GSI/WRF Regional Data Assimilation System and Its Application in theWeather Forecasts over Southwest Asia - Data Assimilation for Atmospheric, Oceanic and Hydrologic Applications - page 605

the SD error is computed as

"

X i X 0 2 # 1=2

N X

1
N

SD D (25.3)

i D 1

In ( 25.1 , 25.2 ,and 25.3 ), N is used rather than N-1 so that a decomposition following
Murphy ( 1988 , eq. (9)) could be applied to the MSE:

MSE D .X 0 / 2 C . / 2 SD (25.4)

Therefore, the total mo del forecast error (e.g. MSE) consists of contributions from
model squared biases

.X 0 / 2 (i.e., systematic error) and squared standard deviation

. / 2 error (i.e., nonsystematic error) in the forecast and observed data. A fraction

is defined to indicate the ratio of systematic error in the total model forecast error as
follows:

SD

E r D .X 0 / 2 =

MSE 100 % (25.5)

In ( 25.5 ), note that if the model bias is less than 50 %, most of the MSE is due to
random, nonsystematic type variability in the errors.

25.5 Forecast Error

Similar to Air Force Weather Agency's (AFWA) operational setup, a 15-km grid
spacing centered over the Southwest Asia (SWA) region (Fig. 25.1 )isusedto
encompass the regions complex topography and associated spatial variability in
surface characteristics. To assess model predictive skill, 48-h (hour) forecasts are
made for each day starting at 00Z for the period of May 1 through May 31, 2006.
Forecasts without data assimilation are labeled CTRL in order to distinguish them
from the forecasts with data assimilation found in Sect. 25.6 . The initial atmospheric
and lateral boundary conditions, including soil moisture and temperature, are
taken from the NCEP Global Forecast System (GFS) real time forecasts with 3-h
intervals, which is gridded to a horizontal resolution of 1 ı 1 ı . Through the WRF

Preprocessing System (WPS), the global soil categories, land use categories, terrain
height, annual mean deep soil temperature, monthly vegetation fraction, monthly
albedo, maximum snow albedo, and slope category are interpolated into the model
grids of the study domain. The physics packages used in the CTRL forecasts are
the WRF Single Moment 5-class (WSM5) microphysics scheme, Yonsei University
planetary boundary layer (YSUPBL) scheme, Noah land surface scheme, Grell-
Devenyi ensemble cumulus scheme, Rapid Radiative Transfer Model (RRTM)
longwave radiation, and the Dudhia shortwave radiation scheme.