Boundary layer parameterization

Arya, S. P. S. (1977). Suggested revision to certain boundary layer parameterization schemes used in atmospheric circulation models. Mon. Weather Rev. 105, 215-227. 

Large, W. G., McWilliams, J. C., Doney, S. C., 1994. Oceanic vertical mixing a review and a model with a nonlocal boundary layer parameterization. Review of Geophysics, 32, 363 03. 

When NMHC are significant in concentration, differences in their oxidation mechanisms such as how the NMHC chemistry was parameterized, details of R02-/R02 recombination (95), and heterogenous chemistry also contribute to differences in computed [HO ]. Recently, the sensitivity of [HO ] to non-methane hydrocarbon oxidation was studied in the context of the remote marine boundary-layer (156). It was concluded that differences in radical-radical recombination mechanisms (R02 /R02 ) can cause significant differences in computed [HO ] in regions of low NO and NMHC levels. The effect of cloud chemistry in the troposphere has also recently been studied (151,180). The rapid aqueous-phase breakdown of formaldehyde in the presence of clouds reduces the source of HOj due to RIO. In addition, the dissolution in clouds of a NO reservoir (N2O5) at night reduces the formation of HO and CH2O due to R6-RIO and R13. Predictions for HO and HO2 concentrations with cloud chemistry considered compared to predictions without cloud chemistry are 10-40% lower for HO and 10-45% lower for HO2. 

Zeman, O., and Tennekes, H. (1977). Parameterization of the turbulent energy budget at the top of the daytime atmospheric boundary layer. J. Atmos. Sci. 34, 111-123. 

Boundary layer models take a similar approach but attempt to extend the parameterization of gas exchange to individual micrometeorological processes including transfer of heat (solar radiation effects including the cool skin), momentum (friction, waves, bubble injection, current shear), and other effects such as rainfall and chemical enhancements arising from reaction with water. 

As Brenguier (2003) noted, a contributing factor to the uncertainty is drizzle in clouds that form in the atmospheric boundary layer (ABL). In particular, this circumstance illustrates the importance of the adequate retrieval of cloud cover dynamics in the ABL. Another problem is connected with consideration (parameterization) of small-scale processes in the ABL and their non-linearity. For instance, aerosols acting as cloud concentration nuclei (CCN) can be determined from upward motions at the cloud bottom which should be reproduced at a spatial resolution (in the horizontal) of the order of 100 m. The present parameterization schemes still do not meet these requirements. 

Typical options for turbulent transport in the boundary layer include a level 2.5 Mellor-Yamada closure parametrization (Mellor and Yamada 1982), or a non-local approach implemented by scientists from the Yong-Sei University (YSU scheme, Hong and Pan, 1996). Transport in non-resolved convection is handled by an ensemble scheme developed by Grell and Devenyi (2002). This scheme takes time-averaged rainfall rates from any of the convective parametrizations from the meteorological model to derive the convective fluxes of tracers. This scheme also parameterizes the wet deposition of the chemical constituents. 

In no case has the gas exchange rate been observed to be linearly dependent on the Schmidt number. Thus, the simplest model of gas exchange, the stagnant boundary layer, is the big loser in the competition to parameterize the mechanism in nature. The most reahstic representation is that of the square root dependency this has been adopted in the interpretation of tracers of gas exchange in nature. 

Kastner-Klein and Rotach [327] investigated a detailed 1 200 scale model of a portion of the city of Nantes, France in a neutral boundary-layer wind tunnel at the University of Karlsruhe, Germany. They used laser-doppler anemometry to measure all components of velocity, turbulence intensity, and turbulent shear at different locations within the city. Subsequently, they compared their data with various parameterization schemes and concluded that in the roughness sub-layer (RSL),... 

The parameterisation has been tested on the city of Basel (Switzerland), Mexico City (Mexico), Copenhagen (Denmark), and verified versus the BUBBLE experiment (Basel Urban Boundary Layer Experiment Rotach et al., 2005 [549]). The verification results (Figure 9.11) show that the urban parameterization scheme is able to catch most of the typical processes induced by an urban surface Inside the canopy layer, the wind speed, the friction velocity and the atmospheric stability are reduced. In the other hand, even if the main effects of the urban canopy are reproduced, the comparison with the measurement seems indicates that some physical processes are still missing in the parameterization. In most of the cases, the model still overestimates the wind speed inside the canopy layer and it can have difficulties to simulate the maximum of the friction velocity which appears above the building roofs. 

Chen, F., Janjic, Z., and Mitchell, K. (1997) Impact of atmospheric surface-layer parameterizations in the new land-surface scheme of the NCEP mesoscale ETA model, Boundary-Layer Meteorol. 85, 391-421. 

In this paragraph the wall function concept is outlined. The wall functions are empirical parameterizations of the mean flow variable profiles within the inner part of the wall boundary layers, bridging the fully developed turbulent log-law flow quantities with the wall through the viscous and buffer sublayers where the two-equation turbulence model is strictly not valid. These empirical parameterizations thus allow the numerical flow simulation to be carried out with a finite resolution within the wall boundary layers, and one avoids accounting for viscous effects in the model equations. Therefore, in the numerical implementation of the k-e model one anticipates that the boundary layer flow is not fully resolved by the model resolution. The first grid point or node used at a wall boundary is thus placed within the fully turbulent log-law sub-layer, rather than on the wall itself [95]. In effect, the wall functions amount to a synthetic boundary condition for the k-e model. In addition, the limited boundary layer resolution required also provides savings on computer time and storage. 

This means that larger scale motions can be explicitly resolved and deterministically forecasted. The smaller scale motions, namely turbulence, are not explicitly resolved. Rather, the effects of those sub-grid scales on the larger scales are approximated by turbulence models. These smaller size motions are said to be parameterized by sub-grid scale stochastic (statistical) approximations or modes. The referred experimental data analyzes of the flow in the atmospheric boundary layer determine the basis for the large eddy simulation (LES) approach developed by meteorologists like Deardorff [27] [29] [30]. Large-Eddy Simulation (LES) is thus a relatively new approach to the calculation of turbulent flows. 

Schumann U (1992) Simulations and Parameterizations of Large Eddies in Convective Atmospheric Boundary Layers. In Proceedings of a workshop held at the European Centre for Medium-Range Weather Eorecasts (ECMWF)... 

In this section the heat and mass transport coefficients for turbulent boundary layers are examined. In this case the model derivation is based on the governing Reynolds averaged equations. In these equations statistical covariances appear which involve fluctuating velocities, temperatures and concentrations. The nature of these terms is not known a priori and their effects must by estimated by semi-empirical turbulence modeling. The resulting parameterizations allow us to express the unknown turbulent fluctuations in terms of the mean flow field variables. It is emphasized that the Reynolds equations are not actually solved, merely semi-empirical relations are derived for the wall fluxes through the inner boundary layer. 

The modeling procedure can be sketched as follows. First an approximate description of the velocity distribution in the turbulent boundary layer is required. The universal velocity profile called the Law of the wall is normally used. The local shear stress in the boundary layer is expressed in terms of the shear stress at the wall. From this relation a dimensionless velocity profile is derived. Secondly, a similar strategy can be used for heat and species mass relating the local boundary layer fluxes to the corresponding wall fluxes. From these relations dimensionless profiles for temperature and species concentration are derived. At this point the concentration and temperature distributions are not known. Therefore, based on the similarity hypothesis we assume that the functional form of the dimensionless fluxes are similar, so the heat and species concentration fluxes can be expressed in terms of the momentum transport coefficients and velocity scales. Finally, a comparison of the resulting boundary layer fluxes with the definitions of the heat and mass transfer coefficients, indiates that parameterizations for the engineering transfer coefficients can be put up in terms of the appropriate dimensionless groups. 

Ideally, the solution of the primitive equations for specified external constraints (e.g., the solar irradiance at the top of the atmosphere) and appropriate boundary conditions (e.g., observed sea-surface temperature) should provide a comprehensive representation in space and time of the atmospheric dynamical system. In practice, however, limitations in computer capabilities impose limits on the spatial resolution of these models, so that small-scale processes, rather than being explicitly reproduced, must be parameterized. The uncertainties associated with these physical parameterizations (e.g., boundary layer exchanges, convection, clouds, gravity wave breaking, etc.) often limit the overall accuracy in the model results. 

Venkatram, A. (1993) The parameterization of the vertical dispersion of a scalar in the atmospheric boundary layer, Atmos. Environ. 21 A, 1963-1966. 

Schumann U (1989) Laige-eddy simulation of the turbulent diffusion with chemical reactions in the convective boundary layer. Atmos Environ 23(8) 1713-1727 Schumann U (1992) Simulations and parameterizations of laige eddies in convective atmospheric boundary layers. In Proceedings of a workshop held at the European Centre for Medium-Range Weather Forecasts (ECMWF) on Fine Scale Modelling and the Development of Parameterization Schemes, 16-18 September 1991, ECMWF Shames IH (1962) Mechemics of fluids. McGraw-Hill, New York... 

Provided that this hypothesis holds the heat and mass transfer rates can be estimated from the rate of momentum transport. It is noted that Sideman and Pinezewski [111], among others, have examined this hypothesis in further details and concluded that there are numerous requirements that need to be fulfilled to achieve similarity between the momentum, heat and mass transfer fluxes. On the other hand, there are apparently fewer restrictions necessary to obtain similarity between heat and low-flux mass transfer. This observation has lead to the suggestion that empirical parameterizations developed for mass transfer could be applied to heat transfer studies simply by replacing the Schmidt number Sct = ) by the Prandtl number (Pr, = and visa versa. To proceed we need to put up dimensionless relations for the heat and mass transfer fluxes in the turbulent boundary layer using a procedure analoguous to the one applied for the momentum flux (5.229) in which the Boussinesq s turbulent viscosity hypothesis is involved. 

The quasilaminar sublayer resistance / b describes the excess resistance for the transfer of matter from the atmosphere to the surfaces of the vegetation, that is, the difference between the resistance for matter and the resistance for momentum. It is primarily associated with molecular diffusion through quasi laminar boundary layers. Several parameterizations for Rb have been developed, but that employed by Brook et al. (1999), which like Equations 7.3 and 7.6 is valid for conditions of neutral atmospheric stability, is particularly easy to apply ... 

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