From the sensitivity studies performed with the Goddard Laboratory for Atmospheres (GLA) analysis/forecast system, it was revealed that the forecast errors in the tropics affect the ability to forecast midlatitude weather in some cases. Apparently, the forecast errors occurring in the tropics can propagate to midlatitudes. Therefore, the systematic error analysis of the GLA forecast system becomes a necessary step in improving the model's forecast performance. The major effort of this study is to examine the possible impact of the hydrological-cycle forecast error on dynamical fields in the GLA forecast system

Baker, Wayman E.

Chen, Tsing-Chang

Corrigan, Martin

Pfaendtner, James

English

NASA Technical Reports Server

d a RIM 
A STUDY MIR SYSTJMTIC ERRORS 
OF THE GLA FORECAST MODEL IN TROPICAL REGIONS ,& - 4’7 e z/2 
Tsing-Chang Chen, Department of Geological and Atmospheric Sciences, Iowa /f3-07& 
State University; Wayman E. Baker and James Pfaendtner, Laboratory for 
Atmospheres, Goddard Space Flight Center; Martin Corrigan, Department of 
Geological and Atmospheric Sciences, Iowa State University tl\ i 
1. 1-ION 
From the sensitivity studies performed by Baker and Paegle (1983) and 
Paegle and Baker (1983) with the Goddard Laboratory for Atmospheres (GLA) 
analysis/forecast system (Kalnay et al., 1983), it was revealed that the 
forecast errors in the tropics affect the forecastability of midlatitudes in 
some cases. Apparently, the forecast errors occurring in the tropics can 
propagate to midlatitudes. Therefore, the systematic error analysis of the 
GLA forecast system becomes a necessary step in improving the model’s forecast 
performance. Our major effort of this study is to examine the possible 
impact of the hydrological-cycle forecast error on dynamical fields in the 
CLA forecast system. 
. 
Twenty-eight 5-day forecasts were performed every two days for both 
Special Obse.rvating Periods (SOP). 
started from OOOOGMT January 5, 1979 and those of SOP!2 from OOOOGMT May 1, 
1979. The initial conditions of these forecast experiments are provided by 
the GLA FGCE III-b analyses (Baker, 1983). The analysis scheme employs a 
successive correction method of the Cressman (1959) type, modified to account 
for differences in data density and statistical estimates of the error 
structure of the observations. Nonlinear normal mode initialization is not 
used in the GLA forecast system, but 8 Matsuno (1966) time-differencing 
scheme is adopted to control the inertial gravity waves excited by the 
imbalance between the mass and motion field. 
The forecast experiments of SOP1 
The ensemble averages of 28 forecasts will be used to illustrate the 
forecast errors. 
3. SURFACE BALANCE AND HYDROWGICAL CYCLE 
After Day-1, the surface heat budget of forecasts (Table la) becomes 
relatively stable in time f o r  both SOP’S. Although the surface shortwave and 
longwave radiation are larger than their annual-mean climatic values, the sum 
of these two surface radiation components results in a smaller net surface 
radiation than climate. Climatologically, the surface (sensible + latent) 
heat flux should be balanced by the net surface radiation. 
computational errors into account, the model’s net surface heat flux is 
small. 
By taking 
The GLA hydrological cycle forecasts of both SOP’S are shown in Table 
https://ntrs.nasa.gov/search.jsp?R=19890005280 2020-03-20T05:02:02+00:00Z
lb. 
smaller than the climate inferred from Jaeger's (1983) estimation of 
Precipitation. The precipitation forecasts significantly exceed the 
evaporation forecasts. Even the hydrological cycle of Day-5 forecasts still 
does not reach equilibrium. During the rpinup of the hydrological-cycle 
forecasts, the sop2 precipitation forecasts exhibit an overshooting at Day-1. 
The GLA forecast system does not employ the nonlinear normal mode 
initialization nor the shallow cumulus convection. The Arakawa's (1972) 
cumulus convection scheme is used in this model. However, the characteristics 
of the GLA hydrological cycle forecasts are also common to the forecast model 
of the European Center for Medium Range Weather Forecast (ECIWWF) analyzed by 
Heckley (1986). 
The global-mean evaporation over the entire forecast period is slightly 
4 .  FORECAST ERRORS OF ZONAGllEAN STATES 
Since the forecasted precipitation exceeds the forecasted evaporation, 
it is expected that the forecasts would become too dry. As shown by the 
Day-5 forecast errors of the zonal-mean specific humidity (qz) (Figure la) 
during SOP2, the middle and lower troposphere are dried out and the planetary 
boundary layer is moistened. The major precipitation exists in the tropics. 
The overforecasted precipitation of both SOP'S also occurs there. Therefore, 
a warm bias of the zonal-mean temperature (TZ) forecasts may be caused by the 
latent heat released by the overforecasted cumulus convection activities over 
the tropics. 
our argument. 
particularly. the midlatitudes of the winter hemisphere. According to the 
thermal wind relationships, the zonal-mean zonal wind (Uz) should also be 
overforecasted in midlatitudes. 
forecast errors during SOP2 behave in a relatively systematic manner. 
low-level tropical eas terl ies and midlat i tude wester 1 i es are over f orecas t ed, 
whi 1 e the high-la t i tude wester 1 i es are under f orecas t ed . 
The Day-3 TZ forecast errors during SOP2 (Figure lb) confirms 
The north-south TZ gradients are also overforecasted, 
As exhibited in Figure IC, the Day-3 Uz 
The 
Our previ,ous study ( m e n  and Baker, 1986) suggested that the atmospheric 
diabatic heating maintains the tropical divergent circulation. The time 
evolution of the forecasted tropical divergent circulation may follow that of 
the precipitation forecasts shown in Table 1. As revealed from the Hadley 
cell portrayed by the mass flux function (#z = J'ooo mb vZdP) forecasts 
P 
(Figure 21, the overshooting of precipitation forecasts reflects in the 
maximum intensity of Hadley cell at Day-1 forecasts. 
Day-5 forecasts, the intensity of Hadley cell becomes weaker when the forecast 
time extends. To be more quantitative, the forecast errors of the zonal-mean 
meridional wind (Vz) show that the southerly and northerly anomalies appear, 
respectively, in the lower and upper tropical troposphere of Day-1 forecasts. 
Evidently, Hadley cell is overforecasted at Day-1. In contrast, the 
upper-level northerly anomalies are replaced by southerly and the lower-level 
southerly anomalies disappear in Day-5 forecasts. This implies that the upper 
branch of Hadley cell is underforecasted at this time. 
By comparing Day-1 and 
Except for the Precipitation and $z overshooting in the sop2 forecasts, 
the salient features of the q,, uz, TZ and V 
to SOP1 forecasts. 
forecast errors are also common z 
5 .  FORECAST ERRORS OF HORIUlNTAL FIELDS 
In accordance with the zonal-mean divergent circulation depicted above, 
the 200-mb divergent circulation [(VDlxv) (200 mb)l forecasts of SOP2 are 
shown in Figure 3. At Day-1 forecasts, three divergence centers are located 
over three tropical continents. The most dominant is the divergent 
circulation associated with the monsoon region. The clear divergent center 
over Central and northern South America at Day-1 forecasts is replaced by a 
relatively weak convergence center at Day-5 forecasts. This significant 
change of divergent circulation explains why the upper branch of Hadley cell 
is underforecasted at this time. Some previous studies, e.g., Silva Dios et 
- al. (1983) demonstrate that the diurnal cycle of cumulus convection is vital 
in maintaining Bolivian high. It seems that the diurnal cycle of the GLA 
cumulus convection scheme over this region does not effectively play its 
designated role. 
the underforecast of east-west Walker circulation. 
The [(VD,xv)(200 mb)] forecast errors during SOPl exhibit 
The major precipitable water (W) exists in low latitudes, particularly 
over three tropical continents and along the ITCZ. The Day-5 W forecast 
errors (Figure 4a) show that the W underforecast previously pointed out occurs 
over the entire tropical global belt between about 30's and 30'N. The 
significant W forecast error over high mountains may be attributed to 
erroneous data. The W underforecast is caused by the precipitation 
overforecast. The water balance equation 
indicates that the precipitation (P) overforecasts should be supported by the 
overforecast of convergence of water vapor flux. 
the divergent component (Q ) and potential function ( x  1 of water vapor flux D 8 
are introduced in Eq. (1). The Day-1 forecast errors of (Q , x  1 (not shown) 
show that the precipitation overshooting corresponds to the overforecast of 
convergence of water vapor flux toward tropical continents and ITCZ where the 
major precipitation exists. After this overshooting, the convergence of water 
vapor flux toward the Asian monsoon region and the region around Central and 
northern South America is underforecasted (Figure 4d). This drastic (Q x 1 
D' Q 
forecast change agrees with that of (VD,xv)(200 mb) shown previously. During 
SOPl, the W forecast errors behave similarly, as those during SOP2 and the 
(Q x 1 forecast errors correspond to the underforecast of east-west Walker 
circulation. 
To facilitate discussion, 
D Q  
D' Q 
Yanai et a l .  (1972) demonstrated that the tropical water vapor and heat 
budgets are closely related to each other through the latent heat. 
positive values of T(300 mb) forecast error (Figure 4c) and tropical 
convergences of (Q , x  ) forecast error for SOPZ Day-5 forecasts are 
relatively consistent. 
heat released due to the precipitation overforecasts is responsible for these 
T(300 mb) forecast errors. 
The 
D Q  
This consistency indicates that the excessive latent 
The comparison between the SOPZ Day-5 U(200 mb) forecasts (not shown) 
and the forecast errors (Figure 4d) shows that either jet streams themselves 
or the equatorward sides of jet streams are overforecasted. "he contrast 
between positive forecast errors of T(300 mb) and U(200 mb) ( F i g .  4d) that the 
thermal wind relationship holds between them indicates this. 
During the forecast spinup, the thermal wind relationship is reached 
through the adjustment by ageostrophic circulation. This physical adjustment 
can be realized through the generation of kinetic energy by ageostrophic flow 
(-V*V+) which is roughly balanced by the divergence of kinetic energy flux 
[-Ve(Vk)]. Their relationship is essentially the kinetic energy equation 
The divergent component [(Vk)DJ and potential function (xm) of kinetic 
energy flux are used. 
side and diverged to the downstream side of the jet where the kinetic energy 
is destroyed by ageostrophic effect. The SOPl Day-5 forecast errors of k(200 
mb) (Figure 5a) are consistent with the observation of the U(200 mb) forecast 
errors shown in Figure 4c. 
(Figure 5b) are opposite to the SOP1 Day-5 (VklD(2O0 mb) forecasts (not 
shown). This situation indicates that the thermal field forecast errors 
possibly alter the ageostrophic circulation forecasts in such a way that the 
generation of kinetic energy in the upstream side is underforecasted. 
Therefore, there is less kinetic energy transported to the downstream sides of 
jet streams to be destroyed. 
The kinetic energy (k) is generated in the upstream 
The SOPl Day-5 forecast errors of (VklD(2O0 mb) 
The tropical divergent circulation is maintained by the diabatic 
heating. In turn, the precipitation forecast errors can cause the divergent 
circulation forecast errors. The planetary-scale interaction between 
divergent (V,) and rotational (V,) may offer another possible adjustment 
process causing the forecast errors of jet streams. Following Chen et al. 
(19881, the interaction between these two flow components can be understood 
through the kinetic energy equations of divergent (kD) and rotational (kR) 
flows: - - vD.V+ , (% equation) ( 3 )  
positive errors of C(%,kR)(2O0 mb) forecast mean that the excessive kD(200 
mb) is converted to maintain the excessive kR(200 mb). 
existing between the U(200 mb) and C(k,,,kR)(200 mb) forecast errors indicates 
that the U(200 mb) forecast errors are possibly caused by those of divergent 
circulations. 
Some consistency 
5. CONCLUDING RWARRS 
The GLA forecast system does not employ nonlinear normal mode 
initialization nor the shallow cumulus convection scheme. The cumulus 
convection scheme proposed by Arakawa (1972) is adopted in this model. The 
systematic errors of thermal and dynamical fields in the GLA forecast system 
differ from those of the ECMWF forecast model, but the GLA's deficiencies of 
moisture and precipitation forecast are common in the ECMWF forecast model 
(Heckley, 1985). According to Tiedtke et al. (19881, the incorporation of a 
shallow cumulus convection is most vital to the improvement of the ECMWF 
forecast performance over the tropics, The impact of the shallow cumulus 
convection on forecasts is one of the future efforts which should be pursued 
in the GLA forecast system. 
6. ACKNOWLEDGEMEXI'S 
This study is supported by the NASA Grant NAG5-355. 
References 
Arakawa, A., 1972: Design of the UCLA general circulation model. Tech. Rpt. 
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Baker, W. E., 1983: Objective analysis and assimilation of observational 
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Chen, T.-C., 1985: Global water vapor flux and maintenance during W E .  
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J. Atmo8. Sci . , 30, 611-627. 
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A study for systematic errors of the GLA forecast model in tropical regions

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