Estimation of the functional form of subgrid-scale schemes using ensemble-based data assimilation: a simple model experiment

PULIDO M., G. SCHEFFLER, J. RUIZ, M. LUCINI AND P. TANDEO

QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY

JOHN WILEY & SONS LTD

Lugar: LOndres; Año: 2016 vol. 142 p. 2974 - 2984

0035-9009

Oceanic and atmospheric global numerical models represent explicitly the large-scale dynamics while the smaller-scale processes are not resolved so that their effects in the large-scale dynamics are included through subgrid-scale parameterizations. These parameterizations model small-scale effects as a function of the resolved variables.  In this work,  data assimilation principles are used not only to estimate the parameters of subgrid-scale parameterizations  but also  to uncover the functional dependencies of subgrid-scale processes as a function of large-scale variables.  Two data assimilation methods based on the ensemble transform Kalman filter (ETKF) are evaluated in the two-scale Lorenz 96 model scenario:  An online estimation that uses the ETKF with an augmented space state composed by  the model large-scale variables and a set of unknown global parameters from the parameterization. The other method  first uses the ETKF to estimate an augmented space state composed by the large-scale variables and by a space dependent model error term.  In a second offline stage, a functional relationship is used to fit the estimated model error as a function of the large-scale model variables in order to develop a parameterization of small-scale dynamics. The online  estimation shows a good performance when the parameter-state relationship is assumed to be quadratic polynomial function.  The offline estimation captures better some of the highly nonlinear functional dependencies found  in the subgrid-scale processes. The nonlinear and nonlocal dependence found in an experiment with shear generated small-scale dynamics is also recovered by the offline estimation method. Therefore, the combination of these two  methods could be a useful tool for the estimation of the functional form of subgrid-scale parameterizations.