198 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
Transport on river networks: A dynamical approach
This study is motivated by problems related to environmental transport on
river networks. We establish statistical properties of a flow along a directed
branching network and suggest its compact parameterization. The downstream
network transport is treated as a particular case of nearest-neighbor
hierarchical aggregation with respect to the metric induced by the branching
structure of the river network. We describe the static geometric structure of a
drainage network by a tree, referred to as the static tree, and introduce an
associated dynamic tree that describes the transport along the static tree. It
is well known that the static branching structure of river networks can be
described by self-similar trees (SSTs); we demonstrate that the corresponding
dynamic trees are also self-similar. We report an unexpected phase transition
in the dynamics of three river networks, one from California and two from
Italy, demonstrate the universal features of this transition, and seek to
interpret it in hydrological terms.Comment: 38 pages, 15 figure
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
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
Revisiting scaling laws in river basins: New considerations across hillslope and fluvial regimes
Increasing availability of high‐resolution (1 m) topography data and enhanced computational processing power present new opportunities to study landscape organization at a detail not possible before. Here we propose the use of “directed distance from the divide” as the scale parameter (instead of Horton’s stream order or upstream contributing area) for performing detailed probabilistic analysis of landscapes over a broad range of scales. This scale parameter offers several advantages for applications in hydrology, geomorphology, and ecology in that it can be directly related to length‐scale dependent processes, it can be applied seamlessly across the hillslope and fluvial regimes, and it is a continuous parameter allowing accurate statistical characterization (higher‐order statistical moments) across scales. Application of this scaling formalism to three basins in California demonstrates the emergence of three distinct geomorphic regimes of divergent, highly convergent, and moderately convergent fluvial pathways, with notable differences in their scaling relationships and in the variability, or spatial heterogeneity, of topographic attributes in each regime. We show that topographic attributes, such as slopes and curvatures, conditional on directed distance from the divide exhibit less variability than those same attributes conditional on upstream contributing area, thus affording a sharper identification of regime transitions and increased accuracy in the scaling analysis
Network robustness assessed within a dual connectivity perspective
Network robustness against attacks has been widely studied in fields as
diverse as the Internet, power grids and human societies. Typically, in these
studies, robustness is assessed only in terms of the connectivity of the nodes
unaffected by the attack. Here we put forward the idea that the connectivity of
the affected nodes can play a crucial role in properly evaluating the overall
network robustness and its future recovery from the attack. Specifically, we
propose a dual perspective approach wherein at any instant in the network
evolution under attack, two distinct networks are defined: (i) the Active
Network (AN) composed of the unaffected nodes and (ii) the Idle Network (IN)
composed of the affected nodes. The proposed robustness metric considers both
the efficiency of destroying the AN and the efficiency of building-up the IN.
We show, via analysis of both prototype networks and real world data, that
trade-offs between the efficiency of Active and Idle network dynamics give rise
to surprising crossovers and re-ranking of different attack strategies,
pointing to significant implications for decision making
Rotated Spectral Principal Component Analysis (rsPCA) for Identifying Dynamical Modes of Variability in Climate Systems.
Spectral PCA (sPCA), in contrast to classical PCA, offers the advantage of identifying organized spatiotemporal patterns within specific frequency bands and extracting dynamical modes. However, the unavoidable trade-off between frequency resolution and robustness of the PCs leads to high sensitivity to noise and overfitting, which limits the interpretation of the sPCA results. We propose herein a simple nonparametric implementation of sPCA using the continuous analytic Morlet wavelet as a robust estimator of the cross-spectral matrices with good frequency resolution. To improve the interpretability of the results, especially when several modes of similar amplitude exist within the same frequency band, we propose a rotation of the complex-valued eigenvectors to optimize their spatial regularity (smoothness). The developed method, called rotated spectral PCA (rsPCA), is tested on synthetic data simulating propagating waves and shows impressive performance even with high levels of noise in the data. Applied to global historical geopotential height (GPH) and sea surface temperature (SST) daily time series, the method accurately captures patterns of atmospheric Rossby waves at high frequencies (3-60-day periods) in both GPH and SST and El Niño-Southern Oscillation (ENSO) at low frequencies (2-7-yr periodicity) in SST. At high frequencies the rsPCA successfully unmixes the identified waves, revealing spatially coherent patterns with robust propagation dynamics
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