A Parameterization of Eddy Transfer Coefficients for Two-Level Seasonal Statistical Dynamical Zonally Averaged Models

Abstract

A parameterization of quasi-geostrophic eddy transport that takes into account the time variation of the eddy transfer coefficients according to Green's theory is studied. A relation proposed by Green connects the vertical integral of the meridional heat flux at 50°N with the second power of the 500 mb temperature difference between the boundaries of baroclinic activity. It is found that the fourth power in this relation, rather than the original second power, is obtained from analysis of zonal/monthly-mean observational data at 500 mb. For the temperature difference at 1 000 mb, however, the same analysis yields a power of 1.5. The differences in the seasonal simulation of different powers in the eddy transfer relation are explored in a two-level statistical dynamical zonally averaged model (SDZAM), and it is found that an appropriate choice of power may be of special importance if the model is devised to simulate the seasonal climate cycle, or to test astronomical changes inducing different seasonalities. With the second power in 500 rob, the particular SDZAM being tested simulates an oversensitivity in the high latitude temperature response to the seasonal cycle/astronomical changes, due to its undersensitivity in the simulation of changes in the meridional eddy heat flux. A comparison of the results of a second power at the surface level vs a fourth power at 500 mb is difficult due to the need to retune the model, but a certain advantage to the latter model is detected.