The impact of droplets’ clustering on the radar backscattering from water clouds

The goal of this thesis is to investigate the clustering effect of droplets in the water clouds. The initial motivation came from the incapability of millimeter-wave cloud radars to always detect low-level liquid water clouds. The observed discrepancy between the value of radar reflectivity factor estimated by radar measurements and the theoretical one predicted by the standard radar scattering theory set under question the applicability of the incoherent Rayleigh scattering assumption in the case of backscattering from water clouds. A possible reason for the violation of the assumption for incoherent Rayleigh scattering is the formation of clusters inside the cloud volume, which behave as coherent structures. Droplets’ clustering has been investigated through three cases: droplets inside the cloud volume totally correlated form one cluster; droplets inside the cloud volume partially correlated form more than one cluster; droplets inside the cloud volume completely uncorrelated do not form any cluster. The patterns of radar backscattered electric field were visualised in the complex plane by using the Random Walks approach which is a tool for studying the statistical properties of electromagnetic waves backscattered by objects containing few scattering centers. To simulate turbulence inside the cloud volume, four different types of motion for the clusters were introduced. Thus, the turbulence model allows the clusters to shift either horizontally, vertically, towards any direction in 3-dimensional space or rotate about a vertical central axis. The induced velocity and acceleration define clusters’ maximum displacement. The particular motions characterized by the maximum displacement, denote various length scales and intensities of turbulence. The impact of these motions on the pattern of backscattered electric field is investigated for the case of totally correlated droplets which form a single cluster. Low degrees of clustering are explored through the patterns of the radar backscattered electric field, but also from the distribution of power resulting from the coherent summation of the individual backscattered fields. The computational tests showed that the probability density function of coherent power backscattered by n=1, 2, 3 clusters is consistent with the probability density function of the distance from the origin in a single-, two-, three-step isotropic Pearson’s random walk over the two-dimensional phase space respectively. Clusters have been considered in alignment to X-axis, Y-axis, Z-axis or randomly arranged in the cloud volume. An analysis on the statistical properties of the backscattered electric field for different arrangements of clusters inside the cloud volume is presented. The computational results of this research showed that the clustering of droplets results in a radar response which deviates from the one predicted by the standard radar theory. The probability density function of the power backscattered by partially correlated droplets differs from the well-known exponential distribution of completely uncorrelated droplets in the absence of clustering. The systematic discrepancies between the mean coherent and incoherent power imply that radar reflectivity sensitivity of cloud radars may not be sufficient for detecting backscattered signals from water clouds.

Subject

droplets clustering
droplets spatial correlation
radar discrepancy
millimeter-wave cloud radar
Pearsons random walk
coherent radar backscatter
water clouds

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master thesis

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