Overview of radar data assimilation in NWP models
Gergely Bölöni
09/10/2008
Content
1. Introduction
2. Radar observations
3. Overview of radar assimilation methods used in NWP
3.1 Radar wind assimilation
3.2 Summary on the impact
3.3 Reflectivity assimilation
3.4 Summary on the impact
4. Status of the AROME radar assimilation
5. Towards LACE radar data assimilation
6. References
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1. Introduction
The purpose of this paper is to make a synthesis of the state of the art radar data assimilation
around the world. This means a description of main differences in the assimilation methods
and a summary of obtained results and impact studies. The status of the AROME radar
assimilation is also summarized.
2. Radar observations (a very simplified description)
Important radar measurements for meteorology are reflectivity and radar wind. Reflectivity is
the backscattered radiation (originally emitted by the radar) from any object along the radar
beam (target) in the direction of the radar. Radar wind is estimated from the phase delay of
the backscattered radiation from moving targets according to the Doppler effect. Radar wind
can be measured only with Doppler radars. Both raw wind and reflectivity measurements are
post-processed in different ways:
Wind:
- VAD (Velocity Azimuth Display), which is an estimated wind profile from radial
wind measurements on all vertical elevation
- Radial wind super-observations, which means a spatial averaging (smoothing) of the
raw data over some pixels in order to get rid of horizontal correlations of observation
errors
- Raw radial winds are also used to be filtered for spatial smoothing
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Reflectivity:
- Cmax, which is the maximum reflectivity value of all elevations above the given pixel
- Column of elevation’s reflectivity values above the given pixel – volume data
- Estimated instantaneous precipitation
- Estimated cumulated precipitation
- Etc…
- Interpolation of any above to a regular grid
One has to mention that the emitted radiation is scattered back not only from the targets in our
interest (orography, birds, insects), which makes necessary to apply an important amount of
extra processing of the raw data (filters, corrections, etc.). These procedures are not detailed
here but literature can be found on the website of ERAD conference 2008 for instance
(http://erad2008.fmi.fi/proceedings/index/index.html).
3. Overview of radar assimilation methods used in NWP
The following figure gives a very general overview of the existing radar assimilation schemes
applied in NWP models.
Doppler Radar data
Wind



Reflectivity



VAD (Velocity Azimuth Display)
Radial wind super-observations
Radial wind (raw data after filtering)
Nudging
Reflectivity
Instantaneous precipitation
Cumulated precipitation
Variational
assimilation
Ensemble
Kalman
Filtering
Updated control variables
Figure 1: Possible ways of assimilating radar information
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3.1 Radar wind assimilation
Radar wind is assimilated with the Variational method (3/4DVAR) in many NWP models
(HIRLAM, UM, AROME, MM5, WRF, ARPS). Most of the applications use radar radial
wind information (Montmerle and Faccani, 2008, Montmerle et al., 2007, Lindskog et al.,
2003) but there are examples of VAD assimilation as well (Lindskog et al., 2003). In case of
VAD, the wind profile is assimilated similarly to radiosonde and wind profiler data (the
observation operator consist of horizontal and vertical interpolations of the model wind to the
location of the radar wind profile values). Radial wind data are often used as superobservations or they are processed with filters in order to smooth the very high-resolution raw
information. The observation operator for radial wind data consist of a projection of the model
wind u and v components at the observation location towards the radar (still in azimuthal
direction):
vh  u sin   v cos
where θ is the azimuth angle of the radar bem. Then vh is projected on the slanted direction of
the radar beam:
vr  vh cos(    )

d cos 

 d sin   r  h 

  arctan
where Φ is the elevation angle of the radar beam, d is the distance from the radar, r is the
radius of the Earth and h is the height of the radar instrument (above the mean sea level). As
in all Variational assimilation, both VAD and radial wind observations are meant to produce
analysis increments in the function of the background and observation errors. Most of the
Variational analysis applications are multivariate, that is radar wind observations produce not
only wind but also pressure, temperature and humidity analysis increments.
3.2 Summary on the impact
The impact of VAD and radial wind super observations were found to be positive in the
synoptic scale (dx~20km) HIRLAM model via general score comparisons (BIAS and RMSE)
(Lindskog et al., 2003). On higher resolution, Montmerle and Faccani (2008) reports an
improvement of short range (up to +6h) precipitation forecasts (False Alarm Rate [FAR] and
Probability Of Detection [POD]) due to radar radial wind assimilation. Xiao et al. (2005) and
Gao et al. (2004) found positive impact of radar wind assimilation in the MM5 / WRF
3DVAR on heavy precipitation case studies. On a supercell case the VDRAS 4DVAR system
(Variational Doppler Radar Assimilation System of NCAR) was found to reproduce well the
storm in focus partly due to the use of radar wind data (Sun 2005).
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3.2 Reflectivity assimilation
Reflectivity or post-processed information from reflectivity is assimilated with different
approaches in different NWP models. The main approaches in use are Nudging, Variational
analysis and Ensemble Kalman Filtering. Contrary to the case of radar wind, the assimilation
of reflectivity information requires complicated observation operators including moist
physics.
(a) Nudging
Nudging in general aims to force the model state towards available observations during the
model integration. This is done by introducing a relaxation term, which measures the
‘observation minus model’ distance. With the Nudging scheme one does not assimilate the
reflectivity itself but the precipitation estimated from it. A popular way of nudging
precipitation information is the Latent Heat Nudging (LHN) (Jones and Macpherson, 1997).
In LHN an extra temperature tendency is added to the thermodynamic equation, accounting
for the latent heating that would generate similar rain in the model as the observation,
according to the model physics:
T
T
 FT  
t
t LHN
RR o
T
   1TLH with  
t LHN
RRm
where F(T) stands for the model physics tendencies, T/tLHN stands for the LHN tendency,
and ΔTLH is the needed latent heat for adjusting the model precipitation (RRm) to the
observed precipitation (RRo) according to the model physics. The scheme implies that first
model and observation rain are compared in the observation points i.e. the observation
operator consist of the model moist physics and an interpolation to the observation points. It is
to be noted, that the full physics can be used and there is no need for its adjoint. Other
nudging schemes adjust the model humidity profile instead of the temperature (i.e. Davolio
and Buzzi, 2004). The adjustment is proportional to the difference between the model and
observed rain and it differs according to the model precipitation type (stratiform or
convective).
(b) Variational assimilation
In Variational assimilation (3/4DVAR), the information from radar reflectivity is taken into
account through a new Jo term, which measures the distance of the background and the radar
information (reflectivity, rain, or derived temperature and humidity profiles). There are
differences however in the observation operators providing the ‘model to reflectivity’
transformation depending on the implementation.
 Direct assimilation: some implementations assimilate directly the reflectivity itself in
the 3/4DVAR. Such examples are the MM5 and WRF implementations (Xiao et al.,
2006). Here the control variable is the total water content (qt), which is first
repartitioned to model rain water (qr), cloud water (qc) and water vapor (qv) through
warm rain physics. The model rain water (qr) is then used to compute simulated
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
‘model’ reflectivity. Jo is then computed in the ‘reflectivity space’ and its gradient is
computed with respect to reflectivity. Finally, the adjoint of the reflectivity operator
and the repartitioning warm rain physics are used to compute the gradient with respect
to the control variable (qt), i.e gradJo and gradJb can be added and a new search of the
minimization can start.
At Meteo-France (AROME) a two-step approach is applied, first providing 1D
humidity pseudo observation profiles derived from reflectivity and second,
assimilating these 1D profiles in the 3DVAR just like radiosonde observations. The
humidity pseudo observations in AROME are generated via a Bayesian method. One
has to know that at Meteo France, reflectivity observations are available as vertical
profiles on several elevations in the location of the radar pixels. The 1D Bayesian
method provides the humidity profile pseudo observation ypo as the linear combination
of background humidity profiles (xi) in the neighborhood of the given radar
reflectivity profile (yz).
y po

 1

exp  Jpo x i 
 2

  xi
1


i
exp  Jpo x j 
 2

where Jpo x   y z  Hz x  R 1 y z  Hz x 
T
One can see that the weight of a given background humidity profile depends on the
departure of its reflectivity equivalent from the observed radar reflectivity profile. The
reflectivity equivalent of the background humidity is provided by the radar simulator,
which models the backscattered signal from the model hydrometeor particles provided
by the full moist physics. A limitation of the 1D Bayesian method is that if there is no
any precipitation in the model near the observed reflectivity there is no chance to find
a good linear combination of neighboring humidity profiles, i.e. a “too dry” humidity
pseudo observation will be proposed. There is an attempt to get rid of this limitation
by forcing saturation in those model grid points, which are in the neighborhood of
observed reflectivity profiles (Montmerle et al., 2007, Watterlot et al., 2008).
At ECMWF a two-step approach is implemented as well (Lopez and Bauer, 2006,
Marécal and Mahfouf, 2003). In there, hourly cumulated rain observations from radars
and gauges are used to produce 1D Total Column Water Vapor (TCWV) observations
via 1DVAR minimization. The 1DVAR control variables are specific humidity and
temperature and the applied observation operator consist of interpolations and of
linearized moist physics, which transforms the model humidity and temperature into
precipitation in order to provide the observation minus background differences in the
1DVAR Jo. The 1DVAR minimization will find first a humidity profile, which fits
both the background and the observations in the variational sense, then the vertical
profile of humidity increments is integrated to TCWV. The TCWV observations are
used in the 4DVAR assimilation. Note, that the 1DVAR method has limitations as
well to produce TCWV pseudo observations if the model background is not rainy. In
this case the cost function used in the 1DVAR:
Jx  
1
x  x B B 1 x  x B   1 y  Hx T R 1 y  Hx 
2
2
is reduced to
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J

1 T 1
y R y
2
which is not depending any more on the model humidity and temperature x as x=xB
and H(x)=0. Another drawback of this method is that the background is used twice
during the analysis (first in the 1D- and second in the 4DVAR), which leads to
relatively weak analysis increments.
The operational JMA 4DVAR assimilates hourly cumulated precipitation with a one
step approach (Koizumi et al., 2005). There a J rain is added to the cost function, which
measures the distance of the model and observed precipitation (note that the observed
precipitation is interpolated onto a regular grid before running the analysis). The
model precipitation is generated with the moist physics of the model. The gradient of
Jrain is projected back to the control variable space with the adjoint of the moist
physics.
(c) Ensemble Kalman Filtering
The EnKF (Ensemble Kalman Filter) and ETKF (Ensemble Transform Kalman Filter) method
were tested at the University of Oklahoma and at NCAR (Synder and Zhang, 2003, Tong and
Xue, 2004). In these tests simulated radar observations were used in storm cases and were
focusing on the impact of flow dependent background errors mostly.
3.4 Summary on the impact
LHN and nudging of precipitation improves the precipitation forecast in the first 6 hours
mainly (Macpherson, 1999, Davolio and Buzzi, 2004). ECMWF reported the slight
improvement of classical scores due to precipitation assimilation (Lopez and Bauer, 2006).
Xiao et al. (2006) could improve the forecast of the Typhoon Rusa by their direct method for
reflectivity assimilation. Several case studies at Meteo France show a slight improvement in
the location and structure of mesoscale precipitating systems when assimilating reflectivity
data (Watterlot et al., 2008). Koizumi et al. (2005) at JMA found positive impact of rain
assimilation on the precipitation up to 18 hours.
4. Status of the AROME radar assimilation
The AROME reflectivity assimilation is technically available in CY33T1. It has already been
tested in a 3h RUC cycling on several cases at Meteo France. A description of the
methodology and the impact can be read in Watterlot et al. (2008), in Montmerle et al. (2007)
or in this paper’s previous sections. The further development will focus on the improvement
of the 1D Bayesian method, the quality control and to take into account the impact of
horizontal correlations of observation and background errors. A complementary information
is that according to the experience at Meteo France, the reflectivity operator is also well
applicable in visual verification of precipitation cases. Namely, the reflectivity operator
provides ‘model reflectivity‘, which is more comparable with the observed reflectivity than
the model precipitation (what we used to compare in general so far).
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5. Towards LACE radar assimilation
Accounting for radar data assimilation in LACE countries, a key issue will be the
preprocessing of radar data in order to feed the ALADIN/AROME radar assimilation system.
Namely, it must be fed with vertical profiles of reflectivity on a high-resolution regular grid.
The possibility of generating such information from the available radars in LACE countries
should be investigated as soon as possible. As an example of what exist presently in Hungary,
reflectivity profiles on a regular grid are available with a 15 minute time frequency with a 8
minute delay due to the data processing. This information is available for all the 3 available
radars separately, however no composite of these information is created at the moment.
Complementary to the investigation of appropriate radar input generation over Central
Europe, radar assimilation tests could be started with pre-prepared data from France. These
tests would be rather learning exercises than real impact studies as no useful information can
be gained from radars in France over Central Europe.
Another good preparation for LACE partners to the technical details of radar
assimilation would be to use the reflectivity operator for verification purposes first. This
would not require radar observation data but only to learn how to make work the reflectivity
operator and generate ‘model reflectivity’ plots.
An important thing to notice is that the reflectivity operator needs microphysics. This
implies that either an ALARO or AROME implementation is needed to use radar information
in the initial conditions. So far only the AROME microphysics have been tested at Meteo
France. A challenge for LACE would be to try what the 1D Bayesian method gives using the
ALARO microphysics.
6. References
Davolio S. and A. Buzzi, 2004: A Nudging scheme for the Assimilation of Precipitation Data
into a Mesoscale Model, Wea. Forecasting, 19, pp 855-871
Gao J., Xue M., Brewster K. and Droegemeier K., 2004: A three-dimensional variational
analysis method with recursive filter Doppler radars, J. Atmos. Ocean. Technol., 21, pp 457469
Jones CD and Macpherson B., 1997: A latent heat nudging scheme for the assimilation of
precipitation data into an operational mesoscale model., Meteorological Applications, 5, pp 116
Koizumi K, Y. Ishikawa and T. Tsuyuki, 2005: Assimilation of Precipitation Data to the JMA
Mesoscale Model with a Four-dimensional Variational Method and its Impact on Precipitation
Forecasts, SOLA, 1, pp 45 –48
Lindskog M, K. Salonen, H. Jarvinen, D.B. Michelson, 2003: Doppler Radar Wind Data
Assimilation with HIRLAM 3DVAR, Journal of Am. Meteor. Soc., 132, pp 1081-1092
Lopez P. and P. Bauer: 2006: “1D + 4DVAR” Assimilation of NCEP Stage-IV Radar and
Gauge Hourly Precipitation at ECMWF, Mon. Wea. Rev., 135, pp 2506-2524
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Macpherson B., 1999: Operational experience with assimilation of rainfall data in the Met
Office Mesoscale model, Met. Atm. Phys., 76, 3-8
Marécal V. and JF. Mahfouf, 2003: Experiments on 4D-Var assimilation of rainfall data using
an incremental formulation, Q.J.R.M.S, 129, pp 3137-3160
Montmerle T. and C. Faccani, 2008: Assimilation of Doppler wind into the French mesoscale
model
AROME,
Proceedings
of
the
ERAD
2008
conference
(http://erad2008.fmi.fi/proceedings/index/session_wednesday.html)
Montmerle T., E. Watterlot, C. Faccani, O. Caumont, M. Jurasek, and G. Haase, 2007:
Regional scale assimilation of radar data at Météo-France. Hirlam Tec. Report on Short
Range Numerical Weather Prediction
Sun, J, 2005: Initialization and numerical forecasting of a supercell storm observed during
STEPS, Mon. Wea. Rev., 133, pp 793Synder C. and F. Zhang, 2003: Assimilation of Simulated Doppler Radar Observations with
an Ensemble Kalman Filter, Mon. Wea. Rev, 131, pp 1663-1675
Tong M. and M. Xue, 2004: Ensemble Kalman Filter Assimilation of Doppler Radar Data
with a Compressible Nonhydrostatic Mode: OSS Experiments, Mon. Wea. Rev., 133, pp
1789-1807
Xiao Q., Kuo, Y-H., Sun J., Lee W-C., Lim E., Guo Y. and Baker, D.M., 2005: Assimilation
of Doppler radar observations with a regional 3D-VAR system: Impact of Doppler velocities
on forecasts of a heavy rainfall case, Journal of Appl. Meteor., 44, pp 768-788
Watterlot E., O. Caumont, S. Pradier-Vabre, M. Jurasek, G. Haase, 2008: 1D + 3Dvar
assimilation of radar reflectivities in the pre-operational AROME model at Météo-France,
Proceedings
of
the
ERAD
2008
conference
(http://erad2008.fmi.fi/proceedings/index/session_wednesday.html)
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