Simulating Reversibility and Assessing Systematic Sources of Errors in Climate Models

A challenge common to weather, climate and seasonal numerical prediction is the need to simulate accurately long range transport and reversible isentropic processes in combination with appropriate determination of sources/sinks of energy and entropy. A means to study a model's accuracy in simulating internal hydrologic processes is to determine its capability to simulate the appropriate conservation of potential and equivalent potential temperature as surrogates of dry and moist entropy under reversible moist adiabatic processes in which clouds form, evaporate and precipitate. Within the experimental design to examine the differences that develop between the equivalent potential temperature as simulated by the governing equations and its proxy simulated by a transport equation, the continuum equations demand the difference vanish at all discrete model information points throughout the simulation. In an extension to an earlier study, zonal-vertical cross sections of the differences, relative frequency distributions of the differences and the vertical structure of systematic differences are examined. In the situation where all biases vanish, measures of numerical accuracy are readily related to the classical triangular distribution of the differences of two random variates. A final consideration is to place the random and systematic components of differences within a probability perspective in which the normal distribution is utilized to assess whether the magnitude of the average difference exceeds that expected to develop from the presence of the random component.