1  Intorduction

At present, Doppler weather radars became the operational standard. Doppler radars provide measurements not only of the radar reflectivity (as conventional radars), but also of the frequency change of backscattered signal, which can be used for determination of radial velocity of the targets (mainly atmospheric precipitation and fluctuations in refractive index of air).

Czech Hydrometeorological Institute operates the Czech Weather Radar Network consisting of 2 weather radars (non-Doppler X-band MRL-5 at Prague-Libus, digitized in 1993, and Doppler C-band Gematronik Meteor 360 AC with Rainbow software installed at Skalky plateau in Central Moravia) [13]. The installation of a new Doppler radar in Central Bohemia (C-band EEC 2500C with EDGE software) is prepared for the end of 1999. Both, the existing Gematronik radar and planned EEC radar, are capable to measure radial Doppler velocities.

2  Theory of Doppler weather radar measurement

2.1  Doppler effect

Atmospheric targets usually are not static. Let us consider a radar with wavelength l observing a target at range r. If radar signal is transmitted with initial phase of j₀ then the phase of returned signal will be j₀ - 4 pr(t)/l. If the target is moving with respect to the radar with a radial velocity v_r, the phase of the signal varies and we have

Thus, the frequency of the echo has a shift due to the Doppler effect f_d = -2 v_r/l. The Doppler frequencies of atmospheric targets do not exceed a few kilohertz. Therefore they are too small with respect to the transmitted frequencies to measure them directly. Doppler signal is derived from comparison of transmitted and received signal. Because the duration of one pulse is only t = 0.5-2ms it's not possible to determime Doppler frequency directly from this one pulse, but it's possible from phases of several consecutive pulses. The Fast Fourier Transformation or method called Pulse-Pair Algorithm (calculation of autocorrelation coefficients of measured phases) is used for calculation of Doppler frequency from serie of phases [4], [11].

2.2  Doppler dilemma

Because the Doppler frequency is not determined from continuous measurements but from discrete ones defined by the pulse repetition frequency f_r, there is limitation on the velocities that a radar can resolve unambiguously. The maximum Doppler frequency that can be measured unambiguously is equal to half of the pulse repetition frequency f_dmax = f_r/2 (also called Nyquist frequency). Consequently, the maximum unambiguous velocity is equal to

Because the velocity speed of radar pulse is approximately equal to the speed of light c, the maximum unambiguous range (defined as a range from which the backscattered signal can be received before next pulse transmission) is given by r_max = c /2 f_r. The echo of a strong target at range r > r_max is interpreted as a new pulse echo target at range r - r_max (ßecond-trip echo"). The combination of this relation with the equation for maximum unambiguous velocity gives equation (also called ëquation of Doppler Dilemma")

Various software algorithms for velocity aliasing removal from radar data exist, but none ensures full recovery. In addition, there is also a possibility of a hardware based extension of the maximum unambiguous velocity interval, which exploits combination of 2 repetition frequencies (with fixed ratio e.g.: 2/3, 3/4, 4/5). A detailed information about the Doppler weather radar theory can be found e.g. in [4], [5], [7], [8], [11], [12].

2.3  VAD Method

A Doppler radar allows the measurement of only one (radial) component of the velocity of the targets. In general case, air movement is 3-dimensional and varies over time and space. Simultaneous measurements with three Doppler radars would have to be performed to describe this movement completely, but typically only data from a single Doppler radar are available. That is why we are forced to make simplifying assumption on the structure of the observed wind field during creation of Doppler products.

The most simple case is to consider a horizontally uniform wind field for both, horizontal and vertical (precipitation fall velocity), components. In such a case, if we make measurement of the velocity along circles centred at the radar by azimuthal scanning at a constant elevation angle (PPI), we get for a constant distance from the radar sinusoidal dependency of the measured radial velocity on the azimuthal angle ("Velocity-Azimuth Display" - fig.1).

Fig. 1: VAD method

Direction of horizontal wind b₀ is given by azimuths of the maximum and minimum measured radial velocity. Horizontal [`(V<sub>h</sub>)] and vertical [`w] components of the velocity speed is obtained from maximum (V₁ = V_rmax) and minimum (V₂ = V_rmin) velocity and elevation angle a:

If this calculation is performed for a fixed elevation angle and several distances from radar, we will get vertical profile of the wind speed and direction. In operational measurement we do not get data from all azimuth angles and velocity-azimuth dependency is not perfectly sinusoidal, that is why [`(V<sub>h</sub>)] and [`w] is estimated by a least square fit or similar method.

The described algorithm is the most simple one but it shows the principles and problems of Doppler radial velocities processing. More complex VAD algorithms assume a local wind field varying almost linearly so that the velocity components could be approximated by a Taylor series expansion limited to first derivatives. The kinematic properties of the local wind field are then determined using the Fourier series expansion. In another algorithm, VVP (Volume Velocity Processing), the data from more elevation angles are considered together in order to get more complex information about wind field parameters. For detailed description of VAD/VVP methods see e.g.: [4], [6] or [12].

3  PPI display of the Radial Velocity

Operational measurement of Doppler weather radars consists of several PPI measurements (measurements with constant elevation angle and varying azimuth) at different elevation angles. The most simple visualisation of these "volume" data is the projection of single PPI into the horizontal plane. The value in each pixel is then expressed by certain colour from a colour or gray scale. The distance from radar r and elevation angle of the corresponding PPI level a give the altitude of displayed target z = r sina.

Such visualisation of a scalar field (as radar reflectivity or rain rate) is clear and intuitive. The same is not true for a vector field such as velocity and, thus, during PPI interpretation, we have to remember that Doppler radar does not measure velocity vector but only magnitude of its radial component.

Fig. 2: Doppler velocity fields simulation

Simulations of PPI visualisation of Doppler velocities for different observed wind fields were created to provide help with operational interpretation of Doppler data in the future [9]. Simulations were done not only for horizontally uniform wind field but also for more complex fields, e.g. divergence, convergence or cyclonic and anticyclonic rotation. Simulation of aliased velocity and frontal discontinuity wind field were also created. Examples of these simulations are shown in fig.2. More information about the Doppler data interpretation can be found in [10], [12].

4  Doppler data processing

Because of these problems we have decided to develop a software package for processing of raw volume data in the Rainbow format and products creation. At present, the first release of this software package (including both reflectivity and Doppler velocity volume data processing, basic reflectivity products creation) is available. This software has allowed us first tests of Doppler data processing.

Fig. 3: Radar reflectivity and Doppler velocity PPI fields from recent operational scan (f_r = 560Hz, r_max = 256km, v_max = 7.37ms^-1)

Fig.3 shows processed reflectivity and Doppler velocity volume data from a scan, obtained with the same set-up as for operational measurements of the radar reflectivity. Because the operational measurement is done up to range of 256 km the maximum unambiguous velocity is only 7.37ms^-1. That is why the velocity aliasing already exists on low elevation measurement when the lower part of atmosphere (with low velocities) is observed.

Fig. 4: Doppler velocity fields measured with modified parameters (f_r: DUAL-PRF 2:3 /533:800Hz/, r_max = 25km, v_max = 21.2ms^-1) displayd by various displays

Fig.4 shows two PPI levels from volume scan (higher elevations) with modified scanning parameters displayed by various methods. The maximum unambiguous velocity is equal to 21.2ms^-1 and we can see that aliasing (very well detectable) exists only at higher ranges (it means higher altitudes). The first tests have already showed that for routine exploitation of Doppler data it will be necessary to modify the existing operational volume scan parameters. The prepared software package enables this.

5  Conclusion and Outlook

Doppler velocity data can provide a lot of useful information for meteorological applications, including ground clutter removal from radar reflectivity data, exploitation of vertical wind profiles, algorithms for detection of dangerous phenomena mainly in convective storms (mesocyclone, downburst).

Doppler weather radar theory, simulations of Doppler data visualisation and the first results of Doppler data processing in the Czech Republic are presented in this article. The work on exploitation of Doppler data from Czech weather radars is in very early stage now. It is aimed for operative aplications in the Czech Hydrometeorological Institute. Main tasks of future work are:

• Incorporation of processing of Doppler data (de-aliasing, PPI, VAD/VVP products, detection algorithms) into the operation of the Czech Weather Radar Network.

• Comparison of Doppler products with the data from aerological soundings and the outputs from Local Area NWP model ALADIN, operated by LACE in the CHMI.

• Preparation of guidelines for the operational interpretation of these data.

• Assessment of the applicability of Doppler radar data as an input into the assimilation (4DVAR) of ALADIN model.

References

[1]

Atlas, D.(ed.),:Radar in Meteorology, American Meteorological Society, 1990

[2]

Battan, L.J.,:Radar Observation of the Atmosphere, The University of Chicago Press, Chicago and London, 1973

[3]

Browning, K.A., Wexler R.: The determination of kinematic properties of a wind field using Doppler radar, J. Appl. Meteor., 7, 1968, p. 105-113

[4]

Doviak, R.J., Zrnic D.S.: Doppler Radar and Weather Observation, Academic Press Inc., San Diego, 1984, 1993

[5]

Eilts, M.D., Smith S.D.: Efficient Dealiasing of Doppler Velocities Using Local Environment Constraints, Journal of Atmospheric and Oceanic Technology, 7, 1990, p. 118-128

[6]

Germann, U.: Vertical wind profile by Doppler weather radars - A new algorithm including de-aliasing, unpublished contribution to the RADHYD project, Locarno, 1998

[7]

Jing, Z., Wiener G.: Two-Dimensional Dealiasing of Doppler Velocities, Journal of Atmospheric and Oceanic Technology, 10, 1991, p. 798-808

[8]

Miller, L.J., Mohr C.G, Weinheimer A.J.: The Simple Rectification to Cartesian Space of Folded Radial Velocities from Doppler Radar Sampling, Journal of Atmospheric and Oceanic Technology, 5, 1986, p. 162-174

[9]

Novak P.: Doppler Radar Measurement of Radial Velocities, Seminar work, Faculty of Mathematics and Physics, Charles University, Prague, 22p.
            - WWW version: http://www.chmi.cz/meteo/rad/pub/sem_dop/

[10]

Federal Meteorological Handbook No.11, Doppler Radar Meteorological Observations. OFCM, NOAA, Dept.of Commerce, Washington D.C. 1991.

[11]

Peters, S.R., Ziegler C.: De-Aliasing First-Moment Doppler Estimates, J. Appl. Meteor., 16, 1977, p. 563-564

[12]

Sauvagot, H.: Radar Meteorology, Artech House, Boston, 1992

[13]

http://www.chmi.cz/meteo/rad/
            - WWW homepage of the Czech Hydrometeorological Institute, Radar Department