Sensitivity analysis and metamodels for the bulk parametrization of turbulent air–sea fluxes. (28th August 2018) - Pelletier, C.; Lemarié, F.; Blayo, E.
Abstract : State‐of‐the‐art climate models rely on bulk formulae arising from the Monin–Obukhov semi‐empirical theory to estimate turbulent air–sea fluxes. The mathematical structure of those formulae implies several difficulties when trying to study the numerical properties of coupling algorithms used for practical applications. This article introduces a methodology for building physically realistic approximations of existing bulk formulae which would also satisfy suitable mathematical properties (explicit character, regularity, differentiability). This is achieved by applying the Sobol' method to compute sensitivity indices in order to reduce the number of inputs and derive a simple metamodel for the parametrization of turbulent air–sea fluxes. Numerical results show excellent agreement between our approximations and the standard bulk formulae. In particular, single‐column simulations using the TOGA–COARE experiment within the LMDZ atmospheric model show negligible changes in numerical results. Abstract : This article underlines subtleties in state‐of‐the‐art bulk formulae regarding their compatibility with standard mathematical coupling algorithms. Data and sensitivity analyses are carried out on bulk formulae, in order to assess their most influential inputs. Using these results, mathematically explicit approximations of classical bulk formulae are built, which benefit from desirable mathematical properties of regularity. As a conclusion, the numerical accuracy of these explicit approximations are tested on the three classical bulk formulae using Sobol' indices for the momentum coefficient. Each rectangle contains the Sobol' indices for one given variable. The hatch pattern distinguishes, for each input and each output, which combination of bulk (COARE, CORE or ECMWF) and index order (first or total) has been represented.