RADAR RADIAL WIND SUPEROBSERVATIONS
METHODOLOGY AND CHARACTERISTICS
By
D. B. Michelson1, K. Salonen2 ,G. Haase1, T. Landelius1, M. Lindskog1 , H. Järvinen2
(1) Swedish Meteorological and Hydrological Institute, (2) Finnish Meteorological Institute
EU-project CARPE DIEM
Contract Nº EVG1-CT-2001-0045
AREA1: Data assimilation and NWP improvements
Work Package 2: Extraction of information from Doppler winds
SUMMARY
A novel processing procedure for radar radial wind data has been developed to assure spatial
and temporal consistency when assimilating the data into a HIgh Resolution Limited Area
Modelling system (HIRLAM). The procedure includes de-aliasing of raw radial wind data,
averaging into so-called superobservations, and a low-pass median time filter of
superobservations. A detailed description of the methodologies used in the processing
procedure, as well as the file format, is given. Furthermore the functionality of the various
components is described and the characteristics of the superobservation product are
investigated.
KEYWORDS: radar radial wind superobservation, filtering, de-aliasing, assimilation
Table of contents
1. Introduction
2. Radars
3. De-aliasing of radar wind velocities
4. Methodology for SO generation
5. Format
5.1 Fundamentals
5.2 Headers
5.3 Data
5.4 Output format
5.5 Example
6. Low-pass time filtering of SO
7. Data characteristics of SO product
7.1 Horizontal averaging
7.2 Variation in time and filtering
7.3 Observation errors
8. Concluding remarks
9. References
10. Appendix
2
1. Introduction
Utilisation of remote sensing data with high spatial and temporal resolution is important for
improving the quality of high resolution limited area weather forecasts. Improved weather
forecasts would be of importance for a better prediction of smaller scale flood events. The
procedure of utilising observations of various types to obtain the best possible initial model
state is normally referred to as data assimilation. A 3D-Var (3-dimensional variational data
assimilation) system is developed for the HIRLAM (HIgh Resolution Limited Area
Modelling) system (Gustafsson et al., 2001; Lindskog et al., 2001).
One type of remote sensing data that has not yet been satisfactorily exploited in numerical
weather prediction, but have a great potential, is radial wind data from ground-based Doppler
radars. Research and co-operation within this area is stimulated through the European Union
funded project CARPE DIEM and the European COST 717 action concerning ``Use of Radar
Observations in Hydrological and NWP models'' (Rossa, 2000). A Doppler radar frequently
scans the surrounding atmosphere and produces spatially radial wind raw data with a spherical
geometry and a high measurement density. A problem when combining these radar data with
a numerical weather prediction model is the different spectrum of scales represented by the
radial wind raw data and by the model respectively. Furthermore, aliasing, clutter and flying
birds are phenomena that require consideration.
To overcome these problems, and enable assimilation of radar radial wind data within
HIRLAM 3D-Var, a processing procedure for raw radar radial wind data is developed. The
procedure includes averaging of raw data into superobservations (hereafter SO), representing
the horizontal scales of the model. Applying a low-pass median time filter may reduce high
frequency variations in the SO data.
In Section 2, the concept of measuring wind data with radars is presented, followed by a
description of an algorithm applied for de-aliasing of raw radial wind data in Section 3. The
methodology used for SO generation is the subject of Section 4, and a detailed description of
the file format containing the radial wind SO is presented in Section 5. Reduction of high
frequency variations is the object of the low-pass median time filter, described in Section 6.
Section 7 deals with data characteristics of the SO product to various parameters. Finally,
some concluding remarks are given in Section 8.
2. Radars
A Doppler weather radar is an active remote sensing instrument which transmits
electromagnetic wave pulses and receives reflected echoes in order to investigate the
properties of the atmosphere. The amplitude of the returning wave pulses is used to estimate
the reflectivity, which can be related to precipitation intensity. The phase shift between the
transmitted and received pulses, i.e. the Doppler shift, is used to estimate the radial wind. The
radar measurements are unfortunately limited in the sense that there is a trade-off between the
maximum unambiguous velocity, Va , and the maximum unambiguous range, Ra . The
unambiguous range Ra is related to the rate at with the radar transmits, i.e. the Pulse
Repetition Frequency ( PRF ), and also the propagation speed of the transmitted
electromagnetic wave ( c ) through
3
Ra 
c
PRF
2
(1)
The ambiguity velocity is dependent on the PRF , and on the wavelength (  ) of the signal
Va 
  PRF
4
.
(2)
Thus Ra and Va are related through
RaVa 
c
.
8
(3)
Obviously, for a fixed  (in accordance with what is technically and practically attainable) in
(3) an increase of Ra can only be achieved by decreasing Va .
As an example, the Swedish radar network consists of 12 Ericsson C-band systems. All
Swedish radars have a  of approximately 5.3 cm (5.65 GHz) and are operated with dual PRF
of 900 and 1200 Hz, respectively. According to (1) to (3) these values should result in Ra and
Va of 167 km and 11.9 m/s, respectively, for 900 Hz, and 125 km and 15.9 m/s, respectively,
for 1200 Hz. However, staggering the two different PRFs can be used to effectively increase
the composite velocity unambiguity value (Doviak and Zrinc, 1993). The resulting range and
velocity composite unanambiguity values ( Rac and Vac ) are 120 km and 48 m/s, respectively.
This established procedure of staggering PRFs is, however, not widely utilised in European
weather radar networks.
Figure 1: Vertical propagation of a one degree radar beam transmitted with an elevation angle of
0.5o, assuming a half-power (-3 dB) beamwidth, as a function of range from the radar.
The raw Swedish radar data have a resolution in the azimuth dimension of 0.86 o (420 per
scan) and in range of 1 km (120 per azimuth gate). For geometrical reasons, this will of course
result in a higher density of raw data closer to the radar than at more distant ranges. Another
related issue is the broadening of the radar beam with increased range from the radar. The
half-power beamwidth of a pulse is the distance from the central axis of the pulse to the point
4
where the intensity has dropped by -3 dB from its value at the central beam axis. The vertical
broadening of the half-power beamwidth with an increasing distance from the radar is
illustrated in Figure 1. Swedish radars collect data in a sequence of scans with increasing
elevation angle, repeated every 15 minutes.
3. De-aliasing of raw radar wind velocities
Velocities higher than the unambiguous velocity will be folded back into the fundamental
velocity interval. This process is called “aliasing”. The observed radial velocity ( Vobs ) is
therefore related to the true velocity through
V  Vobs  2 n Va ,
(4)
where n is an unknown integer called Nyquist number. There exist two main approaches to
tackle the aliasing problem: one is based on improving the measurement technique of the
radar system like staggering PRFs (see above) and one focuses on post-processing methods.
At SMHI a novel de-aliasing algorithm for Doppler radar velocity data has been developed
recently. It is based on a linear wind model ( Vm ), in which the radial wind speed can be
expressed as a function of radar range, azimuth (  ) and elevation angle (  ):
Vm  - u sin   v cos   cos  .
(5)
It should be mentioned that the zonal ( u ) and meridional wind speeds ( v ) are assumed to be
proportional to the horizontal transport of precipitation. For the sake of simplification the
vertical velocity of hydrometeors is neglected. Assuming that the elevation angle and the
distance to the radar are constant, each observation at a given azimuth angle is assigned a
radial velocity.
Figure 2: Two different projections of a perfect radial wind measurement (the Nyquist velocity ( V n ) is
7.875 m/s). Left: classical representation. Right: mapping the observations onto the surface of a torus.
Unfortunately, the resulting curve could have discontinuities due to aliasing difficulties
(Figure 2, left). To avoid this problem, we map the measurements onto the surface of a torus
and yield a continuous parametric curve (Figure 2, right):
5


V

 
 
 e1  a sin Vm
 e2   e3 .
cos Vm

Va 

a 
 
 V




Va
F   
F1
(6)
F2

 
The unit vectors e1 , e2 and e3 describe the geometry of the new system. In a next step the
first component of the tangent vector along all azimuth angles is calculated:
F1


Vm
π 
sin Vm 

 Va 
π
  F2
cos    cos  ,  sin 
Va
 

u
  .
v
(7)
Note that F2 (and F1 respectively) can be transformed to
F2 
   V

 
sin Vm   a sin Vobs  ,

Va 
 Va  

Va
(8)
because Vm  V  Vobs  2 n Va and

 
sin Vm   sin
 Va 



Vobs
 2 n    sin
Va



 
Vobs  .
Va 

Inserting (8) in (7) we arrive at


F1
 
 
 u cos  cos  sin Vobs   v sin  cos  sin Vobs  .

Va 
Va 
 
 




 

D
u a1
(9)
v a2
Using N estimates of D , a1 and a 2 from an area where the model assumption (5) is
reasonable, it is possible to solve for the model velocities u and v using least squares:
u~, v~  arg min
Dk  u a1,k  v a2,k  , k  1, ..., N .
2
(10)
u ,v
Finally, the wind speeds u~ and v~ are inserted in (5) and used to de-alias the observed radial
wind velocities:
~
n  arg min Vobs  2 i Va  Vm , i    2,  1, 0, 1, 2 
i
V  Vobs  2 n Va .
(11)
In order to verify the quality of the new de-aliasing technique, we generated wind profiles
based on the VVP (Volume Velocity Processing) method (Waldteufel and Corbin, 1979).
Typically, the VVP technique is applied to thin layers of data at successive heights to obtain a
6
wind profile. Wind speed and direction can be extracted via a multi-dimensional and multiparameter linear fit of all data in a certain height layer. For a case study, we used single-PRF
data sets from the Finnish radar network, because they are more affected by aliasing than
Swedish data.
Figure 2 shows the maximum azimuthal availability of radial wind observations versus height.
Up to 2900 m height, measurements from all directions are used in the VVP technique.
Above, the number of unique azimuth angles decreases almost linearly.
Figure 3: Maximum azimuthal availability of radial wind observations versus height (   1 ). Each
layer has a thickness of 200 m. Data is measured by Korpo radar (Finland) on December 4, 1999 at
12 UTC.
A comparison of vertical profiles of wind speed and direction produced by commercial radar
software (IRIS) and with SMHI’s new de-aliasing algorithm is presented in Figure 3 (same
case as in Figure 2). Furthermore, wind profiles derived from aliased raw data are shown. The
benefit of de-aliasing is clearly visible. Unfortunately, there is no radiosonde sounding
available for this particularly case. Long-term comparisons (30 hours) between both dealiasing techniques for five different Finnish radars reveal mostly good agreement, although
the methods are quite different. When the IRIS system is implemented at SMHI this year, we
will use its VVP technique to generate wind profiles. Then, differences between the two dealiasing methods might be easier to interpret.
Figure 4: Vertical profile of wind speed (left) and direction (right) derived by IRIS, with SMHI’s new
de-aliasing algorithm, and from aliased raw data (see also Figure 2).
7
Since commercial algorithms provide only one- or two-dimensional wind products, we will
use the new method to correct volume radar data sets as well. These can be applied to
variational assimilation schemes through the generation of SO.
4. Methodology for SO generation
The processing software used to generate radar SO has been developed as an extension
module to the Radar Analysis and Visualisation Environment (Michelson, 1999). Radial wind
SO are generated through horizontal averaging in polar space of the raw polar volume of data.
The polar-to-polar transformation is based on a strategy for improved polar-to-cartesian
transformation (Henja and Michelson, 1999). To minimise horizontal correlations of the SO,
each piece of raw data is allowed to influence one SO only. To avoid averaging of radial
winds with significantly different directions, the horizontal averaging search radius increases
as a function of range, being equal to the horizontal distance between two neighbouring
azimuth gates, until this distance equals the output range bin resolution. This increase in
averaging search radius is illustrated in Figure 5 and the horizontal averaging applied when
generating the super-observations is illustrated in Figure 6.
Figure 5: Horizontal and vertical averaging lengths used when generating radar SO with a geometry
of 105 azimuth gates per scan, 10 km range bin spacing and a 0.9o beamwidth. The vertical measure
describes the pulse volume thickness from a 0.9o elevation angle, whereas the horizontal length is
actually used as a search radius in the interpolation.
To minimise vertical correlations of the SO two scans are constrained not to overlap. Such
non-overlapping scans are iteratively determined such that, starting with the lowest scan, the
closest non-overlapping scan is identified and SO are generated through horizontal averaging;
this scan then becomes the starting point and the closest non-overlapping scan to it is found.
This continues until the highest allowed elevation angle is reached. A number of supporting
variables are derived and written to a file, radial wind variances being among them. A detailed
description of the contents of the file is given in Section 5.
8
Figure 6: Radial wind raw data (left) and SO generated through horizontal averaging (right).
5. Format
5.1 Fundamentals
The file consists of ASCII characters only (ISO-8859-1 character set). All breaks between
variables are given as white spaces. The end of a line is denoted with the "line feed" character
only. In C this is the "\n" character. The term "superob" is referred to both as a single SO and
as a collection of SO from a single radar.
5.2 Headers
The file contains a one-line header with a file identifier followed by date and time strings in
the forms YYYYMMDD HHmm:
SUPEROB 19991210 1200
The time entry denotes the starting time of the original polar volume scan. SO files may
contain data from more than one temporal sampling period by concatenating two or more
files. The temporal delimiter is the identifier line, above. Data from more than one radar can
be held in a SO file. Data are ordered sequentially by radars. Data from each radar is preceded
by a one-line header containing constant information on that radar. A header line containing
information on Radar Norrköping would look like this, for example:
NEWRADAR 16.152 58.583 57 2570 10000.0 0.9 3.429
The header format in C-syntax is
NEWRADAR %6.3f %5.3f %d %d %5.1f %3.1f %5.3f\n
Each radar is thus identified by its location (lon/lat), its height above mean sea level (m), and
its WMO station number. The initial WMO station numbers are taken from the GORN list
prepared by KNMI (October, 1998). The last three numbers are the range bin spacing
(meters), the radar beamwidth (degrees) and the angle between azimuth gates (degrees) in the
volume, all of which are constant throughout that SO.
9
5.3 Data
Following the radar's header are lines containing the SO themselves, with one SO on each
line. The order and meaning of each variable is as follows:
Longitude - of the observation's position above the Earth's surface (degrees)
Latitude - of the observation's position above the Earth's surface (degrees)
Elevation - angle of the radar beam's main axis above the horizon (degrees)
Range - slant range (direct distance) from the antenna (meters)
Azimuth - antenna's clockwise rotation from due north (degrees)
Height - radar beam main axis altitude above mean sea level (meters)
Horizontal averaging length - (meters)
Vertical averaging length - (meters)
Radial wind value - (m/s) Negative values denote winds approaching the radar. Positive
values denote receding winds.
Sample size (n) of measured radial wind values in the interpolation.
Variance (m/s) of the radial wind sample about the mean.
Quality of radial wind value - ?
Obs error of radial wind value - (m/s)
Reflectivity factor - (dBZ)
Sample size (n) of non-zero reflectivity factor values.
Variance (dBZ) of the reflectivity factor values about the mean. The lower bound is -50 dBZ.
Quality of reflectivity factor - ?
Obs error of reflectivity factor - (dBZ)
All positions are valid for the middle of the given range bin in all dimensions.
For all variables EXCEPT reflectivity factor, an unknown value is denoted by 0 (zero). For
mean reflectivity factor, an unknown value is denoted by 255.0.
5.4 Output format
Each SO is written to one line and the variables are ordered according to the list given above.
The specific formatting of each SO is (in C-syntax):
%6.3f %6.3f %4.1f %6d %5.1f %7.1f %7.1f %7.1f %6.2f %4d %7.1f
%2d %5.1f %6.2f %4d %7.1f %2d %5.1f\n
5.5 Example
An example of two SO from Radar Karlskrona, including its header, is:
NEWRADAR 15.613 56.296 122 2666 10000.0 0.9 3.429
15.613 56.341 0.5 5000 0.0 167.1 538.2 78.5 0.15 5 18.8 0 0.0
0.91 13 3.9 0 0.0
15.613 56.521 0.5 25000 0.0 377.1 2691.1 392.7 18.21 58 10.3 0
0.0 19.00 63 36.4 0 0.0
10
6. Low-pass time filtering of SO
A low pass median time filter may be applied to the SO in order to remove high frequency
variations that cannot be represented in the forecast model. For each radar, radar elevation
angle, azimuth angle and range all radial wind SO data within a time window is collected. The
data within the time window are from the series of scans carried out every 15 minutes. The
length of the time window is dependent on the typical time scale of the forecast model.
Figure 7 shows a one-month time series of unfiltered and filtered radial wind data from one
particular point. Raw data are available every 15 minutes, provided there is an echo at the
particular position. The filtering time window is set to 3 h in this example. This means that the
median value out of maximum12 pieces of unfiltered data is chosen within each 3 h interval.
In case of one or less data values within the window no filtered value is produced. Clearly the
high frequency variations have been reduced.
Figure 7: One-month time series of radial wind SO from the radar of Norrköping in Sweden during
July 2000. The series is from the particular SO point with scan elevation angle 0.5 o, azimuth angle
260.6o and range 25 km. Unfiltered data are represented by blue pluses and filtered data by red
circles. Unit: m/s.
7. Data characteristics of SO product
The purpose of the algorithms developed for generation of radar radial wind SO is to have an
observation type suitable for assimilation within the HIRLAM 3D-Var. Therefore it is natural
to utilise also HIRLAM model information for evaluation and demonstration of the properties
of the SO. Within variational data assimilation in numerical weather prediction a so-called
observation operator is applied to project a model state into the observed quantities. The
present version of the observation operator used in the HIRLAM variational data assimilation
for projection into radar radial winds (Lindskog et al., 2000; Lindskog et al., 2001; Salonen,
2002; Salonen, 2002) is described in Appendix. The radial wind observation operator is used
in this section when comparing SO with the corresponding HIRLAM model state equivalents.
11
7.1 Horizontal averaging
Figure 8 shows radial wind raw data, SO with an approximate scale of 10 km and the
corresponding HIRLAM model equivalents for a 6 h forecast at 22 km horizontal resolution.
The example is from the radar of Norrköping at 5 of July 2000, 21 UTC. It can be seen that
the SO represents much better the horizontal scales of the model equivalents than do the raw
data. It should be mentioned that further increasing the horizontal scale of the SO would,
close to the radar, lead to averaging of radial winds with significant different directions,
which is not to recommend. A horizontal averaging scale of roughly 10 km seems to be
appropriate for a forecast model with a horizontal scale of the order of magnitude 10 km.
Figure 8: Radial wind raw data (upper left), SO representing an horizontal scale of approximate 10
km (upper right) and HIRLAM model state equivalents (lower left). Displayed are the 0.5 o elevation
radar scan from the radar of Norrköping in Sweden at 5 of July 2000, 21 UTC. The radial velocities
are given in m/s and the colour bar (lower right) shows the colour coding.
12
7.2 Variation in time and time-filtering
When, choosing the length of the time window of the median filter, the characteristics of the
forecast model should be taken into account. The left part of Figure 9 illustrate the difference
when applying a 1 h time filter to a one month time series of unfiltered data, as compared to
applying a 3 h filter.
Figure 9: One-month time series of radial wind SO from the radar of Norrköping in Sweden during
July 2000 and the corresponding HIRLAM model equivalents. The series is from the particular point
with scan elevation angle 0.5o, azimuth angle 260.6o and range 25 km. To the left: unfiltered data
(blue pluses), data filtered with a 1 h window (red circles) and data filtered with a 3 h window (green
triangles). To the right: data filtered with a 3 h window (green triangles) and model HIRLAM model
state equivalents (black circles). Unit: m/s.
It can bee seen that filtering with either of the time windows reduces significantly the
fluctuations in the unfiltered data. However, the difference is rather small between the results
of the 1 h time filter and the 3 h time filter. The right part of Figure 10 shows for the same
time-period and position the 3h-time filtered SO and the corresponding model equivalents of a
6 h forecast at 22 km horizontal resolution. The filtered observations capture rather well the
time evolution of the model. An advantage of choosing a 3 h time window instead of a 1 h
window is that less data are lost due to only one unfiltered data value within the interval. It is
less likely that there will exist only 1 or less SO in a window consisting of 12 SO than in a
window consisting of 4 SO.
To some extent the of the time filter also has a spatially smoothing effect, since it helps to
reduce non-persistent small scale variations in the unfiltered data. Figure 7 illustrates how the
filtering may remove data that are not consistent with the surrounding. The filtered data show
a better spatial agreement with the corresponding model equivalents.
13
Figure 10: Radial wind raw data (upper left), Radial wind unfiltered SO representing a horizontal
scale of approximate 10 km (upper right) and HIRLAM model state equivalents (lower left). Displayed
are the 0.5o elevation radar scan from the radar of Norrköping in Sweden at 5 of July 2000, 21
UTC. The radial velocities are given in m/s and the colour bar (lower right) shows the colour coding
14
7.3 Estimation of errors
The estimation of observation errors is based on comparisons of SO data with the
corresponding HIRLAM 6 h 22 km forecast model state equivalents over the period from 1
to14 June 1999. During this period, 460000 SO data (unfiltered in time, representing roughly
10 km horizontal resolution) were generated representing four radar sites (Karlskrona,
Leksand, Norrköping and Stockholm), and elevation angles of 0.5o and 1.3o.
There are free parameters associated to each SO (see Section 5), three of which are relevant
for data selection, namely the measurement range, the number of polar bins used in the SO
generation (hereafter NPB) and the variance of the raw radial wind values forming a SO
(hereafter VRW). A small value for parameter NPB indicates that a SO originates from a few,
perhaps isolated, raw data bins, whereas a large value indicates that SO represents a more
homogenous coverage of hydrometeors. A small value for parameter VRW indicates
coherence of the raw data wind values within the SO (note: NPB=1 implies VRW=0),
whereas a large value indicates internal variability of the raw data wind values.
The comparison of SO data with the corresponding model counterparts revealed that the
model counterpart is in average stronger than the observed wind. There is also outliers in the
data. The model counterparts are confined approximately to an interval of +-25 m/s, but SO
may take any value within the unambiguous interval +-48 m/s. Parameters range, NPB and
VRW can be used in attempt to isolate the slow bias and for detecting the outlying data
points. For this purpose, bias and root-mean-square (rms) of the SO background departures
are calculated for different classes of these free parameters. A summary of the findings is that
the slow bias seems to increase with the measurement range, that the outlying data points are
most effectively removed by setting a minimum value for the parameter NPB, and that the
parameter VRW provides a very weak selection criterion.
Figure 11 displays the bias and rms of the SO model departures as a function of the parameter
NPB for data from ranges less than 100 km. The rms in the class of NPB=1-5 is
approximately twice the rms-value of any other class. This provides a clear data selection
criterion. The bias in class of NPB >20 is about -0.52 m/s, and it is a justified data selection
criterion, too.
Finally, the bias and rms of the SO background departures as a function of the parameter
VRW is shown in Figure 12, for ranges less than 100 km and after applying selection criteria
for NPB (>5) and range (< 100 km). No particular selection criterion arises for VRW, and an
ad hoc criterion of VRW<10 m2/s2 is used. This criterion limits the internal variability of the
SO to the typical magnitude of the SO itself.
The bias and rms of all SO model departure are displayed in Figure 13, as function of height,
for two slightly different versions of the HIRLAM observation operator. It can be seen that
the SO data are relatively unbiased with respect to the model and that the rms value is roughly
6 m/s, independent of height.
15
Figure 11: Bias (a) and rms (b) of the SO background departures as a function of VRW.
Figure 12: Bias (a) and rms (b) of the SO background departures as a function of VRW.
16
Figure 13: Bias (a) and rms (b) of the SO background departures as a function of height.
The variance of the SO data model departure, x, is given by:
n

n
 ( yi bi )
( y 2 b 2 )
var( x)  i 1
i
n 1
i

n i 1
(
n 1
n
)2
(12)
where yi are the SO data bi are the corresponding model values and n is the number of SO
data.
The variance of the SO data model departure is the sum of the model error variance,  b2 and
the SO error variance  o2 . Assuming  2 and  o2 has an equal magnitude and estimating
b
var(x) from Figure 13 one can get a rough estimate of the SO error standard deviation,  o ,
through:
17
o 
var( x)

2
62
 4.2
2
(13)
That is the SO observation error standard deviation seems to be of the order of 4 m/s.
It is extremely difficult, if not impossible to determine the spatial variation of SO errors
within the coverage domain of a radar site. Figure 14 displays the rms of the SO model
departures as a function of range. The rms increases somewhat with range, being about 5
m2/s2, but there is no obvious selection criterion based on rms of the SO background
departures. Data from elevation angle of 0.5o behave similarly with respect to bias and rms
error (not shown).
Based on the bias of the SO background departures as a function of range either 50 km or 100
km could be used as a data selection criterion for range. The 50 km range limit is justified by
the smaller bias. However, the tighter is the range limit for SO data, the closer the SO concept
becomes the VAD concept, both being averaging processes of noisy raw data. The motivation
for developing SO is indeed its capability of resolving the non-linear features of the wind
field, which is essential for the meso-scale forecasting. Furthermore, the larger bias at longer
ranges may be due to the deficiencies in the observation operator formulation, and not being a
genuine SO problem. Thus 100 km was chosen as a data selection criterion for range.
Figure 14: Bias (a) and rms (b) of the SO background departures as a function of range.
18
8. Concluding remarks
A processing procedure for radar radial wind data has been developed to assure spatial and
temporal consistency when assimilating the data into the HIRLAM variational assimilation
system. The procedure contains many novel components and is designed to assure spatial and
temporal consistency when assimilating high resolution radial data. The procedure is
advantageous over the traditional Velocity Azimuth Display (VAD) technique (see for
example Michelson et al., 2000, page 61 for an overview of the VAD method) in that spatial
wind structures within the coverage area of each radar can be represented. Therefore radial
wind SO are ideally suited for high resolution limited area assimilation. However the SO
approach require a comprehensive observation handling system and associated quality
control.
The functionality of the processing procedure has been demonstrated and the characteristics
of the methodology and SO product have been evaluated. Emphasis has been on spatial model
scales of the order of magnitude 10 km. When further increasing the resolution to the order of
magnitude 1 km modifications of parameters associated with horizontal and temporal filtering
scales will be required.
The main software for generation of radial wind superobservations (RAVE) is written in C
and PYTHON, while the part handling the de-aliasing is presently coded in OCTAVE. The
software for time-filtering is a stand alone FORTRAN module communicating with the
RAVE software on file level only. The software is in principle portable to any UNIX platform
supporting PYTHON, OCTAVE, C and FORTRAN. The future plan is to re-write the parts
written in OCTAVE to PYTHON, to remove the dependency on too many computing
languages. The software modules are freely available for all HIRLAM member institutes, and
available in accordance with the rules formulated by EUMRTNET SRNWP for anyone else.
19
9. References
Doviak R. J. and Zrnić, D. S., 1993: Doppler Radar and Weather Observations. Second
Edition. San Diego Academic Press, Inc., 562 pp.
Gustafsson, N, Berre, L, Hörnquist, S, Huang, X-Y, Lindskog, M, Navascués, B, Mogensen,
K S and Thorsteinsson, S, 2001: Three-dimensional variational data assimilation for a limited
area model. Part I: General formulation and the background error constraint. Tellus, 53A, 425446.
Henja, A and Michelson, D B, 1999: Improved polar to cartesian radar data transformation.
Preprints AMS 29th Int. Conf. on Radar. Met., 252--255.
Michelson, D B, 1999: RAVE User's Guide. Available from SMHI, SE-601 76, Norrköping,
Sweden. 51 pp.
Michelson, D B, Andersson, T, Koistinen, J, Collier, C G, Riedl, J, Szrurc, J, Gjertsen, U,
Nielsen, A and Overgaard, S, 2000: BALTEX Radar Data Centre Products and their
Methodologies. RMK 90 SMHI, SE-601 76 Norrköping, 76 pp.
Lindskog, M, Järvinen, H and Michelson, D B, 2000: Assimilation of Radar Radial Winds in
the HIRLAM 3D-Var. Phys. Chem. Earth (B), 25, No. 10-12, 1243-1249.
Lindskog, M, Gustafsson, N, Navascués, B, Mogensen, K S, Huang, X-Y, Yang, X, Andræ,
U, Berre, L, Thorsteinsson, S and Rantakokko, J, 2001: Three-dimensional variational data
assimilation for a limited area model. Part II: Observation handling and assimilation
experiments. Tellus, 53A, 447-468.
Lindskog, M., Järvinen, H. and Michelson, D. B., 2001: Development of Doppler radar wind
data assimilation for the HIRLAM 3D-Var, HIRLAM Technical report, 52, January 1999, 74
pp. Available from SMHI, SE-601 76, Norrköping, Sweden. 51 pp.
Rossa, A, 2000: COST-717: Use of Radar Observations in Hydrological and NWP Models.
Phys. Chem. Earth (B), 25, No. 10-12, 1221-1224.
Salonen K., 2002: Latest developments in the observation operator for Doppler radar radial
winds in the HIRLAM 3D-Var. HIRLAM Workshop Report, March 2002, pp. 58-64.
K. Salonen, 2002: Observation operator for Doppler radar radial winds in HIRLAM 3D-Var.
ERAD Publication Series Vol 1, 405-408.
Waldteufel, P. and H. Corbin, 1979: On the analysis of single Doppler radar data. J. Appl.
Meteor., 18, 532-542.
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Appendix
The radial wind observation operator
The radar radial wind observation operator produces the model counterpart of the SO. Starting
from the HIRLAM model wind field, interpolated horizontally and vertically (using a
Gaussian weight function) to the point of the observation (u,v), these are the main features of
the observation operator:
1. Horizontal projection on to the transmitted radar pulse (θ-radar azimuth angle)
vh  u sin   v cos
(14)
2. Vertical projection onto the radar pulse (vh-horizontally projected wind field, φ -radar
elevation angle, α -Earth’s curvature) :
v r  v h cos(   )
(15)
Here α represents the Earth’s curvature in an approximate way, and is calculated through :
  arctan(
d cos 
)
d sin   r  h
(16)
where d is for the range of the measurement from the radar, r is for the radius of the Earth and
h is for the elevation of the radar beam from the mean sea level, respectively.
21