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The upcoming Surface Water and Ocean Topography (SWOT) satellite mission will measure water surface elevation, its spatial and temporal derivatives, and inundated area. These observations can be used to estimate river discharge at a global scale. SWOT will measure a given area on mid-latitude rivers two or three times per 22-day repeat cycle. In this paper, we suggest an interpolation-based method of estimating water height for times without SWOT observations (i.e., in between SWOT overpasses). A local space-time ordinary kriging (LSTOK) method is developed. Two sets of synthetic SWOT observations are generated by corrupting two different types of true river height with the instrument error. The true river heights are extracted from: 1) simulation of the LISFLOOD-FP hydrodynamic model, and from 2) in situ gage measurements from five USGS gages. Both of these synthetic SWOT observations datasets are important for the following reasons. The model-based dataset provides a complete spatiotemporal picture of river height that is unavailable from in situ measurements, but neglects the effects of e.g. human management actions on river dynamics. On the other hand, the gage-based dataset samples only five locations on the river (1,050 km in length), but represents all effects of human management, tributaries, or other influences on river heights, which are not included in the model. The results are evaluated by a comparison with truth and simple linear interpolation estimates as a first-guess. The model-based experiment shows the LSTOK recovered the river heights with a mean spatial and temporal root mean square error (RMSE) of 11 cm and 12 cm, respectively; these accuracies show a 46% and 54% improvement compared to the RMSEs of the linear interpolation estimates. The gage-based experiment shows a temporal RMSE of 32 cm on average; the LSTOK estimates show a 23% improvement over the linear interpolation estimates. The degradation in performance of the LSTOK for the gage-ba- ed analysis as compared to the model-based analysis is apparently due to the effects of human management on river dynamics. Further work is needed to model the effects of human management, and to extend the analysis to consider river tributaries and the main stem of the river simultaneously.