Copula-derived observation operators for assimilating TMI and AMSR-E retrieved soil moisture into land surface models

Assimilating soil moisture from satellite remote sensing into land surface models (LSMs) has potential for improving model predictions by providing real-time information at large scales. However, the majority of the research demonstrating this potential has been limited to datasets based on either airborne data or synthetic observations. The limited availability of satellite-retrieved soil moisture and the observed qualitative difference between satellite-retrieved and modeled soil moisture has posed challenges in demonstrating the potential over large regions in actual applications. Comparing modeled and satellite-retrieved soil moisture fields shows systematic differences between their mean values and between their dynamic ranges, and these systematic differences vary with satellite sensors, retrieval algorithms, and LSMs. This investigation focuses on generating observation operators for assimilating soil moisture into LSMs using a number of satellite-model combinations. The remotely sensed soil moisture products come from the Tropical Rainfall Measuring Mission (TRMM) Microwave Imager (TMI) and the NASA/Earth Observing System (EOS) Advanced Microwave Scanning Radiometer (AMSR-E). The soil moisture model predictions are from the Variable Infiltration Capacity (VIC) hydrological model; the 40-yr European Centre for Medium-Range Weather Forecasts (ECMWF) Re-Analysis (ERA-40); and the NCEP North American Regional Reanalysis (NARR). For this analysis, the satellite and model data are over the southern Great Plains region from 1998 to 2003 (1998-2002 for ERA-40). Previous work on observation operators used the matching of cumulative distributions to transform satellite-retrieved soil moisture into modeled soil moisture, which implied perfect correlations between the ranked values. In this paper, a bivariate statistical approach, based on copula distributions, is employed for representing the joint distribution between retrieved and modeled soil moisture, allowing for a quantitative estimation of the uncertainty in modeled soil moisture when merged with a satellite retrieval. The conditional probability distribution of model-based soil moisture conditioned on a satellite retrieval forms the basis for the soil moisture observation operator. The variance of these conditional distributions for different retrieval algorithms, LSMs, and locations provides an indication of the information content of satellite retrievals in assimilation. Results show that the operators vary by season and by land surface model, with the satellite retrievals providing more information in summer [July-August (JJA)] and fall [September-November (SON)] than winter [December-February (DJF)] or spring [March-May (MAM)] seasons. Also, the results indicate that the value of satellite-retrieved soil moisture is most useful to VIC, followed by ERA-40 and then NARR.