The Technical Note series provides an outlet for a variety of NCAR manuscripts that contribute in specialized ways to the body of scientific knowledge but which are not suitable for journal, monograph, or book publication. Reports in this series are issued by the NCAR Scientific Divisions ; copies may be obtained on request from the Publications Office of NCAR. Designation symbols for the series include: Any opinions, findings, conclusions, or recommendations expressed in this publication are those of the authors and do not necessarily reflect the views of the National Science Foundation.

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A Description of the Advanced Research WRF Version 3

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

If model parameterizations of unresolved physics, such as the variety of upper ocean mixing processes, are to hold over the large range of time and space scales of importance to climate, they must be strongly physically based. Observations, theories, and models of oceanic vertical mixing are surveyed. Two distinct regimes are identified: ocean mixing in the boundary layer near the surface under a variety of surface forcing conditions (stabilizing, destabilizing, and wind driven), and mixing in the ocean interior due to internal waves, shear instability, and double diffusion (arising from the different molecular diffusion rates of heat and salt). Mixing schemes commonly applied to the upper ocean are shown not to contain some potentially important boundary layer physics. Therefore a new parameterization of oceanic boundary layer mixing is developed to accommodate some of this physics. It includes a scheme for determining the boundary layer depth h, where the turbulent contribution to the vertical shear of a bulk Richardson number is parameterized. Expressions for diffusivity and nonlocal transport throughout the boundary layer are given. The diffusivity is formulated to agree with similarity theory of turbulence in the surface layer and is subject to the conditions that both it and its vertical gradient match the interior values at h. This nonlocal “K profile parameterization” (KPP) is then verified and compared to alternatives, including its atmospheric counterparts. Its most important feature is shown to be the capability of the boundary layer to penetrate well into a stable thermocline in both convective and wind-driven situations. The diffusivities of the aforementioned three interior mixing processes are modeled as constants, functions of a gradient Richardson number (a measure of the relative importance of stratification to destabilizing shear), and functions of the double-diffusion density ratio, Rρ. Oceanic simulations of convective penetration, wind deepening, and diurnal cycling are used to determine appropriate values for various model parameters as weak functions of vertical resolution. Annual cycle simulations at ocean weather station Papa for 1961 and 1969–1974 are used to test the complete suite of parameterizations. Model and observed temperatures at all depths are shown to agree very well into September, after which systematic advective cooling in the ocean produces expected differences. It is argued that this cooling and a steady salt advection into the model are needed to balance the net annual surface heating and freshwater input. With these advections, good multiyear simulations of temperature and salinity can be achieved. These results and KPP simulations of the diurnal cycle at the Long-Term Upper Ocean Study (LOTUS) site are compared with the results of other models. It is demonstrated that the KPP model exchanges properties between the mixed layer and thermocline in a manner consistent with observations, and at least as well or better than alternatives.

Oceanic vertical mixing: A review and a model with a nonlocal boundary layer parameterization

A Description of a Three-Dimensional Coastal Ocean Circulation Model

https://ams.confex.com/ams/pdfpapers/71176.pdf

Fully coupled “online” chemistry within the WRF model

Turbulence models centered on hypotheses by Rotta and Kolmogoroff are complex. In the present paper we consider systematic simplifications based on the observation that parameters governing the degree of anisotropy are small. Hopefully, we shall discern a level of complexity which is intuitively attractive and which optimizes computational speed and convenience without unduly sacrificing accuracy. Discussion is focused on density stratified flow due to temperature. However, other dependent variables—such as water vapor and droplet density—can be treated in analogous fashion. It is, in fact, the anticipation of additional physical complexity in modeling turbulent flow fields that partially motivates the interest in an organized process of analytical simplification. For the problem of a planetary boundary layer subject to a diurnally varying surface heat flux or surface temperature, three models of varying complexity have been integrated for 10 days. All of the models incorporate identical empirica...

A Hierarchy of Turbulence Closure Models for Planetary Boundary Layers.

Previously, the authors have studied a hierarchy of turbulent boundary layer models, all based on the same closure assumptions for the triple turbulence moments. The models differ in complexity by virtue of a systematic process of neglecting certain of the tendency and diffusion terms in the dynamic equations for the turbulent moments. Based on this work a Level 3 model was selected as one which apparently sacrificed little predictive accuracy, but which afforded considerable numerical simplification relative to the more complex Level 4 model. An earlier paper had demonstrated that the model produced similarity solutions in near agreement with surface, constant flux data. In this paper, simulators from the Level 3 model are compared with two days of Wangara atmospheric boundary layer data (Clarke et al., 1971). In this comparison, there is an easily identified error introduced by our inability to include advection of momentum in the calculation since these terms were not measured. Otherwise, the ...

A Simulation of the Wangara Atmospheric Boundary Layer Data

A simplified second-moment urbulence closure model, which has been reasonably well tested in various geophysical problems, is used to simulate effects of a tall tree canopy on air circulations in the atmospheric boundary layer. Qualitative simulation of a canopy flow, with nearly constant and low wind speeds in a canopy, but large wind shears near a treetop, and unstable (stable) temperature layers within a canopy during the night (day) are all satisfactory. Strong couplings between the mean and turbulence variables are obvious when simulations performed with and without a canopy in the model are compared with one another.

https://www.jstage.jst.go.jp/article/jmsj1965/60/1/60_1_439/_pdf

A numerical model study of turbulent airflow in and above a forest canopy

Nocturnal drainage flows observed over a nearly two-dimensional ridge called Rattlesnake Hills near Richland, Washington are simulated by using a simplified turbulence closure model in which only turbulence kinetic energy and turbulence length scale equations are solved prognostically. The present model is slightly simpler than a level 2.5 model which has been extensively used in previous simulations of various atmospheric boundary layer phenomena. Wind and temperature profiles computed by the present model are generally in excellent agreement with observations made by towers erected on the slope of Rattlesnake Hills. Strong coupling between the mean and turbulence variables is also demonstrated.

Tetsuji Yamada

Papers

Development of a turbulence closure model for geophysical fluid problems

A Hierarchy of Turbulence Closure Models for Planetary Boundary Layers.

A Simulation of the Wangara Atmospheric Boundary Layer Data

A numerical model study of turbulent airflow in and above a forest canopy

Simulations of Nocturnal Drainage Flows by a q2l Turbulence Closure Model