Sparse regularization for precipitation downscaling

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Authors Ebtehaj, A.M., E. Foufoula-Georgiou, G. Lerman
Paper Category
Paper Abstract Downscaling of remotely sensed precipitation images and outputs of generalcirculation models has been a subject of intense interest in hydrometeorology. The problemof downscaling is basically one of resolution enhancement, that is, appropriately addingdetails or high frequency features onto a low-resolution observation or simulated rainfallfield. Invoking the property of rainfall self similarity, this mathematically ill-posed problemhas been approached in the past within a stochastic framework resulting in ensemble ofpossible high-resolution realizations. In this work, we recast the rainfall downscaling intoan ill-posed inverse problem and introduce a class of nonlinear estimators to properlyregularize it and obtain the best high-resolution estimate in an optimal sense. Thisregularization capitalizes on two main observations: (1) precipitation fields are sparse whentransformed into an appropriately chosen domain (e.g., wavelet), and (2) small-scaleorganized precipitation features tend to recur within and across different stormenvironments. We demonstrate the promise of the proposed methodology throughdownscaling and error analysis of level III precipitation reflectivity snapshots provided bythe ground-based next generation Doppler weather radars in a ground validation sites of theTropical Rainfall Measuring Mission.
Date of publication 2012
Code Programming Language MATLAB

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