A semi-Lagrangian water temperature model for advection-dominated river systems

Abstract

This paper describes a one-dimensional stream temperature model that is computationally efficient and highly scalable in both time and space. The model is developed within the framework of state space structure. The time-dependent equations for the conservation of thermal energy in a flowing stream or river are solved using a mixed Eulerian-Lagrangian, or semi-Lagrangian, numerical scheme. Solutions are obtained by tracking individual water parcels along their flow characteristics and storing the simulated results at discrete points on a fixed grid. Computational efficiency and accuracy of the numerical scheme are demonstrated by comparison of model estimates with observations of stream temperatures from rivers in the Pacific Northwest as well as with results from a closed-form solution of the energy equation. A preliminary analysis of the impact of climate changes on stream temperature in the Columbia River system illustrates the strengths of the semi-Lagrangian method for addressing water quality issues of regional, national, and, ultimately, global scale. Further development of the semi-Lagrangian method has the potential to improve the ability of water quality planners to perform uncertainty analysis, risk analysis, and forecasting for large, complex river systems.