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simplib the analysis by converting this multi-parameter model to a simpler and more
intuitive form.
To begin this SimpWcation process, consider the general formulation equations
presented in Section 2 3.1 In this formulation can be equated to V, the radial
component in the sector, while Vv becomes K, the tangential component. This can
ea~iiy be shown by an appropriate axis rotation. By setting the radial mmpment
to an arbitrary mnstant it is clear that the tangential component is a function of
the changing radial components me& by the radar. Even though this may be
intmtive. this step re& the key parameter in the tangential estimation process-
the linear change in the radial -t varlation over azimuth. Hence, using this
approach, an inwtigation of the effect of this variable only will he considered. This
simpliFxation allows us to consider the e kt of the variation of azimuth only As the
radial anent is held constant the effect of that variable should be minimized with
respect to the azimuthal variation.
With this simplification, the variability of results is studied using three azimuthal
extents. The range inuement war held constant at the arclength used for the direct
radial component averaging, 4.8 km, while the angular extents arere chosen ar IZ',
2(P and 36" (i.e. an odd integral number of nominal radar beamwidthe.). For each
care the point dens,@ is preserved, in that radial data irom each radar cell contains
only one radial component at any range while the sector area is increasing with range.
In ather wrds, for each angular extent the same -her of radial components d
be used to estimate the vector current at each estimation point. However, this may
not be the optimal approach, as mentioned in the previous seetion, since this does
not preserve area. At range of 50 and ZOO 00, the area ewerage is approximately
50 and 2W square kilometar, respmtively, for the 12- ease. Far the 36" case this
corresponds to are- of 150 and 6W square kilometers. An flustration of the size of
these regions with respect to the radar -rage area is show in Figure 4.2.