Proceedings with Extended Abstracts (single PDF file) - Radio ...

as low as 0.55. The Piura 50-MHz radar has a B 6 -~0.74 in its current configuration.A more general form of the radar equation, (1), shows how the range-weighting functionaffects the data obtained by the radar. In (1), the range-weighting function is shown as a functionof the range from the radar, r 0 , and the distance around this range, r. The received power comesfrom the integration of the product of the reflectivity, (r), and the range-weighting function:r0+ ∆rW ( r0, r)Pr( r0) = ∫ η( r)2dr( 1)0rUsing numerical methods, the range-weighting function, |W(r 0 ,r)| 2 , can be calculated.Figure 2 shows the range-weighting function for a 500 m long transmitted pulse and four valuesof the B 6 - product. The range extent of the volume described by the radar output is determinedby the range-weighting function. A way to summarize this is to define the range resolution of theradar as the distance between the -6 dB points (0.25 relative power level) of the range-weightingfunction. Figure 2 shows that when B 6 - is large, e.g. B 6 -=10.0, the range resolution is 500 m fora 500 m long pulse. The matched-filter case, B 6 -=1.04, gives a resolution of 574 m, B 6 -=0.83gives a resolution of 648 m, and a small B 6 - of 0.55 gives a resolution volume that is 877 mbetween the -6 dB points. In casual discussions, the profiler community describes the rangeresolution only as the pulse length, c-/2.2Figure 2. Range weighting functions for a pulse length of 500 m. Four differentreceiver bandwidths are shown. The horizontal line shows the -6 dB level.Equation 1 shows that the response of the radar to signals in space is controlled (inrange) by the range-weighting function and the reflectivity of the atmosphere. The reflectivityproperties of the atmosphere can cause differences in the location of the maximum velocities, asseen in Figure 1 (Johnston et al., 2002). The range-weighting function shown in Figure 2determines the radial portion of the volume that contributes to the radar data at a given point inspace. The antenna response of the radar determines the tangential, or across beam, dimensionsof the volume.When we sample the continuous signal received by the radar at discrete points, the volumerepresented by each sample is determined by the range-weighting function and the antennaresponse. This sampling of the radar signals has nothing to do with the range resolution of theradar. Using the example of a 500-m pulse length and a B 6 - product of 1.04, each data samplewill represent data from a volume that is approximately 574 m deep. The sampling of thereceived signal could be done every 1 m, or every 10 km, and the range represented by eachsample would be a radial distance of 574 m centered at the sample range, assuming uniformreflectivity in the volume (c.f. Johnston et al., 2002).The range-weighting function, which describes the range behavior of a radar, is derivedas the convolution of the transmitted pulse and the receiver impulse response. A different wayto look at the range behavior is to examine the response in the frequency domain, where the rangeresponse can be easily calculated as the product of the transmitted spectrum and the receiver263