An examination of the accuracy of the linearization of a mesoscale model with moist physics

The accuracy of tangent linear and adjoint versions of a primitive-equation model with moist physics is examined with respect to growing perturbations having significant initial magnitudes. The Jacobians for the convective parametrizations are approximated using a perturbation method. These Jacobians are then quality controlled to ensure that the approximations are suitable. Results show that: (1) Linearization of the diabatic moist physics can have a significant impact; (2) even where such impacts are large, the linearized versions of the model can yield good approximations to the nonlinear behaviour for significant perturbations, especially if there is sufficient dynamical influence; (3) poor approximations can be obtained when convection dominates the results; and (4) a straightforward linearization of some parametrization schemes may be inadequate. The results are encouraging for quantitative applications of some moist adjoint models to extratropical cyclones in the winter, but suggest some tangent linear approximations may be unsuitable in the tropics or over continents in the summer, except if qualitative agreements with nonlinear results are sufficient. Detailed comparisons of linear and nonlinear results should be made, particularly using optimal perturbations, prior to any applications of tangent linear or adjoint models.