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

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

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

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 $\ell_{1}$-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

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

The influence of migrating bed forms on the velocity-intermittency structure of turbulent flow over a gravel bed.

Modeling turbulent flows at high Reynolds number requires solving simplified variants of the Navier-Stokes equations. The methods used to close the resulting Reynolds-averaged, or eddy simulation equations usually follow classical theory and, at small enough scales, postulate universal scaling for turbulence that is independent of the velocity itself. This may not be the best way to conceptualize geophysical turbulence. Turbulent intermittency may be defined in terms of the local “roughness” of the velocity signal as measured by pointwise Hölder exponents. This study investigates the joint velocity-intermittency structure of flow over a gravel-bed surface with migrating bed forms. We report clear velocity-intermittency dependence and quantify its nature above the moving bed form profile. Our results imply differences in energy transfer close to bed forms at shorter wavelengths than those forced directly. Hence, progress in modeling flows of geophysical relevance may require a reconsideration of the principles on which turbulence closures are based