The UW Isentropic Analysis and Modeling Group

Welcome to the UW Isentropic Analysis and Modeling Group home page. Our group specializes in the use of isentropic coordinates for the analysis and modeling of atmospheric circulation on regional to global scales. Emphasis is on investigation of the atmosphere's hydologic cycle, atmospheric heating, and regional entropy and energy balance.

 Global Climate Simulation with the University of Wisconsin Global Hybrid Isentropic Coordinate Model  (J. Climate, 2004, ~1 Mb)

I. Isentropic Modeling

    The primary objective of this research is to advance the modeling and understanding of atmospheric processes involving water substances and the transport of inert trace constituents. To achieve this goal, two  global hybrid models based primarily on isentropic coordinates in the vertical have been developed at the University of Wisconsin-Madison (UW). In the first model model the lowest 15% of the model's atmosphere is described by conventional sigma coordinates (normalized pressure) and the remaining 85% by isentropic (entropy) coordinates. In the second, more recently developed model, the vertical coordinate smoothly transitions from terrain following at the earth's surface to isentropic coordinates in the middle troposphere. For comparative purposes, a nominally identical global sigma coordinate model is under parallel development. Channel and regional versions of each model also exist.
    An additional objective is to examine the accuracy and theoretical limits of global climate predictability which are imposed by the inherent limitations of simulating trace constituent transport and the hydrologic processes of condensation, precipitation and cloud life cycles. This objective involves a diagnostic comparison of results from the hybrid isentropic and sigma models described above as well as other "state of the art" general circulation models. Results from a series of numerical experiments indicate that sigma coordinate models fail to simulate the transport of dry and moist entropy with appropriate conservation under reversible moist adiabatic processes as accurately as the UW hybrid model.

    Trace constituent experiments
                       Conservation of Equivalent Potential Temperature
    Model Simulations

    List of publications

II. Isentropic Analysis

Our large-scale research efforts are primarily devoted to diagnostic studies of global and regional energy balance. Emphasis is on investigation of atmospheric heat sources and sinks and hydrologic processes in relation to mass, momentum and energy exchange. A major objective of this work has been to determine the distributions of atmospheric heating from observed data and to document the underlying forcing of global monsoonal circulations. A comprehensive atlas documenting the three dimensional distribution of monthly, seasonally and annually averaged atmospheric heating during the annual cycle of the Global Weather Experiment has been produced and the interannual variability of atmospheric heating investigated.

   Atmospheric heating

   Isentropic Analyses

   List of publications  


III. Theoretical Studies

The above research demonstrates the more accurate numerical representation of water vapor transport and other hydrologic processes in a model based on isentropic coordinates. Additionally, climate models based on isentropic coordinates or specific entropy coordinates enjoy a fundamental advantage over models based on sigma coordinates. Johnson (1997) established for a model without drift that a positive definite source of entropy requires that the simulated climate state be biased cold, and that sigma coordinate model simulations are subject to positive definite aphysical sources of entropy in association with the numerical diffusion/dispersion of energy. Also, since the implicit source of entropy in a sigma coordinate model is determined from a calculation of heating that is separate from the prognostic calculation of temperature, a prognostic error in temperature induces an erroneous aphysical source of entropy. Johnson (1997) further established that a similar positive definite source of entropy does not occur in a model based on isentropic or specific entropy coordinates since the vertical mass and entropy transport is a direct function of the Lagrangian entropy source itself.

In a follow on study entitled "Entropy, the Lorenz Energy Cycle and Climate" Johnson (1998) reconciled the theoretical concepts of available potential energy with the classical thermodynamic concepts of thermodynamic efficiency, the Carnot cycle, and verified that a climate model atmosphere must become cold, thus becoming more efficient in order to simulate a climate state without drift in the presence of spurious positive definite sources of entropy. Globally, an aphysical source of entropy from numerical diffusion/dispersion and other inadequacies of parameterization equivalent to 4% of the entropy source from kinetic energy dissipation corresponds with a biased temperature error of 10C, thus limiting the accuracy of climate model simulations. Increasing the accuracy of climate model simulations through reducing aphysical sources of entropy and cold temperature biases is exceedingly difficult to realize. Theory substantiates that a major source of the positive definite source of entropy comes from the numerical diffusion of water substances and the spurious mixing of moist static energy.

Johnson, D. R., 1999:  Entropy, the Lorenz Energy Cycle and Climate.  In “General Circulation Model Development: Past, Present and Future”
                                    (D. A. Randall, ed.),  Academic Press, pp. 659-720..

Johnson, D. R., 1997: On the "General Coldness of Climate Models" and the Second Law: Implications for Modeling the Earth System. J. Climate,10, 2826-2846.

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