INTERIM REPORT
Cloud Assimilation into the Weather Research and Forecast
(WRF) Model:
Testing Cumulus Physics Parameters
Project Period of Performance
June 6, 2013 – November 30, 2013
Submitted to:
Bright Dornblaser
Texas Commission on Environmental Quality (TCEQ)
Prepared by:
Arastoo Pour Biazar, Richard McNider, Andrew White
Earth System Science Center
National Space and Technology Center
University of Alabama – Huntsville
________________________________________________________________
January 13, 2014
Cloud Assimilation in WRF: Testing Cumulus Physics Parameters
Table of Contents
Table of Contents .......................................................................................................................................................... i
Table of Figures: .........................................................................................................................................................iii
List of Tables: ............................................................................................................................................................. iv
1
SUMMARY........................................................................................................................................................... 5
2
INTRODUCTION ................................................................................................................................................ 6
3
BASELINE SIMULATIONS............................................................................................................................... 9
3.1
4
Methods for Evaluation ..................................................................................................................................... 11
4.1.1
4.1.2
5
Model Configuration ..................................................................................................................................9
METSTAT Evaluation ......................................................................................................................... 11
Evaluating Cloud Simulation Using GOES Observations ................................................................... 12
ALTERNATE ANALYTICAL APPROACH FOR ESTIMATING TARGET VERTICAL
VELOCITY ......................................................................................................................................................... 13
5.1
Rationale and Strategy ............................................................................................................................. 13
5.2
Adjustment of the Model Environment to Support Clouds........................................................................ 13
5.3
Development of Analytical Technique to Estimate Target Vertical Velocity ............................................ 15
5.3.1
Implementation for Under-Prediction Case ........................................................................................ 17
5.3.2
Implementation for Over-Prediction Case ........................................................................................... 18
6
WRF SIMULATIONS ASSIMILATING GOES CLOUD OBSERVATIONS ............................................. 19
6.1
7
8
Program Flow for Assimilation Technique .............................................................................................. 19
RESULTS ............................................................................................................................................................ 21
7.1
Control Simulations .................................................................................................................................. 22
7.2
Simulations with Cloud Assimilation ........................................................................................................ 26
Summary and Conclusions ................................................................................................................................ 30
References .................................................................................................................................................................. 33
Cloud Assimilation into the Weather Research and Forecast (WRF) Model
iii
Table of Figures:
FIGURE 3-1. FIGURE SHOWING THE EXTENT OF DOMAINS USED FOR 36-KM GRID SPACING (CONUS), 12-KM GRID
SPACING (SEUS), AND 4-KM GRID SPACING (TEXAS). ......................................................................................... 10
FIGURE 5-1. CONCEPTUAL DIAGRAM OF CLOUD TO BE CREATED BY THE MODEL. THE AIR PARCEL WITH MIXING RATIO
Q1, PRESSURE P1, AND TEMPERATURE T1 IS TO BE LIFTED TO SATURATION AT CLOUD BASE. ............................... 15
FIGURE 5-2. SCHEMATIC FOR FOUR-VARIABLE NEEDED IN 1D-VAR. ........................................................................... 18
FIGURE 5-3. A DISTRIBUTION OF CLOUD TYPES IN THE WRF MODEL 36 KM SIMULATION: 1) THICK HIGH-CLOUDS
(ALBEDO>0.6, TARGET HEIGHT >5 KM); 2) THICK MID-CLOUDS WHICH HAVE ALBEDO (>0.6) AND TARGET
HEIGHT (<5 KM); 3) HIGH CLOUDS (0.4<ALBEDO<0.6, TARGET HEIGHT >5 KM); 4) MID-CLOUDS
(0.4<ALBEDO<0.6, HEIGHT < 5 KM); 5)THIN HIGH-CLOUDS(ALBEDO<0.4, TARGET HEIGHT>5 KM); 6) THIN MIDCLOUDS (ALBEDO<0.4, TARGET HEIGHT < 5 KM) ................................................................................................. 18
FIGURE 5-4. SCHEMATIC FOR AN ANALYTICAL APPROACH FOR OVER-PREDICTION AREAS ........................................... 19
FIGURE 6-1. SCHEMATIC FOR THE PROGRAM FLOW WHEN ASSIMILATING GOES CLOUD OBSERVATION ...................... 20
FIGURE 7-1. CLOUD FRACTION AND AGREEMENT INDEX (AI) FOR 36 KM WRF SIMULATION (CONTROL). .................. 22
FIGURE 7-2. . CLOUD FRACTION AND AGREEMENT INDEX (AI) FOR 12 KM WRF SIMULATION (CONTROL).................. 23
FIGURE 7-3. CLOUD FRACTION AND AGREEMENT INDEX (AI) FOR 4 KM WRF SIMULATION (CONTROL) ..................... 23
FIGURE 7-4. METSTAT STATISTICS FOR WIND FROM 36 KM CONTROL SIMULATION. .................................................. 24
FIGURE 7-5. METSTAT STATISTICS FOR TEMPERATURE FROM 36 KM CONTROL SIMULATION. .................................... 25
FIGURE 7-6. METSTAT STATISTICS FOR MIXING RATIO FROM 36 KM CONTROL SIMULATION...................................... 25
FIGURE 7-7. METSTAT STATISTICS SHOWING RMSE AND ITS SYSTEMATIC AND UNSYSTEMATIC COMPONENTS FOR
TEMPERATURE AND MIXING RATIO FOR 12-KM CONTROL SIMULATION. .............................................................. 26
FIGURE 7-8. AGREEMENT INDEX (AI) FOR 12-KM SIMULATION. ................................................................................... 27
FIGURE 7-9. METSTAT STATISTICS FOR 12-KM SIMULATIONS. ................................................................................... 28
FIGURE 7-10. AGREEMENT INDEX (AI) FOR 4-KM SIMULATIONS. ................................................................................ 29
FIGURE 7-11. METSTAT STATISTICS FOR 4-KM SIMULATION. ..................................................................................... 30
Cloud Assimilation into the Weather Research and Forecast (WRF) Model
iv
List of Tables:
TABLE 3-1. WRF DOMAIN SETUP FOR 36-, 12-, AND 4-KM GRID SPACING ......................................................................9
TABLE 3-2. WRF CONFIGURATION FOR SIMULATIONS .................................................................................................. 10
TABLE 4-1. CONTINGENCY TABLE USED FOR EVALUATION. ......................................................................................... 13
Cloud Assimilation into the Weather Research and Forecast (WRF) Model
Report Type:
Project Number:
Project Title:
Authors:
Mailing Address:
Report Date:
5
Interim Report
Cloud Assimilation into the Weather Research and Forecast (WRF)
Model: Testing Cumulus Physics Parameters
Arastoo Pour Biazar, Richard T. McNider, Andrew White
Earth System Science Center, University of Alabama in Huntsville,
Huntsville, Alabama 35899
Phone:
(256) 961-7970
Fax:
(256) 961-7755
E-mail:
biazar@nsstc.uah.edu
January 13, 2014
1 SUMMARY
The University of Alabama in Huntsville (UAH) was awarded a contract by TCEQ through a
cooperative agreement to continue work on satellite cloud assimilation in WRF and to
specifically investigate the impact of new improvements in cumulus parameterizations in WRF
on satellite cloud assimilation technique.
The purpose of the cloud assimilation is to improve model location and timing of clouds in the
Weather Research and Forecast (WRF) meteorological model selected for driving photochemical
models in future State Implementation Plans (SIPs). In the past, UAH has developed techniques
using satellite data to improve the spatial location and timing of clouds in WRF while keeping all
other meteorological variables in balance.
Under the current activity UAH was tasked 1) to examine the impact of the new Ma-Tan
triggering function in Kain-Fritsch (KF) cumulus parameterization on cloud simulation relevant
to UAH assimilation technique; and 2) to evaluate the impact of including the radiative feedback
from sub-grid clouds in the radiation calculations on over-all model performance. The following
interim report documents these activities.
The fundamental approach in UAH technique for correcting cloud fields relies on the use of
GOES observations of clouds. Satellite observations are used both to evaluate the model and to
identify the locations of model over- and under-prediction, as well as determining the key
variables (such as vertical velocity) that are needed for cloud adjustment. The technique uses
satellite observations of cloud top pressure and cloud albedo to identify the areas where the
model is under-predicting or over-predicting clouds. Then a target vertical velocity is estimated
and using a one-dimensional variation technique wind fields are adjusted and used as a nudging
field. This approach has been able to improve the simulation of cloud fields in the model in a
sustainable manner as it adjusts the dynamics and creates an environment conducive to cloud
formation or clear sky.
In this technique, the key variables inferred from satellite observations are the target vertical
velocity, the elevation at which this target velocity is realized, and the bottom and top levels for
Cloud Assimilation into the Weather Research and Forecast (WRF) Model
6
vertical velocity adjustment (needed for applying one dimensional variation technique.) Thus,
any change in the model that impacts the radiation field will have direct impact on UAH
technique as it alters the error statistics developed from baseline simulation. The changes
impacting baseline cloud formation also impact UAH technique as such changes may alter the
effectiveness of vertical velocity in convective initiation and also affect model evaluation that
uses the baseline simulation as a reference point.
For the current activity we used two different versions of WRF-v3.3.1. The first one is the
standard release of WRF-ARW that uses Ma-Tan trigger mechanism in KF convective
parameterization. The second model is an experimental version of WRF-v3.3.1 with some
modifications pertaining to the interaction between sub-grid cloud and grid-resolved radiation
field. For KF cumulus option the standard WRF does not account for the impact of sub-grid
cloud when calculating incident short-wave radiation at the surface. Basically what this amounts
to is that when a convective cell is forming overhead, model thinks it is still sunny. Kiran
Alapaty and other scientists at USEPA recently modified WRF to correct this shortcoming.
These modifications will be reflected in the future releases of WRF-ARW. However, with their
permission we are using their modified model in this activity to examine the impact of these
modifications relevant to our work.
In summary, for 36-km simulations over the continental United States (ConUS), there are not
significant differences between the baseline simulation that uses KF with Ma-Tan trigger
mechanism and USEPA modified version as far as near surface meteorological parameters are
concerned.
2 INTRODUCTION
Clouds play a critical role in the production and destruction of pollutants. However, numerical
meteorological models used in the creation of the physical atmosphere in the SIP modeling
process have traditionally had significant problems in creating clouds in the right place and time
compared to observed clouds. This is especially the case during air pollution episodes when
synoptic-scale forcing is weak (e.g. Stensrud and Fritsch 1994).
While the previous activities supported by TCEQ have resulted in improving the radiative effect
of clouds in air quality simulations (Biazar et al., 2007), physical inconsistencies remain a concern
as the insolation and photolysis fields derived from satellite data do not agree with the model clouds. The
purpose of the current activity is to improve model location and timing of clouds in the Weather
Research and Forecast (WRF) meteorological model selected for driving photochemical models
in future State Implementation Plans (SIPs). This activity provides techniques, using satellite
data, to first quantify errors in model clouds, and then to improve the spatial location and timing
of clouds in WRF while keeping all other meteorological variables in balance.
The basic approach is to use a GOES cloud image to determine the cloud truth. The strategy will
be first to examine differences between model clouds and the GOES clouds. Then a vertical
velocity (lifting for the areas where the model under-predicted clouds and subsidence in the areas
where the model over-predicted clouds), cloud top, cloud base, level of maximum vertical
velocity, and top and base levels for variational adjustment are estimated. Using a variational
Cloud Assimilation into the Weather Research and Forecast (WRF) Model
technique (as described in our previous report) new horizontal wind components are estimated
and the model is nudged toward the new wind field. Here in this report we document the new
approach in estimating the target vertical velocity and the relevant parameters for adjusting the
wind field. Details about variational technique were presented in our previous report. We also
briefly present results from the baseline evaluation as they are slightly different from our
previous report. This is due to the correction we made to satellite retrievals.
In the following chapters, first the baseline simulations are documented, and then the technique,
subsequent simulations, and the results will be presented.
7
Cloud Assimilation into the Weather Research and Forecast (WRF) Model
9
3 BASELINE SIMULATIONS
3.1 Model Configuration
WRF simulations in this project span over August 2006. This period coincides with TexAQS-II
field study, has been used for the previous modeling studies, and offers a substantial
observational dataset for model evaluation. Previously, in order to select a baseline simulation
that yields the best performance with respect to cloud simulation, three different set of
simulations using Kain-Fritsch (KF), Grell-Devenyi (GD) ensemble, and new Grell (G) scheme
for convective parameterization were performed to investigate the impact of these schemes on
the overall cloud prediction. KF resulted in the best performance compared to observations.
While the assimilation technique improved the performance (on 36-km grid spacing) regardless
of the cumulus parameterization used, all the subsequent simulations are using KF for cumulus
parameterization.
WRF (version 3.3) was used for simulations over the continental United States (CONUS) and
two nests covering the southeastern US (SouthUS) and East Texas (Texas) (as indicated in
Figure 3-1) for August 2006. The coarse domain has a spatial grid spacing of 36 km x 36 km
horizontally (164 grids in west-east direction and 128 grids in south-north direction) and a nonuniform vertical structure with 42 levels (41 layers) with the top pressure at 50 mb. The nonuniform vertical structure is designed to have high resolution within the boundary layer (and
close to the surface) and near tropopause (8 to 14 km) in order to better explain the stratospherictropospheric exchanges. The nest over southeast US (SouthUS) has 12 km x 12 km horizontal
resolution with 210 grids in west-east direction and 105 grids in south-north direction. The
second nest over East Texas (Texas) has 4 km x 4 km resolution with 165 x 220 grids. Table 3-1
and Figure 3-1 describe the three domains.
Table 3-1. WRF domain setup for 36-, 12-, and 4-km grid spacing
NCEP Eta Data Assimilation System (EDAS) analyses were used in WPS to create the initial
and boundary conditions for the simulations. Table 3-2 summarizes the key options used for the
simulations. WRF FDDA (four dimensional data assimilation) was also utilized to nudge the
model toward analyses data for better performance in the baseline simulation. We strived to
have the configuration of the baseline simulations similar to the common practices in air quality
modeling for the State Implementation Plan (SIP) in Texas. Simulations were performed in 5.5
day segments and re-initialized from analyses for each segment at 0 GMT. The first 12 hr of
each segment is discarded as the spin-up time and the rest of the output is appended to the
previous segments to create a continuous record.
Cloud Assimilation into the Weather Research and Forecast (WRF) Model
10
CONUS
SouthUS
Texas
Figure 3-1. Figure showing the extent of domains used for 36-km grid spacing (CONUS), 12-km grid spacing
(SEUS), and 4-km grid spacing (Texas).
Table 3-2. WRF configuration for simulations
Domain 01
Domain 02
Domain 03
Running period
August, 2006
Horizontal resolution
36 km
12 km
4 km
Time step
90s
30s
10s
Number of vertical levels
42
Top pressure of the model
50 mb
Shortwave radiation
Duhia
Longwave radiation
RRTM
Surface layer
Monin-Obukhov similarity
Land surface layer
Noah (4-soil layer)
PBL
YSU
Microphysics
LIN
KainKainCumulus physics
Fritsch
Fritsch
NO
Grid physics
Horizontal wind
Meteotological input data
EDAS
Analysis Nudging
yes
U, V Nudging Coefficient
3x10-4
1x10-4
3x10-5
T Nudging Coefficient
3x10-4
Q Nudging Coefficient
10-5
Nudging within PBL
Yes for U and V, NO for q and T
10
Cloud Assimilation into the Weather Research and Forecast (WRF) Model
11
4 Methods for Evaluation
The results were evaluated in several ways. The results from the 36-km simulation have been
extensively evaluated in the previous reports. Here we present additional evaluation focusing on
12- and 4-km simulations. The first set of evaluations examines the model results in more detail
using the surface observations. METSTAT was used to create the statistics for key
meteorological parameters and also to examine the time series for selected locations. The second
set of evaluations, involve the use of geostationary satellite observations of clouds to examine
model performance with respect to cloud simulation.
4.1.1 METSTAT Evaluation
This set of evaluations was performed using METSTAT software from Environ
(http://www.camx.com/files/metstat.27oct09.tar.gz). These evaluations attempted to quantify the
model performance with respect to standard atmospheric variables such as wind speed,
temperature, and humidity.
The following statistics were used in the evaluations:
Bias Error: the mean difference in prediction and observation pairings with valid data within a
given analysis region and for a given time period
Gross Error: the mean absolute difference in prediction and observation pairings with valid data
within a given analysis region and for a given time period
Root Mean Square Error (RMSE): the square root of the mean squared difference in
prediction and observation pairings with valid data within a given analysis region and for a given
time period
Systematic Root Mean Square Error (sysRMSE): the square root of the mean squared
difference in regressed prediction and observation pairings within a given analysis region and for
a given time period (the regressed prediction is estimated for each observation from the least
square fit).
Cloud Assimilation into the Weather Research and Forecast (WRF) Model
12
Unsystematic Root Mean Square Error (UnsysRMSE): the square root of the mean squared
difference in prediction and regressed prediction pairings within a given analysis region and for a
given time period
The meaning of UnsysRMSE is a measure of how much of the discrepancy between estimates
and observations is due to random processes or influences outside the legitimate range of the
model. In other words, UnsysRMSE identifies the errors that are not predictable mathematically.
4.1.2 Evaluating Cloud Simulation Using GOES Observations
The second set of evaluations was performed against GOES observations of clouds. While
surface monitors represent point measurements and are not comparable with the model grid
average quantity, satellite observations are aggregated pixel quantity and offer a more
comparable measurement. GOES measures the radiative impact of clouds directly in infrared
and visible channels. For this evaluation work, derived surface insolations from GOES visible
channel were used. A byproduct of surface insolation is cloud reflectance that is readily
available to be used. However, to create a consistent comparable field between the model and
satellite observations, we define an effective cloud index to indicate cloudiness. The effective
cloud albedo is defined as:

I 
 c  1.  
S

0

Where c is the effective cloud index (or cloud albedo), I is the insolation (incident shortwave
solar radiation at the surface), and S0 is the clear sky insolation (S0 is the solar constant). This
quantity will also include the small cloud absorption and indeed will yield a normalized index
when S0 represents the maximum clear sky insolation for any given point and time. S0 is
obtained from a clear sky model simulation. Then, the cloud index is calculated for each hour
(model output time) based on the above formula. The cloud index approaches zero for clear sky
condition and increases toward the limit of 1 for more opaque clouds. While the value of the
index for the model could be different from that of the observations, it can be a good indicator of
cloudiness regardless of the opaqueness of the cloud.
The effective cloud index is used to compare model results to satellite image and to identify
cloudy/clear areas. Using this identifier, we introduce a new metric for model evaluation against
GOES observations. This metric is called the Index of Agreement (AI). Table 4-1 shows the
contingency table used for this index. The table shows the number of grids where both model
and GOES indicate cloudiness (A), number of grids where both model and GOES indicate clear
sky (D), number of grids where the model is under-predicting clouds (B), and number of grids
where the model is over-predicting clouds (C).
12
Cloud Assimilation into the Weather Research and Forecast (WRF) Model
13
Table 4-1. Contingency table used for evaluation.
GOES
WRF
TOTAL
Cloudy
Clear
Cloudy
A
B
A+B
Clear
C
D
C+D
A+C
B+D
A+B+C+D
TOTAL
AI is defined as the percentage of grid points that show agreement between model and GOES
observations. Based on Table 4-1 AI is defined as:
AI = (A+D)/(A+B+C+D)
Where:
A = Number of grid points where both GOES and WRF are cloudy
D = Number of grid points where both GOES and WRF are clear
Total = A+B+C+D = Total number of model grids
The index varies between 0 and 1, where closer to 1 means better performance.
5 ALTERNATE ANALYTICAL APPROACH FOR ESTIMATING TARGET
VERTICAL VELOCITY
5.1 Rationale and Strategy
The overall goal of this project was to have a cloud assimilation technique that will be used in an
operational setting. Thus, operational concerns such as ease of use and computational efficiency
were also important factors for consideration. A major objective of the project was to develop
and implement a new analytical technique for estimating target vertical velocity that can address
the aforementioned concerns.
5.2 Adjustment of the Model Environment to Support Clouds
The initiation and assimilation of clouds in weather forecast models has been the subject of many
investigations. Yet, evidence suggests that there are still major errors in cloud placement. This is
especially true at the spatial scale at which air quality models operate. It is particularly frustrating
in air quality SIP modeling since they are after the fact runs that the observed cloud field is
known from satellite observations but models have significant differences in cloud placement. At
UAH considerable attention has been given to replacing model cloud transmissivity with satellite
Cloud Assimilation into the Weather Research and Forecast (WRF) Model
14
observed transmissivity (McNider et al 1995, Pour-Biazar et al 2007) in air quality models.
These previous activities that directly replaced model transmissivity and cloud tops with satellite
observations provided improvements in model performance. However, it produced a physical
inconsistency in the model system. Insolation and photolysis fields derived from satellite data did
not agree with the model clouds. Thus, locations in the model where deep convection or cloud
venting of the boundary layer was occurring were not consistent with the locations where the
satellites indicated clouds were located. Additionally, cloud water that would impact long wave
radiation or chemistry was in the wrong location.
Rather than adjusting model transmissivity it would be preferred to insert cloud water into the
model at locations where the satellite indicates clouds. Previous attempts at using satellite data to
insert cloud water have met with limited success. For example, Lipton and Modica (1999) used
GOES-7 data to adjust the model relative humidity field in stratiform cloud areas and found a
general improvement in the model simulation but only for about 6 hours.
The problem is that cloud water typically depends on a water vapor and temperature environment
to provide the relative humidity to sustain the cloud liquid water. Conversely, when liquid water
is removed from the model where observations show no clouds, the model will continue to
produce new water. Direct insertion of liquid water can even deteriorate model performance. As
an example, attempting to insert clouds that satellites show at a position where the model is clear
means that you are likely inserting clouds where the model has subsidence (broad-scale
downward motion) as opposed to lifting. Inserting water in this situation where the model has
subsidence will cause evaporation and further subsidence, exactly the opposite of supporting the
clouds that the satellite observes. Yucel et al (2003) discovered that adjustment of the model
dynamics and thermodynamics was necessary to fully support the insertion of cloud liquid water
in models.
In reality, the issue with supporting clouds in models goes beyond thermodynamic support. For
clouds to persist they must have dynamical support through upward vertical motion. This has
been recognized in the weather forecasting community and investigators with NOAA seeking to
produce improved initialization have inserted vertical motion in models where clouds were
observed but not supported (Albers et al. 1996). However, these motions were relatively ad hoc
and the inserted vertical velocities relatively small. The results, though they produced some
improvement, had limited success in changing the cloud statistics after several hours.
In principal the problem of providing the coincident thermodynamic support and dynamical
support could be provided by four-dimensional variational assimilation (4DVAR). 4DVAR
employs a strategy that develops local linear approximations of relationships among all variables
(the tangent linear approximation) (Lopez, 2006). These partial derivatives among all the state
variables (the Jacobian matrix) define the needed relationships so that required changes in
humidity and vertical motions could be found if liquid water were changed from satellite
observations. Variational minimization is coincidently used to reduce the difference between
observations and model values. The development of the Jacobian can be done using tools from
non-linear analysis (McNider et al. 1995b) or by running the model in a forward/backward mode
to determine relationships among the variables. However, the application of 4DVAR to cloud
initialization has been limited by the inability to define the Jacobian for cloud processes. A
14
Cloud Assimilation into the Weather Research and Forecast (WRF) Model
15
survey of the state of science reveals a lack of success in developing 4DVAR for clouds except
for simple representations in very coarse grid models. This is in large part because cloud
processes and cloud initiation are highly non-linear. This is further exacerbated by the fact that
clouds in models are highly parameterized and the relationships have many conditional and onoff switches which make developing the required inter-parameter relationships difficult if not
impossible (Mu and Wang, 2003).
In the present activity we employ a technique originally started under the NASA GEWEX
activity but with further support by NSF and MMS. This technique is basically a statistical
approach to 4DVAR that attempts to develop relationships between satellite-derived cloud
properties and targeted variables internal to the models such as grid scale vertical velocity. As
mentioned above, the air quality problem is generally different from the forecast problem in that
observed clouds are available during the entire period of interest not just at the initialization time.
In effect the technique used here is an engineering attempt to provide the dynamical and
thermodynamical support needed to sustain or clear observed clouds during the air quality
simulation.
As described in our previous report, the key parameters for making such an adjustment are the
target vertical velocity, the height at which this target is reached, and the base and top of the
layer in a model grid column where the adjustment is taking place. These are the key parameters
needed in the variational technique to estimate a new wind field that can create/clear and sustain
the clouds. The following is a description of the analytical approach.
5.3 Development of Analytical Technique to Estimate Target Vertical Velocity
Here we present an analytical technique to estimate the target vertical velocity needed to clear or
create clouds where the model is over-predicting or under-predicting clouds. This technique will
substitute for threshold values previously used that were based on model statistics. To illustrate
the technique we consider a case of under-prediction in which we attempt to create clouds where
the model indicated clear sky. In such a case, we assume that the target cloud conforms to our
conceptual diagram in Figure 5-1.
Figure 5-1. Conceptual diagram of cloud to be created by the model. The air parcel with mixing ratio q1,
pressure P1, and temperature T1 is to be lifted to saturation at cloud base.
Cloud Assimilation into the Weather Research and Forecast (WRF) Model
16
To create cloud in the model, a parcel with mixing ratio of q1, pressure p1, and temperature of
T1 is to be lifted to saturation. The saturation level constitutes the cloud base. The vertical
advection of temperature and moisture are described as:


 w
t
z
q
q
 w
t
z
Discretization of these equations yields:
 2t  t   2t
 2t  1t
 w
dt
dz
q2t  t  q2t
q2t  q1t
 w
dt
dz
Now assuming that at time t+t the parcel reaches saturation at cloud base, we get:
 2t  t  1t
q2t  t  q1t
Furthermore, we impose a condition for saturation. That is at t+t the temperature at the cloud
base is the saturation temperature and relative humidity is 100%, meaning:
Ts  f (T2t  t , q2t  t , P2t  t )  f (T1t , q1t , P2t )
In another word, since the parcel has been lifted to the cloud base, it preserves the moisture and
the potential temperature and only the pressure has changed. Now, the saturation temperature for
each model layer given the pressure P at the cloud base can be calculated as:
e(Ts )  es (Ts )
qP
17.67Ts
]

Ts  243.5
qP
243.5 ln(
)
6
.
112

Ts 
qP
17.67  ln(
)
6.112
 6.11 exp[
16
Cloud Assimilation into the Weather Research and Forecast (WRF) Model
17
Since the cloud top is known from the satellite observation, then a search from some layer below
the cloud top down to the boundary layer can identify the layer in which temperature and
moisture are adequate to reach saturation when lifted (saturation temperature will be greater than
or equal to the actual temperature). When such layer is identified, then the difference in height
between the cloud top and this layer is calculated and the vertical velocity can be estimated as:
W 
z
t
We also envision the situations where the atmosphere is so dry that the search fails and we do not
find any layer in the column to satisfy our condition. In such cases moisture adjustment is
needed to produce observed clouds. Assuming that the moisture in the boundary layer is
responsible for the observed clouds, by knowing the location of the parcel (level 1) the desired
moisture can also be estimated.
The same conceptual approach is implemented for removing erroneous clouds. For removing
clouds the parcel is assumed to be saturated at cloud top and contains cloud water (model cloud)
and will be moved down in the column until the relative humidity falls below a threshold value.
5.3.1 Implementation for Under-Prediction Case
In this case we assume that the missing clouds are in developing stage, which tend to have large
updraft at the cloud base. We expect a large enough positive vertical velocity at the cloud base
using the advection terms of temperature and moisture. We further assume that the vertical
velocity can assist a parcel at the potential layer to be lifted to saturation within 30 minutes.
Figure 5-2 shows a schematic indicating the key variables needed for the variational technique
(1D-VAR). 1D-VAR needs four key parameters. These are 1) the top for the adjustment
(wadj_top, where the vertical velocity approaches zero); 2) the bottom for adjustment (wadj_bot,
where the vertical velocity approaches zero); 3) the target vertical velocity (Target W); and 4)
the target height (Target-H) at which Target-W is reached. wadj_top is the layer corresponding
to the cloud top height that is indicated by GOES observed cloud top temperature. For Target-H
we developed an empirical simple linear relationship between cloud albedo and cloud depth
based on model statistics. This is an area that needs to be revisited in the subsequent studies.
Target H = Wadj_top x (1-cloud albedo)
Wadj_bot is determined by searching the model layers below Target-H and finding the layer that
can be lifted to saturation. Target-W then can be calculated by
Target W = (wadj_top – wadj_bot)/1800s
The equation for Target_W assumes that the parcel is lifted to saturation within 30 minutes.
Cloud Assimilation into the Weather Research and Forecast (WRF) Model
18
Figure 5-2. Schematic for four-variable needed in 1D-VAR.
Based on the statistics developed previously, a typical maximum vertical velocity in cloudy grid
cells for the 36-km simulation is about 2 m/s. To achieve this threshold in 30 minutes, a cloud
depth of at least 3600 m is needed.
Figure 5-3 represents the distribution of cloud types in the WRF 36 km simulations. More than
85 % of clouds have target heights below 5 km.
Figure 5-3. A distribution of cloud types in the WRF model 36 km simulation: 1) thick high-clouds
(albedo>0.6, target height >5 km); 2) thick mid-clouds which have albedo (>0.6) and target height (<5 km); 3)
high clouds (0.4<albedo<0.6, target height >5 km); 4) mid-clouds (0.4<albedo<0.6, height < 5 km); 5)thin
high-clouds(albedo<0.4, target height>5 km); 6) thin mid-clouds (albedo<0.4, target height < 5 km)
5.3.2 Implementation for Over-Prediction Case
In the case of over-prediction, subsidence is introduced to evaporate and remove clouds. The
advantage in this case is that the information about the erroneous cloud is obtained from the
model. The cloud top in this case is defined as the highest model layer with cloud water. The
18
Cloud Assimilation into the Weather Research and Forecast (WRF) Model
19
target-H is the height of the layer with the maximum cloud water. The lower layer for
adjustment (wadj_bot) is the closest layer to the surface with minimum relative humidity. As
before, the difference between top and bottom heights for adjustment provide the depth needed
for the estimation of vertical velocity.
Figure 5-4. Schematic for an analytical approach for over-prediction areas
6 WRF SIMULATIONS ASSIMILATING GOES CLOUD OBSERVATIONS
The new analytical technique was implemented in WRF and simulations using this technique
were performed. The period of simulation and model configuration for different domains was
explained in Chapter 3. However, simulations assimilating satellite cloud observations require
frequent updates to the nudging fields provided as input to the model. This was done in order to
minimize the modifications needed in WRF by using all available tools within WRF system. In
this effort most of the tools and scripts developed for cloud adjustment are external to the WRF
modeling system and only interact with the model through WRF standard data files.
6.1 Program Flow for Assimilation Technique
In these simulations WRF is run in its standard configuration for a retrospective case study. As
described in Chapter 3, analysis nudging is used in these simulations. The assimilation period
spans over 14:00-23:00 GMT. This was chosen to ensure that the observations cover the entire
continental United States during the assimilation period. For each day the model is run to time
t1, cloud field is compared to the satellite observations, vertical velocity is estimated, new U and
V components are estimated by employing the variational technique, U and V in the analysis are
replaced with the new estimates, and finally the model is restarted from time t0 and will continue
the simulation to time t2 where this whole process is repeated.
Cloud Assimilation into the Weather Research and Forecast (WRF) Model
20
Figure 6-1. Schematic for the program flow when assimilating GOES cloud observation
20
Cloud Assimilation into the Weather Research and Forecast (WRF) Model
21
For the nudging to be active at each given time, the model needs the nudging fields for two
consecutive times (prior to and after the given time) in order to interpolate the fields to the
current time. The piecewise simulations ensures that the model is nudged a wind field that is
conducive to creation of the observed field. Figure 6-1 shows the program flow paradigm. A
critical factor in this process is the bookkeeping, data file management, and the insertion of new
information in the data files. This is done by a series of Linux scripts and FORTRAN programs.
The process is automated, but still needs feedback from an independent user. We look forward
to work and interact with TCEQ to test the system.
The model reverts back to default setting when the satellite data is missing. Since all the
interactions with the model are external to WRF modeling system, the risk of introducing
unforeseen errors when using this system is minimized. Currently, the technique is implemented
for one-way nesting only. While there is not any theoretical hindrance for using this technique in
two-way nesting, due to operational difficulties we have developed the scripts/codes to be used
in one-way nesting. In the future, if necessary, this technique can be extended to work in twoway nesting simulations.
The simulations were performed for all three domains. In the first set of simulations, the
assimilation was performed on the mother domain and results used to provide the lateral
boundary conditions for the nest. This was to test how the improvements can propagate from a
coarser grid to a finer grid. The 36-km simulation over continental U.S. served as the coarsest
grid spacing. For 12-km grid spacing, three simulations were performed. The first simulation
was the control simulation in which as described in Chapter 3. The second simulation used the
lateral boundary condition provided from the assimilation simulation for 36-km domain. The
third simulation for 12-km domain assimilated GOES cloud observations.
A similar set-up was used for the 4-km simulations. That is, the first simulation used the default
setting with the lateral boundary condition provided from the control 12-km simulation. The
second simulation was performed using the lateral boundary condition provided from a 12-km
simulation with assimilated cloud. And the third simulation assimilated satellite clouds.
7 RESULTS
The results from these simulations were evaluated against surface weather monitors as well as
GOES observations (as described in Chapter 4.) We should also note that the satellite retrievals
used in the previous study and for the first set of simulations in this study had a low bias in the
brightness count as they were not corrected for sensor degradation. Parallel to the work in this
project, the retrieval code was corrected and the data reprocessed. After the first set of the
simulations for this project, the corrected data set was available and we started using it. This
meant that we repeated all the simulations with the new data. Use of the new data not only
slightly changed the results; it also impacted the agreement index used in the evaluation. We
attributed the difference to the calibration issue in GOES retrievals. Only recently we realized
that the new data set is not as complete as the old data set (due to unavailability of raw satellite
images for certain hours.) Since most of the missing data are during the assimilation window
Cloud Assimilation into the Weather Research and Forecast (WRF) Model
22
(daytime), this has adversely affected our results here. Thus, what is presented here should not
be construed as the best results that can be obtained from the assimilation technique.
7.1 Control Simulations
Figure 7-1 is daily averaged cloud fraction and Agreement Index (AI) during 15 ~ 22 GMT for
36-km control (CNTRL) simulation. AI is based on cloud albedo and is the number of
clear/cloudy grid cells in the model that agree with observation divided by the total number of
grids. The cloud fraction and AI for 36 km simulation in the figure is slightly different with
previous report because we increased the averaging time from 18~23 GMT to 15~22 GMT.
Figure 7-1. Cloud fraction and Agreement Index (AI) for 36 km WRF simulation (Control).
Figure 7-2Figure 7-3 show AI and cloud fraction for 12-km and 4-km simulations. In all three
domains, high AI is associated with low cloud fraction. This shows the difficulty of the model in
creating clouds. Also evident from the figures is that the model underestimates cloud fraction for
36- and 12-km domains. However, the 4-km domain shows a reasonably good agreement with
observation with respect to cloud fraction, but with low AI due to the mismatch in cloud
location.
22
Cloud Assimilation into the Weather Research and Forecast (WRF) Model
Figure 7-2. . Cloud fraction and Agreement Index (AI) for 12 km WRF simulation (Control).
Figure 7-3. Cloud fraction and Agreement Index (AI) for 4 km WRF simulation (Control)
23
Cloud Assimilation into the Weather Research and Forecast (WRF) Model
24
Figure 7-4 Figure 7-6 show the statistics for wind, temperature, and mixing ratio from the 36-km
control simulation. Wind speed has positive bias during a month of August while temperature
and humidity are negatively biased. For wind speed, systematic and unsystematic RMSE are
comparable in magnitude. However, for temperature and mixing ratio unsystematic RMSE is
dominant. This means that the random scatter in data about their mean is as large (for wind) and
larger (for temperature and mixing ratio) than the pair-wise scatter around surface observations.
These patterns are repeated for sub-domains thus limiting our ability to reduce errors.
Figure 7-4. METSTAT statistics for wind from 36 km control simulation.
24
Cloud Assimilation into the Weather Research and Forecast (WRF) Model
25
Figure 7-5. METSTAT statistics for temperature from 36 km control simulation.
Mixing Ratio (g/kg)
0
Bias
-0.2
36km.cntrl
8/04 8/05 8/06 8/07 8/08 8/09 8/10 8/11 8/12 8/13 8/14 8/15 8/16 8/17 8/18 8/19 8/20 8/21 8/22 8/23 8/24 8/25 8/26 8/27 8/28
-0.4
-0.6
-0.8
-1
Days
Mixing Ratio (g/kg)
2.5
RMSE
2
36km.cntrl.RMSE
36km.cntrl.SysRMSE
36km.cntrl.UnsysRMSE
1.5
1
0.5
0
8/04 8/05 8/06 8/07 8/08 8/09 8/10 8/11 8/12 8/13 8/14 8/15 8/16 8/17 8/18 8/19 8/20 8/21 8/22 8/23 8/24 8/25 8/26 8/27 8/28
Days
Figure 7-6. METSTAT statistics for mixing ratio from 36 km control simulation.
Figure 7-7 shows Root Mean Square Error for 12-km control simulation. As evident in the
figures, for both temperature and mixing ratio, the unsystematic error is dominant. The error for
Cloud Assimilation into the Weather Research and Forecast (WRF) Model
26
temperature is generally less than what was observed for the 36-km simulation, but the error for
mixing ratio is comparable to the 36-km simulation. Another observation here is the correlation
between temperature and mixing ratio errors and the periodic behavior from one peak to the next.
Temperature (K)
3
12km.cntrl.RMSE
12km.cntrl.SysRMSE
12km.cntrl.UnsysRMSE
RMSE
2.5
2
1.5
1
0.5
0
8/04 8/05 8/06 8/07 8/08 8/09 8/10 8/11 8/12 8/13 8/14 8/15 8/16 8/17 8/18 8/19 8/20 8/21 8/22 8/23 8/24 8/25 8/26 8/27 8/28
Days
Mixing Ratio (g/kg)
12km.cntrl.SysRMSE
2.5
12km.cntrl.UnsysRMSE
2
RMSE
12km.cntrl.RMSE
1.5
1
0.5
0
8/04 8/05 8/06 8/07 8/08 8/09 8/10 8/11 8/12 8/13 8/14 8/15 8/16 8/17 8/18 8/19 8/20 8/21 8/22 8/23 8/24 8/25 8/26 8/27 8/28
Days
Figure 7-7. METSTAT statistics showing RMSE and its systematic and unsystematic components for
temperature and mixing ratio for 12-km control simulation.
7.2 Simulations with Cloud Assimilation
The first set of simulations considering the impact of assimilation on 12-km run only replaced
the lateral boundary conditions used in the control run with one extracted from the 36-km
simulation with cloud assimilation. This was to test how the assimilation in a coarser grid can
impact a sub-domain through the lateral boundary conditions. The results from this simulation
are labeled “assimBDY12” in the following figures. The second set of simulations for the 12-km
domain assimilated GOES cloud information as described in the preceding chapter. The results
from this simulation are labeled “assim” in the figures.
Figure 7-8 shows the agreement index (AI) for all three simulations over 12-km domain. With
respect to this metric assimilating clouds in the 36-km domain and providing lateral boundary
condition to 12-km simulation has a minimal impact on model performance. Perhaps this can be
explained by the extent of the 12-km domain within the 36-km domain as seen in Figure 3-1.
12-km domain is large enough that any impact from advection of the clouds through the lateral
boundary will be dissipated long before its impact can be realized in the interior of the domain.
26
Cloud Assimilation into the Weather Research and Forecast (WRF) Model
27
Agreement Index for TX12 simulation
WRF.cntrl
WRF.assimBDY36
WRF.assim
0.90
0.85
0.80
AI
0.75
0.70
0.65
0.60
0.55
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
Days in August
Figure 7-8. Agreement Index (AI) for 12-km simulation.
Figure 7-9 shows the METSTAT statistics for the 12-km simulation. The figure shows the bias
in wind speed, temperature, and mixing ratio compared to surface weather stations. Both
assimBDY and assim simulations do not show a significant deviation from the control
simulation. For temperature, assimBDY generally increases the bias while the assimilation run
reduces the bias. With respect to temperature, assimilation run performs better in some of the
days compared to others. This is due to the fact that for most of the days the dominant factor for
warm bias is the inherent nighttime bias in the model. Therefore, a daytime correction in
temperature only shows a significant impact when the nighttime warm bias is low.
Mixing ratio is negatively correlated with the temperature and shows a negative bias with
assimBDY having larger negative bias than the assim simulation. Overall, even the
improvements in assim simulation are not significant and are only seen on few days.
Overall, for the 12-km simulations, assimilation improves the model performance while the
impact of lateral boundary condition from a coarser domain with satellite assimilation is not
significant. The assimilation simulations at 12-km grid spacing still needs some fine tuning.
There several problems encountered during these simulations that have not been completely
resolved. Most of these problems dealt with the estimation of vertical velocity and its effective
distribution within the column. For this reason the nudging coefficient was reduced, while
perhaps limiting the magnitude of vertical velocity through a better estimation of cloud depth
and/or time scale for cloud formation would be more appropriate.
Cloud Assimilation into the Weather Research and Forecast (WRF) Model
Bias
Wind Speed (m/s)
TX12.cntrl
TX12.assimBDY36
28
TX12.assim
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
8/04 8/05 8/06 8/07 8/08 8/09 8/10 8/11 8/12 8/13 8/14 8/15 8/16 8/17 8/18 8/19 8/20 8/21 8/22 8/23 8/24 8/25 8/26 8/27 8/28
Days
Temperature (K)
TX12.cntrl
TX12.assimBDY36
TX12.assim
1.4
1.2
Bias
1
0.8
0.6
0.4
0.2
0
8/04 8/05 8/06 8/07 8/08 8/09 8/10 8/11 8/12 8/13 8/14 8/15 8/16 8/17 8/18 8/19 8/20 8/21 8/22 8/23 8/24 8/25 8/26 8/27 8/28
Days
Mixing Ratio (g/kg)
TX12.cntrl
TX12.assimBDY36
TX12.assim
0
-0.2
Bias
-0.4
8/04 8/05 8/06 8/07 8/08 8/09 8/10 8/11 8/12 8/13 8/14 8/15 8/16 8/17 8/18 8/19 8/20 8/21 8/22 8/23 8/24 8/25 8/26 8/27 8/28
-0.6
-0.8
-1
-1.2
-1.4
Days
Figure 7-9. METSTAT statistics for 12-km simulations.
The simulations for 4-km domain reveal a different picture. As shown in Figure 7-10 the
agreement index does not exhibit a significant change for all three simulations (CNTRL,
assimBDY, and assim). While for some days there are increases of up to 5% (e.g., August 22) in
AI for assimilation simulation over the control simulation, there are many days that AI is almost
unaffected. Examining individual scenes, it seems that at this grid spacing some special
treatment is required.
Figure 7-11 shows a snap shot of insolation for 19 GMT on August 10, 2006. The top panel is
from GOES observations while the lower panel shows images from two WRF simulations with
cumulus parameterization turned on and off. Without cumulus parameterization the model is
performing better and is able to reproduce the individual convective cells inland close to the
coastal areas. But the larger system offshore to the southeast is not well realized. While our
technique is not adequate to correct for individual cells with short time scale at this resolution, it
should be able to help in realizing the larger system.
28
Cloud Assimilation into the Weather Research and Forecast (WRF) Model
29
Agreement Index for TX04 simulation
WRF.cntrl
WRF.assimBDY12
WRF.assim
1.00
0.95
0.90
0.85
AI
0.80
0.75
0.70
0.65
0.60
0.55
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
Days in August
Figure 7-10. Agreement Index (AI) for 4-km simulations.
Figure 7-11. Insolation at 4-km grid spacing for 19 GMT on August 10, 2006. The top figure shows GOES
observation, while the lower panel are from WRF simulations with cumulus parameterization (KF) turned on
(lower left), and no cumulus parameterization (lower right).
Cloud Assimilation into the Weather Research and Forecast (WRF) Model
30
Figure 7-12 shows METSTAT statistics for 4-km simulation. With respect to wind speed,
providing the lateral boundary condition from 12-km assimilation run yields a better
performance by reducing the wind speed bias, while assimilating GOES clouds is not
consequential and for some days it even increases the bias. The same can be said for temperature.
However, for mixing ratio the picture is mixed and the impact is minimal.
Bias of Wind Speed (m/s)
1.2
1
0.8
0.6
TX04.cntrl
0.4
TX04.BDY12
TX04.assim
0.2
0
8/04
8/05
8/06
8/07
8/08
8/09
8/10
8/11
8/12
8/13
8/14
8/15
8/16
8/17
8/18
8/19
8/20
8/21
8/22
8/23
8/24
8/25
8/26
8/27
8/28
Bias of Temperature (K)
2.5
2
1.5
TX04.cntrl
1
TX04.BDY12
TX04.assim
0.5
0
8/04
8/05
8/06
8/07
8/08
8/09
8/10
8/11
8/12
8/13
8/14
8/15
8/16
8/17
8/18
8/19
8/20
8/21
8/22
8/23
8/24
8/25
8/26
8/27
8/28
8/20
8/21
8/22
8/23
8/24
8/25
8/26
8/27
8/28
Bias of Humidity (g/kg)
1
0.5
0
-0.5
TX04.cntrl
8/04
8/05
8/06
8/07
8/08
8/09
8/10
8/11
8/12
8/13
8/14
8/15
8/16
8/17
8/18
8/19
TX04.BDY12
TX04.assim
-1
-1.5
-2
Figure 7-12. METSTAT statistics for 4-km simulation.
8 Summary and Conclusions
This report documented UAH’s efforts in assimilating clouds in WRF using GOES observation.
An alternate simple approach for estimating vertical velocity was devised, implemented in WRF,
and tested for a month long simulation over August 2006. The new technique analytically
estimates the vertical velocity needed to create/remove clouds in the model in accordance to
GOES observations. This eliminates the need for developing model statistics that are case
dependent (as described in previous report).
Furthermore, we performed simulations on 36-, 12-, and 4-km grid spacing that covers
continental United States on the coarser grid and focuses on Texas on the finer grid. The
simulations not only evaluated the impact of assimilation in each domain, but also used to
30
Cloud Assimilation into the Weather Research and Forecast (WRF) Model
31
investigate how the assimilation on a coarser grid impacts the fine grid through the lateral
boundary conditions.
For the simulations documented in this report we used the latest retrievals in which GOES
imager data was reprocessed in order to account for sensor degradation. While using this latest
product offered more accurate cloud information, it wasn’t as complete as the old data set. We
are reprocessing the data for missing hours for a follow-up investigation.
Overall, the improvements in cloud simulation were more pronounced and more significant in
the 36-km simulations. There are several reasons for this. First, the spatial scale and temporal
scale of the grid resolved clouds for 36-km grid scaling is comparable to the GOES hourly cloud
information we use for adjustment. Our current technique does not account for advection of
clouds. It assumes that a storm system that develops within one hour stays in the same general
area. It is more likely that a storm system that is spread over several 36-km grids to develop and
stay in the same general area. As we get to the finer grids, we approach the spatial scale of
individual convective cells that can be moved over several grid cells due to advection. The
second reason is that for 36-km, the statistics we developed in our prior investigation was used as
a guide for our assumptions for estimating key variables used in the adjustment of vertical
velocity. We have not evaluated our assumptions against model statistics for finer grids.
Satellite data assimilation did not improve wind speed bias in any of the simulations, but reduced
temperature and mixing ratio bias for 36- and 12-km simulations. For 4-km simulation,
assimilating satellite data didn’t improve model performance with respect to these key state
variables. However, using assimilation in 12-km simulation that provided the lateral boundary
condition for the 4-km simulation reduced the bias in wind speed, temperature and mixing ratio.
From these results, it seems that concentrating on better performance for 12-km simulation will
have a more significant impact on 4-km simulation. This is in part due to the small spatial extent
of the 4-km domain that leads to the dominant role of horizontal advection and makes the impact
of lateral boundary condition more significant. Overall, the improvements we see in these
simulations are promising and there seems to be room for even more improvements.
Cloud Assimilation into the Weather Research and Forecast (WRF) Model
33
References
Albers, S. C., J. A. McGinley, D.L. Birkenheier, and J.R. Smart, 1996: The local analysis
and prediction system (LAPS): Analyses of clouds, precipitation, and temperature. Wea. Forecasting,
11, 273-287.
Diak, G. R. and C. Gautier, 1983: Improvements to a simple physical model for estimating insolation
from GOES data. J. Appl. Meteor., 22, 505–508.
Lipton, A.E., and G.D. Modica, 1999: Assimilation of Visible-Band Satellite Data for Mesoscale
Forecasting in Cloudy Conditions. Mon. Wea. Rev., 127, 265-278.
Lopez, P., 2007: Cloud and Precipitation Parameterizations in Modeling and Variational Data
Assimilation: A Review. J. Atmos. Sci., 64, 3766–3784.
McNider, R. T., A. J. Song, D. M. Casey, P. J. Wetzel, W. L. Crosson, and R. M. Rabin, 1994: Toward a
dynamic-thermodynamic assimilation of satellite surface temperature in numerical atmospheric
models. Mon. Wea. Rev., 122, 2784–2803.
McNider, R.T., A. Song, and S.Q. Kidder, 1995a: Assimilation of GOES-derived solar insolation into a
Mesoscale model for studies of cloud shading effects. Int. J. Remote Sens., 16, 2207-2231.
McNider, R. T., X. Shi, M. Friedman, and D. E. England,1995b: On the predictability of the
stable atmospheric boundary layer, J. Atmos. Sci., 52, 1602-1614.
Mu, M., and J. Wang, 2003: A Method for Adjoint Variational Data Assimilation with Physical “On–Off”
Processes. J. Atmos. Sci., 60, 2010–2018.
Pour-Biazar, Arastoo, Richard T. McNider, Shawn J. Roselle, Ron Suggs, Gary Jedlovec, Soontae Kim ,
Daewon W. Byun, Jerry C. Lin, Thomas C. Ho, Stephanie Haines, Bright Dornblaser, Robert
Cameron. (2007), Correcting photolysis rates on the basis of satellite observed clouds, J. Geophys.
Res, 112, D10302, doi:10.1029/2006JD007422.
Stephens, G.L., 1978: Radiation profiles in extended water clouds. Part II. Model Parameterizations.
J.Atmos. Sci., 35, 2123-2132
Stephens, Graeme L., Deborah G. Vane, Ronald J. Boain, Gerald G. Mace, Kenneth Sassen,
Zhien Wang, Anthony J. Illingworth, Ewan J. O'Connor, William B. Rossow, Stephen L.
Durden, Steven D. Miller, Richard T. Austin, Angela Benedetti, Cristian Mitrescu, and
CloudSat Science Team, 2002: The CloudSat mission and the A-train: A new dimension of
space-based observations of clouds and precipitation. Bull. Amer. Meteorol. Soc., 83, 17711790, doi:10.1175/BAMS-83-12-1771
Yucel, I., W. J. Shuttleworth, X. Gao, and S. Sorooshian, 2003: Short-term performance of MM5 with
cloud-cover assimilation from satellite observations. Mon. Wea. Rev., 131, 1797–1810.