We inquire whether an empirical weather forecasting scheme can profitably incorporate a possible nonlinear relationship between observed predictands and predictors. We analyze a set of twice–daily hemispheric 500 mb height fields into truncated series of spherical harmonies. From each act of spherical-harmonic coefficients, we predict the coefficients 24 h in advance by integrating the barotropic vorticity equation in spherical-harmonic form. We then establish linear regression equations for predicting the same coefficients, using as predictors the coefficients which represent the observed height fields, and, in some instances, the numerically predicted height fields. We find that the empirical schemes which incorporate nonlinearity by using the numerically predicted fields perform considerably better than those which do not. Abstract We inquire whether an empirical weather forecasting scheme can profitably incorporate a possible nonlinear relationship between observed predictands and predictors. We analyze a set of twice–daily hemispheric 500 mb height fields into truncated series of spherical harmonies. From each act of spherical-harmonic coefficients, we predict the coefficients 24 h in advance by integrating the barotropic vorticity equation in spherical-harmonic form. We then establish linear regression equations for predicting the same coefficients, using as predictors the coefficients which represent the observed height fields, and, in some instances, the numerically predicted height fields. We find that the empirical schemes which incorporate nonlinearity by using the numerically predicted fields perform considerably better than those which do not.