<title>Spaceborne Doppler precipitation radar: system configurations and performance analysis</title>

Abstract

Knowledge of the global distribution of the vertical velocity of precipitation is important in the study of energy transportation in the atmosphere, the climate and weather. Such knowledge can only be directly acquired with the use of spaceborne Doppler precipitation radars (DPR). Although the high relative speed of the radar with respect to the rainfall particles introduces significant broadening in the Doppler spectrum, recent studies have shown that the average vertical velocity can be measured to acceptable accuracy levels by appropriate selection of radar parameters. Furthermore, methods to correct for specific errors arising from non-uniform beam filling (NUBF) effects and pointing uncertainties have recently been developed. In this paper we will present the results of the trade studies on the performances of a spaceborne Doppler radar with different system parameters configurations. Particular emphases will be placed on the choices of: 1) the PRF vs. antenna size ratio, 2) the observational strategy, 3) the operating frequency; and 4) processing strategy. The results show that accuracies of 1 m/s or better can be achieved with the currently available technology. DOPPLER VELOCITY MEASUREMENTS FROM SPACEBORNE RADARDoppler velocity measurements require coherent processing of the radar signal. It follows that two consecutive radar echoes must be correlated in order to allow the measurement of the relative phase shift (and therefore of the Doppler frequency shift) without ambiguity.A Doppler radar transmitting one pulse every T S seconds can measure without ambiguity the Doppler velocity of a single target in the range ±v m where v m is the Nyquist limit imposed by the finite sampling:(1) where is the radar operating wavelength and PRF = 1/T S is the Pulse Repetition Frequency. A Precipitation Radar measures the echo returned by the distributed target consisting of all hydrometeors within a radar volume of resolution, therefore, in general, the Doppler signal is described through its Doppler velocity spectrum P(v) which can be expressed as:[ ] ( ) + = r r r r p r p

Spaceborne Doppler Radar Measurements of Rainfall: Correction of Errors Induced by Pointing Uncertainties

“…In fact, assuming that the error introduced by the pointing uncertainty is independent of all other sources of error, and modeling all errors as random variables with Gaussian distribution, one can simply sum their variance to obtain the overall variance of the estimate. For example, it was shown in Tanelli et al (2004) that a root-mean-square error (rmse) better than 0.75 m s Ϫ1 on vertical velocity estimates can be obtained by NDPR for a signal-to-noise ratio (SNR) Ͼ 10 dB and by ignoring pointing errors. To satisfy the 1 m s Ϫ1 overall requirement, one should impose rms( ␣ ) Ͻ 0.66 m s Ϫ1 .…”

“…A second simple model is useful to assess the effect of NUBF on the observed surface Doppler velocity: one could assume that the apparent (i.e., attenuated) surface reflectivity Z X (x), expressed in dBZ, varies linearly within the radar footprint. Following an approach similar to that used in the CFT (Tanelli et al 2004) to correct for turbulence-induced offsets, one obtains…”

“…The CFT technique, described in Tanelli et al (2004) and briefly recalled here, aims at removing the NUBFinduced bias from the estimates of rainfall average vertical velocity by estimating the first moment of the tracks of the rainfall distributed targets projected in the along-track satellite position/Doppler velocity (x-) plane. Figure 4 shows a sequence of periodograms measured by a Doppler radar for the range cell intersecting the sea surface in the first case study discussed in section 5.…”

“…Although the high relative speed of an orbiting radar with respect to the rainfall particles introduces significant broadening in the Doppler spectrum, recent studies (Tanelli et al 2002(Tanelli et al , 2004 have proven that the average vertical velocity can indeed be measured to the 1 m s Ϫ1 accuracy level by the proper selection of radar parameters. The parameters and configuration for a representative 14-GHz nadir-pointing spaceborne Doppler precipitation radar (NDPR; see appendix C for a complete list of acronym and symbol definitions) employed in this study are shown in Table 1.…”

“…In section 4, the application of the combined frequency-time (CFT) algorithm to sea surface Doppler spectra is described. The CFT algorithm, originally developed to correct for the NUBF-induced bias in vertical velocity measurements of rainfall (Tanelli et al 2004), is applied in this paper also to analyze the sea surface Doppler spectrum and correct for the pointinginduced bias in vertical velocity under uniform beam filling (UBF) and nonuniform beam filling conditions. Figure 1 shows the geometry of the problem and introduces the vector notation used throughout this paper.…”