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The linear parts of the terms governing the fastest and relaxation processes. In practice, both the demoving gravity waves are then time-averaged using coupling and overrelaxation processes account for ž2 = (x++1 + X-1)/2, X ~15% of the total computation time of a model fore(A1) cast. where X represents any variable and 7 signifies quan- tities evaluated at time tAt. Thus ax/at becomes REFERENCES Brown, J. A., Jr., and K. A. Campana, 1978: An economical time-differencing system for numerical weather prediction. at 2At At Mon. Wea. Rev., 106, 1125-1136. Campana, K. A., 1974: Status report on a semi-implicit version Except for the gradient of 6 in (3.1) and (3.2), of the Shuman-Hovermale model. NOAA Tech. Memo. the equations have now been reduced to two group NWS NMC-54, 22 pp.* [NTIS COM-74-11096/AS). ings of terms—those computed explicitly at time 1978a: Addition of orography to the semi-implicit version of the Shuman-Hovermale model. NOAA Tech. Memo. T i and those that are time-averaged (ū, özt, īļ, ī? V NWS NMC-62, 14 pp.* [NTIS PB-286009]. poa, Ps“, pro', 3). The gradient of is reduced 1978b: Semi-implicit higher order version of the Shumanto these terms by first eliminating the wind diver- Hovermale model. NOAA Tech. Memo. NWS NMC-61, 50 gence in modified (3.3) via the continuity equation. pp.* [NTIS PB-286012). Then the resulting solution for it is substituted into Crowley, W. P., 1968: Numerical advection experiments. Mon. Wea. Rev., 96, 1-11. the equation of state (3.7) to obtain a?', which in Fawcett, E. B., 1969: Systematic errors in operational baroclinic turn is used in the hydrostatic equation (3.6) to ob- prognoses at the National Meteorological Center. Mon. Wea. tain 72 as a function of the desired terms. Rev., 97, 670-682. Schematically, Eqs. (3.1), (3.2), modified (3.3) and Gerrity, J. P., Jr., 1973: Numerical advection experiments with higher order, accurate, semimomentum approximations. (3.5) become Mon. Wea. Rev., 101, 231-234. 1977: The LFM model-1976: A documentation. NOAA u21 + PSU EU, (A2) Tech. Memo. NWS NMC-60, 68 pp.* (NTIS PB-279419). duction of truncation error in numerical weather prediction ü2t models. Mon. Wea. Rev., 100, 637-643. + PSV = EV, (A3) and S. Scolnik, 1973: A semi-implicit version of the Shuman-Hovermale model. NOAA Tech. Memo. NWS 12t + PST NMC-53, 44 pp.* (NTIS COM-73-11323). (A4) Kwizak, M., 'and Robert, A. J., 1971: A semi-implicit scheme q21 = EQ, (A5) for grid point atmospheric models of the primitive equa tions. Mon. Wea. Rev., 99, 32-36. where EU, EV, ET and EQ contain terms computed Merilees, P. E., 1975: The effect of grid resolution on the in stability of a simple barotropic model. Mon. Wea. Rev., explicitly at time 7 and PSU, PSV and PST con 103, 101-104. tain various combinations of the time-averaged Miyakoda, K., R. F. Stricker, C. J. Nappo, P. L. Baker and , quantities p.“, ps“, pr“ and ö 82 G. D. Hembree, 1971: The effect of horizontal grid resoluThe sequence of operations during each time step tion in an atmospheric circulation model. J. Atmos. Sci., 28, 481-499. begins with the computation of EU, EV, ET and EQ. Sela, J., and S. Scolnik, 1972: Method for solving simultaneous Then a set of Helmholtz equations are solved to Helmholtz equations. Mon. Wea. Rev., 100, 644-645. obtain po,ps, pro and the four nonzero 72. In ma- Shuman, F. G., 1962: Numerical experiments with the primitive trix form these equations are equations. Proc. Int. Symp. Numerical Weather Prediction, Tokyo, Japan Meteor. Agency, 85-107. m272 CP + EP F, (A6) and J. B. Hovermale, 1968: An operational six-layer primi tive equation model, J. Appl. Meteor., 7, 525-547. where the square matrices Cand E are only functions Teweles, S., and H. Wobus, 1954: Verification of prognostic of Ax, At and basic state and therefore, need only charts. Bull. Amer. Meteor. Soc., 35, 455-463. be computed at the beginning of the forecast. P is Wellck, R. E., A. Kasahara, W. M. Washington and G. DeSanto, 1971: Effect of horizontal resolution in a finite-difference a column vector of the unknowns and F a column model of the general circulation. Mon. Wea. Rev., 99, 673– vector of the forcing functions (computed explicitly 683. at time 7). Solutions to (A6) are then substituted Williamson, D. L., 1978: The relative importance of resolution, into (A2), (A3) and (A4) to give uạt, öz, iat. Solu accuracy, and diffusion in short-range forecasts with the NCAR global circulation model. Mon. Wea. Rev., 106, 69tion of (A1) for all variables gives their values at 88. time t + 1. and G. L. Browning, 1973: Comparison of grids and difThe Helmholtz equations (A6) are decoupled ference approximations for numerical weather prediction using an interative process described by Sela and over a sphere. J. Appl. Meteor., 12, 264-274. Scolnik (1972), and then each equation is solved independently using a Liebmann over-relaxation scheme. On the IBM 360/195 double precision arith- * Available from the National Meteorological Center, Washmetic (64-bit word) is required for the decoupling ington, DC 20233. Page 3
18 (2%) Relative 36 h pressure changes were assigned to each model anticyclone and corresponding verificaSOUTH tion in the working sample of 568 cases where the Fig. 4. Observed position of surface anticyclones relative to anticyclone existed at the initial time. Fig. 6 shows . forecast position. Numbers in parentheses indicate the portion of the distribution of verification pressure changes as anticyclones observed in a specific compass direction from the a function of model forecast. Overall there was a forecast position. slight tendency for the model to underforecast pres sure increases in intensifying anticyclones and overa. Motion errors estimate pressure decreases in weakening anti cyclones. Of the 568 anticyclones observed at initial time, and forecast and observed at verification time, some 428 cases were classified as “moving” anticyclones left of forecast track in which there was a forecast displacement of at 38% 16% least 1° latitude (12 h)- [or ~333 km (36 h)-] in any (590) (530) direction. For each of these 428 moving anticy- slower faster forecast track than than clones, 36 h forecast and observed displacements forecast forecast 16% were computed relative to a spherical earth. From (490) (405) this information, a displacement error was determined for each anticyclone, defined to be the dis right of forecast track tance between forecast and verification positions, (a)All moving anticyclones as well as a measure of the angular error or the angle between each forecast anticyclone track and 50% 24% 17% its corresponding verification track. (660) (550) (555) (680) The results of this analysis are presented in Fig. 5 according to observed anticyclone displacements relative to their forecast track for the entire sample 18% 8% 30% 17% (340) (365) (415) (455) of moving anticyclones and for subdivisions of the 428 cases into southeastward and northeastward (b) SE- OCEANIC (d) NE- OCEANIC 40% 9% 16% (545) (325) (520) (415) fore, 168 anticyclones were classified as southeastward moving and continental, 118 as southeastward moving oceanic, 87 as northeastward moving oce 29% 22% 40% 17% (460) (455) (700) (200) anic, and 55 as northeastward moving continental. Overall, there was a tendency for observed anticyclones to move to the left of their forecast track, (c) SE - CONTINENTAL (e) NE - CONTINENTAL while 68% of all anticyclones were forecast to move Fig. 5. (a) Observed displacement of all moving anticyclones too fast. Mean displacement error for all these anti- relative to their forecast displacement (arrow). The percentages cyclones was 517 km. are the portion of all moving anticyclones observed in a particular The fast bias in model anticyclones was found in quadrant relative to the forecast motion (i.e., faster or slower Page 4
cyclone east of New England. At the same time the western lobe of this cyclone is overemphasized. Again there is too much surface trough into the cold air southeast of New England. The consequence of this error in the forecast is to place excessive easterly geostrophic flow across the northern Appa510 504 lachians with weaker easterly geostrophic flow along 516 the coast as opposed to the observed coastal south easterly geostrophic flow maximum. Although the 08112 model was very valuable in indicating another significant storm in a region still recovering from a major ice and snow storm three days earlier, it erred 24 -Н H in the magnitude of the threat of frozen precipita24 tion to the coastal cities of the northeastern United 540 States because of the failure to properly predict the southeasterly surface flow. 552 The same forecast also produced major errors in the central part of the country as can be seen from 12 36h LFM II 5649 a predicted strong 992 mb cyclone on the Montana0000 GMT North Dakota border versus a much weaker ob- 1/17/ 78 served 1007 mb center on the Colorado-Wyoming Fig. 14. As in Fig. 12 except for 0000 GMT 17 January 1978. border. The tendency for excessive lee cyclogenesis is a carry-over from the earlier six-layer PE model as documented by Leary (1971). at verification time, no doubt accompanied by more Note another example of the spurious reduction quiescent weather than indicated by the poor model in central pressure (1048– 1034 mb) of the cold northforecast. Note also that the central pressure in the western Canadian anticyclone. cold northwestern Canadian anticyclone is too low Our final examples involve the 7L-PE forecasts. by 8 mb. Figs. 20-22 shows the 36 h 7L-PE, LFM II surface Another example can be seen from Figs. 18 and 19 and thickness forecasts and the corresponding veriwhich depict the 48 h LFM II (36 h LFM II fore- fication map for 0000 GMT 10 February 1978. Both cast unavailable to us) surface and thickness fore- models placed a surface anticyclone in the upper cast and the corresponding verification map for 0000 Midwest with the LFM II slightly faster. In contrast GMT 18 January 1978. The LFM II forecast is the observed anticyclone was stronger with the surslightly too fast with the eastern lobe of the anti- face center remaining in Canada. The cyclone east Page 5
that plagued the 6L-PE for short-wave systems has been largely eliminated in the 7L-PE and LFM II models. It can still be observed to a lesser degree, however, in some very short-wave features such as the cyclone that was forecast to influence the Florida and offshore waters area in Figs. 20–22. The overall reduction of truncation error in the current opera tional NMC models has resulted in considerable im3522 provement in the forecast of large-scale circulation seo features. This improvement is evident both visually La 92 and in terms of the standard statistical measures. Some characteristic errors do persist, however, 542 including excessive lee cyclogenesis, a fast bias with transitory anticyclones, excessive or incorrect weak ening of surface anticyclones, and underforecasting 12 of oceanic storms and overforecasting of anti cyclones beneath cold midtropospheric troughs and 564 in elevated terrain regions. It is difficult to be pre48-h LFM I cise about the quantitative source of such errors 0000 GMT as direct evidence is hard to come by. Inadequate vertical resolution is likely a significant source of FIG. 18. LFM II 48 h surface and 1000 - 500 thickness prog- numerical error for many smaller scale transient feanosis, valid 0000 GMT 18 January 1978. Otherwise as in tures of limited tropospheric depth. An example Fig. 12. would be the weak transitory cyclones that propa gate along quasi-stationary baroclinic zones. 6. Discussion Initial analysis uncertainties are a major source of error that are relatively independent of the model In an attempt to put our results into perspective resolution. Bosart (1978) has discussed this problem it is convenient to divide error sources into three in terms of the effect of erroneous eastern Pacific categories: 1) initial analysis uncertainties, 2) incor- 500 mb height and wind analyses resulting from serirect model physics and 3) numerical effects. For ous satellite temperature retrieval errors on LFM example, truncation error, would be lumped into the II forecasts. The downstream effect of such errors is latter category. Note that the persistent slow bias often rather significant. The trade-off of model reso Page 6
failure to properly forecast downstream oceanic cy- National Meteorological Center until January 1978. clogenesis (Leary, 1971) may result in inadequate The period of record was the six-month winter seabaroclinicity between the cyclone and the upstream son from October 1969 through March 1970 and inanticyclone center. Note that the 500 mb trough volved daily 36 h prognoses verifying at 1200 GMT along 60°W is deeper than forecast with a consequent over the Northern Hemisphere. The principal findenhancement of the northerly surface flow in Fig. 9. ings are as follows: Forecast amplitudes of the associated mid-tropo 1) Model forecast sea level pressures were genspheric trough and ridge systems may therefore be underdeveloped, contributing to the underforecast- erally too low over the Atlantic and eastern Pacific ing of surface pressure in the upstream anticyclone. Oceans and eastern North America, and too high One might further speculate that if sensible heating over western North America, the western Great Plains and in elevated terrain. is underestimated by the model in the wake of oce 2) Model errors in the 1000-500 mb thickness anic cyclogenesis and overestimated near the upstream anticyclone, then the overall lower tropo forecasts over anticyclone centers were generally spheric model baroclinicity is reduced between the too cold throughout the hemisphere. The origin of the error is uncertain. two systems. Correspondingly, model cold advection in the lower troposphere and associated sinking too low in response to the thickness errors . 3) Model 500 mb height forecasts were generally motion and surface pressure rises would be underestimated. Another way of saying the same thing with a tendency for the model to place these sys 4) Model anticyclones were generally too fast, is that model isobars are displaced away from anti tems too far into cold downstream thickness cyclones toward cyclones, reducing the model surface pressure gradient relative to observed. troughs, corresponding to negative thickness errors Another characteristic error which also persists observed anticyclone track tended to lie to the left on the average over the forecast anticyclones. The in present day operational models is the tendency of the forecast displacement, particularly so for to predict excessive anticyclogenesis in cold 1000– 500 thickness troughs (recall Figs. 8 and 10). In every southeastward tracking anticyclones over oceanic case from our six-month data sample such overpre regions. diction was associated with a model forecast con 5) Little seasonal variability was seen in speed fluent 500 mb trough brought about by excessive and track errors except for a slightly enhanced model model slowness with the southern part of the trough. fast bias in December-January. The spurious northeast-southwest tilt in the south 6) Surface pressure in model anticyclones crossern end of the model trough apparently resulted in ing the Atlantic coastline while moving northeastexaggerated differential anticyclonic vorticity ad ward was particularly apt to be underforecast. The vection in the mid and upper troposphere near the cause may be related to excessive model boundarytrough axis leading to excessive surface pressure layer sensible heat flux in the oceanic regions in rises below. This same physical effect might possibly lower level baroclinicity in the model, or model the vicinity of the anticyclone center, improper be a factor in the model-exhibited fast bias, particu- failure to produce significant mid and upper tropolarly with a weak anticyclonic system such as shown a in Fig. 11, with the model tending to incorrectly spheric ridging in the wake of an underforecast major place the surface anticyclone too far into the down- cyclone event in the western Atlantic ocean basin. stream cold thickness trough. 7) Model anticyclones tended to be considerably Excessive surface troughing within a cold air mass overforecast while located in spurious cold 1000– just upstream from the surface anticyclone location 500 mb thickness troughs. The error is coincident (see Figs. 14, 16 and 18) is a final example of a with model development of excessive northeastparticularly vexing error that persists today. The ori southeast tilts in the southern end of mobile midgin of the error is unknown. Inspection of the 700 tropospheric short waves. The resulting confluent and 500 mb forecasts for these and other cases (not nature of the southern ends of these troughs resulted shown) tends to disclose the presence of a weak in enhanced differential anticyclonic vorticity adshort-wave trough of small amplitude upstream of vection into the trough axis and corresponding exhe surface troughing. On the contrary the evidence cessive surface pressure rises. for such troughs on the verification maps is con- Finally, some selected cases were presented for siderably more tenuous. more recent 7L-PE and LFM II model forecasts. The problem of truncation error has been greatly 7. Conclusions alleviated in the current operational models. How ever, transitory anticyclones are still forecast too A study has been completed of errors in the fore- fast. Excessive loss in central pressure is still noted asts of surface anticyclones by the six-layer primi- for cold continental anticyclones away from eleive equation model employed operationally by the vated terrain as well as for anticyclones crossing Page 7
Fig. 4. Observed (A) and predicted (B) mean maps of 1000 mb geopotential heights, negative regions shaded, and the error map (C) (i.e., the predicted minus the observed). Contours in all maps are at 30 m intervals. Negative areas of height error in (C) are shaded. The loci of small segmented lines mark the mountain areas.
tion is lower by 41% than that of the observed, in shown in Figs. 4 and 5, together with their forecast contrast to the 25% reduction in the case of January. errors SZ Z pred – Z obs. The observed patterns Z The secondary maximum that is associated with the in these figures closely resemble the climatological polar frontal jet was not well-produced. The major maps obtained by Crutcher and Jenne (1970). cause for these deficiencies is the coarse-grid resolu- In the 1000 mb map, the height error is positive tion of the model for both horizontal and vertical toward the pole and negative toward the equator directions and, in part, the excessive horizontal dif- with a node near 30°N. The largest error is found fusion. Compared with January, July has an appreci- between Turkestan and the Himalayas, and also ably reduced intensity of KE both in the observa- over the North Sea and northern Canada. The tions and predictions, indicating that the baroclinic former error may largely be due to improper heat process in the middle latitudes is inactive in summer balance at the surface and also related to the model's and also reflecting the fact that the cyclone genera- weakness in simulating capability of the Asian montion is less. soon, which comes from the prohibited interhemi spheric exchange over the Indian Ocean. In fact, d. Hemispheric geopotential fields the global models of Manabe and Holloway (1975) Height fields both for the observation and the pre- and Stone et al. (1977) successfully simulated the diction averaged for 10 days and over 12 cases are pattern east of the Caspian Sea (though Manabe
Fig. 5. As in Fig. 4 for 500 mb except mean height contours are at 60 m intervals and height error contours are at 30 m intervals. Page 8
cyclones are less than in January or, particularly, in April. It is also typical in July that there are more cyclone paths over eastern Siberia and China. The correspondence between prediction and observation is somewhat poorer in July than in January. There is reasonable agreement between forecast and observation in the tracks over North America, the North Atlantic, the North Pacific and central Siberia. However, the movement of cyclones over China is very different from the observation (see also Kasahara (1977) for the result of the NCAR model.] Reed and Kunkel (1960) mentioned that cyclones develop along the northern shore of Siberia, Alaska and Canada in summer, and that these cyclones frequently invade the central Arctic. Fig. 7 agrees with this description. In the tropical region, there are cyclone displacements directed clockwise in the observation map. They correspond to the paths of easterly waves which travel westward in trade winds in the tropical Pacific, central Africa, Caribbean Sea and the east Asian monsoon area. However, they are almost entirely missing in the prediction, partially due to the effect of the equatorial wall. Newton (1956) discussed the lee cyclogenesis over the central eastern slopes of the Rocky Mountains. In our prediction period this phenomenon occurred quite often and was not well predicted. For the present numerical model, one of the most difficult problems is simulating the rapid development of cyclones in the lee of mountains and the subsequent develop- function of height. January (above) and July (below). The ordinate Fig. 9. Time evolution of the rms temperature error (°C) as a ment of cutoff lows [or at the side of mountains, is scaled in equal pressure intervals (mb) at the right, and scaled Genoa cyclones, for example (see, Egger, 1972; by the nine levels at the left. Mesinger, 1977; Bleck, 1977)). According to the study of Blackmon, the rms field c. Error in geopotential height is largely contributed by a slowly varying part Fig. 8 is the rms error of 1000 mb height defined (period > 10 days) of spatially medium-scale waves, and yet the contribution from waves of periodicity by (E(dz)?]1/2, where E is the ensemble mean of 12 4-10 days is not negligible either. In contrast to cases. As expected, substantial errors are located the winter case, the activities of not only the largemostly in relatively higher latitudes, compared with scale slowly varying part but also the small-scale those of January. (cyclone) part of atmospheric disturbances affect The magnitude of the July rms error is smaller significantly the rms errors in the summer case. than the January error; the maximum in July is In Fig. 8 other large rms errors appear in the sub105 m, whereas it is 180 m in January. The largest tropics, i.e., 10°N over Africa, 20°N in the Atlantic errors occur in four regions, i.e., the Iceland-Eng- and ~5-10°N in the western Pacific. land-Norway area, near the Caspian Sea, northern Canada and the Kamchatka area. d. Temperature error development If one compares this map with the rms geopotential field (not error but natural variance) produced Fig. 9 is the growth with time of the rms temby Blackmon (1976), there is a striking resemblance, perature error [E(87)]1/2, as a function of vertical a although his map is for 500 mb and his period is level, based on six cases each for January and July. from 15 May to 14 September. This correspondence The January pattern in Fig. 9 is the same as that in implies that the geographical locations of these er- Part I, except that the pressure coordinate was taken rors may not necessarily be special for this particular for the ordinate in this paper. model, but they are rather intrinsic in the sense that The errors seem to start near the surface and they were produced by inherited instability of the at- tropopause levels, develop quickly in the lower mosphere in the respective months. troposphere (~4 days) and somewhat slowly at the Page 9
enstrophy spectrum of -1.5 power at midlatitudes general circulation in the model solution, such as instead of a – 1 power, implying that spectral resolu- high levels of eddy kinetic and potential energies, tion may not be sufficient for the vorticity calcu- and Ferrel as well as Hadley cells, which are closer lation. to the observation. Smagorinsky derived the formulation of his vis3) THE STAGGERED GRID cosity based on a heuristic assumption: the Reynolds stress is proportional to deformation of flow and Arakawa and Lamb (1977; see, also, Mesinger and the energy spectrum obeys the – 5/3 law. InterestArakawa, 1978) argued that the A-lattice which our ingly, Lilly (1967), and Deardorff (1973) obtained model uses leads to an erroneous wave dispersion Smagorinsky's formula from the theory of turbulent relation and inefficient geostrophic adjustment in the closure by discarding many terms, and also found finite-difference solution. A more direct description that the coefficient for temperature diffusion is much of the disadvantages of the A-lattice system may be larger than the coefficient for momentum. a statement that it enforces a redundant calculation The coefficient varies with the grid size AS generating multiple-computational modes of solu- adopted. As was mentioned earlier, experiences of tion, which might give an adverse effect rather than real-data forecasts are that less influence of the suban improvement of the solution. The shredded flow pattern mentioned earlier may grid-scale viscosity on the lower wavenumbers is more desirable. In this view together with the reason be related to the problem above. In other words, of economy, Hoskins, (personal communication) the shredded pattern is the consequence of using the A-lattice, but the A-lattice is not the generator of proposed an empirical k V4 viscosity and Williamson the shredded pattern. (1978) suggested V2K V2 viscosity. According to our experiment, K94 viscosity gives better forecasts than Smagorinsky's nonlinear viscosity (Gordon, 4) THE MOUNTAIN TREATMENT personal communication). A proper treatment of pressure gradient terms in the equations of motion in sigma-coordinate is es- 6) THE LAND-SEA DRAG AND THERMAL CONTRAST sential to the accurate inclusion of the topographic According to a sensitivity study on surface layer effect (Mesinger, personal communication; Kasa processes (Delsol et al., 1971), the land-sea contrast hara, 1977). In this respect, the 1967 version model of drag and thermal diffusion is most influential on may not be satisfactory (see Miyakoda, 1973). A the forecast of extended range, compared with other finite-difference treatment of the term of adiabatic processes such as the Monin-Obukhov process verexpansion/contraction (-wa) in the temperature sus the neutral process and the diurnal variability equation must be consistent with the formulation of versus the nondiurnal treatment. Garratt (1978) has the pressure-gradient terms (Corby et al., 1977). reviewed the observational data of the drag coeffiMoreover, Arakawa and Lamb (the following ma- cient, summarizing that the neutral drag coefficient terial that replaces Section III-C of their 1977 paper) re Cpy referred to 10 m/height is Cpx x 103 = 10 over ported that schemes of potential enstrophy con land and Cpx x 103 = 0.75 + 0.067 V over sea, servation are very effective for accurate inclusion where V is the wind speed (m s-?). Over mountainous of the effect of the large-scale mountain barrier, and areas, the form drag arising from flow over rugged suggested that the deficiency in the simulation of the topography is considerable, but the effect is not inultralong waves in conventional models may be rec cluded in CDx above. tified. Burridge and Haseler (1977) have already in Note that the impact of the differential drag on the corporated this feature in the model of the European large-scale flow is only appreciable on the forecasts Centre for Medium-Range Weather Forecasts, and beyond 6 days. the model was implemented for the test prediction of medium-range weather evolution (see Gauntlett 7) “MOIST CONVECTIVE ADJUSTMENT”' et al., 1977). Miyakoda (1975) made a comparison test by includ5) THE SUBGRID-SCALE VISCOSITY ing or excluding some processes in or from a pre diction model. The conclusion is that the water Smagorinsky's (1963) nonlinear viscosity has been vapor effect is very important in improving the used in our model. We found this viscosity is useful medium-range forecast. Heat released by condensabecause of the highly scale-selective dissipation par- tion activated the flow pattern and the forecast score ticularly compared with the formula KV2. A power- was thereby improved over the forecast without ful dissipation for the high-wavenumber flow is re- water vapor processes. quired to obtain an overall favorable forecast. For the parameterization of ensemble cumulus Francis (1975) demonstrated that the removal of convection, the moist convective adjustment scheme very small-scale disturbances allows more active has been incorporated in the 1967 version model. The scheme is a simple and reasonably good param- scheme, and concluded that the former produced eterization. Yet the “shocking” generated by the the shallower penetrative convection. Hollingsscheme seems harmful for the meteorologically sig- worth then suggested that this difference leads to a nificant part of numerical solutions, and the effect large impact on the baroclinic instability in the midmay be aggravated by use of the nonstaggered grid. dle latitudes. Hollingsworth (1977) pointed out that the scheme of moist convective adjustment produces a seem Page 10
Sahara desert, and the trough over the central U.S.S.R. spectral model is particularly good in the score of has been deepened by the new model. It is also về(Z - Zn). This is not inconsistent to the expectaimportant to note that the midlatitude westerlies no tion that the spectral model supposedly handles the longer extend into the tropics. vorticity calculation better. Previously, Gordon (1976) had made a preliminary comparison of a specc. Numerical approximation comparison tral model with a global finite-difference model (N 48) for one case of March 1965. Also, the rms In the following, in order to clarify the relative error of 500 mb geopotential in that test was meascapability of the 1967 version model, a comparison urably lower in the spectral model up to the tenth of this model with a recently constructed model, day. Simmons and Hoskins (1975) summarized their i.e., a spectral model, will be presented. It may be comparison experiments using a somewhat idealized interesting to see how a model which is free from initial condition, as that a spectral model gives a more some of the above deficiencies performs in short accurate representation of amplitudes and phases in range and medium-range forecasts. a growing wave than does a finite-difference model, The spectral transform model was constructed by but smaller scale changes such as those of frontal Gordon and Stern (1974) as a general circulation structure are resolved better by a finite-difference model based on Bourke's (1972) barotropic model, model. Baede and Hansen (1977) mentioned that in which uses the spherical harmonic functions as well comparative 10-day forecasts with the spectral and as the transform grid. Therefore, this model is en- grid-point models each with judicious space resodowed with the characteristics of enstrophy con- lution there is little to choose between the two servation for two-dimensional terms and of precise models, though anomaly correlation coefficients estimation of lateral pressure and geopotential gradi- suggests a slightly better performance of the grident terms in the equations of motion (however, the point model. Baumhefner and Downey (1978) contemperature in front of the term V Inps, where pg cluded from their study of model-intercomparison is the surface pressure, is free to be specified in that a spectral model (Canada) has good forecast the vertical). The space resolution in the spectral skill in large- and medium-scale baroclinic disturb model is “R30L9'', which means that the spectral ances. However, they also stated that the GISS representation is truncated in rhomboidal fashion finite-difference model is more capable of minimizof order 30 and that there are nine vertical levels. ing the error associated with planetary-wave feaThe rhomboidal truncation 30 means that M = J tures than the Canadian spectral model (the GISS 30 for m<J and n = \m| + J for Ym, i.e., model uses the Arakawa finite-difference scheme, , , the same wavenumbers are contained both for the i.e., quasi-enstrophy conservation using the B-lattice). zonal and meridional directions. The grid numbers at the so-called Gaussian latitudes between pole and 8. Conclusions equator is N = 40; this grid size corresponds to ~242 km. The physics in the spectral model are Application of the GFDL 1967 version prediction almost comparable to those in the 1967 version model to 12 summer cases and the analysis of the model except that the soil moisture has been improved and the land-sea drag contrast is included. resulting forecasts, together with the supplementary An example of the predicted geopotential height moisture and the comparative forecasts with a spec experimental prediction for the sensitivity of soil maps in both models is given in Fig. 23. The initial tral model, leads to the following conclusions: time is 1200 GMT 16 July 1968. It appears that the spectral model performs reasonably well, particu- 1) The July forecasts are overall poorer than the larly at day 8, and seems more skillful than the January forecasts. The prediction is inferior for the finite-difference model, although the difference is lower part of the troposphere, suggesting that the not large. The averaged skill scores for three cases physical effects near the earth's surface are complex also are shown in Table 3, where the initial times in summertime. for the additional cases are 3 July 1966 and 19 July 2) The prediction of the middle troposphere (say, 1969, both for 1200 GMT. The rms error of Z (geo- 500 mb height) in July is slightly worse up to 5 days potential height), the correlation coefficients for the than that in January. But the deterioration beyond height anomaly, and the correlation coefficients of 5 days is not severe; the rms skill score remains the Laplacian of height anomalies, V?(Z - Zn), are above persistence for the entire two-week period, shown for the hemisphere poleward of 20°N; they and the correlation for height anomalies stays above are slightly, but consistently, better in the spectral zero. The difference from the January case in this model than in the 1967 version finite-difference respect comes from the better forecast of the planemodel. On the other hand, the S1 score over the tary-scale waves. United States is worse in the spectral model. It may 3) The July stratospheric prediction was a combe interesting to note that the performance of the plete failure with the nine-level model. The tropo Page 11
Acknowledgments. The authors wish to thank tary boundary layer. Workshop on Micrometeorology, Drs. J. Smagorinsky and T. C. Gordon for valuable D. A. Haugen, Ed., Amer. Meteor. Soc., 271-311. Delsol, F., K. Miyakoda and R. H. Clarke, 1971: Parameterized discussions; Drs. W. Bourke, F. Mesinger and Mr. processes in the surface boundary layer of an atmospheric D. Baumhefner for criticism of the manuscript draft; circulation model. Quart. J. Roy. Meteor. Soc., 97, 181-208. and Dr. J. Brown for supplying the NMC program Druyan, L. M., R. C. J. Somerville and W. J. Quirk, 1975: Exto calculate the si skill score and Messrs. J. tended-range forecasts with the GISS model of the global Chludzinski, I. Shulman and W. Stern for program atmosphere. Mon. Wea. Rev., 103, 779-795. Egger, J., 1972: Numerical experiments on the cyclogenesis in ming and technical assistance. Gratitude is also ex- the Gulf of Genoa, Beitr. Phys. Atmos., 45, 320-346. pressed to Mrs. B. Williams, Messrs. P. G. Tunison Fjørtoft, R., 1953: On the changes in the spectral distribution and J. N. Conner for typing and graphical assistance. of kinetic energy for two-dimensional non-divergent flow. Tellus, 5, 225-230. Francis, P. E., 1975: The use of a multipoint filter as a dissipaREFERENCES tive mechanism in a numerical model of the general circula tion of the atmosphere. Quart. J. Roy. Meteor. Soc., 101, Arakawa, A., 1966: Computational design for long-term numeri- 567-582. cal integration of the equations of fluid motion: two-dimen- Garratt, J. R., 1977: Review of drag coefficients over oceans sional incompressible flow. Part I. J. Comput. Phys., 1, 119- and continents. Mon. Wea. Rev., 105, 915-929. 143. Gauntlett, D. J., D. M. Burridge and K. Arpe, 1977: Compariand W. H. Schubert, 1974: Interaction of cumulus cloud tive extended range numerical integrations with the E.C.M.W.F. ensemble with the large-scale environment, Part I. J. Atmos. global forecasting model 1: The N24, non-adiabatic experiSci., 31, 674-701. ment. Int. Rep. 6, Res. Dept., European Centre for Medium-, and V. R. Lamb, 1977: Computational design of the basic Range Weather Forecasts, Bracknell, U.K., 86 pp. dynamical processes of the UCLA general circulation model. Gordon, C. T., 1976: Verification of the GFDL spectral model. Methods in Computational Physics, Vol. 17, General Cir- Weather Forecasting and Weather Forecasts: Models, Sysculation Models of the Atmosphere, J Chang, Ed., Academic tems, and Users, Vol. 2, Notes from a Colloquium SumPress, 173-265. mer, 1976, conducted jointly by the Advance Study Program, Arpe, K., L. Bengtsson, A. Hollingsworth and Z. Janjić, 1976: Numerical Weather Prediction Project, and Environmental A case study of a 10-day prediction. Tech. Rep. No. 1, and Societal Impacts Group of the National Center for At- -, and W. Stern, 1974: Spectral modelling at GFDL. The Baede, A. P. M., and A. W. Hansen, 1977: A ten-day high- GARP Programme on Numerical Experimentation --Report puting Symp. Environmental Sciences, Thomas J. Watson Phillips, N. A., 1978: A test of finer resolution. Office Note 171, Research Center, Yorktown, NY, 195-210. Page 12
was selected based on the “highest probability” within the central computer system and the few mesrule. As indicated in the research methodology, the oscale predictors in the model can be easily derived, classification of intensity in the 10-year data sample utilizing the series of equations developed by Philwas based upon the maximum observed lake-effect lips (1972). The model will be further evaluated snowfall within the lake-effect snowbelt. Therefore, during the 1978–79 lake-effect snowfall season. It the forecasts generated during these two inde- is hoped that this model, or one similar to it, will be pendent winter seasons were for the maximum ex- considered for possible implementation within the pected snowfall to the lee of the lake. On this specific lake-effect snowbelt sometime in the near future. day, a maximum of 13 cm (5 inches) was observed to the lee of Lake Erie. Acknowledgments. Appreciation is extended to the entire staff of the Techniques Development Laboratory, National Weather Service, Silver 5. Verification of forecasts and evaluation of the model Spring, Maryland, for their assistance and the use of The observed snowfall amounts were made avail- their facilities in the development of this forecast able from the Environmental Data Service, National model. Climatic Center, Ashville, North Carolina, and were REFERENCES compared to the forecast snowfall amounts. It is difficult to measure the relative success of this fore- Baker, D., 1976: The mesoscale temperature and dewpoint cast product for there are no other operational lake fields of a very cold airflow across the Great Lakes. Mon. effect intensity forecast models available for com Wea. Rev., 104, 860-867. Dewey, K., 1975: The prediction of Lake Huron lake-effect parative purposes. A measure of this model's snowfall systems. J. Appl. Meteor., 14, 3-7. success can be illustrated, however, through a sub 1977: Lake-effect snowstorms and the record breaking jective evaluation of the forecast verifications. 1976-77 snowfall to the lee of Lakes Erie and Ontario. Table 3 illustrates that less than 17% of the veri Weatherwise, 30, 228-231. Eichenlaub, V., 1970: Lake-effect snowfall to the lee of the fications were more than one classification category Great Lakes— its role in Michigan. Bull. Amer. Meteor. from the predicted intensity of snowfall. And the Soc., 51, 403-412. forecast error exceeded two classification cate- Epstein, E., 1969: A scoring system for probability forecasts gories only 2% of the time. It is significant to of ranked categories. J. Appl. Meteor., 8, 985-987. note that on no occasion was there a complete Falconer, R. L., L. Lansing and R. Sykes, 1964: Studies of the weather phenomena to the lee of the eastern Great Lakes. failure of the model (i.e., a forecast of category 1 Weatherwise, 17, 256-261. with a verification of category 7). Although neither Jiusto, J. E., and M. Kaplan, 1972: Snowfall from lake-effect a forecast nor a verification of a 24 h snowfall storms. Mon. Wea. Rev., 100, 62-66. greater than 60 cm occurred during the two winter Lavoie, R. L., 1972: A mesoscale numerical model of lake-effect storms. J. Atmos. Sci., 29, 1025-1040. seasons, this intensity category was retained (and Miller, R. G., 1962: Statistical prediction by discriminant listed in Table 3) due to its occurrence within the analysis. Meteor. Monogr., No. 25, Amer. Meteor. Soc., 10-year data base. 1-54. Muller, R., 1966: Snowbelts of the Great Lakes. Weatherwise, 19, 248-257. 6. Conclusions Paine, D., and M. Kaplan, 1971: The linking of multi-scaled The last few years have seen the development and energy sources creating a severe local winter storm. Pre prints Seventh Conf. Severe Local Storms, Kansas City, partial implementation of Automation of Field Amer. Meteor. Soc., 299-306. Operations and Services (AFOS). Part of the func- Peace, R. L., and R. B. Sykes, 1966: Mesoscale study of a laketioning of the AFOS system will be the availability effect snowstorm. Mon. Wea. Rev., 94, 495-507. of minicomputer facilities within the individual fore- Phillips, D., 1972: Modification of surface air over Lake Ontario in winter. Mon. Wea. Rev., 100, 662-670. cast offices. This will allow the development of -, and J. Irbe, 1978: Lake to land comparison of wind, localized or regional forecast models which can be temperature and humidity on Lake Ontario during the utilized in the few regions where required without International Field Year for the Great Lakes. Atmospheric ying up the National Meteorological Center com Environment Service-Canada, Publ. CLI-2-77, 51 pp. Richards, T., H. Dragert and D. McIntyre, 1966: Influence of puter facilities. It is anticipated that there should atmospheric stability and over-water fetch on winds over be an improvement in forecast accuracy once these the lower Great Lakes. Mon. Wea. Rev., 94, 448-453. ocal and regional guidance products are made avail- Rieck, R., A. Sadowski, and J. Harrell, Eds., 1976: National ible within the AFOS system. There is no centrally Weather Service Forecasting Handbook No. 1—Facsimile produced lake-effect intensity guidance product. Products. U.S. Department of Commerce, NOAA, Washington, DC. Cherefore, the individual forecast offices have had to Strommen, N., 1975: Seasonal change in the axis of maximum ely on local experience for the forecasting of lake lake-snow in western Lower Michigan. Ph.D. dissertation, :ffect activity. The model described in this paper Michigan State University, 113 pp. an produce an automated forecast of lake-effect Page 13
modulated by traveling easterly waves (Burpee and composite radar echo distribution. The location of Dugdale, 1975; Aspliden et al., 1976; Reed et al., 1977; the cloud clusters as identified from satellite photos Payne and McGarry, 1977; Thompson et al., 1979), in Fig. 2 are also marked on Fig. 3. Practically no we shall also include in our description phases of radar echoes were observed at 1800 GMT 3 Septemthe 700 mb easterly waves over the A/B array for ber (Fig. 3a). The w distribution shows upward moeach of the six clusters under discussion. We use tion in the southeastern part of the A/B area with a Reed and Recker's (1971) terminology; wave cate- maximum w of -1.2 ub s-1. Clusters A and B formed gory 2 is centered on the region of the maximum in this upward motion area after 3 and 6 h, respecnorthly wind component, category 4 on the trough, tively, and the maximum w increased to –2.2 ub s-1 category 6 on the region of maximum southerly at 0000 GMT 4 September (Fig. 3b). The pattern component and category 8 on the ridge; categories of the w distribution stayed more or less the same in 1, 3, 5 and 7 occupy intermediate positions. the next 24 h, during which time the arch-shaped Fig. 2 shows the sequence of cloud activity as radar echo squall line cluster C moved through the seen in satellite infrared images. At 1800 GMT 3 southeastern part of the A/B area (Figs. 3c-3e). September, the area around the west edge of A/B At 0000 GMT 5 September (Fig. 3f), downward array was free of convection (Fig. 2a). A close in- motion occupied the southern half of the A/B area spection of hourly sequence satellite photographs where cluster C was in its decay stage. In contrast, reveals that cluster A was generated around 2100 the northern part of the A/B area showed strong GMT 3 September 60 km south of the ship Oceanog- low-level upward motion preceding the formation of rapher. It continued to develop in the next 3 h and cluster E and the advection of cluster D into this at 0000 GMT 4 September cluster B started to form area (Fig. 3g). The maximum w increased to more just west of cluster A (Fig. 2b). Both clusters A than -6 ub s-1 by 1200 GMT 5 September (Fig. and B were produced in the ridge area (wave cate- 3h) and the area of upward motion occupied almost gory 8) of the easterly wave passing through the the entire A/B area as clusters D and E intensiGATE A/B array area. fied. The low-level vertical velocity decreased Cluster A was decaying at 0600 GMT (Fig. 2c) rapidly during the next 6 h as clusters D and E as cluster B continued to enlarge and move west- entered their dissipation stage. The formation and ward. Cluster C was generated at 1200 GMT (Fig. 2d) intensification of cluster F during the period 0600– to the northeast of the A/B array and moved south- 1800 GMT 6 September was again accompanied westward. A detailed analysis of cluster C by Houze by low-level upward motion in the southern part of (1977) indicated that cluster C was a tropical squall the A/B area (Figs. 3j-31). line system consisting of a squall line along the lead- While the analysis scheme does not resolve any ing edge with a trailing anvil cloud region. Cluster divergence or vertical motion field with a scale 5400 C moved completely inside the A/B array area at km, the computed low-level upward motion area 1800 GMT (Fig. 2e). Cluster D, which formed does correlate with the area of radar echoes, as a around 2100 GMT to the east of A/B array, moved reasonable analysis scheme should. These results westward to the location at 9°N, 20°W at 0000 GMT also give a clear indication that the formation of 5 September. Two cloud bands formed in the next these cloud clusters are preceded either by meso3 h, one north of the Vanguard and the other over scale low-level convergence or by the enhancethe Gilliss and Quadra. Both lines became active ment of the low-level convergence. at 0600 GMT (Fig. 2g) and produced cluster E. Cluster D continued to develop and was connected c. The meridional cross section of w with cluster E at 1200 GMT (Fig. 2h). Both clusters D and E formed just west of the trough of a passing The w field, as described earlier, was computed easterly wave, in categories 2 and 3 of the easterly from the ocean surface to the 100 mb level at 25 mb wave. Cluster D gradually decayed after 1800 GMT intervals. The vertical distribution of w through the (Fig. 2i). The A/B area was clear when cluster F meridional cross section along 22°W is shown in formed near the Oceanographer and the Researcher Fig. 4 to compare the cross-sectional variation of at 0600 GMT 6 September (Fig. 2j), in wave cate- the w field with the convective activity. The reason gory 5. Cluster F intensified during the next 6 h for the selection of this longitude was the frequent (Fig. 2k) but weakened rather quickly after that convective activity observed along this cross sec(Fig. 21). tion for the period under consideration. At 1800 GMT 3 September (Fig. 4a) upward mob. A comparison of low-level vertical velocity with tion in the southern part of the A/B array was radar echo distribution confined only to low levels. As had been discussed earlier and shown in Fig. 2, cluster A did not develop Fig. 3 shows the horizontal distribution of the until 3 h later. At 0000 GMT 4 September (Fig. 4b), vertical velocity (w) at 900 mb superimposed on the the upward motion associated with cluster A and the Page 14
Fig. 4. Time sequence of the vertical velocity (ub s-') in the north-south vertical cross section through 22°W.
formation of cluster B already extended through the first observed on satellite pictures. Cluster C entire troposphere with a maximum velocity more entered the mature stage at 1800 GMT (Fig. 4e) and, than -3 ub s-l at 450 mb. The dissipation of at that time, the magnitude of the maximum verticluster A and the simultaneous enhancement of cal motion increased to more than -6 ub s-1 and cluster B at 0600 GMT (Fig. 4c) produced an w was located in the upper troposphere around 400 mb. distribution having the maximum vertical velocity By 0000 GMT 5 September (Fig. 4f), cluster C had around 700-800 mb layer. The maximum vertical almost passed the southern part of the cross section velocity had already reached more than - 4 ub s-1 of 22°W and entered its dissipation stage. Downward and was located around the 600 mb level at 1200 motion developed in the low levels while upward GMT (Fig. 4d), when the squall line cluster C was motion remained in the upper atmosphere. At the
fied by the anticyclonic outflow in the 200 mb level shown by Houze (1977, Figs. 5b-5c). Even though the intense convection of the squall line cluster C covered only part of the area being considered, its influence showed up in the vertical motions computed from the large scale data of A/B array. The vertical motion pattern sequence of the squall line cluster C was also similar to that of -1.5 clusters D and E, which were not squall lines. -1.5 0 1-2.0 -1.5 d. The area-averaged w The temporal variation of the area-averaged w for the period from 1800 GMT 3 September through 0000 GMT 7 September is shown in Fig. 5. The features in 5 and 6 September are quite similar to FIG. 5. Time-height cross section for the A/B-scale area-averaged those reported earlier by Nitta (1977). There are vertical velocity (ub s-'). several interesting features in Fig. 5. same time, upward motion was observed in the 1) There are three major upward motions during northern part, reflecting the advection of cluster D this period occurring at 1800 GMT 4 September, into the A/B array. 1500 GMT 5 September and 1200 GMT 6 September. The formation of cluster E and the enhancement As had been indicated earlier, these upward moof cluster D at 0600 GMT (Fig. 4g) produced an tions are associated with clusters C, D and F reintense upward motion with a maximum of more spectively. The maximum values of the area averthan -6 ub s-1 at 600 mb. Downward motion aged w associated with these clusters are -2.3, was observed both to the north and south sides of the -2.9 and -2.1 ub s-1, respectively. The correupward motion area. As cluster D continued to de- sponding maximum values of w shown in Fig. 4 at velop and merged with cluster E at 12 GMT (Fig. times close to the occurrence of these maxima w 4h), strong upward motion extended up to the 200 are -6.2, -5.2 and -4.2 ub s-1 at 1800 GMT 4 mb level. Cluster D was at its dissipating stage at September, 1200 GMT 5 September and 1800 GMT 1800 GMT (Fig. 4i). The low-level vertical velocity 6 September, respectively. Therefore the maximum had weakened considerably by this time while the value of w resolved by this analysis is approxiupward motion in the upper levels remained strong. mately 2-3 times the corresponding maximum No significant vertical motion was observed in the value of the area-averaged w. next 6 h. 2) The tilt sequence radar photographs showed At 0600 GMT 6 September (Fig. 4j), low-level that the area covered by very deep clouds associupward motion was present in the southern part of ated with the cluster F is less than that associated the A/B array. The location of the maximum upward with cluster D and E. This fact is reflected in the motion was approximately the location where vertical extent of the upward motion area shown cluster F formed. Cluster F intensified in the next in Figs. 4 and 5. 6 h and weakened rather quickly after that time 3) There are two maxima of w associated with (Figs. 4k-41). The magnitude of vertical motion cluster D. This was caused by the divergence at midassociated with cluster F was smaller and not well dle levels. The presence of a divergence layer cenorganized. tered at 500-600 mb levels, in addition to the These results indicated a distinct difference of the major outflow layer at 200–300 mb levels, is also mesoscale upward motion pattern during the de- evident at the developing and mature stages of the veloping, mature and dissipating stages of cloud life cycle composited by Frank (1978). In a case of clusters. Upward motion always existed in the lower weaker clusters such as cluster F, the low-level atmosphere during the developing stage and ex- convergence layer was capped by the divergence tended to the entire troposphere during the mature layer above. Thompson et al. (1979) noted that the stage. Downward motion started in the lower at- presence of middle-level divergence is evident even mosphere while upward motion remained in the in the mean state averaged over the entire Phase upper troposphere as clusters entered their dissipat- III period. ing stage. These differences were also observed 4) There is a weak descending motion in the layer in the composite cluster structure using B-scale 100–250 mb prior to the development of the major data by Frank (1978). The mesoscale upward motion upward motion. Frank (1978) also showed similar in the upper troposphere during the mature and the downward motion in the upper troposphere 3 h dissipating stages of cluster C was also exempli- before the first stage of the development of a com
Fig. 6 shows the thermodynamic structure of the atmosphere at the Oceanographer and the Poryv at 1800 GMT 3 September, a few hours prior to the formation of cluster A. The sounding at the Oceanographer indicates a very moist layer below 750 mb with relative humidity higher than 90%. Above this level moisture decreased rapidly with height, and the air was very dry in the layer between 700 and 550 mb. The temperature profile indicates a moist adiabatic lapse rate in the layer between 950 and 750 mb, and conditionally unstable between 750 and 550 mb. It was stably stratified above 450 mb. In contrast, the Poryv sounding indicates that a very stable layer was present around 800 mb. This stable layer was also observed at all A/B and B ships at this time except the Oceanographer and Researcher. Thus, the area near the Oceanographer already possessed the potential for the formation of a cloud cluster at that time. A close examination of the environmental conditions at 0300 GMT 6 September indicates that the predeveloping conditions for cluster F were quite similar to those for the clusters A and B. The conditionally unstable atmosphere was present in both cases with high moisture content at low levels in the area of the subsequent cluster formation. A stable layer was present near 800 mb in other areas. The surface wind field around the location of cloud cluster genesis was also quite similar to that at 1800 GMT 3 September. However, cluster F ultimately failed to develop into a cluster as vigorous as clusters D and E. This may give an indication that a favorable thermodynamic structure alone is not a sufficient condition for the subsequent growth of a strong cloud cluster.
f. A comparison of the estimated rainfall rate Earlier diagnostic analysis on cloud ensemble properties by Yanai et al. (1973) and by Ogura and Fig. 6. The vertical profiles of temperature and mixing ratio at Cho (1973) showed that the cloud ensemble ef 1800 GMT 3 September at the Oceanographer (a) and the fects can be estimated from larger scale upper air Poryv (b). and surface data. They designated the cloud heating and drying effects computed this way as Qi - Qx heat flux or the evaporation rate gives the estimated Qr and Q2, respectively. The vertical integration of precipitation rate [Eqs. (12)-(13), Yanai et al., either Q. - Qr or Q2 plus the appropriate surface 1973].
The horizontal distribution of precipitation rate resolution of vertical velocity, which was the was estimated in this analysis by vertically integrat dominant factor in the estimated rainfall rate, was ing the profiles of Q2. The Qi - Qr profiles were about 400 km. The spatial variation of the comnot used to avoid the uncertainty in Qr. The sur- puted rainfall rate therefore represents an average face evaporation rate was estimated from the bulk of a (400 km)2 area centered on the grid point. On aerodynamic formula using the mean hourly boom the other hand, the radar-estimated rainfall rate data on the Dallas, Gilliss, Oceanographer and has a resolution of about 30 km. The estimated Researcher. The drag coefficient was assumed to rainfall rate in this analysis, therefore, is not exbe 1.4 x 10-3. pected to correspond to the radar-estimated patTwo periods of the estimated rainfall pattern tern in every detail. However, as shown in Fig. 7a, (0600-1800 GMT 4 September and 0600-1800 the results of this analysis give heaviest precipitaGMT 5 September) average over 12 h are shown in tion in the southeast part of the B array during the Fig. 7. The average rainfall pattern estimated from period 0600-1800 GMT 4 September. This is acturadar data by Hudlow (1977) during these two ally in fair agreement with the radar-estimated patperiods are also shown in the same figure for tern in Fig. 7b. Little precipitation is observed in comparison. Only the estimated precipitation in the the northern part of the B array during this period in B array is shown here because the estimate from both Figs. 7a and 7b. During the period 0600-1800 radar is not available outside the B array. These GMT 5 September (Figs. 7c and 7d), there was heavy B two periods were selected due to the vigorous precipitation in the northern part of the B array in convective activity in these periods as shown both the rainfall estimates from radar and from this in Fig. 5. analysis. However, the analyzed results showed a Comparison of the rainfall rates estimated from smoother rainfall smoother rainfall pattern with the maximum radar and from this analysis must be done with centered at the northeast part of the Barray. caution. As discussed in Section 2, the horizontal The estimated rainfall rate from radar, on the other
the 3 h from 1800 to 2100 GMT, the convergence hand, had two maxima: one in the west part and the area moved toward the north and weakened. The other outside the northeast part of the B array. cloud activity also weakened. Calculated and radar-estimated rainfall are in agree At 0000 GMT 12 August (Fig. 10), the surface ment to the extent that neither show precipitation confluence line was oriented WSW-ENE in the over the southern part of the array. middle of the area occupied by the Oceanographer The overall pattern of the precipitation rate esti and Researcher. The convergence area was present mated in this analysis therefore agreed reasonably south of the confluence line, with the maximum well with the radar-estimated pattern. Small-scale value of -3.5 x 10-5 5-1. The flow was divergent variations of the radar-estimated precipitation did in the northern part of the A/B area. Deep clouds B not correspond well with the analysis. This dis- formed a line structure in the area of convergence. crepancy was expected due to the difference in the horizontal resolution in the two estimates.
This period was selected mainly because a wellorganized line of convection, which we refer to as the ITCZ rainband, developed near the surface confluence line on 12 August. The surface flow fields and the computed divergence prior to the organization of the ITCZ rainband are shown in Figs. 8-10. At 0600 GMT 11 August (Fig. 8), the confluence line was oriented east-west over the Researcher. A well-defined band of convergence with a width of 300 km was present along this line. The maximum convergence was -2.7 x 10-5 5-1 and scattered convective clouds were developing in this area of convergence. During the next 12 h, the convergence area moved slowly toward the south and the convergence strengthened. Correspondingly the convective activity also increased (Fig. 9). However, convective clouds observed at 1800 GMT did not develop to an organized convective system, in contrast to the situation on the next day. During
Page 15
of w in the lower troposphere during the dissipa- A and B formed in the wave ridge and cluster F tion stage was also observed. It is interesting to formed behind the wave trough. An inspection of the note that the patterns of the w-field during the surface weather maps indicates that clusters A, B developing, mature and dissipating stages of the and F formed to the south of the surface confluence ITCZ convection (Figs. 136-13c) were similar to line. So did the intense rainband described in secthe corresponding patterns of a squall line cluster C tion 4 (Fig. 10). Analyzing pre-GATE data, Sadler (Figs. 4d-4f) and of clusters D and E (Figs. 4g-4i) in (1975) concluded that the major convective cloudiprevious section. However, Fig. 13c may indicate ness was embedded in the westerly flow south of the limitation of spatial resolution in this analysis as the surface trough line. Estoque and Douglas (1978) well. The nearly homogeneous horizontal distribu- composited 25 cases during GATE Phase II referring tion of w in the southern side shown in Fig. 13c to the surface confluence line when the satellite is not realistic. The analysis of more dense surface images indicated that the ITCZ clouds were oriented data at 1200 GMT showed a reasonably concentrated a in long east-west line rather blob type clusters. convergence pattern beneath the convective area, They found a close correspondence between the as should be expected. maxima of cloudiness and measured precipitation, with both being about 1° south of the surface 5. Concluding remarks confluence axis. It is hoped that continuing analysis of GATE data will provide a better description of In this work, the divergence and the vertical organized convective systems and increase the velocity within the GATE A/B array were calculated understanding on the interaction between largefrom GATE surface and upper air wind data. Even scale fields and organized convective systems. though the data resolution limited the resolvable scale to 400 km, the results of the analysis showed a Acknowledgments. This work was supported good correlation between the vertical velocity field jointly by the National Science Foundation and the and the deep cloud activities as viewed by radar National Oceanic and Atmospheric Administration and infrared satellite images. In all cases considered, under Grants ATM73-00238 A04 and ATM78-11642. the mesoscale low-level convergence and, conse- The Research Board of the University of Illinois quently, upward motion was present or enhanced also provided computer support. prior to or at least in the initial stage of the development of convective systems. A low-level inversion REFERENCES was absent in the area of subsequent convective development in contrast to areas of no organized Aspliden, C. I., Y. Tourre and J. B. Sabine, 1976: Some climatoconvective activity. During the mature stage of logical aspects of West African disturbance lines during GATE. Mon. Wea. Rev., 104, 1029-1035. either a cloud cluster, a squall line or an ITCZ rain Burpee, R. W., and G. Dugdale, 1975: A summary of weather band, upward motion in the upper troposphere systems affecting western Africa and eastern Atlantic invariably increased in magnitude and became a during GATE. GATE Rep. No. 16, ICSU/WMO, Geneva, maximum in the profiles. They also show similar 2.1-2.42. Cline, A. K., 1973: Curve fitting using splines under tension. rapid decrease in upward motion in the lower tropo Almos. Tech., No. 3, National Center for Atmospheric sphere during the dissipating stage. Research, 60-65. The area of analysis is currently been expanded Cressman, G., 1959: An operational objective analysis system. to include data prepared by the Synoptic-Scale Mon. Wea. Rev., 94, 367-374. Subprogram Data Center. The purpose is to relate Estoque, M. A., and M. Douglas, 1978: Structure of the inter tropical convergence zone over the GATE area. Tellus, the convergence areas detected inside the A/B array 30, 55-61. to larger scale flows, with the hope of understand- Frank, W. M., 1978: The life-cycle of GATE convective systems. ing the processes responsible for generating con- J. Atmos. Sci., 35, 1256-1264. vergence. Modulation of convective activity by Houze, R. A. Jr., 1977: Structure and dynamics of a tropical squall-line system. Mon. Wea. Rev., 105, 1541- 1567. travelling easterly waves has been convincingly Hudlow, M. D., 1977: Precipitation climatology for the three established (Burpee and Dugdale, 1975; Aspliden phases of GATE. Preprints Second Conf. Hydrometeorolet al., 1976; Reed et al., 1977; Payne and McGarry, ogy, Toronto, Amer. Meteor. Soc., 290-297. 1977; and other contributions presented at the Martin, D. W., 1975: Characteristics of west African and AtGATE Workshop, 25 July-12 August 1977 at the lantic cloud clusters. GATE Rep. No. 14, WMO, Geneva, 182-192. National Center for Atmospheric Research). There Nitta, T., 1977: Response of cumulus updraft and downdraft are other processes to be considered which give rise to GATE A/B-scale motion system. J. Atmos. Sci., 34, to low-level convergence. One of them is the possi- 1163-1186. Page 16
a. Subcloud wind components the directional change from westerly to easterly Before examining the wind and moisture condi- during the day appears well-established before the tions on days preceding and following hail and com usual onset of large clouds. This strongly sugparative no-hail days, it is informative to examine gests that the forcing in this instance was not due the variation of subcloud wind components ob- primarily to the influence of local convection. The served at Sterling during the day of the event. Fig. 2 main effect of storm-scale convection in the late shows the evolving vertical profiles of mean u afternoon upon the environment, near the surface, and v component wind speeds associated with the very likely would be westerly and northerly outconvective activity categories previously defined. flow. Yet such an effect is not apparent, in the mean, These have been averaged over all three NHRE for the hail cases at 2300 GMT (1700 MDT in hail seasons, 1972-74, and the number of cases in Fig. 2). This suggests that any local convection each category is listed in Table 1. Increasing con did not dominate the soundings in this respect. vective activity is shown ranging from clear day The v component wind speed profiles shown on cases in the top row to hail day cases at the bottom. the right-hand side of Fig. 2 exhibit a more southerly The times indicated by the coding in the legend trend as convective activity increases. The thunderof Fig. 2 are local times (Mountain Daylight Time), storm and hail classes have a distinct southerly comand may be converted to GMT by the addition of 6 h. ponent, whereas the remaining classes have mean Immediately apparent in the left-hand side of northerly or nil component. The difference between Fig. 2 is a diurnal trend of the mean u component the mean hail and no-hail v wind components late in . direction from westerly to easterly as the day pro the afternoon is statistically significant at the 0.5% ceeds. This trend is apparent in all classes of con level of significance. vective activity depicted, except perhaps the rain The terrain surrounding Sterling is essentially flat shower days. A diurnal reversal of low-level wind to the south and east. The land rises gradually to direction has long been noted in the sloping plains the west and also to the north, where it intersects east of the Rockies. Bleeker and Andre (1951) an escarpment of 150 m height lying along the inferred such an east-west pattern from the diurnal Nebraska border (about 40 km north of Sterling). oscillation of divergence aloft. Bonner and Paegle This feature does not directly affect wind direction (1970) and Paegle and Rasch (1973) modeled measured at Sterling (see Fig. 1). diurnally varying boundary layer winds over sloping Considering both components, the prevailing terrain and obtained realistic results (see also wind direction at Sterling for the clear, cumulus Blackadar, 1957; Hoecker, 1965). congestus and rainshower convective classes is The diurnal trend of the u component in Fig. 2 of westerly to northwesterly. Also, the mean wind the present work is most prominent on mean hail speed for these classes shows a tendency to diminish days (bottom row). A stronger easterly component, during the 1400–2300 GMT period. The wind direcwhich sharply distinguishes these days from the tion is mainly southwesterly to southeasterly for mean no-hail days, especially in the afternoons, the thunderstorm and hail cases, with a tendency begins developing early in the day. The resulting for the mean wind speed to increase during these difference in the u component wind speed between days. It is possible to infer the associated synoptic u mean hail and no-hail cases is strongest at the sur regime from these wind directions, but not potential face, while apparently little difference exists be moisture advection. The moisture present at Stertween them at the level of the mean cloud base. In ling in the subcloud layer in the late afternoon of terms of statistical significance, at 25 mb above the the day of the event is shown in the next section. surface at 2300 GMT, there is less than one chance in a thousand of the indicated difference arising b. Subcloud mixing ratio purely by chance. The convection during the later portion of the day Fig. 3 shows vertical profiles of subcloud mixing may have influenced these winds, but the trend of ratio at Sterling in the late afternoon for the five cate Page 17
Great Plains region, often accompanying cyclo- Acknowledgments. The author thanks Carl Mohr, genesis east of the Rocky Mountains. The approach Gretchen Jahn and Barbara Horner for their proor development of such systems in association with gramming contributions to this study; Dale Nieman hailfall in northeast Colorado can also be inferred and William Cobb for their assistance with the procfrom the mean divergence and positive vorticity essing and analysis of data; and Griffith Morgan, advection aloft reported by Modahl (1979). Alex Long and Andrew Heymsfield, as well as the The primary importance of the low-level southerly anonymous reviewers, for their helpful reviews of wind patterns over the Plains lies in the moisture this manuscript. The NCAR Graphics Department advection. The moisture transport may be consider- staff and Steve Connolly of NHRE are also thanked ably enhanced by the low-level jet suspected to be for their preparation of the figures. embedded in this circulation (e.g., Means, 1954; Pitchford and London, 1962; Bonner, 1968). There are yet other implications for hail-bearing storm REFERENCES occurrence and behavior: 1) the circulation could Beckwith, W. B., 1960: Analysis of hailstorms in the Denver serve to enhance baroclinity; 2) lifting through up- network, 1949-1958. Physics of Precipitation, Geophys. slope, easterly component movement could further Monogr. No. 5, Amer. Geophys. Union, 348–353. reduce airmass stability; 3) the circulation could Blackadar, A. K., 1957: Boundary layer wind maxima and their significance for the growth of nocturnal inversions. Bull. provide the large moisture supply required for mas Amer. Meteor. Soc., 38, 283–290. sive, long-lasting storms which form in northeast Bleeker, W., and M. J. Andre, 1951: On the diurnal variation of Colorado and travel eastward through the night; precipitation, particularly over Central United States, and 4) the advection of modified-maritime airmass and its relation to large-scale orographic circulation systems. aerosols may have further implications for cloud Quurt. J. Roy. Meteor. Soc., 77, 260-271. Bonner, W. D., 1968: Climatology of the low-level jet. Mon. microphysics. Wea. Rev., 96, 833-850. winds over the south-central United States in summer. 4. Conclusions Mon. Wea. Rev., 98, 735–744. Browning, K. A., and G. B. Foote, 1975: Airflow and hail The environmental settings of low-level wind and growth in supercell storms and some implications for hail moisture content preceding, attending and follow- suppression. Quart. J. Roy. Meteor. Soc., 102, 661-695. ing hail and no-hail days in northeast Colorado Crow, E. L., P. W. Summers, A. B. Long, C. A. Knight, G. B. Foote and J. E. Dye, 1976: Final Report, National Hail undergo distinctly different patterns of evolution. Research Experiment Randomized Seeding Experiment On hail days, a strong upslope surge of shallow, 1972-74, Vol. I, p. 11. (Available from the National low-level easterly flow develops which is signifi- Center for Atmospheric Research, Box 3000, Boulder, CO cantly larger than that developing on no-hail days. 80307). The low-level winds also increase from a southerly Hoecker, W. H., 1965: Comparative physical behavior of southerly boundary-layer wind jets. Mon. Wea. Rev., 93, direction, beginning as much as 24–36 h in advance 133-144. of hail occurrence in the NHRE region. The low- Longley, R. W., and C. E. Thompson, 1965: A study of the level winds also tend to increase from a southerly causes of hail. J. Appl. Meteor., 4, 68-82. direction prior to hail-less thundershowers, but with Madden, R., E. Zipser, E. Danielsen, D. Joseph and R. Gall, out, in the mean, development of a strong easterly 1971: Rawinsonde data obtained during the Line Islands Experiment. NCAR TN/STR-55, Vol. 1. [Available from the component. Southerly winds appear to diminish National Center for Atmospheric Research, Box 3000, sharply or become northerly during the 12-24 h Boulder, CO 80307). after the end of a hail episode. Preceding and dura Mahrt, L., 1977: Influence of low-level environment on severity of High Plains moist convection. Mon. Wea. Rev., 105, ing comparative periods of insignificant convection, 1315-1329. the low-level winds are westerly to northwesterly. Means, L. L., 1954: A study of the mean southerly windLow-level moisture content in the mean appears to maximum in low levels associated with a period of summer change gradually, in concert with the pattern of precipitation in the middle west. Bull. Amer. Meteor. Soc., southerly and easterly winds prior to hail, and change 35, 166-170. Modahl, A. C., 1979: Synoptic parameters as discriminators little, if at all, prior to comparative no-hail periods. between hailfall and less significant convective activity in Synoptic features are clearly associated with pro northeast Colorado. J. Appl. Meteor., 18 (in press). nounced convection—thunderstorms and hail — in Morrissey, J. F., and F. J. Brousaides, 1970: Temperaturethe NHRE region, and there is indication that meso induced errors in the ML-476 humidity data. J. Appl. scale features in the u component wind field may Meteor., 9, 805-808. Paegle, J., and G. E. Rasch, 1973: Three dimensional charbe unique to hail occurrence. The results in this acteristics of diurnally varying boundary layer flows. Mon. paper point to the need for a more detailed study Wea. Rev., 101, 746-756. of the low-level wind and moisture settings and their Palmén, E., and C. W. Newton, 1969: Atmospheric Circulaevolution. Soundings at 3 h intervals on a 24-hour tion Systems, Their Structure and Physical Interpretabasis along a cross section from the Rockies east Page 18
4. Eyewitness observations Eyewitness accounts and photography collected FIG. 8. The track of the east Tulsa tornado and the locations from the public confirmed our radar-based impres- of photographs, the National Weather Service (NWS) Office and sions of these storms. Storm C's passage through downtown Tulsa. Okmulgee was variously reported as a brief rainshower or the fall of just a few large raindrops. remained on the foundations of some houses were Tornado photographs taken from different angles the carpet and the bed frame; the walls and roof indicate very little precipitation falling from the base had been deposited a short distance away in the of the cloud. Photographs also show that the tornado direction of translation. Other houses still had inapparently formed from a shallow flanking cloud terior walls or plumbing fixtures intact (Fig. 9). As line behind the main cumulonimbus (Fig. 7). Bates far as we could tell, all the debris was displaced (1968) also observed tornadoes pendant from downstream (relative to tornado translation). On flanking cloud lines. the fringes of the path, there were a few signs of Fig. 8 shows the track of the tornado which struck low-level radial inflow (such as the direction from east Tulsa and the camera sites for photography col which sheet metal had been wrapped around trees). lected by us from the general public. All photog A swimming pool, which lay in the midst of the raphers, including No. 7 who was 8 km northwest worst damage, suffered no detectable water loss and No. 9 who was 7 km west-southwest, had from the tornado passage. clear unobstructed views of the tornado. Only Photography (Fig. 10) shows that the tornado's light rain fell at all the photographers’ locations life cycle was similar to that of the Union City either just before, during or immediately after the tornado (Moller et al., 1974; Golden and Purcell, tornado. Near the path, 0.5-2 cm hail fell at points 1978). Debris started rising from the surface before 2, 3 and 6 before the tornado. Baseball-size hail the condensation funnel reached the ground. The was reported in downtown Tulsa (13 km west). At mature stage was marked by maximum funnel size. location 7 and the National Weather Service Office, 5 cm stones fell while the tornado was in progress. Photographs reveal a dark precipitation shaft northeast of the tornado; in all other directions little precipitation is visible. These observations are consistent with the absence of a hook echo on the WSR-3 radar. Thus, visual evidence and eyewitness reports confirm that 1) the tornadoes occurred on the rear flanks of the storms, and that 2) little precipitation was falling from Storm C around 1630.
5. Tornado-scale features
Although its path was short (2.5 km) the Tulsa tornado severely damaged brick houses, a church, theater, shopping center and apartments. All that
Fig. 9. Damaged house in Tulsa. Page 19
ди δυ 1 + = lim k.v X dr, (1) B' where A = SSsdo is the area of the surface S, k a unit vector normal to S, do a differential surface area, Fig. 2. Geometric configuration for three different methods of and dr the differential of the position vector along evaluating the line integral definitions (see text for details). the curve I which bounds S and lies in the horizontal plane. In applying the differential definition to real ing between rawinsondes over the contiguous data, many problems arise. As pointed out in Sec- United States). tion 1, interpolation of winds to a uniform grid is a The vertical component of vorticity can be siminon-unique process. Further, a conventional cen- larly defined through an integration procedure: tered difference always underestimates the true derivative (via multiplication by a diffraction func av au 1 Š = k·V X v = lim $ v•dr. (2) tion, as shown by Hamming (1962, p. 318)]. A ax ду A → A third error source stems from the limited accuracy of the data itself. Morel and Necco (1973) have Since the rotation of wind vectors 90° to the right shown that the total uncertainty of the computa- produces a wind field with vorticity equal to the tion can be greater than 100%. divergence of the original field (Saucier, 1955, p. The integral definition eases these constraints. 339), comments on the divergence estimates are Since line integrals are being evaluated, an initial directly applicable to vorticity, and evaluation interpolation of the winds is not necessary. Rather, techniques are similar. it is assumed that an individual wind measurement represents an average value along a portion of the b. Method of evaluation path of integration. Also, the “roughing” inherent Bellamy (1949) has developed a method of estiin numerical differentiation is replaced by the mating divergence via an integral technique. For "smoothing” of integration. However, the increased the curve T, a triangle is selected with vertices at the number of “data points” available (Ceselski and wind observation points (points A, B, C, in Fig. 2). Sapp, 1975) allows a compensating resolution in The winds are then allowed to displace the vertices crease in the interpolated fields. While there is still for a time interval dt. Since divergence is equal to uncertainty in the computations, Eddy (1964) has the percentage increase in area enclosed by the concluded that the noise level in the meteorologi curve per unit time, an estimate of its value is cally important part of the spectrum is significantly immediately obtained. This method assumes that the less than the true value. It must be pointed out that wind varies linearly along each leg of the triangle. the limit in the defining equation implies that the Under the linearity assumption, a direct evaluacomputed divergence is the average value within the tion of the line integrals in Eqs. (1) and (2) is possible. spatial curve considered and not a true point value. The mean wind along each leg of the triangle is Thus, a horizontal scale is attached to each esti- considered to be the component average of the mate. Morel and Necco (1973) have shown that the values at the two vertices. It is informative to note spectrum is adequately measured for wave lengths that this divergence estimate differs from that obgreater than about 400 km (the approximate spac- tained by the Bellamy method. Direct evaluation of the line integral yields a change in area equal to the hatched portions in the figure. The Bellamy method А B considers not only this expansion, but also an addi tional area around each vortex (stippled portions of Fig. 1. Schematic example of non-uniqueness problem figure). The magnitude of the difference between in vector interpolation. these results is directly proportional to the time increment dt chosen for the Bellamy method. As filtering and smoothing to the interpolation scheme st approaches zero, the two methods converge to used to grid the randomly spaced data, where the the same answer. Page 20
b. Variational adjustment of a preliminary wind [{ – k:V x vjdơ analysis By making an adjustment to a preliminary wind dt. analysis (generally obtained via component inter (21) an polation), it is possible to obtain a final wind field that has the “measured” divergence and vorticity That is, the difference between the measured dicontent. At the same time, the difference between vergence (or vorticity) and that obtained via difthe preliminary wind analysis and the final result ferentiation of the wind field is totally contained in is also minimized. This adjustment can be cast as a the normal derivative of 12 (or ^,) across the boundvariational problem (Sasaki, 1970). The required ary, or equivalently in the change of the normal (or functional is tangential) wind component at the boundary. Thus, Neumann conditions require a preknowledge of the J 2 \,: V wind field along the boundary. Additional elucidation of the boundary conditions + 12(7.v – D)]do, (12) comes from the requirements that where: v(x,y) final analyzed horizontal vector wind y Vlado V(x,y) preliminary horizontal vector wind Š(x,y) measured vertical component of vorticity FĎ(x,y) measured horizontal divergence [2(v – V) – k x ^,]do ) λι, λ, Lagrange multipliers. After setting the first variation of Eq. (12) to zero Vido and applying Green's theorem, the Euler-Lagrange (EL) equations are found to be lindt. (23) v – ý = 12[V/2 + k x 14,1, ) (13) V•v = s, (14) Eqs. (22) and (23) emphasize that the two Lagrange multipliers are not independent; the specification of k:7 x v = ]. (15) one multiplier along the boundaries puts internal The associated natural boundary conditions (NBC) restrictions upon the other multiplier. This suggests that use of any exotic boundary specification for the multipliers may be self-defeating. Consequently, lov•dt = 0, (16) the simplest specification which satisfies the NBC, i.e., λι |r = λα(r = 0, 12 r = 0 (24) 12k.dv x dt = 0. 0 (17) seems to be reasonable. The implications of this boundary condition can be seen by noting that By combining Eqs. (13), (14) and (15), it is found Eq. (13) requires that the Lagrange multipliers must satisfy V21, = 2[Ě – k:7 x v], (18) 122[k X ] V212 = 2[Ď - •v]. (19) 2ndt + 112 lidt. () The problem reduces to solving Eqs. (18) and (19) under the constraints of the NBC [Eqs. (16) and (17)]. Thus, when condition (24) is used, the total areaThere are myriad potential ways that the NBC can averaged velocity of the final wind analysis is equal be satisfied. However, by considering the integral to that of the preliminary one. This restriction is constraints upon the system, the options become not as harmful as it first appears since, at the expense limited. First note of noise in the analyzed field (and thus the derived
= [ {kx [2(v – ) – TA]}do = 4 Page 21
Table 2. Statistical error analysis comparison between Gauss- where m is the metric coefficient determined by the ian interpolation and variational adjustment of divergence and analysis grid geometry. These are Poisson equavorticity. tions for the wind components and can be numeriVariational cally solved under the restrictions of the NBC. wind adjustment Gaussian The NBC will be satisfied when either Algebraic Algebraic X / (31) All data points (73) interior to domain or dvlr = 0. (32) u-component 0.47 0.20 0.53 0.00 v-component 1.80 0.48 1.21 0.02 Because of the interrelationship between V•v and Speed 1.06 0.63 0.79 -0.34 k:x v, Eq. (31) does not provide viable boundary Vector 1.86 1.56 1.32 1.15 conditions. Thus, solution requires condition (32). This will be satisfied if the winds along the boundary Excluding data within one grid increment of boundary, 62 data points remain are specified via an independent analysis. The validity of this wind retrieval technique is u-component 0.45 0.24 0.51 0.01 tested using the same experiment employed in the v-component 1.67 0.50 1.18 -0.11 Speed 1.01 0.63 0.79 -0.40 last section. The pattern in the analyzed comVector 1.73 1.47 1.28 1.13 ponent fields is similar to that of the analytically defined data. Fig. 11 shows the retrieved v-comExcluding data within two grid increments of boundary, ponent; this should be compared to Fig. 10a. Gradi51 data points remain ents in the retrieved field are quite similar to those u-component 0.37 0.24 0.49 -0.03 which actually exist. However, definite discrepancies U-component 1.60 0.65 1.24 -0.05 between the defined field and the analyzed field are Speed .99 0.66 0.85 -0.43 present, especially near the boundaries. Error Vector 1.64 1.39 1.34 1.20 statistics obtained by comparing the analyzed field to the observations for this method and for Excluding data within three grid increments of boundary, the Gaussian component analysis scheme are given 46 data points remain in Table 2. As the domain of comparison is moved u-component 0.35 0.24 0.48 -0.06 away from the boundary (Shukla and Saha, 1974), v-component 1.33 0.40 1.27 -0.07 the variational technique improves relative to the Speed 0.84 0.55 0.85 -0.50 Vector 1.38 1.22 1.36 1.21 standard method. The vorticity of the final wind analysis is shown Page 22
Atlantic Hurricane Season of 1978
Miles B. LAWRENCE
(Manuscript received 29 January 1979)
A summary of the 1978 Atlantic hurricane season is presented including detailed accounts of individual storms. There were 11 named storms this year of which five reached hurricane force. Three storms made landfall along the Gulf of Mexico coastline, two in the United States and the other in Mexico. Hurricane Greta affected portions of Central America.
1. General summary to speculate on the combined effect of the absence of hurricane activity and the dramatic population Eleven systems were named as tropical storms increase along our coastline. It is this writer's during the 1978 hurricane season, and five of these opinion that the prolonged absence of a major became hurricanes. Tracks and summaries of these hurricane, in the long run, is not a state of affairs storms are given in Fig. 1 and Table 1, respectively. about which a community should be excessively In addition, there was one unnamed subtropical storm during January 1978, also included in the grateful, because the resultant apathy might be a major factor in a future hurricane disaster. track chart and summary table. The trend in operational hurricane track foreSix of the 11 named storms originated from casting at the National Hurricane Center has been a tropical waves which moved off of the African coast. The other five were initiated as baroclinic develop- track forecasting has not improved at a rate subject of concern in recent years. It appears that ments, i.e., old cold fronts, upper level cold lows, etc. commensurate with advances in computer techComparison of this season's statistics to long-term nology, satellite observations, etc. Verification averages indicates a slightly higher-than-normal statistics for 19782 continue to support the notion number of storms for 1978. In contrast, there were that, at best, forecast accuracy remains on the 307 hurricane hours in 1978, where a hurricane hour is counted for each hour that a storm has wind speeds plateau reached in the early 1970's . While there is no single, simple explanation for > 64 kt. The 30-year average is 620 hurricane hours. this situation, one topic that appears to be quite Thus, while there were more individual storms than normal, the amount of time during which hurricane- meteorological fields on the synoptic and hurricane relevant concerns the operational analysis of various force winds were present was far less than normal. storms made landfall along the coastline of the objective analysis of the 500 mb geopotential height Inspection of Fig. 1 shows that three tropical scales, in the vicinity of a given storm. In particular, the National Meteorological Center's western Gulf of Mexico. Except for extreme rain- fields are of great concern. These fields are used as fall over central Texas from the remnants of Tropical input data to all of the operational statistical-synoptic Storm Amelia, there were no other noteworthy and statistical-dynamical prediction schemes for events in connection with these storms. Hurricane Greta raked over the sparsely populated utilized as the primary synoptic guidance by the tropical cyclone track forecasting. These are also northeast coast of Honduras with 115 kt winds, but hurricane forecaster. Therefore, any degradation of the storm's intensity diminished to below 100 kt by the accuracy of these height fields will have an the time of landfall in Belize. Limited damage reports adverse impact on the prediction schemes. indicate that this was not a disastrous storm. The U.S. East Coast and most of Florida have been spared from a major hurricane for many 2 A comprehensive evaluation of hurricane forecasting accuyears, and this year was no exception. It is interesting racy at the National Hurricane Center is contained in a report Page 23
A point of interest is that Cora was identified 1831 08A078 14A-H 05311 29761 MA14N43W-1 as a tropical storm and then a hurricane solely on the basis of satellite pictures. Maximum wind speed and minimum pressure obtained from satellite intensity classification techniques were 80 kt and 980 mb during the period 0000–0600 GMT 9 August. Hurricanes Doris and Gladys in 1975 are the only other Atlantic storms to have been upgraded to hurricane status based on satellite pictures alone. (Operational reconnaissance procedures restrict the use of aircraft during times when a storm is far out at sea and does not pose an immediate threat to land.) Rapid dissipation as Cora moved into the southeast Caribbean is not an unexpected event in this area. The entrainment of continental air from South America limits convective processes in the storm and strong tradewind easterlies produced by the geographic heat low disrupts the low-level circulation. Large-scale criteria were generally favorable otherwise for intensification, and yet the circulation Fig. 6. Visible satellite picture of Cora at 1831 GMT 8 August 1978 completely disappeared within 24 h, which indicates from GOES 2 (12 n mi resolution). the significance of continental influences. There have been no reports of damage or casualties in connection with this storm. near the point of landfall. Twenty-five kt winds were reported from Tampico and Tuxpan on 7 August as the center approached the coast. Satellite data d. Tropical Storm Debra, 26–29 August indicated that rainfall associated with this storm decreased rapidly after landfall. There have been The origins of Debra can be traced to an upper neither casualties nor significant damage attributed tropospheric low-pressure system which formed over southwest Florida on 25 August. For 36 h, this to Bess. low drifted southwestward, reaching a position just c. Hurricane Cora, 7-11 August north of the Yucatan Peninsula, simultaneously penetrating down into the lower troposphere. A weather disturbance moved off of the African Meanwhile, cloudiness, which appeared to be coast on 4 August. It continued westward along the associated with a tropical wave, moved from the intertropical convergence zone for two days; then northwest Caribbean to the vicinity of the Yucatan a circular cloud mass shifted northward and devel- Peninsula. This cloudiness interacted with the lowoped into a tropical depression. This depression level vorticity center generated by the low from intensified to tropical storm strength on 8 August Florida, resulting in the formation of a tropical at a location almost 1000 n mi west of the Azores. depression at 1200 GMT 26 August, at a position The storm further intensified to a hurricane later ~400 n mi south of New Orleans. the same day. This is based on satellite pictures This depression first moved toward the west and that indicated the formation of an eye. One of these then northward as the western extension of a highpictures is shown in Fig. 6. Cora was now moving pressure ridge weakened over Texas and Louisiana. on a course slightly south of due west at about Slow strengthening occurred and the system was 20 kt and this motion continued as the storm moved upgraded to Tropical Storm Debra at 1800 GMT on into the extreme southeast Caribbean. the 28th on receipt of reconnaissance data of 40 kt On 9 August, Cora weakened while still east of the surface winds. Debra was an immediate coastal Lesser Antilles. The first reconnaissance flight into threat and gale warnings were posted from Galveston, Cora took place on the afternoon of the 9th and Texas, to Grand Isle, Louisiana, issued at 1800 GMT 55 kt winds were the highest measured. The on the 28th. weakening trend continued and squalls to around The storm's maximum intensity (50 kt surface 40 kt were reported on the islands of Barbados and winds and 1000 mb central pressure) was reached St. Lucia as Cora crossed the Windward Islands at 0000 GMT 29 August, just before landfall. Fig. 7 on the 10th and 11th. On the 11th, Cora lost all shows Debra's appearance while approaching the evidence of circulation and was downgraded to a coast and it is evident from the picture that this tropical wave. It continued into the southwest was not a particularly well-defined cloud system. Caribbean and dissipated. In addition, most of the high winds associated Page 24
with the storm were found well east of the center. 1831 28A078 14A-H 03371 13701 MA27N92W-1 Automatic observation stations mounted on offshore platforms in the Gulf of Mexico measured sustained winds of 40-45 kt for several hours, as Debra passed 100–150 n mi to the west. Fig. 8 depicts low-level winds measured by a NOAA aircraft flying through the storm (note that the maximum winds are displaced some 1.5° of longitude from the circulation center). After moving onshore, Debra accelerated northnortheastward across west central Louisiana and into Arkansas, where the residual low-pressure system combined with a frontal trough on 29 August. The resulting frontal wave was tracked across the Ohio Valley for the next three days. Tides in connection with this storm ranged from 1 ft above normal at Corpus Christi to 2.2 ft at Galveston and 4-5 ft on the Louisiana coast from west of Atchafalaya Bay through Vermilion Bay. The greatest total rainfall reported was 10.81 inches at Freshwater Bayou Lock, Louisiana. Fig. 7. Visible satellite picture of Debra at 1831 GMT 28 August Amounts of 6 inches or more occurred in southwest 1978 from GOES 2 (1/2 n mi resolution). Louisiana, southwest Mississippi, Arkansas, and later in southern Missouri and Illinois, as the remnants of Debra became a frontal wave. A Atlantic Ocean. On 28 August, within this previously summary of the meteorological storm data is given baroclinic zone, satellite pictures suggested a in Table 3. cyclonic turning of low-cloud elements at a position Tornados occurred in Texas, Louisiana and , ~500 n mi southeast of Bermuda. Ship and Mississippi. One death was attributed to the satellite data allowed the determination that a Mississippi tornado and another death was reported tropical depression had formed at this location by to have occurred on an offshore oil rig. Total 0000 GMT 30 August. storm damage caused by Debra is considered to The depression headed toward the west-northwest be minimal. An estimated 3000 or more persons at a speed of 10–15 kt along the periphery of the were evacuated from low-lying coastal sections of Atlantic subtropical high-pressure ridge. A ship Louisiana. report of 47 kt wind just north of the center at 2000 GMT on the 30th indicated that tropical storm e. Hurricane Ella, 29 August-5 September intensity had been reached several hours earlier. Ella's formation occurred within a decaying, Almost 24 h later, another ship reported a sea quasi-stationary frontal zone over the central North level pressure of 980 mb and 70 kt winds, which Page 25
1831 290C78 14A-H 03342 19922 MA27N73W-1 Kendra is shown in Fig. 17 while located just east of the northern Bahamas. But by late on the 30th, Kendra encountered strong upper level westerlies, which separated the dense convection from the low-level circulation. Weakening ensued and Kendra was downgraded to a tropical storm at 0000 GMT 31 October. A few hours later, surface winds had decreased to below gale force, and there was little tropical cloud structure in evidence. However, a 1008 mb surface low persisted and accelerated northeastward. This low deepened on the next day, under the influence of a strong upper trough moving off of the U.S. East Coast. The system was finally absorbed by another extratropical low over the northeast North Atlantic. Gale warnings were required along the North Carolina coast on the 30th and 31st, as a result of the interaction between Kendra and an intense polar anticyclone over the northeast United States. Significant damage from this storm was restricted Fig. 17. Visible satellite picture of Kendra at 1831 GMT to the predepression stage, which produced the 29 October 1978 from GOES 2 (12 n mi resolution). heavy rains over Puerto Rico, 12 inches in the Ponce area and 18 inches in the Humacao area of southern By this time, however, there was no longer any Puerto Rico. There was one death and about 1000 evidence of a surface circulation near the area of families sheltered. Newspaper reports listed damages the storm remnants. at about $6 million, all water-related. No death or damage reports have been received in connection with Juliet. 3. Subtropical storm of 18–22 January k. Hurricane Kendra, 28 October-3 November There was one system identified as a subtropical storm during 1978. It occured in January and historical Disturbed weather was observed over the eastern records (Neumann et al., 1978) indicate that this is Caribbean for several days during late October. the first time that a tropical or subtropical cyclone Some locations in Puerto Rico measured over 18 of at least storm intensity formed in this month (a inches of rain during the period 22–27 October. A tropical wave which left the African coast on 15 October reached the eastern Caribbean on the 21st 1531 21 JA78 14A-1 and appears to have been a factor in initiating this 03261 25241 MB21N57W-1 persistent weather disturbance. Concurrent with the activity described above, cloudiness associated with an old frontal zone slipped southward to merge with the rain-producing system in the general vicinity of Puerto Rico. Eventually, the disturbed weather shifted northwestward and satellite pictures showed a very concentrated convective area to the north of Hispaniola during the night of 27–28 October. During 28 October, subsequent pictures revealed increasing organization. A depression developed just east of the Bahamas that afternoon. Kendra was named as a tropical storm at 0000 GMT on the 29th. This is based on satellite imagery as well as a ship report of 999 mb and winds to 60–70 kt. Hurricane status was reached on the afternoon of the 29th, when a reconnaissance plane estimated 70 kt surface winds. There was little change in strength during the next Fig. 18. Visible satellite picture of unnamed subtropical storm at 24 h as the hurricane moved north-northeastward. 1531 GMT 21 January 1978 from GOES 2 (1 n mi resolution). Page 26
formance of formula (3) on data for 1970–77 is that Table 5. Errors in hindcasting using Eq. (4). Year Error those during 1970–77. Support for this hypothesis 1949 6.1 1964 4.3 may be found by comparing the statistics of H for the 1950 -1.6 1965 6.3 two periods (Table 4). The probability is less than 1951 -0.8 1966 5% that a mean of a sample of eight, differing 1952 2.2 1967 -13.9 by 11.6 or more from 55.2, could arise from a 1953 - 15.3 1968 4.2 population defined by the data for the period 1949– 1954 4.1 1969 11.2 69. The standard deviation for the later period was 1955 18.0 1970 2.5 substantially higher, mainly due to the occurrence of 1956 -1.0 1971 - 13.5 4.8 1972 two years (1973 and 1977) that were drier than the 1958 1973 - 20.9 driest year in the earlier period. Winter 1978 (not included in the analysis) was comparable in dryness 1959 -0.9 1974 -3.3 1960 -3.1 1975 19.0 to 1973. These results suggest that the rainfall data 1961 4.9 1976 - 14.9 for 1970–77 belong to a significantly different 1962 -4.3 1977 -21.2 population than those for 1949-69. 1963 The multiple-regression analysis was repeated using the whole period 1949–77. The mean value of H was 52.0 and its standard deviation 15.3, and the best relationship was given by 3) Statistical relationships, even of high signifi cance, may be of little help in providing predicH = 51.6 + 1.1(S, -S3) – 0.8(S3 - S6) – 0.6S3, tion formulas because of artificial predictability and changes in physical influences from one period to 0.74. ) (4) another. This is similar to (3), except that Sg is now making a significant contribution, which is not surprising in Acknowledgments. I thank Klaus Wyrtki, Tom view of the evidence from earlier work cited. But Schroeder and Bernard Meisner for comments. This the total contribution of all three factors is much less research has been supported by the National Science than for the period 1949–69. When we examine the Foundation as part of the North Pacific Experiment values of the errors for each year when Eq. (4) is of the International Decade of Ocean Exploration. used (Table 5), we find that there were nine years in This support is gratefully acknowledged. which the error was greater than nine units, and seven of these occurred in the last 11 years. The chi REFERENCES squared test shows that this distribution would occur Davis, R. E., 1976: Predictability of sea surface temperature by chance on only 1% of occasions. This result and sea level pressure anomalies over the North Pacific provides further support for the hypothesis that the Ocean. J. Phys. Oceanogr., 6, 249-266. SST gradients in the North Pacific that were im- Fishing Information, 1973–1977: U.S. Department of Commerce, Southwest Fisheries Center, La Jolla, CA. portant factors in Hawaiian winter rainfall in the Markham, C. G., and D. R. McLain, 1977: Pacific sea-surface 1950's and 1960's were relatively much less im- temperature related to rain in California. Nature, 269, portant in the 1970's. 501-504. Meisner, B. N., 1976: A study of Hawaiian and Line Islands 6. Conclusions rainfall. UH-MET 76-04, Dept. of Meteorology, Uni versity of Hawaii, 83 pp. 1) Hawaiian winter rainfall was closely related to Murdoch, J., and J. A. Barnes, 1968: Statistical Tables for two sea surface temperature differences in the North Science and Engineering. Macmillan, 32 pp. Namias, J., 1972: Large-scale and long-term fluctuations in Pacific during the 1950's and 1960's, and less some atmospheric and oceanic variables. Nobel Symposium closely related also to the equatorial east Pacific 20, D. Dyrssen and D. Jagner, Eds., Wiley, 27-48. SST. These relationships imply physical linkages; Newell, R. E., and B. C. Weare, 1976: Ocean temperatures future studies of atmospheric circulations may help and large-scale atmospheric variations. Nature, 262, 40-41. us to understand these linkages. Ratcliffe, R. A. S., and R. Murray, 1970: New lag associations 2) The relationships with the SST differences between North Atlantic sea temperature and European were much weaker in the 1970's. This implies that pressure applied to long-range weather forecasting. Quart. the physical influences on Hawaiian winter rainfall J. Roy. Meteor. Soc., 96, 226-246. were quantitatively different. This “climatic change” Wright, P. B., 1977: The Southern Oscillation: Patterns and |
Which of the following are sources of computational error in computer model forecasts?
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