1. De-aliasing of Doppler radar winds
using a torus mapping
G. Haase and T. Landelius
Swedish Meteorological and Hydrological Institute
This presentation focuses on de-aliasing of Doppler winds.
The study is financed in part by the European project CARPE DIEM.
It contributes also to the COST-717 action entitled “Use of Radar Observations in Hydrological and NWP models”.

2. Doppler wind measurements
Quality control
(e.g. de-aliasing)
An important goal of the new de-aliasing algorithm is to improve the assimilation of radial winds.
Since commercial algorithms provide only one- or two-dimensional wind products, we will use the new method to correct polar volumes as well.
The de-aliasing component is new in the assimilation cycle.
The polar volumes can be applied to variational data assimilation schemes through the generation of so-called superobservations.
A superobservation is an intelligently generalized observation created through smoothing in space, based on high resolution data.
The proper software including the observation operator for the NWP model is already implemented at SMHI.
The proposed de-aliasing method is expected to improve the NWP forecasts.
Currently, only VAD profiles are assimilated operationally into the HIRLAM model.
Assimilation into NWP models
(e.g. VAD profiles, superobservations …)

3. Aliasing problem Doppler “dilemma”
One of the inherent characteristics of Doppler radars is the so called “Doppler dilemma”:
Increasing the maximum unambiguous velocity, decreases the maximum unambiguous range, and vice versa.
The effect is greater for short wavelength radars.
Because range ambiguities contaminate both the reflectivity and radial wind data, they are more difficult to correct.
If a robust velocity de-aliasing method is developed, the Nyquist velocity can be small even when the wind is very large.
By this means, range-ambiguous returns can be effectively minimized.
The velocity jumps in the PPI image are clearly visible.
Blue/green: winds towards the radar
Red/yellow: winds away from the radar
PRT = 1/PRF

4. De-aliasing algorithm
Linear wind model:
The new method is based on a linear wind model, in which the radial wind speed in a specified height interval can be expressed as a function of
azimuth and elevation angle.
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.
Unfortunately, the resulting curve could have discontinuities due to aliasing difficulties.

5. De-aliasing algorithm
Linear wind model:
Map the measurements onto the surface of a torus
To avoid this problem, we map the measurements onto the surface of a torus and yield a continuous parametric curve.

6. Case study
Hemse (Sweden): 2 July 2003, 10:47 UTC

7. Validation New algorithm Siggia & Holmes total sample size 504000
# valid observations
388147
maximum velocity
35.6 m/s
# falsely reconstructed
obs. (vn= 47.6 m/s)
obs. (vn= 7.6 m/s)
100
17205
CPU time
90 s
34 s
In order to make a validation of the new de-aliasing algorithm as realistic as possible, we decided to apply Doppler measurements from an existing radar network.
Their distribution is a priori more natural than for a synthetically generated wind field.
In the validation process, the Doppler data are aliased to a wind speed lower than the Nyquist velocity.
Afterwards, the method's de-aliasing capability to reconstruct the original wind field is examined.
The Doppler data are provided by the Swedish radar network.
Although the Nyquist velocity is relative high (48 m/s), we consider only data sets with a maximum wind speed of 36 m/s to be sure that the
observations are not aliased.
The radial velocities observed by the radar in Hemse within a measurement radius of 100 km, fulfill this requirement.
The sample comprises single measurements whereof are valid.
The de-aliasing experiment with a Nyquist velocity of 47.6 m/s (Swedish radar network) provides a perfect reconstruction of the wind field.
If the maximum unambiguous velocity is reduced to 7.6 m/s, as it is for the lowest elevation angles of the Finnish radar network, 100 single measurements are reconstructed falsely.
This might be caused by erroneous observations or the linear wind assumption.
Both are sensitive to small Nyquist velocities.
The computational costs depend on the sample size of the radar observation.
However, they are currently too high for real-time applications.
But they will probably decrease by converting the routines to C.
Additionally, we compared the novel de-aliasing method with a technique developed by Siggia and Holmes 1991.
It is implemented in the commercial radar software package IRIS which will probably be available at SMHI at the end of this year.
The number of falsely reconstructed observations is more than two magnitudes larger than with our algorithm.

8. Application 1: Wind profiles (VVP)
Vantaa (Finland): 4 December 1999, 12:00 UTC
First, we applied the de-aliasing algorithm to the generation of wind profiles based on the VVP method.
For a case study, we used measurements from Vantaa radar in Finland, because they are more affected by aliasing than Swedish data.
A comparison of the wind speed profiles generated by commercial radar software (SIGMET's IRIS package) and our new algorithm (SMHI) is presented in this figure.
Please keep in mind that both techniques use the same (aliased) radar radial wind observations as input.
It is clearly visible that the two curves almost coincide.
Long-term comparisons (30 hours) between both de-aliasing algorithms for five Finnish radars reveal mostly good agreement.
Unfortunately, there is no radiosonde sounding available for the radar location in Vantaa (Finland).
Instead, the radiosonde observation for Tallinn (Estonia) is shown (approximately 100 km distance from Vantaa).
Although the vertical resolution is much lower than for the radar measurements, structures in the wind speed and direction fields are similar.
The HIRLAM (High Resolution Limited Area Model) forecast (22 km grid point spacing, no assimilation of radar winds) reveal the same trend as the radar observations, however not as detailed.
Therefore, forecasts would probably benefit from an assimilation of de-aliased radar radial winds.

9. Application 2: Superobservations
Karlskrona (Sweden): 3 December 1999, 18:30 UTC
D. B. Michelson

10. Summary accurate & robust post-processing algorithm
(elimination of multiple folding)
no additional wind information needed
(independent data source)
improve quality of wind profiles and superobservations for data assimilation
potential for further reduction of computational costs (real-time applications)
See transparency.