Inspired by the Skamarock et al. 1995 work on the preconditioned Krylov solvers for Helmholtz equations on staggered C-grids, Piotr Smolarkiewicz, in collaboration with Steven Thomas (visitor, Rechere Prevision Numerique, Montreal, Canada), developed a family of ADI-type preconditioners for complex elliptic equations emerging in nonhydrostatic anelastic two-time-level models cast in rotating curvilinear reference frames and discretized on nonstaggered A grids. These preconditioners employ customized pentadiagonal solvers equivalent to the celebrated tridiagonal Thomas' algorithm suitable for the C-grid. This work lead to an alternate nonhydrostatic model on the sphere, as well as to a substantial acceleration of the nonhydrostatic small-scale semi-Lagrangian/Eulerian model EULAG.

Smolarkiewicz, Vanda Grubišic (visitor, Yale University), and Len Margolin (Los Alamos National Laboratory) continued the study (an eight-year project funded by the DOE CHAMMP program) of nonoscillatory forward-in-time (NFT) methods suitable for modeling the global dynamics of the atmosphere and the oceans. In 1996 they developed an alternative variant of the three-dimensional nonhydrostatic, anelastic, semi-Lagrangian NFT model on the mountainous sphere that uses vertical ADI-type preconditioners for the pressure solver, and therefore dispenses with pressure decomposition into hydrostatic and nonhydrostatic parts of the original code. This is a much simpler model than that reported in 1996 using hydrostatic pressure for the first guess in the full three-dimensional nonhydrostatic elliptic problem. The new variant contains two optional fluid algorithms: the explicit (Runge-Kutta type) and implicit (trapezoidal rule) schemes for integrating terms controlling propagation of internal gravity waves. For the computational stability, the latter option admits large time steps characteristic of semi-implicit semi-Lagrangian models.

Grubišic and Smolarkiewicz, in collaboration with Robert Sharman (visitor, UCLA) and Zbigniew Sorbjan (visitor, Marquette University) developed turbulence modules adequate for the NFT semi-Lagrangian/Eulerian nonhydrostatic fluid model. They established several optional designs of the SGS models, including the simple Smagorinsky model and a more complex TKE approach following Schumann (1991; Theoret. Comput. Fluid Dynamics). They performed numerous LES simulations of boundary layers on both the vector and MPP architectures to investigate the suitability of the approach. One of the unique aspects of their SGS models is an accurate treatment of lower boundary conditions dispensing with the traditional meteorological approximation of gentle slopes.

The availability of the 24 processor, 1 gigabyte memory J9 Cray (Ouray) allowed the Parallel Clark-Hall Model to yield high fidelity simulations for both the windstorm and tropical convection studies, and 512³ simulations of fundamental turbulence using the Kerr spectral model.

The windstorm-modeled simulations utilized five levels of interactive nested grids and a large-scale data to initialize the model. The total number of grid points for each domain (x-y-z) were (34x34x63), (66x66x50), (82x82x50), (162x162x72), and (242x242x74) totaling 6.9 million nodes with 29 variables per node. The model simulation used approximately 2000 CPU hours using 16 processors for about 140 hours equivalent wall clock time to simulate three hours of high resolution simulation time. For the physics of this flow, see the descriptions elsewhere in the current report. For more on the 512³ turbulence simulations, see the links on the Boundary Layer and Turbulence Group web pages.

Future developments to move the Clark-Hall code onto a distributive memory system such as the T3D are in progress. Multi-processing interface (MPI) commands were added to the Kerr spectral model so that this code can now be run in a fully parallel mode.

In a collaborative effort, NCEP, NOAA/FSL, CAPS, the division and university scientists began the development of a new mesoscale forecast model that will advance the understanding and prediction of important mesoscale weather, and promote closer ties between the research and operational communities. The model is intended to be accurate and efficient across a broad range of scales (cloud to synoptic), and to be well suited for applications ranging from idealized research to operational forecasting. The model will be freely distributed and supported as a "community" model for the benefit of university researchers, and to facilitate the transfer of research advances into operational forecasting.

An important first step in this project is to reach a consensus on the best numerical techniques to use for integrating the dynamical nonhydrostatic equations. For this purpose, Zavisa Janjic (NCEP), John Brown and Stanley Benjamin (NOAA/FSL), David Dempsey (San Francisco State University), and Ming Xue (CAPS) visited MMM during the year and worked with Joseph Klemp, William Skamarock, and Jimy Dudhia to evaluate alternative numerical approaches and select those best suited for the new model. Specific numerical components of the model system are initially being evaluated using idealized simulations, with priority emphasis on performance with horizontal grids in the range between one and ten kilometers. Studies thus far have focused primarily on the choice of vertical coordinate, treatment of terrain, grid staggering, and time integration techniques.

For the vertical coordinate, the comparative advantages of a height-based versus a hydrostatic-pressure coordinate are being considered. Prototype solvers for the time-split nonhydrostatic equations were constructed for both vertical coordinates, and their comparative accuracy and efficiency are being evaluated for a variety of applications. To incorporate terrain in the model, the tradeoffs between a terrain-following sigma type coordinate and a step-mountain treatment for terrain are being investigated. Research focused on techniques to reduce the errors in computing the horizontal pressure gradient force in the vicinity of steep terrain with the sigma coordinate, and techniques, such as the shaved cell approach, to reduce the alteration of terrain shape that occurs with the step mountain condition. For grid staggering, the C grid versus the B or E grid is being evaluated. For the targeted range of horizontal grids, the C grid provides a generally more accurate treatment of inertia-gravity waves without compromising the accuracy of larger-scale rotational modes. Techniques are also being explored for improving the treatment of inertia-gravity waves on the B grid through a "deaveraging" procedure on the horizontal divergence. In considering the time-integration, both semi-implicit and time-splitting techniques appear to be viable; however, time-splitting is favored at present since its efficiency may be less sensitive to the particular application and it is simpler to code. Time-splitting can be done either through partial or complete splitting. Here, comparative simulations indicate that partial splitting may better control the spurious growth of nondivergence.

To bring the remaining numerical issues to closure, the group plans to develop testbed models for the alternative numerical approaches and design additional idealized test cases to critically evaluate their behavior.

The adaptive grid model COMMAS (COllaborative Model for Multiscale Atmospheric Simulation), using the generalized adaptive grid interface constructed by Skamarock and Ming Xue (visitor, CAPS), and a cloud model constructed by Louis Wicker (Texas A&M University) is being used for simulations of midlatitude mesoscale convective systems, supercell storms, coastal currents, and frontogenesis associated with unstable baroclinic waves. It incorporates a new split-explicit time integration method for integrating the elastic nonhydrostatic equations, developed by Wicker and Skamarock. The new integration scheme offers several advantages over the traditional Leapfrog-based split explicit approaches, including two-time-level simplicity and a decreased need for explicit computational filtering.

Within the context of the WRF model development project, the COMMAS model is used to evaluate various code-design approaches for parallel processing applications on cache-based shared memory multiprocessor computer architectures. Wicker and Skamarock, with computational assistance from Robert Wilhelmson (NCSA), found that memory structure and loop order could be optimized in such a way so as to produce reasonable efficiencies over several tens of processors. The memory ordering, with columns innermost in memory addressing, is also most natural for the implementation of physical parameterizations within models and suggests that, for non-vector machines, a coding paradigm somewhat different than that employed for vector machines may prove most efficient.

Also within the context of the WRF model development project, Skamarock, Benjamin and Reiner Bleck (University of Miami) examined hybrid coordinate model formulations for the nonhydrostatic compressible equations. The hybrid coordinate takes the form of a terrain-following sigma-like coordinate near the surface and relaxes to an isentropic coordinate (or any other specified coordinate) aloft. Within the nonhydrostatic framework, the isentropic coordinate aloft must be relaxed to avoid coordinate singularities that may arise in simulations of convection and breaking waves, and methods controlling the smoothness of the coordinate surfaces are showing promise in tests with breaking mountain waves. Integration methods being examined in the context of a hybrid model include both semi-Lagrangian semi-implicit and Eulerian split-explicit techniques (see figure).

Under the leadership of Jimy Dudhia, Version 2 of MM5 continued to be improved with several new releases over the past year. The MRF PBL scheme described in the FY96 Annual Scientific Report was officially released to the user community in December 1996. Another new PBL scheme, the NCEP Eta model's Mellor-Yamada scheme, was tested in MM5. Janjic made this code available in the spring of 1997. Other changes released in MM5 include efficiency improvements in advection and the incorporation of David Stauffer's (Pennsylvania State University) ramping function for data assimilation.

Dudhia continued his collaboration with John Michalakes (Argonne National Laboratory) to develop a same-source parallel version of MM5 that can run on distributed memory machines. Michalakes developed a pre-compiler that can operate on standard MM5 code to produce a code enhanced by parallelization directives. Daniel Hansen is helping to bring this development to the standard MM5 system.

Dudhia's and David Gill’s collaboration with Wesley Jones (SGI) is leading to shared-memory parallelization improvements that demonstrated 10 Gflops performance for a full-physics numerical simulation on a 128-processor Origin 2000. This work would also be beneficial in the use of MM5 on NCAR's HP Exemplar machine. In collaboration with Paul Chen (iMSC) and DEC, Gill developed a version of MM5 that will operate on NT (as opposed to UNIX) operating systems. This allows the MM5 to be used effectively on PC-level platforms.

The MM5 Modeling System pre-processing codes also underwent much development coordinated by Wei Wang and were released as part of the version 2 system which includes using the CVS (Concurrent Versions System) tool for code maintenance. Work continued toward adapting these programs for use on platforms other than Crays. Most of them can now be run on workstations. Yong-Run Guo, Kevin Manning, Gill, and Wang continued development of these pre- and post-processing programs (Terrain, Datagrid, Rawins, Interp, and Graph).

The scarcity and quality of upstream data often limit the accuracy of forecasts for the western U.S. over the Pacific Ocean. An intriguing potential remedy for this problem is the use of adaptive observing strategies, in which movable observing platforms (such as manned or unmanned aircraft) provide additional observations in those specific regions where, depending on the character of the flow at a given time, analysis errors are likely to be large and to grow rapidly.

Adaptive observation strategies were tested during the Fronts and Atlantic Storm Track Experiment (FASTEX) in January and February. Kerry Emanuel (Massachusetts Institute of Technology) and Christoph Snyder, together with investigators from NCEP, NRL, European Centre for Medium-Range Weather Forecasts, Meteo-France, and PSU, provided support and direction for this effort. Aside from difficulties in obtaining clearance to drop sondes from above 28,000 feet (so that few sondes were launched from above the tropopause), operations were generally successful, with 13 flights of the NSF-sponsored Lear 36, nine flights of USAF C-130's, and four flights of the NOAA G4 devoted to adaptive observations.

Analysis of FASTEX intensive observation periods (IOPs) is in progress and is being led by Istvan Szunyogh and Zoltan Toth (NCEP). Forecasts for each IOP are being re-run (using the operational data assimilation scheme) first as "controls," without any FASTEX data, and then including the adaptively sampled data. Preliminary results demonstrate that in almost all cases the largest forecast differences resulting from FASTEX adaptive observations lie in the expected verification region. These results also show that both analysis and forecast differences are generally small (< 5 mb in surface pressure, for example). The reasons for such small differences are not completely clear, but likely reflect both the challenge to the operational data assimilation scheme of closely spaced dropsoundings in a normally data-sparse area and the generally high quality of forecasts during the experiment.

All adaptive observational strategies employed during FASTEX, indeed all strategies proposed to date, are at least in part heuristic. This motivated L. Mark Berliner (Ohio State University, formerly director of the Geophysical Statistics Project, NCAR), Z.-Q. Lu (GSP), and Snyder to explore the mathematical foundations for adaptive observations. They showed that the natural formulation is a problem in statistical design; from this formulation, it is clear that one seeks to minimize, over all feasible "arrangements" of observations, some norm of the forecast error covariance matrix, and that this minimization depends fundamentally on the statistics of analysis errors associated with the standard observational network. They also show, in the limit of small measurement error, that heuristic approaches suggest observational deployments that differ from the true optimal if the analysis error statistics are nontrivial, that is, if they are spatially correlated and inhomogeneous.

Dudhia continued to collaborate with David Parsons (ATD) on completing a data assimilation study over a ten-day period for a region covering the ARM Southern Great Plains site in Oklahoma and Kansas during June 1993. The study includes evaluating the mesoscale-model-derived four-dimensional dataset against observations as well as making use of the high-resolution 6.67-km-gridded data to derive mean diagnostic properties of precipitation events, such as Q1 and Q2, that are useful for the evaluation of precipitation and radiation parameterization schemes used in general circulation models.

The data were released to collaborators at Lawrence Livermore National Laboratory. (Richard Cederwall, Martin Leach) who investigated analysis techniques given limited observational networks. Work was also completed in collaboration with Jon Petch (visitor, CGD) on using these data to drive a single-column version of CCM3 to investigate the impact of hydrometeor fluxes on the single-column behavior. Since many single-column model studies have been driven by lateral fluxes based on observational analyses, hydrometeor advection is generally neglected. By using a mesoscale-model-derived four-dimensional dataset, this assumption could be evaluated and it was determined that there are cases when hydrometeor advection contributed significantly to the SCM time evolution.

Yong-Run Guo, in collaboration with Ying-Hwa Kuo, Xiaolei Zou, Dudhia, and Parsons, performed four-dimensional variational data assimilation (4DVAR) experiments using precipitable water (PW) measurements derived from 14 ground-based GPS stations concentrated over the Oklahoma/Kansas area. The PW data at 30-min temporal resolution were used in a 6-h assimilation period for two cases of squall line events. The results showed that the assimilation of GPS PW data helped improve the timing and intensity of the convective systems. However, the positive impact of PW assimilation was quickly lost after the assimilation period ended. This was attributed to the relatively small area coverage of the GPS network. Additional experiments are being conducted to incorporate PW observations from the GOES.

A GPS/MET proof-of-concept experiment became a reality on 3 April 1995 when a small satellite carrying a modified GPS receiver was launched into Earth's orbit to demonstrate the feasibility of active limb sounding of the Earth’s neutral atmosphere and ionosphere using the radio occultation method. On 22 October 1995 a GPS/MET occultation took place over northeastern China where a dense network of radiosonde observations was available within an hour of the occultation. The GPS/MET refractivity profile showed an inflection and the corresponding temperature retrieval displayed a sharp temperature inversion around 310 mb. Kuo and collaborators performed a subjective analysis based on radiosonde observations and showed that the GPS/MET occultation went through a strong upper-level front. The inflection in the refractivity profile and the sharp frontal inversion seen in the GPS/MET sounding were verified closely by a radiosonde located about 150 km to the east of the GPS/MET occultation site. A similar frontal structure was also found in other nearby radiosonde observations. These results showed that high quality GPS/MET radio occultation data can be obtained even when the occultation goes through a sharp temperature gradient associated with an upper-level front.

In close collaboration with Mikhail Gorbunov and Sergey Sokolovsky (Institute of Atmospheric Physics, Moscow, Russia) and Simon Rosenfeld (NCEP), Zou and Francois Van den Berghe developed a procedure to directly assimilate the raw refraction angle data from the GPS/MET satellite using the NCEP global spectral model. This procedure is based on the so-called raytracing technique. Electromagnetic ray paths are explicitly modeled in the real satellite configuration using the three-dimensional refractivity field provided by the NCEP model. Refraction angles are computed from the ray geometry. This procedure was applied to simulate all the occultations available between 12:00 and 24:00 UTC on 11 October 1995 (54 soundings). Statistics show that the model compares very well with observations with a slight trend toward overestimation. The tangent linear approximation and the adjoint of the raytracing code were developed so that the complete GPS/MET observation operator can be used in three- and four-dimensional variational data assimilation systems. This software is now being implemented in the current NCEP 3-DVAR operational system. Experiments are being conducted to assess the impact of GPS/MET data on operational numerical weather prediction.

Over the past year Zou and Wei Huang continued to develop a mesoscale 4DVAR system based on the MM5 model and its full physics adjoint. Considerable effort has been devoted to code clean-up and standardization. The MM5 4DVAR system was ported to workstations. The standard version of the MM5 4DVAR system can now be operated on either the Cray computer or workstations, which allow a wide range of university users to take advantage of this important research tool. Zou, Van den Berghe, Manuel Pondeca (visitor, Florida State University), Kuo, and Huang also wrote documentation and a users' guide for the MM5 4DVAR system. Zou, Van den Berghe, Huang, Pondeca, and Guo conducted an adjoint model tutorial in July 1997 to introduce the university scientists to the system.

In collaboration with Wang-Shu Wu (NCEP), Nils Gustafsson (Sweden) and Philippe Courtier (Centre National d'Etude Spatiale, France), Van den Berghe, Zou, and Joseph Chang (visitor, Central Weather Bureau, Taiwan) started the development of a MM5 3DVAR system to complement the MM5 4DVAR system. The 3DVAR system takes into account the error statistics of the background analysis that is also needed for a complete 4DVAR system. In order to establish the necessary error statistics, they computed the difference between all the MM5 24-hour and 12-hour forecasts valid for the same time during a one-month period based on the MM5 real-time forecast system established by James Bresch (visitor, University of Washington). A mean error was then computed by averaging on all the differences. This mean error provided useful statistics which are needed to build the background covariance matrix for MM5 3DVAR and 4DVAR systems, which will be developed in the coming year.

In collaboration with George Modica and Alan Lipton (Phillips Laboratory), Qingnong Xiao (visitor, Nanging University, China) and Zou developed the tangent linear and adjoint codes for the 6-channel SSM/I satellite rainfall observations. They performed a MM5 4DVAR experiment to assimilate such data into the ERICA IOP4 storm, and showed that the SSM/I satellite observations can be used to improve the moisture analysis over the ocean and improve the short-range prediction of marine cyclones. They are extending their work for the assimilation of GOES 8 radiance data.

Juanzhen Sun and N. Andrew Crook (joint appointment with RAP) continued the work on assimilation of radar data into a convective scale numerical model. The convective scale data assimilation system was further examined using radar data from CaPE. The retrieved dynamical and microphysical fields were compared with measurements made by two aircraft penetrating the storm at different heights. Reasonable agreement was found in terms of the general structure and strength of the fields. The sensitivity of the retrieval system to several factors was examined, including the neglect of the grid point time difference in a radar volume, the inclusion of the background information, and the relation used to derive the rain water mixing ratio from reflectivity observations.

Sun and Crook applied the adjoint retrieval technique to WSR-88D radar observations to obtain three-dimensional wind and temperature fields in the boundary layer. In addition to the radial velocity data, the reflectivity was used as a tracer in the retrieval. A parameterization of raindrop terminal velocity was included in the reflectivity equation to take into account the falling of raindrops. In two case studies using Memphis WSR-88D radar data, it was demonstrated that the technique was able to determine the location and the boundary layer convergence through both the wind and temperature fields.

Mei Xu (visitor, University of Georgia), in collaboration with Crook and Sun, examined the sensitivity of the wind and temperature retrieval within the boundary layer to the knowledge of the flow above. Numerical simulations of a collapsing cold pool were performed and "radar observations" of radial velocity were constructed from the whole or parts of the simulated data. Retrieval experiments were then conducted using the "radar observation" and the adjoint model to recover the perturbation wind, temperature fields of the PBL features, and the upper level gravity waves with or without the data above the PBL. Forecasting merits of the model initialized with the retrieved fields were also examined.

When observations of the entire domain (up to 16 km in the vertical) were used, the method was able to retrieve the boundary layer features and the upper level gravity waves accurately with relative errors of 0.1 percent for the horizontal winds, 1 percent for the vertical velocity and 20 percent for the temperature field. When observations were available only in the PBL (assuming a PBL height of 3 km), the technique showed a certain degree of robustness. While retrieval of the upper level features was severely affected by lack of upper-level observation, the main PBL features can be recovered with a slightly degraded accuracy. When the retrieved fields were used in a forecast test, the lack of upper level gravity wave initialization further affected the forecast PBL features at a later time.

Crook and Sun investigated the correlation between storm growth and low-level divergence and buoyancy. The 30-minutes change in reflectivity was used as the measure of the storm growth. The divergence and temperature fields were determined by the adjoint technique. A correlation analysis was performed on two cases of thunderstorm development from Memphis WSR-88D data. The analysis indicated a correlation of around 0.5 between reflectivity growth and fields of convergence and buoyancy. These fields, when used in conjunction with other predictors, may be able to provide useful forecasts of storm growth and decay.

Bresch continued improving a real-time forecast system running on the Division's multi-processor computers. Forecasts are produced twice daily and are made available on the World Wide Web to forecasters, researchers, and the general public. The forecasts supported field operations of a thunderstorm anvil shading experiment conducted by Jerry Straka (University of Oklahoma) and the May-June subVORTEX field experiment over the southern plains administered by Erik Rasmussen (visitor, NSSL). Special output was provided by request to the Air Force Weather Agency (formerly AFGWC) and the National Weather Service offices in Goodland, Kansas and Minneapolis, Minnesota. The real-time model proved most effective in ferreting out model faults as well as serving as a testbed for new parameterizations. Shortly after NCEP's MRF PBL scheme was added to MM5 by Song-You Hong (NCEP), it was debugged and tested in the real-time system. In collaboration with Dudhia, Bresch added a simple bucket scheme to predict soil moisture availability, as well as a forecast update cycle to better initialize soil moisture. The potential benefits of having a state-of-the-science real-time system to both researchers and forecasters were demonstrated by MM5's successful 9-km forecast of the 28 July 1997 Fort Collins flood. MM5 predicted a large rainfall maximum near Fort Collins (see figure). Bresch used the real-time system to investigate the sensitivity of the forecast of this case to horizontal resolution and presence of monsoon moisture. It was found that while the storm's updraft source was the nearly saturated low-level upslope, the moisture above 600 mb was essential for its development as well. When model resolution was increased to 3 km, the rainfall was better located close to Fort Collins. The real-time MM5 forecasts for 27 May 1997 provided stronger clues than the operational models that tornadoes were a threat in the Jarrell, Texas, area.

Davis, Dudhia, Skamarock, David Dempsey (visitor, San Francisco State University), and Hsiao-Ming Hsu (RAP) conducted tests of MM5 with emphasis on its performance over complex terrain. Idealized simulations were performed. Spurious flow accelerations were noted near steep slopes, with errors in velocity greatly exceeding those in other numerical models. Several factors were found to contribute, including treatment of the thermodynamic equation and pressure gradient force. Dempsey and Davis tested various pressure gradient force (PGF) schemes within MM5. Davis worked with Dudhia, Skamarock, Dempsey, and Hsu to test improvements to MM5 such as 1) addition of an absorbing sponge in the lower stratosphere (with Robert Sharman, RAP); 2) diffusion of deviations from the initial state; 3) use of potential temperature advection instead of temperature advection; and 4) introduction of high-resolution (3 km) land-use data (with Teddie Keller, RAP).

Davis worked with several MMM and RAP staff members to implement a high-resolution (1.1 km grid spacing), operational forecast system for TECOM of the Army. The prototype produced twice daily forecasts over the area of west central Utah, with emphasis on flows dominated by local topography and variations in surface characteristics.

Jordan Powers continued to develop and apply a coupled mesoscale modeling system comprised of the MM5, the Princeton Ocean Model, and the GLERL-Donelan Wave Model. The coupled system was developed as a tool for better simulating phenomena dependent on mesoscale air-sea interaction. It is being used to investigate the effects of 1) incorporating detailed sea state and surface temperature data from marine models into the MM5 and 2) using high-resolution atmospheric mesoscale model output to drive marine models. System developments included new roughness modeling approaches and new roughness parameterizations based on sea state and wave age.

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