Apart from the inuence of instrumentation eects and meteorological parameters on the accuracy of the wind{eld determination, the accuracy of the wind{eld is also aected by the location of transmitter, receiver, and target (dened by ) and the number of Doppler velocity measurements, vmn, achieved in the same area by
n receivers. The inuences of instrumentation eects, signal processing, and meteo- rological parameters on the quality of the wind{eld are similar for bistatic and for monostatic Doppler radar systems and will not be discussed in detail in this section. In this work, only the inuence of and n on the standard deviation of the hori- zontal wind{eld is discussed. Hereafter, the standard deviations of the horizontal wind{eld refer exclusively to the geometrical impact.
In the following discussion, the velocity variance of the horizontal wind{eld,
2
jVhj, determined by the bistatic multiple{Doppler radar network at Oberpfaen-
hofen, is compared to the velocity variance achieved by the monostatic dual{Doppler wind{eld processing. The latter is performed with POLDIRAD and the operational C-band Doppler radar of the German Weather Service (DWD) on Mount Hohen- peienberg about 37 km south{west of OP (hereafter 'radar HP'). In addition, it is shown how an overdetermination of the equation system to calculate the wind{ eld reduces 2
jVhj compared to dual{Doppler wind{eld processing for the bistatic
Doppler radar network in OP.
The variance of the estimates of (u;v) independent of the wind{velocity can be expressed by taking the second power of Eq. (2.34) and Eq. (2.35).
It is assumed that monostatic and bistatic receivers have the same variance in the Doppler velocity measurement (only instrumental error), 2vm1 =2vm2 =:::=2vmn.
Within a bistatic network, the measured apparent velocity,va, has to be projected
onto the direction
e
. Therefore, the variance of the i0th Doppler velocity has to beprojected as well, which leads to 2vmi =2vei =2vai cos;2(
2.7 Accuracy of the wind{eld determination 29 In the following, the horizontal distribution of the standard deviation of the hor- izontal wind{velocity is discussed for
Cases 1 { 3
. Figure 2.13 illustrates the stan- dard deviation for all three cases normalized by the radial velocity standard deviation which is for most weather radar systems 1 ms;1.The following discussion is focused on the bistatic Doppler radar network at OP. The standard deviation of the Doppler velocity measurement using POLDIRAD can be assumed to be 0.8 ms;1, a value which is applied to the following discussion.
Case 1:
In monostatic multiple{Doppler installation, the radial velocities, vtj,measured by each individual monostatic Doppler radar are combined [cf. Eq. (2.37) and Eq. (2.38)] to a wind{vector. The unit vectors of two vtj's intersect at an angle
called the intersection angle. This angle is identical to the angle.
For monostatic dual{Doppler radar processing consisting of POLDIRAD and radar HP, the distribution of the standard deviation12 of 0
jVhj at ground level is
illustrated in Figure 2.13(a). The horizontal wind{eld can be measured with a stan- dard deviation of 1.2 m s;1 { 1.6 ms;1 within the monostatic dual{Doppler radar
network. This range corresponds to an intersection angle ranging between 50 and
140. The minimum value of0
jVhjis at an intersection angle of 90
. If the intersection
angle approaches 180 or 0,0
jVhj becomes innite [cf. Fig. 2.13(a)].
Case 2:
Here we discuss the accuracy of the horizontal wind{eld using bistatic dual{Doppler processing consisting of POLDIRAD and the bistatic receiver system Lagerlechfeld [cf. Fig. 2.13(b)]; and bistatic quadruple{Doppler processing consist- ing of POLDIRAD and the three bistatic receivers at Lichtenau, Lagerlechfeld, and Ried [cf. Fig. 2.13(c)]. Within a bistatic multiple{Doppler radar system, ve and vtare combined. The intersection angle between these two vectors is identical to =2 (Fig. 2.3).
For a bistatic dual{Doppler radar system, the distribution of 0
jVhj is illustrated
in Fig. 2.13(b). A minimum of 0
jVhj within the bistatic dual{Doppler network is
reached at an intersection angle of about 100. 0
jVhj ranges at ground level between
1.9 ms;1 and 3.2 ms;1 which is within 25
=2 70
. If the intersection angle,
=2, approaches 90 or 0, 0
jVhj becomes innite [cf. Fig. 2.13(b)].
Additional receivers result in overdetermination of the horizontal wind{eld. For bistatic quadruple{Doppler processing, 0
jVhj ranges from 1.2 ms
;1 to 2.0 ms;1 at
ground level [Fig. 2.13(c)]. These values are comparable to the standard deviation of monostatic dual{Doppler processing [Fig. 2.13(a)]. As a result, the standard deviation can be reduced by about 1 ms;1in bistatic quadruple{Doppler compared to a bistatic
dual{Doppler processing [cf. Figs. 2.13(b) and 2.13(c)]. The eect of an innite0 jVhj
at = 0 or 90 in a dual{Doppler system is reduced in a quadruple{Doppler system
because the transmitter{receiver baseline is covered by the additional receivers.
Case 3:
Here, the monostatic radar acts as a transmitting source only insofar as the bistatic Doppler velocity measurements are used to determine horizontal wind{ eld [Fig. 2.13(d)]. Within the observation area,0jVhjranges between 1.3 ms
;1 and
12To avoid confusion with the standard deviation of the horizontal wind{velocity, denoted as
jV
h
j, the standard deviation at a certain grid{point is symbolized by
0
jV h
30 Monostatic versus bistatic Doppler radar
(a) (b)
(c) (d)
Figure 2.13:
Spatial distribution of the 0jVhj normalized by the radial velocity standard
deviation of 1ms;1 for (a) monostatic dual{Doppler processing; (b) bistatic dual{Doppler
processing; (c) bistatic quadruple{Doppler processing and; (d) bistatic triple{Doppler pro- cessing with only bistatic receivers. Note that the maximum contour line is set at a value of ten.
2.8 Optimal arrangement for the bistatic receiver 31