River discharge is an essential component of the terrestrial water cycle which helps to assess the human consumption of fresh water, biochemistry, and carbon cycle. Even though large-scale river routing models were used to estimate river discharge; they consist of non-negligible uncertainties. However, with the emerging amount of river related remote sensing data, which can be combined, through data assimilation, with global-scale river routing models to estimate river discharge accurately. Comparing simulated water surface elevation (WSE) with the satellite altimetry data remains challenging and can introduce large biases. In order to evaluate the data assimilation performance using erroneous models, we conducted several experiments namely, direct, anomaly, and normalized assimilations to examine the ability of data assimilations using satellite altimetry data. The hydrological data assimilation was performed using a physically-based empirical localization method. As an alternative to direct data assimilation we used anomaly data assimilation to overcome the large biases in simulated WSE and observed satellite altimetry. In addition, we found that the modelled WSE distribution and observed are considerably distinct. Therefore, a normalized data assimilation was carried out as well to realize better data assimilation using satellite altimetry data. River discharge was improved in 38%, 36%, and 50% of the gauging stations in direct, anomaly, and normalized assimilation experiments, respectively. In these experiments, the normalized data assimilation performed better than anomaly and direct data assimilation due to the large biases and differences in the WSE distributions. With the upcoming Surface Water and Ocean Topography (SWOT) satellite mission, the ability of data assimilation to estimate accurate river discharge would be enhanced with the methods developed here.
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