Accurate estimation of the position of the departure points (d.p.) is crucial for the accuracy of a semi-Lagrangian NWP model. This calculation is often performed applying an implicit discretization to a kinematic equation solved by a fixed-point iteration scheme. A small number of iterations is typically used, assuming that this is sufficient for convergence. This assumption, derived from a past theoretical analysis, is revisited here. Analyzing the convergence of a generic d.p. iteration scheme and testing the ECMWF Integrated Forecast System (IFS) model, it is demonstrated that 2–3 iterations may not be sufficient for convergence to satisfactory accuracy in a modern high-resolution global model. Large forecast improvements can be seen by increasing the number of iterations. The extratropical geopotential error decreases and the simulated vertical structure of tropical cyclones improves. These findings prompted the implementation of an algorithm in which stopping criteria based on estimated convergence rates are used to “dynamically” stop d.p. iterations when an error tolerance criterion is satisfied. This is applied consistently to the nonlinear forecast, tangent linear, and adjoint models used by the ECMWF data assimilation system (4DVAR). Although the additional benefit of dynamic iteration is small, its testing reinforces the conclusion that a larger number of iterations is needed in regions of strong winds and shear. Furthermore, experiments suggest that dynamic iteration may prevent occasional 4DVAR failures in cases of strong stratospheric cross-polar flow in which the tangent linear model becomes unstable.
Inter/Extrapolation-Based Multirate Schemes: A Dynamic-Iteration Perspective
