309 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
A multi-sensor data-driven methodology for all-sky passive microwave inundation retrieval
We present a multi-sensor Bayesian passive microwave retrieval algorithm for
flood inundation mapping at high spatial and temporal resolutions. The
algorithm takes advantage of observations from multiple sensors in optical,
short-infrared, and microwave bands, thereby allowing for detection and mapping
of the sub-pixel fraction of inundated areas under almost all-sky conditions.
The method relies on a nearest-neighbor search and a modern sparsity-promoting
inversion method that make use of an a priori dataset in the form of two joint
dictionaries. These dictionaries contain almost overlapping observations by the
Special Sensor Microwave Imager and Sounder (SSMIS) on board the Defense
Meteorological Satellite Program (DMSP) F17 satellite and the Moderate
Resolution Imaging Spectroradiometer (MODIS) on board the Aqua and Terra
satellites. Evaluation of the retrieval algorithm over the Mekong Delta shows
that it is capable of capturing to a good degree the inundation diurnal
variability due to localized convective precipitation. At longer timescales,
the results demonstrate consistency with the ground-based water level
observations, denoting that the method is properly capturing inundation
seasonal patterns in response to regional monsoonal rain. The calculated
Euclidean distance, rank-correlation, and also copula quantile analysis
demonstrate a good agreement between the outputs of the algorithm and the
observed water levels at monthly and daily timescales. The current inundation
products are at a resolution of 12.5 km and taken twice per day, but a higher
resolution (order of 5 km and every 3 h) can be achieved using the same
algorithm with the dictionary populated by the Global Precipitation Mission
(GPM) Microwave Imager (GMI) products.Comment: 12 pages, 9 Figure
Variational Data Assimilation via Sparse Regularization
This paper studies the role of sparse regularization in a properly chosen
basis for variational data assimilation (VDA) problems. Specifically, it
focuses on data assimilation of noisy and down-sampled observations while the
state variable of interest exhibits sparsity in the real or transformed domain.
We show that in the presence of sparsity, the -norm regularization
produces more accurate and stable solutions than the classic data assimilation
methods. To motivate further developments of the proposed methodology,
assimilation experiments are conducted in the wavelet and spectral domain using
the linear advection-diffusion equation
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
Compressive Earth Observatory: An Insight from AIRS/AMSU Retrievals
We demonstrate that the global fields of temperature, humidity and
geopotential heights admit a nearly sparse representation in the wavelet
domain, offering a viable path forward to explore new paradigms of
sparsity-promoting data assimilation and compressive recovery of land
surface-atmospheric states from space. We illustrate this idea using retrieval
products of the Atmospheric Infrared Sounder (AIRS) and Advanced Microwave
Sounding Unit (AMSU) on board the Aqua satellite. The results reveal that the
sparsity of the fields of temperature is relatively pressure-independent while
atmospheric humidity and geopotential heights are typically sparser at lower
and higher pressure levels, respectively. We provide evidence that these
land-atmospheric states can be accurately estimated using a small set of
measurements by taking advantage of their sparsity prior.Comment: 12 pages, 8 figures, 1 tabl
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