Numerical sensitivity of the ECMWF model to Semi-Lagrangian departure point iterations

Computing the departure points (d.p.) is a fundamental calculation in a semi-Lagrangian numerical model. Most models compute these using a fixed point iteration scheme with a small number of iterations assuming that this is sufficient to converge. This assumption is tested here and results show that, for the long timesteps the ECMWF model IFS uses, convergence is not entirely satisfactory and improvement in forecast skill can be achieved by increasing the number of these iterations. There is a notable improvement in the vertical structure of tropical cyclones but also in the extra-tropical winds.

The impact of increasing the d.p. iterations in the IFS tangent linear (TL) model of the 4DVAR data assimilation system is also tested. Surprisingly, increasing the iterations in the TL model occasionally excites an instability in the stratosphere in regions of strong jets. This seems to happen when iterations do not converge to a fixed point. An algorithm is proposed here in which stopping criteria based on convergence rate are used to terminate iterations when such a non-converging situation is anticipated. Testing shows that this is sufficient to prohibit development of this instability and it is possible to run the 4DVAR system with increased number of d.p. iterations consistently with the nonlinear forecast model.