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Blandine Bianchi, Peter Jan van Leeuwen, Robin J. Hogan, and Alexis Berne

for the main sources of errors (e.g., Germann et al. 2006 ). Since the state vector in Eq. (9) is in terms of the natural logarithm of the rain rate, the normal assumption for the errors in x is equivalent to the lognormal assumption for the distribution of errors in rain rate [for an alternative approach see for example Fletcher and Zupanski (2006) ]. To obtain the forward rain gauge and microwave link observations, after exponentiating the state values, we use as the forward model for the

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Konstantinos M. Andreadis, Ding Liang, Leung Tsang, Dennis P. Lettenmaier, and Edward G. Josberger

microwave satellite observations have been available since the late 1970s and have been used extensively for snow depth and cover extent estimation ( Tait 1998 ; Grody and Basist 1996 ; Josberger and Mognard 2002 ). Nonetheless, retrievals of snow parameters from passive microwave satellite observations are hindered by several factors. Hardware configurations on current operational satellites produce relatively coarse spatial resolutions (dependent on frequency, 27 km × 17 km for 18.7 GHz, and 14 km

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T. J. Bellerby

microwave overpass but update estimates once they are bracketed by both a previous and subsequent observation. For the general Lagrangian algorithm described by Eq. (3) , the conditional distribution P u ( R ; x , t ) of observed rainfall with respect to the satellite information used to derive the estimate is given by Here P ( R| …) is a conditional distribution of rainfall characterized only by the previous and subsequent microwave rain-rate observations and their respective lags t − t 1 and t

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Maheshwari Neelam, Rajat Bindlish, Peggy O’Neill, George J. Huffman, Rolf Reichle, Steven Chan, and Andreas Colliander

-based estimates and (ii) the PMW adjustment to the IR depends on adjustments interpolated from surrounding areas to the areas where PMW observations have been screened out due to snowy/icy surfaces ( Huffman 2019 ). The IMERG algorithm utilizes a combination of PERSIANN, CMORPH, and CORRA algorithms. It is worth mentioning that PERSIANN estimates the precipitation based on infrared brightness temperature image (as input) and artificial neural network (as a model), while CMORPH is mainly based on microwave

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Weijing Chen, Chunlin Huang, Zong-Liang Yang, and Ying Zhang

, and ecohydrology ( Bisselink et al. 2011 ; Dorigo et al. 2017 ; Ford et al. 2014 ; Martínez-Fernández et al. 2016 ; Ray and Jacobs 2007 ; Wanders et al. 2014 ; Zhang and Jia 2013 ). Moreover, integrating microwave observations with a land surface model by data assimilation has been widely used to acquire more accurate soil moisture. The performance of assimilating the retrieved soil moisture products from microwave sensors has varied in different regions according to previous studies ( Crow

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Shanshui Yuan, Laiyin Zhu, and Steven M. Quiring

: Estimation of tropical cyclone intensity in the North Atlantic and northeastern Pacific basins using TRMM satellite passive microwave observations . J. Appl. Meteor. Climatol. , 58 , 185 – 197 , . 10.1175/JAMC-D-18-0094.1 Jones , P. W. , 1999 : First- and second-order conservative remapping schemes for grids in spherical coordinates . Mon. Wea. Rev. , 127 , 2204 – 2210 ,<2204:FASOCR>2.0.CO;2 . 10

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David T. Bolvin, George J. Huffman, Eric J. Nelkin, and Jackson Tan

rivers, as well as the global energy and water cycle. Rain gauges have been the vanguard of precipitation observation, but coverage over land is sparse in much of the world ( Kidd et al. 2017 ) and even more sparse over open ocean. Over the last several decades, satellite-based precipitation estimates have proven extremely useful in providing excellent spatial and temporal coverage not available with surface observations. As satellite estimates are based on indirect observation of precipitation at

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Michael Durand and Steven A. Margulis

the usefulness of these methodologies, most snow data assimilation has been limited to direct-insertion schemes that do not take into account the uncertainty in the observations. Assimilation of passive microwave remote sensing observations to update a modeled estimate of SWE has not been reported in the literature. d. Motivation and science questions General application of a data assimilation methodology requires only assumptions about the measurement and model input uncertainty, and implicitly

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M. Tugrul Yilmaz and Wade T. Crow

nature of soil moisture in land surface models . J. Climate , 22 , 4322 – 4335 . Parinussa, R. M. , Holmes T. R. H. , Yilmaz M. T. , and Crow W. T. , 2011 : The impact of land surface temperature on soil moisture anomaly detection from passive microwave observations . Hydrol. Earth Syst. Sci. , 15 , 3135 – 3151 . Reichle, R. H. , and Koster R. D. , 2004 : Bias reduction in short records of satellite soil moisture. Geophys. Res. Lett., 31, L19501, doi:10.1029/2004GL020938

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Nasrin Nasrollahi, Kuolin Hsu, and Soroosh Sorooshian

1. Introduction Reliable estimation of precipitation is important to predict and manage water resources, hazard preparedness, and climate studies ( Ajami et al. 2008 ; AghaKouchak and Nakhjiri 2012 ; Anderson et al. 2008 ). However, spatial and temporal variability of precipitation makes it difficult to rely on sparse gauge point measurements, especially for remote regions. Higher spatial and temporal resolutions as well as global coverage of satellite observations are the main advantages of

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