A Synergy Method to Improve Ensemble Weather Predictions and Differential SAR Interferograms

Abstract

A compensation of atmospheric effects is essential for mm-sensitivity in differential interferometric synthetic aperture radar (DInSAR) techniques. Numerical weather predictions are used to compensate these disturbances allowing a reduction in the number of required radar scenes. Practically, predictions are solutions of partial differential equations which never can be precise due to model or initialisation uncertainties. In order to deal with the chaotic nature of the solutions, ensembles of predictions are computed. From a stochastic point of view, the ensemble mean is the expected prediction, if all ensemble members are equally likely. This corresponds to the typical assumption that all ensemble members are physically correct solutions of the set of partial differential equations. DInSAR allows adding to this knowledge. Observations of refractivity can now be utilised to check the likelihood of a solution and to weight the respective ensemble member to estimate a better expected prediction. The objective of the paper is to show the synergy between ensemble weather predictions and differential interferometric atmospheric correction. We demonstrate a new method first to compensate better for the atmospheric effect in DInSAR and second to estimate an improved numerical weather prediction (NWP) ensemble mean. Practically, a least squares fit of predicted atmospheric effects with respect to a differential interferogram is computed. The coefficients of this fit are interpreted as likelihoods and used as weights for the weighted ensemble mean. Finally, the derived weighted prediction has minimal expected quadratic errors which is a better solution compared to the straightforward best-fitting ensemble member. Furthermore, we propose an extension of the algorithm which avoids the systematic bias caused by deformations. It makes this technique suitable for time series analysis, e.g. persistent scatterer interferometry (PSI). We validate the algorithm using the well known Netherlands-DInSAR test case and first show that the atmospheric compensation improves by nearly 40% compared to the straightforward technique. Second, we compare our results with independent sea level pressure data. In our test case, the mean squared error is reduced by 29% compared to the averaged ensemble members with equal weights. An application demonstration using actual Sentinel-1 data and a typical test site with significant subsidence (Mexico City) completes the paper.