Development and Application of an Evaluation Method for 

the WRF Mesoscale Model 

by Teizi Henmi, Robert Flanigan, and Richard Padilla 

ARL-TR-3657 September 2005 

Approved for public release; distribution is unlimited. 
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ARL-TR-3657 September 2005 

Development and Application of an Evaluation Method for 

the WRF Mesoscale Model 

Teizi Henmi, Robert Flanigan, and Richard Padilla 

Computational & Information Sciences Directorate 

Battlefield Environment Division 

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Development and Application of an Evaluation Method for the WRF Mesoscale Model 

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6. AUTHOR(S) 

Teizi Henmi, Robert Flanigan, and Richard Padilla 

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U.S. Army Research Laboratory 

Computational and Information Sciences Directorate 

Battlefield Environment Division (ATTN: AMSRD-ARL-CI-EM) 

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Approved for public release; distribution is unlimited. 

13. SUPPLEMENTARY NOTES 

14. ABSTRACT 

This report establishes automated methods of obtaining and archiving initialization and time-dependent lateral condition data for the Weather 

Research and Forecast (WRF) mesoscale model. The data includes Eta forecast data, MADIS surface data, and upper-air sounding data. 

Statistical analysis methods that compare surface and upper-air data between model calculation and observation have also been established 

and are described in detail. In this study, the WRF was applied to model domains surrounding the National Training Center in southern 

California. A set of 24-hr forecast data of 2-way, coupled domains (with grid resolutions of 18 and 6 km) were statistically compared with 

surface and upper-air observation data. 

15. SUBJECT TERMS

mesoscale, statistical evaluation, WRF 

16. SECURITY CLASSIFICATION OF:

19a. NAME OF RESPONSIBLE PERSON

Teizi Henmi 

a. REPORT 

U 

b. ABSTRACT 

 U 

c. THIS PAGE 

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17. LIMITATION 

 OF 

 ABSTRACT 

SAR 

18. NUMBER 

 OF 

 PAGES 

36 19b. TELEPHONE NUMBER (Include area code) 

505-678-3519

Standard Form 298 (Rev. 8/98) 

Prescribed by ANSI Std. Z39.18 

ii 
Contents 

List of Figures iv

Summary 1

1. Introduction 3

2. Model Domains and Physics 4

3. Data 5

3.1 Input Data 6 

3.2 Data for Comparison 7 

3.2.1 Surface Data 7 

3.2.2 Upper-Air Sounding Data 7 

4. Reading WRF Output File 7

5. Analysis Program 9

5.1 Wind Velocity Components 9 

5.2 Height 9 

5.3 Temperature 10 

5.4 Dew-Point Temperature 10 

5.5 Rotating Horizontal Wind Vector Components 11 

6. Comparison with Observed Data 12

6.1 Surface Data 12 

6.2 Upper-Air Data 13 

7. Statistical Comparison Program 16

7.1 Surface Data 16 

7.2 Upper-Air Data 17 

8. Comparison Results 18

8.1 Surface Data 18 

iii 
8.2 Upper-Air Data 21 

9. Summary and Conclusion 24

References 25

Acronyms 26

Distribution List 27

List of Figures 

Figure 1. WRF model domains covering the NTC in southern California.......................... 4 

Figure 2. The locations of Eta grid data (*), surface observation data from the 

Meteorological Assimilation Data Ingest System (MADIS) (S), and upper-air 

sounding data (U) in the model domains. ...................................................................... 6 

Figure 3. A script file designed to read a WRF output file in netCDF format and 

convert it into ASCII format.......................................................................................... 8 

Figure 4. Horizontal and vertical grids of the WRF. ........................................................... 9 

Figure 4. An example of surface data comparison. ........................................................... 13 

Figure 5. An example of a vertical profile comparison between observation and 

model forecast data ...................................................................................................... 14 

Figure 6. Vertical profiles of temperature and dew-point temperature for upper-air 

sounding data and WRF forecast data for station DRA at 1200 UTC, 23 February 

2005.............................................................................................................................. 15 

Figure 7. Same as figure 6, except for wind speed and wind direction. ............................ 15 

Figure 8. A time-series of MD, CC, and AD for temperature. .......................................... 18 

Figure 9. Same as figure 8, except for dew-point temperature.......................................... 19 

Figure 10. Same as figure 8, except for wind speed. ......................................................... 20 

Figure 11. A time-series of RMSVE and MWDDF for domains 1 and 2. ........................ 21 

Figure 12. Vertical profiles of MD for temperature, dew-point temperature, and wind 

speed for station NKX for a 12-h forecast period........................................................ 22 

Figure 13. Vertical profiles of AD of temperature, dew-point temperature wind speed, 

and wind vector components, u and v, for station NKX for a 12-h forecast period. ... 23 

iv 
Summary 

This report establishes automated methods of obtaining and archiving initialization and 

time-dependent lateral condition data for the Weather Research and Forecast (WRF) 

mesoscale model. It also establishes statistical analysis methods that compare WRF 

forecast data with observation data. 

The WRF was applied to the model domains surrounding the National Training Center in 

southern California. A set of 24-h forecast data of 2-way coupled domains (with grid 

resolutions of 18 and 6 km) were statistically compared with surface and upper-air 

observation data. For surface temperature, domain 2 (6-km grid resolution) produced 

better statistical agreements with the observation data than domain 1 (18-km grid 

resolution). 

For dew-point temperature, there were no significant differences between time-series of 

statistical parameters for domains 1 and 2. For wind speed and vectors, domain 1 

produced statistically better agreements between calculation and observation than 

domain 2. 

Vertical profiles of meteorological parameters were also compared between calculation 

and observation. From that, the following could be inferred: 

• The mean absolute difference (AD) of temperature was about 2 °C throughout the 

model’s vertical depth. 

• The ADs for dew-point temperature were substantially greater than 2 °C. 

• The ADs of wind speed were 5 m/s or greater, but gradually increased with height. 

There were no systematic biases in vertical profiles of temperature, dew-point 

temperature, and wind speed. 

1 
INTENTIONALLY LEFT BLANK. 

2 
1. Introduction 

The Weather Research and Forecast (WRF) model is a weather forecasting system with 

fully compressible, non-hydrostatic equations. The WRF version 2 has multiple-nesting 

capability with one-way and two-way coupling. Details of the WRF version 2 have been 

described by Skamarock et al. (2005). 

In a previous study (Henmi, 2004), forecasting skills of surface meteorological 

parameters of two mesoscale models, the Mesoscale Model Version 5 (MM5) and 

WRF version 1.3, were statistically evaluated over two different geographical areas: Utah 

and western Texas. A triple-nested MM5, with grid resolutions of 45, 15, and 5 km, 

respectively, was used over the Utah area. The WRF version 1.3, which does not have 

multiple-nesting capability, was used with a 5-km grid resolution. Over the Utah domain, 

the WRF domain covered an area similar to the MM5 domain 3. 

Using the 40-km Eta forecast data freely available from the National Center of 

Environmental Prediction (NCEP), forecast calculations of both the MM5 and the WRF 

were carried out and the results were compared with surface observation data. 

Both models tended to over-forecast temperature and dew-point temperature, although 

the correlation coefficients between forecast and observation were fairly high. The 

statistical parameters for the MM5 were slightly better than those for the WRF. For both 

the MM5 and the WRF, the statistical parameters for wind vector components were 

inferior to those of temperature and dew-point temperature, although the WRF values 

were slightly better than the MM5 values. 

For this study, the model domains of the WRF were set over the area surrounding the 

National Training Center (NTC) located in southern California (figure 1), in order to 

accomplish the following objectives: 

1. To develop the methods for using and statistical evaluating the WRF. 

2. To make a statistical comparison between the WRF forecast output of 

domains 1 and 2 for surface and upper-air meteorological parameters. 

3 
2. Model Domains and Physics 

WRF double-nested computational domains, depicted in figure 1, were used. 

Figure 1. WRF model domains covering the NTC in southern California. 

Both domains are centered at 35.30° N. and 116.63° W. Domain 1 has 55-by-55 grid 

points with an 18-km grid resolution, and domain 2 has 61-by-61 grid points with a 6-km 

grid resolution. Two-way coupling is used. 

The WRF can use a number of different physics options. For this study, the following 

physics options were used: 

• Planetary boundary layer (PBL): A new scheme, known as the Yonsei University 

PBL, was used. It has an explicit representation of entrainment at the PBL top, 

which is derived from large eddy simulation modeling. This scheme partially 

corrects the problem of too much entrainment in the early phase of PBL growth and 

also adds non-local momentum mixing to provide a realistic wind profile in the 

PBL (Dudhia, 2004). 

• Precipitation parameterization: The WRF single-moment three-class was used 

(Hong et al., 2004). In this scheme, the ice crystal number concentration is 

dependent on ice mass content rather than temperature, giving realistic ice crystal 

concentrations and sizes that are compatible with the fall speeds. 

4 
• Cumulus parameterization: A modified version of the Kain-Fritch (1990, 1993) was 

selected. This scheme utilizes a simple cloud model with moist updrafts, including 

the effects of detrainment, entrainment, and cloud microphysics. A minimum 

entrainment rate is imposed to suppress widespread convection in marginally 

unstable, relatively dry environments. Shallow (non-precipitating) convection is 

allowed for any updraft that does not reach minimum cloud depth for precipitating 

clouds; this cloud depth varies as a function of cloud-base temperature. In this 

version, the entrainment is allowed to vary as a function of low-level convergence. 

• Radiation parameterization: For long-wave radiation, the rapid radiative transfer 

model (RRTM) (Mlawer et al., 1997) was used. The RRTM is a spectral-band 

scheme that uses preset tables to accurately represent long wave processes due to 

water vapor, ozone, CO2, and trace gases (if present), as well as accounts for cloud 

optical depth. For short-wave radiation, a scheme based on Dudhia (1989) was 

used. 

• Ground temperature scheme: The five-layer, soil temperature model used in the 

MM5 was used for the WRF as well. 

3. Data 

The following datasets are necessary for forecast computation in the WRF and for 

comparison with the model output. Automated methods to obtain and archive data have 

been developed. 

5 
Figure 2. The locations of Eta grid data, surface observation data from the Meteorological 

Assimilation Data Ingest System (MADIS), and upper-air sounding data in the 

model domains. 

NOTE: * = Eta grid data, S = surface observation data, and U = upper-air sounding data. 

Terrain contour lines are drawn at every 200 m in height. 

3.1 Input Data 

Forecast data by a large-scale forecast model are required for initialization and timedependent lateral condition data to run the WRF. 

An automated method to obtain and archive the 40-km Eta (now North American 

Mesoscale (NAM)) model data in a gridded binary (GRIB) format was developed, and 

the data was archived for future use. The data are freely available from the NCEP FTP 

site: ftpprd.ncep.gov. 

6 
3.2 Data for Comparison 

3.2.1 Surface Data 

Hourly surface meteorological data are obtained from the Meteorological Assimilation 

Data Ingest System (MADIS) of the National Oceanic and Atmospheric Administration 

(NOAA) Forecast System Laboratory (FSL) (http://www-sdd.fsl.noaa.gov/MADIS). 

Daily data are produced by assembling hourly data for a forecasting period. The data file 

contains the name of the station, latitude (φs), longitude (ψs), and meteorological 

parameter value (xs). Temperature, dew-point temperature, wind speed, and wind 

direction data are also included in the file. 

An automated method to obtain MADIS data has been developed, and daily data 

consisting of hourly datasets have been archived. 

3.2.2 Upper-Air Sounding Data 

Upper-air sounding data are obtained from the archive library on the University of 

Wyoming, Atmospheric Sciences Department’s Web site: 

http:/weather.uwyo.edu/upperair/sounding.html. 

4. Reading WRF Output File 

The WRF produces only one output file in the netCDF format 

(http://www.unidata.ucar.edu) and contains many time-dependent, two-dimensional, and 

three-dimensional meteorological parameters. 

For the current approach, the forecasted parameters necessary for our use were converted 

from netCDF to ASCII format so that the analysis program could easily read them. 

Figure 3 is an example of a script file designed to read a WRF output file in netCDF 

format and convert it into an ASCII file. 

7 
# Dumping WRF output data to ascii files for Surface. 

# 2-D parameters 

# Q2, QV at 2m 

ncdump -v Q2 wrfout_d02_2004-10-07_12:00:00>Q2_wrf.file 

# T2 Temperature at 2 m 

ncdump -v T2 wrfout_d02_2004-10-07_12:00:00>T2_wrf.file 

# TH2, Potential temperature at 2 m 

ncdump -v TH2 wrfout_d02_2004-10-07_12:00:00>TH2_wrf.file 

# U10, U at 10 m 

ncdump -v U10 wrfout_d02_2004-10-07_12:00:00>U10_wrf.file 

# V10, V at 10 m 

ncdump -v V10 wrfout_d02_2004-10-07_12:00:00>V10_wrf.file 

# HGT, Terrain height 

ncdump -v HGT wrfout_d02_2004-10-07_12:00:00>HGT_wrf.file 

# XLAT, Latitude 

ncdump -v XLAT wrfout_d02_2004-10-07_12:00:00>XLAT_wrf.file 

# XLONG, Longitude 

ncdump -v XLONG wrfout_d02_2004-10-07_12:00:00>XLONG_wrf.file 

# RAINC, Accumulated total cumulus precipitation (mm) 

ncdump -v RAINC wrfout_d02_2004-10-07_12:00:00>RAINC_wrf.file 

# 

# 3-D parameters 

# Pressure 

ncdump -v P wrfout_d02_2004-10-07_12:00:00>P_wrf.file 

# PB, Base state pressure at half levels 

ncdump -v PB wrfout_d02_2004-10-07_12:00:00>PB_wrf.file 

# Water Vapor 

ncdump -v QVAPOR wrfout_d02_2004-10-07_12:00:00>QVAPOR_wrf.file 

# Perturbation geopotential 

ncdump -v PH wrfout_d02_2004-10-07_12:00:00>PH_wrf.file 

# Base state geopotential 

ncdump -v PHB wrfout_d02_2004-10-07_12:00:00>PHB_wrf.file 

# U, U wind 

ncdump -v U wrfout_d02_2004-10-07_12:00:00>U_wrf.file 

# V, V wind 

ncdump -v V wrfout_d02_2004-10-07_12:00:00>V_wrf.file 

# T, Perturbation potential temp. 

ncdump -v T wrfout_d02_2004-10-07_12:00:00>T_wrf.file 

Figure 3. A script file designed to read a WRF output file in netCDF format and convert it into ASCII format. 

In figure 3, “ncdump” is a netCDF program. For instance, “ncdump –v P wrfout-d02-

2004-10-07_12:00:00>P_wrf.file” means to read the data of pamameter P from the 

wrfout-d02-2004-10-07_12:00:00 file and write the data onto the P_wrf.file file in ASCII 

format. Here, the WRF is initialized at 1200 UTC, 07 October 2004 and the data is for the 

domain 2. 

Running this script produces one file for each parameter. 

8 
5. Analysis Program 

Figure 4. Horizontal and vertical grids of the WRF. 

The WRF uses a C grid staggering for variables, as shown in figure 4 (Skamarock, 2005). 

In the grid, velocity components (u, v, w) are staggered at one-half grid length from the 

thermodynamic variable θ. 

5.1 Wind Velocity Components 

Given the grid location of potential temperature θ by (i, j, k, t), wind vector components 

u, v, and w at (i, j, k) are calculated by 

 u(i, j, k, t)=0.5(u(i-1/2, j, k, t) +u(i+1/2, j. k, t)) (1) 

 v(i, j, k, t)=0.5(v(i, j-1/2, k, t) + v(i, j+1/2, k, t)) (2) 

 w(i, j, k, t)=0.5(w(i, j, k-1/2, t) + w(i, j, k+1/2, t)) (3) 

5.2 Height 

The WRF output file contains base state and perturbation geopotentials (Ф and Ф’). 

Vertical height Z(i, j, k, t) is calculated by 

Z(i, j, k, t)=(Ф(i, j, k, t) + Ф’(i, j, k, t))/g (4) 

where g is the gravitational acceleration (9.81 m/s2). 

9 
5.3 Temperature 

In the model, potential temperature is used as a temperature variable, but for comparison 

with observed data, it is convenient to use temperature. The WRF output file contains the 

perturbation potential temperature θ’ from 300 °K, 

Θ = θ’ + 300.0. (5) 

Pressure P is the sum of the base state pressure PB and the perturbation pressure P’: 

 P=PB + P’. (6) 

Thus, temperature T is calculated as 

κ

θ ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ =

P

P T

0

 - 273.16 (7) 

where P0 is standard pressure (1,000 mb) and 

C

R

p

κ = d (8) 

where Rd is the gas constant for dry air and Cp is the specific heat at constant pressure. 

5.4 Dew-Point Temperature 

The moisture variable in the WRF is expressed by a mixing ratio, but in observational 

data, the moisture variable is usually given in terms of dew-point temperature 

To calculate dew-point temperature from the WRF output mixing ratio, the following 

steps are taken: 

1. Tetan’s empirical formula of mixing ratio Q (g/kg) is given as (Yamada and 

Bunker, 1989) 

⎥

⎥

⎦

⎤

⎢

⎢

⎣

⎡

−

− •= 86.35

16.273

exp

8002.3

T

T

d

d

P Q (9) 

 where Q is the mixing ratio (g/kg), P is pressure (mb), and Td is dew-point 

temperature (°K). 

2. From equation 9, the dew-point temperature is derived as 

27.17

16.27327.1786.35

−

− = AxxA Td (10) 

 where A is given by 

10 
⎥

⎦

⎤ ⎢

⎣

⎡ = 8002.3 log PxQ A . (11) 

5.5 Rotating Horizontal Wind Vector Components 

Since the horizontal wind vector components u and v in the WRF output file are along the 

model coordinate system, they are rotated to the west-to-east and the south-to-north 

components. 

In our applications, the Lambert conformal mapping system was used as a model 

coordinate system. The following procedures were taken to rotate from (u, v) to (ut, vt). 

Here (u, v) are the x- and y-components of the horizontal wind vector of the model 

coordinate, and (ut, vt) are the true west-east and south-north components of the 

horizontal vector. 

Let us express the latitude and longitude of grid points by φ(i, j) and ψ(i, j), and the center 

latitude and longitude of the model domain by φc and ψc . 

A constant for model domain, cone is defined as 

c cone = sin(φ ). (12) 

For each grid point, Δψ=ψ(i, j) – ψc is calculated. 

For Δψ>180.0, 

Δψ=Δψ -360.0. (13) 

For Δψ≤-180.0, 

Δψ=Δψ + 360.0. (14) 

If φ(i, j)≤0.0 

α=-Δψ•cone (15) 

and for φ(i, j)>0.0 

α=Δψ•cone. (16) 

Horizontal wind vector components (ut, vt) are calculated as 

 ) t vu ∗= α + u ∗ cos()sin( α (17) 

and 

 ) t vv ∗−= α + u ∗ sin()cos( α . (18) 

11 
After these calculations, the WRF forecast output data are compared with surface and 

upper-air observation data for statistical evaluation. 

6. Comparison with Observed Data 

6.1 Surface Data 

The program checks if the latitude and longitude (φs and ψs) of an observation station is 

within the model domain and surrounded by four grid points of the model. If surrounded, 

the model value of an arbitrarily parameter Xm, corresponding to Xs, is computed using the 

following: 

( ) ( ),( ),(),1(

)),(),1(( ),( 1 ji jijijiXjiX X jiX s ψψ

ψ ψ

−∗

−+ ) + − += (19) 

( )

( ) ))1,(( ),()1,1( )1,( 2 +−∗

−++

++ − jiXjiX + )1,()1,1(

( )

++= ji jiji jiXX s ψψ

ψ ψ

 (20) 

( ) )),(( ),()1,1(

12

1 ji jiji m XX s φφ

φ φ − −+−

+= − XX (21) 

Figure 4 shows an abbreviated table of comparison, showing station names, latitudes, and 

longitudes, as well as interpolated and observed values for temperature, dew-point 

temperature, and the horizontal wind components. Values for wind components—um and 

us, and vm and vs—are recorded in columns 4 through 7. 

12 
2 376 Temperature 

AP156 34.86 -118.17 15.6 14.4 

AP263 34.30 -118.51 13.4 14.4 

CEKC1 34.27 -118.15 9.3 8.3 

CNAC1 33.88 -117.55 15.4 15.5 

CTLC1 34.32 -117.84 4.5 4.4 

GMTC1 34.64 -118.41 11.0 6.1 

CMP12 36.11 -115.15 15.6 15.9 

OWENS 36.80 -118.20 5.0 11.3 

UP013 36.50 -114.76 -999.0 16.6 

UP183 35.66 -115.36 13.1 12.8 

OWENS 36.80 -118.20 5.0 10.5 

 2 344 Dew Pt Temp 

AP156 34.86 -118.17 2.1 5.2 

AP263 34.30 -118.51 8.9 9.4 

AP516 36.03 -115.02 4.3 5.5 

AP541 33.87 -117.83 11.3 8.0 

CMP12 36.11 -115.15 4.5 2.3 

OWENS 36.80 -118.20 2.0 0.6 

OWENS 36.80 -118.20 2.0 1.3 

 2 356 Wind component 

AP156 34.86 -118.17 2.2 2.5 2.2 2.5 

AP263 34.30 -118.51 3.5 2.2 2.9 1.6 

AP516 36.03 -115.02 0.2 -0.9 0.2 -2.0 

AP541 33.87 -117.83 2.9 0.9 0.5 0.3 

ONYC1 35.67 -118.06 2.3 1.4 1.0 1.7 

CMP12 36.11 -115.15 0.8 -0.7 0.3 -0.8 

OWENS 36.80 -118.20 0.7 -1.2 -0.4 2.4 

OWENS 36.80 -118.20 0.7 0.0 -0.4 1.8 

Figure 4. An example of surface data comparison. 

6.2 Upper-Air Data 

In order to make a comparison between vertical profiles of upper-air sounding data and 

model forecast data, the following procedures are taken: 

1. The vertical data of the four grid points surrounding the location of an upper-air 

sounding station are interpolated to the heights of the sounding data. 

2. At each height of sounding data, the bilinear interpolation method described in 

equations 19 through 21 is used to obtain the vertical profile of the model forecast 

corresponding to observed upper-air sounding data. 

13 
Figure 5 shows a portion of the file containing a vertical profile comparison between 

observation and model forecast data. The first line shows the latitude and longitude of an 

upper-air station. The second line shows that there are 52 vertical levels of observation. 

Column 1 is the height above sea level for the upper-air observation. Columns 2 through 

9 are for observation, showing pressure, temperature, dew-point temperature, wind vector 

the u and v wind components, relative humidity, wind direction, and wind speed. 

Columns 10 through 14 are for the WRF model forecast, showing pressure, temperature, 

dew-point temperature, and the u and v wind components. 

Figures 6 and 7 show the vertical profiles of upper-air sounding data and interpolation 

data from model output for station DRA (Mercury, NV) at 1200 UTC, 23 February 2005. 

Figure 5. An example of a vertical profile comparison between observation and model forecast data 

14 
Figure 6. Vertical profiles of temperature and dew-point temperature 

for upper-air sounding data and WRF forecast data for station 

DRA at 1200 UTC, 23 February 2005. 

Figure 7. Same as figure 6, except for wind speed and wind direction. 

15 
7. Statistical Comparison Program 

After files, such as those shown in figures 4 and 5, are produced for numerous different 

forecast periods, statistical comparison studies can be made between the observation and 

forecast data. 

7.1 Surface Data 

In this study, statistical parameters are used to compare observation and model forecast 

data of temperature and dew-point temperature at the 2-m level, and horizontal wind 

vector components, u and v, at the 10-m level. Such statistical parameters are calculated 

hourly. 

Mean Difference (MD) 

MD is expressed as 

( )

mn

xx

MD

m

j

n

i

∑∑ jiojip

= =

−

= 1 1

,,,,

 (22) 

where the subscripts o and p represent observation and prediction, respectively; the 

subscript i represents the i

th surface station; the subscript j represents the jth forecast day; 

n is the number of surface stations; and m is the total number of forecast days. 

A nonzero MD indicates bias. For instance, if the MD value is positive, it indicates that 

the model tends to over-forecast. 

Mean Absolute Difference (AD) 

AD is expressed as 

mn

xx

AD

m

j

n

i

∑∑ jiojip

= =

−

= 1 1

,,,,

. (23) 

Root Mean Square Error (RMSE) 

RMSE is expressed as 

( )

mn

xx

RMSE

m

j

n

i

∑∑ jiojip

= =

−

= 1

2

1

,,,,

. (24) 

Good agreements between observation and forecast are, in general, related to small 

values of AD and RMSE. 

16 
Root Mean Square Vector Error (RMSVE) 

RMSVE is calculated using 

[ ] ( )( )

mn

vvuu

RMSVE

m

j

n

i

∑∑ jiojip jiojip

= =

−+−

= 1 1

2

,,,,

2

,,,,

. (25) 

This parameter measures the differences of both wind speed and wind direction. Good 

agreements of wind vectors are related to small values of the RMSVE. 

Correlation Coefficient (CC) 

CC is expressed as 

∑∑

∑∑

= =

= =

∗

∗

= m

j

n

i jiojip

m

j

n

i

jiojip

yy

yy

CC

1 1

2

,,

2

,,

1 1

,,,, ( )

 (26) 

where 

pjipjip −= xxy ,,,, (27) 

ojiojio −= xxy ,,,, (28) 

mn

x

x j i

jip

p

∑∑= = = 1 1

,,

m n

 (29) 

mn

x

x j i

jio

o

∑∑= = = 1 1

,,

m n

 (30) 

7.2 Upper-Air Data 

Upper-air comparison data, such as shown in figure 6, are calculated at heights specific to 

each sounding. For statistical evaluation, it is necessary to use data interpolated to predefined heights. Using a linear interpolation method, both observed and forecasted data 

are computed at pre-defined heights. 

MD and AD are calculated for each pre-defined height for upper-air sounding stations 

located within the model domain. 

17 
8. Comparison Results 

WRF forecast calculations were intermittently carried out during a period from December 

10, 2004 to February 28, 2005. Thirty-three 24-h forecast calculations were made during 

that time. 

8.1 Surface Data 

The forecast data from domains 1 and 2 were compared with the MADIS surface 

observation data. A comparison was made each hour during a 24-h forecast period. 

Figure 8 shows a time-series of MD, CC, and AD for temperature during a 24-h period. 

Figure 8. A time-series of MD, CC, and AD for temperature. 

NOTE: The thick lines are for domain 1 and the thin lines are for domain 2. 

18 
Although the time-series of MD of temperature for domain 2 is slightly greater than that 

for domain 1, the time-series of CC and AD show that the forecast output of domain 2 

produced better agreements with the observation data than those of domain 1. 

A time-series of the statistical parameters for dew-point temperature are shown in figure 

9. Contrary to the temperature statistics, the statistics for dew-point temperature show 

little difference between domains 1 and 2, although there was a slight improvement of 

AD for domain 2 over domain 1. 

Figure 9. Same as figure 8, except for dew-point temperature. 

19 
Figure 10 shows a time-series of MD, CC, and AD for wind speed. MD for domain 1 is 

smaller than that for domain 2, CC for domain 1 is greater than that for domain 2, and 

AD for domain 1 is smaller than that for domain 2. 

A time-series of RMSVE and MWDDF are shown in figure 11. The values for both 

RMSVE and MWDDF for domain 1 are smaller than those for domain 2. 

Therefore, from figures 10 and 11, it can be inferred that the wind fields of domain 1 are 

statistically better than those of domain 2. 

Figure 10. Same as figure 8, except for wind speed. 

20 
Figure 11. A time-series of RMSVE and MWDDF for domains 1 and 2. 

8.2 Upper-Air Data 

Vertical profiles of MD and AD are obtained for three upper-air stations―DRA 

(Mercury, NV), NKX (San Diego, CA), and VBG (Vandenberg Air Force Base, CA)―

located within domain 1 (see figure 2). Figure 12 is the vertical profiles of MD for 

temperature, dew-point temperature, and wind speed for a forecast period of 12-h for 

NKX. Vertical profiles of AD are also shown in figure 13 for the same time period and 

station. These are the mean values obtained from 33 different cases. 

Similar figures are obtained for the other stations and for different time periods, but are 

not shown in this report. 

Figure 12 shows that the WRF did not significantly over- or under-predict the three 

variables throughout the vertical layers of the atmosphere for station NKX. 

From figure 13, the following can be inferred: the ADs of temperature throughout the 

vertical layers were 1 to 2 °C, but for dew-point temperature, the ADs were significantly 

21 
larger. For wind speed and the wind vector components u and v, the ADs stayed around 

5 m/s, but showed a gradual increase with height. 

Figure 12. Vertical profiles of MD for temperature, dew-point temperature, and wind speed for 

station NKX for a 12-h forecast period. 

22 
Figure 13. Vertical profiles of AD of temperature, dew-point temperature wind speed, and 

wind vector components, u and v, for station NKX for a 12-h forecast period. 

23 
9. Summary and Conclusion 

We have established automated methods of obtaining and archiving initialization and 

time-dependent lateral condition data for the WRF. These data include Eta (NAM) 

forecast data, MADIS surface data, and upper-air sounding data. 

We also established statistical analysis methods that compare WRF forecast data with 

observation data. This report described methods of comparing surface as well as upperair data between model calculation and observation. 

The WRF was applied to model domains surrounding the NTC in southern California. In 

this study, a set of 24-h forecast data of 2-way coupled domains, with the grid resolutions 

of 18 and 6 km, were statistically compared with surface and upper-air observation data. 

For surface temperature, domain 2 (a 6-km grid resolution) produced better statistical 

agreements with observations than domain 1 (an 18-km grid resolution). 

There were no significant differences between time-series of statistical parameters for 

domains 1 and 2. However, for wind speed and vectors, domain 1 produced statistically 

better agreements between calculation and observation than domain 2. 

Vertical profiles of temperature, dew-point temperature, and wind speed and vector 

components were compared between calculation and observation. From that the 

following could be inferred: 

• The ADs for temperature were about 2 °C throughout the model’s vertical depth. 

• The ADs for dew-point temperature were substantially greater than 2 °C. 

• The ADs for wind speed were 5 m/s or greater, but gradually increased with height. 

There were no systematic biases in vertical profiles of temperature, dew-point 

temperature, and wind speed. 

24 
References 

Dudhia, J. A Numerical Study of Convection Observed During the Winter Monsoon 

Experiment Using a Mesoscale Two-Dimensional Model. J. of Atmos. Sci., 1989, 46, 

3077–3107. 

Dudhia, J. The Weather Research and Forecast Model Version 2.0: Physics Update, 

WRF/MM5 Summer Workshop, Extended Abstract, National Center for Atmospheric 

Research, 2004. 

Henmi, T. Statistical Studies of Mesoscale Forecast Models MM5 and WRF; ARL-TR3329; U.S. Army Research Laboratory: White Sands Missile Range, NM, 2004. 

Hong, S.Y.; Dudhia, J.; Chen, S.H. A Revised Approach to Ice Microphysical processes 

for the Bulk Parameterization of Cloud and Precipitation. Monthly Weather Rev., 

2004, 132, 103. 

Kain, J.S.; Fritch, J.M. A One-Dimensional Entraining/Dtraining Plume Model and its 

Application in Convective Parameterization. J. of Atmos. Sci., 1999, 47, 2784–2802. 

Kain, J.S.; Fritch, J.M. Convective Parameterization for Mesoscale Models: The KainFritch Scheme. The Representation of Cumulus Convection in Numerical Models, K. 

A. Emanuel and D. J. Raymond, eds.; American Meteorological Society, 1993, p 246. 

Mlawer, E.J.; Taubman, S.J.; Brown, P.D.; Iacono, M.J.; Clough, S.A. Radiative Transfer 

for Inhomogeneous Atmosphere: RRTM, A Validated Correlated-k Model for the 

Long-Wave. J. of Geophysical Res., 1997, 102 (D14) 11163–11182. 

Skamarock ,W.C.; Klemp, J.B.; Dudhia, J.; Gill, D.M.; Barker, D.M.; Wang, W.; Powers, 

J.G. A Description of the Advanced Research WRF Version 2; NCAR/TN-468+STR; 

Mesoscale and Microscale Meteorology Division, National Center for Atmospheric 

Research: Boulder, CO, 2005. 

Yamada, T.; Bunker, S. A Numerical Model Study of Nocturnal Drainage Flows with 

Strong Wind and Temperature Gradients. J. of Applied Meteorology, 1989, 82, 

407–430. 

25 
Acronyms 

AD absolute difference 

CC correlation coefficient 

DRA Mercury, NV, station 

FSL Forecast System Laboratory 

GRIB Gridded Binary 

MADIS Meteorological Assimilation Data Ingest System 

MD mean difference 

MM5 Mesoscale Model Version 5 

MWDDF mean wind direction difference 

NAM North American Mesoscale model 

NCEP National Center of Environmental Prediction 

NKX San Diego, CA, station 

NOAA National Oceanic and Atmospheric Administration 

NTC National Training Center 

PBL planetary boundary layer 

RMSVE root mean square vector error 

RRTM Rapid Radiative Transfer Model 

VBG Vandenberg Air Force Base, CA, station 

WRF Weather Research and Forecast model 

26 
Distribution List 

 Copies 

US ARMY RESEARCH LAB 3 

AMSRD ARL CI BE 

ATTN T HENMI 

R FLANIGAN 

R PADILLA 

WSMR NM 88002-5501 

US ARMY RESEARCH LAB 1

ATTN IMNE ALC IMS 

MAIL & RECORDS MGMT

ADELPHI MD 20783-1197

ADMNSTR 1 

DEFNS TECHL INFO CTR 

ATTN DTIC OCP ELECT CPY V MADDOX 

8725 JOHN J KINGMAN RD STE 0944 

FT BELVOIR VA 22060-6218 

US ARMY RESEARCH LAB 2 

AMSRD ARL CI OK TL TECHL LIB 

2800 POWDER MILL ROAD 

ADELPHI MD 20783-1197 

US ARMY RESEARCH LAB 1 

AMSRD CI OK TP TECHL LIB 

APG MD 21005 

TOTAL 8 

27 
INTENTIONALLY LEFT BLANK. 

28