G601 A7 A67 1 978 c.2 000119
PROCEEDINGS OF AN ARCTIC PHYSICAL OCEANOGRAPHY WORKSHOP
October 10-11,1978
at the
Institute of Ocean Sciences, Patricia Bay Sidney, B.C.
Institute of Ocean Sciences, Patricia Bay
Sidney, B.C.
1979 •
This is a manuscript which has received only limited circulation. On citing this report in a bibliography, the title should be followed by the words "UNPUBLISHED MANUSCRIPT" which is in accordance with accepted bibliographic custom.
• CON TEN T S
Page
INTRODUCTION 1
PROGRAM 1
INFORMAL INFORMATION EXCHANGE 2
GENERAL DISCUSSION 5
LIST OF PARTICIPANTS 6
APPENDICES : 10
A. F. G. Barber. Arctic Oceanography: Some Knowns and Unknowns B. T. S. Murty and M. C. Rasmussen. Plans for Numerical Modelling of Circulation Associated with Sills in the Canadian Arctic Archipelago C. Knut Aagaard. Summary of Invited Talk D. V. R. Neralla. Sea Ice Prediction Programs and a Methodology at the Atmospheric Envi ronment Servi ce, Canada ..
- 1 -
INTRODUCTION In recent years, the distribution of Arctic Oceanographers in Canada has changed; many of them work as contractors and for offshore resource extraction industries. It seemed timely to collect most of these relatively rare oceanographers from Industry, Government and Universities under one roof - primarily to meet each other and to find out what each of us is doing. The Workshop, held on October 10 and 11,1978, did just that. The hoped-for workshop component - to develop a rationale for long-term Arctic oceanographic research - of necessity has to be a topic for future discussions. There was too much else to learn. The Workshop was organized by Allen R. Milne and Tad S. Murty.
PROGRAM. October 19, 1978. 0830 Registration 0900 P. W. Nasmyth Welcome A. R. Mi 1ne Workshop theme and overview of Oceanography related to resource de ve 1opment. 0935 F. G. Barber Knowns and unknowns in Archipelago oceanography 1010 B REA K 1040 T. S. Murty Numerical Modelling 1120 E. L. Lewi s Instrumentation and Logistics 1200 L U N C H (at lOS Cafeteria) 1315 Information Exchange and Workshops (Moderator: A. R. Milne) "Programs and Problems" - each participant to give a 5-minute, informal presentation. 1500 B REA K 1530 "Programs and Problems" - conti nuati on. 1700 B REA K for DIN N E R 1930 Wine and Cheese Social at lOS October 11, 1978. 0830 Invited speaker - Knut Aagaard, University of Washington 0915 "Programs and Problems" continuation. 1000 B REA K 1020 "Programs and Problems" - cont., and Wrap-up. 1230 End of organized program. - 2 -
INFORMAL INFORMATION EXCHANGE. Each attendee had an opportunity to speak on his current work and interests related to Arctic Oceanography. Apart from time allotted to invited speakers, all of the time was devoted to this part of the program; consequently, the hoped-for opportunity to deal with future plans and programs did not arise. It would seem that this function could be the responsibility of an individual or small committee benefiting from the stimulation of the workshop. Topics and speakers were as follows: (Apologies, in advance, are due to those participants whose comments were not recorded and to those whose main points of discussion are not accurately noted). Clive Mason, Bedford Institute of Oceanography: Work is proceeding on ice forecasting in the Gulf of St. Lawrence. Related to EAMES (Eastern Arctic Marine Environmental Survey), the Bedford Institute of Ocean ography has oceanographic interests in Baffin Bay and Davis Strait; also off Labrador, related to EMR permit areas. Regarding the archiving of data, it should all reside with M.E.D.S. (Marine Environmental Data Service). Considerable data is now with Universities and industrial contractors. Regarding archiving the latter, there is some mistrust as to its quality. V. R. Neralla, Atmospheric Environment Service, Toronto. (See attached paper). Real-time sea-ice prediction models are now under development. M. B. Danard, University of Waterloo and Atmospheric Dynamics Inc. Discussed were three projects: (1) Predicting winds in the Beaufort Sea; (2) Modelling of surface winds in Barrow Strait (on behalf of Defence Research Establishment Esquimalt) and (3) Climatology in Davis Strait. T. S. Murty, Institute of Ocean Sciences. Discussed were wind-generated and tidal-circulation models for the whole of the Northwest Passage (Parry Channel), Baffin Bay and Davis Strait system. Touched on was the possibility of developing a model for the whole Canadian Arctic Archipelago. A. R. Milne, Institute of Ocean Sciences. Current-meter moorings in Parry Channel were discussed in the context of providing 'ground-truth' data for T. Murty's numerical models of water circulation. Heavy stress was put upon the need for year-round monitori ng of water-mass movements and their identification. Discussed was possible relationships between the Archipelago ice climate and oceanography.
S. Prinzenberg, Canadian Centre for Inland Waters (OAS, Burlington). Work in Hudson Bay, James Bay and Hudson Strait was described, as well as more recent work over the Barrow Sill. - 3 -
Steven Peck, Canadi an Centre for Inl and Waters (OAS, Burl i ngton). Described was data from two current meters deployed in Penny Strait on behalf of DINA. Plans for 1979 include a program of air/sea inter action studies in the Sverdrup Basin, funded by the Energy Research and Development Program. Parts of this program include : the development of an ice model by Dr. Neralla, and the deployment of sets of current meters, under ice, to examine vertical current structures. Hopes are to develop a joint AES-OAS five-year program for the Sverdrup Basin. Brian Smiley, Institute of Ocean Sciences. Described assessment of risk to wildlife from offshore drilling proposed for Lancaster Sound. Impacts likely are best guesses which are difficult to defend legal istically,at Public Hearings. Assumed threats to wildlife must be based on a firm ice and oceanographic climate.
Lyn Lewi s, Insti tute of Ocean Sci ences. Briefly covered was a description of : Current measurements in various Archipelago channels, supported by Polar Gas Project funds; investigations of mixing processes in deep Arctic fjords; seasonal changes in Bridport Inlet oceanography (supported by Petro-Canada); past and completed work in Greely Fjord on Ellesmere Island; work on deep water oil-well blowouts in conjunction with the University of Alberta at Calgary; the study of polynya air/sea interactions and oceanography (in conjunction with the Boundary Layer Group at AES, Toronto); mine-tailings work (by Bob Sudar); instrumentation development of various types; finally, the preparation of a manual on CTD measurements as a commitment to a SCOR Committee of which he is a member. Robert Lake, Institute of Ocean Sciences. Following on discussions by Lyn Lewis, described in detail were current meter measurements in Byam and Austin Channels. Mean bottom currents, trending southward, appear to increase by almost an order of magnitude during the winter months. Currents measured in Wellington Channel agree well with Murty's numerical model. Adam Kerr, OAS, Ottawa. He described the terms of reference for a study he is conducting on long-range plans for Arctic research within OAS. He is directly responsible to ADM/OAS, Mr. G. Ewing, for this study. Dave Grant, Petro-Canada (Melville Shipping Limited), Montreal. He described his connection and invol vement with the Arctic Pilot Project [a proposal to transport Melville Island and offshore gas by liquid natural gas (LNG) icebreakers through Parry Channel on a year-round basis]. He described programs which measure ice ridges and other ice climate· features. A numerical model has been developed (ARCTRANS), into which ice features and icebreaker characteristics are built in order to determine delivery parameters. Alex Beaton, Ice Forecasting Central, Ottawa. Operational ice fore casting procedures were described. Aids include LANDSAT and NOAA photographs in near real-time, aircraft reconnaissance and water temperature and salinity data.- the latter to assist in forecasting - 4 -
freeze-up and break-up. This is not always available, particularly in the far north. In addition to winds, ocean-current data is needed to estimate ice drift adequately. The reconnaissance aircraft is equipped with: side-looking radar (SLAR), a LASER profilometer (for measuring ice-ridge heights and wind-wave amplitudes), an infrared line scanner (for estimating ice thickness), and a radiation thermometer. Martin Vanieperen, Panarctic Oils Limited. Considerable work on the motion of landfast ice has been done, but is not yet public information. Oceanographic data has been obtained at all offshore, thickened ice- pl atforms. George Hobson, Polar Continental Shelf Project of EMR. Described was EMR's upcoming LOREX Project (Lomonosov Ridge Experiment), beginning April, 1979 and involving geological and geophysical studies. Ocean ographers from the University of Washington have some involvement in the Project. The status of the North Water Project was covered. He is the new Chairman of the Canadian Committee on Oceanography's (C.C.O) Sub-Committee on Arctic Oceanography (SCAO). Bodo De Lange-Boom, Seakem Oceanography Limited, Sidney, B. C. Icebergs and sea ice were tracked by a radar at the S.E. corner of Devon Island during late Spring, Summer and Fall, 1978, under contract to Petro-Canada. Eric Sadler, Ice Research Group, Defence Research Establishment Pacific. The Robeson Channel Oceanography erogram has been completed. Fourteen current meters were deployed in Fury and Hecla Straits, along with six tide gauges. Some current-meter data is available for the eastern end of Hudson Strait. David Fissel, Arctic Sciences Limited, Sidney, B. C. For the past two years, ice-drift work and 'oceanography has focussed on Lancaster Sound and Baffin Bay. At present (1978), under contract to Petro-Canada, work is concentrating at the mouth of Lancaster Sound and the adjoining Northwest part of Baffin Bay. This summer, 14 out of 15 current-meter moorings were recovered. Seven moorings were redeployed for over wintering. Similar work will extend to March, 1980. Other complementary field work included satellite-tracking of icebergs and surface currents (RAMS buoys), CTD's and the detailled tracking of surface currents relative to oil-slick modelling requirements. Harold Serson, Ice Research Group, Defence Research Establishment Pacific. Concerning locations where continuous year-round oceanographic data could be COllected, an 'ice-plug' located between Meighan Island and Axel Heiberg Island in Sverdrup Channel last broke out in 1961, and has remained in place since that time. Elton Pounder, McGill University. CTD's and current measurements obtained over the Barrow Sill in the spring of 1977 were described. Analysis is being completed. - 5 -
Humfrey Melling, Institute of Ocean Sciences. Fifteen RAMS (Random Access Measurement System) buoys were air-dropped by TWin Otter in locations around the Beaufort Sea's rim in the winter of 1977-78. Ice drift has been tracked during the ensuing year.
GENERAL DISCUSSION. Major points brought out in the general discussion were Possibility of establishing synoptic oceanographic stations in Archipelago waters Lack of year-round oceanographic data in the Archipelago Concern regarding quality of data obtained by industry and its suitability for archiving at M.E.D.S.
Optimism regarding revival of the C.C.O. Sub~Committee on Arctic Oceanography (s.c.A.d.) and its possible role in spearheading program development Suggestion that Arctic Oceanography Workshops, in the future, could be scheduled to coincide with Canadian Meteorological and Ocean ographic Socities (C.M.O.S.) General Assemablies. - How does one get industrial, oceanographic data made public? - A long-term objective for oceanographic programs in the Archipelago could be related to the sea-ice cover in the context of climate change. Also, factors such as ice-growth, decay and drift could be better understood if water mass movements and the oceanic heat input were known. lIST OF PARTICIPANTS ARCTIC PHYSICAL OCEANOGRAPHY WORKSHOP, OCTOBER 10 and 11, 1978. Name Organization Address Dr. P. W. Nasmyth Institute of Ocean Sciences P. O. Box 6000, 9860 West Saanich Road, SIDNEY, B. C. V8l4B2. Dr. David Farmer Institute of Ocean Sciences SIDNEY, B. C. (as above) Mr. Michael Foreman Institute of Ocean Sciences SIDNEY, B. C. (as above) Dr. Falconer Henry Institute of Ocean Sciences SIDNEY, B. C. (as above) Mr. Stephen Hill Institute of Ocean Sciences SIDNEY, B. C. (as above) Mr. Robert A. lake Institute of Ocean Sciences SIDNEY, B. C. (as above) '" Dr. E. lyn lewis Institute of Ocean Sciences SIDNEY, B. C. (as above) Dr. Humfrey Melling Institute of Ocean Sciences SIDNEY, B. C. (as above) Mr. Allen R. Milne Institute of Ocean Sciences SIDNEY, B. C. (as above) Dr. Tadepalli S. Murty Institute of Ocean Sciences SIDNEY, B. C. (as above) Mr. Brian D. Smiley Institute of Ocean Sciences SIDNEY, B. C. (as above) Mr. Fred Ba rbe r Ocean &Aquatic Sciences 240 Sparks Street, Affairs Branch - Environmental (7th Floor West), Studi es, Dept. Fi sheries & Oceans OTTAWA, Ontario. K1A OE6. Dr. J. R. Wilson Marine Environmental Data Centre, 240 Sparks Street, Ocean & Aquatic Sciences, (7th Floor, West), Dept. Fisheries & Oceans OTTAWA, Ontario. K1A OE6. LIST OF PARTICIPANTS (Continued) Name Organization Address Mr. Adam Kerr Assistant Deputy Minister's 240 Sparks Street, Office, Ocean & Aquatic Sciences, (7th Floor, West), Dept. Fisheries & Oceans OTTAWA, Ontario. K1A OE6. Dr. V. R. Neralla Atmospheric Environment Service, 4905 Dufferin Street, Dept. Fisheries & Oceans DOWNSVIEW, Ontario. M3H 5T4. Dr. Steven Peck Canada Centre for Inland Waters, 867 Lakeshore Road, Dept. Fisheries & Oceans BURLINGTON, Ontario, L7R 4A6. Dr .. Pri nzenberg Canada Centre for Inland Waters, 867 Lakeshore Road, Dept. Fisheries & Oceans BURLINGTON, Ontario, L7R 4A6. Mr. A. P. Beaton Ice Central, Trebla Building, Dept. Fisheries & Oceans 473 Albert Street, " OTTAWA, Ontario, K1A OH3. Dr. George Hobson Polar Continental Shelf Project, 4th Floor, City Centre Towers, Dept. Energy, Mi nes & Resources 880 Wellington Street, OTTAWA, Ontario, K1A OE4. Dr. Joh n Keys Dept. Indian & Northern Affairs, Les Terrasses de la Chaudiere, (Northern Environmental Protection OTTAWA, Ontario, K1A OH4. Branch) Dr. Eric Sadler Defence Research Establishment Fleet Mail Office, Pacific (DREP), Ice Research Group, ESQUIMALT, B. C. Dept. National Defence Dr. Maurice Danard University of Waterloo WATERLOO, Ontario. (Dept. Mechanical Engineering), and President, Atmospheric Dynami cs Inc. LIST OF PARTICIPANTS (Continued) Name Organization Address Prof. Knut Aagaard University of Washington SEATTLE, Wa. 98195, (Department of Oceanography) U. S. A. Dr. L. K. Coachman University of Washington SEATTLE, Wa. 98195, (Department of Oceanography) U. S. A. Dr. R. B. Tripp University of Washington SEATTLE, Wa. 98195, (Department of Oceanography) U. S. A. Dr. E. R. Pounder McGill University Rutherford Physics Building, (Ice Research Project) 3600 University Street, MONTREAL, P. Q. H3A 2T8. Dr. Harold L. Snyder C-CORE (Centre for Cold Ocean Memorial University of Resources Engineering) Newfoundl and, St. John's, Newfoundland. 00 AlB 3X5. Mr. Dave Grant Melville Shipping Limited 1801 McGill College, Suite 1020, MONTREAL, P. Q. H3A 2N4. Mr. Larry Allen Petro-Canada Exploration Inc. 650 Guinness House, 727 - 7th Avenue, S. W., CALGARY, Alberta. T2P OZ6.
Mr. Fran~ois Aubin Petro-Canada Exploration Inc. 650 Guinness House, 727 - 7th Avenue, S. W., CALGARY, Alberta. T2P OZ6. Dr. Martin Vanieperen Panarctic Oils Limited 703 - 6th Avenue, S. W., CALGARY, Alberta. T2P OT9. lIST OF PARTICIPANTS (Continued)
Name Organization Address Mr. Tom Yao Maclaren Marex Inc., Wi ndmi 11 Pl ace, Consulting Engineers &Scientists 1000 Wi ndmi 11 Road, DARTMOUTH, N. S. B3B 1l7. Dr. Wilson E. Russell NORDCO limited (Newfoundland P. O. Box 8833, Oceans Research & Development ST. JOHN'S, Newfoundland, Corpora ti on) AlB 3T2. Capt. Simon T. Culshaw NORDCO Li mited lower 534 - 8th Avenue, S. W., CALGARY, Alberta, T2P lE8. Dr. Savithri Narayanan Dobrocky-Sea tech l i mi ted 130 Kingston Street, VICTORIA, B. C. V8V lV4. '" Mr. Michael C. Rasmussen Dobrocky-Seatech limited 130 Kingston Street, VICTORIA, B. C. V8V lV4. Dr. John Marko Arctic Sciences limited 9860 West Saanich Road, SIDNEY, B. C. V8l4B2. Dr. David Fissel Arctic Sciences limited 9860 West Saanich Road, SIDNEY, B. C. V8l4B2. Dr. Clive S. Mason Bedford Institute of Oceanography, DARTMOUTH, N. S. (Coastal Oceanography) B2Y 4A2. Mr. Bodo De langeBoom Sea kern Oceanography ltd. 9817 West Saanich Road, SIDNEY, B. C. Dr. Harold Serson Defence Research Establishment Fleet Mail Office, Pacific (DREP), Ice Research Group, ESQUIMAlT, B. C. Dept. National Defence.
~ 10 ~
A P PEN DIe E S A, B, C & D
A P PEN D I X A.
F. G. BARBER. Arctic Oceanography Some Knowns and Unknowns
Arctic oceanography: some knowns and unknowns
F.G. Barber
Contents
1. Foreword
2. 1ntroduct ion
3. Water level data
4. Discussion
5. References
6. Appendices
6.1 Fish population in the Hudson Bay system, a speculation
6.2 Initiation and prevention of a glacier, a speculation
1. Forword
Some of the ideas I would like to talk about this morning were de rived from study of water level data at various sites in the archipelago, al though we are testing some of the concepts through application of existing numerical models. We have concluded that a cover of fastice can (1) 1 imit the input of energy from the atmosphere (wind mainly) by an order of magnitude and as well can (2) alter the frequency of modes of free oscillations, (3) modify the character of shallow-water constituents and (4) in two areas in particular, the Hudson Bay system and Amundsen Gulf, the ice cover can modify the main tidal constituents significantly. We bel ieve we understand in a general way how the ice cover achieves these effects, but for the present will limit the description to data from Tuktoyaktuk, noting that a descrip tion for other sites may be available soon (Godin and Barber undated). The suggestion that 1 would like to leave with you now is that we should antici pate a distinct alteration in regime in areas where an annual ice COVer is characteristic, for example an alteration from a winter pattern of surface current to a summer pattern. As far as I know such an alteration has not been shown to occur, although there is indirect support in a number of aspects including the freshwater budget and particularly in the Aidjex study (eg Hibler and Tucker 1977 p 130).
2 . I n trod uc t i on
As an initial response to Allan's request, I reviewed the result of the 1969 workshop (Anon. 1969) and my contribution to it (Barber 1969). It is quite clear I believe that in several specific aspects considerable pro- f 2 g ress has been ach i eved dur i ng the interval. Two wh i ch seem (to me) to s till need attention are the manner in which support in physical oceanography is provided to contingencies and the extent that local people are involved in oceanographic programmes.
I have found it curious that quite often we have been expected to respond meaningfully to questions in the context of the oceanography of northern waters which had not yet been resolved at more southern locations, where there were a great deal more data and many more studies. Two examples are Strathcona Sound and the Beaufort Sea; there are others. In somewhat similar vein, we need to recognise that we still lack a fundamental under standing of the world ocean, as well as parts of it, indeed we are quite un certain about the sequence of events which led to the distributions observed in the modern world ocean. Munk (1966a) noted this and the consequence that oceanographers have directed attention to lesser and apparently more tract able problems. He said (p II)
This lack of an orderly and systematic approach towards understanding the oceans is to oceanographers at once a source of despai r and of exciting challenge.
After this initial review my inclination was to speak to you to the theme "How did the Arctic Ocean get the way it is?" - partly I suppose to refute Allan's idea that we tend to forget about change - but I soon found that with but a few exceptions, one of which I will return to'later, the work would be similar to th'H already achieved for the Pacific (Munk 1966 b). In addition there have been a number of good reviews by agencies in North America and U.S.S.R. relating to large programmes in meteorology, oceanography and glaciology (see eg Anon. 1974 a; b; 1976; Treshnikov et al. 1974). I then decided to attempt to examine the theme Allan had suggested.
As you can imagine I found it difficult to deal adequately with the "Knowns and unknowns" in our' understanding of the oceanography of our north ern areas. As ",'ell it seemed somewhat presumptuous that one attempt to de scribe the unknown; nevertheless, I soon determined that the topic was too extensive to treat in the time avai lable and ,.as led to I imit drastically my contribution: I decided to emphasize one particular feature about which I would I ike to know more and I expect you would as well. This is the role of the ice cover - not the nature of the ice COver but the consequences.
First I would note' briefly some biological consequences of an ice cOVer about which we have speculated; speculations which are gradually being accepted. With the idea that a layer of freshwater could have been widely distributed under a perennial ice cover and so have led to some of the so called "reI ict s~ecies" in the arctic (Barber and Murty 197]), I have sug gested that the Pacific salmon, in particular tre pink salmon, originated from the arctic char during a period the land bridge at BerIng Strait existed. This has led in turn to a rather novel concept concerning the development of ocean migration in Pacific salmon based on Langmuir circulations and to the idea that the paucity of certain pink salmon populations, ie of the off-year run, is due to predation. These are of no immediate concern here and it would be premature to say more about them, except that they began with a physical distribution which could only develop and persist in the presence of ice cover. Similarly I have conjectured that present fish distributions in Hudson Bay are 3
akin to accident in that fish in neighbouring low-salinity coastal areas are prevented from becoming establ ished there by the high salinity in Hudson Strait. Subsequently I have suggested that the arctic cisco be introduced into James Bay and southern Hudson Bay (see 6.1).
The idea of introducing the cisco was one of a number of undertakings by man which I perceived could eventually alter (increase) the rather limited resource base of the Hudson Bay system and I enlarged on this to the extent that I foresaw that some management of the system in the oceanographic sense might be achieved. However, I have become much less sanguine about the pos sibility of management as it seemed likely that oceanographic conditions in Hudson Bay favour the development of a glacier, ie there is I ittle point in trying to improve the region if a glacier is to occupy the region again. Recently then I have been examining several models of glacier growth and of ways man might intervene to prevent such growth and, while it seems now that intervention would be possible there are more than a few unknowns, most of which relate to the consequences of an ice cover (see 6.2).
In the Foreword I suggested that in the presence of fastice the energy input from atmosphere to ocean is much reduced and that the conse quences are probably significant to major current patterns. While this re sult initially came out of study of the freshwater budget of the Beaufort Sea and archipelago, it has been strongly supported by study of water level data.
3. Water level data
It is of interest that Gabriel Godin has been able to complete a co tidal map for all Canadian coastal areas including the arctic, although he emphasizes' that for some arctic areas the available data are marginal at best. For example there are few data in Foxe Basin, Committee Bay and east Amundsen Gulf, while along the coast of the archipelago bordering on the Arctic Ocean there are no data. However, in some areas we have been able to examine the influence of the ice cover on free oscillations and it is clear that a great deal of information or understanding of particular regions can be achieved in this way. In addition gauge records contain information about barotropic transports and the length and time scales OVer which the transport may be coherent. One can say that much more data are required, more current data, more met data and more sea level data; however, available material should be studied, particularly as the transport through the passages of the archipel ago may be largely barotropic and hence likely strongly correlated with sea level data.
An obvious site where such relations may be apparent in the gauge records is Barrow Strait and as a particularly good body of data appears to exist there we are in process of an examination. We began with data observed at nearby Port Leopold in 1848 which Ross (1854) bel ieved showed the influence of variations of atmospheric pressure. The residuals after low-passing clearly show evidence of periodicities at the scale of days. Most power occurred at .08 cpd (12 d) with lesser peaks at .20 cpd (5 d), .33 cpd (3 d) and .58 cpd (1.7 d). There is I ittle power in the latter peak, but it is noted because it occurs in the residuals at Resolute; as do each of the other peaks. The possibil ity that these periodicities might have an association with fluctuations of transarchipelago transport was I bel ieve made first by Bailey (1957) over 20 years ago. 4
Figure. Spectral analysis of the mean dai ly water level (low pass) a.t Resolute for 1975 'in the form of overlapping segments, each of 15 days and shifted by 1.5 days.
o;'.o~o-~o;"'.t~0-~0'-'.2~0-~0;"'.3~0-~0'-'. 4:::0-~0;". 5:::0-~0'-'.6:::0-~0;". ,:::o--'o"'.e:::o'--'o7-.,;;;o'---:'\ '. 00 CYc/OAY 5
Of courSe we have also examined data from Resolute and as an initial assessment we obtained power spectra for the low pass of each of March and September of 1975 and it is seen that no marked difference occurred, although there is significantly more power at low frequency in March. Considerable power exists at about .10 cp 12 h (5 d) in September and of a number of other peaks in each record one at .23 cp 12 hr (2.2 d) is most obvious. The peak at 15 cp 12 h (3.3 d) in March is not seen in September, but may exist as part of the broad peak at about .10 cp 12 h in September.
At this point it seemed 1 ike·ly that the longer period variation might be evident in a presentation of the data in the form of overlapping segments. In this there is considerable power throughout the year, not con tinuously but in bursts, between about .08 cpd (12 d) and .3 cpd (3 d). Peaks at .125 (3 d) and .25 (4 d) are seen frequently and may be related to normal modes of the system, perhaps the latter is an harmonic. A point here is that for Barrow Strait in 1978 some useful insights might be achieved were current speed data available there - everything else seems to be in place including a numerical model.
4. Discussion
I would emphasize that while our studies of water level data are in a preliminary stage, they do appear to support the contention that a signif icant alteration of regime occurs with annual period. The change of regime appears in part responsible for the maintenance of the low-sal inity water within the Beaufort Sea Gyre, ie for the gyre itself, and for the development and persistence "f areas of open water in winter (polynia) within the archi pelago. Models or schemes, of each have been attempted but remain incomplete because of uncertainties in relatively simple aspects of heat and volume budgets. Specifically we need to know the manner in which the winter surface deficit is met, whether by sensible heat or ice formation; and of the signif icance of ice export. In one approach we appl ied a box model to several areas (Beaufort Sea, Baffin Bay) in an attempt to determine whether unusual amounts of ice were being formed; however, with the lack of winter data the results remain uncertain. In Hudson Bay, where the excess of ice export over import is bel ieved close to zero, the box model was instructive and led to the speculation concerning the initiation of a glacier mentioned above.
Finally, there are many other aspects not touched upon here which may receive attention later in the workshop, but I would note that I have not spoken directly to one of the sub-themes mentioned by Allan in his first work shop announcement ie the "constant annual cl imate assumption". I must say that I had not been aware that this·assumption was being made, except as nec essary perhaps in the development and appl ication of budget techniques (volume, salt and heat), for on the contrary, we know that the water in the archipelago and the Hudson Bay system is of very recent origin, within 8,000 years BP. However, in one respect I agree with the comment, for I see little in present programmes which would provide long-term information; eg of the kind avail able for certain Norwegian fiords (Saelen 1967). We attempted to establish such a programme at Pond Inlet based on individuals there. It seems that one such programme, ie at one locality, should receive support, but I would not want to champion any particular programme at this point in our workshop. 6
5. Re fe rences
Anonymous. 1969. Informal proceedings of the workshop on research topics on ice-drift and oceanography in the arctic archipelago. Second Canad ian Oceanographic Symposium. Victoria November. Def. Res. Est. Pac:49 p.
1971. Ice summary and analysis 1969; Hudson Bay and approaches. Canadian Meteorological Service: 47 p.
1974 a. U.S. contribution to the Polar Experiment (POLEX). Part I, POLEX-GARP (NORTH): 119 p. Part 11 (SOUTH: 33 p. Nat. Acad. Sciences.
1974 b. Southern Ocean dynamics - a strategy for scientific explor ation. 1973-1983: 52 p. and Antarctic Glaciology - guidel ines for U.S. programme planning 1973-83: 66 p. Nat. Acad. Sciences.
1976. Scientific plan for the proposed Nansen Drift Station. Polar Research Board. Nat. Acad. Sciences: 247 p.
Bailey, W.B. 1957. Oceanographic features of the Canadian archipelago. J. Fish. Res. Bd. Canada 14(5) :731-769.
Barber, F.G. 1967. A contribution to the oceanography of Hudson Bay. Marine Sciences Br. Man. Rep. Ser. No. 4:69 p.
1969. Letter to A.R. Milne, December 31. MSB file 1225-1:7 p.
1970. Oil spills in ice: some cleanup options. Arctic 23(4) :285-286.
1972. On the oceanography of James Bay. Marine Sciences Br. Man. Rep. Series No. 24:1-96.
Barber, F.G. and T.S. Murty. 1977. Perennial sea ice: speculations COncern ing physical and biological consequences. In Polar Oceans. M.J. Dunbar (ed):257-267.
Broecker, W.S. 1975. Floating glacial ice caps in the Arctic Ocean. Science 188(4193) :1116-8.
Donn, W.L. 1967. Causes of the ice ages. Reprint Sky and Telescope 33(4) :7p.
Godin, G. and F.G. Barber. undated. Variability of the tide at some sites in the Canadian arctic. Submitted to Arctic.
Hays, J.D. 1973. The ice age cometh. Saturday Review of the Sciences. Apri 1 :29-32.
Hays, J.D., J. Imbrie and N.J. Shackleton. 1977. A reply to D.L. Evans and H.J. Freeland. Science 198:p 530.
Hibler, W.O. and W.B. Tucker. 1977. An examination of the viscous wind driven circulation of the arctic ice cover over a two-year period. Aidjex Bull. No.37:95-131. 7
Ives, J.D. 1978. The maximum extent of the Laurentide Ice Sheet along the east coast of North America during the last glaciation. Arctic 31(1):24-53.
Lee, H.A. 1968. Quaternary geology. In Science, History and Hudson Bay, 2. C.S. Beals and D.A. Shenstone eds:503-543.
Libby, W.F. 1967. Climatology conference, a letter. Science 192:843.
Maykut, G.H. and N. Untersteiner. 1969. Numerical prediction of the thermo dynamic response of arctic sea ice to environmental changes. Rand Corp. Memorandum RM-6093-PR:173 p.
Mercer, J.H. 1970. A former ice sheet in the Arctic Ocean? Palaeogeography, Palaeoclimatology, Palaeoecology 8:19-27.
Munk, W.H. 1966a. The abyssal Pacific. Univ. Newcastle upon Tyne. Fifth Marchon Lecture:11 p.
1966b. Abyssal recipes. Deep-Sea Res. 13:707-730.
Newell, R.E. 1974. Changes in the poleward energy flux by the atmosphere and ocean as a possible cause for ice ages. Quat. Res. 4:117-127.
Ross, J.C. 1854. On the effect of the pressure of the atmosphere on the mean level of the ocean. Trans. Roy. Soc. 144:285-296.
Saelen, O.H. 1967. Some features of the hydrography of Norwegian fjords. In Estuaries AAA Pub. No.83:63-71. G.H. Lauff (ed).
Thompson, H.A. 1968. The cl imate of Hudson Bay. ~ C.S. Beals (ed.) Science, History and Hudson Bay. Dept. Energy, Mines and Resources, Ottawa: 263-286.
Treshnikov, A.F. and four. 1974. The POLAR EXPERIMENT - polar problems in the global context. The Arctic and Antarctic Research Institute, Leningrad: 58 p.
Weyl, P.K. 1968. The role of the oceans in climatic change: a theory of the ice ages. Meteorological Monographs 8(30):37-62.
6. Appendices
6.1 Fish population in the Hudson Bay system, a speculation
(As this will likely soon become available in the Technical Report Series of the Fisheries Research Board it is not included here).
6.2 Initiation and prevention of a glacier, a speculation
Ice ages have been the normal condition during the last several million years, with temperate climates enduring only about 5 per cent of the time. (Libby 1976).
7 8
It is generally accepted that ice-covered oceanic areas experience a deficit in their annual surface heat budgets; a deficit which is balanced by a coupling through currents to adjacent ocean areas. We can foresee that in some of these areas the amount of heat transported by the currents could be altered, in particular could be reduced which, if surface conditions be un altered, would require an increase in the volume or thickness of ice. We speculate that in a region like the Hudson Bay system. the heat transported by currents could become so small that a perennial ice cover could become char acteristic and eventually, Hudson Bay could again become the centre for growth of a glacier.
In a recent review Ives (1978) conjectured that the last glaciation, the Laurentide, may not have been as extensive as some believe; nevertheless, his interpretation (see his figure 2) indicates a formidable distribution of glacial ice. Lee (1968) briefly reviewed a number of hypotheses concerning the increase in the amount of ice on land around Hudson Bay and in the follow ing we propose yet another. It will be evident that several explanations of the causes of ice ages (Donn 1967 p 4; Weyl 1968; Mercer 1970; Newell 1974; Broecker 1975) contain parts of our mechanism and it seems that aspects of these theories might have been incorporated into our scheme. We might for example have pursued the development of a perennial ice cover over the Hudson Bay system which grew further seaward to extend over much of the North Atlantic, as in Weyl 's scheme. We chose however to exploit aspects peculiar to the region and the strong I ikel ihood that Hudson Bay was the centre for the earlier glaciation. A novelty is that we visualize intervention by man to prevent a particular condition, ie to prevent a perennial ice cover over Hudson Bay, seen as a necessary step to the growth of a glacier there.
That the glaciation of the Laurentide was centered over Hudson Bay led to the consideration that the mechanism for the initiation of a glacier, and perhaps its subsequent growth, might have a connection with the ocean ography: the annual surface deficit, the annual ice cover little or none of which is exported and the uncoupling from the ocean by strong tidal mixing all contribute to the character of the system. A portion of the surface water moving seaward in the estuarine circulation, because of the tidal mixing in and adjacent to Hudson Strait, is returned to Hudson Bay as part of the inflow. Thus the annual surface deficit of the bay may in part be met by heat absorbed (stored) in the surface' layer during summer, ie after the ice cover is dispersed. The timing and extent of these periods are known to vary and it is known too that ice usually lingers longest in the southwest part of the bay where, in the season of 1969, a portion of the ice nearly survived the summer (Anon. 1971). In a prel iminary examination of the possible impact of hydro-electric development I envisaged that the persistence of the ice was due to a change of wind strength and direction each summer, ie from a cold, dry northwesterly flow to a rather weaker movement of warm, moist air from the southwest (Barber 1972). As the latter air moves over the ice cover it becomes cold and stable, with much cloud and fog and hence less absorption of shortwave radiation, less ice melt and continued high surface albedo. This general movement of air is believed to be strongly coupled to global processes (Thompson 1968) and we speculate that a small change in the present pattern, to less persistent northwest winds in spring and early summer to more frequent flows from the southwest and south, could cause a decrease in the amount of ice melted in the southwest and eventually to a perennial ice cover there. 9
It was recognised that the persistence of the ice led to relatively low surface temperature and reduced seasonal heat storage, as compared with other parts of the bay, and that the influence was reflected in a reduced heat content of the surface outflow. Thus, the increased persistence of ice would lead to a reduction of heat in the outflow, of heat in the inflow and of the heat available to meet the surface deficit. -2 -1 The deficit was calculated to be about 700 g cal cm year in the water adjacent to Churchill (Barber 1967) and although supported by somewhat independent calculations of salt and volume budgets, perhaps only the small size is significant. For the purpose here we take the value as a measure of the present capability of the system to meet a deficit at the surface; a capability which seems relatively small in comparison to the Arctic Ocean and Baffin Bay where deficits appear close to an order of magnitude larger. And of course in neither of these areas does a significant part of the ocean con tribution appear to originate within each area, ie there is little feedback. I foresee then that the extent of perennial ice would continue to increase as the contribution of the ocean continued to decrease. The ice, which is not exported as is much of the ice formed in the Arctic Ocean and Baffin Bay, would eventually reach an equil ibrium thickness governed mainly by the char acter of the annual surface radiation balance (Maykut and Untersteiner 1969). This balance determines the extent ablation occurs each season; should abla tion be less than the annual precipitation as snoW a glacier would result (Broecker 1975). As an increased amount of snow would be associated with the change in global circulation, ie of a relatively moist air from the southwest, the development of a glacier seems 1 ikely.
A glacier over Hudson Bay would be considered undesirable, so that were it believed possible to avoid the condition, appropriate measures would likely be taken. The extent that man might intervene is dependent on the time scale; the slower the natural process the greater the 1 ikel ihood that inter vention is possible. Perhaps there is some optimum length of time over which man's activity would be practical (in the engineering sense) and the change measureable and recognisable as being due to man. Such may be a feature of our scheme in that the existence of a perennial ice cover may represent a stage both critical to the initiation of a glacier and possible of control.
Of a variety of ways in which control might be achieved - waste heat from "spent" nuclear reactors, alterations to or removal of the coupl ing to the world ocean, change of surface albedo - I have been led to speculate that a sign i fi cant dec rease of albedo cou 1d be ach i eved by pump i ng seawa te r on to the surface cover of snow and ice, which reduction would increase ablation so as to be greater than precipitation.
Experience is limited to pumping spilled oil (with water) onto a cover of fastice in June (Barber 1970), which formed large, shallow pools over the surface. The oil in these pools was subsequently disposed of by burning, but an initial objective of pumping was to attempt to enhance the evaporation of the (diesel) oi 1. We were aware of the heat budget impl ications, but were not able to obtain significant data except that we noted the influence of the pools with regard to albedo during periods of precipitation as snow: the form ation of pools not only altered the albedo but also the potential to store heat.
., "I 10
Maykut and Untersteiner (1969 p 133) showed that understanding of the influence of the melt pond was deficient and concluded that a "programme to define the characteristics and behaviour of melt ponds is needed". This situation does not seem to have changed significantly. In addition our under standing of particular aspects of the Hudson Bay system remains quite 1 imited, so that the elevation of the thesis presented here from the speculative, is not yet possible. However, one cannot but be aware of the known extent of the ice ages, as noted at the outset, and of the sombre warnings of climates to come, eg Hays (1973). There is growing evidence that the timing of the succession of the ice ages may be predictable but that their extent is not, ~ee Hays et al. 1977), so that the extent, or amplitude, of any ice age may turn on a subtle, but perhaps critical sequence, as we envisage the perennial ice cove r to be.
,I ". A P PEN 0 I X B
T. S. MURTY and M. C. RASMUSSEN. Plans for Numerical Modelling of Circulation Associated with Sills in the Canadian Arctic Archipelago.
if
PLANS FOR NUMERICAL MODELLING OF CIRCULATION ASSOCIATED
WITH SILLS IN THE CANADIAN ARCTIC ARCHIPELAGO
T. S. Murty and M. C. Rasmussen
, ·"1 I,j-
A B S T R ACT
Plans for a hierarchy of models to study the circulation and internal hydraulic jumps associated with sills in the Canadian Arctic Archipelago are discussed.
ill;
- 1 -
1. INTRODUCTION An examination of a hydrographic chart of the Canadian Arctic Archipelago shows that there are several sills of varying sizes and s,lopes in the vari ous water bodi es compri sing the Arcti c Archi pe 1ago. Recently, Farmer (1978) showed in connection with his studies on Babine Lake, that when sills are present, the circulation in the presence of stratification could be quite complicated due to the presence of features such as internal hydraulic jumps (or internal undular surges) associated with the thermocline. However, it should be pointed out that internal hydraulic jumps are possible even when sills are not present; but sills are potential sources for these jumps.
In real water bodies, if there are sills present, usually there is more than one and, as can be seen from Figure 1, in a hypothetical case with two symmetrical sills, two symmetric internal jumps may be generated. After some time, these jumps may propagate and merge and give rise to complicated slopes of the thermocline, as can be seen from Figure 2. Thus, it is obvious that thermocline movements and mixing problems cannot be truly understood in numerical models without allowing for the possibility of formation of internal jumps.
In circulation problems, one has to distinguish between rigid lid and free surface models, because this top boundary condition could be important in determining. the nature of the circulation (Lick et al, 1978). Long (1965) showed that, when the Boussinesq approximation is made, drastic differences in the results could occur, depending upon which boundary condition is used - 2 -
at the top. The Arctic water bodies, because of their surface ice-cover during most of the year, offer a natural and unique laboratory for testing the rigid lid versus free surface models.
It has been pointed out by several authors that, a model in which the pressure field is treated as hydrostatic cannot be valid once the jump forms. Beyond this stage, the pressure field has to be treated as non- hydrostatic. In connection with a scale analysis for the mid-latitude cyclone systems, Holton (1972) pointed out that, hydrostatic approximation is not merely to show that the vertical acceleration is small compared to gravity, but since it is only the horizontally-varying pressure field that is directly coupled to the velocity field, one has to show that, the horizontally-varying pressure field is in hydrostatic balance with the horizontally-varying density field.
In terms of free surface and interfacial displacements, Proudman (1953) showed that, for the hydrostatic approximation to be valid, the following criteria have to be satisfied for a two-layer model (taking the origin of the ~ axis at the undisturbed free surface and pointing downwards). For the free surface
(1) and for the interface
( 2) where h and hi respectively are the thicknesses of the upper and lower layers, - 3 -
l p and pi are the densities, nand n are the deviations of the free surface and the interface from their respective equilibrium positions, and g is gravity. By putting in appropriate numerical values, it can be shown, for exampl e, in the 1aboratory experiment conducted by the Coas ta 1 Ocean'ography section on internal hydraulic jumps, that, while criterion (1) is valid, criterion (2) is not valid.
Figure 3 shows an internal hydraulic jump simulated through a hydrostatic model. Since non-hYdrostatic pressure field is not present in this model, the dispersion seen here could be attributed either to rotation or to numerical dispersion. In principle, by using suitable finite-difference forms, numerical dispersion can be suppressed. For narrow water bodies, such as the Babine Lake, rotation is not important. Hence, the only source for dispersion is the non-hydrostatic pressure field, and any internal hydraulic jump model, to be correct physically, should include this. In the meteor ological literature, it has been demonstrated that, without the inclusion of the non-hydrostatic pressure field, one cannot simulate lee waves on the down stream side (or lee side) of mountains.
2. HYDROSTATIC MODELS One of the models which has been successfully used in the simulation of internal hydraulic jumps is patterned after Simons (1978). We will simply summarize the relevant equations for the case of f = 0, ~ = 0, and v = O. ay Thus, we only have one horizontal dimension (along the axis of the water body). The momentum and continuity equations are
aU + ( 3) at - 4 -
and £!l+~=O at ax (4 ) where U = hu is the mass transport in the upper layer in the x direction, h is the depth of the upper layer, D(x) is the total depth, E = ,6.p/p is the density difference across the interface, and TX is the x component of the wind stress.
Simons (1978) showed that the jump moves with the non-dimensional speed C where
C = 3(1-2r), / r(l-r).------K . J ra (l-ro) , -ll-6 r O-r)Jl':-K2 (5) /ra (l-ro) i -' where K (6 ) where r is the ratio of the upper layer depth to the total depth, u* is a non-dimensional upper layer velocity, and subscript 0 refers to the undisturbed state.
The results of simulations shown in Figures 1 to 3 are based on this model. It should be exphasized that, if the non-linear advective term uau in the x-momentum equation is not present, then the thermocline will ax not steepen enough to form a jump - as can be seen from Figure 4.
Another interesting result from the observations of the Coastal Oceanography section is, when multiple interfaces are present, there is a jump on each interface. In a three-layer situation with two interfaces, the jumps on these
, 1.. ( - 5 -
interfaces are of different amplitude and out of phase. We hope to simulate the two-interface problem using the following model which is based upon Houghton and Isaacson (1970).
With reference to Figure 5, let PI' pi, P3, respectively, be the densities of the top, middle and bottom layers and let H(x) be the height of the sill. Let the top layer be considered passive so that the only parameter of interest will be its density. Let the thicknesses of the middle and bottom layers, respectively, be H2 and H3 and let u2 and U3 be the velocities initially imposed in these layers. Define
PI P2 = sand - = r (7) P 3 P 3
Then the equations of motion and continuity for the middle layer are
dU2 : S \ dH 2 + u - + g 1 - - 1- 2 dX \ r / dX
s s dH + g, 1 + g, 1 = 0 ( 8) r \ r dX and 2 dH + ~X \ u2H2 = 0 (9) dt
The same equations for the lower layer are
dU3 U dU3 dH 2 + 3- + g(r - s) dt dX ax dH + g( 1 - s) dH3 + g (1 - s) = 0 (10) ax dX and dH3 + L (U3H3 = 0 (11 ) dt dX .' - 6 -
We plan to solve this set of four equations for the four unknowns, uz, u3' H2 , H3 , using the two-step Lax-Wendroff scheme, as was used in the Simons model.
3. NON-HYDROSTATIC MODELS
Proudman (1953) gave analytical solutions for the case when the
pressure field is treated as non-hydrostatic. Assuming as above, f = 0,
a/ay = 0 and v = 0, the equations of motion in the x and ~ directions and the continuity equation are (with the origin for the ~-axis at the undisturbed free surface and pointing downwards)
1 aP (12 ) au u~ + w~ = - -- at + ax a~ p ax
aw waw 1 aP + u,aw + = - -- + g ( 13) at ax a~ p a~
aw Q..u + = 0 (14 ) ax a~
At the free surface ~ = - no
ana + uono + at ax 'II = 0 (15 ) For the linearized problem, the solutions are r X ' t \ a-cos 27r I - T' (16 ) " _27r1:/'A P = P + g p ~ + a·e cos ( 17) a [ '\ 27r1:/'A "x t \ 27ra - cos 27r -- -T J: (18 ) u = Ie 'A! 27ra _2 7r 1:/'A t w = - T e sin 27r f - T (19) where a is the amplitude, 'A is the wavelength, T is the period, and
Pa is the atmospheric pressure. - 7 -
When the non-linear terms are included, under the third approximation Proudman (1953) gave the following solutions: " . \ 'x t 2 .'x t'; no = a· cos 27r I --- '+ 7Ta COS41T! - - _ ! :.A T; - A :A\ T't, '. cos 611'~ - t) (20) A I "
-211~/A P = P + ~ + a[l + liM;: a gp f 2 \ A ' J e cos 21r'~ - 1'.1 1 '.A T; r I ( 21) I - 1Ia 2 e -411Z/A ~ )
-211~/A ' x - t \ u = 211a e cos 211 - T ,A I) ( 22)
. \ 2 i , 5 '1Ia ' -211'f./A , x t --- I e sin 211, - (23) 2 • A• .J . A - I I
These above solutions are for the homogeneous case. For the two-layer problem, solutions can be worked out similarly.
The numerical model which we plan to use is patterned after Lin and Apelt (1970). The momentum equations in the x and 'f. directions and the continuity equations are; i a P 2 P ; au + u ~ + w .£.l!.) = + 110 "V U (24) 0: at ax a~ ax I. \ 2 Po: aw + u aw + w aw \ = - aP - pg + 110 v w (25) :,at ax a~ " a'f. '. ,
au + aw = 0 (26) ax a'f.
The thermal energy equation is
poep ( aT + u~ + w aT) = Ko- where 110 and Ko are the eddy dynamic viscosity and therTllill conductivity. - 8 - From (24) to (26) the vorticity equation can be formed. ( 28) where the vorticity ~ is defined as ~ .: aw (29 ) ax and v ~ ~o is the kinematic eddy viscosity. The equation of state is Po 1 aT ~ -_1 ~ To ax Po ax (30) A stream functi on 'I' can be defined such that u ~ ~ w ~ - 2.t a;! , ax ( 31 ) 2 Then ~ ~ -'V 1jJ ( 32) Define K ~ Ko ( 33) p-:Cp where K is the eddy thermal diffusivity and Cp is the specific heat at constant pressure. Next, the equations will be non-dimensionalized using the following scheme u* ~ u w* ~ '!!- , x* = ~ , t* ~ t [j' U L (L7U) ~* ~_~_ , 1jJ* ~L, T*~ T-To (34) (uIL) UL .6. T where L is a characteristic length, U is a characteristic velocity and ~.T is a characteristic temperature difference. The non-dimensional forms of the vorticity equation, thermal energy equation and the relation connecting the vorticity and the stream function are (* denotes a non- dimensional quantity) : ~* + u*~* + w*~* ~ (35) at* ax* a;o:* - 9 - aT* + u*aT* + w*aT* = at"* ax* a;!* (36 ) ( 37) where the Prandtl number Pr , the Reynolds number Re, and the Froude number Fr are defined as P = r "K Re = UL " Fr = U (38) .; gL·I'T To NOTE that Fr = 1 where Rj is the Richardson number. '-R .. "' 1 Equations (35) to (37) are three equations for the three unknowns ,*, T* and ~*. Once ~* is known, one can calculate u* and w* .. 4. DENSITY AS A VERTICAL COORDINATE. In section 2~ we pointed out that, since hydrostatic assumption means, the horizontally-varying pressure field has to be in hydrostatic balance with the horizontally-varying density field, one can think of using density as a vertical coordinate in preference to;!. In meteorological literature, the so-called sigma coordinates are extensively used. In the oceanographic context also, some studies have been made using the sigma coordinates (e.g. Freeman et al, 1972). Although the sigma coordinates enable one to take the topography into consideration in a convenient way, for the sill problem, sigma coordinates are not appropriate. The reason is, when the sigma coordinates are used, the water on one side of the sill is forced to climb over the sill to the other side. However, in nature, this need not happen. With density as a vertical coordinate, there is no such unrealistic movement of the water. Also, the water bodies are stratified with respect to density and hence density as a vertical coordinate is very natural. - 10 - Starr (1945) derived the equations in density coordinates. In a Cartesian system, x, y, and density, p, the non-hydrostatic equations of motion are, with the inclusion of the Coriolis force, p.~. du = pfv ~ + ~. ~ _ ~. ai! ap dt ap ax ap ax ap (39 ) p ~ . dv = - pfu.~ + ai! aP - aP ai! (40) . ap dt ap ay ap ay ap P.2.1. . dw = - pg ai! aP ap dt ap ap ( 41) where 0.1,1 = au + u.£..l!. + v i1\J dt at ax ay dv = av + u~ + vav 1 dt at ax ay ( ( 42) dw = aw + u aw + vaw dt at ax ay I The continuity equation is d ai! ai! ' a,u - p = - p - + av ( 43) dt ap. ap ax ay . \ The equations (39) to (43) are four equations for the four unknowns, u, v, i!, and P. NOTE that once i! is known, w is simply di!/dt. These equations can be written for a multi-layer system also - 11 - ACKNOWLEDGMENTS. I thank Dr. D. Farmer for introducing me to the internal hydraulic jump problem, Dr. R. W. Stewart for suggesting the use of the density coordinates, Dr. T. J. Simons for kindly sending me a copy of his Computer Program on the two-layer hydrostatic model, Dr. D. Houghton for sending me a copy of his three-layer hydrostatic model program and Sheila Osborne for typing this report. REFERENCES. Farmer, D. M. (1978). Observations of Long Non-linear Waves in a Lake. J. of Physical Oceanography, Vol. 8, pp. 63-73. Freeman, N. G., A.M. Hale and M.B. Danard (1972). A Modified Sigma Equations' Approach to the Numerical Modelling of the Great Lakes Dynamics. J. of Geophysical Res., Vol. 77, No.6, pp. 1050-1060. Holton, J. R. (1972). Introduction to Dynamic Meteorology. Academic Press, New York. 319 pp. Houghton, D. D. and E. Isaacson (1968). Mountain Winds. Studies in Numerical Analysis, Vol. 2, pp. 21-52. Lin, J. T. and C.J. Apelt (1973). Stratified Flow over a Vertical Barrier. Proc. Third Int. Conf. on Numerical Methods in Fluid Mechanics, Vol. II, July 3-7,72. University of Paris. Edited by Henri Cabannes and Roger Temam, Springer-Verlag, Berlin. pp. 176-183. Long, R. R. (1965). On the Boussinesq Approximation and its Role in the Theory of Internal Waves, Tellus, Vol. 17, pp.46-52. Proudman, J. (1953). Dynamical Oceanography. Methuen Co., Ltd., London. 409 pp. Simons, T. J. (1978). Generation and Propagation of Downwelling Fronts. Journal of Physical Oceanography, Vol. 8, pp. 571-581. Starr, V. P. (1945). A quasi-Lagrangian System of Hydrodynamical Equations. J. of Meteorology, Vol. 2, No.4, pp. 227-237. THG UHER i100EL RT HGUR 8 5 INITIAL WIND N I I o T-----I ~ N 0'.00 a.DD tt.DD di.DD Z4.DD JO:OO--- ~1i.DD 4t.O':' lh.DO S~.:JO SIl.!1D ii6.0!l ----n-:DD 'h.oo 114.00 96.00 96.00 Ihz.oo loe.oo OISTANCE FRaM SOUTH SHBRE (KNI I I g I I --T------i I I ~. %0 ~, i fL.. ---_. A i ~g. I 0- I ~ I ~~o. I =- I o I o I I I I o~--:-ai:J-- - !L~c ----iB:-5il---Tl.iia-- . jo-:-~o- ~s.'Cio--'F.ao-- -.I! :ac--- --;1-:- '-0· ·--~c .oa--"""·ss--:---o-o---ll.tIO- ---jll:Co---e... .-00-·-"9"6--:00 11&.00 lbz.oo ·~i"-:-;j"c D!sr~~~~ ~~:~ ~~~TH s~~~~ (~NJ FIGURE 1. Two internal hydraulic jumps associated with two sills of same dimensions. Note that the jumps are also of equal dimensions. ,'.' .... -.) \.' TWG LRYER ~1GDEL RT HGUR 26 s INITIAL WIND N I 4 I ~,--+------,-.------n-----I ." irAI \ 'I ~ U o ~o ~, ~o ~. ~ ~ o o ~ W ill_DO e_oo I~_OD Ih_oo 2:4_00 36.00 ,h_oo .i_oo 4h_DO 54.00 156.00 IHi_aD "lZ_OO .,&.00 84.00 9b.oo 9t.OO Ibz.oo Ibll_Ct' DISTANCE FR8H SBUTH SHaRE (~Nl I I g I I ~r--T------i I I g I I ~ci\ : A A: ~g I I ,,-e;, I ~l r'l~"l g~ ~ 0':"iiO ------a:co i~.co 1&.00 i'6.oa·-~ ~h DC 42,00 ,h.oo 64.00 110.00 IIh.oo .,i.oo 71i.DO ei'i-:ocr--go,OO 9&.00 \"D"Z:OOL1iS:Oo DISTRNCE ffUH1 SOUTH SHe,~E O\MI FIGURE 2. Same as Figure 1, except at a later time when the two jumps merged. The asymmetry is due to the direction of the imposed wind. TWB LAYER MBDEL AT DRY 1 p HBUR 20 INITIAL ~IND __ 1I ~ 1 T------I 1 1 ~ 1 1 x ~ w.~ 1 I ~ :1 "0 1 w· z" 1 ~ u. ~. ~~ ..,~ .00 .:'.00 sb.OQ st.oo st.ao ,b.DD ''''.00 4b.ca ~.oo st.oD tll.oo '::'.00 .00 16.00 1t..Oo II',OC ,',DO 0',1]0 DISTANCE FRB~ NaRTH SHORE IKHl 1 1 1 :r--+------~ I ., I ..:.: ~:~~- " 8.00 I&.Do-lIb-:Qo -i;;&.00- It-oa' .11.0-0- .."-.00 - ~b.OO--- -~- '~--:QO --1:8.00- - tY";Oo -ib.~- IB.QO- It--:aD - 11.00 4.00 -~D.OO OISlR,'tCE FRaN NSRTH SHeRE I K/1J FIGURE 3. A numerical simulation of an internal hydraulic jump. The dispersion could be due to three reasons; (a) numerical, (b) rotation, (c) non hydrostatic pressure field. In this simulation, the third factor is not present. 9. , --.J S:.) ~;.:; TWB LRYER MODEL RT HBUR 20 INITIAL HIND 1 1 1 :",--T-- : ------~------1: ;::~ 1 1 1 1 -~ ~I i!'w- 1 1 e., 1 1 1 1 1 1 1 .. 1 1 1 ~ U1 .L.oo ii.OD lb.oo is.DO ".on ii.oo .. '.i.oo $6.00 si.oo n.on ti.ao u.!lC z6.00 dioDe n.DO .'.00 ... 00 O!.OD DISTRNCE F~3M N~RTH SHDRE t~Ml 1 1 1 = --T------: ; 1 1 ~ 1 ~. 1 1 1 1 1 1 1 i 1 1 .. I 1 l:co li.oo 113.':10 5I.OD It.DO 41i.O~ ~- 46.ro 3'.00 n.on zi":"C'C u.co EO.llol~~--__:r_:_~~--i:~-·~_i.DQ DHi1;:;."i~::: F~:l11 N~RTH liH::JRE [101l FIGURE 4. Simulation with a linear model to show that the interface cannot steepen sufficiently to form a jump. - 16 - LRYEP. 1 (PAM/Vii) ~ LAYER 2- f'l. 1 Uz. liz. ~ LAYEP. 3 x FIGURE 5. Schematic diagram of a passive three-layer hydrQstatic model as used by Houghton and Isaacson. A P PEN D I X C KNUT AAGAARD. Summary of Invited Talk. I Summary of Invited Talk Arctic Physical Oceanography Workshop Sidney, B. C., 10-11 October, 1978 Knut Aagaard Department of Oceanography University of Washington Seattle, Washington 98195 The relationship between waters of the Canadian Arctic and those of adjacent seas is a dynamic one in which processes in adjacent seas influence Canadian waters and vice versa. Furthermore the Canadian Arctic Archipelago is probably as complicated an ocean area as any in the world, not least because of its geometry. It is useful to think of the hydrographic structure in the classic sense, dating from Nansen's time, with two layers being of interest: the upper (or mixed or surface) and the Atlantic layer. The upper layer is cold and of relatively low salinity. It actually extends down to about 200 m, and it's certainly not mixed, but is rather characterized by a salinity gradient. Below this is the Atlantic layer which is characterized by tempera- tures several degrees above the ~reezing point, i.e., it is an enormous reservoir of sensible heat, the integrity of which is maintained solely by the salinity stratification, limiting the effectiveness of vertical transfer. In the Canadian Arctic, this water is probably several 10's of years old, in terms of it's entry time into the Arctic ocean. My thesis is that there are considerable variations with time in the characteristics and location of these waters, that these variations occur at very low frequencies, and that while such variations may be important (say, to the ice distribution or plant and animal life) we don't know what the consequences are. Consider the upper layer. In the simplest view, we can consider its characteristics to represent a see-sawing between the addition of fresh water -2- at the surface, principally through runoff, and the addition of salt at a dept.h of some hundreds of meters through the Atlantic water influx. Seasonally, significant stirring is achieved through convection driven by freezing. Some simple TS considerations suggest that the vertical mixing may be more effective than has been supposed. (We might well hypothesize that a number of factors and processes affect vertical mixing, including edge effects and shelf processes). Examples from the Alaskan Beaufort Sea show the kind of changes that can occur over very large areas and for very long times. One of the remarkable things about the Canadian Arctic is the enormously long shoreline, in effect a tortuous shelf (with surface exchange, wind effects, and tidal currents) on which waters can be changed and mixed. We don't even know the sense of the cross-shelf circulation in such areas, i.e., whether they constitute a source or a sink of density for the Arctic Ocean. Some recent examples from northern Alaskan waters show that both senses of circulation can exist in winter. In the Beaufort Sea, dense saline water can move onto the shelf Over large areas and its effects persist for long periods of time. In the Chukchi Sea, on the other hand, freezing produces a salty, cold water on the shelf. This corresponds to the classic view of the shelf role in winter (large area/volume ratio), but the water formed is of such an extreme type that it is denser than any water in the Arctic basin. Are there similar occurrences in the Canadian Arctic? Another matter of interest in the upper layer is the cycling of fresh water. The residence time for fresh water in the Arctic Ocean is about ten years, with the water deriving partly from Arctic rivers and partly from the North Pacific. Long-term river gaging shows the persistence of anomalies for periods of five years or so, which is comparable to the residence time. As for the North Pacific influence, reactive silicon and phosphorus budgets indicate that the Pacific water is principally discharged through the archipelago, with perhaps 60 percent going through Lancaster Sound. In this connection we know that there -3- can be long-term changes in the hydrography of the northern Bering shelf. From recent long-term current measurements in the Chukchi and northern Bering seas we also know that the "very lowest measurable frequencies con- tain high energy levels. Similarly with the Atlantic water, we know that at its point of inflow there are very large low-frequency variations in both temperature and transport. Again we don't know the effect of such variability, although comparison of ice concentrations north of Spitsbergen and Franz Josef Land show cons i- derable variations from year to year. My conclusion is that the Arctic seas are restless ones. It's important to find out what this restlessness does to the Canadian Arctic. While the 10,000,000 square km of ice-covered Arctic Ocean seem enormous and permanent, the ocean is really a very small one. A P PEN D I X D v. R. NERALLA. Sea Ice Prediction Programs and a Methodology at the Atmospheric Environment Service, Canada. SEA ICE PREDICTioN PROGRAMS AND A METHODOLOGY AT THE ATMOSPHERIC ENVIRONMENT SERVICE, CANADA V. R. Nerall a Atmospheric Environment Service Downsview, Ontario, Canada October 1978 ,/ '';, Abstract The research programs at the Meteorological Services Research Branch (MSRB) for the prediction of sea ice motion and other relevant studies are discussed. A real-time, short range small scale ice pre diction methodology is developed and the results are briefly discussed. The incorporation of variable compactness in the internal ice resistance formulation in the momentum equation is also discussed. A simple method to calculate the time dependent compactness is devised and computed compactness is compared with daily composite ice cover charts prepared at the Ice Forecasting Central, Ottawa. 1. MSRB* Research Program in Ice Predi.ction Methodology The purpose of developing a comprehensive research program in ice prediction methodology is: (i) to have available a plan of action for meeting antici- pated needs and future operational requirements in ice prediction for which AES has operational responsibilities, (ii) to assist in identifying where external support for carrying out specific projects on ice prediction methodology should be directed and identifying where external support is required, (iii) to consolidate many R&D projects on ice prediction into an integrated and comprehensive program, (iv) to advance required prediction procedures for implemen- tation in the AES Environmental Prediction System or for implementation in Special Environmental Prediction Systems operated for industry on a cost recovery basis. The program contributes substantially to Ice Covered Waters projects and is designed to meet future demands for ice prediction in respect to: (i) Support for general marine navigation in Arctic waters infested by ice (floes, bergs, packs) for ice breakers, ore carriers, supply vessels, natural gas and oil tankers, etc. (ii) Support for safe and optimum routing through ice for special marine navigation associated with energy transportation and *MSRB stands for Meteorological Services Research Branch of the Atmospheric Environment Service (AES), Canada 37 -2- including LNG transport and AML transport i.n ice covered waters of the Arctic, (iii) oil drilling from offshore platforms in Arctic where the presence of floes, bergs, and packs and their movement poses a threat to the environment and operations. (iv) Support from weather and other environmental predictions in the Arctic (e.g., prediction of ice boundaries, floe concentrations etc., for determining fetch and damping factors for prediction of waves and superstructure icing etc.). The prediction items include 1) floe motion, 2) leading edges of ice pack, 3) concentration of floes and pack, 4) ridging and rafting, 5) icebergs, 6) freeze-up and break-up, 7) fast ice motion and 8) forma tion and closing of leads. 2. Ice Prediction in the Proposed Computerized Forecast System The first report of the National Detailed Design provides specification of a computer supported forecast system as it expected to evolve through the 1980"s. There are several aspects of ice pre diction that are covered under the Environmental Prediction System. (i) Short range floe concentration at the boundaries of ice packs and floe motion prediction, predictions will be based on dynamical forcing using most of the important stresses. (ii) Prediction of freeze-up and break-up on a seasonal basis over specified areas. (iii) Large scale analysis and prediction techniques continue to be manual, but incorporating all the available observations such as ice reconnaissance and sate" ite imagery etc: 3ff ·3- 3. Dynamical Ice Prediction Development at MSRB In order to assist the Arctic offshore activities, a real-time, short range small scale dynamical prediction model of ice motion has been developed at the Atmospheric Environment Service (AES) (Neralla et "al 1975, 1977). This model is incorporated into the computerized support system (CPSS) (Clodman and Muller, 1975). The CPSS is a complex set of computerized prediction modules designed to provide a variety of real- time environmental forecasts. Because the prediction methodology is relatively simple, it has the following advantages: 1. It can run operationally on mini computers available at regional forecast offices 2. Since the model requires only little input, it can be used over data sparse areas, and 3. With practically no changes in the model, it can be easily adapted to different areas of drilling operations, in particular for the floating oil rig locations. The model-generated drifts are compared with observed ice floe drifts obtained from the satellite imagery. 3.1 Description of the model The equation for horizontal motion of an ice floe is given by (1) where Pi' hi and Vi are respectively the density, thickness and velocity of ice, t is the time, ~a is the tangential wind stress at the air-ice 3'1 -4- interface, ~w is the water stress at the water-ice interface, CF is the Coriolis force, -+P is the pressure gradient force due to tilting G of the sea surface and R is the internal ice resistance. Assuming the motion to occur under balanced forces, equation (1) becomes (2 ) In order to obtain a reasonable solution, an accurate knowledge of all stresses is needed. Figure 1 shows the arrangement of velocities and forces in- cluded in the model. Considering a small area, the steady-state equation, for an isolated floe where the internal ice resistance is zero, becomes ->- ->- "* 'ai + 'wi + ~F = 0 (3) where ~ai is the wind stress at the air-ice interface and ~wi is the water stress at the water-ice interface. The different terms can be expressed as ,->- a ->- ai = Pa Cd Vai V.al (4) -+, w -+ wi = - Pw Cd Vwi Vwi (5) -, V = V V. (6) ai a 1 Vwi = Vi Vw (7) where C~ and C~ are respectively the air to ice and water to ice drag coefficients. 4D .. -5- Following Reed and Campbe 11 (1962) we incorporated water currents calculated from surface stresses. The procedure is based on the requirements of continuity of mixing length and the eddy viscosity at the interface between boundary and spiral layers. The main difference between our method and Reed and Campbell's is that the latter assumed The relationship between Vw and Vwi is 3/2 V = BV . (8) W Wl where B = ko [In h;~O ] _3/2 [f(h+ZO)]-\ (9 ) where ko is the von Karman constant, h is the thickness of the boundary layer and Zo is roughness length of the underside of the ice. The theoretical water currents are thus obtained and incor- porated into the formulation. From the balance of forces and velocity vectors we arrive at an expression for ice velocity. 3.2 Internal Ice Resistance In the ice prediction problems, the treatment of internal ice resistance is one of the important features of the model. Campbell (1965) and Doronin (1970) have treated the ice floes as a film of highly viscous fluid. Recent studies by Hibler (1977) showed that if the stress, '1/ -6- rate of strain relation were smoothed over a day or longer, the viscous law appeared a good approximation i.n modeling the ice dynamics. The internal ice resistance is expressed as p.h. "i/' (K"i/ V.) (10 ) R = 1 1 1 where K is the horizontal eddy viscosity coefficient for ice floes. Campbell assumed K to be constant while Doronin assumed a realistic form K = KH C where C is called compactness (fraction of area covered by ice). 3.3 Compactness of ice A simple method is next devised to compute compactness (Neralla and Liu, 1978) over a given area. By assuming constant ice density and thickness over the area, the compactness, C is obtained from ac + at = -"i/' (CV) + Si (11 ) where Vi is the ice drift, Si is the sources and sinks in the given area (e.g., freezing, melting or precipitation deposited on the ice). We have neglected thermodynamic processes by assuming the mass changes over a period of a few days are small. Concentration CN is related to compactness by (12 ) -7- The ice drift is obtained by solving equation (2). Since the area under study is small, we have neglected PG in equation (2). If 5 denotes fraction of land area of a grid point, then the maximum value of C is C=l when 5=0 and C=l-S when 5>0. If the compactness at a grid point is less than 0.1 then, R is neglected in the computations. The solution of Reed and Campbell as modified by Neralla et al (1977) is used as initial conditions. No slip boundary condition for -+Vi and no diffusive boundary condition for C are used. The modified Liebmann successive over-relaxation technique (Carnahan et al, 1969) with a projection method to control the non-linear form is applied (Neralla and Liu, 1978) for solving the momentum equation. 3.4 Results Based on recent sea ice studies, appropriate, parameters are assumed and used for testing the model. The details can be found in Neralla et al (1977). The observed ice drifts are obtained from ERTS imagery. The surface winds over the area of interest are obtained from a mesoscale one level primitive equation model (Danard, 1977). Table 1 shows the comparison between observed and model-generated ice velocities. The underestimates of computed ice velocities presumably result from the underestimates of diagnosed surface winds. For testing the internal ice resistance formulation, we I3 assumed the compactness C=l.O and KH=3.3xlO gm S-l for all cases. Since the ice velocities over the given area are uniform, the Laplacian -8- 'of ice velocities is very small. This is'probably the reason for small differences in computed ice velocities and deviation angles between these last two columns in Table 1. Next, the compactness is obtained by integrating the continuity and momentum equations. The time step used in the computa tions is 24 hrs. Figures 2 to 6 show, for each case, the initial, predicted and observed values of compactness. With a steady large-scale flow over the area of interest, the agreement of model predictions with observations for cases in late July (Figs. 2 and 3) is reasonable. The predicted distribution of compactness (in particular, 0.5 isopleth) in figures 2 to 5 agrees well with the observed distribution. The model performance for the period 24-29 August 1975 (Fig. 6) is only marginal, presumably due to abrupt changes in winds caused by a fast moving intense weather system. Although predictions agree reasonably well with observations, it would be more realistic to incorporate the sources and sinks term in the continuity equation for compactness. However, the present results from the simple formulation demonstrate the applicability of the technique for short-term forecasting of compactness over a small area. 3.5 Summary and Conclusions A real-time, short range small scale dynamical ice prediction model is developed. The calculated values of ice velocities are compared with satell i te deri ved floe motions. Although the results are encouragi ng, it has been emphasized that the incorporation of variable compactness is realistic in the formulation of internal stress. A simple method is devised to compute compactness over a given area. We have neglected sources and sinks terms by assuming the mass changes over a period of a few days are small. However, we plan to incorporate this in our future modification of the model. Five day integrations, with a time step of 24 hrs., have been carried out using data obtained from the daily composite ice charts pre pared at the Ice Forecasting Central, Ottawa. The preliminary results of the model are encouraging. For computing ice drifts incorporating internal ice resistance with variable compactness, the methodology developed here will be used. Acknowledgements I am grateful to Mr. O.K. Smith, Director, Meteorological Services Research Branch, and Mr. E.C. Jarvis, Chief, Forecast Research Division, for their encouragement. The manuscript was typed by Mrs. A.M. Kimmel. The research was supported by the Atmospheric Environment Service, Canada. References Campbell, W.J., 1965: The wind-driven circulation of ice and water in a polar ocean. J. Geophys. Res., Vol. 70, pp. 3279-3301. Carnahan, B., H.A. Luther, and J. Wilkes, 1969: Applied Numerical Methods. John Wiley, New York, 604 pp. Clodman, J., and F.B. Muller, 1975: Real-time environmental prediction system. Department of the Environment, Victoria, B.C., Canada. Beaufort Sea Technical Report #20, 138 pp. Danard, M., 1977: A simple model for mesoscale effects of topography on surface winds. Mon. Wea. Rev., Vol. 105, pp 572-581. Doronin, Yu. P., 1970: On a method of calculating the compactness and drift of ice floes. Translated from Russian in AIDJEX Bulletin, No.3, pp. 22-39. Hibler III, W.D., 1977: A viscous sea ice law as a stochastic average of plasticity. J. Geophys. Res., Vol. 82, pp. 3932-3938. Neralla, V.R., S. Venkatesh and M.B. Danard, 1975: Ice Motion in the Beaufort Sea. Proceedings of the Symposium on Modeling of Transport Mechanisms in Oceans and Lakes. Canada Center for Inland Waters, Burlington, Ontario 6-8 October, 1975. Neralla,· V.R., W.S. Liu, S. Venkatesh and M.B. Danard, 1977: Techniques for predicting sea ice. Preprints, Vol. II. Symposium on Sea Ice Processes and Models, September 6-9, 1977, Seattle, Washington, p II - 46 to II - 55. (Also to appear in the proceedings). Neralla, V.R., and W.S. Liu, 1978: A simple model to calculate the compactness of ice floes. Paper presented at the symposium on Dynamics of Large Ice Masses, conducted by the International Glaciological Society, August, 1978, Ottawa. Reed, R.J., and W.J. Campbell, 1962: The equilibrium drift of ice station Alpha. J. Geophys. Res., Vol. 67, pp. 281-297. Table 1. Observed and computed ice speeds (Vi' em S-1) and angular dgviation (0., deg) for Modell (excluding R) and Model 2 (including R) Observed Comruted Case Mode 1 1 Model 2 0. V. 0. V. 0. Vi 1 1 1 26.7 1 29.8 44 28.8 44 2 9.3 47 6.2 64 6.2 64 3 18.5 65 12.3 62 12.3 62 4 7.5 192 5.2 68 5.2 69 5 11.6 119 10.7 62 11.4 62 6 12.7 56 7.0 36 7.0 36 7 9.5 0 16.1 55 16.1 55 8 9.3 101 7.3 99 7.3 99 9 48.7 14 61.6 46 56.3 44 10 10.4 11 4.1 91 3.9 91 11 16.2 68 7.3 52 7.2 52 12 23.1 45 7.3 99 7.3 99 13 19.7 32 5.5 84 5.3 83 14 6.9 25 14.0 56 13.7 56 Average 16.4 55 13.9 65 13.4 65 Average error -2.5 10 -3.0 10 (Comp .- obs. ) x t> rJ f l--J / / V> / < ...,o u / OJ > / 'r U -0 $: o /-;1 OJ - t> ~ > Ll C ------... 1U OJ'" \I<-__~">-:-- U < o 4- 4- o EO <- en'" <0 o 0, 'IS ~o 1.0 0·5 FiU. 2 Compactness (a) at initial time, 21 July 1975, (il) 5- \ ·0 \ 0·5 ,_)0 ~ II ~-I-" . :;:r:-< a (r r ~ \ /' \·0 \·o~ ''----- 0 . 5- \''"~ ..~ :.;/.-::-.:::>-~I '-__ • ~• /" ./"';-:'.-.J .1 _ J , b Cr(' fi g. 3 Compactness (a) at initial time, 24 ,JlIly 1975, (b) 5-day fore cost valid. for 29 ,July 1"175 ilnd (c) 'observed at 29 ,July 1975. / 1·0 1.0 Fi 1'0 .' ~. r i (I. 5 CO(lIpactncss (a) at ini·tiil-l tillie, 19 /lU(just 197:>, (b) 5-t!ay l()n~CdSL vol it! for ,,~ I\uuust 1975 dnJ (c) observ~d ill ,,~ I\uyust 1975. I'O~ ~ - 0-5 J:''.., J,~~~" -' 2~O ,,--. VL--- [ c )~ F i ~. 6 COlllpactness (a) at initial tilile. 24 I\U'lIJst 1975. (b) 5-day f()I'L'c~st 'val id for 29 1\11~IJSt 1975 a'rl"d (c) observed al 29 I\u