On polynomial predictions for river surface elevations

This paper addresses the issue of river level prediction through the use of polynomial regression models, employing solely elevation data and inflow forecasts. A variety of models are considered, including an approximation of elevations by a quadratic function of inlet discharge and position. Additionally, a novel approach founded upon the notion of virtual stations is introduced. It is demonstrated that when a station possesses an adequate quantity of surface elevation data, the elevations at that station can be accurately predicted by linear, quadratic, or cubic models as a function of inlet discharge. In the event that elevation data are not concentrated at a finite number of stations, the method of “virtual stations” is introduced. This method entails the establishment of new stations at strategically selected locations, for which virtual elevation data are derived from the existing stations. An algorithm is provided for the determination of the positions where the virtual stations should be located. Arguments are presented to explain why this procedure produces adequate predictions of surface elevations, but is unlikely to be as efficient in predicting flow rates. The results of comprehensive numerical experiments demonstrate the potential utility of this proposal as a tool for making predictions when the physical characteristics of the river are uncertain.