COOPERATIVE INSTITUTE FOR MESOSCALE METEOROLOGICAL STUDIES THE UNIVERSITY OF OKLAHOMA Final Report for Cooperative Agreement NA67RJ0150 July 1, 1996-June 30, 2001 Peter J. Lamb, Director Randy A. Peppler, Associate Director John V. Cortinas, Jr., Assistant Director I. Introduction The University of Oklahoma (OU) and NOAA established the Cooperative Institute for Mesoscale Meteorological Studies (CIMMS) in 1978. Through 1995, CIMMS promoted cooperation and collaboration on problems of mutual interest among research scientists in the NOAA Environmental Research Laboratories (ERL) National Severe Storms Laboratory (NSSL), and faculty, postdoctoral scientists, and students in the School of Meteorology and other academic departments at OU. The Memorandum of Agreement (MOA) between OU and NOAA that established CIMMS was updated in 1995 to include the National Weather Service (NWS). This expanded the formal OU/NOAA collaboration to the Radar Operations Center (ROC) for the WSR-88D (NEXRAD) Program, the NCEP (National Centers for Environmental Prediction) Storm Prediction Center (SPC), and our local NWS Forecast Office, all located in Norman, Oklahoma. Management of the NSSL came under the auspices of the NOAA Office of Oceanic and Atmospheric Research (OAR) in 1999. The Norman NOAA groups at that time became known as the NOAA Weather Partners. Through CIMMS, university scientists collaborate with NOAA scientists on research supported by NOAA programs and laboratories as well as by other agencies such as the National Science Foundation (NSF), the U.S. Department of Energy (DOE), the Federal Aviation Administration (FAA), and the National Aeronautics and Space Administration (NASA). This document describes the significant research progress made by CIMMS scientists at OU and at our NOAA collaborating institutions during the five-year period July 1, 1996-June 30, 2001. During this period, CIMMS concentrated its efforts and resources on the following five principal research themes: (1) basic convective and mesoscale research, (2) forecast improvements, (3) climate effects of/controls on mesoscale processes, (4) socioeconomic impacts of mesoscale weather systems and regional-scale climate variations, and (5) Doppler weather radar research and development. 1 II. Research Progress 1. Basic Convective and Mesoscale Research Dynamic Meteorology Balanced and Unbalanced Dynamics Balanced and unbalanced dynamics were studied for three-dimensional substructures embedded in balanced nonlinear symmetric circulations. Four types of unstable modes were identified. The Type I mode was characterized by horizontally tilted bands, similar to the tilted primary mode obtained previously by other investigators. The remaining three modes were highly three-dimensional and emerged consecutively as the base-state Richardson number decreased significantly below the critical value. These modes resembled many observed three- dimensional substructures embedded in frontal rainbands. Balanced dynamics were also studied relating to cold fronts passing over a three-dimensional mesoscale mountain ridge. A hyperbolic differential equation was derived for the movement of the surface cold front. This equation was shown to be useful for understanding the topographic effects on the evolution of fronts. Unbalanced dynamics were studied in terms of departures from viscous semigeostrophy (SG) in baroclinic Eady wave and fronts. The unbalanced perturbation was found to be generated mainly by a vector forcing defined by the SG Lagrangian time derivatives of two ageostrophic wind components in the cross-frontal and along-frontal directions. In the case of free-slip boundary condition, the along-frontal wind forcing is weaker than the cross-frontal one and the unbalanced perturbations are generated largely as a linear response in the form of inertial gravity waves to the forcing. In the case of nonslip boundary condition, the along-frontal wind-forcing component is slightly stronger than the cross-frontal forcing, but the unbalanced perturbations are generated in the form of enhanced planetary-boundary-layer pumping immediately ahead of the front and in the form of inertial gravity waves in the warm sector further away from the front. An idealized two-fluid model of density current in constant shear previously used was extended and tested with ARPS (Advanced Regional Prediction System) model simulations. The numerical results agreed closely with the theoretical analyses. The simulated flow features could be described in terms of locally (small-scale) balanced and unbalanced dynamics. Semigeostrophic Eady Waves The geostrophic coordinate transformation was applied to the viscous semigeostrophic (SG) Eady wave solution. In the transformed SG space, the inversion of the geostrophic potential vorticity (GPV) becomes a linear problem, so the development of the Eady wave can be clearly interpreted by the interaction between the upper and lower GPV anomalies. The generation of interior GPV anomaly plumes along the upper and lower fronts in the viscous SG solution can be easily interpreted through its analogy to the intrusion of frontal discontinuities into the interior fluid of the inviscid solution after the surface front collapses. The SG solutions obtained for the baroclinic Eady wave fronts with two types (free-slip and non-slip) of boundary conditions were analyzed in terms of generation of cross-frontal temperature gradient in the boundary layer. The non-slip semigeostrophic solution was compared 2 with the Ekman-layer model solution to quantify errors in the vertical motion estimated by the Ekman-pumping in the frontal boundary layer during the mature stage of the frontogenesis (near and after the time of inviscid frontal collapse). Adjoint Theory and Methods The classic adjoint theory derived for differentiable systems of equations has been found not to be applicable to systems with parameterized discontinuities. To overcome this, the classic theory was generalized, and the generalized adjoint formulations were further developed to deal with various complex situations in numerical models. Problems can be avoided by introducing coarse-grain tangent linearization and adjoint theory without modifying the traditional discretization, although the coarse-grain gradient check can be performed only for finite perturbations. Generalized adjoint formulations with modified discretization and generalized coarse-grain adjoint theory were derived for a vector system of equations that contains parameterized on/off switches. With vector examples, it was shown that the conventional adjoint minimization may have a convergence problem in multi-dimensional space. The problem can be solved by the generalized adjoint with modified discretization or by the generalized coarse-grain adjoint without modifying the traditional discretization in the forward model. The ability to retrieve two-dimensional horizontal wind fields from WSR-88D radars has been studied. An adjoint-method wind retrieval technique containing predictive equations for reflectivity and radial wind was used. In particular, the potential to retrieve horizontal winds at 500 m from a case involving a non-precipitating outflow boundary was investigated. This research is unique to past single-Doppler radar retrieval studies in that WSR-88D data were used as input to the retrieval technique. Research radars used during field projects, which typically observe the atmosphere at higher resolutions both spatially and temporally than do operational WSR-88D radars, were primarily used here to validate single-Doppler retrieval techniques. In addition, the adjoint-method technique is unique in that a first guess to the retrieval solution is provided through the Velocity-Azimuth Display (VAD) technique. Through the application of the first guess, the adjoint-method retrieval technique has proven to retrieve wind flow with accuracy. Data Assimilation A new variational method was developed for Doppler radar data assimilation in combination with other observations. The method uses a set of mesoscale model equations as weak constraints. The equations are discretized in time using an implicit scheme to synchronize the model's time steps with the radar volume scans. The assimilation is cycled every model time step in association with each new volume scan. The method was tested with simulated radar data. It was found that the adjusted fields can reach high accuracy if the observations, model constraints and initial fields are sufficiently accurate. Because the NEXRAD radar network provides only single-Doppler scanning over most areas in the U. S., research efforts have been undertaken to develop various methods for meteorological parameter retrievals from single-Doppler observations. These previous efforts, however, were focused mainly on retrievals with no background information. To optimally use the background field provided by high-resolution model forecasts, basic research was conducted to examine (i) how the previous retrieval methods should be upgraded in consistency with the 3 general formulation derived for the conditional maximum likelihood estimate based on theoretical considerations, and (ii) how the theoretical formulations should be simplified under certain assumptions to make the analyses and related computations feasible. Along with these studies, prototype 3.5dVAR and simple-adjoint 4dVAR (S4dVAR) packages were developed for Doppler radar data assimilation in combination with other observations. The packages were tested with NEXRAD and