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
and modeling of atmospheric circulation on regional to global scales.
is on investigation of the atmosphere's hydologic cycle, atmospheric
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
goal, two global hybrid models based primarily on isentropic
in the vertical have been developed at the University of
(UW). In the first model model the lowest 15% of the model's atmosphere
is described by conventional sigma coordinates (normalized pressure)
the remaining 85% by isentropic (entropy) coordinates. In the second,
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
global sigma coordinate model is under parallel development. Channel
regional versions of each model also exist.
An additional objective is to examine the accuracy
and theoretical limits of global climate predictability which are
by the inherent limitations of simulating trace constituent transport
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
the transport of dry and moist entropy with appropriate conservation
reversible moist adiabatic processes as accurately as the UW hybrid
Conservation of Equivalent Potential Temperature
II. Isentropic Analysis
Our large-scale research efforts are primarily devoted to diagnostic
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
been to determine the distributions of atmospheric heating from
data and to document the underlying forcing of global monsoonal
A comprehensive atlas documenting the three dimensional distribution of
monthly, seasonally and annually averaged atmospheric heating during
annual cycle of the Global Weather Experiment has been produced and the
interannual variability of atmospheric heating investigated.
III. Theoretical Studies
The above research demonstrates the more accurate numerical
of water vapor transport and other hydrologic processes in a model
on isentropic coordinates. Additionally, climate models based on
coordinates or specific entropy coordinates enjoy a fundamental
over models based on sigma coordinates. Johnson (1997) established for
a model without drift that a positive definite source of entropy
that the simulated climate state be biased cold, and that sigma
model simulations are subject to positive definite aphysical sources of
entropy in association with the numerical diffusion/dispersion of
Also, since the implicit source of entropy in a sigma coordinate model
is determined from a calculation of heating that is separate from the
calculation of temperature, a prognostic error in temperature induces
erroneous aphysical source of entropy. Johnson (1997) further
that a similar positive definite source of entropy does not occur in a
model based on isentropic or specific entropy coordinates since the
mass and entropy transport is a direct function of the Lagrangian
In a follow on study entitled "Entropy, the Lorenz Energy Cycle and
Climate" Johnson (1998) reconciled the theoretical concepts of
potential energy with the classical thermodynamic concepts of
efficiency, the Carnot cycle, and verified that a climate model
must become cold, thus becoming more efficient in order to simulate a
state without drift in the presence of spurious positive definite
of entropy. Globally, an aphysical source of entropy from numerical
and other inadequacies of parameterization equivalent to 4% of the
source from kinetic energy dissipation corresponds with a biased
error of 10C, thus limiting the accuracy of climate model simulations.
Increasing the accuracy of climate model simulations through reducing
sources of entropy and cold temperature biases is exceedingly difficult
to realize. Theory substantiates that a major source of the positive
source of entropy comes from the numerical diffusion of water
and the spurious mixing of moist static energy.
Johnson, D. R., 1999: Entropy, the Lorenz Energy Cycle and
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"
the Second Law: Implications for Modeling the Earth System. J.
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