Conservation of Equivalent Potential Temperature

    For accurate simulations of condensation and precipitation, first order considerations demand that a model be capable of conserving potential temperature (PT) and equivalent potential temperature (EPT) prior to the condensation process and EPT during the condensation process.  These constraints require that the joint distributions of mass, temperature and water vapor be properly simulated.  If any one of these distributions is poorly resolved, the condensation process will not be simulated accurately.   The following experiment studies the relative capabilities of the models to simulate reversible moist processes.
    In this experiment, EPT is calculated at each model grid point from the initial data, inserted into the initial atmosphere and treated as an inert trace constituent (tEPT) through a 10 day integration.  Large scale condensation is allowed to occur and the condensed water goes to form clouds. A separate continuity equation is included for cloud water.  Once formed, evaporation of clouds is allowed but precipitation is not.  All other model physics are turned off. Under the conditions of this experiment, EPT should be conserved and the difference tEPT - EPT should be zero initially and forever at each model grid point. Non zero values indicate that the model fails to appropriately conserve equivalent potential temperature. The degree of non conservation is given by the magnitude of  tEPT-EPT.

    The following compares model simulations from the UW hybrid isentropic coordinate model and the NCAR CCM3. The UW hybrid isentropic model had a horizontal resolution of 2.8125 degrees which corresponds closely with that of the T42 spectral resolution (2.8 degree gaussian grid) of CCM3. Both models have 18 vertical layers.  The animations show a side by side comparison of the difference field tEPT-EPT in degrees K for a lower tropospheric layer (750-800 Mb) from the UW hybrid model and the CCM3. The differences are shown for 00 hour through day 10.

            Conservation of Equivalent Potential Temperature - 3 hour data (3.5 Mb)

            Conservation of Equivalent Potential Temperature - 6 hour data (2.2 Mb)