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• Organized cloud systems and large-scale dynamics
• Cloud systems and microscale processes

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• Advanced multi-purpose numerical models

 

Anelastic model for geophysical flows: dynamic grid deformation

Joseph Prusa (Iowa State University) and Smolarkiewicz continued the development of an adaptive grid-refinement approach, embedded in the framework of a nonhydrostatic anelastic model, for simulating a broad range of geophysical flows using Eulerian/semi-Lagrangian nonoscillatory forward-in-time (NFT) numerical methods. The key prerequisite of the adaptive grid is a continuous time-dependent curvilinear-coordinate remapping that enables mesh refinement indirectly, via dynamic change of the metric coefficients, while retaining advantages of Cartesian mesh calculations (speed, low memory requirements, and accuracy), conducted fully in the computational domain. The focus of the past year has been an advective grid adaptation technique. Compared to more traditional elliptic grid generators, the advective approach proposed is faster and more straightforward in its implementation for time dependent grids. These properties follow from the use of MPDATA to integrate a posited, prognostic equation for grid increments. Also, the NFT properties of MPDATA mimicked nested grids by propagating step changes in grid resolution. Test results that simulate a traveling stratospheric inertio-gravity wave packet (Movie 4) demonstrate the potential and the efficacy of the approach for tracing targeted flow features, and dynamically adjusting to prescribed undulations of model boundaries.

A nonhydrostatic NFT model for oceanic research

Smolarkiewicz, Frank Bryan (NCAR/CGD), and Matthew Hecht (Los Alamos National Laboratory) developed a nonoscillatory forward-in-time (NFT) nonhydrostatic model for simulating a broad range of oceanic circulations. The model employs the Boussinesq approximation and linearized constitutive equation for seawater. These two assumptions, common in the simulation of oceanic flows, facilitated the design of a fully second-order-accurate NFT numerics with implicit treatment of internal gravity waves. The latter enhances the computational stability and accuracy of the model. Since the model has been cloned from the all-scale atmospheric model EULAG, it inherits all the benefits of the NFT approach, and most of the technical advancements, including: accurate representation of rapidly-rotating strongly-stratified flows past complex bathymetry, explicit/implicit turbulence modeling, optionality of the semi-Lagrangian (trajectory wise) and Eulerian (control-volume wise) transport schemes, mesh refinement capability via deformable coordinates, and high-performance computer programming. Smolarkiewicz, and a Naval Research Laboratory (NRL) team lead by Alex Warn-Varnass, have collaborated on research projects which demonstrate the efficacy of the model, including: the western-boundary-current separation (DNS scenario mimicking laboratory experiments, Movie 5 and the evolution of coastal solitons (LES of mesoscale circulations in the Messina Straits.

	To view the movie, place mouse over image. Alternately, for slower connections, you may use the links below to download the movie. Dye tracer movie (animated GIF) Dye tracer movie (AVI format) Dye tracer movie (MPEG format)
Movie 5. Animation of the simulated flow of a dye tracer, injected into the rotating, flat-bottomed domain along with inflowing water at the bottom left and flowing out at the upper right. Frames are separated in time by about 3 seconds, with the total length of the simulation spanning about 5 minutes.

Upper boundary conditions for nonhydrostatic models

Nils Wedi of the European Center for Medium Range Weather Forecasts (ECMWF) and Smolarkiewicz continued development of a novel class of upper boundary conditions for nonhydrostatic models of atmospheres and oceans. Typically, nonhydrostatic atmospheric models attempt to mimic an infinite atmosphere, whereas nonhydrostatic oceanic models incorporate rigid-lid approximation. Either condition assumes simplistic mathematical representation of the true conditions, and over-constrains admissible atmospheric/oceanic circulations. Wedi and Smolarkiewicz relaxed the standard assumptions to allow for undulating smooth material boundaries, an approximation that is sound in the long-wave limit. The key technical prerequisite of their development is the extension of the classical terrain-following coordinate transformation of Gal-Chen and Somerville (1975) onto time-dependent curvilinear upper boundaries, and its efficient numerical coding in a generic Eulerian/semi-Lagrangian NFT nonhydrostatic model format. A series of simulations with the finite-amplitude undulations of the upper boundary predicted from the shallow-water equations - a physical scenario relevant to ocean models (see Movie 6) - and the validation against corresponding simulations of ''real shallow water'' (incompressible non-Boussinesq fluid with a 1/1000 density jump) clearly demonstrate the utility of the approach.

	To view the movie, place mouse over image. Alternately, for slower connections, you may use the links below to download the movie. Simulated flow movie (animated GIF) Simulated flow movie (AVI format)
Movie 6. Simulated flow (contours of vertical velocity) of a homogeneous nonhydrostatic Boussinesq fluid with the free-surface upper boundary conditions. The height of the surface is predicted by integrating shallow-water equations, and it is incorporated into a nonhydrostatic model via time-dependent curvilinear coordinate transformation.

Spectral preconditioners for nonhydrostatic atmospheric models

The elliptic problems in semi-implicit nonhydrostatic atmospheric models are difficult. Typically, they are poorly conditioned, nonseparable, contain cross derivative terms, and often are nonsymmetric. Collaboration between NCAR researchers Steven Thomas (NCAR/SCD), Joshua Hacker, Smolarkiewicz, and Roland Stull (University of British Columbia) has led to a class of effective Krylov methods - a conjugate residual (GCR) algorithm preconditioned with a 3D direct solver (using standard tridiagonal inversion in the vertical). They have developed a horizontal spectral preconditioner as an alternative to a more standard, and simpler, line-Jacobi relaxation scheme. However, the efficacy of the spectral preconditioner requires neglecting the cross derivative terms, and homogenization (e.g., averaging) metric coefficients over the computational domain. Because such a compromise causes a substantial departure of the preconditioner from the original elliptic operator, it is not obvious whether it leads to a competitive solver a priori. They evaluated the robustness of the proposed approach over a broad range of representative meteorological applications (see Movie 7) and they documented its superior performance in the context of a three-time-level, semi-implicit, semi-Lagrangian, all-scale weather-prediction/research model.

	To view the movie, place mouse over image. Alternately, for slower connections, you may use the links below to download the movie. Isotherms movie (animated GIF) Isotherms movie (AVI format)
Movie 7. Isotherms of a 3D convective thermal. The loop covers 450 s in 30 s intervals. GCR solver performance with both the DCT and line Jacobi preconditioners are shown as running totals of iterations and CPU seconds. The contour interval is 0.1 K.

Correction algorithms for Vaisala radiosondes

Vaisala radiosonde relative humidity measurements are known to be inaccurate at cold temperatures in the upper troposphere, yet these measurements are fundamentally important to a wide range of research activities, including: initializing numerical models or evaluating model results; performing radiative transfer calculations; validating ground-based or satellite water vapor retrievals; and developing water vapor and cloud parameterizations. Larry Miloshevich developed a numerical inversion algorithm to correct for the time-lag error that results from slow sensor response at cold temperatures, based on laboratory measurements of the temperature-dependence of the sensor time-constant. Miloshevich applied a correction algorithm for time-lag known bias errors to a dataset of 40 humidity profiles, measured simultaneously by Vaisala radiosondes and the reference-quality NOAA/Climate Monitoring Diagnostics Library cryogenic hygrometer (Fig. 32), demonstrating that the corrections largely remove the temperature-dependent dry bias, and reduce the variability. The example corrected humidity profile in Figure 33 (red) shows that the time-lag correction recovers vertical structure in the profile at cold temperatures, showing what appears to be a tropopause cirrus layer, approximately 1 km thick, that is undetectable in the original measurements (blue).

Figure 32. Statistical analysis of 40 Vaisala RS80-H humidity profiles as compared to simultaneous measurements by the reference-quality NOAA/CMDL cryogenic hygrometer. The mean and standard deviation (red curves) of the difference between the hygrometer measurements and the corresponding uncorrected (left) or corrected (right) radiosonde measurements are shown in %RH as a function of temperature.

Figure 33. Vaisala RS80-H humidity sounding after correction for sensor time-lag error and known bias errors (red), showing a probable tropopause cirrus layer that is not readily apparent in the original data (blue). The dashed curve is ice-saturation, and an asterisk indicates the tropopause.