Russell L. Elsberry Applications oi Department of Meteorology Naval Postgraduate School Tropical Cyclone Models Monterey, Calif. 93940
Abstract and Eastern Pacific hurricanes (Sanders et al., 1977). A The extensive research in tropical cyclone modeling during the balanced barotropic model for typhoon movement pre- 1960s and 1970s has resulted in a number of applications for diction has been run by the Japan Meteorological real-time track prediction. A review of the characteristics of Agency. Similar barotropic models are also being de- these 3-dimensional dynamical models is given, including a veloped in India (Singh and Saha, 1976), Taiwan discussion of procedures for initializing and tracking the (Tsay, 1977), and the Phillipines. In some cases the model storm. Some limited verifications of track forecasts are described. An outlook for the future is presented; both in initial fields are based on hand analyses. Until objective terms of numerical model improvements, and for large-scale analysis schemes arc developed and tested with the and inner-scale data required to implement the improved models on an operational basis, it is unlikely that these models. models will have a practical application.
1. Introduction 2. General description of models At the Sixth Technical Exchange Conference in 1970, S. Rosenthal of the National Hurricane Research Laboratory reported results from the first 3-dimensional A few of the physical characteristics of some selected numerical model with the physical processes and hori- baroclinic models are shown in Table 1. The National zontal resolution necessary to resolve tropical cyclones. Meteorological Center (NMC) Moveable Fine Mesh Since that time a number of 3-dimensional models have (MFM) has been used on an operational basis for several been developed—both for research purposes and for years (Hovermale and Livezey, 1977). A Tropical operational prediction of tropical cyclone tracks. The Cyclone Model (TCM) has been operationally tested characteristics of these operational models, and those for Pacific Ocean storms at the Fleet Numerical being tested with operational data, will be reviewed. Weather Center (FNWC), as described by Hinsman Some of this material must be considered as interim (1977) and Mihok and Hinsman (1977). The model since several of the models to be described are in various (Madala and Hodur, 1977) being developed jointly by stages of development and testing. After describing the Naval Research Laboratory (NRL) and the Naval generally the characteristics of the models, I shall Environmental Prediction Research Facility (NEPRF) discuss the initial fields that are required and the is intended to replace the FNWC-TCM after further methods of tracking the model tropical cyclone. An testing with operational data. Following this, a nested evaluation of the track forecasts will then be presented. grid version is to be developed and tested by NRL and Some of the results or conclusions based on rather NEPRF. Some limited testing of the Pennsylvania limited sample sizes may have to be reexamined in the State University (PSU) mesoscale model for several light of additional cases. The last section of this paper western Pacific typhoon cases is being done at the Naval will be concerned with the outlook for the future and Post-graduate School (NPS). The primary purpose of will focus on some of the data problems that are being these tests (Hacunda, 1978) is to compare the predic- encountered in the operational use of fine-scale tropical tions with the FNWC-TCM and NRL/NEPRF models cyclone models. using the same input data. Anthes (1978) has shown that the PSU mesoscale model (with 60 km resolution) This survey is limited to 3-dimensional models, and improved the forecasts in 32 cases over Europe and the thus excludes a number of barotropic models that have United States. These further tests over data-sparse proved very useful for tropical cyclone motion fore- oceans, together with the different physics represented casts. Experience with these models has helped antici- by typhoon circulations, will provide additional in- pate the types of problems that will occur during opera- formation regarding the applicability of these fine mesh tional implementation of the more complex baroclinic models. The last model listed in Table 1 is the Japanese models. The best known of the barotropic models is Meteorological Agency (J MA) movable multiply- the SANBAR model, which was developed by Sanders nested grid (MNG) developed by Ookochi (1978). and Burpee (1968) and subsequently modified by Pike This model has been tested on a few typhoons approach- (1972) and by Sanders et al. (1975). Various versions of ing Japan. this model have been extensively tested with Atlantic The entries in Table 1 suggest wide variances in model characteristics, and consequently it is not possible 0003-0007/79/070750-13$07.25 to evaluate directly the differences in the model pre- © 1979 American Meteorological Society dictions. The FNWC and JMA models have minimal
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TABLE 1. Characteristics of several baroclinic models being applied for prediction of tropical cyclone motion based on operational data (see text for explanation).
Lateral Vertical Number Grid size Number Relocatable boundary Agency-Model coordinate of layers (km) of points grid conditions*
NMC-MFM * OW—One-way interaction; TW—Two-way interaction. vertical resolution with only three layers, which are Each of these models must be provided time-de- able to represent the inflow, outflow, and an inter- pendent values along the outer boundaries from some mediate layer of the mature typhoon circulation. Al- other prediction model. The interface boundary condi- though the NRL/NEPRF and PSU/NPS models have tion is of the one-way (OW) type (Phillips and Shukla, improved resolution with five layers, only the NMC- 1973), in that no feedback of information is provided MFM has adequate vertical resolution. However, it from the tropical cyclone model to the hemispheric should be noted that the tendency for tropical observa- model. An early version (Hinsman, 1977) of the FNWC- tions to be distributed in two layers—near the surface TCM model was in a channel, and thus required no and at predominately jet aircraft levels—makes initiali- information from the larger scale model after the initial zation of a 10-layer model rather difficult. time. Hodur and Burk (1977) have demonstrated that It has been known for some time that finer spatial one-way boundary conditions improve the TCM fore- grids are required to predict tropical circulations than casts during recurvature situations. The JMA nested are commonly used for mid-latitude prediction models. grid model has two-way interaction conditions for the Except for the FNWC-TCM model, each of the models inner grids. This requires a simultaneous integration on in Table 1 attempts to resolve the inner structure of the all grids rather than a sequential integration as in one- tropical cyclone circulation. It is generally assumed way integration. Various interface boundary conditions that the primary interaction between the vortex and have been employed to permit mass, momentum and the steering current can be resolved on the 60 km grid energy to flow between the grids (Elsberry, 1978). Al- used by the NMC and NRL/NEPRF models. How- though these conditions can never be perfect because ever, to attempt intensity forecasts one must resolve of the differences in resolvable waves with different the inner region of the typhoon (Elsberry, 1975 ; Jones, grid lengths, it appears that acceptable numerical solu- 1977a). This will require a nested grid arrangement be- tions have been obtained (see e.g., Anthes, 1976; Jones, cause the entire domain cannot be covered with the 1977a,b; Sobel, 1976). approximately 10 km resolution that will be necessary Note that the requirement in every case for lateral for the innermost grid. The second characteristic that boundary conditions from a hemispheric model places will be required for intensity forecasts will be an ability an important operational constraint on these tropical to move the inner grids with the storm. The JMA model cyclone forecast models. The normal procedure would possesses both of these characteristics, although the be to await the completion of the hemispheric forecast inner grid presently has only 36 km resolution. The model run. Allowing for the collection and analysis of other models in Table 1 have a uniform grid lattice the initial data, this means that the tropical model will that generally covers at least a 3000 km square. Even not be initiated until 6 h or more after map time (/0). this may be inadequate for 72 h forecasts of fast-moving Consequently the model guidance may not actually be storms. All of the models can be positioned at the initial used by the forecaster until to + 12 h. For example, time to minimize the chance that the expected storm Jarvinen (1977) points out that the SANBAR forecast motion will bring the storm center near the boundaries. is not available to the National Hurricane Center until Only the NMC model has the capability of being re- to + 4 h, and the 48 h NMC-MFM forecast appears at located during the forecast. This relocatability feature to + 8 h. Likewise, Mihok and Hinsman (1977) have allows one to keep the storm near the center of the attempted to reduce the greater than to + 9 h lag time domain, away from adverse boundary effects, and con- for the FNWC-TCM. They used a channel version of sequently permits a smaller domain size. As the grid is the TCM (note that this requires lateral boundary relocated, some fine-mesh values along the leading edge conditions only at the initial time) at to + 4 h with must be interpolated from the coarse-mesh hemispheric initial data primarily based on a 12 h forecast. The forecast values. This introduces some additional noise overall average difference in forecast error between the in the region of the boundary. earlier run and a later run with more complete data was Unauthenticated | Downloaded 10/11/21 01:38 AM UTC 752 Vol. 60, No. 7, July 1979 TABLE 2. Provision of initial fields for several baroclinic tropical inability to track cumulus cloud elements within the cyclone models (see Table 1 and text for explanation). general region of the cirrus canopy. Better spatial resolu- tion and a large increase in the number of clouds that Agency- may be tracked has been achieved by reducing the model Initialization method Storm-scale data area that the satellite views. The images may then be NMC-MFM Reverse balance (V —> <£) 2-d spin-up received every three minutes rather than each 30 FNWC-TCM Reverse balance Tangential minutes and smaller cloud elements can be followed for wind bogus 15 minutes to estimate the velocities. Rodgers et al. NRL/NEPRF Reverse balance Tangential (1978) were able to track about 6-10 times the usual wind bogus PSU/NPS Reverse balance Tangential number of clouds in this way, including some low-level wind bogus cumulus between breaks in the cirrus overcast. This JMA/MNG Balance ( Unauthenticated | Downloaded 10/11/21 01:38 AM UTC Bulletin American Meteorological Society 753 FIG. 2. Comparison of track errors between the official JTWC and the Tropical Cyclone Model (TCM) forecasts FIG. 1. Tangential wind speed versus radius from Kurihara during 1977. Positive values indicate TCM errors are smaller and Tuleya (1974) model (solid line), the NMC spun-up (see text and 1977 Annual Typhoon Report for explanation vortex during 1975 (dash-dot line) and modified distribution of data base versus warning time comparisons). used at NMC in 1976 (dashed line) from Hovermale et al. (1977). not well represented by the existing observations. This field is diagnosed from the thicknesses between the is frequently revealed by a systematic bias in the pre- geopotentials at the various levels. With the inclusion dicted speed and direction. Pike (1972) has previously of only the tangential wind components, and assuming treated this problem for the SANBAR model by simply no frictional terms, the initial wind fields will be non- replacing the initial wind field within 555 km of the divergent. Consequently some time will elapse before center by the observed storm motion. The difference be- a realistic vertical motion, and latent heat release, field tween the actual and the TCM-predicted storm motion will develop in the model. The JMA-MNG contains an after 6 h was used by Shewchuk and Elsberry (1978) initial symmetrical surface pressure and temperature to adjust the initial wind fields near the center. A trial bogus to represent the storm circulation on the inner and error procedure was necessary to determine the grids. After deriving geostrophic wind fields (reduced relative magnitudes of the zonal and meridional com- by a factor of 0.5 to account for curvature effects) that ponents of the adjustment. Operational implementation correspond to the geopotential fields, a radial wind field during the 1977 typhoon season appears to have re- is also superposed. Because of the imposed low-level sulted in improved forecasts relative to the 1976 season convergence and upper-level divergence, and the geo- (Mihok and Hinsman, 1977). The adjusted TCM fore- strophic assumption, these initial fields will not be in casts based on the same map time were better than the balance. A period of adjustment will thus be necessary, official Joint Typhoon Warning Center (JTWC) fore- although this would presumably be shorter than in the casts in all forecast periods (see Fig. 2). If account for cases without initial divergence. the nearly 12 h lag in receiving the forecasts is made by A superior method of minimizing the initial shock, as comparing the TCM forecasts with an official forecast well as incorporating various types of observations, is made 12 h later, the TCM results are only beginning the dynamic initialization scheme of Hoke and Anthes to approach the official forecasts in the 72 h time frame (1976, 1977). During the preforecast integration period (Annual Report, Joint Typhoon Warning Center, the predictive equations with all of the physical proces- 1977). This emphasizes the need for improving the ses are supplemented by terms that drive the model timeliness of the dynamical forecasts. atmosphere toward the observations. At the completion of the dynamic initialization phase, the terms which "nudge" the model parameters toward the observations are set to zero and the forecast proceeds. Although tested 4. Tracking the model tropical cyclone with only a single case, the dynamic initialization scheme appears to have advantages over forecasts with A number of observational studies (see references in static initialization. The primary disadvantage is the Lewis and Black, 1977) have indicated oscillations along extra computer resources that are required for the pre- the storm path. Lewis and Black (1977) decomposed forecast integration. However, this may be necessary time series of radar eye positions into displacements to make optimum use of the varied types of observa- perpendicular and parallel to a smoothed track. The tions, including off-time cloud motion vectors and cross-track oscillations had magnitudes of about =L 20 reconnaissance data. Kurihara and Tuleya (1978) have km and two dominant periods of 7-12 h and approxi- proposed a dynamic initialization for the hurricane mately 24 h. Numerical models also predict oscillatory planetary boundary layer, which will be important for tracks, although the mechanisms may not be the same intensity forecasts. as in nature. Jones (1977a) has shown that the vortex There is some evidence that the steering flow is also path is trochoidal and that the mean vortex motion is Unauthenticated | Downloaded 10/11/21 01:38 AM UTC 754 Vol. 60, No. 7, July 1979 TABLE 3. Methods for positioning tropical cyclone centers in TCM is only run if the reported maximum wind speed selected models (see Table 1 and text for explanation). is greater than 25 m s_1 (Mihok and Hinsman, 1977). W'eaker storms are not well represented by the bogus Agency-Model Positioning method wind in the TCM, and the weak storm circulation tends NMC-MFM Low-level vorticity maximum to be dispersed during the forecast because of the FNWC-TCM Minimum in streamfunction coarse spatial resolution in the model. It should be NRL/NEPRF Minimum in streamfunction emphasized that storms that move from east to west PSU/NPS Streamline/surface pressure centers are easier to forecast than are storms that recurve JMA-MNG Surface pressure centers (Jarrell et al., 1978). Consequently the number of each kind of forecast can affect the statistics, and this is particularly important if only a few cases are available. about 5° to the right of the steering current. This ap- A second difficulty in establishing long-term error pears to be due to boundary layer frictional drag forces statistics is that these developmental models are con- on the vortex, as suggested by Kuo (1969), because no tinually being modified. Sometimes large changes are variation in the Coriolis parameter was included in the made in the models between seasons. In most cases a Jones model. Therefore in each of the numerical tropical complete comparison between the old and the revised cyclone models there is a problem of determining the versions cannot be made because the historical data are storm track on the basis of a few center positions at 12 h incomplete, or the necessary resources (computer and intervals. As the grid resolution improves—for example, human) are not available. Such comparisons would be in the JMA-MNG—the model track should show more helpful for interpreting the effects of the model changes of the trochoidal path and the center locations will have and improving our physical understanding of the model to be determined more frequently. predictions. This is particularly important if the fore- The methods used for estimating storm positions in caster is to determine when to use the dynamical model the tropical cyclone models are listed on Table 3. One guidance versus the other techniques that are available. should recall the grid resolutions for each model (see An example of the magnitude of track errors from Table 1). It is possible to interpolate quite precisely the NMC-MFM for the 1976 hurricane season is given the position of all extrema in any scalar field such as in Table 4 (from Table 1 of Hovermale and Livezey, vorticity, stream function, or pressure. However, the 1977). One should note that the sample size is small asymmetries that result from representing an intense, and diminishes with the forecast interval because nearly circular wind field on a rectangular grid may not verification data are lacking after landfall. Hovermale justify great precision. It is possible that the location and Livezey treat the sparse data cases separately, of a minimum could be displaced somewhat erratically which in the mean have much larger errors at 36 and only one or two time steps later. The surface pressure 48 h. Nevertheless, the total sample shows that the center and the vorticity maximum will not necessarily NMC-MFM predictions are quite good and do not be coincident, especially for weak storms. It would seem decay in time as rapidly as do some other schemes. advisable to use the vorticity center since the pressure This advantage of dynamic models is evidently due to fields tend to adjust to the wind field on these small the incorporation of large-scale synoptic changes that space scales and at low latitudes. The reasoning impact the tropical cyclone at the longer time intervals. (Shewchuk, 1977) behind the use of a stream function Another example (Hovermale, private communication) center in the FNWC-TCM rather than the maximum was the performance of the NMC-MFM model for 20 vorticity location is that the solution of the Poisson consecutive times with Hurricane Fico in the eastern equation tends to smooth the irregularities in the field, Pacific during 1978. The 24 and 48 h vector errors of and consequently storm positions that are more con- 135 and 291 km must be considered as very good, since servative in time are obtained. official 24 h forecast errors are typically 185-260 km. Of course one should compare these model errors with the comparable official forecasts, because Fico was a 5. Some verification statistics TABLE 4. Mean vector errors in nautical miles of hurricane There are several factors that complicate the discussion forecasts from the MFM (NMC hurricane model) during of forecast errors with the dynamical tropical cyclone the 1976 season (Hovermale and Livezey, 1977). models. The first is the small number of cases that are available for comparison with the best track, which is Forecasts determined from postseason analysis. Because the excluding Forecast sparse Sparse models are expensive and may cause delays in the period data cases data cases Total cases delivery of other products, they may not be run every (h) (N) (N) (N) 12 h unless the tropical cyclone threat is imminent. For example, the primary objective of the NMC-MFM is 12 71 (11) 62 (4) 68 (15) to improve landfall forecasts of storms threatening the 24 102 (10) 135 (4) 126 (14) 36 96 (9) 250 (4) 143 (13) United States. A number of potential cases are not run 48 119 (8) 365 (4) 201 (12) because the storm is not fully developed. The FNWC- Unauthenticated | Downloaded 10/11/21 01:38 AM UTC Bulletin American Meteorological Society 755 TABLE 5. Track error (km) statistics at 24 and 48 h for selected found a correlation between cases with large model 1977 typhoons for official (JTWC), NMC-MFM, and errors and initial wind fields that were ill-defined. FNWC-TCM (prepared by J. Shewchuk, JTWC). Hovermale and Livezey (1977) also noted that "sparse data" cases resulted in larger errors with the NMC- NMC- FNWC- Official MFM TCM MFM. Systematic tests with improved versions of the model can illustrate some of the model-related errors. Typhoon 24 h 48 h 24 h 48 h 24 h 48 h For example, Hodur and Burk (1977) improved the FNWC-TCM by providing for open boundary condi- Vera-1 178 107 294 289 106 111 tions rather than a channel configuration. This model Ivy 226 472 109 248 — — Dinah-1 181 778 356 559 152 285 improvement resulted in a decrease of 48 h errors from Thelma 159 707 96 148 146 574 602 to 448 km (N = 38) and 72 h errors from 1026 to Jean 126 578 339 441 — — 654 km (N = 28). Dinah-2 206 437 56 385 250 270 Babe 583 — 282 885 437 — Dinah-3 204 693 115 324 52 350 Vera-2 300 444 254 181 143 52 6. What about the future? Gilda 243 407 183 580 100 376 Babe 191 782 217 198 196 726 a. Improvements in numerical aspects Homogeneous 250 544 206 333 176 343 Sample I (N = 8) We have not treated in detail the numerical aspects of the dynamical models. One of the goals for future very well-behaved storm in a region with nearly con- tropical cyclone prediction is to improve the horizontal tinuous geostationary satellite coverage. and vertical resolution beyond that shown in Table 1. The use (Kerlin, private communication) of the For the same domain size, an increase in horizontal NMC-MFM on selected Western Pacific typhoons resolution by a factor of two requires eight times the during 1977 allows some preliminary comparisons with computer resources. In the past the improvements in the FNWC-TCM and the official JTWC forecasts. computer technology have produced machines with Statistics for these (and other) forecast techniques were this order of increased capability. For example, the verified by J. Shewchuk (JTWC) on the basis of introduction of the NMC-MFM was made possible by warning positions, rather than on the best track (see the acquisition of a more powerful computer. However, Table 5). This introduces some uncertainties but the it is clearly not going to be possible to decrease the general comparisons are not changed. The individual spatial resolution to the approximately 10 km required 24 and 48 h forecast errors are shown because the sample for representing motions on the scale of the hurricane is so small. Note that the official forecast deteriorates eye by virtue of improved computers alone. rapidly from 24 h to 48 h in most of the cases. There are Advances in nested grid simulations of various several cases in which the dynamical models have smaller scale atmospheric phenomena have been made smaller errors at 48 h than at 24 h. This probably indi- in recent years (Elsberry, 1978). The strategy in these cates that the model tracks are somewhat irregular and models is to represent only the localized regions of large cross the actual track during the period. One generally gradients with fine resolution, and to resolve the regions finds that the dynamical models have the same tend- with smaller gradients on a somewhat coarser grid. The encies and seem to be closer to each other than to the chief advantage of the nested grid model is economic. official forecasts. It is not clear to what extent the official If the inner grids are permitted to move with the atmo- forecasts were guided by the FNWC-TCM (recall the spheric phenomena of interest, the innermost grid need nearly 12 h lag in the receipt at JTWC of the model only cover a very small fraction of the total domain. prediction). Because of the eight-fold increase in computer time for The FNWC-TCM predictions are not available in twice the horizontal resolution, the inner domains all periods. Mean values for a homogeneous sample of require the major fraction of the computer resources. nine 24 h and eight 48 h forecasts are given at the bot- Depending on the domain sizes, it is possible to reduce tom of Table 5. Considerable caution is advised in computing times by a factor of more than five over the using these values because of the small sample. At most requirements of a uniform grid model. The primary one can safely say that the dynamical models produce disadvantage of the nested models is the more rapid comparable results. It would also seem that 48 h guid- contamination of the solutions on the inner grids be- ance based on the dynamical models would be useful to cause the boundaries are closer to the feature of in- the forecasters if it could be received in a timely fashion. terest. Errors in the solutions at the interfaces propagate Additional cases must be provided to the forecaster to into the region, so some consideration must be given to permit determination of the conditions for which the producing the best possible solution on the outer grids dynamical guidance should be accepted or discarded. as well. The research model of Jones (1977a, b) has When that occurs, the official forecasts will again im- demonstrated the feasibility of representing the intense prove on this form of guidance. tropical cyclones on a nested grid. The streamlines and It is difficult to separate numerical model-related isotachs predicted on the 30 km grid of the Jones model errors from the data-related errors. Elsberry (1977) are shown in Fig. 3. Note that the overall pattern is Unauthenticated | Downloaded 10/11/21 01:38 AM UTC 756 Vol. 60, No. 7, July 1979 the air-ocean fluxes, the processes in the planetary boundary layer (PBL) are crucial. Most of the research and operational models have used a relatively crude PBL model in which the surface fluxes are determined by bulk formulas and the PBL depth is constant. Anthes and Chang (1978) have incorporated an improved PBL model with better vertical resolution and a parameteri- zation of the vertical mixing that depends on shear and stability. This stability dependence produces a more realistic response of the hurricane model to changes in sea-surface temperature. The fluctuations in intensity in the Anthes and Chang experiments are less pro- nounced than in a similar model with a conventional bulk parameterization of the hurricane PBL. Another important physical process in the tropical atmosphere is the release of latent heat. Considerable uncertainty remains as to the proper representation of the latent heat transport. Yamasaki (1977) and Rosenthal (1978) have abandoned the parameterization of the latent heat release in terms of the large-scale variables. Rather, they add equations that specifically treat the cloud water and rainwater. Contrary to the FIG. 3. Boundary layer streamlines and isotachs on 30 km grid at 24 h from the model of Jones (1977a,b). Position of earlier theoretical treatments, this does not result in an 10 km grid is denoted by four crosses. unstable solution with unlimited growth on the scale of the grid interval (less than 20 km). The nonlinearity of the vertical heat redistribution during the various representative of a tropical cyclone, and that the flow stages of the cloud development evidently prevents a crosses quite smoothly from the 30 km grid onto the continued growth of the cloud at the same location. 10 km grid (indicated by crosses). As noted in Table 1, Jones and Trout (1977) are utilizing this explicit treat- the JMA-MNG model is in a quasi-operational phase, ment of the clouds on a 12-level, 3-dimensional, nested and a nested version of the NRL/NEPRF model is tropical cyclone model. planned. A movable nested mesh model is also being The NMC-MFM and NRL/NEPRF models use a constructed at the Geophysical Fluid Dynamics Labo- modified version of the Kuo (1965) scheme, whereas ratory, NOAA, to study tropical disturbances (Kurihara et al., 1977). It is also possible to use various numerical differencing schemes to improve the efficiency of present models. Madala (1977) is using split semi-implicit techniques to increase the time step in the NRL/NEPRF model. In the split semi-implicit model, the terms governing the first few fastest moving modes in the solution are treated implicitly. The advantage gained in taking larger time steps will be lost unless an efficient direct elliptic solver is used for the 2-dimensional Helmholtz equation for each implicitly treated mode. The use of the direct solver enables Madala to integrate the semi-implicit model up to six times faster than an analogous explicit model with no pressure gradient averaging. Consequently the combination of the split semi-implicit technique and a nested grid arrangement has great promise for an efficient and more complete numerical model compared to those presently being run. b. Improvements in representation of physical processes With the development of finer resolution models, it FIG. 4. Instantaneous rate of convective heating (°C/day) becomes even more important that the physical proc- in the mid-troposphere after 12 h prediction at 00 GMT esses are well represented in the models. Because the 9 November 1977. The axes are labeled as grid intervals with strength of the storm depends on the rate of inflow and spacing of 120 km (Hacunda, 1978). Unauthenticated | Downloaded 10/11/21 01:38 AM UTC Bulletin American Meteorological Society 757 FIG. 5. (a) Initial wind (full barb, 50 m s-1) at Unauthenticated | Downloaded 10/11/21 01:38 AM UTC 758 Vol. 60, No. 7, July 1979 FIG. 6. Similar to Fig. 5 except using weak wind bogus. sistent. This is in contrast to the reversion-to-clima- A weak storm bogus wind as in Fig. 1 results in the tology feature of the present FNWC wind field analysis, initial wind and pressure fields in Fig. 6a. Note that the which can result in unrealistic analyses in and adjacent cyclonic area introduced by the bogus wind is much to data-void regions. smaller, and the maximum winds are less than 25 m s_1. Although this intensity is much less than in the actual storm, it is more realistic in terms of the gradients that d. Improvements in fine-scale data can be represented on the 120 km grid. Likewise, the It was mentioned previously that some type of bogus depiction of the surrounding wind field is more repre- data is necessary to define the inner regions of the sentative of the true flow. The 24 h forecast for the tropical cyclone. Experience has shown that the result- weak storm bogus is given in Fig. 6b. The maximum ing initial fields should not depart too significantly from wind speed is now slightly in excess of 25 m s-1, and it real conditions (see Fig. 1). Hacunda (1978) tested two occurs at a larger radius, as in Fig. 5b. After only 24 h bogus winds in the PSU/NPS model described in the prediction of the storm center based on an intense Table 1. The initial low-level winds and pressure fields vortex is about 180 km farther north than for the case for the stronger bogus wind are shown in Fig. 5a. At with the weak vortex. Similar excessive northward dis- first glance the wind and pressure gradients appear very placements with strong bogus winds were found in all realistic. However, it is important to note that only five cases treated by Hacunda (1978). A vortex that is alternate gridpoints (resolution of 120 km) are plotted. too large or intense compared to the actual vortex can Consequently the full wind barb to the east of the storm lead to significant westward and northward accelera- center is equivalent to 50 m s_1 at 240 km, and is com- tions due to the variations in the Coriolis parameter parable to the values in the bogus wind used in the (Hovermale et al., 1977). It follows that the environ- NMC-MFM during 1975 (see Fig. 1). Note also that mental flow in the model must be as close as possible the areal domain of the implied cyclonic circulation to observations, but the true interior flow cannot be associated with the typhoon is very large, with a trough realistically represented on a 60 km grid. extending to the northeast corner of the grid. The 24 h Not only is there a problem with how many data forecast based on the bogus wind in Fig. 5a is displayed from the inner regions of the storm can be incorporated in Fig. 5b. The initial wind maximum of 50 m s-1 can- in the 60 km models, the distribution of these observa- not be sustained on the 120 km grid, and a marked tions can have a severe impact on the initial fields. reduction in intensity occurs. There is also a spreading Walters (1978) tested the effect of unequal distribution of the maximum wind region, which appears typically of data by using an analytic representation of the vortex in these relatively coarse mesh models. The storm cir- as in Fig. 7a. This wind field can be completely re- culation at 24 h affects most of the domain. The cir- covered by the objective analysis scheme if sufficient culation pattern in the northeast corner produced a data are provided. However, there is a lack of "observa- precipitation maximum that intensified the trough and tions" in the northeast quadrant of the storm. The wind contributed to the recurvature of the storm. field that is produced with the limited observations is Unauthenticated | Downloaded 10/11/21 01:38 AM UTC Bulletin American Meteorological Society 759 FIG. 7. (a) Analytic solution of a vortex superposed on a basic current used by Walters (1978) to evaluate effect of data distribution indicated by squares, (b) Wind field derived from the 37 observations using an objec- tive analysis scheme. Correct typhoon location from the analytic solution is indicated by typhoon symbol. shown in Fig. 7b. Whereas the large-scale aspects of the (and degraded) vortex wind distributions. Additional flow are reproduced, the unequal distribution of the data in the near-environment of the storm will permit a data results in a sizeable displacement of the vortex realistic blending of the bogus vortex with the large- center to the southwest. scale flow. As indicated above, some care must be taken An unequal distribution of data is quite likely to to assure that the data distribution does not result in a occur during the crucial periods of landfall. An economic distortion of the vortex. More sophisticated models with analysis by Neumann (1975) indicated the largest fine resolution nested grids will require, and be able to benefits are to be obtained from improved forecasts of use, more data near the center of the storm. landfall. There is normally a large difference in data coverage over the ocean relative to the land areas. Thus the dynamical models that use observations near the e. Statistical modification of model predictions center may be adversely affected by the unequal dis- tribution. Robert Burpee of the National Hurricane and One of the common features in the dynamical models Experimental Meteorology Laboratory of NOAA has has been the tendency for the track direction to be proposed augmentation of the reconnaissance coverage better than the speed (Hovermale, 1976 ; Shewchuk and in the area from 150-1500 km of the center. An example Elsberry, 1978). In general the model displacement is for a hurricane located off the Atlantic coast is shown in Fig. 8. The addition of dropwindsonde data at and below 400 mb to the existing observations would im- prove the specification of the atmospheric circulation patterns throughout the troposphere. Factors such as storm location, aircraft capability and dropwindsonde design must be considered in determining specific flight tracks. If dropwindsondes are made at the indicated locations, one would expect significant improvements in the wind analysis in the near-environment of the storm. It appears likely that near-environmental data of the type shown in Fig. 8 are the most important for the existing dynamical models. First, it is a region in which the cyclonic envelope of the storm interacts with the basic current to determine the 12 to 36 h track. Data coverage is generally inadequate in this domain be- tween the center of the storm where the largest winds occur and the far environment. It is important to note that even the 60 km resolution models cannot use FIG. 8. Proposed flight tracks and dropwindsonde locations detailed wind profiles near the storm center. Only the (X) for a hurricane located at 30°N, 75°W. Darkened circles center location must be known with any degree of ac- designate locations of the regular rawinsonde network (R. curacy, because the present models use some idealized Burpee, personal communication). Unauthenticated | Downloaded 10/11/21 01:38 AM UTC 760 Vol. 60, No. 7, July 1979 too slow. If this proves to be a systematic bias, it should for tropical cyclone forecasting should be improved be possible to develop statistical regression equations during the Global Weather Experiment and with the to adjust the model-predicted track. Work along these advent of the global forecast models. Cloud motion lines is in progress at the Naval Postgraduate School vectors from the global satellite coverage are par- using the output of the FNWC-TCM. ticularly important. Additional aircraft reconnaissance It is conceivable that these statistical modifications will also be very beneficial, especially in those cases of the relatively crude FNWC-TCM predictions could where the data can be transmitted directly to the fore- result in errors no larger than the more sophisticated cast centers via communication satellites. The chief NMC-MFM or NRL/NEPRF models. That is, the problem will be to provide data in the inner regions. It information content of the present observational net- appears that the present models are quite sensitive to work (without aircraft reconnaissance) may not justify relative humidity changes of only 5% in the lowest models with further reductions in grid size. It has been layers. Obtaining such accurate humidity measurements suggested (Sanders et al., 1977) that the primary inter- may pose severe problems. Likewise, the specification actions (advective effect) between the vortex and the of the wind field is very important. Near the center of basic current can be represented on a coarse grid (say the tropical cyclone the wind can change rapidly in 150 km). The interaction of the radius of maximum wind space and time. A good distribution of the observations scale circulations with the basic current may be a with respect to the center, as well as the observations secondary effect. The inner regions can only be resolved in the near-environment of the storm, must be provided. on a relatively fine grid. Initialization of the model on Finally, there are still important problems as to how to this scale with actual data will require aircraft recon- incorporate these data into the models and yet deliver naissance, and this may not be replaced with bogus the predictions to the tropical cyclone forecaster in a data. The by-product of an intensity forecast may timely fashion. It seems likely that such dynamical result, but this will clearly require a quantum jump in model guidance is the best hope for significantly im- resources and data to accomplish. It may be reasonable proving the prediction of tropical cyclone tracks be- to do a parallel development of a combined dynamical- yond 24 h. statistical approach. An efficient coarse resolution model will be required so that one can obtain the large number of cases necessary to develop stable statistical equations. Acknowledgments. The long-term support of the Naval Air Systems Command, the Naval Environmental Prediction Research Facility, and the Fleet Numerical Weather Central is gratefully acknowledged. The cooperation and assistance of numerous personnel at the latter two agencies, and at the 7. Summary Naval Postgraduate School, have made possible the develop- ment of the U.S. Navy Tropical Cyclone Model. Constructive Several 3-dimensional numerical models to predict the comments on this manuscript were provided by G. J. Haltiner, R. A. Anthes, and R. M. Hodur. motion of tropical cyclones have been used opera- tionally, or are currently being tested with operational data. Although there is a problem with the timeliness of References the predictions that are delivered to the forecasters, the dynamical guidance at 48 and 72 h appears superior to Anthes, R. A., 1976: Numerical prediction of severe storms— the official forecasts in many important cases. Further certainty, possibility or dream? Bull. Am. Meteorol. Soc., improvements in various aspects of these numerical 57, 423-430. models can be expected in the next few years, if the , 1977: A cumulus parameterization scheme utilizing a sophisticated research models are applied to the opera- one-dimensional cloud model. Mon. Wea. Rev., 105, 270-286. tional tropical cyclone track prediction problem. Spe- , 1978: Tests of a mesoscale model over Europe and the cific goals include better horizontal and vertical resolu- United States. Naval Postgraduate School Tech. Rept. NPS tion, and improved representation of the physical proc- 63-78004, Monterey, Calif., 107 pp. esses. These new dynamical models will require addi- , and S. W. Chang, 1978: Response of the hurricane tional computer resources. However, nesting the grids boundary layer to changes of sea surface temperature in a and more efficient numerical differencing schemes will numerical model. J. Atmos. Set., 35, 1240-1255. permit a better utilization of those resources. Elsberry, R. L.,1975: Feasibility of an operational tropical If finer resolution (say 10 km) models are developed, cyclone prediction model for the western North Pacific one can consider intensity forecasts as well as track area. Naval Postgraduate School Tech. Rept. NPS- 5lEs7505l, Monterey, Calif., 56 pp. forecasts. A deterministic prediction of maximum wind , 1977: Operational data tests with a tropical cyclone speed appears doubtful when one considers the natural model. Naval Postgraduate School Tech. Rept. NPS- variability, and thus predictability, of these maxima. 63Es77031, Monterey, Calif., 28 pp. However, the general distribution of wind speed, say , 1978: Prediction of atmospheric flows on nested grids. -1 -1 the radii of 25 m s and 15 ms s winds in various Computational Techniques for Interface Problems, Vol. 30. quadrants, may be possible. Appl. Mech. Div., Am. Soc. Mech. Engr., New York, 67-86. Even with a better representation of the physical Hacunda, M. R., 1978: Tests of the Penn State mesoscale processes in the models, the major limitation appears model with tropical cyclones. M.S. Thesis, Naval Post- to be input data. Specification of the large-scale data graduate School, Monterey, Calif., 80 pp. Unauthenticated | Downloaded 10/11/21 01:38 AM UTC Bulletin American Meteorological Society 761 Harrison, E. J., Jr., 1973: Three-dimensional numerical 11th Technical Conference on Hurricanes and Tropical simulations of tropical systems utilizing nested finite grids. Meteorology {Miami Beach), AMS, Boston, pp. 484-489. J. Atmos. Set., 30, 1528-1543. Madala, R. V., 1977: Semi-implicit and split semi-implicit Hinsman, D. E., 1977: Preliminary results from the Fleet integration schemes for tropical cyclone prediction models. Numerical Weather Central tropical cyclone model. Pre- Preprints, 11th Technical Conference on Hurricanes and prints, Third Conference on Numerical Weather Prediction Tropical Meteorology {Miami Beach), AMS, Boston, pp. {Omaha), AMS, Boston, pp. 19-34. 96-98. Hodur, R. M., and S. D. Burk, 1977 : Incorporation of one-way , and R. M. Hodur, 1977: A multi-layer nested tropical interactive boundary conditions in the Fleet Numerical cyclone prediction model in sigma coordinates. Preprints, Weather Central tropical cyclone model. Preprints, 11th 11th Technical Conference on Hurricanes and Tropical Technical Conference on Hurricanes and Tropical Meteo- Meteorology {Miami Beach), AMS, Boston, pp. 101-103. rology (Miami Beach), AMS, Boston, pp. 116-121. Mathur, M. B., 1978: A case study of analyses and forecasts Hoke, J. E., and R. A. Anthes, 1976: Initialization of numeri- over tropics with NMC operational models. Office Note 187, cal models by a dynamic-initialization technique. Mon. Wea. National Meteorological Center, Washington, D.C., 15 pp. plus figures. Rev., 104, 1551-1556. Mihok, W. F., and D. E. Hinsman, 1977: Tropical storm fore- , and , 1977: Dynamic initialization of a three- casts during 1977 using the Fleet Numerical Weather Cen- dimensional primitive-equation model of hurricane Alma of tral Tropical Cyclone Model. Preprints, 11th Technical Con- 1962. Mon. Wea. Rev., 105, 1266-1280. ference on Hurricanes and Tropical Meteorology {Miami Hovermale, J., 1976: First season storm movement charac- Beach), AMS, Boston, pp. 401-404. teristics of the NMC objective hurricane forecast model. Neumann, C. J., 1975: A statistical study of tropical cyclone National Meteorological Center, Washington, D.C. (Un- positioning errors with economic applications. NO A A Tech. published manuscript.) Memo. NWS SR-82, Washington, D.C., 21 pp. (NTIS No. , and R. E. Livezey, 1977: Three-year performance char- COM-75-11362). acteristics of the NMC hurricane model. Preprints, 11th Ookochi, Y., 1978: Preliminary test of typhoon forecast with Technical Conference on Hurricanes and Tropical Meteo- a moving multi-nested grid (MNG). J. Meteorol. Soc. Japan, rology {Miami Beach), AMS, Boston, pp. 122-125. 56, 571-583. , S. H. Scolnik, D. G. Marks, 1977: Performance charac- Phillips, N. A., and J. Shukla, 1973: On the strategy of com- teristics of the NMC movable fine mesh model (MFM) bining coarse and fine grid meshes in numerical weather pertaining to hurricane predictions during the 1976 hur- prediction. J. Appl. Meteorol., 12, 763-770. ricane season. National Meteorological Center, Washington, Pike, A. C. 1972: Improved barotropic hurricane track pre- D.C. (Unpublished manuscript.) diction by adjustment of the initial wind field. NO A A Tech. Jarrell, J. D., S. Brand, and D. S. Nicklin, 1978: An analysis Memo. NWS SR-66, Washington, D.C., 16 pp. of western North Pacific tropical cyclone forecast errors. Rodgers, E., R. C. Gentry, W. Shenk, and V. Oliver, 1978: Mon. Wea. Rev., 106, 925-937. Benefits of using short interval satellite images to derive Jarvinen, B. R., 1977: Comparison of initial analysis schemes winds for tropical cyclones. NASA Tech. Memo. 79594, on the barotropic hurricane model (SANBAR). Preprints, Washington, D.C., 32 pp. 11th Technical Conference on Hurricanes and Tropical Rosenthal, S. L., 1978: Numerical simulation of tropical Meteorology {Miami Beach), AMS, Boston, pp. 397-400. cyclone development with latent heat release by the re- Joint Typhoon Warning Center, 1977: Annual Typhoon solvable scales. I. Model description and preliminary results. report, Guam, 923 pp. J. Atmos. Sci., 35, 258. Jones, R. W., 1977a: Vortex motion in a tropical cyclone Rosmond, T., 1978: A review of global numerical weather pre- model. J. Atmos. Sci., 34, 1518-1527. diction. Air Weather Serv. Tech. Rept. 79/001, Proceedings , 1977b: A nested grid for a three-dimensional model of a of the 8th Technical Exchange Conference, Scott AFB, 111., pp. 29-37. tropical cyclone. J. Atmos. Sci., 34, 1528-1553. Sanders, F., and R. W. Burpee, 1968: Experiments in baro- , and J. Trout, 1977: 12-level, three-dimensional, nested tropic hurricane track forecasting. J. Appl. Meteorol., 7, grid, tropical cyclone model. Presented at the 11th Tech- 313-323. nical Conference on Hurricanes and Tropical Meteorology, , A. C. Pike, and J. P. Gaertner, 1975 : A barotropic model (Miami Beach), AMS, Boston. for operational prediction of tracks of tropical storms. J. Kuo, H.-L., 1965 : On formation and intensification of tropical Appl. Meteorol., 14, 265-280. cyclones through latent heat release by cumulus convec- , A. L. Adams, N. J. B. Gordon, and W. D. Jensen, 1977: tion. J. Atmos. Sci., 22, 40-63. A study of forecast errors in a barotropic operational model , 1969: Motions of vortices and circulating cylinder in for predicting paths of tropical storms. Preprints, 11th shear flow with friction. J. Atmos. Sci., 26, 390-398. Technical Conference on Hurricanes and Tropical Meteo- Kurihara, Y., and R. E. Tuleya, 1974: Structure of a tropical rology {Miami Beach), AMS, Boston, pp. 389-396. cyclone developed in a three-dimensional numerical simula- Shewchuk, J. D., 1977: Development of a biasing scheme to tion model. /. Atmos. Sci., 31, 893-919. improve initial dynamical model forecasts of tropical , and , 1978: A scheme of dynamic initialization of cyclone motion. M.S. thesis, Naval Postgraduate School, the boundary layer in a primitive equation model. Mon. Monterey, Calif., 93 pp. Wea. Rev., 106, 114-123. , and R. L. Elsberry, 1978: Improvement of short-term , M. A. Bender, and G. J. Tripoli, 1977: A movable dynamical tropical cyclone motion prediction by initial nested mesh primitive equation model. Preprints, 11th field adjustments. Mon. Wea. Rev., 106, 713-718. Technical Conference on Hurricanes and Tropical Meteo- Singh, S. S., and K. Saha, 1976: Numerical experiments with rology {Miami Beach), AMS, Boston, pp. 99-100. a primitive equation barotropic model for the prediction of Lewis, B. M., and P. G. Black, 1977: Spectral analysis of movement of monsoon depressions and tropical cyclones. oscillations of radar-determined hurricane tracks. Preprints, J. Appl. Meteorol., 15, 805-810. Unauthenticated | Downloaded 10/11/21 01:38 AM UTC 762 Vol. 60, No. 7, July 1979 Sobel, J. P., 1976: Nested grids in numerical weather predic- Walters, T. P., 1978: Improvements in tropical cyclone tion and an application to a mesoscale jet streak. Ph.D. motion prediction by incorporating DMSP wind direction thesis, Pennsylvania State University, University Park, Pa. estimates. M.S. thesis, Naval Postgraduate School, Mon- Tsay, C.-Y., 1977: Numerical predictions of typhoon tracks terey, Calif., 72 pp. in the area of Taiwan and its vicinity. Preprints, 11th Yamasaki, M., 1977 : A preliminary experiment of the tropical Technical Conference on Hurricanes and Tropical Meteo- cyclone without parameterizing the effects of cumulus con- rology (Miami Beach), AMS, Boston, pp. 405-412. vection. J. Meteorol. Soc. Japan, 55, 11-30. • announcements State solar education directories nation. This National Directory may be purchased from the Superintendent of Documents, U.S. Government Printing Increasing national interest in solar energy is being demon- Office, Washington, D.C., 20402, Stock number: 061-000- strated by a wide variety of solar-related courses and pro- 00210-3, for $4.75. The state directories can be ordered by grams now offered by postsecondary institutions. The calling toll-free request lines of the National Solar Heating Department of Energy's Solar Energy Research Institute and Cooling Information Center: (tel: 800-523-2929); from (SERI) has compiled information on these educational Pennsylvania (tel: 800-462-4983); from Alaska and Hawaii offerings in a series of State Solar Energy Education Direc- (tel: 800-523-4700). Requestors may order copies only for tories now available free of charge. Information in these states in which they reside. directories was gathered from a national survey of more than 3200 colleges, universities, vocational-technical schools, and community and junior colleges. The data collection effort was coordinated by SERI's Academic Programs and Data Input data for solar systems Base Systems Branches. Some 700 postsecondary institutions are now offering solar The National Climatic Center has prepared and published courses. The state directories contain detailed information for the Department of Energy a 192-page compilation of on each. In addition to the name, address, and telephone climatological data for 248 U.S. stations. The publication, number of each school with solar offerings, the state directories Input Data for Solar Systems, contains tables of monthly also provide the instructor's name, course, and department and annual normals (1941-70) of temperature and of total number; the number of credits offered; whether the course is heating and cooling degree days for those stations with graduate or undergraduate; topics covered; number of times available data. Also included in the tables are corresponding the course has been taught; and average course enrollment. values of average daily global solar radiation on a horizontal In addition, information is supplied for each program and surface, based upon corrected (rehabilitated) hourly measure- curriculum offered. ments for 26 stations, and similar derived values for 222 The state directories are subsets of the first edition of the additional stations. Most of the statistics are based upon a National Solar Energy Education Directory, released in March 24- to 25-year period, generally from 1952-76. Copies of the 1979, that contains identical information for the entire publication are available for a $2.00 handling charge. Address requests to: Director, National Climatic Center, Federal 1 Note of registration deadlines for meetings, workshops, Building, Asheville, N.C. 28801 (tel: 704-258-2850, ext. 683; and seminars, deadlines for submittal of abstracts or papers for requests about the same data on magnetic tape, call to be presented at meetings, and deadlines for grants, pro- ext. 203). posals, awards, nominations, and fellowships must be re- ceived at least three months prior to deadline dates.—News Ed. Continued on page 769 Unauthenticated | Downloaded 10/11/21 01:38 AM UTC