Tom H. Zapotocny

A Comparison of Simulated Precipitation by Hybrid Isentropic-Sigma and Sigma Models

Abstract The primary objectives of this study are threefold: 1) to compare simulators of dry and moist baroclinic development from 10-and 22-layer hybrid isentropic-sigma coordinate models with those from 11-, 27-, and 35-layer sigma coordinate models; 2) to examine the ability of the models to transport water vapor and simulate equivalent potential temperature θe; and 3) to compare predictions of the timing, location, and amount of precipitation. A models capability to predict precipitation sterns from the accuracy of its simulation of the joint distribution of mass, potential temperature, and water vapor throughout the model domain. In a series of experiments to compare simulations of precipitation, several analytic distributions of water vapor are specified initially. The water vapor distributions include a “cylinder”extending vertically throughout the atmosphere and “lenses” within isentropic, sigma, and isobaric layers. The effect of increased horizontal resolution are also studied. Results indicate...

Development and initial test of the University of Wisconsin global isentropic-sigma model

Abstract The description of a global version of the University of Wisconsin (UW) hybrid isentropic-sigma (θ − σ) model and the results from an initial numerical weather prediction experiment are presented in this paper. The main objectives of this initial test are to 1) discuss θ − σ model development and computer requirements, 2) demonstrate the ability of the UW θ − σ model for global numerical weather prediction using realistic orography and parameterized physical processes, and 3) compare the transport of an inert trace constituent against a nominally “identical” sigma (σ) coordinate model. Initial and verifying data for the 5-day simulations presented in this work were supplied by the Goddaird Earth Observing System (GEOS-1) data assimilation system. The time period studied is 1–6 February 1985. This validation experiment demonstrates that the global UW θ − σ model produces a realistic 5-day simulation of the mass and momentum distributions when compared to both the identical σ model and GEOS-1 verif...

A Comparison of Inert Trace Constituent Transport between the University of Wisconsin Isentropic–Sigma Model and the NCAR Community Climate Model

Abstract Five- and 10-day inert trace constituent distributions prognostically simulated with the University of Wisconsin (UW) hybrid isentropic–sigma (θ–σ) model, the nominally identical UW sigma (σ) model, and the National Center for Atmospheric Research Community Climate Model 2 (CCM2) are analyzed and compared in this study. The UW θ–σ and σ gridpoint models utilize the flux form of the primitive equations, while CCM2 is based on the spectral representation and uses semi-Lagrangian transport (SLT) for trace constituents. Results are also compared against a version of the CCM that uses spectral transport for the trace constituent. These comparisons 1) contrast the spatial and temporal evolution of the filamentary transport of inert trace constituents simulated with the UW θ–σ and σ models against a “state of the art” GCM under both isentropic and nonisentropic conditions and 2) examine the ability of the models to conserve the initial trace constituent maximum value during 10-day integrations. Results ...

Numerical Uncertainties in the Simulation of Reversible Isentropic Processes and Entropy Conservation

Abstract A challenge common to weather, climate, and seasonal numerical prediction is the need to simulate accurately reversible isentropic processes in combination with appropriate determination of sources/sinks of energy and entropy. Ultimately, this task includes the distribution and transport of internal, gravitational, and kinetic energies, the energies of water substances in all forms, and the related thermodynamic processes of phase changes involved with clouds, including condensation, evaporation, and precipitation processes. All of the processes noted above involve the entropies of matter, radiation, and chemical substances, conservation during transport, and/or changes in entropies by physical processes internal to the atmosphere. With respect to the entropy of matter, 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 moi...

Global Climate Simulation with the University of Wisconsin Global Hybrid Isentropic Coordinate Model

Abstract The purpose of this study is to briefly describe the global atmospheric University of Wisconsin (UW) hybrid isentropic–eta coordinate (UW θ–η) model and document results from a 14-yr climate simulation. The model, developed through modification of the UW hybrid isentropic–sigma (θ–σ) coordinate model, employs a vertical coordinate that smoothly varies from terrain following at the earths surface to isentropic coordinates in the middle to upper troposphere. The UW θ–η model eliminates the discrete interface in the UW θ–σ model between the PBL expressed in sigma coordinates and the free atmosphere expressed in isentropic coordinates. The smooth transition of the modified model retains the excellent transport characteristics of the UW θ–σ model while providing for straightforward application of data assimilation techniques, use of higher-order finite-difference schemes, and implementation on massively parallel computing platforms. This study sets forth the governing equations and describes the vert...

Numerical Uncertainties in Simulation of Reversible Isentropic Processes and Entropy Conservation: Part II

Abstract The objectives of this study are 1) to provide the framework for an in-depth statistical analysis of the numerical uncertainties in the simulation of conservation of entropy, potential vorticity, and like properties under appropriate modeling constraints, and 2) to illustrate the discriminating nature of the analysis in an application that isolates internal numerical inaccuracies in the simulation of reversible atmospheric processes. In an earlier study the authors studied the pure error sum of squares function as a quadratic measure of uncertainties by summing the squared differences between equivalent potential temperature as simulated by the nonlinear governing equations for mass, energy, water vapor, and cloud water and its counterpart simulated as a trace constituent. Within the experimental design to examine a models capabilities to conserve the moist entropy, the continuum equations demand that the differences between equivalent potential temperature θe and proxy equivalent potential temp...

Numerical Investigations with a Hybrid Isentropic–Sigma Model. Part I: Normal-Mode Characteristics

Abstract In a validation experiment of a hybrid isentropic–sigma coordinate primitive equation model developed at the University of Wisconsin (the UW θ−σ model), an initial value technique is used to investigate numerically the normal-mode characteristics of baroclinically amplifying disturbances over a spectrum of meteorologically significant wavelength. The experiments are designed to determine the impact of coupling an isentropic-coordinate free atmospheric domain to a sigma-coordinate planetary boundary layer (PBL) on the normal-mode characteristics. The growth rate and phase speed spectra of the most unstable normal modes are obtained for an analytically prescribed zonal flow field. The evolution and vertical structure of the kinetic energy, energy conversions, growth rates, and geopotential fields are investigated. Several modifications have been made to earlier versions of the UW θ−σ model to overcome noise introduced by adjustments associated with emerging and submerging grid volumes at the sigma–...

Joint distributions of potential vorticity and inert trace constituent in CCM2 and UW θ‐σ model simulations

This letter describes an experiment that examines the ability of the University of Wisconsin (UW) hybrid isentropic-sigma (θ-σ) and sigma (σ) coordinate models and the NCAR Community Climate Model 2 (CCM2) to transport and conserve the joint distributions of isentropic potential vorticity (P θ ) and a source-free inert trace constituent related to the initial distribution of P θ , called proxy ozone (O 3 ), during 10-day isentropic integrations. Under the idealized conditions of this experiment, the governing equations for the atmospheric continuum require that the initial joint distribution of P θ and O 3 be conserved, thereby establishing a test of model accuracy from statistical comparisons of paired values of O 3 and P θ . Any decrease in the initial correlation of unity of P θ and O 3 after integration is an objective measure of a models skill. Results show that correlation coefficients for the UW θ-σ model remain higher than those from CCM2 and the UW σ model, demonstrating an inherent advantage in the simulation of trace constituent transport relative to dynamical processes in isentropic versus sigma coordinate models.

Numerical Investigations with a Hybrid IsentropicσSigma Model. Part II: The Inclusion of Moist Processes

Abstract The main goals of this paper are 1) to demonstrate the feasibility of incorporating a prognostic equation for water vapor and diabatic processes in the University of Wisconsin θ−σ model discussed in Part I, 2) to document methods applied to overcome difficulties stemming from the inclusion of moist processes and 3) to present results illustrating the effects of latent heat release on baroclinic development. The results confirm earlier studies that a prognostic equation for water vapor and the diabatic component of latent heat release may be included in a hybrid model. However, the modifications made in this study were important for eliminating spurious supersaturation and release of latent heat within grid volumes emerging and submerging through the interface between sigma and isentropic model domains. The results demonstrate the hybrid models robust nature and potential for use in prediction. For this demonstration, model simulations of an analytically specified synoptic-scale wave that amplifi...

Inert Trace Constituent Transport in Sigma and Hybrid Isentropic–Sigma Models. Part I: Nine Advection Algorithms

Abstract The University of Wisconsin hybrid isentropic–sigma (θ–σ) coordinate channel model and the nominally identical sigma (σ) model are used to test the relative capabilities of nine trace constituent transport algorithms. The nine are “standard” second-order finite differencing, the standard with two local “borrow and fill” fixers, the standard with a global fixer, four conservative flux-integrated approaches, and the conservation of second-order moments (CSOM). Transport of two analytically specified initial trace constituent distributions is simulated within a common initial atmosphere, which includes a baroclinically amplifying synoptic-scale wave. Two different vertical resolution θ–σ models and four vertical resolution σ models provide excellent test beds for comparison of the transport algorithms because their 48-h predictions of standard synoptic fields are virtually identical. Although no analytic solution exists against which detailed comparisons can be made, the constraint of adiabatic cond...