Use of Differentiable and Nondifferentiable Optimization Algorithms for Variational Data Assimilation with Discontinuous Cost Functions

Abstract

Abstract Cost functions formulated in four-dimensional variational data assimilation (4DVAR) are nonsmooth in the presence of discontinuous physical processes (i.e., the presence of “on–off” switches in NWP models). The adjoint model integration produces values of subgradients, instead of gradients, of these cost functions with respect to the model’s control variables at discontinuous points. Minimization of these cost functions using conventional differentiable optimization algorithms may encounter difficulties. In this paper an idealized discontinuous model and an actual shallow convection parameterization are used, both including on–off switches, to illustrate the performances of differentiable and nondifferentiable optimization algorithms. It was found that (i) the differentiable optimization, such as the limited memory quasi-Newton (L-BFGS) algorithm, may still work well for minimizing a nondifferentiable cost function, especially when the changes made in the forecast model at switching points to the...