Higher-order Turbulence Closure Model Research Articles

Elucidating Model Inadequacies in a Cloud Parameterization by Use of an Ensemble-Based Calibration Framework

AbstractEvery cloud parameterization contains structural model errors. The source of these errors is difficult to pinpoint because cloud parameterizations contain nonlinearities and feedbacks. To elucidate these model inadequacies, this paper uses a general-purpose ensemble parameter estimation technique. In principle, the technique is applicable to any parameterization that contains a number of adjustable coefficients. It optimizes or calibrates parameter values by attempting to match predicted fields to reference datasets. Rather than striving to find the single best set of parameter values, the output is instead an ensemble of parameter sets. This ensemble provides a wealth of information. In particular, it can help uncover model deficiencies and structural errors that might not otherwise be easily revealed. The calibration technique is applied to an existing single-column model (SCM) that parameterizes boundary layer clouds. The SCM is a higher-order turbulence closure model. It is closed using a multivariate probability density function (PDF) that represents subgrid-scale variability. Reference datasets are provided by large-eddy simulations (LES) of a variety of cloudy boundary layers. The calibration technique locates some model errors in the SCM. As a result, empirical modifications are suggested. These modifications are evaluated with independent datasets and found to lead to an overall improvement in the SCM’s performance.

Flow dynamics in Athens area under moderate large-scale winds

The purpose of the present paper is to study the wind regime in Greater Athens Area (GAA) during a day when the sea breeze was opposing a moderately strong synoptic-scale flow. The approach adopted in the present study is to analyze data from a field campaign and from numerical model simulations. The field data used in the analysis are from the MEDditerranean CAmpaign of PHOtochemical Tracers-TRAnsport and Chemical Evolution (MEDCAPHOT-TRACE) which took place in the GAA during the period 20 August–20 September 1994. The numerical simulations were performed using a three-dimensional, higher-order turbulence closure model. All model equations are transformed to a terrain-following coordinate system, which enables studies of flow over complex terrain. The results from the simulations compare reasonably well with the field data. The analysis of the field data and the numerical simulation results reveals that, under the present conditions, the temporal and spatial variations of the wind field are not as pronounced as in days with weak synoptic background flow. A sea breeze circulation is developing over the sea and reaches the shoreline but is counterbalanced by the opposing synoptic flow and it does not penetrate deeply over the land. The characteristics of the sea breeze systems developing in GAA under weak large-scale ambient winds are presented in a companion paper.

Anatomy of the sea-breeze circulation in Athens area under weak large-scale ambient winds

The city of Athens is located near an irregular coastline and is surrounded by moderately high mountains. The complex structure of the sea breezes developing in Greater Athens Area (GAA) during a day with weak large-scale ambient winds is examined using consolidated field data and results from numerical model simulations. The data used in the analysis are from the MEDditerranean CAmpaign of PHOtochemical Tracers-TRAnsport and Chemical Evolution (MEDCAPHOT-TRACE) which took place in the GAA during the period 20 August–20 September 1994. The numerical simulations were performed using a three-dimensional, higher-order turbulence closure model. All model equations are transformed to a terrain-influenced coordinate system, which enables studies of flow over complex terrain. A full diurnal cycle has been simulated for the typical sea-breeze day of 15 September 1994. Major characteristics of the sea-breeze circulation including surface wind pattern, inland penetration of the sea-breeze front and vertical extension and intensity as well as diurnal variation of the vertical eddy thermal diffusivity are identified and discussed. Model predictions show a good agreement with the comprehensive data set.

Boundary layer dynamics in an urban coastal environment under sea breeze conditions

A three-dimensional, higher-order turbulence closure model is applied to simulate the boundary layer dynamics in Attica peninsula, where the city of Athens is located. All model equations are transformed to a terrain influenced coordinate system, which enables studies of flow over complex terrain. Major characteristics of the sea breeze circulation including vertical extension and intensity as well as the growth rate of the thermal internal boundary layer are identified and discussed. Model predictions agree fairly well with measured profiles at one location and measured surface winds in the center of Athens. In addition to the basic simulations, a series of sensitivity tests has been performed in order to evaluate the relative importance of the various input parameters. It was found that some parameters (topography, the amplitude; of the diurnal variation of the temperature over the land) have relatively larger impact on the development of sea breeze circulation over the Athens basin than others. The sea breeze circulation developing at the east side of the Attica peninsula is particularly sensitive to the input geostrophic wind.

Numerical Simulation on the TIBL Structure in Shoreline Areas with a 2D Higher-Order Turbulence Closure Model

Abstract A 2D higher-order turbulence closure model for research on the structure of the thermal internal boundary layer (TIBL) has been developed in this paper. The mean quantities (temperature and wind), as well as their turbulent moments and their distribution under the TIBL, were computed. Results of numerical simulation show that under the initial condition of onshore flow and surface temperature on land being higher, than on water. 1) the profile of the TIBL on shore can be identified by the distributions of the mean wind and temperature, and during the integration hours there is an unstable stratified region over land that extends upward and inland gradually; 2) the shape of the profiles of the TIBL is roughly in concordance with observed profiles, but there are some differences, obviously, between the results computed by the formula of h ∼ x1/2 and the results of the numerical experiment; and 3) u′2, v′2, w′2, and u′w′, θ′w′ and their general features are well reproduced by the model. It is shown that the numerical model is feasible and effective.

A numerical study of floe in Athens area using the MIUU model

The flow regime in Greater Athens Area (GAA) io numerically investigated by a mesoscale, higher-order turbulence closure model. The model is three-dimensional, hydrostatic, and with a terrain following coordinate system. It has been developed at the Department of Meteorology in Uppsala (MIUU). The numerical investigation was performed within the frame of the Athenian Photochemical Smog Intercomparison of Simulations (APSIS) and the day chosen for simulation is May 25, 1990. Although the geostrophic wind was kept constant throughout the simulation period, the simulated wind fields in the lower layers are quite variable both in time as well as in space. The major characteristics of the flow field during day-hours, are identified and discussed.

APPLICATION OF A HIGHER-ORDER TURBULENCE CLOSURE MODEL TO PLANE JET

Abstract This paper presents performance tests of a higher-order turbulence closure model for the predictions of turbulent shear flows. Computations of the momentum and temperature fields in the flow domain being considered entail the solutions of the Reynolds-averaged transport equations containing the second-order turbulence fluctuating products. Computations of the Reynolds stresses are performed with three closure models and the k-c model (one of the Boussinesq viscosity models). Computations of the second-order temperature velocity products are achieved by closing the pressure-heat flux term. These predictions are compared with three sets of experimental data. Several advantages have been observed in using the higher-order transport equations for evaluating Reynolds stresses; considerable improvement is achieved when higher-order turbulence closures are employed. This is because the Boussinesq viscosity model assumes that turbulence is isotropic and thus overpredicts the transverse normal component o...

Some parameterizations of the nocturnal boundary layer

The evolution and structure of a steady barotropic nocturnal boundary layer are investigated using a higher-order turbulence closure model which includes equations for the mean quantities, turbulence convariances, and the viscous dissipation rate. The results indicate that a quasi-steady nocturnal PBL might be established in 4–10 hours after transition, depending on surface cooling rate. The latter is assumed to be constant in the model. The emphasis is on prediction of eddy viscosity, nocturnal mixing-layer depth, and the stability-dependent universal functions in the geostrophic drag and heat transfer relations. The model predictions are parameterized in the framework of the PBL similarity theory and compared with observations and results of other models.

The Moist Boundary Layer with a Higher Order Turbulence Closure Model

A one-dimensional higher order turbulence closure model is used to investigate moisture structure within the diurnally varying planetary boundary layer. The diurnal character of the moist boundary layer as a whole and a variety of micrometeorological features are examined in a series of experiments having differing lower boundary conditions on the moisture field. In one case, midafternoon surface evaporation and turbulent moisture transfer to higher levels act as competing processes in determining low-level moisture content. A double wave in low-level daily specific humidity results (specific humidity minima in early morning and midafternoon). In another experiment, a moisture inversion develops when there is a strong nocturnal moisture flux to the surface such as occurs with dew formation. A simple, analytic method of calculating the moist layer's growth rate is compared with the numerical results. The analytic method provides good flux estimates when the shoulder in the specific humidity profiles (where the moisture lapse first sharply deviates from its mixed-layer value) is treated as being the top of the moist boundary layer. The specified initial moisture distribution has a considerable lapse above 0.5 km. However, during the afternoon a well-mixed moist layer develops despite dry air entrainment above and surface moisture influx from below. This suggests that rapid growth into a dry environment cannot explain the coincidence of strong moisture lapses with thermally well-mixed regions.

Local advection of momentum, heat, and moisture in micrometeorology

The local advection of momentum, heat and moisture in micrometeorology due to a horizontal inhomogeneity in surface conditions is numerically investigated by a higher-order turbulence closure model which includes equations for the mean quantities, turbulent fluxes, and the viscous dissipation rate. The application of the two-dimensional model in this paper deals with the simulation of the flow from an extensive smooth dry area to a grassy wet terrain. The mean wind speed, temperature, and humidity distributions in the resulting internal boundary layer downstream of the surface discontinuity are determined such that the energy and moisture balances at the Earth's surface are satisfied. Numerical calculations of the mean temperature and humidity profiles are compared with available observed ones. The results include the advective effects on turbulent flux distributions, surface energy balance, evaporation rate, and Bowen ratio. The sensitivity of the predicted mean profiles and turbulent flux distributions to the surface relative humidity, thermal stratification, and the roughness change is discussed.