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

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

Global Precipitation Nowcasting of Integrated Multi-satellitE Retrievals for GPM: A U-Net Convolutional LSTM Architecture

This paper presents a deep learning architecture for nowcasting of precipitation almost globally every 30 min with a 4-hour lead time. The architecture fuses a U-Net and a convolutional long short-term memory (LSTM) neural network and is trained using data from the Integrated MultisatellitE Retrievals for GPM (IMERG) and a few key precipitation drivers from the Global Forecast System (GFS). The impacts of different training loss functions, including the mean-squared error (regression) and the focal-loss (classification), on the quality of precipitation nowcasts are studied. The results indicate that the regression network performs well in capturing light precipitation (below 1.6 mm/hr), but the classification network can outperform the regression network for nowcasting of precipitation extremes (>8 mm/hr), in terms of the critical success index (CSI).. Using the Wasserstein distance, it is shown that the predicted precipitation by the classification network has a closer class probability distribution to the IMERG than the regression network. It is uncovered that the inclusion of the physical variables can improve precipitation nowcasting, especially at longer lead times in both networks. Taking IMERG as a relative reference, a multi-scale analysis in terms of fractions skill score (FSS), shows that the nowcasting machine remains skillful (FSS > 0.5) at the resolution of 10 km compared to 50 km for GFS. For precipitation rates greater than 4~mm/hr, only the classification network remains FSS-skillful on scales greater than 50 km within a 2-hour lead time

Spatial Scale Gap Filling Using an Unmanned Aerial System: A Statistical Downscaling Method for Applications in Precision Agriculture

Applications of satellite-borne observations in precision agriculture (PA) are often limited due to the coarse spatial resolution of satellite imagery. This paper uses high-resolution airborne observations to increase the spatial resolution of satellite data for related applications in PA. A new variational downscaling scheme is presented that uses coincident aerial imagery products from “AggieAir”, an unmanned aerial system, to increase the spatial resolution of Landsat satellite data. This approach is primarily tested for downscaling individual band Landsat images that can be used to derive normalized difference vegetation index (NDVI) and surface soil moisture (SSM). Quantitative and qualitative results demonstrate promising capabilities of the downscaling approach enabling effective increase of the spatial resolution of Landsat imageries by orders of 2 to 4. Specifically, the downscaling scheme retrieved the missing high-resolution feature of the imageries and reduced the root mean squared error by 15, 11, and 10 percent in visual, near infrared, and thermal infrared bands, respectively. This metric is reduced by 9% in the derived NDVI and remains negligibly for the soil moisture products

Dynamical Precipitation Downscaling for Hydrologic Applications Using WRF 4D-Var Data Assimilation: Implications for GPM Era

The objective of this study is to develop a framework for dynamically downscaling spaceborne precipitation products using the Weather Research and Forecasting (WRF) Model with four-dimensional variational data assimilation (4D-Var). Numerical experiments have been conducted to 1) understand the sensitivity of precipitation downscaling through point-scale precipitation data assimilation and 2) investigate the impact of seasonality and associated changes in precipitation-generating mechanisms on the quality of spatiotemporal downscaling of precipitation. The point-scale experiment suggests that assimilating precipitation can significantly affect the precipitation analysis, forecast, and downscaling. Because of occasional overestimation or underestimation of small-scale summertime precipitation extremes, the numerical experiments presented here demonstrate that the wintertime assimilation produces downscaled precipitation estimates that are in closer agreement with the reference National Centers for Environmental Prediction stage IV dataset than similar summertime experiments. This study concludes that the WRF 4D-Var system is able to effectively downscale a 6-h precipitation product with a spatial resolution of 20 km to hourly precipitation with a spatial resolution of less than 10 km in grid spacing—relevant to finescale hydrologic applications for the era of the Global Precipitation Measurement mission