Ardeshir M. Ebtehaj

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 [called the shrunken locally linear embedding algorithm for retrieval of precipitation (ShARP)] relies on a regularization technique and makes use of two joint dictionaries of coincident 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 neighbor classification rule, whereas the estimation scheme is equipped with a constrained shrinkage estimator to ensure the stability of retrieval and some physical consistency. The algorithm is examined using coincident observations of the active precipitation radar and the passive microwave imager onboard the 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, particularly 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.

Downscaling Satellite Precipitation with Emphasis on Extremes: A Variational 1-norm Regularization in the Derivative Domain

The increasing availability of precipitation observations from space, e.g., from the Tropical Rainfall Measuring Mission (TRMM) and the forthcoming Global Precipitation Measuring (GPM) Mission, has fueled renewed interest in developing frameworks for downscaling and multi-sensor data fusion that can handle large data sets in computationally efficient ways while optimally reproducing desired properties of the underlying rainfall fields. Of special interest is the reproduction of extreme precipitation intensities and gradients, as these are directly relevant to hazard prediction. In this paper, we present a new formalism for downscaling satellite precipitation observations, which explicitly allows for the preservation of some key geometrical and statistical properties of spatial precipitation. These include sharp intensity gradients (due to high-intensity regions embedded within lower-intensity areas), coherent spatial structures (due to regions of slowly varying rainfall), and thicker-than-Gaussian tails of precipitation gradients and intensities. Specifically, we pose the downscaling problem as a discrete inverse problem and solve it via a regularized variational approach (variational downscaling) where the regularization term is selected to impose the desired smoothness in the solution while allowing for some steep gradients (called ℓ1-norm or total variation regularization). We demonstrate the duality between this geometrically inspired solution and its Bayesian statistical interpretation, which is equivalent to assuming a Laplace prior distribution for the precipitation intensities in the derivative (wavelet) space. When the observation operator is not known, we discuss the effect of its misspecification and explore a previously proposed dictionary-based sparse inverse downscaling methodology to indirectly learn the observation operator from a data base of coincidental high- and low-resolution observations. The proposed method and ideas are illustrated in case studies featuring the downscaling of a hurricane precipitation field.

Evaluation of ShARP Passive Rainfall Retrievals over Snow-Covered Land Surfaces and Coastal Zones

AbstractUsing satellite measurements in microwave bands to retrieve precipitation over land requires proper discrimination of the weak rainfall signals from strong and highly variable background Earth surface emissions. Traditionally, land retrieval methods rely on a weak signal of rainfall scattering on high-frequency channels and make use of empirical thresholding and regression-based techniques. Because of the increased surface signal interference, retrievals over radiometrically complex land surfaces—snow-covered lands, deserts, and coastal areas—are particularly challenging for this class of retrieval techniques. This paper evaluates the results by the recently proposed Shrunken Locally Linear Embedding Algorithm for Retrieval of Precipitation (ShARP) using data from the Tropical Rainfall Measuring Mission (TRMM) satellite. The study focuses on a radiometrically complex region, partly covering the Tibetan highlands, Himalayas, and Ganges–Brahmaputra–Meghna River basins, which is unique in terms of it...

Microwave retrievals of terrestrial precipitation over snow‐covered surfaces: A lesson from the GPM satellite

Satellites are playing an ever-increasing role in estimating precipitation over remote areas. Improving satellite retrievals of precipitation requires increased understanding of its passive microwave signatures over different land surfaces. Snow-covered surfaces are notoriously difficult to interpret because they exhibits both emission from the land below and scattering from the ice crystals. Using data from the Global Precipitation Measurement (GPM) satellite, we demonstrate that microwave brightness temperatures of rain and snowfall transition from a scattering to an emission regime from summer to winter, due to expansion of less emissive snow cover. Evidence suggests that the combination of low- (10-19 GHz) and high-frequency (89-166 GHz) channels provide the maximum amount of information for snowfall detection. The results demonstrate that, using a multi-frequency matching method, the probability of snowfall detection can even be higher than rainfall—chiefly because of the information content of the low-frequency channels that respond to the (near) surface temperature.

Variational data assimilation via sparse regularisation

This paper studies the role of sparse regularisation 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 transform domains. We show that in the presence of sparsity, the -norm regularisation produces more accurate and stable solutions than the classic VDA methods. We recast the VDA problem under the -norm regularisation into a constrained quadratic programming problem and propose an efficient gradient-based approach, suitable for large-dimensional systems. The proof of concept is examined via assimilation experiments in the wavelet and spectral domain using the linear advection–diffusion equation.

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.

Soil moisture background error covariance and data assimilation in a coupled land-atmosphere model

This study characterizes the space-time structure of soil moisture background error covariance and paves the way for the development of a soil moisture variational data assimilation system for the Noah land surface model coupled to the Weather Research and Forecasting (WRF) model. The soil moisture background error covariance over the contiguous United States exhibits strong seasonal and regional variability with the largest values occurring in the uppermost soil layer during the summer. Large background error biases were identified, particularly over the southeastern United States, caused mainly by the discrepancy between the WRF-Noah simulations and the initial conditions derived from the used operational global analysis data set. The assimilation of the Soil Moisture and Ocean Salinity (SMOS) soil moisture data notably reduces the error of soil moisture simulations. On average, data assimilation with space-time varying background error covariance results in 33% and 35% reduction in the root-mean-square error and the mean absolute error, respectively, in the simulation of hourly top 10 cm soil moisture, mainly due to implicit reductions in soil moisture biases. In terms of correlation, the improvement in soil moisture simulations is also observed but less notable, indicating the limitation of coarse-scale soil moisture data assimilation in capturing fine-scale soil moisture variation. In addition, soil moisture data assimilation improves the simulations of latent heat fluxes but shows a marginal impact on the simulations of sensible latent heat fluxes and precipitation.

Coping with model error in variational data assimilation using optimal mass transport

Classical variational data assimilation methods address the problem of optimally combining model predictions with observations in the presence of zero-mean Gaussian random errors. However, in many natural systems, uncertainty in model structure and/or model parameters often results in systematic errors or biases. Prior knowledge about such systematic model error for parametric removal is not always feasible in practice, limiting the efficient use of observations for improved prediction. The main contribution of this work is to advocate the relevance of transportation metrics for quantifying nonrandom model error in variational data assimilation for nonnegative natural states and fluxes. Transportation metrics (also known as Wasserstein metrics) originate in the theory of Optimal Mass Transport (OMT) and provide a nonparametric way to compare distributions which is natural in the sense that it penalizes mismatch in the values and relative position of “masses” in the two distributions. We demonstrate the promise of the proposed methodology using 1-D and 2-D advection-diffusion dynamics with systematic error in the velocity and diffusivity parameters. Moreover, we combine this methodology with additional regularization functionals, such as the l1-norm of the state in a properly chosen domain, to incorporate both model error and potential prior information in the presence of sparsity or sharp fronts in the underlying state of interest.

Combined Assimilation of Satellite Precipitation and Soil Moisture: A Case Study Using TRMM and SMOS Data

AbstractThis paper presents a framework that enables simultaneous assimilation of satellite precipitation and soil moisture observations into the coupled Weather Research and Forecasting (WRF) and Noah land surface model through variational approaches. The authors tested the framework by assimilating precipitation data from the Tropical Rainfall Measuring Mission (TRMM) and soil moisture data from the Soil Moisture Ocean Salinity (SMOS) satellite. The results show that assimilation of both TRMM and SMOS data can effectively improve the forecast skills of precipitation, top 10-cm soil moisture, and 2-m temperature and specific humidity. Within a 2-day time window, impacts of precipitation data assimilation on the forecasts remain relatively constant for forecast lead times greater than 6 h, while the influence of soil moisture data assimilation increases with lead time. The study also demonstrates that the forecast skill of precipitation, soil moisture, and near-surface temperature and humidity are further...

A multi-sensor data-driven methodology for all-sky passive microwave inundation retrieval

Abstract. 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.