Study of the attenuation error structure

The interest of studying the error covariance matrices of radar rainfall estimates has recently increased, with the aim to improve the characterization of the uncertainty inherent into radar rainfall estimates, necessary for radar assimilation into numerical models and for some probabilistic applications.

Two alternative ways to obtain this matrix have been recently explored: (a) studying the overall error structure by analyzing the residuals between radar estimates and an independent source of rainfall measurements (usually rain gauges); (b) studying separately, by simulation, the structure of the different sources of errors affecting radar measurements and, as a second step, the cross-covariances between them. Although the first approach gives us a straightforward way to characterize the total uncertainty (though one that is affected by the uncertainty of the “reference”), the second provides more understanding of the errors themselves, but requires assumptions used for the simulations.

Following the second approach, this work focuses on characterizing the structure of the errors due to signal attenuation by rainfall. In particular, our main purpose has been to obtain the distribution of the Path Integrated Attenuation (PIA) as a function of the path length through rainfall and the ACF of the PIA field. Secondly, we investigate the cross-correlation between errors due to attenuation and those due to the variability of drop size distributions.

To carry out this work, DSD measurements obtained with a POSS disdrometer have been used to simulate radial profiles of rainfall observed at attenuated wavelengths. In the simulation, the T-matrix method scattering has been used to account for drop deformation.