Generation of High‐Resolution Water Surface Slopes From Multi‐Mission Satellite Altimetry

Abstract

For nearly three decades, satellite radar altimetry has provided measurements of the water surface elevation (WSE) of rivers. These observations can be used to calculate the water surface slope (WSS), which is an essential parameter for estimating flow velocity and river discharge. In this study, we calculate a non time‐varying high‐resolution WSS of 11 Polish rivers based on multi‐mission altimetry observations from 11 satellites in the period from 1994 to 2023. The proposed approach is based on a weighted least squares adjustment with an additional Laplace condition and an a priori gradient condition. The processing is divided into river sections not interrupted by dams and reservoirs. After proper determination of the WSE for each river kilometer (bin), the WSS between adjacent bins is calculated. To assess the accuracy of the estimated WSS, it is compared with slopes between gauge stations, which are referenced to a common vertical datum. Such gauge stations are available for 8 studied rivers. The root mean squared error (RMSE) ranges from 4 mm/km to 77 mm/km, with an average of 27 mm/km. However, the mean RMSE decreases to 11 mm/km when the 2 mountain rivers are excluded. The WSS accuracies are also compared with slope data sets based on digital elevation models, ICESat‐2 altimetry, and lidar. For 6 rivers the estimated WSS shows the highest accuracy. The improvement was particularly significant for mountain rivers. The proposed approach allows an accurate, non time‐varying high‐resolution WSS even for small and medium‐sized rivers and can be applied to almost any river worldwide.