An adaptive ensemble Kalman filter for assimilation of multi-sensor, multi-modal water temperature observations into hydrodynamic model of shallow rivers

Abstract There is lack of knowledge in assimilation of multi-sensor, multi-modal water temperature observations into hydrodynamic models of shallow rivers, specifically, (a) how does accuracy of shallow river model improve after assimilation of in-situ and remotely sensed temperature observations, and (b) how can data from disparate sensors and sources be assimilated into the prediction model without significant increase in computational burden. Multi-sensor, multi-modal observations used in this study are obtained from in-situ monitoring devices in the river with limited spatial coverage but dense temporal resolution, and from Landsat-7 satellite that has better spatial coverage but limited temporal coverage. Use of remotely-sensed observations from satellites poses the challenge that the physical region represented by satellite data does not directly correspond with the physical domain of the river simulated in hydrodynamic models. Satellites detects the skin water temperature, whereas numerical models estimate the bulk temperature in the surface layer that may be multiple meters in thickness. Furthermore, for rivers narrower than the resolution of satellite data, the temperature of each cell represents the weighted average temperature of land and water. These factors introduce biases into the updated numerical model, thereby impeding appropriate management of temperature, water quality, and aquatic ecology. We implemented an efficient ensemble Kalman filter method using Latin-Hypercube sampling to assimilate multi-sensor water temperature observations into the hydrodynamic model of the Lower Klamath River located in northern California. Assimilation of remote sensing data from Landsat-7 improved the model prediction for the entire river. The average spatial error was reduced from 2.59 °C to 0.66 °C (i.e., 75% improvement). In-situ data assimilation reduced the error at the observation location, however, error in the water temperature predicted by the updated model reverted in less than two days to the same level as that of an un-updated model. On the other hand, it is not computationally efficient to assimilate all of the available data into the model as they become available. In order to overcome these challenges, in-situ data were adaptively assimilated into the model whenever the error exceeded a maximum allowable error. Adaptive assimilation of in-situ data for the Lower Klamath river application occurred one to three times per day, and reduced the average daily error up to 58% compared to assimilation of in-situ data only once each day.