to any promising scheme to get an accurate measure of the radiative temperature of the sun over all wavelengths.

It is also rather surprising to me how many astronomers will consider remarks like that as unworthy of serious attention. Why should the solar constant vary, astronomers often say when I broach the subject with them.

I would like now to give some more or less indirect evidence that there is a real possibility, if not a probability, that the solar constant does in fact change. My intention is not to prove that the solar constant changes -- we can't do that -- but to indicate that the possibility it changes is a very real and present possibility, and we ought to be checking into it. Allied with this, of course, is the question, if the solar constant changes, on what time scales does it change? This is very important too.

Solar constant changes may include micropulsations from second to second. If so, one might suppose that these are statistical fluctuations associated with turbulence on the surface of the sun. The area of the sun being as big as it is, and the elements of turbulence (exhibited by granules, etc.) being so small, you would expect that, statistically, this would lead to almost nothing in the way of net fluctuation over the whole disc of the sun. But how about longer-period fluctuations? On the assumption that 159

...... The Solar Inconstant

sunspots themselves are some kind of index of the solar constant -- perhaps the way that measle spots are an indication of fever in the patient who has measles -- let's look at some statistics on sunspots to see what would be a reasonable guess as to the time scales involved.

Figure I shows something that is "old hat" to almost all of us. It is s-imply the chronology from about 1750 of the annual mean relative sunspot numbers. Of course, the eleven-year cycle is the most prominent thing about it, but we see also that there are longer-period variations of sunspot numbers that are really quite spectacular. For example, from 1900 to 1960, the average sunspot number (integrated over each eleven-year cycle) has no less than tripled. If we go back further in history, we see other rather remarkable ups and downs in the average number too.

Figure 2 shows what the power spectrum of these numbers looks like. This spectrum makes it quite clear that we have two -- at least two -- time scales of solar variability to worry about. The most prominent of these, of course, is the eleven-year cycle, and there is some evidence of the second harmonic of this. The other peak out to the left, at wavelengths of around 90 years, which was discovered a long time ago by Gleissberg [1] and others, is very prominent in sunspot data and there is some evidence that this particular cycle goes back many centuries. There are thought to be longer-period cycles too, one roughly twice this 90-year period. There are, in fact, supposed to be 200-year, 400, 600, 2 0 and even 00-year cycles in solar activity, but I am not going to talk about those.

There is some statistical evidence of meteorological variations that follow solar activity on these same scales of time, which are at least consistent with the hypothesis that the solar constant changes with sunspot number. This evidence is not, however, established on comfortably high levels of statistical significance, and as you know there is a big story to that. In saying that these meteorological relations are consistent with the idea of changes in the solar constant, by the way, I do not mean to preclude that the meteorological variations might alternatively be explained equally well by changes in ultraviolet radiation (through their effect on ozone).

There are many studies that could be cited as evidence of an eleven-year variation in meteorological processes. (In some, the variation stood up very well for years and then broke down: you 160

Summary Paper, Topic C ..

have heard about things like that.) I will cite just two representative studies here. Figure 3, taken from Brier [2], involves an index "W" which defines in objective terms how wintry the northern-hemispheric sea-level pressure pattern looks as opposed to how summery it looks. Brier used 40 years of historical pressure- map data. He classified the pattern for each month of each year in terms of this index, and correlated the index with sunspot numbers. He found that there was a consistent negative correlation between sunspot number and this wintriness index. This result is qualita- tively consistent with the notion of an increase of solar constant with increasing sunspot number. There are two statistical components in the sunspot data -- one, the eleven-year cycle, and the other, long-term trends. If you remove the long-term trends in both pressure patterns and sunspots, as Brier did, you bring your correlations down to about half of what they are with the trends, but still they are quite consistently negative, which adds further confirmation to the idea that we are looking at a real solar/tropospheric relationship.

Figure 4 shows the kind of thing that tantalizes meteorologists. This is from a study by Carapiperis [3] indicating the frequency of Etesian winds in Athens as a function of time, in relation to sunspot numbers. No smoothing has been done on these data, according to Carapiperis. The correlation here is really quite remarkable, and what makes it all the more remarkable to me is that, back in 1948 the same author published an earlier paper claiming such a relationship to sunspot number, and the relationship has held up in the years since.

In addition, we have intriguing evidence of meteorological variations on the scale of 80 to 90 years that seem to correspond quite well to the Gleissberg solar cycle of the same length.

Figure 5 will show you one illustration of this, taken from Xanthakis [4]. This is a time series spanning fifteen successive eleven-year solar cycles (about 170 years of data). The heavy line shows the variation of mean sunspot numbers in each eleven- year cycle up through the 1938 maximum, and the other curves are a measure of the distribution of monthly mean surface temperatures within each eleven-year sunspot cycle, at various places in Europe and Scandinavia. I won't take the time to define what this measure is exactly, except to say that it is one of a number that together rather completely describe the annual march of temperature at these places.

Figure 6 shows another illustration of long-term meteorological variations. In this figure are shown 40-year moving averages, 161

•••• •••...... The Solar Inconstant

computed by Lamb [5], of the longitudes of the trough just off the east coast of the United States in the North Atlantic, and the ridge off the coast of Europe in the Atlantic, since around 1800. They reflect an oscillation of longitude which is just about 80 to 90 years in length.

Figure 7 shows yet another indication of the same extraordinary thing, taken from Lamb [6] . Here we see the annual frequency (in days) of west winds over the British Isles, in each year since 1873 (the light curve is not smoothed in any way). You can see how this frequency systematically increases from 1880 up to about 1920 and then decreases again up to 1960. I don't really know if this is an 80 to 90 year cycle or not, but it certainly looks like one. This is the sort of thing we can see in climatic data that really has me wondering; perhaps it has you wondering too.

But are phenomena like this really consistent with the idea that the solar constant increases in parallel with sunspot number? I could give you a number of arguments that they are. I will illustrate these arguments first with Fig. 8 which shows a comparison of certain changes in the temperate-latitude zonal- westerlies index (and also the subtropical zonal-easterlies index), at the 700-mb level, based on 16 years of data. In Fig. 8 we see two values under each index; the changes labeled "Predicted by Analogue" were the outcome of an analog scheme to infer what changes of solar constant would do, based on an analogy with seasonal changes of the circulation (Mitchell, unpublished). I cannot take the time to outline here how this analog was devised, but I think that it is a reasonably realistic approach to the problem. You can see that, on the basis of this analog, the temperate index isn't much affected by changes of solar radiation. For an increase of 200 in sunspot number one may infer a 0.2 knot increase in the westerlies index, whereas the regression on actual sunspot numbers yields a 0.1 knot decrease. While these numbers are very small and they are not statistically significant or anything like that, the nature of this result is interesting in that it suggests so small a solar effect on the temperate-latitude westerlies when these are measured in the accustomed way (between 35 and 550 N).

The subtropical easterlies index predicted by the analog is an increase of 0.5 knots per 200 increase in sunspot number, and the actual increase regressed on sunspot number is 0.7 knots. This is a rather close agreement, and the magnitudes are large enough to be of quite general meteorological interest. 162

Summary Paper, Topic C ......

Figure 9 shows a somewhat different view of the results one gets from the same type of analog system (relating the presumed effect of solar-constant changes to seasonal changes in circulation). Here the dashed curve is the change in meridional pressure profile around the entire hemisphere for high sunspot years minus low. This dates back to the studies of Wexler and Clayton; you can see this rather familiar pattern where during maxima of the eleven-year cycle you find an excess of pressure in the highest latitudes and a deficit in the middle latitudes. In comparison with this, the solid curve in the figure represents the effect of a 1% increase of insolation (by analog). Now you can argue whether this comparison means very much because almost any way you perturb the atmosphere it tends to oscillate in this kind of mode. Professor Lorenz demonstrated that years ago. So the pattern of pressure changes in the figure may not mean as much as the agreement in amplitudes of change that we are comparing here. Once again we have this curious consistency with the idea that the solar constant is changing with sunspot number by a reasonable amount, of the order of 17o.

If we don't want to trust the meteorological data for this kind of inference as to solar-constant changes, what can we say about the likelihood of solar-constant changes from the astronomical point of view?

First we should mention the direct observational evidence of solar-constant changes. The most venerable of these, of course, is the work done by Abbot and others of the Smithsonian Institution. Figure 10 shows an example of the kind of thing Abbot has come up with [7]. This graph, which refers to a certain period of years happens to be very difficult to reproduce in other solar cycles, but it is indicative,at least,of a possible 0.2% change of solar constant with sunspot-number changes of about 150.

Figure 11 shows what comes out of the data of the Lowell Observatory Solar Variations Project, where the photometric magnitude of outlying planets has been measured for 12 years relative to the magnitudes of background stars [8]. This kind of approach gets around many of the difficulties that Abbot en- countered in correcting for atmospheric transmission. Still, there are plenty of problems in trying to adduce solar-constant changes from this sort of indirect evidence. However, I would like to show you the chronology of the magnitude values for Neptune (Fig. 11), which is the more reliable of the two planets studied at Lowell for looking at this sort of thing. (The other planet is Ura-

of much value.) At the top of this figure we have the sunspot number 163

.. •.. ..•...... The Solar Inconstant

changes. Figure 11 indicates a change in blue magnitude of 0.02, which is equivalent to a 1.4% increase of solar constant over a cycle where the sunspots ranged in number between 2 and 200. This is equivalent to about a 0.3% change of solar constant for a sunspot-number change of 40, which agrees almost perfectly with the net long-term trend of 0.3% in the Smithsonian data, as reported by Aldrich and Hoover [9], during which time (1925-1951) mean sunspot number increased by about 40.

In this connection, I think it is interesting that Opik [10] has looked at the Smithsonian solar-constant data and discovered that the inter-annual changes of solar constant (as computed by the Smithsonian) are only slightly smaller than the inter-monthly variations. One would expect the inter-annual variations to be about 3 to 4 times smaller, if the sun is constant. Opik therefore concludes that there are real changes in the solar constant over relatively long periods of time, and that the Smithsonian data are adequate to show this.

There is observational evidence of luminosity changes of other solar-type stars as well. G. Jackisch and others in recent years (see [10]), who studied near-solar type stars, found that about 17% of them varied in luminosity more than could be accounted for by changes in atmospheric transmission. Since these stars were observed on many different nights, it was possible by statistical analysis to separate out the effect of atmospheric transmission changes. Opik notes that almost 80% of all stars that have been measured in this way are intrinsically variable by at least 5% and some of the remaining 20% may also be variable to a lesser extent.

It would seem, then, that "microvariability"of stars is a rather common phenomenon. As a matter of fact the sun and solar- type stars are more constant than other types of stars, and so the relative variations are smaller but they may still easily amount to 1% on the basis of astronomical evidence.

There are observable physical characteristics of the solar surface that also suggest intrinsic changes of heat flux from the sun. An example of this is shown in Fig. 12 taken from [11] which depicts the long-term trend of penumbra-umbra ratios of average- sized sunspots (labelledg,), and the trend of the difference of of penumbra-umbra ratio between average-sized and large sunspots (1 - 92 )* I won't interpret the full significance of these statistics here, but you will notice that there has been a rather systematic change over the period of record (from 1880 to about 1940). This change is in the direction of decreasing penumbra- 164

Summary Paper, Topic C ......

to-umbra ratios which can be interpreted as meaning an increase in the strength of convection on the sun. An increased convection, in turn, would almost certainly mean an increase in luminosity of the sun.

It should also be mentioned that the number of granules on the solar surface has been found by Maeris and Elias [12] to nearly double from sunspot minimum to maximum; during maximum they are much brighter and during minimum they are relatively quiescent.

There is a most curious variation in the distribution of heliographic latitude of sunspots over the longer-term 80- to 90- year solar cycle [13]. In a certain quarter of the cycle we find a predominance of spottedness in the northern solar hemisphere. Forty years later the predominance in spottedness is in the southern hemisphere, and then 40 years or so later in the northern hemisphere again. The greatest and the least total activity tend to come at times when spottedness is about equal in the two hemispheres.

A final thought I would like to leave with you concerns the theory of the solar interior. Figure 14 is a rough, schematic cross-section of the sun, according to modern astrophysical con- cepts. This shows an outer convective shell which is in turbulent unrest, and an inner "mantle" (which may extend all the way to the center of the sun) in which the heat flux is almost entirely by radiation. According to theory, there is no turbulence in the mantle, although there well may be slow large-scale overturning of the entire solar interior. Some astronomers believe there is also a central core which is convectively active, where most of the heat transfer again is by convection rather than by radiation. Of course I am not an astrophysicist and I don't claim to know much about this. However, I have tried to do some reading into the theory of stellar interiors and in the course of my reading I have been struck by the fact that astronomers are constantly referring to different kinds of instability in the sun. A few astronomers refer to radiative instability. They say that the mantle, as I have called it here, is perhaps in radiative equilibrium, but that it would be more correct to say that this equilibrium is metastable. Slight perturbations, it seems, might very quickly induce turbulence in that region. The outer convective shell is believed to be gravitationally unstable and Rubashev [14] (among others) has commented that this layer may be quite sensitive to the tidal influence of the planets, and things of this sort. 165

••.•. • ••..•.. . •. •...... The Solar Inconstant

Then there is something known as -circulatory instability. This seems to be concerned with the fact that the larger-scale motions in the outer convective shell are an order of magnitude more rapid than those in the interior. At the boundary between these two regions of the sun, which is supposed to be a rather abrupt boundary, this could lead to certain kinds of dynamic instability, again on a large scale.

And finally we have the fact that the angular momentum of solar rotation is a function of depth into the sun, as well as a function of heliographic latitude. This permits several oppor- tunities for different kinds of rotational instability to come in.

I think these cursory remarks are enough to indicate that there are many possibilities for changes of solar constant to arise in a complex organism like the sun, where we apparently have the oppor- tunity for so many forms of instability to arise.

My closing thought will be concerned with a rather simple- minded ad hoc argument regarding the question of the reality of solar-constant changes.

What goes on at a time when a very large sunspot crosses the face of the sun, such as the huge spot seen on April 7, 1947, which covered 0.55% of the solar disk? It is generally acknowledged that the black body radiation from sunspots is only about half of what it is from the surrounding undisturbed surface. This would apparently mean that, as that huge spot seen in 1947 passed across the visible solar disk, there was a decrease of solar constant of about 0.27o. This would be highly significant to terrestrial meteorology if true! One can, in fact, argue on the basis of the statistical relationship between sunspot areas and sunspot number, that in the average eleven-year solar cycle one should expect a 0.1 to a 0.2% change of solar constant over the cycle which is just out of phase with the sunspot number. I don't really believe that there is this kind of change in solar constant accompanying sunspot number and you don't either. But how do we know this isn't a reasonable way to look at the problem? We know that we are getting deficient radiation from the region of sunspots, so how can we be so sure that the rest of the sun makes up the difference, and makes it up almost perfectly? I'd prefer to see some proof that such an assumption is really valid.

In conclusion I would say that, in the first place, the lower atmosphere probably doesn't care too much what the upper atmosphere is doing. I think of the atmosphere as being something like a dog 166

Summary Paper, Topic C ......

-- the high atmosphere is the tail, and the tail can wag very happily along up there in response to solar activity without diverting the dog from his intended destination. Some people want to make the dog a kangaroo -- in which case its tail may play a more important role; but I suspect the atmosphere is more like a dog. In any case if we are interested in relationships between the lower atmosphere and solar events, then it seems reasonable that we should be looking deeper into the sun than we have done hitherto. It may well turn out that the astronomer is misled who thinks that the sun is like the sea -- if there is a storm raging on the surface all he has to do is dive a few hundred feet below in a submarine and everything will be quiet and tranquil. Perhaps the sun is like the sea, but it seems a bit questionable to me!

Let me close with a simple appeal: Let's try as best we can, and as soon as we can, to get that thermometer up there in space and take the sun's temperature, and to do this at regular intervals thereafter until we are sure whether or not the solar constant is really as constant as we seem so willing to assume. This, I sub- mit, is a project deserving of the very highest priority in our national space program.

References

1. Gleissberg, W.: Die Haufigkeit der Sonnenflecken, Chapter 3, Akademie - Verlag, Berlin, 1952.

2. Brier, G. W.: "Forty-year Sea Level Pressure and Sunspots," Tellus, 4, No. 3, 262-269, 1952.

3. Carapiperis, L. N.: "The Etesian Winds. III. Secular Changes and Periodicity of the Etesian Winds," UPOMNEMATA TOU ETHNIKON ASTEROSKOPEION ATHENON, Ser. II (Meteorology), No. 11, 13 pp, 1962.

4. Xanthakis, J.: "Study of the Mean Monthly Air Temperatures during the Successive Sunspot Cycles," Archiv fuer Meteorologie, Geophysik und Bioklimatologie, Serie A, 9, No. 1. 54-77, 1956. 167

...... The Solar Inconstant

5. Lamb, H. H.: "On the Nature of Certain Climatic Epochs which Differed from the Modern (1900-39) Normal," in Changes of Climate, UNESCO Arid Zone Research,No. 20, Paris, 125-150, 1963.

6. Lamb,. H. H.: "Frequency of Weather Types," Weather, 20, No. 1, 9-12, 1965.

7. Abbot, C. G.: "On Sterne and Dieter's Paper, 'The Constancy of the Solar Constant'," Smithsonian Contributions to Astrophysics, 3, No. 3, 13-21, 1958.

8. Serkowski, K.: The Sun as a Variable Star, II, Lowell Observatory Bull. No. 116, Flagstaff, 69 pp, 1961.

9. Aldrich, L. B. and W. H. Hoover: "The Solar Constant," Science, 116, No. 3024, 2, 1952.

10. Opik, E. J.: "Microvariability of the Sun and Stars," Irish Astro- nomical Journal, 6, 174-182, 1964.

11. Nord0, J.: A Comparison of Secular Changes in Terrestrial Climate and Sunspot Activity, Videnskaps-AkademietsInstitut for Vaer-og Klimaforskning, Oslo, Rep. No. 5, 14 pp, 1955.

12. Maeris, C. and D. Elias: "Sur une Variation du Nombre des Granules Photospheriques en Function de l'activite'Solaire," Annales d'Astrophysique, 18, No. 2, 143-144, 1955.

13. Bell, Barbara and J. G. Wolbach: "North-south Asymmetry in Solar Spottedness and in Great-storm Sources," Smithsonian Contributions to Astrophysics, 5, No. 12, 187-208, 1962.

14. Rubashev, B. M.: "Problems of Solar Activity," NASA Technical Translation F-244, NASA, Washington, D.C., 393 pp, 1964. 168

Summary Paper, Topic C.

Annual average Zurich relative sunspot number (1750 to date) 220 -- 220 200 Low-pass filtered moving average 200 -- 200 ——- -—- 11-year moving average

ISO - ISO

1« -16

40 ~140

? 0120 1

0 00

61 - A 1• go

0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~8

1740 1760 1760 1800 1820 1040 1860 1880 1900 1920 1940 1960 960 DATE Fig. 1 -- Series of annual averages of Zurich relative sunspot number, and same series after being smoothed by each of two methods. Dashed curve: result of smoothing by "ordinary" 11-year moving average. Solid curve: result of smoothing by "low-pass" filter with weights determined by binomial coefficient method with}k- 100.

Fig.:K~o s '-uIIljs I8 I 0 2 30f1 46 ^^ 90^

0 A

0 —10 2.0 — 30— AA

PERI oD CYLc^c.S PER 17^ (eARS Fi.2-- Power spectrum of annual mean Zurich relative sunspot numbers, 1700-1960. Maximum lag of analysis m-88 years; only low- frequency half of spectrum shown. 169

...... The Solar Inconstant

0.4

r _.°t - t ^TIMOsNR5movt=X,;

-0.2.

-0.6 .

-0.O .

Ml MI UwNS APH MBERtMw ,SSU AvN CM C Fig. 3 ---- Correlations ofof index Wsunspots, with sunspots, and beforeafter and after removal of the trend during the periodof record 1899-1938, calendareach

I GiO

OAVS O E E SIN I

------. SUNSPOT NUMBERS s ,·

150-

140-

130

120

110

so I 100 ''I*« 'I *

. ,i

60 l

ISBM 1900 1010 1020 1090 1040 1060 Fig.Annual 4 -- number of sunspots and Etesian winds in Athens, 1893-1961. 170

Summary Paper, Topic C...... TiM facle Ior Go ft ti IV V W Vil V/i K' XI XIt Wit XIV XVI < I i J 1 I I I I I I I I

/ ,A -.9-

cu70 - i 60- \ ~i/ / -. j.„-6 60- 60 1820-59 ^ ^ 1820- 1840-79- 1

20~~~~~~~~~~~~~~~~~~-

10- -1 IU III V V Vi Vii V/l/ Kx Xi Jr#Ki XI V XV - 77i0e scale o0r NE

Fig. 5 -- Variation of mean sunspot number N, andsmeasure of annual march of surface temperature ei0 in successive 11-year sunspot cycles. N = continuous line.

0(----0 Values of er for Vienna 0.0 Values of e for Copenhagen A ---A I it ifi Prague i.Af it if Oslo x __ i of it it Berlin x --- x if it if it Bergen

7d'W60 50 40 30 20 10 0 10PE

I I 10-3 1780-18191900-39 -- I I 1780 -1819

1800-39 1800M-39

1820-59 - 1820 -59

1840-79 -1840 -79

8660-99- 1860 - 99

1880-191 -18800-1919

1900-39 -1900-39

1920-59 (3 i)1920-59 70"W 60 50 40 30 20 10 0 IeE ridge FRig. 6 -- ongitudes of the semi-permanent surface pressure trough and 171

. . . . 0,,.. . . •. . .The Solar Inconstant

2 0 82 0 0 0

170- • • • • • • • • • 1pi70

ISO- ISO

i3o- n^ 130^1^

90 1 RI ^~~ ~ ~~~ 110

70- • ••• •• 70 0 0 Q 0 0

Ta-.• • • •• • • • fr70

Fig. 7 -- Annual frequency of west-wind type of circulation over British Isles, 1873-1963. Heavy curve is 10-year moving average.

CHANGE OF ANNUAL MEAN 700-MB ZONAL WIND ( 0 - 180W )

TEMPERATE INDEX ( 35 - 55ON ) Predicted by analogue* + 0.2 kts Regressed on sunspot number# - 0.1 ( r =.-.04 )

SUBTROPICAL INDEX ( 20 - 35N ) Predicted by analogue* + 0.5 Regressed on sunspot number# + 0.7 ( r - +.22)

* assuming 2 per cent increase of solar constant # assuming increase of sunspot number from 0 to 200, based on 16 yrs of data 1944-1959 0 Fig. 8 -- Changes of annual mean 700-MB zonal wind (0 - 180 W) predicted by analog for postulated change of solar constant and regressed on sunspot number. 172

Summary Paper, Topic C.

CHANGE OF MERIDIONAL SEA LEVEL PRESSURE PROFILE 1.5 ——————I——

1.0 -

S9 .5I \\ z I ^\

0)~~~~~\ w 0.

-.5- 0----O HIGH SUNSPOT YEARS MINUS LOW, 1899-1938 (20 YEARS EACH GROUP) A-—&CHANGE DUE TO 1% INCREASE OF INSOLATION

-1.0 —1—— 111— g 70 60 50 40 30 20 10 0 LATITUDE (N)

Fig. 9 -- Change of meridional sea level pressure profile, 0 - 3600 in northern hemisphere, predicted by analog for postulated change of solar constant and "observed" for high sunspot years minus low sunspot years.

-22

/ / /

123 I/

1^8______

—' ^~~~~~~~~~~~~~~~~~en inldeiasahgru %\ I-o(TA number near each point

Fig10--Sunpo nube vesu soa costnt.iBasedronb mfonthly ma Smtsnanvle in peio 194 Mthroeugho1950. rop* 173

••sl .•.••••I .. •••••e » . « The Solar Inconstant

200 SUNSPOT NUMBER ISO (MARCH -JUNE)

100

50 -8. 2

0^ ^ ).24

NEPTUNE MAGNITUDE 2.5

1954 5G c58o62 19

Fig. 11 -- Variation of planetary blue magnitude of Neptune, and mean sunspot number around time of each opposition when magnitude measurements were made, 1954-1963.

7.^J Ite /"o

Fig. 12 -- Histograms showing the variation of giand(g 1 - Cj)' 1878-1945. Upper histogram shows mean sunspot number -JT for comparison. (See text.) 174

Summary Paper, Topic C ......

, r o r vT r 0 T r r r s POTCYCLEI 9 10 II I 1 3 14 I - IT I Is9

*-_

zow.~~~~OOE

I 0T0 spotted b area,/A~ N + 5, of the whole sun. spotted area, N+S. of the whole sun. b.b, Relative spotted area ofnorthern the and southern hemispheres, expressed by the ratio q = (N- S)/(N+S).Z"~~~~~~~~~~~~~~~~~~~~1+ Dark shaded areas indicate

Fig. 13 -- Variation of solar spottedness with time. a,Annual average

Fig. 14 -- Structure of the Sun (highly schematic). Arrows represent hypothetical internal circulations. 175

CLIMATIC EVIDENCE ON PROBABLE PHYSICAL NATURE OF SOLAR DISTURBANCE OF CLIMATIC PATTERNS

Hurd C. Willett Massachusetts Institute of Technology

Today I would like to present some observational and statistical facts, of which some are old and some are new. The data are organized for presentation and discussion for the purpose of em- phasizing certain ideas. With respect to long-term solar weather relationships (i.e., climatic), there is probably a different physical relationship governing the 80- to 90-year cycle than that which is associated with the double sunspot cycle. Some may be skeptical of the evidence, but it appears that the 80- to 90-year solar-climatic relationship reflects changes in the effective solar constant -- that is, a variation of the actual solar heating of the atmosphere. That doesn't necessarily mean changes in the solar constant itself, but in the effectiveness with which solar energy is received by the earth and its atmosphere. Now with respect to the double sunspot cycle (the 22-year cycle), the evidence is less convincing but it is fairly clear that there is not a direct insolational effect. Rather, there appears to be an effect on the transparency or the greenhouse effect of the atmosphere and in particular on the absorption of the outgoing terrestrial radiation.

In the tropics there was reported many years ago by Koppen, Walker and others a strong negative correlation between temperature and the 11-year sunspot cycle. Examination of the pattern associated with this relationship reveals that it exists primarily in the intertropical convergence belt. It appears that the lower temperatures noted during high sunspot years are probably a reflection of the increased convective activity with associated cloudiness and precipitation. In the sub-tropics the evidence is that there is a positive correlation between sunspot number and temperature.

Over India the negative correlation between sunspot number and temperatures at lower elevations is particularly strong. But at Leh, which is in an arid climate at 10,500 ft elevation, there is a slight positive correlation between sunspot number and temperature. 176

Hurd C. Willett ......

However, owing to the scarcity of hemispheric climatic data in tropical latitudes, the following discussion is concerned primarily with climatic data in extra-tropical latitudes, and with the 80- to 90-year and double sunspot solar climatic cycles.

80- to 90-Year Cycle

Regarding the 80- or 90-year climatic cycle, the evidence is convincing that it is a reflection of variation of the effective solar constant. However, after all these years we still have no reliable measurement of this most fundamental quantity. (The existing Smithsonian solar constant measurements unfortunately are useless for this purpose.) I believe that the effective variation of the solar constant probably lies in the visible spectrum absorbed in the upper atmosphere; or, the variation of the transparency of the atmosphere may be most important. Pre- cisely which one of these is most effective cannot be positively answered.

Evidence of the 80- to 90-year solar-climatic cycle is illustrated in Fig. 1 and explained in detail in [1]. It is interesting to note that the shape of the hemispheric profiles for both the standardized seasonal departure of sea-level pressure and of thickness is very similar for the four seasons of each 20-year period shown. Notice the large degree of negative correlation between sea-level pressure and thickness, which ranges from -0.94 for the winter profiles to -0.72 for the summer profiles. During the 1900 to 1919 quarter of low sunspot activity the pressure profile indicates the expected above-normal strength of the mid- latitude zonal westerlies. Note the seasonal progression of the region of maximum anomalous coolness, from 250 N in winter to 350 N in summer and back again. There is no question that this is a direct reflection of solar heating. During the period 1920 to 1939 the pressure and temperature (thickness) profiles indicate a shift toward high latitude zonal characteristics of the hemispheric circulation patterns as-reflected by the warming at high latitudes. The last 20-year period shows a fall in temperatures at high latitudes to normal or slightly below normal with considerably above normal values at subtropical latitudes. Notice again at low latitudes the seasonal progression of anomalous warmth with the sun. The temperature anomalies (particularly in low latitudes) shown on these 20-year seasonal profiles probably represent the thermal driving force of the changes in hemispheric circulation patterns of the 80- to 90-year climatic cycle. These changes obviously are responsive to the sun and follow the 80- to 90-year sunspot cycle. 177

...... Solar Disturbance of Climatic Patterns

Table 1, taken from a paper of Mitchell [2], completely confirms (on the basis of station mean temperature data) not only the thickness profiles of Fig. 1, but also the geographical patterns of thicKness corresponding to the patterns of the actual surface temperature anomalies for the same period. To illustrate this, note in Table 1 the 200 to 300 and the 300 to 400 belts for the summer season. For 1900 to 1920 they were quite cold, and warmed up continuously for the two following 20-year periods.

Figures 2, 3, and 4 present cumulative trend curves of standardized departures of seasonal mean temperatures for selected stations across the western plains averaged by latitudinal zones [1]. The summer season for the southerly section shows much the strongest correlation with the solar-climatic cycle. The western plains were previously shown [3] to be sensitive to the double sunspot cycle and, as shown here, the 80- to 90-year cycle is clearly evident.

By the expression of the time variance of temperature over the continental United States in the form of empirical orthogonal functions, some interesting relations between the 80- to 90-year cycle of solar activity and temperature variance are seen. This analysis was made along the lines of Gilman's [4] work back in the middle to late 1950s. Table 2 shows some of the results. It contains the tabluated variances for each of the first three functions. Here U1 (the continentality function) represents a continent-wide variation of temperature centered over mid- continent, U2 (the meridional function) represents an E-W temperature contrast, and U3 (the zonal function) represents a N-S temperature variation in the period 1899 to 1962.

Table 2 shows the variance accounted for by each of the first three functions when their computation is broken down into 20-year periods corresponding to the four phases of the 80- to 90-year cycle. Each function is clearly identified except that during the first 20 years (1880 to 1899) the meridional function is not detectable.

In the last 20-year period the meridional function (U1 ) is most prominent, while the zonal function (U2 ) is rather low like the preceding period. The continentality function (U1 ) predominates during that first period, explaining 61% of the variance, while during the last period (1940 to 1959) this function (U2 ) explains only 21% of the variance. During the 1900 to 1919 period U1 contains less of the variance, the zonal component (U2 ) continues moderately high, and the meridional function becomes evident as U3. By the last 20-year period the meridional function (now U1 ) has come up to explain 47% of the variance, and the zonal function 178

Hurd C. Willett ......

has dropped to U3 . In terms of temperature patterns the results here are in agreement with what should be expected. The continental function, probably corresponding to wave number 2, completely predominates the control of variance during the earlier low-latitude zonal phase of the 80- to 90-year cycle, while by the final cellular blocking phase of the cycle the meridional function, probably corresponding to wave number 4 of the general circulation, has rather completely taken over control of the variance.

In examinations of the empirical orthogonal functions in relation to solar activity indices, it is the temperature which has the best correlation. Precipitation was less satisfactory, while the U1 or continentality function correlated quite well, but none of these correlations were overwhelmingly significant. An interesting point is that a rather large number (more than half) of temperature function correlations, particularly those above the 17o level, occurred during June and July or the period centered around the summer solstice. There is a sharp drop in the correlations during August which is not easily explained. Another interesting point is that the temperature correlation is not reflected at all in the pressure functions or precipitation. Again the evidence agrees with other analyses of the 80- to 90-year solar climatic cycle which indicate that the relationship is most significant at lower latitudes and during the summer season; apparently this reflects fluctuations of the effective solar constant.

Double Sunspot Cycle

Now let us look at the double sunspot solar-climatic cycle which I have suggested above probably reflects a change in the transmissive properties of the atmosphere (greenhouse effect). I believe that this climatic effect is mostly due to a modification of the transparency of the atmosphere to outgoing terrestrial radiation, since unlike the longer (80- to 90-year) cycle the double sunspot cycle manifests itself most strongly in middle and high latitudes and during the winter season. The double sunspot cycle is reflected most clearly by irregular cellular blocking patterns in mid- and high latitudes in winter during the major maximum half of the double sunspot cycle, in contrast to relatively steady zonal patterns during the minor maximum half of the cycle. The general circulation trends toward blocking circulation patterns in passing from sunspot minimum to major maximum, and toward relatively steady zonal patterns in passing from minimum to minor maximum. This difference is probably related to the facility with which continents can cool radiationally during the major and the minor maximum phases of the double sunspot cycle. 179

...... Solar Disturbance of Climatic Patterns

As possible explanations of changes of the transmissive properties of the atmosphere, there are at least three possibilities. The most likely is a variation in ozone with changing sunspot regimes. The changes of total ozone may be a direct photochemical effect of the sunspot regime or they may reflect changes in the state of the upper circulation induced by sunspot activity. Another factor may be water vapor. This explanation seems less likely, but any high level changes in the amount of water vapor again would most likely be an effect of solar-caused changes of the upper circulation rather than a cause. Or, perhaps the important factor is condensed water vapor in the form of cirrus cloudiness or haze. There is some early work which relates cirrus clouds to sunspot activity.

With these preliminary remarks, let us look first at some relations between solar indices and sea-level pressure. Shown by the solid curves in Fig. 5 are the seasonal difference profiles of mean standardized departures of sea-level pressure between the six seasons of maximum and six seasons of minimum mean value of four indices of solar activity selected from the 1899 to 1962 period. The four solar indices are as follows:

SSN - relative sunspot number

Aumb/Aws - the ratio of total area of sunspot umbrae to the area of the whole spots

C. - geomagnetic character figures

AD - a magnetic declination index

Note that there is a striking similarity for the four seasonal difference profiles for each of its solar indices. Also note that for all four seasons at 700N there is a maximum in pressure with large Ci's, while at low latitudes pressure is less than normal with the higher Ci's. This corresponds to short-term effects of sudden bursts of geomagnetic activity. All four sets of seasonal difference profiles in Fig. 5 indicate consistent relationships between the zonal distribution of seasonal mean pressure on the northern hemisphere and oppositely extreme states of solar activity. 180

Hurd C. Willett ......

The outstanding feature of the double sunspot cycle climatic reaction is that illustrated in Fig. 6. This figure contains for the winter season and for the summer season, difference profiles of the change of the mean seasonal standardized departures of sea- level pressure, of pressure contour heights, and of thickness (i.e., temperature) in passing from sunspot minimum to major maximum, in contrast to that from minimum to minor maximum. Nine seasonal values of standardized departure are contained in each of the phase means between which changes and difference of change are taken.

Note that the difference of the change trend is similar for both seasons, but that it is outstandingly stronger during the winter season. The relative trend toward low index (cellular blocking) patterns going into the major maximum is outstanding, particularly during the winter season in middle and higher latitudes. Note also the trend toward relative coldness in the high latitudes and relative warmth in the low latitudes in passing to the major maximum. This corresponds exactly to the trend of change of the zonal distribution of temperature and pressure in passing from the third (high latitude zonal) to the fourth (cellular blocking) phase of the 80- to 90-year cycle. This fact suggests strongly that it is the major maximum type of solar activity that dominates the general circulation patterns of the last, or cellular blocking, phase of the 80- to 90-year climatic cycle.

Several elements that vary significantly during the double sunspot cycle are shown in Table 3, along with the phase variation of ozone and several solar indices. The standard deviation of the gridpoint standardized departures of seasonal mean sea-level pressure shows a strong relation of the year-to-year variance of these departures to the phase of the double sunspot cycle, with greatest variance as might be expected at the major maximum (MM) phase of irregular cellular blocking, and minimum variance at the minor maximum (M) phase of steady zonal patterns. The upper level contour heights show an almost parallel and even more significant relation of variance to the double sunspot cycle. All significance levels indicated in this table are based on the F-test of between group to within group variance, where the groups are the nine seasonal values that go into each of the eight phase means.

Note that the frequency of cyclogenesis and anticyclogenesis, based on six annual totals for each of the eight phases of the 181

...... Solar Disturbance of Climatic Patterns

double sunspot cycle from 1899 to 1939, follow an oppositely phased cycle of change. This cycle suggests strongly that it is greater frequency of cyclones and anticyclones that feeds the necessary energy into the more steady zonal circulation patterns of the minor sunspot maximum.

The day-to-day variance of Boston maximum and minimum temperatures also shows a highly significant relation to the double sunspot cycle, more significant for the maxima than for the minima, as might be expected if the effect is solar-induced. In this case the opposite extremes of day-to-day variance occur at the two minima of the double sunspot cycle.

Also included in Table 3 are the variations of three solar indices, and of total atmospheric ozone. As might be expected, the significance of the double sunspot cycle of the relative sunspot number proves to be highly significant, but surprisingly enough the cycle of mean latitude of solar spottedness (N + S) is even more significant. Also surprising is the fact that the double sunspot cycle of total ozone, in spite of its short record, tests as more significant than that of Ci, which is generally accepted without question.

Particularly to be noted in Table 3 is the lag of Ci one phase after M, whereas the strongest maximum falls directly on MM. It is interesting to note that both ozone and N + S, which presumably are both significantly related to geomagnetic activity, show the same phase displacement at M relative to MM that is shown by Ci . Furthermore, both the year-to-year variance of sea- level pressure and of contour heights, as well as that of cyclogenesis and anticyclogenesis, all show acyclical anomalies at phase MM exactly as does Ci, and in the sense that would be expected from the apparent inducement of cellular blocking circulation patterns by geomagnetic activity.

Conclusions

1. The 80- to 90-year climatic cycle consists primarily of a rising trend of temperature. In the lower latitides, 200 to 400 N, this rising trend is strongest, and continues from the second through the third and the fourth quarter (1940 to 1959) of highest solar activity. This long trend of rising temperature appears to be associated with an increase of the effective solar constant, quite possibly of the solar constant in the visible spectrum. 182

Hurd C. Willett ......

2. Superposed on the 80- to 90-year climatic cycle is the double sunspot climatic cycle, that becomes most pronounced during the latter active half of the 80- to 90-year cycle. It is characterized primarily by a relatively zonal steadier state of the general circulation during the minor maximum half of the cycle, and by a more cellular blocking or variable climatic stress pattern during the major maximum half. Relative coldness in the higher latitudes and warmth in middle and lower latitudes characterizes this climatic stress pattern, and probably gives its character to the fourth or final phase of the 80- to 90-year cycle.

3. Most probable causative factor of the double sunspot climatic cycle is variation in the transparency of the atmosphere to outgoing terrestrial radiation, the atmosphere being more transparent at the major maximum phase, less at the minor.

Such variations of transparency can more plausibly be explained by variations of total atmospheric ozone, less readily by variable turbidity produced by high cirrus haze or cloudiness.

4. A second possible causative factor in the double sunspot climatic cycle might be a change of vertical stability at the top of the troposphere, however produced, in the sense shown by the Lorenz-Kraus model to produce cold season instability (an intensified index cycle) of the zonal westerlies. This explanation would require increased instability aloft at the major as opposed to the minor sunspot maximum, at the same time that the lower troposphere during the cold season is shown to be colder poleward of 55°N and warmer equatorward.

Discussion

Visitor: Do you believe the atmosphere can respond in a short time to variations in the solar constant?

Willett: Yes, possibly models such as Kraus' could demonstrate atmospheric response.

Mitchell: I believe it is safe to say that the response of the atmosphere to rapid changes in the solar constant will depend upon the initial state of the atmosphere. Therefore it would only be for the slower changes in the solar constant that there would be systematic changes in the atmosphere.

Willett: This is probably the case. 183

.•...... •.•. . . Solar Disturbance of Climatic Patterns

Mitchell: For slow changes in the solar constant the oceans will have a chance to participate more fully in the temperature and circulation changes, and this must make an important difference.

Willett: I hope to have some information in this regard soon. I am working on this problem at the present time and I am convinced that the oceans do not play a major role.

Kraus: On short time scales the variability of the atmosphere is much greater than that of the ocean, but on longer time scales the oceans become relatively more important.

Willett: We would like to compare notes with you -- one of my students is making use of your weather ship data. One of the areas we need data from is the tropical South Pacific.

References

1. Willett, H.C.: "Solar-Climatic Relationships in the Light of Standardized Climatic Data," Journal of the Atmospheric Sciences, 22, 120-136, March 1965.

2. Mitchell, M.: "On the World-wide Pattern of Secular Temperature Change," Arid Zone Research, 20, UNESCO, Paris, 1963.

3. Willett, H.C.: "Climatic Trends of Temperature and Precipi- tation in the Continental United States," Proceedings of the Eastern Snow Conference, 1959-1960.

4. Gilman, D.L.: Empirical Orthogonal Functions Applied to 30-day Forecasting, Massachusetts Institute of Technology, Scientific Report No. 1, Contract AF19(604)-1283, 1957. 184

HurdC. Willett . . . . . * o0 . O . o0 0 o

Table Mean temperature by pentads, expressed as departures in _F from 1 1 to 959 pentad each 100 latitude band from 800N to 600 S (Source: Ref [21 reproduced by permission of UNESCO)

Table 2A -- Reduction of variance of 20-year winter-season functions

Table 2B -- Reduction of variance by three principle function patterns 185

. . .. .• « Solar Disturbance of Climatic Patterns

Table 3 -- Distribution of selected weather elements and solar indices by phases of the double sunspot cycle 186

Hurd C. Willett .o . . . . . d o

Fig. Hemispheric profiles of 20-year means of seasonal departures of sea-level pressure (full line) and of thickness, Tv (broken

point means of standardized seasonal departures.)

tures, averaged for selected stations 187

†.•••••• ••. • • Solar Disturbance of Climatic Patterns

Fig. 3 -- Cumulative totals of winter season standardized departures of temperatures, averaged for selected stations

Fig.1 4 oaso-Cmltv umrsesnsadrie eatrso

Fig. tCmulrative,toalsrge ofosmmr seasone statindadzddpatrso 188

Hurd C. Willett......

Fig. 5 -- Mean seasonal pressure difference profiles for maximum minus minimum solar index extremes. (Units are standard deviations of seasonal mean pressures or contour heights, 1899-1962.)

Fig. 6 -- Mean seasonal hemispheric difference profiles, change from sunspot minimum to major maximum minus change from sunspot minimum to minor maximum, i.e., [((MM-m) - (M-mm)]. (Abscissae

standardized seasonal departures.) 189

STRATOSPHERIC CIRCULATION AND AURORAL ACTIVITY

W. 0. Roberts National Center for Atmospheric Research

Introduction

There is a long and spotty history of researches and speculations purporting to relate auroral activity to the large-scale features of the stratospheric or tropospheric circulations. A wide diversity of studies has suggested that these circulations are noticeably more meridionally developed or "blocked" when major auroras or related geomagnetic disturbances have occurred some days before. A similar trend shows in mean statistics for whole months or seasons when severe geomagnetic disturbances have been unusually frequent in the accompanying periods.

None of these studies has been conclusive of a genuine relationship. Some of the work on the subject has been faulty in statistical approach, or has been over-interpreted. In fact, the whole literature of solar and cosmic influences on weather has been a weird assortment of fact and fancy, leading sound workers to pause before entering so strange an arena. But to me there do appear some solid clues to associations that deserve an imag- inative probing for mechanisms of cause and effect. Moreover, sound advances will be more likely when statistical studies are carried out in pursuit of specific physical working hypotheses, no matter how speculative these may be.

A Few Recent Relevant Works Based on Relative Frequencies of Various Circulation Patterns

l. Willett [1] has noted an interesting apparent effect during periods of the largest geomagnetic disturbance, at years near major maxima of solar activity (which have recently tended to alternate with minor maxima at intervals of just over 10 years). Such major geomagnetic disturbance periods (thus also major auroral activity periods), he notes, tend to display an aggravated thermal contrast between continental and maritime air. And such periods tend to favor cellular blocking patterns as contrasted with zonal flows. 190

W. 0. Roberts ......

2. Borisova and Khesina [2] have noted the greater frequency of 500 mb meridional and anticyclogenic processes at periods of high solar activity, especially at very high latitudes over the Barents and Kara seas. It is unfortunate that upper level circulation and temperature data tend to be sparse at higher latitudes, because this is where the effects appear to be most pronounced.

3. Some years ago Bodurtha [3] noted a markedly greater frequency of blocking situations in high solar activity periods. And there are many other similar results (for example, see Sazonav and Gnevyshev [4]).

There seems to me to be a greater prospect of finding and understanding an auroral -- weather connection, if there is one, through study of day-to-day relationships. In this way individual case statistics build up rapidly enough (for example, in a single winter) to begin to be significant of a relationship. In a short time, thus, independent data regimes can be used to test discover- ies or hypotheses. Moreover, one can, in day-to-day studies hope to use modern data exclusively, and data from higher levels and latitudes. Thus I shall speak here only of some selected few studies involving short-term relationships.

1. Shapiro Paper on 1899-1945 North American Data [5]. This work was stimulated by a one-year 500-mb study [6] that suggested that pressure patterns over North America changed ab- normally fast (declined in persistence) about a week to two weeks after a geomagnetic disturbance. This idea turned up from an unexpected and perhaps coincidental tendency for forecast "busts" on an experimental GRD numerical forecast to follow a series of remarkable geomagnetic storms that year.

Surface barometric pressure data for the 46-year period showed, on the average, a rapidly decreasing persistence correlation index some 8 to 14 days after geomagnetic disturbance. The index, moreover, fell from an apparently significant peak in persistence some three to five days after major geomagnetic activity. The persistence index used was simply the average correlation value for a network of stations over North America, computed in this way: The pressure was averaged for each station for a three-day period of the same station. The period-to-period correlation value was then, by superposed epoch methods, averaged first for the days that accompanied magnetic storms, then for the first day after, then the second to the n-th day. The range of n was from -12 to +19. 191

...... Stratospheric Circulation and Auroral Activity

Figure 1 reproduces one of the graphs from that paper.

2. Later Work by Shapiro and Colleagues. Shapiro [7] later examined, by an analogous method, the average persistence index for the same years (1899-1945) for a network of European stations. Again he found a rise to a peak persistence a few days after the geomagnetic disturbances, followed by a steady decline, though to a value less far below the mean than for North America.

Later work by Shapiro and Ward [8] examined a new period (1945-1953) for the 500-mb level. Here the work was done for 0 0 0 latitude circles ringing the hemisphere at 30 N, 45 N and 60 N. The 45°N circles showed an average persistence rise in the few days after the geomagnetic disturbance dates, consistent with the North American and European results of the 1899-1945 studies. At 60°N a rise occurred after the geomagnetic storm dates, but the higher persistence values continued for about 10 days. The effects were shown to result from the longer wave components of the circu- 0 lation. Nothing significant appeared at 30 N. Shapiro and Ward considered the result to be consistent with an effect on the large- scale circulation in days immediately after geomagnetic upsets. I feel that this study, though positive, was a less sensitive test for the kind of effects sought in the earlier papers.

3. High Altitude Observatory Work on Stratospheric Trough Development. Work at HAO by Norman Macdonald and others since 1956, gave attention to 300-mb levels, and to a circulation index tied to individual low pressure troughs as they moved in the ° general circulation between 1800 and 0 in the western half of the northern hemisphere [9].

We found an effect involving troughs that were first identified in a "target area" overlying the Gulf of Alaska (a sector 0 bounded by 120°W and 1800, north of 40 N) on the second to fourth day after the onset of severe auroral or geomagnetic disturbances. For winter half-years we systematically identified every trough found in the target area and measured a "trough index" expressing the trough's depth-to-width ratio on every successive day it could be traced as it migrated eastward on our maps of the half-hemisphere. "Key Troughs" first found in the target area on the day 3 + 1 from auroras, systematically grew to larger trough index values than the troughs first in the target area on other dates. We allowed a variable lag time, attributing to the key troughs (and the others) the largest trough index, whenever it maximized. 192

W. 0. Roberts.

Key troughs tended to maximize on the average, about eight days after the geomagnetic storm dates, and by then they had usually reached, in this easterly drift, somewhere near the middle of the North American Continent.

The half years 1956-57, 1957-58 and 1958-59 showed exactly similar effects, and in each year the significance level was of the order of 17o, giving a highly convincing combined level of significance. Each year involved about 65 troughs, of which over one-half of the largest ones were aurora-associated, compared with a one-third chance expectation.

Subsequent unpublished data suggest the same result at lower significance level in 1959-60, followed by a nearly random distribution in 1960-61 and 1961-62. In these latter years the auroral activity and geomagnetic disturbance activity was far lower. Other unpublished work by Macdonald, after he had left HAO, also showed that there appeared no comparable trough development in other sections of the northern hemisphere.

Twitchell [10] subsequently and entirely independently analyzed 1960-61 500-mb data, using the same trough index as we did but with a somewhat different geomagnetic and statistical analysis. He found results consistent with our 1956-59 data -- namely a systematic trend to larger troughs over North America some eight days after geomagnetic storms, as also found in our analysis.

Speculations on Mechanisms

In outline, I now offer a suggested chain of events to explain these apparent effects on upper level troughs. The mechanisms suggested are, step by step, susceptible of observational or analytical test -- and for each step in the chain it would be profitable to try to invent and to test alternative hypotheses:

1. The solar corpuscular energy involved in aurora production over the Gulf of Alaska is the initiating cause. The energetic solar particles precipitate, during the major auroral disturbances involved, some hundreds of kilometers south of the normal auroral belt.

(a) Recent theoretical and observational studies can delineate energies, atmospheric penetration levels, etc., for this auroral energy, the relationship to the magnetospheric tail, ionospheric auroral electrojets, etc. 193

...... Stratospheric Circulation and Auroral Activity

(b) The auroral particle energy flux is small compared with the solar constant (order of 1000 ergs/cm2 /sec) and very small compared with stratospheric circulation energies, ruling out dynamical effects of direct heating.

2. The auroral energy produces freezing nuclei at stratospheric levels over the Gulf of Alaska, and these nuclei trigger post-auroral cirrus cloudiness.

(a) The link of auroral X-rays or other secondary effects to freezing nuclei is purely speculative. I can suggest no specific mechanism at this time.

(b) The air over the Gulf of Alaska is probably, on occasion, moist and supercooled, in a circumstance where freezing could easily be triggered. (One should note that if this is so, deliberate artificial triggering might be possible, as well as randomly initiated or aurora-initiated triggering.)

3. The warm surface levels resulting from the Japan current (whether or not covered with low stratus) provide an energy source for initiating a dynamical change via radiation blanketing by the aurora-induced cirrus.

(a) The warm surface normally radiates its 10/.-peaked black body radiation to space through the transparent, even if moist, stratospheric air.

(b) When cirrus (ice) forms, the 10 water vapor window is partially closed, and this radiation is partially trapped, resulting in a new heat source at and below the cirrus deck.

4. When the circulation is only conditionally stable, this added heat initiates dynamical instability, which ends in major trough growth. These events could perhaps occur particularly readily in the transitional period from winter to spring, as large circulation breakdowns become probable.

In discussing these speculative mechanisms I have not leaned heavily on the often reported observational relations between atmospheric halos and geomagnetic storms, nor the reported relations between auroras and cirrus in Scandinavia. But modern observational 194

W. 0. Roberts ...... • • • • . • • • • • .

techniques could probably give unequivocal answers to the reality of such associations in just a few years. Moreover, day-by-day IR satellite maps at 10 for the Gulf of Alaska would very directly test the suggested mechanism. A single winter half-year, at appropriate high geomagnetic storm period, should be adequate to give fairly strong evidence pro or con.

Nordberg [11] has already shown, from TIROS satellite data, that the Aleutian stratosphere was, during the week-long periods analyzed, warmer than expected, suggesting that the underlying warm surface had produced a heating effect. If day-to-day data, not yet available, should show a large variability as well as average warming, the variability will be a most interesting possible source of dynamical effects downwind. It would be interesting to explore whether such possible circulational responses could now be numerically modelled. A postulated heating function consistent with the above speculative chain of events could probably be stipu- lated, even in the absence of actual satellite IR data, as an initial state condition for a differential model analysis with and without the postulated cirrus heating. It would be interesting to see if such a heat source could reasonably make the difference between a cellular block and a more zonal flow pattern.

Discussion

Cole suggested that it would be of interest to repeat the analysis with a more modern criterion of strongest auroras over the Gulf of Alaska; perhaps the amplitude of magnetic bays at auroral or sub-auroral latitudes would be better, for example.

Rooth suggested that the cold Siberian continental mass upwind from the warm winter oceanic region of the Gulf of Alaska might also conspire to make the North American trough development situation uniquely favored.

Sparkman's work was mentioned briefly. In this, the surface barometric pressure trends of downwind stations in the three to six subsequent days appeared to drift in opposite directions when the geomagnetic stations showed "positive" gradients as compared to "negative" ones. A positive gradient was the situation when the western geomagnetic station (on the same latitude) had a higher diurnal variation than the eastern station of the pair. The work suggested a response of downwind surface pressures to differences of zonal currents at the ionospheric levels responsible for the geomagnetic parameters. 195

...... Stratospheric Circulation and Auroral Activity

Mitchell emphasized that the apparent geomagnetic effects on the circulation delineated by Shapiro involved the largest-scale elements of the circulation.

Mitchell mentioned Manabe and Strickler's work [12] in the USWB on the effect of clouds on radiative heating -- and emphasized that, according to these authors, significant heating may occur only when (cirrus) clouds exist at levels above the tropopause level itself. Discussion suggested that the radiative effect of a cirrus deck at a cold, high level should be given further study.

Discussion pointed up the special interest of the Gulf of Alaska area for blocking action. And when strong warm blocking anticyclones occur, the effects go to very high altitudes. Effects may go as high as 70 to 80 km. Temperature data in these circum- stances would be of great value. Perhaps the cause of the associations are below, in meteorology, rather than above in geomagnetism.

References

1. Willett, H.C.: "Solar-Climatic Relationships in the Light of Standaridzed Climatic Data," Journal of the Atmospheric Sciences, 22, 120-136, 1965.

2. Borisova, L.G. and B.G. Khesina: Proceedings of the Central Institute of Weather Forecasting: Problems of Long-Range Weather Forecasts, No. 124, 28-32, Moscow, 1963.

3. Bodurtha, F.T., Jr.: "An Investigation of Anticyclogenesis in Alaska," Journal of Meteorology, 9, 118-138, April 1952.

4. Gnevyshev and Sazonav: "Pressure Variations and Solar Activity," Astronomical Journal of the USSR, 41, 937, 1964.

5. Shapiro, R.: (on 1899-1945 North American data) Journal of Meteorology, 13, 335-340, 1956. 196

W. 0. Roberts ......

6. Shapiro, R.: (one-year, 500-mb study) Journal of Meteorology, ll, 424-425, 1954.

7. Shapiro, R.: (on 1899-1945 European data) Journal of Meteorology, 16, 569-572, 1959.

8. Shapiro, R. and F. Ward: (1945-1953 500-mb data) Journal of the Atmsopheric Sciences, 19, 60-65, 1962.

9. Macdonald, N. and W.O. Roberts: "Further Evidence of a Solar Corpuscular Influence on Large-Scale Circulation at 300 mb," (work at HAO by Norman Macdonald and others since 1956) Journal of Geophysical Research, 65, 529-534, February 1960.

10. Twitchell, P.F.: "Geomagnetic Storms and 500 mb Trough Behavior," Bulletin de Geophsique, No. 13, 69-84, Montreal, avril 1963.

11. Nordberg, W., et. al.: (TIROS data) NASA report X -- 651- 64-115, May 1964.

12. Manabe, S. and R.F. Strickler: "Thermal Equilibrium of the Atmosphere with a Convective Adjustment," Journal of the Atmospheric Sciences, 21, 361-385, 1964. 197

a •••••o•Stratospheric.•• Circulation and Auroral Activity

I~~~~~~I l l l I U l l l lI' 1I I i i il .40z — HIGH .39 PERSISTENCE .38 0 -I36 U. 3 a .35 z.UJ o 33

1- .32 ______tt -o — ______

Qn .31 0- .30 — \T_ PERSISTENCE .29 - \ .28 -12-10-8 -6-4-2 0 2 4 6 8 10 12 14 16 18 DAY

Fig. I --. Mean persistence correlation, 1899-1945, with twelve years .of maximum sunspot number eliminated, for days minus 12 to plus 19 from dates of large increase in geomagnetic activity (after Shapiro, [5J). Lines shown are at the 57o significance level. I 199

FURTHER DISCUSSIONS ON NOCTILUCENT CLOUDS

Haurwitz: Ben Fogel of the University of Alaska told me that he has observed three or four cases of the following sequence of events:

1. Several nights of good display of noctilucent clouds.

2. A good aurora.

3. No noctilucent clouds on the following several nights.

He wondered if this had something to do with heating at the 80 to 100 km level?

Roberts: This goes along with the results of Vestine who reported, many years ago, a negative correlation between years of frequent noctilucent clouds and high solar activity. I have thought that this might represent auroral heating at 80 km, but I have never felt secure about the reliability of the noctilucent cloud statistics.

London: This observation would be very interesting if it is borne out. It would be an indication of where a possible direct reaction can occur. I think one thing that should be looked for is the timing of this sort of thing because I think there are at least two mechanisms by which the heating to evaporate noctilucent clouds would occur:

1. Particles coming in and losing their kinetic energy -- this reaction would be a delayed one.

2. The UV radiation (1500 to 3000 A) might affect ozone concentrations at about 80 km. Heating at this level is very sensitive to ozone concentration. This would produce an immediate reaction.

So, I'm suggesting that the observations might help in de- ciding which mechanism if any is operating.

Shapiro: Is there any observational evidence of variations in this portion of the spectrum?

No such evidence is available but an experiment is being designed to look at this.

Rooth: I would argue that heating at the mesopause would suppress convection in the mesosphere - - and that these vertical motions are essential to formation and maintenance of these clouds.

201

SOLAR CORPUSCULAR EMISSION EFFECTS ON THE TERRESTRIAL ATMOSPHERE

Keith Cole High Altitude Observatory

Introduction

This talk will not cover solar origin or space propagation of plasma bundles, solar wind, low energy cosmic rays, nor the configuration of interplanetary magnetic fields, interesting as these topics are.

I will speak of effects within the magnetosphere, with emphasis on geomagnetic and auroral phenomena. In particular, I wish to indicate the nature, magnitude, and distribution of the heating of the earth's upper atmosphere at times of magnetic disturbance. Of necessity this talk will not go into details, but adequate references will be provided. A good general reference in this field is the work of Rubashev [l].

The Phenomena of Geomagnetic Disturbances

Let me start by referring you to Fig. 1, showing the relation between the velocity of ionized solar wind particles and the planetary magnetic disturbance index Kp from Snyder et. al. [2]. The solar wind is composed of ionized particles emitted by the hot solar corona -- as discussed by Parker [33 and others.

Magnetic disturbances are measured by the three-hourly maximum range of the intensity vector of the magnetic field. The average value of this range so derived from a special selection of stations, by Bartels, was chosen to be representative of solar corpuscular emission -- and is called Kp. The frequency distribution of Kp values during the last part of 1958 peaked at low values near 2 [41; high values of 8 and 9 were relatively uncommon. Zero values were also very rare during that period.

Conventionally the magnetic disturbance of solar origin is attributed to the stream of electrically neutral but fully ionized plasma ejected from the sun [5] and this view is supported by the correlation of solar wind speed with Kp. The classical attempt to develop this idea was that of Chapman and Ferraro [63. Recent 202

Keith Cole ......

attempted extensions of the theory starting from the basic premise of fully ionized streams as the active agency are those documented in Refs. [7-11] . These latter attempts put great emphasis on polar ionospheric events.

Akasofu [12] has suggested, also, that the neutral hydrogen which accompanies the ionized particles has an important part in geomagnetic storms and auroral phenomena and that the neutral particles penetrate deep into the magnetosphere before acquiring a charge from earth's proton atmosphere and then becoming trapped. I shall not discuss this hypothesis, which has been criticized by Hunten and Brandt [13] .

The intensities of the various magnetic field components of a disturbance are assumed separable into various components of the "disturbance field" D (departure from the "quiet"). Several components are currently recognizable on physical grounds, thus:

D = DM + DI + Dt + Dcf + Dg

DM = a component caused by outward stress on the geomagnetic field due to trapped particles (or ring current) [14, 15]

DI = a field component due to ionospheric currents concentrated most intensely at the auroral zone [16] and the magnetic equator [17].

Dt = effect due to current sheet in the magnetospheric tail under solar wind impact [11, 18].

Dcf = currents flowing on the surface carved out of the solar plasma by the geomagnetic field interaction with the solar wind [6].

Dg = disturbance due to ground currents induced by the other variations; it may amount to 0.4 of the other components [5].

In polar regions there are nearly always some auroras, even in quiet times, during the IGY for example. Magnetic traces in auroral and low latitude zones differ during both quiet and disturbed times. During disturbances the auroral zone traces are jagged, with dominant periods in the 100-minute range, whereas at low latitude traces are more smoothly varying with the dominant period of about a day. 203

••••••••.•...... Solar Corpuscular Emission Effects

The polar region jaggedness is usually considered to be due principally to ionospheric currents (and therefore are largely DI) in the auroral belt at altitudes of about 100 to 150 km. The smoother low latitude effect, even though many forms are possible, is held to involve principally Dcf, DM and Dg though some contribution from DI cannot always be neglected. DM is probably considerably larger than the Dt in the magnetospheric tail [ill .

Atmospheric Energetics Associated with Geomagnetic Disturbances

1. General

Much of the energy associated with many of the different D components ultimately shows up as heat and motion in the atmosphere. But there are other facets of the problem of the energetics of magnetic storms. Here is a partial list of the phenomena which consume significant amounts of energy:

(a) Dissipation of electric currents flowing in the ionosphere, magnetosphere, seas, and ground.

(b) Corpuscular bombardment of the atmosphere, manifesting itself in ionization, visible aurora, electromagnetic wave absorption, ultraviolet, infrared and radio emissions.

(d) Radiation to space of electromagnetic and hydromagnetic waves, heat, and earth gases.

In view of the fact that index Kp is related closely only to the first item, the solar wind correlation observed by Neugebauer and Snyder is surprisingly good. Maybe if a more comprehensive index were designed to cover all the energy sinks during times of magnetic disturbance an even better correlation with the solar wind speed could be obtained.

As Green and Barth [19] have shown, some 40% of the incident beam of 30 kilovolt auroral electrons goes into producing ultraviolet light. This might affect, for example, the ozone layer, for a good amount of energy goes into the 2000 to 3000 A wavelength band. 204

Keith Cole ......

Whether this is sufficient to trigger some meteorological phenomenon in the lower atmosphere may be a profitable avenue of inquiry.

Let's look at the energetics of auroras of different strengths. The energies, resulting principally from 1 to 100 kev electrons are shown in the table:

Intensity Brightness Class Photon Intensity Particle Energy Flux at 5577 A (kR) (ergs cm-2 sec-1 ) weak I 1 4 average II 10 40 bright III 100 400 very bright IV 1000 4000

Note: 1 kR = 106 photons cm'2 sec 1l

The last column of the table is made by taking Chamberlain's [20] luminosity efficiency of 57o. This energy, however, is in fine filaments over selected parts -- not the whole average over the auroral zone. By visual observations one can see that whereas the whole of the sky may be covered with an auroral glow of strength 0-I, only in a small portion of the sky is the auroral brightness II and III. Nobody has really gotten at the total fluxes involved in the various sizes of auroral displays. This is quoted usually as the corpuscular bombardment energy, but there's no good index for it.

This corpuscular bombardment involves protons and electrons penetrating to different depths. Thus (see [21] for a review),

Particle Depth of Penetration (km)

1 Mev protons 110

50 key electrons 110 205

.•...... Solar Corpuscular Emission Effects

These produce ions and generate X-radiation aurora and provide heat for the electron gas.

2. Joule Heating in Upper Atmosphere

I suggest there's another matter to look into, with important energetics -- having to do with dissipation of energy of ionospheric currents which are most intense in the vicinity of auroras. These currents flow at the 100 to 200 km level and give rise to D1 . Classically they are closely related to the so-called DS component of magnetic disturbance. I have made energy studies of this [22-27]. The joule dissipation is given by

,. Q J where = 0 and where o-1, 2 are the Pedersen and Hall electrical conductiv- ities [28]. I have used two models for the auroral ionospheric electrojets.

Model A: infinite sheet of current, j = 2 x 10-8AH

Model B: jet of current, j = 5 x 10-8AH

The symbol AH refers to changes in the horizontal component of the geomagnetic field. The size of the jet assumed in Model B was 100 km wide, with a specific reasonable ion distribution with height [27]. Results of heating in ergs cm3 sec - 1 are shown in the table below.

AH Model 50 y 200y 1000

A 6 x 10-8 3 x 10-7 3 x 10- 6

B 3 x 10- 7 2 x 10- 6 2 x 10- 5 206

Keith Cole ......

This is a significant effect compared with the whole corpuscular auroral zone heating mechanism. Most of the heat due to current dissipation is deposited above 120 km altitude, whereas most of the heat due to corpuscular bombardment appears to be deposited below 120 km [29] . It should perhaps be considered in this seminar. Also better estimates of these currents merit observational effort, particularly to determine their size and position.

3. Auroral Acceleration Process?

Now let's look at the magnetosphere, and the origin of auroral particles. The neutral sheet in the magnetospheric tail downstream from the solar wind may play a role [11] but the details are still mysterious. In a few seconds you must accelerate particles to high enough energies to penetrate the atmosphere to the 100 km altitude and lower, and produce the normal active and fluctuating aurora, x-rays, etc. The required energy is more than is resident in the energetic magnetospheric plasma in the same tube of force. What accelerates the particles? Are they accelerated in situ -- as many now think?

In the tail regions there appears to be a reservoir of moderately energetic particles (200 to 1000 ev). How are these triggered into the atmosphere to make auroras? How do particles get onto lines of force which extend only to 2 earth radii (i.e., L- value of 2) to make auroras during large storms? Does the neutral sheet extend to these L-values at these times?

4. Decay of a Magnetospheric Ring Current

Now let's look at the magnetospheric ring current energies. The ring current causes Dm and is classically associated with the Dst main and recovery phases. It appears to have associated with it an aurora different in character from the normal active aurora associated with DI [30] . The kinetic energy of the trapped particles is given by [15]

B 3 Err 207

••••• .••.•...... Solar Corpuscular Emission Effects

AB = Change of magnetic field at equator

B = magnetic field at the equator

En = kinetic energy of trapped particles in magnetosphere

Em = constant (magnetic energy of geomagnetic field external to the earth)

For a storm where AB = -100l you need magnetospheric trapped kinetic energy En = 3 x 1022 ergs.

The dissipation of the magnetospheric ring current is a most interesting thing which I have recently studied. I suggest that the ring current sits on lines of force nearer the equator than the auroral zone, at L values where IGY observations have revealed the high level (300 to 400 km) stable auroral red arc (hereafter called SAR-arc) [31-33] . This arc is in the F region, is 500 km broad, and runs round the night side of the earth in both hemispheres at a conjugate magnetic latitude. It appears to be morphologically distinct from normal visible aurora, the latter being very active and fine-structured. The position of the SAR-arcs in relation to the magnetospheric ring current is sketched in Fig. 2.

This aurora is strong in 6300 A and has a 10-hr time constant which matches the Dst time constant. Higher latitude auroras have time constants of minutes and seconds. I suggest that the ring current is associated with the SAR-arc, and in fact that the SAR- arc is the site of the major sink of energy for the ring current.

Assume the SAR-arc arises from excitation of atomic oxygen by thermal electrons in the F region, according to e + 0--0 (1 D). The 0 (lD) radiates the 6300 A emission. The intensity of the 6300 A line is given by

1(6300) = f A(Te) ne n(0) dh where

Te = electron temperature in the F region

ne = electron density

n(0) = atomic oxygen density

A(Te) = coefficient of excitation of 0 to ^Dstate. 208

Keith Cole ......

Knowing I, ne, n(0) we can find Te* We then calculate the cooling rate Q(e) of electrons in the arc by considering all possible collisions of electrons with other atmospheric con- stituents. Thus,

Q(e) = cooling rate of electrons

= ne An(0)+ B n(N 2) + C n(0 2) +D ni} where, for example, ne B n(N2 ) gives the rate of cooling of electrons by collision with molecular nitrogen. As an example, in a 100 Y storm 1(6300) is 10 kR and this yields, for two hemispheres,

J Q(e) dv ^ 101 ergs/sec

where the integral should be interpreted as extending over the volume occupied by the SAR-arcs.

This integral can be related to the decay of energy of the ring current. The kinetic energy of the particles in this current, for a 100 -storm, is E ^ 3 x 1022 ergs. The time-constant for the decay of this storm is about 105 sec. Hence, dEn/dt ^ 3 x 1017 ergs sec . So we conclude this fits with the idea that the SAR-arc is the site of a major sink of energy for the ring current.

This amount of heating is less than 10" ergs cm~3 sec"- during an auroral storm; so the integrated heat dissipation rates attributable to Daland Dm are about the same. Many people seem to have thought that ring current processes were far more energetic than the auroral belt processes.

Now, I suggest that the ring current and its red aurora is simply a product of processes associated with normal aurora -- which has moved south and injected particles deep into the magnetosphere that give Dst and red auroral arc [341 . Normal auroral latitudes during quiet times are 800; IGY auroras averaged at about 700 and the red arc sits nearer 500. But big storms move down to 500 too, and red arcs have been seen slowly decaying after large auroral displays have occupied the same region and then receded again poleward. Thus effort should be applied, now, on the birth of the ring current in auroral morphology. 209

••...•.•...... Solar Corpuscular Emission Effects

Elsewhere [35] I've suggested the following method for creating the ring current and the stable auroral red arc: Geomagnetic fluctuations have associated with them a random sequence of electrostatic fields which pump plasma from the outer to the inner magnetosphere and energize it in the process. This gives the ring current. The ring current decays as follows: Energetic particles ('-l kev in a 100Y storm) cool by coulomb collisions with a thermalised component of the plasma (at temperature about 10,0000 K). Heat conduction along the magnetic lines of force from this magnetospheric thermalised plasma raises the temperature of F-region electrons to about 35000 K. The neutral particles in the stable auroral red arc provide a sink for this conducted heat.

Conclusion

I have discussed heating of the atmosphere associated with dissipation of magnetic disturbances. The two principal latitude belts for the heating are:

1. Auroral Zone: Ionospheric currents in the ionospheric E region dissipate energy (associated with DI) principally above 100 km altitude, most intensely at 140 km, in auroral electrojets. The heat dissipated this way is at least comparable in magnitude and may well exceed the heating caused by corpuscular bombardment.

2. Lower Latitude: The stable auroral red arc appears to be the site of a sink of energy for a magnetospheric ring current (associated with DM). The heat is deposited in the F region (250-400 km altitude).

Contrary to opinion expressed in the literature, the energy consumed in auroral zone processes is thought to be greater than that consumed by the ring current. 210

Keith Cole ......

References

1. Rubashev, B.M.: "Problems of Solar Activity," NASA Technical Translations TTF-244, December 1964.

2. Snyder, C.W., M. Neugebauer and U.R. Rao: "The Solar-wind Velocity and its Correlation with Cosmic Ray Radiations and with Solar and Geomagnetic Activity," Journal of Geophysical Research, 68, 6361-6370, 1963.

3. Parker, E.N.: "Dynamics of the Interplanetary Gas and Mag- netic Fields," Astrophysical Journal, 128, 664-676, 1958.

4. Cole, K.D.: "Variation of Upper Atmosphere Densities with Solar Activity," Journal of the Physical Society of Japan, 17, Supp A-I, Part I, 185-187, 1962.

5. Chapman, S. and J. Bartels, Geomagnetism, 2 V., Clarendon Press, Oxford, 1962.

6. Chapman, S. and V.C.A. Ferraro: "A New Theory of Magnetic Storms," Terrestrial Magnetism, 36, 77-97, 171-186, 1931; 37, 147-156, 421-429, 1932; 38, 79-96, 1933.

7. Piddington, J.H.: "A Theory of Polar Geomagnetic Storms," Geophysical Journal of the Royal Astronomical Society, 31, 314-332, 1960.

8. Dungey, J.W.: "InterplanetaryMagnetic Field and the Auroral Zones," Physical Review Letters, 6_, 47-48, 1961.

9. Axford, W.I., and C.O. Hines: "A Unifying Theory of High- latitude Geophysical Phenomena and Geomagnetic Storms," Canadian Journal of Physics, 39, 1433, 1464, 1961.

10. Cole, K.D.: "On Solar Wind Generation of Polar Geomagnetic Disturbance," Geophysical Journal of the Royal Astronomical Society, 6, 104-114, 1961.

11. Axford, W.I., H.E. Petschek, and G.L. Siscoe: "Tail of the Magnetosphere," Journal of Geophysical Research, 70, 1231- 1236, 1965. 211

...... Solar Corpuscular Emission Effects

12. Akasofu, S.I.: "A Source of the Energy for Geomagnetic Storms and Auroras," Planetary and Space Science, 12, 801-832, 1964.

13. Hunten, D.M. and J.C. Brandt, to be published, 1965.

14. Singer, S.F.: "A New Model of Magnetic Storms and Aurorae," Transactions of the American Geophysical Union, 38, 175, 1957.

15. Parker, E.N.: "Dynamics of the Geomagnetic Storm," Space Science Reviews, 1, 62-99, 1962.

16. Birkeland, K.: "Expedition Norvegienne de 1889-1900, Resultats Magnetiques," Vidensk Skrifter I Mat. Naturo. K1., 1-80, Christiana, 1901.

17. Baker, W.G. and D.F. Martyn: Philosophical Transactions of the Royal Society A, 246, 281, 1953.

18. Ness, N.F.: "The Earth's Magnetic Tail," Journal of Geophysical Research, 70, 2989-3005, 1965.

19. Green, A.E.S., and C.A. Barth: "Calculations of Ultraviolet Molecular Nitrogen Emissions from the Aurora," Journal of Geophysical Research, 70, 1083-1092, 1965.

20. Chamberlain, J.W.: Physics of the Aurora and Airglow, Academic Press, New York, 1961.

21. Oguti, T.: "Inter-relations Among the Upper Atmosphere Disturbance Phenomena in the Auroral Zone," Japanese Antarctic Research Expedition Reports, Series A, No. 1, 1963.

22. Cole, K.D.: "Joule Heating of the Upper Atmosphere," Australian Journal of Physics, 15, 223-235, 1962.

23. Cole, K.D.: "A Source of Energy for the Ionosphere," Nature, 194, 95, 1962.

24. Cole, K.D.: "Orbital Acceleration of Satellites during Geomagnetic Disturbance," Nature, 194, 42, 1962.

25. Cole, K.D.: "Atmospheric Blow-up at the Auroral Zone," Nature, 194, 761, 1962. 212

Keith Cole ......

26. Cole, K.D.: "Damping of Magnetospheric Motions by the Ionosphere," Journal of Geophysical Research, 68, 3231-3235, 1963.

27. Cole, K.D.: "Joule Heating of the Ionosphere over Halley Bay," Nature, 199, 444-445, 1963.

28. Chapman, S.: "The Electrical Conductivity of the Ionosphere: A Review," II Nuovo Cimento Supp 4, 4, Series X, 1385-1412, 1956.

29. Mcllwain, C.E.: "Direct Movement of Particles Producing Visible Auroras," Journal of Geophysical Research., 65, 2727-2748, 1960.

30. Cole, K.D.: On the Dst Main Phase of a Magnetic Storm and Certain Associated Phenomena," in Physics of Geomagnetic Phenomena, S. Matsushita and W.H. Campbell, editors, Academic Press, 1965.

31. Barbier, D.: "L'activite"Aurorale aux Basses Latitudes," Annales de Geophysigue, 14, 334-335, 1958.

32. Duncan, R.A.: "Photometric Observations of Subvisual Red Auroral Arcs at Middle Latitudes," Australian Journal of Physics, 12, 197-198, 1959.

33. Roach, F.E. and E. Marovich: "A Monochromatic Low-latitude Aurora," Journal of Research of the National Bureau of Standards, 63D, 297-301, 1959.

34. Cole, K.D.: "On the Depletion of Ionization in the Outer Magnetosphere during Magnetic Disturbance," Journal of Geophysical Research, 69, 3595-3601, 1964.

35. Cole, K.D.: "Stable Auroral Red Arcs, Sinks for Energy of Dst Main Phase," Journal of Geophysical Research, 70, 1689-1706, 1965. 213

.•*•••••*•••*•••••Solar Corpuscular Emission Effects

700.

40 ' 2 0 7, p * 4 F d * * - /

T l i to

UJ*

\f) 5^00~"

4 '- 4-*4

The lineois th leastesquaesulinear fihto th points.

each day. 214

Keith Cole ......

GE~l iNGETIC. A0'T

MoAPMAL- AMRI)rkO IIttb

NMORMML. AVRORA AWI4 IoWOSIOPERIC £LE.CTZOJET5 ^> MAGMeTOSJ0P^ C 1RING CURR.EkT

Fig. 2 -- Sketch of the position of the SAR-arcs in relation to the magnetospheric ring current, normal aurora, and ionospheric electrojets. 215

SOLAR ACTIVITY AND RADIO NOISE

J. W. Warwick University of Colorado

Solar Emission in General

The sun's opaque photosphere radiates the principal energy of the sun in a steady emission similar to a 60000' K black body of 1.4 x 106 km diameter. Most effects of the sun, such as the prime light and heat distribution on earth, come from this and from the variable geometry of points on earth relative to the sun.

The sun's variable energy, however, comes mostly from the corona, flares, particle and plasma emission, the chromosphere and the prominences. These solar atmospheric phenomena produce complex radio emissions and far-UV emissions, magnetic field interactions, etc. The effects of these variable solar occurrences are of great terrestrial significance -- particularly in the high atmosphere.

The Corona

Let's look first at the normal corona. The first figure illustrates schematically several of its features. The corona can be seen in the light of some 30 or so highly ionized atomic emissions (like 5303 A of Fe XIV) or in a continuous spectrum that resembles the sun's integrated white light.

Figure I perhaps gives an erroneous impression, however, because it fails to show the steep and generally steady radial decrease of coronal intensity. To a first approximation, the "white light corona," the main feature seen at total solar eclipse, declines rapidly outward from the sun's edge by e-fold in a couple hundred thousand kilometers.

Coronal isophotes do not show the streamers as strikingly as the diagram does. Instead, the polar plumes and equatorial streamers are perturbations on a fairly smooth, almost circular pattern, characterized by a slightly different law of radial intensity fall-off, and by stronger intensities as well. 216

J. W. Warwick ......

The white light corona or "K-corona" originates in free-free scatter (Thompson scatter) of photons from the solar black body radiation (at .6,000 K) by free electrons of the sun's corona -- which consists mainly of ionized hydrogen.

The corona is a hot gas, highly tenuous, and relatively slowly changing. It co-rotates with the sun, roughly once every 27 days (the sun, of course, does not rotate with the same period at all latitudes).

S. Chapman some ten years ago [1] first examined an ideal coronal model that was entirely static and had no magnetic fields. His corona had T = 1060 K at its base, a temperature maintained from below in a still-unknown manner. (Observations of several sorts indicate the lower corona to be this much hotter than the photospheric layer, the opaque solar surface.) In a highly significant and innovative paper (rejected by the journal to which it was first submitted) Chapman considered thermal conduction running radially out along the thermal gradient into space; he concluded that it was not unreasonable to consider coronal T's as high as 1050 K at the distance of the earth. In fact, his principal motivation was the possibility that this hot corona, surrounding the earth on all sides, might be a significant heat source for the ionosphere.

Chapman deliberately ignored UV radiation losses from the coronal gases. This is probably a safe assumption (although the question has been reopened recently). His ignoring the magnetic field effect on thermal conduction was also probably not serious, since the coronal magnetic fields probably lie radially out from the sun and therefore don't impede the conductive heat flow.

However, he also ignored coronal gas dynamics, which was important. Parker [2] and many others have now issued an important series of significant results extending Chapman's point of view to include dynamic effects.

Parker coined the term "solar wind" to describe the steady flow past the earth of expanding coronal material characterized in his models by v - 500 km/sec, and -~1l0-100 proton electron 3 pairs cm~ , resulting from near-sun temperatures of T '2 x 1060 K, and densities of 108 particles per cm3 .

Space observations confirm Parker's models. Also, recent radar observations of the sun suggest values for the coronal expansion within 2 solar radii. 217

•* • •• • •• • •••. Solar Activity and Radio Noise

Magnetic field structure near the sun probably parallels the complicated observed forms. The physics is of particular interest at the singular point just above the coronal loops, at an altitude of about 250,000 km from the sun, and at the base of a coronal streamer. Here we must assume that the magnetic field 2 energy density H /8.,f (H = magnetic field force) is about equal to the thermal energy n K T (K = Boltzmann constant, n = particle density). The field lines change from closed loop-like structures, to open, linear ones, in this region where H is about 0.1 gauss. The moving plasma here begins to draw out the magnetic field lines. So far, we have no good theory to explain the source of coronal material or temperature.

Solar Flares and their Effects

Close to the sun, in a low latitude, near an active sunspot region at the solar limb (edge), the coronal structure may be radial, but will more often possess a closed loop structure like that sketched in Fig. 2. The region may spread 100 or 200 in latitude. Here we assume the loops parallel the magnetic field, rooted in the photosphere, and of sufficient force (up to a few hundred gauss) that they control the gas motions. In the photosphere, in sunspots, the fields reach a few thousand gauss.

These regions give rise to flares, fluctuating plages and other active solar region phenomena. From these bursts of activity often come terrestrial magnetic storms after 18 to 36 hr. The radio emission effects are varied and spectacular. There is good evidence that strong changes in the solar wind flow result from these events.

Flares are abrupt outbursts of brilliantly radiating hydrogen Balmer alpha (6563 A) and related lines. Typically, flares are seen on the disk, and not up in the corona (i.e., not in coronal emission lines or electron scatter white light). Little change in the shapes of the coronal structures occurs even during a major flare, though major changes in its brightness often do result. Shown below is a typical sunspot and plage region, and the crosshatched part shows a typical flare size and location.

-WI 1~00,00\^ ^ 218

J. W. Warwick ......

Flares involve a local density increase. If one views in Ha there are sometimes big ejections of matter (spray prominences). Typical flares extend in HQ to 20,000 km or more above the solar surface. The brightness rise times can be as abrupt as a few seconds. A twenty-fold increase of intensity in the center of Ha is not unusual. The decays are slower -- tens of minutes up to several hours.

Quite commonly in the later phases of major flares H-alpha loop prominences form with shapes that parallel the loops of the surrounding corona. Paradoxically, the hydrogen gas streams down along both arms of the loop toward the sun. The loops disappear at low levels and reform at successively higher levels as time passes. They have been studied since the early 1930s,. Densities in these loops are of the order of 1011 to 101 particles cm-3 . Since they show in Ha they are probably at 1040 K or so, thus far cooler than the corona, and, of course, far denser. The magnetic field obviously generates strongly controlling forces. The very hottest coronal regions, characterized by yellow coronal line emission (Ca XV) and by temperatures perhaps above 4 x 1060 K, form immediately above these H-alpha loops.

Recently, Moreton [3] of Lockheed Solar Observatory discovered propagating outwards from the large flares a kind of excitation wave -- visible in minor wavings and fluctuations in the chromospheric structure. The waves move along the solar surface to distances as great as a solar radius or more, at speeds as high as 2000 km/sec. One explanation offered by Freidrich Meyer, of the Max Planck Institute for Physics and Astrophysics in Munich, proposes that the disturbance is a coronal wave trapped at the interface between the chromosphere and corona.

Sometimes very large, high, but otherwise stable prominences suddenly elevate and lift off into space -- giving a spectacular sight when viewed in lapsed motion. They are not always or even usually associated with flares.

Radio Noise from the Sun

If you look at the sun in wavelengths from the centimeter to decimeter range (--I cm to -.30 cm) you see primarily thermal radiation from the hot coronal and chromospheric plasma. The electron densities and magnetic fields are such that the corona is opaque at these wavelengths only in active centers such as coronal condensations. At wavelengths larger than about one meter, where the corona is opaque, you observe the hot thermal radiation of the corona only. 219

...... Solar Activity and Radio Noise

At times of flares you get non-thermal emission in all wavelengths, from centimeter waves right out to wavelengths of many km.

In the centimeter to decimeter range the non-thermal flare- related source is usually synchrotron emission associated with very energetic electrons spiralling in the strong local magnetic fields.

In the meter and decametric range (tens of meters) more complex sources seem to be responsible, for example, plasma oscillations and low-frequency synchrotron emission.

The noise morphology is interesting. One kind of emission -- "slow drift" emission -- apparently involves an exciting source moving .1000 km/sec over a range of heights from 100,000 km up to 2 or 3 solar radii. The radio frequency (of the plasma oscillation) drifts as the electron density changes in the solar atmospheric environment through which the exciting source drifts. The source may be a solitary wave, for example, an Alfve'n shock. Following slow drift bursts there often appears synchrotron emission over a wide wavelength range. "Fast drift" radio noise bursts occur much more frequently. Moving outward at speeds of 1/10 to 5/10 the velocity of light, they also seem to represent plasma oscillations varying in frequency with the environmental density. These appear at coronal heights of a hundred thousand kilometers out to distances even greater than 10 solar radii. The fast drift bursts frequently occur without flares. They very probably represent actual particle streams created in active centers.

These radio phenomena all originate in the corona. But no radio noise phenomena can be uniquely tied to the major solar particle events observed at the earth. The whole gamut of phenomena usually accompanies a major flare.

Crucial Questions to be Answered

1. What is the source of the coronal density and heat?

Bright and hot coronal concentrations generally center around flare-active regions and the looped prominence regions. But when flares stop, the coronal region lingers on. Moreover, the corona shows only a very localized increase after a flare -- so it seems that the flare alone isn't the source. 220

J. W. Warwick ......

My own model says the coronal heat is entirely from the very fast particles (neutral plasma stream) generated in the 0.2 to 0.4 C energy range in an active region. The radio evidence often showed, for example, in late May and June of this year a nearly steady succession of fast-drift bursts probably from a single region. The corona grew during this period, and I suggest that this days- to weeks-long flux of fast particles created and heated the corona.

Acoustic waves are inadequate. Hydromagnetic waves are too hard to pin down as a possible source at this stage of knowledge (too many free parameters).

2. What are geomagnetic storm and other terrestrial effects of particle streams?

The geomagnetic storm effect results from a density or speed discontinuity (or both) carried outward in the solar wind from sun to earth. The changing impact of this discontinuity on the geomagnetic field produces at least the initial part of the storm.

But the details are both complex and uncertain. Prediction remains wide open. Big events with the gamut of radio (and optical) effects are pretty sure to produce terrestrial consequences, including a geomagnetic storm, a day or two later.

The sun-earth space is apparently threaded by a spiral field (water-hose geometry) with fields of a few gammas (one y = 10- gauss). The fastest particles generated by the sun appear to follow the "tracks," but particles of lesser energy can come from anywhere on the solar disk.

There are problems also with the fact that some of the fast particles (protons with speeds of 0.1 c) are stored for longer times than their straight-line transit times sun-to-earth -- and continue to arrive at earth for many hours after solar flares.

3. How are solar fast particles accelerated? What is the origin of a flare?

There may be possibilities of explosive release of "twists" in strong magnetic fields in the solar atmosphere. These unstable shapes may be generated by fluid dynamical properties of the photospheric gas. Another possibility is that the particles are created 221

...... Solar Activity and Radio Noise

elsewhere in the sun than in situ in the chromosphere and corona, and are merely trapped there as a result of the complicated magnetic field shapes.

The escape of particles from these flaring regions may occur in kinks, associated with Alfven shock waves, moving out through the trapping region and on up into the high corona.

Accurate magnetic field observations on a short time base over the areas of active regions during major flare effects are clearly a high priority item for the coming solar maximum -- but the observations are not easy.

References

1. Chapman, S.: "Notes on the Solar Corona and the Terrestrial Ionosphere," Smithsonian Contributions to Astrophysics, 2, 1-11, 1957.

2. Parker, E.N.: Interplanetary Dynamical Processes, Inter- science, New York, 1963.

3. Moreton, G.E., and R.G. Athay: "Impulsive Phenomena of the Solar Atmosphere. I. Some Optical Events Associated with Flares Showing Explosive Phase," Astrophysical Journal, 133, 935-945, 1961. 222

J. W. Warwick ......

\\ / , -SINGULAR POINT

WORTH4 Pove \I '~ OCORONAL RAY T= Z- 5xlo o'

WI NO S OLNR

P1"OTOSP"\ERE o000 K (ARLY LACK BODY) / / \

P OLAR COROklAL PLUMES Fig. 1 -- The normal corona

SUWSPOTS AHI V ACTIVE PLUGE REGIOWI

// ~"CH R.OMO PHERE

PHOTOS PHAER:E—

Fig. 2 -- Closed loop structure of the corona 223

INFLUENCES OF THE SATELLITE 10 ON JUPITER'S ATMOSPHERE

James W. Warwick University of Colorado

To me the influence of To, the first Galilean satellite of Jupiter, is a striking demonstration of a connection between a planet's atmosphere and a satellite -- and thus it may have relevance to your consideration of the moon's apparent influence on the earth's rainfall.

Jupiter has twelve known satellites. The four "Galilean satellites" were discovered by Galileo with his early telescope, near the start of the 17th century. lo, the nearest of these to Jupiter, is only six Jupiter-radii away. Its size and mass are similar to our moon's, and it moves in a circular orbit, in the equatorial plane of Jupiter.

Io, in its 42½-hr orbit, displays an event-to-event hour-by-hour connection, amounting essentially to control of the radio noise emission of Jupiter in the 10-40 Mc frequency range. Other Jupiter radio frequency emissions, however, are not measurably affected by To.

The influence of To on Jupiter radio noise has the following main features:

1. To, in two positions in its orbit relative to earth, "turns on" the emission in the 10-40 Mc range (decametric range) that arises from one main sharply localized source fixed on the surface of Jupi- ter, and a weaker less localized source.

2. Radio emission in this range almost surely will occur when there is a favorable positioning of the radio source on Jupiter's surface and the satellite's orbit as shown in Fig. 1. Two configurations provide favorable conditions in which noise is almost certain to occur: (1) when Io is at the 90 point, and the fixed source S is in the sector between that point and the earth-Jupiter line; and (2) when To is at the 240 point, and 0 the source S' lies between 240 and the earth-Jupiter line.

3. Jupiter radio emissions in the higher frequency range near 2000 Mc show no perturbation by To. This emission originates, in all probability, from synchrotron emission from energetic electrons trapped in Jupiter's radiation belts. This is just at the level where To orbits, even though there is no apparent influence. 224

James W. Warwick ......

4. The to-controlled emission very probably results from precipitation of fast protons and electrons into Jupiter's atmosphere. It is a mystery why this is the emission subject to Io's influence.

5. The fixed source on Jupiter very probably coincides with the stronger pole of the general Jupiter magnetic field, which is in- clined about 8 to the rotation axis of Jupiter and has one of the two following characteristics: (1) it is either a dipole with one pole near the surface of Jupiter (the center is away from the equatorial plane) or (2) the field is asymmetric, being grossly distorted from a dipole, with the stronger, more concentrated pole the one responsible for the source.

The periodicities of this 10-40 Mc emission of Jupiter have been studied for many years. The rotation of Jupiter has long been known, but only about a year ago did the to influence emerge -- when Keith Bigg, of Australia, discovered it in data taken there, and established it even more convincingly in my own data here. At first I was convinced that his finding was a spurious beat phenomenon of the terrestrial observing periods, Jupiter's rotation, etc., but I believe its reality now to be unequivocally established. There is a nearly one-to-one correspondence of favorable geometry and the noise -- and the data permit rejection of alternative explanations of the periodicity.

Other facts:

1. The source is not the famous red spot of Jupiter.

2. The noise has a sporadic character from minute to minute.

3. I have reported a short-term positive solar activity relation with this 10-40 Mc radiation, but this is not universally accepted.

4. The emission spectrum has interesting variations related to the geometry of to and the source.

5. The other satellites show no clear effects at all in spite, I think, of the recent paper by Lebo, Smith, and Carr [1]. 225

'•''••••••.•••••••••••••..... lo Influence

Mechanisms

In respect to mechanisms, I suspect satellite-plasma-particle- magnetic field interactions are involved, and not tidal influences. The fact that the favorable lo phases are not 1800 apart is a part of the argument. lo, of course, does have the strongest tidal effect of the satellites, a tidal force comparable to the earth- moon effect.

0 The fact that the noise is not at 180 -opposed positions of To is very securely established and holds even though lo is in the equatorial plane of Jupiter, in a circular orbit, and the plane of the orbit is always nearly parallel to the earth-Jupiter line (never more than 2.90 out).

The polarization of the 10-40 Mc emission is always right-handed (above 20 Mc), which also suggests that the Jupiter source is of one polarity. The radio emission in the 10-40 Mc range is often very narrow-band, encompassing only 2 to 3% of the central frequency (extremely high Q of "transmitter"), and the frequency of the band depends on the geometry within the permitted range. This suggests emission at the gyrofrequency of the electrons involved, instead of emission at the plasma frequency, which would vary as the electron density varied.

We suspect the 90 and 2400 peaks are two lobes of the emission pattern of a transmitter that has the geometry of a conical sheet of emission generated by To (Fig. 2). The emission goes into an angle controlled by the magnetic field in Jupiter's polar regions. Whether this is by reflection or because of the physical nature of the generation is not known, but some of the emission comes off in a direction parallel to Jupiter's equatorial plane. It is clear that at all positions around Jupiter, Io must generate the emission. In most of these locations, however, the emission goes off at an angle to the equatorial plane and therefore cannot be observed by us on earth.

Discussion:

Warwick stated that Io is believed by Dollfus to rotate syn- chronously (like our moon) once per orbital revolution -- this conclusion is based on his recent drawings of Io's surface markings, even though To subtends only about one second of arc. 226

James W. Warwick ......

To produce these effects Io probably must have a magnetic field. It might acquire a magnetic field mainly as a result of its having a mild electrical conductivity. The idea is that Io would then trap a part of Jupiter's magnetic field. A comparable mechanism has been proposed to explain the moon's influence on the solar wind.

No other planets show a satellite effect on radio emission -- but no other planets are known to have anything like Jupiter's decametric emission.

The solar wind, Warwick stated, extends at least as far as Jupiter. The white corona shows a streamer structure from quite low elevations out to around 30 solar radii and probably beyond. The plasma flux thus dominates the magnetic fields beyond a distance of only a few solar radii from the sun. Jupiter's radiation belts extend out a distance depending on the Jupiter field strength and the solar wind there. Warwick has estimated this Jupiter magnetosphere to extend 50 Jupiter radii, but this is not a secure estimate. As seen from earth this would subtend 0.5 on the sky and all the Galilean satellites would be inside.

The solar plasma impact on the earth's or Jupiter's magnetic field is supersonic vis a vis the thermal speed of the particles, and exceeds the hydromagnetic speed in the gas. There exists a shock wave between the wind and the magnetosphere. This was predicted by Kellogg and Axford [2,3] and later confirmed by observation. A bow wave forms and behind this is a turbulent region which extends some thousands of km, where conditions may provide the source of trapped radiation belt particles. Some similar mechanism probably operates on Jupiter.

Near earth there is a plasma coming from H and He diffusion upward to 1000 to 2000 km height; this is probably the ambient plasma responsible for the magnetosphere. Alternatively or in addition there may be a different source: maybe the plasma that causes the main phase of magnetic storms consists of neutral particles as suggested by Akasofu [4]. These questions are still open.

Warwick's theory is that Jupiter's 10-40 Mc emission orginates in a singularity region of the magneto-ionic dispersion relation -- but it will get out only if the magnetic field along the ray path stays reasonably high while the plasma density gets very low. He believes that upward diffusion of plasma from Jupiter, as Ellis has proposed [5,6] is not a source of Jupiter's magnetosphere. 227

•••••••••••••.T...... lo Influence

Brier mentioned that Bigg's study of the Io-Jupiter radio noise came about from an effort to understand the earth-moon rainfall influences. Alas, several pointed out, far from simplifying the understanding of the lunar-earth rainfall effect, it seems to have opened new realms of questioning about radio noise, magnetosphere, etc., in Jupiter, and may be of no value for its original purpose.

References

1. Lebo, G.R., A.G. Smith, and T.D. Carr: "Jupiter's Decametric Emission Correlated with the Longitude of the First Three Galilean Satellites," Science, 148, 1724-1725, June 25, 1962.

2. Kellogg, P.J.: "Flow of Plasma around the Earth," Journal of Geophysical Research, 67, 3805-3811, September 1962.

3. Axford, W.I.: "The Interaction between the Solar Wind and the Earth's Magnetosphere," Journal of Geophysical Research, 67, 3791-3796, September 1962.

4. Akasofu, S.I.: "A Source of the Energy for Geomagnetic Storms and Auroras," Planetary and Space Science, 12, 801-833, September 1964.

5. Ellis, G.R.A.: "Cyclotron Radiation from Jupiter," Australian Journal of Physics, 15, 344-353, September 1962.

6. Ellis, G.R.A.: "The Radio Emissions from Jupiter and the Density of Jovian Exosphere," Australian Journal of Physics, 16, 74-81, March 1963. 228

J. W. Warwick ......

SO0 ~~~~~~ •

^0 -(UPITER)—- —- -—70

I~~~~~ - RANGE oF 1. FAVORAB.E. IBo, POS^ TION1G —O OFIC -OO±ZO0 T \ L T O PoSITION C A TTH OF^" O^ O

lo PERIOD = ^V/Z VK

3UPIT ER 5OUOCE P V t COO ) $I,55mIt

Fig. I — Favorable positions of Jupiter radio source in relation to Io's orbit 229

**^ 10 0• 0 0 0 0 0 • •• •• •• . loI Influence

DIPOLE -L£KE LIINE OF FORCE THE O-TCV, LtWS OF I Co4JTAItOitJ r o FORCFE, W~iC C4 cOJSE-CUT.IELY COPTAIKJ To SOUP-rrR ROTTATS PAST THE SATELLITE

/ ~~~JU^TFI ( o / ^r \~~~~~~~~~~~~~~~~~~~~~

JUPiTE15R'LcEQUATORIAL PLAtJC (ALSO PLAKJ^ OF: loIS OPBQ T)

Fig. 2 -- Conical sheet of emission generated by Io