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Abstract. This paper presents the results of the ensemble Riemannian data assimilation for relatively high-dimensional nonlinear dynamical systems, focusing on the chaotic Lorenz-96 model and a two-layer quasi-geostrophic (QG) model of atmospheric circulation. The analysis state in this approach is inferred from a joint distribution that optimally couples the background probability distribution and the likelihood function, enabling formal treatment of systematic biases without any Gaussian assumptions. Despite the risk of the curse of dimensionality in the computation of the coupling distribution, comparisons with the classic implementation of the particle filter and the stochastic ensemble Kalman filter demonstrate that, with the same ensemble size, the presented methodology could improve the predictability of dynamical systems. In particular, under systematic errors, the root mean squared error of the analysis state can be reduced by 20 % (30 %) in the Lorenz-96 (QG) model. 

Abstract. In this paper, we present an ensemble data assimilation paradigm over a Riemannian manifold equipped with the Wasserstein metric. Unlike the Euclidean distance used in classic data assimilation methodologies, the Wasserstein metric can capture the translation and difference between the shapes of square-integrable probability distributions of the background state and observations. This enables us to formally penalize geophysical biases in state space with non-Gaussian distributions. The new approach is applied to dissipative and chaotic evolutionary dynamics, and its potential advantages and limitations are highlighted compared to the classic ensemble data assimilation approaches under systematic errors. 

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. 

In-depth knowledge about the global patterns and dynamics of land surface net water flux (NWF) is essential for quantification of depletion and recharge of groundwater resources. Net water flux cannot be directly measured, and its estimates as a residual of individual surface flux components often suffer from mass conservation errors due to accumulated systematic biases of individual fluxes. Here, for the first time, we provide direct estimates of global NWF based on near-surface satellite soil moisture retrievals from the Soil Moisture Ocean Salinity (SMOS) and Soil Moisture Active Passive (SMAP) satellites. We apply a recently developed analytical model derived via inversion of the linearized Richards’ equation. The model is parsimonious, yet yields unbiased estimates of long-term cumulative NWF that is generally well correlated with the terrestrial water storage anomaly from the Gravity Recovery and Climate Experiment (GRACE) satellite. In addition, in conjunction with precipitation and evapotranspiration retrievals, the resultant NWF estimates provide a new means for retrieving global infiltration and runoff from satellite observations. However, the efficacy of the proposed approach over densely vegetated regions is questionable, due to the uncertainty of the satellite soil moisture retrievals and the lack of explicit parameterization of transpiration by deeply rooted plants in the proposed model. Future research is needed to advance this modeling paradigm to explicitly account for plant transpiration.