Applications of second-moment turbulent closure hypotheses to geophysical fluid problems have developed rapidly since 1973, when genuine predictive skill in coping with the effects of stratification was demonstrated. The purpose here is to synthesize and organize material that has appeared in a number of articles and add new useful material so that a complete (and improved) description of a turbulence model from conception to application is condensed in a single article. It is hoped that this will be a useful reference to users of the model for application to either atmospheric or oceanic boundary layers.

http://fap.if.usp.br/~hbarbosa/uploads/Teaching/Modclim2010a/MellorYamada1982.pdf

Development of a turbulence closure model for geophysical fluid problems

This paper proposes a revised vertical diffusion package with a nonlocal turbulent mixing coefficient in the planetary boundary layer (PBL). Based on the study of Noh et al. and accumulated results of the behavior of the Hong and Pan algorithm, a revised vertical diffusion algorithm that is suitable for weather forecasting and climate prediction models is developed. The major ingredient of the revision is the inclusion of an explicit treatment of entrainment processes at the top of the PBL. The new diffusion package is called the Yonsei University PBL (YSU PBL). In a one-dimensional offline test framework, the revised scheme is found to improve several features compared with the Hong and Pan implementation. The YSU PBL increases boundary layer mixing in the thermally induced free convection regime and decreases it in the mechanically induced forced convection regime, which alleviates the well-known problems in the Medium-Range Forecast (MRF) PBL. Excessive mixing in the mixed layer in the presenc...

/pdf/a-new-vertical-diffusion-package-with-an-explicit-treatment-11t7nq83se.pdf

A New Vertical Diffusion Package with an Explicit Treatment of Entrainment Processes

A Description of the Fifth-Generation Penn State/ NCAR Mesoscale Model (MM5), NCAR/TN-398+STR

The Hybrid Single-Particle Lagrangian Integrated Trajectory model (HYSPLIT), developed by NOAA’s Air Resources Laboratory, is one of the most widely used models for atmospheric trajectory and dispersion calculations. We present the model’s historical evolution over the last 30 years from simple hand-drawn back trajectories to very sophisticated computations of transport, mixing, chemical transformation, and deposition of pollutants and hazardous materials. We highlight recent applications of the HYSPLIT modeling system, including the simulation of atmospheric tracer release experiments, radionuclides, smoke originated from wild fires, volcanic ash, mercury, and wind-blown dust.

/pdf/noaa-s-hysplit-atmospheric-transport-and-dispersion-modeling-2wocdjl6c5.pdf

NOAA’s HYSPLIT Atmospheric Transport and Dispersion Modeling System

Abstract A two-dimensional version of the Pennsylvania State University mesoscale model has been applied to Winter Monsoon Experiment data in order to simulate the diurnally occurring convection observed over the South China Sea. The domain includes a representation of part of Borneo as well as the sea so that the model can simulate the initiation of convection. Also included in the model are parameterizations of mesoscale ice phase and moisture processes and longwave and shortwave radiation with a diurnal cycle. This allows use of the model to test the relative importance of various heating mechanisms to the stratiform cloud deck, which typically occupies several hundred kilometers of the domain. Frank and Cohen's cumulus parameterization scheme is employed to represent vital unresolved vertical transports in the convective area. The major conclusions are: Ice phase processes are important in determining the level of maximum large-scale heating and vertical motion because there is a strong anvil componen...

Numerical study of convection observed during the Winter Monsoon Experiment using a mesoscale two-dimensional model [presentation]

Wind and temperature profiles for a wide range of stability conditions have been analyzed in the context of Monin-Obukhov similarity theory. Direct measurements of heat and momentum fluxes enabled determination of the Obukhov length L, a key independent variable in the steady-state, horizontally homogeneous, atmospheric surface layer. The free constants in several interpolation formulas can be adjusted to give excellent fits to the wind and temperature gradient data. The behavior of the gradients under neutral conditions is unusual, however, and indicates that von Karman's constant is ∼0.35, rather than 0.40 as usually assumed, and that the ratio of eddy diffusivities for heat and momentum at neutrality is ∼1.35, compared to the often-suggested value of 1.0. The gradient Richardson number, computed from the profiles, and the Obukhov stability parameter z/L, computed from the measured fluxes, are found to be related approximately linearly under unstable conditions. For stable conditions the Richar...

Flux-Profile Relationships in the Atmospheric Surface Layer

Results from a boundary layer experiment conducted over a flat site in northwestern Minnesota are discussed Wind and temperature fluctuations near the ground were measured with AFCRL's fast-response instrumentation on a 32 m tower Measurements between 32 m and the inversion base zi were made with MRU probes attached at five different heights to the tethering cable of a 1300 m2 kite balloon The daytime convective boundary layer appears to be well-mixed with evidence of significant heat and momentum entrainment through the capping inversion The spectra of velocity components are generalized within the framework of mixed-layer similarity The characteristic wavelength for w increases linearly with height up to z = 0l zi following free convection prediction, but approaches a limiting value of 15 zi, in the upper half of the boundary layer The characteristic wavelengths for u and v are maintained at approximately 15 zi down to heights very close to the ground This limiting wavelength correspo

Turbulence Structure in the Convective Boundary Layer

The spatial resolution appropriate for the simulation of deep moist convection is addressed from a turbulence perspective. To provide a clear theoretical framework for the problem, techniques for simulating turbulent flows are reviewed, and the source of the subgrid terms in the Navier‐Stokes equation is clarified. For decades, cloud-resolving models have used large-eddy simulation (LES) techniques to parameterize the subgrid terms. A literature review suggests that the appropriateness of using traditional LES closures for this purpose has never been established. Furthermore, examination of the assumptions inherent in these closures suggests that grid spacing on the order of 100 m may be required for the performance of cloud models to be consistent with their design. Based on these arguments, numerical simulations of squall lines were conducted with grid spacings between 1 km and 125 m. The results reveal that simulations with 1-km grid spacing do not produce equivalent squallline structure and evolution as compared to the higher-resolution simulations. Details of the simulated squall lines that change as resolution is increased include precipitation amount, system phase speed, cloud depth, static stability values, the size of thunderstorm cells, and the organizational mode of convective overturning (e.g., upright towers versus sloped plumes). It is argued that the ability of the higher-resolution runs to become turbulent leads directly to the differences in evolution. There appear to be no systematic trends in specific fields as resolution is increased. For example, mean vertical velocity and rainwater values increase in magnitude with increasing resolution in some environments, but decrease with increasing resolution in other environments. The statistical properties of the simulated squall lines are still not converged between the 250- and 125-m runs. Several possible explanations for the lack of convergence are offered. Nevertheless, it is clear that simulations with O(1 km) grid spacing should not be used as benchmark or control solutions for resolution sensitivity studies. The simulations also support the contention that a minimum grid spacing of O(100 m) is required for traditional LES closures to perform appropriately for their design. Specifically, only simulations with 250- and 125-m grid spacing resolve an inertial subrange. In contrast, the 1-km simulations do not even reproduce the correct magnitude or scale of the spectral kinetic energy maximum. Furthermore, the 1-km simulations contain an unacceptably large amount of subgrid turbulence kinetic energy, and do not adequately resolve turbulent fluxes of total water. A guide to resolution requirements for the operational and research communities is proposed. The proposal is based primarily on the intended use of the model output. Even though simulations with O(1 km) grid spacing display behavior that is unacceptable for the model design, it is argued that these simulations can still provide valuable information to operational forecasters. For the research community, O(100 m) grid spacing is recommended for most applications, because a modeling system that is well founded should be desired for most purposes.

https://opensky.ucar.edu/islandora/object/articles%3A17616/datastream/PDF/view

Resolution Requirements for the Simulation of Deep Moist Convection

In mesoscale modeling the scale l of the energy- and flux-containing turbulence is much smaller than the scale Δ of the spatial filter used on the equations of motion, and in large-eddy simulation (LES) it is much larger. Since their models of the subfilter-scale (SFS) turbulence were not designed to be used when l and Δ are of the same order, this numerical region can be called the “terra incognita.” The most common SFS model, a scalar eddy diffusivity acting on the filtered fields, emerges from the conservation equations for SFS fluxes when several terms, including all but one of the production terms, are neglected. Analysis of data from the recent Horizontal Array Turbulence Study (HATS) shows that the neglected production terms can be significant. Including them in the modeled SFS flux equations yields a more general SFS model, one with a tensor rather than a scalar eddy diffusivity. This more general SFS model is probably not necessary in fine-resolution LES or in coarse-resolution mesoscale...

Toward Numerical Modeling in the “Terra Incognita”

Equations for the conservation of Reynolds shear stress and the two components of heat flux (velocity-temperature covariance) in the homogeneous atmospheric surface layer are derived. The behavior of the production and turbulent transport (flux divergence) terms in each budget is determined directly from measurements obtained over a wide range of stability conditions during the 1968 Kansas field program of AFCRL. The data are presented in the dimensionless form suggested by Monin-Obukhoy similarity theory, and follow universal functions quite well. The theory is extended to the “local free convection” regime which exists under very unstable conditions, and specific power law forms are predicted. Several of these are verified and values are given for the proportionality factors in the power laws. The flux divergence terms are small, implying that in each budget the local production and destruction rates are in balance. The third moments which represent the vertical fluxes of stress and heat flux a...

John C. Wyngaard

Papers

Flux-Profile Relationships in the Atmospheric Surface Layer

Turbulence Structure in the Convective Boundary Layer

Resolution Requirements for the Simulation of Deep Moist Convection

Toward Numerical Modeling in the “Terra Incognita”

Local Free Convection, Similarity, and the Budgets of Shear Stress and Heat Flux.