Evaluation and application of polarimetric radar data for the measurement of rainfall

Abstract

The measurement of rainfall using weather radar technologies is an important application in our daily life. Rainfall measurement is important in hydrology and flash flood prediction. Physically-based methods rely fundamentally on the precipitation model, namely, models for the drop size distribution (dsd), drop shape, and drop orientation (or, canting). Traditionally, surface disdrometer, aircraft imaging probes and profilers (a vertical pointing Doppler radar usually operating in the VHF or UHF bands) are used in studying the dsd variability. However, these instruments have limited spatial and temporal resolution. On the other hand, scanning radar can offer measurements with high spatial and temporal resolution. Dual-polarization radar technologies which use the back scatter and forward scatter based measurements at two polarization states (horizontal and vertical) have progressed dramatically in recent decades. However, the accuracy of the precipitation model has not been systematically addressed; this thesis seeks to more fully address the basic model assumptions and the related issue of accuracy. In the first part of this thesis, we propose an areal rainfall algorithm which uses differential propagation phase shift (ϕdp). In this algorithm, we assume that the R-Kdp relationship is 'locally' linear in a small Kdp interval. We show that the random noise and measurement fluctuations can be reduced significantly by averaging rainfall over an area. Since Kdp is a function of the mean axis ratio of drops, we apply a "β correction" as proposed by Gorgucci et al. (1999, 2000) [16, 17]. The β is the slope of equivalent spherical diameter of drop versus the mean axis ratio which can change due to drop oscillations and canting in different rainfall types. By comparing the estimated areal rainfall rate with areal gage rainfall rate, we show that the "β correction" method can significantly reduce the bias in accumulation over an area. Since the β is associated with mean axis ratio, and axis ratio is a function of equivalent spherical diameter of drops, it implies that the β should include information about drop size. In the following chapter, we use β along with Zh and Zdr to retrieve dsd parameters of a normalized gamma model following Bringi et al. (2002) [11]. After retrieving the gamma dsd parameters, we propose a polarimetrically-based Z-R algorithm of the form Z = αR1.5, where the coefficient can be continuously adjusted. We compare radar retrieved dsd data with profiler dsd data, and the pol-based Z-R relation with gage rain rate from two long duration rain events from Brazil and Florida. In chapter 4, we study the drop orientation (or, canting angle) distribution. We first examine the effects of drop oscillation on drop orientation, and then study the relation between the drop orientation distribution and the canting angle distribution. Since polarimetric radar observations are based on the polarization plane, we need to convert drop orientation angles to canting angles. Based on the natural behavior of drop orientation (i.e., azimuthal symmetry), the canting angle should have zero mean. So we only estimate the standard deviation of canting angle (σβ) from the polarimetric data. We study two existing σβ estimators; the first one based on the ratio of maximum and minimum of cross-power, namely, ρ4 method and the second proposed by Ryzhkov (2001) which use LDR and Zdr data. A new algorithm is also proposed which we call the "simplified ρ4 method". In addition, we propose another algorithm to estimate op using the asymmetric ratio (Asy). The asymmetric ratio is defined as the ratio of two eigen values of the Graves power matrix. We test the stability of these four algorithms and also show that these algorithms are not sensitive to the dsd and canting angle distributions. In the end, we apply the Ryzhkov method and the simplified ρ4 algorithm to three rain events. The results for σβ appear to be reasonable, and even though the two algorithms do not agree with each other for low Zdr values, we are able to explain the differences.