On the enhanced temporal coherency of radar observations in precipitation

In this work, the authors present observations of enhanced temporal coherency beyond that expected using the observations of the standard deviation of the Doppler velocities and the assumption of a family of exponentially decaying autocorrelation functions. The purpose of this paper is to interpret these observations by developing the complex amplitude autocorrelation function when both incoherent and coherent backscatter are present. Using this expression, it is then shown that when coherent scatter is present, the temporal coherency increases as observed. Data are analyzed in snow and in rain. The results agree with the theoretical expectations, and the authors interpret this agreement as an indication that coherent scatter is the likely explanation for the observed enhanced temporal coherency. This finding does not affect decorrelation times measured using time series. However, when the time series is not available (as in theoretical studies), the times to decorrelation are often computed based upon the assumptions that the autocorrelation function is a member of the family of exponentially decaying autocorrelation functions and that the signal decorrelation is due solely to the Doppler velocity fluctuations associated with incoherent scatter. Such an approach, at times, may significantly underestimate the true required times to decorrelation thus leading to overestimates of statistical reliability of parameters

A scalable approach for Variational Data Assimilation

Data assimilation (DA) is a methodology for combining mathematical models simulating complex systems (the background knowledge) and measurements (the reality or observational data) in order to improve the estimate of the system state (the forecast). The DA is an inverse and ill posed problem usually used to handle a huge amount of data, so, it is a large and computationally expensive problem. Here we focus on scalable methods that makes DA applications feasible for a huge number of background data and observations. We present a scalable algorithm for solving variational DA which is highly parallel. We provide a mathematical formalization of this approach and we also study the performance of the resulted algorith

On the condition number of Gaussian sample-covariance matrices

The authors examine the reasons behind the fact that the Gaussian autocorrelation-function model, widely used in remote sensing, yields a particularly ill-conditioned sample-covariance matrix in the case of many strongly correlated samples. The authors explore the question numerically and relate the magnitude of the matrix-condition number to the nonnegativity requirement satisfied by all correlation functions. They show that the condition number exhibits explosive growth near the boundary of the allowed-parameter space, simple numerical recipes are suggested in order to avoid this instability