Geoscience Reference
In-Depth Information
Downscaling Satellite Precipitation with Emphasis
on Extremes: A Variational
'
1
-Norm Regularization
in the Derivative Domain
E. Foufoula-Georgiou
A. M. Ebtehaj
S. Q. Zhang
A. Y. Hou
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•
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Received: 1 April 2013 / Accepted: 5 November 2013 / Published online: 11 December 2013
Springer Science+Business Media Dordrecht (outside the USA) 2013
Abstract The increasing availability of precipitation observations from space, e.g., from
the Tropical Rainfall Measuring Mission (TRMM) and the forthcoming Global Precipita-
tion Measuring (GPM) Mission, has fueled renewed interest in developing frameworks for
downscaling and multi-sensor data fusion that can handle large data sets in computationally
efficient ways while optimally reproducing desired properties of the underlying rainfall
fields. Of special interest is the reproduction of extreme precipitation intensities and gra-
dients, as these are directly relevant to hazard prediction. In this paper, we present a new
formalism for downscaling satellite precipitation observations, which explicitly allows for
the preservation of some key geometrical and statistical properties of spatial precipitation.
These include sharp intensity gradients (due to high-intensity regions embedded within
lower-intensity areas), coherent spatial structures (due to regions of slowly varying rainfall),
and thicker-than-Gaussian tails of precipitation gradients and intensities. Specifically, we
pose the downscaling problem as a discrete inverse problem and solve it via a regularized
variational approach (variational downscaling) where the regularization term is selected to
impose the desired smoothness in the solution while allowing for some steep gradients
(called
'
1
-norm or total variation regularization). We demonstrate the duality between this
geometrically
inspired
solution
and
its
Bayesian
statistical
interpretation,
which
is
