5 research outputs found
Variational Downscaling, Fusion and Assimilation of Hydrometeorological States via Regularized Estimation
Improved estimation of hydrometeorological states from down-sampled
observations and background model forecasts in a noisy environment, has been a
subject of growing research in the past decades. Here, we introduce a unified
framework that ties together the problems of downscaling, data fusion and data
assimilation as ill-posed inverse problems. This framework seeks solutions
beyond the classic least squares estimation paradigms by imposing proper
regularization, which are constraints consistent with the degree of smoothness
and probabilistic structure of the underlying state. We review relevant
regularization methods in derivative space and extend classic formulations of
the aforementioned problems with particular emphasis on hydrologic and
atmospheric applications. Informed by the statistical characteristics of the
state variable of interest, the central results of the paper suggest that
proper regularization can lead to a more accurate and stable recovery of the
true state and hence more skillful forecasts. In particular, using the Tikhonov
and Huber regularization in the derivative space, the promise of the proposed
framework is demonstrated in static downscaling and fusion of synthetic
multi-sensor precipitation data, while a data assimilation numerical experiment
is presented using the heat equation in a variational setting
Shrunken Locally Linear Embedding for Passive Microwave Retrieval of Precipitation
This paper introduces a new Bayesian approach to the inverse problem of
passive microwave rainfall retrieval. The proposed methodology relies on a
regularization technique and makes use of two joint dictionaries of
coincidental rainfall profiles and their corresponding upwelling spectral
radiative fluxes. A sequential detection-estimation strategy is adopted, which
basically assumes that similar rainfall intensity values and their spectral
radiances live close to some sufficiently smooth manifolds with analogous local
geometry. The detection step employs a nearest neighborhood classification
rule, while the estimation scheme is equipped with a constrained shrinkage
estimator to ensure stability of retrieval and some physical consistency. The
algorithm is examined using coincidental observations of the active
precipitation radar (PR) and passive microwave imager (TMI) on board the
Tropical Rainfall Measuring Mission (TRMM) satellite. We present promising
results of instantaneous rainfall retrieval for some tropical storms and
mesoscale convective systems over ocean, land, and coastal zones. We provide
evidence that the algorithm is capable of properly capturing different storm
morphologies including high intensity rain-cells and trailing light rainfall,
especially over land and coastal areas. The algorithm is also validated at an
annual scale for calendar year 2013 versus the standard (version 7) radar
(2A25) and radiometer (2A12) rainfall products of the TRMM satellite
Coping with model error . . .
We introduce a method to handle model uncertainty in data assimilation Optimal mass transport is used to quantify mismatch between forecast and states The promise of our method is demonstrated in advection-diffusion dynamic