IMPLEMENTATION OF COUPLED SKIN TEMPERATURE ANALYSIS AND
BIAS CORRECTION IN THE NASA/GMAO FINITE-VOLUME
DATA ASSIMILATION SYSTEM (FVDAS)
Jon D. Radakovich1, Michael G. Bosilovich2, Jiun-dar Chern3, Arlindo da Silva2,
Ricardo Todling2, Joanna Joiner2, Man-li Wu2, and Peter Norris3
1 NASA Global Modeling and Assimilation Office, SAIC, Greenbelt, MD
2 NASA Global Modeling and Assimilation Office, Greenbelt, MD
3 NASA Global Modeling and Assimilation Office, GEST, Greenbelt, MD
1. INTRODUCTION
Surface skin temperature is a critical state
because it reflects the surface radiative properties
and energy budget and can dictate convective
initiation. In addition, a reliable skin temperature
field from the operational GMAO fvDAS (Global
Modeling and Assimilation Office finite-volume
Data Assimilation System) is a key requirement
from scientific instrument team users. However,
generating an accurate skin temperature product
is a difficult problem due to the sensitivity in the
parameter to error and bias in clouds, radiation,
soil moisture, and precipitation. In an effort to
improve the skin temperature in the fvDAS we
have employed a two-fold approach via the
integration
of
the
state-of-the-art
NCAR
Community Land Model (CLM) version 2.0 landsurface model (Dai et al. 2002; Zeng et al. 2002)
into the assimilation system, and through skin
temperature analysis and bias correction.
Previously, the fvDAS performed an uncoupled
skin temperature analysis and bias correction
based on GMAO TOVS (TIROS Operational
Vertical Sounder) skin temperature observations.
In this study, a new method of coupled skin
temperature analysis and bias correction (BC) has
been developed so the bias correction term is
passed directly to the land-surface model and
considered a forcing term in the solution to the
energy balance.
2. MODELS & ASSIMILATION SYSTEM
2.1 The Community Land Model (CLM2)
The CLM2 provides a comprehensive
physical representation of soil/snow hydrology and
thermal dynamics and biogeophysics. The CLM2
was developed collaboratively by an open

1
Corresponding Author Address: Jon D. Radakovich, Science
Applications International Corporation, Global Modeling and
Assimilation Office, NASA GSFC Code 610.1, Greenbelt, MD
20771, jrad@gmao.gsfc.nasa.gov
interagency/university group of scientists, and
based on well-proven physical parameterizations
and numerical schemes that combine the best
features of three previous land surface models:
Biosphere-Atmosphere Transfer Scheme (BATS;
Dickinson et al. 1993), the NCAR Land-surface
Model (LSM; Bonan 1996), and the IAP94 snow
model (Dai and Zeng 1996).
The CLM2 is a one-dimensional point
model that uses sub-grid scale tiles. The CLM2
has one vegetation layer with a photosynthesisconductance model to realistically depict
evapotranspiration (Bonan 1996). There are 10uneven vertical soil layers with the bottom layer at
3.43-m and water, ice, and temperature states in
each layer. The CLM2 features up to five snow
layers depending on the snow depth with water
flow, refreezing, compaction and aging allowed. In
addition, the CLM2 utilizes two-stream canopy
radiative transfer, the Bonan lake model (1996),
topographic enhanced streamflow based on
TOPMODEL (Beven and Kirkby 1979), and
turbulence is considered above, within, and below
the canopy.
A number of experiments were executed
in order to improve the representation of surface
processes in the CLM2. Modifying the drag
coefficient under the canopy allowed for a
reduction of the warm and dry bias. Also, changes
to the interception scheme and sub-surface runoff
produced a more realistic interception loss ratio,
and increased the canopy throughfall leading to
more soil infiltration and resulting plant
transpiration.
2.2 The NASA/NCAR fvGCM and the fvDAS
The GMAO has collaborated with NCAR
to produce the NASA/NCAR finite-volume Global
Climate Model (fvGCM; Lin and Rood 2002),
which is a unified climate, numerical weather
prediction, and chemistry-transport model suitable
for data assimilation, with the GMAO’s finitevolume dynamical core and NCAR’s suite of
physical parameterizations
The GMAO’s finite-volume dynamical core
is capable of resolving atmospheric motions from
meso- to planetary-scale with a terrain-following
Lagrangian control-volume vertical coordinate
system (Lin 1997; Lin and Rood 1999). The
fvGCM dynamical core formulation includes a
genuinely
conservative
Flux-Form
SemiLagrangian (FFSL) transport algorithm (Lin and
Rood
1996)
with
Gibbs
oscillation-free
monotonicity constraint on sub-grid distribution.
There is a consistent and conservative transport of
air mass and absolute vorticity, and subsequent
superior transport of potential vorticity by the FFSL
algorithm (Lin and Rood 1997). In turn, the mass,
momentum, and total energy are conserved when
mapping from the Lagrangian control-volume to
the Eulerian fixed reference coordinate. The
physical parameterizations of the fvGCM are
based on NCAR Community Climate Model
version 3.0 (CCM3) physics. The NCAR CCM3
parameterizations are a well-balanced set of
processes with a long history of development and
documentation (Kiehl et al. 1998). The moist
physics package includes the Zhang and
McFarlane (1995) deep convective scheme, which
handles updrafts and downdrafts and operates in
conjunction with the Hack (1994) mid- and shallow
convection scheme. For the radiation package,
the longwave radiative transfer is based on an
absorptivity-emissivity formulation (Ramanathan
and Downey 1986) and the shortwave radiative
parameterization uses the -Eddington method
(Briegleb
1992).
The
boundary-layer
mixing/turbulence parameterization utilizes the
“nonlocal” formulation from Holtslag and Boville
(1993). In addition, the NCAR WACCM (Whole
Atmosphere Community Climate Model) gravity
wave drag is used (Sassi et al. 2003). The
scheme includes parameterizations for orographic
gravity waves and a spectrum of traveling gravity
waves.
The fvDAS first utilizes a Statistical Quality
Control (SQC) system to screen the observational
data through checks against the background field
prior to the assimilation. The fvDAS analysis is
performed by the Physical-Space Statistical
Analysis System (PSAS; Cohn et al. 1998). The
PSAS algorithm obtains the best estimate of the
state of the system by combining observations
with the forecast model first guess. The analysis
equation, which encapsulates the PSAS scheme,
is

wa  w f  K wo  Hw f

(1)
where wa denotes the analyzed field, wf represents
the model forecast first guess field, wo is the
observational field, K is the weights of the
analysis, and H is the interpolation operator which
transforms model variables into observables. In
the fvDAS framework, the grid space O – F
(observed skin temperature minus the forecast
first guess skin temperature) values are input to
PSAS. The analysis increments (wa = K(wo – H
wf)), are then produced directly on the model grid,
thereby preserving the balance relationships
implied by the error covariance formulations.
3. SKIN TEMPERATURE ASSIMILATION & BC
In addition to producing analysis
increments, the observations can be used to
reduce the long-term bias of the model through
bias correction. For the skin temperature bias
correction, a variant of the Dee and da Silva
(1998) bias correction scheme was implemented
where,
wa  K wo  Hw f  b f 
(2)
wa  w f  bk 1  wa
(3)
bk  bk 1    wa
(4)
f
f
f
bkf is the updated bias estimate, bk-1f is the bias
estimate based on the previous analysis increment
(wk-1a) and wa is the analysis increment at time
tk. We found however that this scheme was
inadequate if the bias correction term is only
applied at the analysis times. Since the skin
temperature has a small heat capacity,
adjustments from the analysis increment and bias
correction applied only at the analysis time can
quickly dissipate. The bias generation mechanism
associated with the surface skin temperature acts
very rapidly. As a result, an incremental BC
scheme was introduced, where a BC term is
added to the surface energy balance at every
timestep to counteract the subsequent forcing of
the analyzed skin temperature back to the initial
state. For this scheme, bf is computed as in (4)
and the BC term is calculated as,
fb 
bf

.
(5)
where  is the period between analysis times. The
surface temperature is solved by iteration of the
energy balance. Since the temperature increment
is included in the iteration, all budget terms that
are a function of surface temperature adjust to the
presence and magnitude of the increment at every
time step.
The bias correction term was added to the
energy balance for the canopy and for the top
layer soil/snow surface, and then updated at the
analysis times. Initial results indicated that it was
necessary to include the heat capacity terms for
the soil/snow and canopy in the bias estimation.
In addition, there was a mapping of the grid-space
bias term to the CLM2 tile space. The minimal
variance formulation was used in order for the
dominant tiles of the grid-cell to be more greatly
influenced by the bias correction.
The incremental bias correction (IBC)
scheme effectively removed the time mean bias,
but did not remove bias in the mean diurnal cycle.
To account for this deficiency a diurnal bias
correction (DBC) scheme was developed, where
we modeled the time-dependent bias as,
b f (t )   (a j cos  j t  b j sin  j t ) , (6)
j
and estimated the Fourier coefficients.
a j  a j  wa cos  j t
(7)
b j  b j  wa sin  j t .
(8)
We determined that at a minimum it is necessary
to keep diurnal (1=2/24h) harmonics.
4. RESULTS
The motivation for this study is
demonstrated in Figure 1, which shows the
surface skin temperature from an off-line landsurface model with coupled skin temperature
assimilation and bias correction.
The skin
temperature from the experiment with assimilation
only (blue line) reveals the rapid dissipation of the
analysis increment after the analysis time due to
the small heat capacity of the skin temperature.
The skin temperature from the experiment with
incremental bias correction (green line) shows the
benefit of the inclusion of the bias term at every
timestep, and so the experiment closely follows
the observations (black line).
Figure 1. One-day cycle of surface skin temperature from a
point. Remotely sensed skin temperature (black), model
simulation (red), model with assimilation only (blue) and model
with assimilation and incremental bias correction (green).
The coupled skin temperature technique
was tested in the fvDAS CLM2 framework and run
at 1 x 1.25 horizontal resolution with 55 vertical
levels for May through September 2001. The July
2001 period will was the focus for this study. The
atmospheric analysis is performed every 6 hours,
while the surface temperature analysis is done
every 3 hours. The surface temperature bias
estimate is updated in step with the atmospheric
bias correction at a 6-hour frequency. Several
experiments were performed in order to evaluate
the methodology.
The 3-hourly surface skin
temperature
observations
from
ISCCP
(International Satellite Cloud Climatology Project;
Rossow and Schiffer, 1991) were used for the
surface analysis and bias correction. The ISCCP
skin temperature is much more dense than the
GMAO TOVS so we hope to better simulate the
diurnal cycle of the skin temperature.
The
experiments (Table 1) included a control (CTL)
where an uncoupled analysis of ISCCP skin
temperature was performed, Experiment One
(EXP1; Equation 5), where there was an analysis
of ISCCP skin temperature along with coupled
incremental bias correction, and Experiment Two
(EXP2; Equations 6-8), where there was an
analysis based on ISCCP along with coupled
diurnal bias correction.
Figure 2 shows the July 2001 global
monthly-mean standard deviations and biases
between the experiments and the ISCCP
observations for the analysis and the background.
The standard deviations decrease gradually with
each successive improvement to the methodology.
The coupled bias correction results in a ~0.6 K
reduction of the warm bias with respect to ISCCP,
while nearly all of bias is eliminated in the analysis
due to the bias correction. The impact of the DBC
is most visible in the monthly-mean diurnal cycle,
which will be discussed later.
elimination of the spatial differences in EXP2 when
compared EXP1.
Analysis
Table 1: Description of experiments.
Experiment
CTL
EXP1
EXP2
Description
fvDAS with uncoupled ISCCP analysis
fvDAS with coupled ISCCP analysis and IBC
fvDAS with coupled ISCCP analysis and
DBC
3
2.5
Bias
2
(K)
StdDev
1.5
1
Figure 3. July 2001 monthly-mean surface skin temperature
differences (K) for the analysis (ANA) with the control (CTL)
and experiment (EXP2) versus the ISCCP observations.
0.5
0
BKG-CTL
BKG-EXP1
BKG-EXP2
ANA-CTL
ANA-EXP1
ANA-EXP2
-0.5
Background
Figure 2.
July 2001 global monthly-mean surface skin
temperature biases and standard deviations (K) between the
experiments and ISCCP observations for the analysis (ANA)
and background (BKG).
The July 2001 monthly-mean skin
temperature for the analysis and the background
from the ISCCP coupled diurnal bias correction
experiment (EXP2) was compared against the
control run (Figures 3-4). The comparisons of the
analysis (Figure 3) show that with assimilation and
bias correction the skin temperature closely draws
to the ISCCP observations. In addition, there is an
impact in the background skin temperature (Figure
4) due to the coupled bias correction, which
reduces the warm bias and the standard deviation
with respect to ISCCP. However, the effect of the
coupling is not robust enough to eliminate the
inherent bias in the model. The improvement
resulting from the coupled DBC (EXP2) compared
to the IBC (EXP1) is revealed in Figures 5-6,
which show the skin temperature differences for
the analysis and the background against the
ISCCP observations for the daytime component of
the monthly-mean diurnal cycle.
Notice the
reduction in the standard deviation and the
Figure 4. July 2001 monthly-mean surface skin temperature
differences (K) for the background (BKG) with the control (CTL)
and experiment (EXP2) versus the ISCCP observations.
Analysis
There was also an impact in other
background diagnostic fields such as the 2m
temperature and specific humidity, sensible and
latent heat flux, sea-level pressure, winds, the soil
moisture, and precipitation. In Figure 7, the warm
colors represent improvement compared to the
control in the EXP2 background monthly-mean 2m
air temperature against observed station air
temperature. There is an overall improvement
globally in the 2m temperature due to the DBC,
especially over eastern North American and
Western Europe. This is a very positive result
given that the station air temperature is a
completely independent observation source and it
shows the coupling has a beneficial influence in
other fields.
Figure 5. July 2001 surface skin temperature differences (K)
for the analysis (ANA) with the control (CTL) and experiments
(EXP1 & EXP2) versus the ISCCP observations for the daytime
component of the monthly-mean diurnal cycle.
Background
Figure 6. July 2001 surface skin temperature differences (K)
for the background (BKG) with the control (CTL) and
experiments (EXP1 & EXP2) versus the ISCCP observations
for the daytime component of the monthly-mean diurnal cycle.
Figure 7. July 2001 improvement (red) in the background
(BKG) monthly-mean 2 m air temperature (K) for the
experiment (EXP2) versus control (CTL) against observed
station air temperature.
In addition, we have another independent
validation source, which is the CEOP (Coordinated
Enhanced Observing Period; Bosilovich and
Lawford, 2002) in situ reference site dataset. As
seen in Figure 8, the CEOP in situ data include
stations at many different locations around the
world representing varied climate regimes.
Ultimately, CEOP will also include a range of
operational analysis datasets that can be used to
evaluate the surface energy balance with land
data assimilation. The CEOP dataset allows for
comparison of observed surface pressure, surface
temperature, sensible and latent heat flux, winds,
specific humidity, and the radiative fluxes. The
July 2001 monthly-mean diurnal cycle of energy
fluxes for the Rondonia CEOP in situ site were
compared with the background from the EXP2 and
CTL (Figure 9).
The plot includes the net
downward radiative flux (Rn), the sensible heat
flux (Hs), the latent heat flux (LE), and the ground
heat flux (Hg). The simulated sensible and latent
heat flux improved due to the coupled diurnal bias
correction in EXP2. The ground heat flux is the
residual from the energy balance and the increase
in EXP2 is caused by the contribution from the
bias term. In Figure 10, the July 2001 monthlymean diurnal cycle of skin temperature and the 2
m temperature for the Rondonia site were
compared with the background from the EXP2 and
CTL.
The diurnal bias correction causes a
significant reduction in the daytime warm bias in
the skin temperature and the 2 m temperature and
more closely matches the CEOP observations.
CTL
EXP2
Figure 10. Monthly-mean diurnal cycle of the surface skin
temperature (black) and 2 m temperature (red) for the
Rondonia CEOP in situ site.
5. SUMMARY
Figure 8. Station locations of the CEOP reference sites.
CTL
EXP2
Figure 9. Monthly-mean diurnal cycle of the energy fluxes
(W/m2) for the Rondonia CEOP in situ site. Observations are
the dotted lines and the plots include net radiation (black),
sensible heat flux (red), latent heat flux (blue) and the ground
heat flux (green).
In this study, a new technique of coupled
skin temperature analysis and bias correction was
implemented in the GMAO fvDAS (Global
Modeling and Assimilation Office finite-volume
Data Assimilation System). The bias correction
term is passed directly to the land-surface model
and considered a forcing term in the solution to the
energy balance. Both incremental and diurnal
bias correction techniques were applied where the
bias correction term is added to the surface
energy balance at every timestep to counteract the
subsequent forcing of the analyzed temperature
back to the initial state.
Experiments were
conducted based on remotely-sensed skin
temperature
observations
from
ISCCP
(International Satellite Cloud Climatology Project;
Rossow and Schiffer, 1991). Results have shown
that there is an impact in the background skin
temperature that reduces the bias compared to the
ISCCP observations assimilated. In addition, the
surface meteorology is strongly influenced, with
positive impacts to the 2 m air temperature when
compared to station observations. Furthermore,
there was improvement in the skin temperature, 2
m temperature, and sensible and latent heat flux,
compared to the CEOP (Coordinated Enhanced
Observing Period; Bosilovich and Lawford, 2002)
in situ reference site dataset.
6. REFERENCES
Adler, R. F., G. J. Huffman, A. Chang, R. Ferraro,
P. Xie, J. Janowiak, B. Rudolf, U.
Schneider, S. Curtis, D. Bolvin, A. Gruber,
J. Susskind, P. Arkin, and E. Nelkin, 2003:
The
Version-2
Global
Precipitation
Climatology Project (GPCP) Monthly
Precipitation Analysis (1979-Present). J.
Hydrometeor., 4, 1147-1167.
Beven, K. J., and M. J. Kirkby, 1979: A physically
based variable contribution area model of
basin hydrology. Hydrol. Sci. Bull. 24, 4369.
Bonan, G. B., 1996: A land surface model (LSM
version 1.0) for ecological, hydrological,
and atmospheric studies. NCAR Tech.
Note NCAR/TN-417+STR, 150 pp.
Bosilovich, M.G., and R. Lawford, 2002:
Coordinated Enhanced Observing Period
(CEOP) International Workshop. Bull.
Amer. Meteor. Soc., 83, 1495–1499.
Briegleb, B. P., 1992: Delta-Eddington
approximation for solar radiation in the
NCAR Community Climate Model.
J.
Geophys. Res., 97, 7603-7612.
Cohn, S. E., A. da Silva, J. Guo, M. Sienkiewicz,
D. Lamich, 1998: Assessing the effects of
data selection with the DAO Physicalspace Statistical Analysis System. Mon.
Wea. Rev., 126, 2913-2926.
Dai, Y., X. Zeng, R. E. Dickinson, I. Baker, G.
Bonan, M. Bosilovich, S. Denning, P.
Dirmeyer, P. Houser, G. Niu, K. Oleson, A.
Schlosser, and Z.-L. Yang, 2002: The
Common Land Model (CLM). Bull. Amer.
Meteor. Soc., 84, 1013–1023.
_____, and _____, 1996: A land surface model
(IAP94) for climate studies.
Part I:
Formulation and validation in off-line
experiments. Adv. Atmos. Sci., 14, 433460.
Dee, D. P., and A. da Silva, 1998: Data
assimilation in the presence of forecast
bias. Q. J. R. Meteorol. Soc., 124, 269295.
Dickinson, R. E., A. Henderson-Sellers, and P. J.
Kennedy, 1993: Biosphere-Atmosphere
Transfer Scheme (BATS) version 1e as
coupled to the NCAR Community Climate
Model. NCAR Tech. Note NCAR/TN387+STR, 72 pp.
Hack, J. J., 1994: Parameterization of moist
convection in the National Center for
Atmospheric
Research
Community
Climate Model (CCM2).
J. Geophys.
Res., 99, 5551-5568.
Holtslag, A. A. M., and B. A. Boville, 1993: Local
versus nonlocal boundary-layer diffusion
in a global climate model. J. Climate, 6,
1825-1842.
Kiehl, J. T., J. J. Hack, G. B. Bonan, B. A. Boville,
D. L. Williamson, and P. J. Rasch, 1998:
The National Center for Atmospheric
Research Community Climate Model:
CCM. J. Climate, 11, 1131-1149.
Lin, S.-J., and R. B. Rood, 1996: Multidimensional
Flux Form Semi-Lagrangian Transport
schemes. Mon. Wea. Rev., 124, 20462070.
_____, 1997: A finite-volume integration method
for computing pressure gradient forces in
general vertical coordinates. Quart. J.
Roy. Meteor. Soc., 123, 1749-1762.
_____, and R. B. Rood, 1997: An explicit fluxform semi-Lagrangian shallow water
model on the sphere. Quart. J. Roy.
Meteor. Soc., 123, 2531-2533.
_____, and _____, 1999: Development of the joint
NASA/NCAR General Circulation Model.
Preprints, 13th Conf. on Numerical
Weather Prediction, Denver, CO.
_____, and _____, 2002: A “vertically Lagrangian”
finite-volume dynamical core for global
models. (Submitted to Mon. Wea. Rev.)
McFarlane, N. A., 1987: The effect of
orographically excited wave drag on the
general
circulation
of
the
lower
stratosphere and troposphere. J. Atmos.
Sci., 44, 1775-1800.
Radakovich, J.D., P. R. Houser, A. da Silva, and
M. G. Bosilovich, 2001: Results from
global land-surface data assimilation
methods. Preprints, 5th Symposium on
Integrated
Observing
Systems,
Albuquerque, NM, 132-134.
Ramanathan, V., and P. Downey, 1986: A
nonisothermal emissivity and absorptivity
formulation for water vapor. J. Geophys.
Res., 91, 8649-8666.
Rossow, W.B., and R.A. Schiffer, 1991: ISCCP
Cloud Data Products. Bull. Amer. Meteor.
Soc., 72, 2–20.
Sassi, F., B.A. Boville, B. Eaton, R.R. Garica, and
R.G. Roble, 2003: Model description and
user guide for WACCM1b.
(http://acd.ucar.edu/models/WACCM/WAC
CM1b-1.pdf)
Zeng, X., M. Shaikh, Y. Dai, R. E. Dickinson, and
R. Myneni, 2002:
Coupling of the
Common Land Model to the NCAR
Community Land Model. J. Climate, 15,
1832-1854.
Zhang, G. J., and N. A. McFarlane, 1995:
Sensitivity of climate simulation to the
parameterization of cumulus convection in
the Canadian Climate Centre general
circulation model.
Atmos.-Ocean, 33,
407-446.