A Comparison of the Impact of Two Time-differencing Schemes on the NASA-GLAS Climate Model

This paper presents evidence of the sensitivity of a general circulation Model (GCM) to the time-differencing scheme employed when the physical parameterizations and space discretization are not changed. For this purpose, two time-marching schemes-the leapfrog and the Matsuno schemes-are analyzed and tested on the National Aeronautics and Space Administration–Goddard Laboratory for Atmospheric Studies (NASA-GLAS) fourth-order GCM in terms of the stability and behavior of 2-month-averaged fields. Linear analysis suggests that Rossby waves are slightly damped and slightly accelerated when the Matsuno scheme is used and that these effects are scale selective, being smallest for the longest waves. It also suggests that such waves are accelerated less and are not damped when the leapfrog scheme is used. An empirical orthogonal function analysis of the meridional component of velocity at 46°N, keeping at least 70% of the variance, reveals less shortwave activity in the numerical solution with the Matsuno scheme but does not lend support to the conclusion that the waves are accelerated less in the solution with the leapfrog scheme. The two-dimensional Eliassen-Palm (E-P) flux divergence and the eddy-induced mean meridional circulation are found to be stronger in the simulation with the leapfrog time-differencing scheme than in the one with the Matsuno scheme, suggesting that the transient-wave activity is damped by the Matsuno scheme. On the other hand, the three-dimensional stationary-wave activity flux in the Northern Hemisphere simulated with the Matsuno scheme is more intense than that simulated with the leapfrog scheme, indicating that the stationary waves are more robust in the integration with the Matsuno scheme. The GCM precipitation when integrated with the leapfrog scheme is much more intense over the tropical western Pacific and the northeastern Pacific and less intense over the western North Atlantic Ocean. The kinetic energy of waves with wavenumber greater than 9 simulated by the Matsuno scheme is consistently smaller than that obtained by the leapfrog scheme. These results give evidence that climate simulations are sensitive not only to physical parameterizations of subgrid-scale processes but also to the numerical methodology employed.