R. H. SIMPSON AND ROGER A. PIELKE*

Introduction whereas the extratropical wave cyclone has a broader more homogeneous swath of damaging winds. A small Economic losses due to hurricanes in the United States change in the hurricane track may cause a major shift currently averagesmore than $800 million a year! and in the coastal threat (see e.g., Brand and Blelloch, 1975). the trend over the last three decades (see Fig. 1 next Thus, one of the greatest challenges in hurricane fore- page) is exponentially upward? This reflects the en9r- casting is the prediction of , and most of the mous increases in construction along the hurricane- forecast improvement resources have been devoted to vulnerable coastlines as Americans migrate to the sea- the problems of movement and landfall. shore. Over the same period the annual loss of life in Hurricane forecasting comprises three closely related hurricanes has steadily diminished. If this is a measure but (at present) independent prediction tasks, the failure of increasing effectiveness of the hurricane warning of anyone of which may vitiate the success of the service, it is also a frail statistic. There are at least three others. These tasks are: (1) the prediction of movement reasons: first is the increasing numbers of people direct- and landfall; (2) the simulation of the storm surge3 in- ly exposed to hurricanes, many of whom have never cluding inland and riverine flooding; and (3) the predic- experienced one (N. L. Frank, 1974); second, the near- tion of extreme winds and areal extent of damaging plateau reached some years ago in prediction skill winds. Of these three, the greatest progress has been (R. H. Simpson, 1973) which persists despite the prog- made in the simulation of profiles 0 eles- ress which continues to be made in understanding hur- nianski, 1968, 1972). The least progress has been made ricane structure and the energy transformations which in predicting development or change in circulation drive it (J. Malkus and H. Riehl, 1960; LaSeur and strength. In fact, the modeling of development has ~een Hawkins, 1963). Finally, the great killer hurricanes are so ponderous and the initial value problem so intract- rare and comprise not only a critical challenge to the able that nearly all prediction models designed for experience and wits of the forecaster (R. Simpson, operational use seek only to forecast movement. 1971), but also to the formulation of the dynamic In the sections which follow we shall trace the prediction models upon which he is ever more de- progress in developing prediction techniques primarily pendent each year; models which, because of a num- for movement and landfall. We will examine the reasons ber of limiting factors described in this paper, are better why forecast skills have plateaued and what roadblocks able to predict the run-of-the-mill hurricane than the must be removed before significant new improvements extreme event. can be expected. However, the related oceanographic The hurricane poses a more difficult problem of problems relating to the sea-air interface, and the hy- modeling and of warning than do storms of temperate drologic problems of flash and riverine flooding due to latitudes because most of the hurricane's destructive excessive rains are beyond the scope of this paper and forces are concentrated within 20-50 miles of its center, are treated only inferentially.

*See end of article for authors' affiliations and addresses. 3 An abnormal rise in sea level due to the influence of hurricane 1 , 1975: Hurricane preparednessbtief- pressuregradients and wind stresseson the sea. ing documents (slides). Similar terms which are common to the vQcabulariesof fluid 2Por a summar) of the 1975 hurricane seasonwith an illustra- dynamicists and are essential to the discussionin this text are tion of storm tracks see Mon. Wea. Rev., April 1976, Vol. 104 defined in "Glossary of Meteorology," 1959: Amer. Met. Soc., (Dollar amounts are adjusted to 1957-59 values). , Mass.

601 APPLIED MECHANICS REVIEWS

(/) z 2000 ~ 2- 0 <( (/) ..J II: ..J W 0 a- 0 u. u. 0 0 U) II: Z w 0 ~aJ ..J :: 1 ~ 1000 aJ

1910 1930 1950 1970 1910 1930 1950 1970 FIG.1 TRENDS IN HURRICANE RELATED DAMAGE AND DEATHS IN THE U.S. (5-YEAR AVERAGES)

The Conceptual Problem in Predicting Movement performance of the model with hurricanes which are Before the advent of dynamic prediction models, hur- rapidly intensifying as they approach the coast, as in ricane movement was regarded conceptually as a re- Celia (1970), Carmen (1974), Eloise (1975), and the sponse to a "steering current" in the environment, and hurricane of September, 1947. In such cases the development of prediction methods sought to iden- the influence of the developing vortex on its own move- tify and relate the properties of a steering level or layer ment may turn out to be significant. If so, another to the direction and speed of movement of the hurricane means must be found to deal with the initial value center. For example, Norton (1948) used the prevailing problem if such sophisticated primitive equation models wind direction and speed "at the top of the hurricane" are to cope with anomalous movement of the "bad as an index to movement of the vortex. Dynamically, actor," high-risk hurricanes more effectively than the however, the hurricane moves as a complex response simpler barotropic or statistically founded models which to the net forces imposed by environmental circulations can, at best, provide results of uncertain value in such interacting with the entire vortex (Beebe and Simpson, cases. 1976). An unresolved problem is the degree to which The earliest conceptual model to provide objective the vortex circulation may influence its own movement. predictions of hurricane movement was developed by The evidence suggests that when a hurricane circu- H. Riehl, et al. (1956). Riehl considered that the best lation approaches steady state, its movement is almost index to steering of the hurricane was the geostrophic wholly determined by the dynamics of environmental flow of the environment at the level of nondivergence. circulations.4 Hovermale (1975), in 'his development of Zonal and meridional components of geostrophic mo- a new hurricane prediction model for use at the National tion were calculated for the 500 mb surface (-5.5 km) Meteorological Center draws upon this evidence to solve using a large rectangular grid which enclosed the vortex. the very difficult problem of initializing his model. He This was used as input to a regression relation based fIrst removes the vortex and replaces it with one which upon historic data to obtain the westward and north- ward displacements of the vortex for the succeeding is artificially spun up. While further details of this procedure will be dis- 24-hour period. The method worked surprisingly well cussed in a later section, we remark here that the jus- in a research environment but, operationally, suffered tification of this procedure will be severelytested in the from the subjectivity of hurried hand analyses of the 500 mb geopotential fields. During the late 1950's and early 1960's the search "NHEML Field Program Plans-1975 4e.g., NOAA, 1975: for methods less sensitive to subjective circulation {Hurricane)," p. 50.

602

3000' APPLIED MECHANICS REVIEWS

analyses led to the use of statistical screening to iden- clons (Garstang and Betts, 1974; Garstang, 1975), which tify predictors from surface charts. Veigas, et al. (1959) imply that dynamic interactions between cumulus-scale and R. G. Miller (1958) used a large storm-centered circulations and those of much larger scale in the en- grid to screen for predictors of 24-hour displacements. vironment supply a brake to the growth of disturbances. This research produced an operational model known as The explosive development of disturbances, and the T-60 (Veigas, 1961, 1962) which, despite the fact that rapid growth of hurricanes into extreme events-present- it took no cognizance of upper-level circulations, dis- ly beyond the reach of operational models-comprise played good skill with westward-moving hurricanes, and serious problems in hurricane prediction and warning: blazed the trail for development of a heirarchy of the first, because the skills of most models are at lowest ebb more powerful models that followed. These included in cases where there are development extremes, and one by B. I. Miller and Paul Moore (1960); and the second, because significant changes in strength and size NHC-64 model by B. I. Miller and P. chase (1966). The of the hurricane strongly influence the distribution of latter attempted to incorporate the better features of storm surge and tidal flooding at landfall, and hence, the work of Riehl and of Veigas, and is the foundation the need for evacuating coastal residents. upon which the subsequent statistically founded meth- ods, described in the next section, have evolved. The ap- Progress with Statistically Founded Prediction Models plication of these models was primarily responsible for a significant increase in forecast skills at the National Statistically founded methods for predicting move- Hurricane Center in the early 1960's. (Dunn, et al., ment are of two types, one employing historical in- 1968). formation whose application depends upon current ob- The problem of predicting hurricane development, servations only as regards the location of storm center from to the extreme event with and of its instantaneous movement. The second uses winds up to 100 mps, remains one of the most difficult statistical analogs or screening techniques to obtain pre- and intractable problems in meteorology. As such, it is dictors related to circulation characteristics, usually usually treated operationally as a separate problem, over a scale much larger than the hurricane environment. presently handled only through diagnostic, subjective The multivariate results are then applied to current reasoning. This deserves at least brief attention here. analyses or to short-period circulation prognoses to de- Conceptually, organized tropical rain disturbances, termine hurricane displacements for successive12-hour releasing abundant supplies of latent heat, develop periods up to 72 hours. dangerous winds and become tropical storms only when It is interesting to note that, historically, such meth- the vertical circulation of mass succeedsin systematical- ods seem to begin with bold attempts to apply purely ly storing latent heat through a deep tropospheric kinematic or dynamic concepts to current data to ob- column. The most obvious inhibiting factor is a pro- tain a prediction, the operational weaknessesof which nounced vertical shear of the horizontal wind which dis- lead to modifications which incorporate statistical con- perses the latent heat laterally (W. Gray, 1967; R. and straints. Then, as more is learned of hurricane structure J. Simpson, 1976). and energetics, in the next generation of methods the While more than 100 tropical disturbances, some- researcher once more patronizes his urge to employ times called hurricane "seedlings," move westward purely dynamical procedures to current analyses, only across the tropical Atlantic each year, less than 10 per- to find once again a need to apply statistical constraints cent develop sustained winds of gale force and acquire or statistical processing of the dynamical data. It is in- names (Frank, 1973). The numerical simulation of this .teresting to contemplate whether, in connection with process encounters difficulty in parameterizing the ef- the development of the more sophisticated dynamical fect of cumulus convection, both in the disturbance models to be discussedin the section below, this cyclical and in the developed hurricane. This is largely due to process in the sequence of prediction methodologies the fact, demonstrated by Gray and Shea (1973), that may now have ended. the warm core, the heart of the hurricane "heat engine" The NHC-64 method, by far the most skillful and ob-jective is not generated by a simple redistribution of latent heat operational method used prior to 1957, was re- released by convection, but rather by a combination of vised by B. I. Miller, et al. (1968), and became known adiabatic heating from downward motions associated as NHC-67. This employs predictors from the 1000- , with the convection and the release of latent heat (Shea 700- , and SOO-mbsurfaces and produces center posi- and Gray, 1973). This combination is a much more tions for successive 12-hour intervals up to 72 hours. difficult process to parameterize. NHC-67 is still in use at the hurricane center in , A further complication in modeling the initial growth mainly because its predictions of northward displace- of disturbances is currently unfolding from the results of ment during recurvatures are more dependably skillful field experiments in the BOMEXs and GATE6 expedi- than from any other technique presently available. This method has been adapted for use in the Pacific by 5Barbados Oceanographic and Meteorological Experiment. both the Japanese and the People's Republic of China. 6Atlantic Tropical Experiment of the Global Atmospheric Re- In the late 1960's Renard, et al. (1968, 1973) de- searchProgram. veloped a statistically constrained dynamical method

603 APPLIED MECHANICS REVIEWS

FIG.2 REDUCTION IN VARIANCE,AFTER NEUMANN,1975

which returned to the concept of a steering level. This initial constraint, the model computes the most probable method uses digital computer procedures for the analysis track for a 72-hour movement using as analogs the of standard geopotential surfaces (850- , 700- , 500- , historic tracks of hurricanes which had passed near the 300-mbs) and for objectively filtering out perturba- current position with about the same movement vector tions with a scale size of 100s of km including the hur- and at about the same calender date. As an additional ricane vortex, which is reduced to a point entity. It output, it computes and constructs a family of ellipses then moves the point vortex geostrophically in the enclosing areas in which the storm center has a 50 per- large scale flow for a 72-96 hour period. The observed cent probability of residing after 12, 24, 36, 48, and vector error in position after 12 hours of such move- 72 hours. ment is subtracted from the computed position at sub- The remarkable skill of this purely statistical model, sequent 12-hour intervals to obtain a track up to 80 despite the fact it ignores the current and predicted hours in advance. circulations in the path of the hurricane as well as its This method, which of course assumes persistence size and strength, has encouraged its adoption as an of large scale circulations, tends to work well where per- objective tool for identifying coastal sectors which sistence is a good predictor, and when the correct steer- require hurricane watches. The "watch" sector is the ing level can be selected. However, because the method coastal segment located between the two tangents con- predicts a hierarchy of tracks-one for each standard necting the 50 percent probability ellipses for 24 and geopotential surface-and leaves the choice to the 48 hours, respectively, as the latter ellipse passesin- judgment of the forecaster, and because the more dif- land. Similar analog methods have been developed by ficult predictions occur when persistence is not a good Jarrill and Wagoner (1973) for use in the Pacific and predictor, the method has not gained wide operational Indian Oceans. use although it is still used experimentally or as fore- The principal shortcoming of HURRAN and other caster guidance in some areas. analog methods is the limited usefulness in cases of Until 1967, nearly all objective prediction models highly anomalous movements. To alleviate this con- provided outputs which were essentially deterministic straint, Neumann (1972) developed an auxilIary method and offered no means for the user to evaluate the un- known as CLIPER which drew its predictors solely from certainties of predicted positions. In response to a re- CLImatology, and PERsistence (of past motion). The quirement of NASA for probabilistic information on output similar to HURRAN, is a most probable track hurricane tracks, Hope and Neumann (1970) developed for the following 72 hours accompanied by a family of an analog model known as HURRAN. The only current probability ellipses. In operational use it soon became information used by this model is the direction and clear that the combined use of HURRAN and CLIPER speed of movement the preceding 12 hours. With this provided more reliable predictions of zonal movement

604 APPLIED MECHANICS REVIEWS than did any of the alternate prediction methods, in the equations which represent the influence of the while NHC-67 provided more reliable predictions of subgrid scale on the resolvable scale. In order to close meridional movement. the system of equations it is necessaryto parameterize Logically, the next step in procedure development these terms, which is generally done by assuming the was to forge a marriage of the three methods. Neumann, subgrid scale contributions are functions of the resolv- et al. (1972) accomplished this task, which culminated able variables. in the astonishing result illustrated in Fig. 2 (after Current computer storage and speed restrict the mini- Neumann, 1975a). This shows the reduction in variance mum mesh size for a particular problem. In the caseof a by the predictors from persistence (P), from climatology hurricane, the domain of the model must be several (C), and from circulation dynamics (8). Predictors from thousand kilometers on a lateral side and extend ver- persistence both for zon~ and meridional movement ac- tically at least to the tropopause in order to include count for larger reductions of variance th~ from either sufficient coverage of the hurricane and its environment. climatology or circulation dynamics, but the three to- To eliminate the need for averaging the equations one gether account for almost an 80 percent reduction for would need to describe the field of motion with a zonal movement and 70 percent for meridional move- resolution of about one centimeter! This need grows ment for a 24-hour forecast. (The curious increase in from the reality that the atmosphere in motion cannot variance reduction with time in curve (8) is due to sev- be described dynamically in terms of a single scale of eral problems of initialization, including the exact loca- motion. It comprises a hierarchy of motion scales rang- tion of the hurricane center). ing from the small v.iscousto that of the large planetary The most recent improvement in statistical dynamical waves. Of course a resolution of one centimeter is un- models has been the incorporation of predictors by achievable. It would require approximately 1.4 X 1023 Neumann and Lawrence (1975) (and subsequently by data points for a minimal domain of 3000 X 3000 X 15 Neumann and Randrianarison (1976) for the Indian km and a computer capability that is inconceivable Ocean) from prognostic charts of 500 mb circulation within current technology, not to mention the problems for 24, 36, and 48 hours in advance of forecast time. of initializing such a model. Even with resolutions of This procedure was attempted by Veigas (1966) with- 10 km (horizontal) and 1 km (vertical), a hurricane out success due to the poorer quality of machine prog- model would need approximately 1.35 X 106 grid nostic charts during the early 1960's. points to resolve the entire domain uniformly, again With the skills presently achievable with statistically well beyond present computer capabilities.S founded models, especially for hurricanes with regular Because of this limitation, hurricane simulation has tracks, and with results presented in probabilistic for- taken one of the three following approaches: (1) resolve mat, the principal challenge for the more sophisticated the hurricane in detail in an idealized larger scale en- purely dynamical models is to predict dependably the vironment, (2) resolve the dynamics of the environ- more anomalous movements and explosive develop- mental flow and treat the hurricane as an idealized ments, and the heavy precipitation after a hurricane vortex, or (3) a combination of 1 and 2, where the passes inland which frequently generates riverine and spatial and temporal asymmetrics of the large scale flash flooding. flow are treated, with hurricane dynamics expressed rather crudely. Progress with Dynamically Founded Numerical In the fIrst category, two forms of models have been Prediction Models utilized-asymmetric and axisymmetric representations. In the axisymmetric model, variations in the azimuthal As opposed to the statistical prediction models, the direction are neglected, permitting much more eco- dynamic models of hurricane movement are developed nomical calculations as opposed to the more complete directly from basic physical principles. These include three-dimensional asymmetric simulations. As shown Newton's second law of motion for a rotating earth, the by Anthes, et al. (1971) and Kurihara (1975), axisym- first law of thermodynamics, and the ideal gas law, as metric versions are valid tools to investigate many as- well as conservation relations for mass and for watec pects of mature hurricanes for a uniform large scale substance in its three phases. Unfortunately, since these environment. For instance, Rosenthal's (1970) axisym- differential relationships are valid only on a scale in the metric model demonstrated that the use of a 10 km atmosphere of a few centimeters at most; and because horizontal grid provides a significantly better simula- they are a set of nonlinear partial differential equations tion of hurricane dynamics than a 20 km grid. Anthes which cannot be solved by standard analytic techniques, (1974a) has used an axisymmetric model to demon- they must be averaged over a volume corresponding to strate the advantages of dynamic initialization and to the space-time grid mesh in a numerical model. Aver- aging of nonlinear equations, however, introduces terms 8Up to eight variables are needed for at least two time levels at each grid point in the numerical solution of the time de- - pendent equations which corresponds to 2.16 X 107 com- 7 A scale much larger than the molecular scale but small enough puter storage locations. The time levels are determined by the that higher order Taylor series terms in the differential rela- incremental time steps used in the marching solution of the tions are insignificant. prognostic equation.

605 APPLIED MECHANICS REVIEWS

show that, for the idealized storm without azimuthal maximum achievable accuracy in storm position fore- inhomogeneities, observations of winds and tempera- casts of 125 km at 24h and 500 krn at 72h. ture near the center of the storm at low levels provide As contrasted with the first category, these models the most valuable initial data for hurricane models. have been developed for operational use in predicting On the other hand, the asymmetric version allows storm track alone. Without incorporating synoptic scale the development of azimuthal variations in the hur- baroclinic effects and, more importantly, an effective ricane flow fields. As found by Anthes (1972), features resolution of the hurricane vortex, the crucial de- apparently related to the spiral in actual termination of explosive intensification and of radial hurricanes develop due to dynamic instability in the alterations in storm tracks is not possible. layer, and rotate cyclonically as they propa- The third category represents the initial attempts gate outward from the center. Kurihara and Tuleya to adequately resolve hurricane dynamics, yet retain (1974) found a similar feature in their asymmetric a dynamic asymmetrical large scale flow field. The model which developed near the center of the storm model of B. I. Miller, et al. (1972) used horizontal and propagated outward with diminishing amplitude, resolutions as small as 75 hm to predict the move- which they attribute to the movement of internal ment and strengthening of in 1970 and gravity waves. Anthes, et al. (1971) found that the Hurricane Alma in 1962, as well as a nondeveloping development of asymmetries in the hurricane out- tropical system. Miller found that the model was able flow is correlated with hurricane intensification. to predict deepending (as in Alma), but not the ex- In all of these models, the influences of subgrid- plosive intensification observed in Celia. He attributed scale motions due to deep cumulus activity was found the error to lack of adequate resolution. Both track to be essential for the realistic development and suste- and intensity of Alma were well predicted. Mathur nance of hurricanes. Anthes (1974b) presents an ex- (1974, 1975) incorporated a fine mesh grid (hori- cellent summary of this topic as well as other aspects zontal resolution of 37 km) inside a coarser mesh of the dynamics and energetics of hurricanes in idealized (horizontal resolution. 74 km) in order to simulate environments. Hurricane models in this format have the development of Hurricane Isbell in 1964. The fille been used as research tools to improve the physical mesh was centered over the storm and its vicinity, understanding of hurricanes and to investigate means while the coarser mesh was used to represent the to mitigate their intensity (Rosenthal, 1974). larger scale environment. The predicted movement Kasahara (1959) and Birchfield (1960), developed and rate of intensification of the initial disturbance the fIrst models under the second category listed above. agreed favorably with the observations. Kasahara's model assumed barotropic nondivergent Krishnamurti and Kanamitsu (1973) have used motion where the hurricane vortex was subtracted from the Florida State University's tropical prediction his analyzed fields, and the dynamic equations inte- model (Krishnamurti, et al., 1973) to simulate the grated forward in time. After the evolution of the steer- movement and intensity of a nondeveloping easterly ing flow, the tropical system was advected as a point wave with a horizontal resolution of 2 X 2 degrees of trajectory. Forecasts from his model tended to deflect latitude. The solution agreed favorably with observa- storms to the right of their actual paths and to slow tions up to periods of 72 hours. Ceselski (1974) ap- them excessively, particularly after recurvature. Hubert plied this model to the development of Hurricane (1959) attributed this error to the unrealistic flat grad- Alma (1962) and, like Miller, et al. (1972), obtained ients which remained after subtracting the vortex, par- excellent agreement with the observed movement and ticularly in cases where the vortex was in an area of intensity. Ceselski emphasized the importance of the dilatory flow. Birchfield developed a similar barotropic upper-level outflow in intensifying the system. model, but employed a fme grid over the hurricane cir- Hovermale (1975) is developing a model at the culation in order to resolve some of the vortex-environ- National Meteorological Center for operational use, ment interaction. He found that truncation errors con- which predicts dynamic changes in the synoptic en- tribute significantly to the errors of predicted move- vironment and allows intensification of an arbitrarily ment of the hurricane. specified vortex. The model domain moves relative to More recently, Sanders and Burpee (1968), and the earth's surface and has a horizontal grid resolu- Sanders, et al. (1975) have developed a barotropic pre- tion of 60 krn. In the first season of testing (1975), diction model for operational application at the National the model predicted storm path more accurately than Hurricane Center (NHC). The procedure begins by com- speed. The model appears to have a distinct advan- puting pressure weighted mean winds for the layer tage over the statistical models because of its filler 1,000-100 mb and analyzes stream functions over a large resolution, which enablesit to predict much of the observ- fIXed domain as input to the prediction model. The ed mesoscale variations when the calculations are per- initial wind field in the vicinity of the hurricane is de- formed over land in a region of denser data coverage. termined as the sum of the steering flow, derived from Jones (1976), as reported by Rosenthal,9 is testing the best estimate of storm motion, and winds due to an a meshed hurricane model with two inner grids having idealized vortex. A horizontal grid resolution of 165 krn is used. Sanders, et al., felt that this approach has a 9perso nal com munica tio n.

606

~ APPLIED MECHANICS REVIEWS resolutions of 10 km and 30 kIn, respectively, and 4. The influeilce of radiational flux divergence on moving with the hurricane center, together with an the dynamics and thermodynamics of the hur- outer grid of 90 km resolution which moves at a uni- ricane must be considered. Recent day and night form speed relative to the earth. The nested grids are infrared satellite imagery from th.e Synchronous fully interactive and permit high resolution near the Meteorological Satellite (SMS-l), for example, storm core, where previous work by Rosenthal (1970) indicates a diurnal variation of cirrus cloud cover demonstrated it is most needed, but retain a large in a hurricane.l0 domain by use of the coarser grid beyond the storm. The successful incorporation of the above physical The model has not been applied to actual situations; processesinto a hurricane track and development model however, results with ideal initial conditions have been is a many-year task, and will require contributions from the entire spectrum of the meteorological community very encouraging. as well as collaboration with oceanographers. Nonethe- Assessment of the Modeling Problems less, the pay-off in improved forecasts of occurrence, and of landfall alone for the extreme event, will make The models in the third category represent attempts the task worth pursuing. In the near future, however, to synthesize advancements in the fIrst two. It is in this the principal use of dynamic models will be to forecast category that improved forecasts of the anomalous hur- track (particularly recurvature) and the flood-producing ricane and the extreme event are possible. But, as evi- rains which occur after landfall, where the results will dent from the above work, both the details of the hur- be most accurate-north of about the 20th parallel in ricane dynamics and of the larger scale flow are essen- regions of denser observational data. tial for accurate predictions. Successful accomplishment of this goal will necessitate the following improvements Summary and Outlook to the models: 1. Observational data are required with improved The ability to achieve greater skill from statistically spatial resolution over the oceans in the vicinity founded prediction models appears to hinge large upon of the tropical system, and at low levels near the improvements in the initial center location data. Neu- center of storm. For the significantly asymmetric mann (197 5a,b), in a study of errors in the probabilistic tropical system and for the developing distrubance, prediction methods, identified as the most important representative measurements at all regions in the source of error the mislocation of the initial position disturbed environment may be necessary. Hori- of the hurricane (average error 38 km). This problem zontal winds and temperatures, based on Anthes' can apparently be overcome only by using reconnais- (1974) results, appear to be of vital importance. sance aircraft with more sophisticated equipment and Sea surface-temperature distributions must also be flight procedures than are presently available. The available. It is the concensus of hurricane modelers benefits, however, are large and he makes a convincing that the acquisition of these data to initialize the case for an annual potential savings of at least $5.5 models is a necessary ingredient to improve-d hur- million in preparednesscosts alone! ricane predictions. Further reductions in variance for the present meth- 2. A more realistic means must be found to represent ods will depend upon enlarging the existing body of de- cumulus activity in the model-simulated hurricane pendent data, or upon the acquisition of predictors and its environment. This parameterization must which relate more explicitly to the interaction between include dynamic as well as thermodynamic inter- the vortex and its environment. The latter may become actions if the caseof explosive intensification is to possible as better means are found to apply information be properly handled in a synoptic baroclinic at- from satellites to this problem. The satellite is one of mosphere. Horizontal fluxes of heat, moisture, the few tools by which changes in hurricane strength can and momentum, not only associated with cumuli be frequently and effectively monitored qualitatively. but also in the clear air, must be represented realis- However, it provides, at present, little information of tically in the -wall area. prognostic worth for input to numerical prediction 3. The entire planetary boundary layer must be models, either statistically or dynamically founded. parameterized accurately for horizontal non- The most important problems which must be faced homogeneous nonsteady conditions and must be in the further development of dynamical prediction coupled with the ocean.The influence of seaspray, models are, in our opinion: (1) the initial value prob- in the region of strong winds, for instance, must lem, and (2) more accurate physical representations be included in the boundary-layer formulations of the planetary boundary layer, including sea-air in- of moisture flux. Realistic topography and land- teraction, and of cumulus-cloud interactions with the air interactions and their influence on the bound- larger-scale environment. The replacement of the real ary layer must be included in order to simulate vortex with a spun-up artifice may produce realistic extreme events such as flooding and severe thun- derstorms, which may occur after landfall (as in lOpersonal communication from W. Woodley. Publication in Camille (1969), Beulah (1967), and Agnes (1971). press.

607 APPLIED MECHANICS REVIEWS track prediction under conditions of near steady state, Dunn, G. E., Cecil Gentry, and Billy Lewis, 1968: "An eight- but is unlikely to do so under conditions of anomalous year experiment in improving forecasts of hurricane mo- movement or explosive development, the two condi- tion." Mon. Wea. Rev., 96: 708-713. Frank, Neil L., 1973: "Atlantic tropical systems of 1972." tions which most need to be handled skillfully by the Mon. Wea. Rev., 100: 334-338. more sophisticated physical models. These conditions Frank, Neil L., 1974: "The hard facts about hurricanes." NOAA are associated with the most dangerous warning cases Magazine,4: 4-9. and are unlikely to be handled with dependable skill, Garstang, M., 1975: "Final report to Office of Climate Dy- even by later generations of statistically founded namics (GARP) National ScienceFoundation." Garstang, M., and Alan Betts, 1974: "A review of the tropical models. boundary layer and cumulus convection: structure, param- On the brighter side, dynamical models, which may eterization, and modelling." Bul/. of Amer. Meteor. Soc., in the future use a system of nested grids moving with 55: 1195-1205. the hurricane, may possibly provide sufficient resolu- Gray, Wm., 1967: "The mutual variation of wind shear and baroclinity in the cumulus atmosphere of the hurricane." tion to represent realistically the hurricane and its en- Mon. Wea. Rev., 95: 55-73. vironment. If so, they could show significant skill in Gray, Wm., and D. J. Shea, 1973: "The hurricane's inner core predicting well in advance the excessive hurricane rains region, II thermal stability and dynamic characteristics." which occur after landfall, rains which depend mainly Journ. of Atmos. Sci., 30: 1544-1564; AMR 27 (1974), upon orographic and baroclinic processes and some- Rev. 8015 Hope, J. R., and C. J. Neumann, 1970: "An oper~tional tech- times lead to heavy lossesof life and property from such nique for relating the movement of existing tropical cy- floods as occurred in hurricanes Diane (1955), Agnes clones to past tracks," Mon. Wea. Rev., 93: 925-933. (1972), and Camille (1969). Within reach ultimately, Hovermale, J. B., 1975: "First season storm movement char- if 'appropriate means can be found to initialize the acteristics of the NMC objective hurricane forecast model." model, should be the prediction of such dangerous ex- Paper presented at Twelfth Annual NOAA (NWS Hurricane Warning Service Evaluation Conference, December, 1975, plosive intensifications as were observed in Camille Coral Gables,Florida. (1969), Celia (1970), and Eloise (1975). Hubert, L., 1959: "An operational test of a numerical predic- tion model for hurricanes." Mon. Wea. Rev., 87: 222-228. Acknowledgments Jarrell, J. D. and R. A. Wagoner, 1973: "The 1972 Typhoon Analog Program," ENVPREDRSCHFAC Technical Paper No. 1-73, Naval Postgraduate School, Monterey, California, Some of the information about individual prediction 38 pp. models and their performance was supplied by our col- Jelesnianski, C. P., 1968: "Numerical computations of storm leagues Rick Anthes, Neil Frank, John Hovermale, surges with bottom stress." Mon. Wea. ~ev., 94: 740-756. Robert Jones, Yoshio Kurihara, Charles Neumann, Jelesnianski, C. P., 1972: "SPLASH (Special Program to List Stanley Rosenthal, and Fred Sanders. The authors are Amplitudes of Surges from Hurricanes); Part I-Landfall grateful for this and for the advice and opinions sup- Storms." NOAA Tech. Memo., NWS 1DL-46. Jones, R. W., 1976: "A nested grid for a three-dimensional plied during our discussions with each. The opinions model of a ." Draft manuscript, NHEML, expressed herein, however, are those of the authors and NOAA, Coral Gables,Florida. do not necessarily represent a consensus. Kasahara, Y., 1959: "A comparison between geostrophic and nongeostrophic numerical forecasts of hurricane movement with the barotropic steering model." Jour. of Meteor., 16: 371-384. Bibliography Krishnamurti, T. N., and M. 'Kanamitsu, 1973: "A study of a Anthes, R. A., 1972: "The development of asymmetries in a coasting easterly wave." Tel/us, 25: 568-585. three-dimensional numerical model of the tropical cyclone." Krishnamurti, T. N., M. Kanamitsu, B. Ceselski, and M. Mathur, Mon. Wea. Revs., 100: 461-476. 1973: "Florida State University's tropical prediction model," Anthes, R. A., 1974a: "Data assimilation and initialization of Tel/us, 25: 523-535. hurricane prediction models." journ. of Atmos. Sci., 31: Kurihara, Y., 1975: "Budget analysis of a tropical cyclone 702-719. simulated in an axisymmetric numerical model." Jour. of Anthes, R. A., 1974b: "The dynamics and energetics of mature Atmos. Sci., 32: 25-59. tropical cyclones." Rev. of Geophysics and Space Physics, Kurihara, Y., and R. E. Tuleya, 1974: "Structure of a tropical 12: 495-522. cyclone developed in a three-dimensional numerical simula- Anthes, R. A., J. W. Trout and S. L. Rosenthal, 1971: "Com- tion model." Jour. of Atmos. Sci., 31: 893-919. parisons of tropical cyclone simulations with and without LaSeur, N. E., and H. F. Hawkins, 1963: "An analysis of hur- the assumption of circular symmetry." Mon. Wea. Rev., ricane Cleo (1958) based data from research reconnaissance 99: 759-766. aircraft." Mon. Wea.Rev., 91: 694-709. Beebe, R., and R. H. Simpson, 1976: "Hydro meteorological Mathur, M. B., 1974: "A multiple grid primitive equation model aspects of stalling and meandering hurricanes," Proceedings to simulate the development of an asymmetric hurricane AMS Conf. on Hydrology, Ft. Worth, Apri11976. (Isbell 1964)." Jour. of Atmos. Sci., 31: 371-393. Birchfield, G. E., 1960: "Numerical prediction of hurricane Mathur, M. B., 1975: "Development of banded structure in a movement with the use of a fine grid." joum. of Meteor., numerically simulated hurricane." Jour. of Atmos. Sci., 32: 17: 405-414. 512-522. Brand, Samson and J. W. Blelloch, 1975: "Cost effectivenessof Malkus, J., and H. Riehl, 1960: "On the dynamics and energy Typhoon Forecast Improvements." Bull. Amer. Meteor. Soc. transformations in steady-statehurricanes." Tel/us, 12: 1-20; 56: 352-361. AMR 13 (1960), Rev. 6724. Ceselski, B. F., 1974: "Cumulus convection in weak and strong Miller, B~ I., and Paul Moore, 1960: "A comparison of hurricane tropical disturbance." joum. of Atmos. Sci., 31: 1241-1255. steeringlevels." Bull. of A~er. Meteor. Soc., 41: 59-63.

608 APPLIED MECHANICS REVIEWS

Miller, B. I., and P. P. Chase, 1966: "Prediction of hurricane "Forecasting the motion of North Atlantic tropical cy- motion by statistical methods." Mon. Wea. Rev., 94: 399- clones by the objective MOHATr scheme." Mon. Wea. Rev. 405. 100: 206-214. Miller, B. I., E. C. Hill and P. P. Chase,1968: "A revised tech- Riehl, H., W. H. Haggard, and R. W. Sanborn, 1956: "On the nique for forecasting hurricane motion by statistical meth- prediction of 24-hour hurricane motion." Jour. of Meteor., ods." Mon. Wea. Rev., 96: 504-548. 13: 415-420. Miller, B. I., P. P. Chase and B. R. Jarvinan, 1972: "Numerical Riehl, H., 1974: "Computer simulation of hurricane develop- prediction of tropical weather systems." Mon. Wea. Rev., ment and structure." Chapter 15, Weather and Climate 100: 825-835. Modification, John Wiley and Sons, New York, 841 pp. Miller, R. G., 1953: "The screening procedure." Travellers Sanders, F., and R. W., Burpee, 1968: "Expetiments in baro- Weather Research Center, Final Report, contract no. AF19 tropic hurricane track forecasting." Jour. of Applied Meteor., (GO4)-1590: 89-96. 7: 313-323. Neumann, C. J., 1972: "An alternate to the HUR,RAN tropical Sanders, F., A. C. Pike and J. P. Gaertner, 1975: "A barotropic cyclone forecast system," NOAA Tech. Memo. NWS SR-62: model for operational prediction of tracks of tropical 24 pp. storms." Jour. ofApplied Meteor., 14: 265-280. Neumann, C. J., 1975a: "The effect of initial data uncertainties Simpson, R. H., 1973a: "Hurricane prediction: progress and on the performance of statistical tropical cyclone prediction problem areas." Science, 181: 899-907. models." NOAA Tech. Memo. NWS SR-81. Simpson, R. H., 1973b: "The decision processin hurricane fore- Neumann, C. J., 1975b: "A statistical study of tropical cyclone casting." NOAA Tech. Memo. NWS-TM-SR53. - positioning errors with economic applications." NOAA Tech. Simpson, R. H., and J. Simpson, 1976: "Hurricane development Memo. NWS SR-81. and movement." McGraw-Hill Encyclopedia of Science, 4th Neumann, C. J., J. R. Hope and B. I. Miller, 1972: "A statistical Edition (In Press). method for combining synoptic and empirical cyclone pre- Veigas, K. W., 1961: "Prediction of 12- , 24- , and 36-hour dis- diction systems." NOAA Tech. Memo. NWS SR.63, 32 pp. placement of hurricanes by statistical methods." Travellers Neumann, C. J., and M. Lawrence, 1975: "An experiment in the Weather Research Center, Final Report. Contract No. Gwb statistical-dynamical prediction of tropical cyclone motion." 9807. 36 pp. Mon. Wea.Rev., 103: 665-673. Veigas, K. W., 1962: "Development of prediction equations for Neumann, C. J., and E. A. Randrianarison, 1976: "Statistical hurricane movement." Travellers Weather Research Center, prediction of tropical cyclone motion over the southwest Final Report on contract No. Cwb 10170. 59 pp. Indian Ocean." Mon. Wea. Rev., 104: (Jan.). Veigas, K. W., 1966: "The development of a statistical-physical Norton, Grady, 1949: "A soliloqy on hurricane forecasting." hurricane prediction model." Travellers Weather Research National Hurricane Center, Unpublished Manuscript. Center. Final Report, Contract No. Cwb-10966. Renard, R., 1968: "Forecasting the motion of tropical cyclones Veigas, K. W., R. G. Miller and G. M. Howe, 1959: "Probabilistic using a numerically derived steering current and its-biases." prediction of hurricane movements by synoptic climatology." Mon. Wea. Rev., 96: 453-469. Travellers Weather Research Center, Occasional Papers in Renard, R., S. G. Colgan, M. J. Daley, and S. K. Rinard, 1973: Meteorology, No.2, 54 pp.

Prof. R. H. Simpson Department of Environmental Sciences University of P. O. Box 5508 Charlottesville, V A 22903 Prof. Roger A. Pielke Department of Environmental Sciences Center for Advanced Studies University of Virginia Charlottesville, V A 22903

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