Analysis of Spurious Surface Temperature at the Atmosphere–Land Interface and a New Method to Solve the Surface Energy Balance Equation

Solving the surface energy balance equation is the most important task when combining an atmospheric model and a land surface model. However, while the surface energy balance equation determines the interface temperature between the models, this temperature is often oscillatory and without physical significance. This paper discusses the spurious mode of surface temperature. The energy balance equation is solved by the linearization around the surface temperature in most models. When this conventional scheme is used, oscillation of surface temperature occurs, caused by the exclusion or poor consideration of the surface temperature dependence of the turbulent transfer coefficient at the surface. By more strictly solving the surface energy balance equation, no spurious mode appears. However, it is often difficult to obtain such a solution because the equation is highly nonlinear. Indeed, the Newton–Raphson method at times cannot find the convergence solution. To overcome this difficulty, a new method based on a modified Newton–Raphson method is proposed to solve the surface energy balance equation. As confirmed by conducting a long-term climate simulation, the new method can robustly obtain the true solution with reasonable computational efficiency.