Doppler Weather Radar
Iwan Holleman / Hans Beekhuis
Contents:
Introduction:
KNMI operates two C-band Doppler weather radars which are amongst others used for obtaining wind profiles. For this, the radars are performing Doppler volume scans, consisting of ten elevations, four times per hour. Under the assumption of a linear wind field within the analyzed volume, profiles of the wind speed and direction, vertical velocity, and divergence can be extracted from the volume data. Several signal processing algorithms, like Velocity Azimuth Display (VAD) and Volume Velocity Processing (VVP), have been developed previously. The data quality and availability of Doppler radar wind profiles obtained using different wind profile algorithms will be assessed in this project.
Principle of Doppler Radar:
A Doppler radar uses electromagnetic waves to investigate atmospheric properties: the amplitude of waves are used to estimate the reflectivity and the phase of the waves are used to estimate the radial wind. A schematical view of a Doppler measurement by a pulsed radar is depicted below:
The radial velocity of scattering particles is determined from their observed phase difference between successive radar pulses. The radar receiver determined the in-phase (I) and quadrature phase (Q) signals with respect to the transmitted signal. The I and Q signals can be visualized in the complex plane:
By calculation of the Fourier Transform of the I and Q signals as a function of transmitted pulse number, the Doppler velocity spectrum can be obtained. Below an example of such a velocity spectrum is shown. The KNMI radars cannot measure this velocity spectrum, and they directly extract the mean velocity and velocity width.
Because a Doppler radar uses phase differences to determine the radial velocity, there is a maximum velocity that can be determined unambiguously. This maximum velocity is called the Nyquist velocity and it can be expressed as:
where PRF is the Pulse Repetition Frequency of the radar pulses and lambda is the wavelength of the radar (5 cm for C-band). The timelag between two successive radar pulses, and thus the PRF, also determines the maximum range that can be resolved unambiguously. This leads to the fundamental equation for the maximum (Nyquist) range and maximum velocity of a Doppler radar:
where c is the speed of light. For measurements with a Doppler radar, a trade-off, therefore, has to be made between the maximum velocity and the maximum range. For a typical C-band weather radar and a maximum range of 150 km, a maximum velocity of only 12 m/s is obtained. Velocities higher than the maximum velocity will be folded back into the fundamental Nyquist interval (aliasing). The measured radial velocity Vm is, therefore, related to the true velocity by:
where n is an unknown integer called Nyquist number. Velocity aliasing can in principle be identified in radar images by detecting abrupt velocity changes of about 2 Vnyquist between neighbouring measurements. In this case, the basic assumption is that the true wind field is sufficiently smooth and regular; this is true for the greater part of the weather situations with the exception of mesocyclones, tornado vortices or highly sheared environments.
Aliasing problems can largely be circumvented by applying different measurement techniques, like dual-PRF or staggered PRT (Pulse Repetition Time). The operational Doppler radars of KNMI have the capability of using the dual-PRF technique. During a dual-PRF measurement, radial winds are measured with alternating high and low PRFs. By combining the measured velocities at low and high PRF, the maximum unambiguous velocity can be extended by about a factor of three. The dual-PRF technique has the disadvantage that, especially in situations with high turbulence or shear, isolated de-aliasing errors remain in the velocity data. At KNMI a detailed analysis of dual-PRF velocity data has been performed and correction algorithm for the production of high quality velocity data has been developed. See for more details: Analysis and Correction of Dual-PRF Velocity Data (407kb)
Wind Profiles:
Radial velocity data are not straightforward to interpret, so some further processing is required before they can be presented to users. Also for assimilation into NWP models, some further processing of the velocity data is required either via the extraction of a representative wind profile or via averaging of raw radial wind data to the grid size of the model.
Doppler radars are recording volume scans, i.e., reflectivity and radial velocity data as a function of range, azimuth, and elevation. The radar geometry used to measure these volume scans for wind profile extraction is shown schematically below. The range, azimuth, and elevation have been indicated in the figure.
Wind profiles can be obtained from single-site radar data under the assumption of a linear wind model. In this model the wind field (U,V,W) in the vicinity of the radar (at x = 0 and y = 0) is expressed as:
V(x,y,z) = v0 + x dv/dx + y dv/dy + (z-z0) dv/dz
W(x,y,z) = w0 + (z-z0) dw/dz
Using this linear wind field, the radial wind can be calculated as a function of range, azimuth (phi), and elevation (theta). In addition to the movement due to the wind field, the hydrometeors have a vertical velocity (Wfinal) due to gravity. For a uniform wind field this results in:
When Doppler radar data is displayed at constant range and elevation (theta), the radial wind as a function of azimuth (phi) will have the form of a sine. The wind speed and direction can be determined from the amplitude and the phase of the sine, respectively. This technique is called Velocity-Azimuth Display (VAD), and it was introduced by R. Lhermitte (1961), and K. A. Browning and R. Wexler (1968).
From the volume scans, different VADs can be extracted as a function of height, and a wind profile at the radar site can thus be obtained. Extraction of the vertical air velocity (w0) using the VAD technique is troubled by interference of the divergence of the local wind field and of the terminal velocity of the precipitation.
Instead of processing, for each height, a single VAD or a series of VADs, one can also process all available volume data in a certain height layer at once. This so-called Volume Velocity Processing technique (VVP) has been introduced by P. Waldteufel and H. Corbin (1979). Using the previous equations of the linear wind model, the radial wind can be calculated for all points within a layer centered at height z0 as a function of Range (R), azimuth (phi), and elevation (theta):
+ SHEAR/2 R cos(theta) sin(2phi) + STRETCH/2 R cos(theta) cos(2phi)
+ dw/dz (z-z0) sin(theta) + du/dz (z-z0) sin(theta) sin(phi) + dv/dz (z-z0) sin(theta) cos(phi)
where DIV is the divergence, SHEAR is the shearing deformation and STRETCH the stretching deformation of the wind field. Via a multi-dimensional and multi-parameter linear fit, the parameters of the linear wind field can be extracted. The VVP technique is typically applied to thin layers of data at successive heights to obtain a wind profile.
The radars in De Bilt and in Den Helder perform a Doppler volume scan every 15 minutes, and wind profiles are extracted from the volume scans using the VVP algorithm. The wind profiles are collected and are plotted in time-height diagrams. These diagrams allow for on-line montoring of the wind field and also reveal the wind changes associated with passage of a low/high pressure system or a front. For real-time and archived wind data of De Bilt go to wind profiles and of Den Helder go to wind profiles.
An example of time-height plot of wind profiles at De Bilt is shown in the figure below. The wind barbs of the radar are given in black, the radiosonde winds in red, and the Hirlam winds in blue.
Clutter and Birds:
Radial wind measurements, just like reflectivity measurements, can be heavily affected by normal or anomalous propagation clutter. Clutter signal can be suppressed to a large extent from the reflectivity and radial wind data by reducing the echo power around zero radial velocity using discrete filtering techniques in the time or frequency domains. All operational Doppler radars apply this kind of filtering before the radial velocity is determined.
Apart from precipitation, non-hydrometeor targets such as insects and birds are detected by Doppler radar as well. While insects can provide a help in defining the boundary layer wind, birds are mainly a problem for velocity retrieving algorithms. Erroneous wind data due to bird migration can be recognized by inconsistency of the wind data with respect to radiosonde or NWP winds. For information on birds and bird migration take a look a the website of Stichting Vogel Onderzoek Nederland (SOVON).
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Hans Beekhuis