Mellor Yamada Model Research Articles

Assessing turbulence and mixing parameterizations in the gray-zone of multiscale simulations over mountainous terrain during the METEX21 field experiment

Multiscale numerical weather prediction models transition from mesoscale, where turbulence is fully parameterized, to microscale, where the majority of highly energetic scales of turbulence are resolved. The turbulence gray-zone is situated between these two regimes and multiscale models must downscale through these resolutions. Here, we compare three multiscale simulations which vary by the parameterization used for turbulence and mixing within the gray-zone. The three parameterizations analyzed are the Mellor-Yamada Nakanishi and Niino (MYNN) Level 2.5 planetary boundary layer scheme, the TKE-1.5 large eddy simulation (LES) closure scheme, and a recently developed three-dimensional planetary boundary layer scheme based on the Mellor-Yamada model. The simulation domain includes complex (i.e., mountainous) terrain in Nevada that was instrumented with meteorological towers, profiling and scanning lidars, a tethered balloon, and a surface flux tower. Simulations are compared to each other and to observations, with assessment of model skill at predicting wind speed, wind direction and TKE, and qualitative evaluations of transport and dispersion of smoke from controlled releases. This analysis demonstrates that microscale predictions of transport and dispersion can be significantly influenced by the choice of turbulence and mixing parameterization in the terra incognita, particularly over regions of complex terrain and with strong local forcing. This influence may not be apparent in the analysis of model skill, and motivates future field campaigns involving controlled tracer releases and corresponding modeling studies of the turbulence gray-zone.

Diagnosis of Second-Order Turbulent Properties of the Surface Layer for Three-Dimensional Flow Based on the Mellor–Yamada Model

Abstract Accurate representation of heterogeneous surface layer processes is essential for numerical weather prediction (NWP) with sub-kilometer grid spacing. NWP models such as the Weather Research and Forecasting (WRF) Model generally use second-moment turbulent models for parameterizing the planetary boundary layer (PBL). The most common parameterizations follow Mellor–Yamada and account for the vertical turbulent mixing only; that is, standard PBL parameterizations are one-dimensional (1DPBL). The horizontal diffusion of momentum is parameterized based on Smagorinsky’s model for numerical stability. Although the combination of 1DPBL and 2D Smagorinsky parameterizations is successful at coarse grid resolutions (e.g., grid-size dx ∼ 12–2 km), it does not represent well the effect of horizontal turbulence as gridcell size decreases (<1 km). To reconcile the representation of vertical and horizontal turbulent mixing, a full three-dimensional PBL scheme (3DPBL) based on the Mellor–Yamada model was implemented in WRF. The 3DPBL uses the horizontal and vertical turbulent fluxes diagnosed from the flow gradients to handle the turbulent mixing. These gradients cannot be directly calculated near the surface. Therefore, the 3DPBL parameterization is coupled herein to a second-order diagnostic model of the three-dimensional turbulent fluxes in the surface layer. Several adjustments to the original Mellor–Yamada model, including a modified length scale, were introduced to capture flow anisotropy and dependence on stability conditions. The results are compared against data from the Wind Forecast Improvement Project 2 (WFIP2) for different weather regimes and using different grid resolutions to examine stability and scale dependency.

Prediction of gradient‐based similarity functions from the Mellor–Yamada model

AbstractGradient‐based implicit similarity functions are derived theoretically from a few variants of the Mellor–Yamada algebraic turbulence‐closure model under assumptions of local equilibrium conditions in a stably stratified shear flow. The solutions are compared with empirical functions presented by Sorbjan. Good agreement is found in the range of gradient Richardson number extending up to around 0.2. The gradient‐based scaling framework offers better accuracy and reliability than the traditional Monin–Obukhov framework, as it circumvents the problems of small values of fluxes and cross‐correlations. It is also possible to separate the specification of the master length‐scale from the calculation of similarity functions describing second moments and dissipation rate. The related discussion of model performance at higher is included. It is unclear whether the current countermeasures against spurious flow decoupling reflect the observed features of turbulence in the very stable regime, due to the apparent breakdown of the Richardson–Kolmogorov energy cascade, as found by Grachev et al.

An Extension of the Mellor–Yamada Model to the Terra Incognita Zone for Dry Convective Mixed Layers in the Free Convection Regime

The terra incognita (TI) or grey zone arises in conventional planetary boundary-layer parametrizations when the grid resolution of a numerical model is comparable to the size of the energy-containing turbulent eddies \(\sim \)1 km or less. Here, we investigate a simple, plausible extension of the Mellor–Yamada (MY) level-3 scheme for TI-scale grid size using a large-eddy simulation (LES) as a benchmark. Horizontal filtering of the benchmark simulation data for the dry convective mixed layer in the free convection regime yields subfilter-scale components whose statistics are then retrieved for various filter sizes. This leads to a modified MY level-3 scheme for TI-scale grid sizes. The proposed TI scheme incorporates: (1) modification of various length scales in the conventional MY scheme by an empirical function that depends on the horizontal grid size normalized by the convective boundary-layer height; (2) a new length scale for horizontal turbulent fluxes; and (3) a linear relationship between the local dissipation length and subfilter-scale turbulent kinetic energy. A posteriori tests of the proposed TI scheme show a much improved performance compared with the conventional MY level-3 scheme. The ratio of the grid-scale to the subgrid-scale turbulent intensity is comparable to that obtained from the filtered LES solutions. Sensitivity tests show that the modification of the dissipation length scales has the largest impact, while the new length scale for horizontal fluxes also proves important. A simulation that includes all of the above modifications results in the optimum performance.

On the application of a new formulation of nonlinear eddy viscosity based on anisotropy to numerical ocean models

The present paper explores the derivation of an alternative nonlinear eddy viscosity formulation based on Reynolds stress anisotropy and its implementation to numerical ocean models. This formulation takes into account the vorticity in addition to the mean strain rate. The proposed formulation does not include the stability function method which is a common approach in eddy viscosity calculations used in the present state-of-the-art numerical ocean models. Instead, it depends on the second invariant of anisotropy. Initially, the performance of the formulation is checked through a simple channel flow simulation. Consequently for model calibration, an idealised experiment of mixed-layer entrainment into stably stratified flow has been simulated and compared to empirical data. For sensitivity studies related to shear and stable stratification, concept of steady-state Richardson number is applied for homogeneous shear layer. Finally, the performance of the new formulation is tested by implementing it into one-dimensional General Ocean Turbulence Model. Furthermore, a realistic oceanic test case of a storm has been investigated considering different physical processes for the Fladenground Experiment (FLEX’ 76) in the northern North Sea and the results have been compared to the measured data. The main results signify that the overall performance of the nonlinear eddy viscosity model with a different value of steady-state Richardson number is as good as the Mellor–Yamada model in terms of predictability, and the eddy viscosity and diffusivity profiles follow the principle of law of the wall. Additionally, the present formulation does not require computing the stability functions and the ease of implementation into numerical ocean models gives the present formulation an upper hand over the existing formulations in the field of turbulence modelling in oceanography.

Assessment of mixed layer models embedded in an ocean general circulation model

The atmospheric mixed layer obtained using the Mellor–Yamada model grows slower and becomes shallower than observed, which motivated Nakanishi and Niino (J Meteorol Soc Jpn 87:895–912, 2009) to present a modified version of the Mellor–Yamada model. In this study, incorporating each of the Mellor–Yamada and the Nakanishi–Niino models into an ocean general circulation model, we evaluate its performance in the ocean. Comparing the numerical results with the observed ones in the western North Pacific, the Nakanishi–Niino model is shown to exhibit a better performance than the Mellor–Yamada model under strong wind forcing and sea surface cooling during winter and after passage of typhoons during summer.

Software for evaluating sediment-induced stratification in open-channel flows

Open channel flow containing sediment suspension subjects itself to a density gradient in the vertical direction, i.e. density self-stratification, due to the tendency for suspended sediment to settle. Velocity and concentration profiles under the effect of density stratification may differ significantly from the conventional logarithmic and Rousean distributions associated with open channel flow. It is hence important to include this effect into flow computations in order to accurately predict flow characteristics such as the resistance coefficient, near-bed sediment concentration, flow and sediment discharge. In this study we introduce a software, StratSedOC, for such purpose. The application contains a user-friendly interface which allows users to evaluate and visualize the differences in the velocity, concentration and eddy viscosity profiles when stratification effects are taken into account. In addition to the standard logarithmic/Rousean formulation, the model uses three turbulence closures, i.e. an algebraic model (Smith–McLean) and two differential models (k-ε and Mellor–Yamada). The software application can also be used to study the effect of sediment mixtures on flow stratification under different boundary conditions for near-bed sediment concentration. Comparison among the model and experimental results suggests that the Mellor–Yamada model predicts a damping effect on the eddy viscosity which is similar to the Smith–McLean model, while the k-ε model consistently predicts weaker stratification effects. Based on this result, a modified boundary condition for the k-ε model is then proposed.

Importance of the subgrid-scale turbulent moist process: Cloud distribution in global cloud-resolving simulations

This study investigated the turbulent transport process within the nonhydrostatic icosahedral atmospheric model (NICAM), a global cloud-resolving model (GCRM), with particular focus on the spatial reproducibility of cloud characteristics in NICAM simulations. A turbulent closure model was applied, based on level 2 of the model developed by Nakanishi and Niino ([Nakanishi, M., and Niino, H., 2006: An improved Mellor–Yamada level-3 model: its numerical stability and application to a regional prediction of advection fog. Boundary-Layer Meteorol., 119, 397–407.]; a revised version of the original Mellor–Yamada model), together with a subgrid-scale condensation process. NICAM simulations were conducted for boreal summer of 2004 using mesh sizes of about 14 km and 7 km. Simulated cloud amounts and radiative budget were compared with observed data. The results confirmed an improvement in the spatial distribution of low clouds that develop in offshore regions of subtropical continents compared to past NICAM experiments ([Iga, S., Tomita, H., Tsushima, Y., and Satoh, M., 2007: Climatology of a nonhydrostatic global model with explicit cloud process. Geophys. Res. Lett., 34, L22814, doi:10.1029/2007/GL031048.]). A sensitivity study of subgrid-scale clouds in the turbulent closure scheme revealed that the turbulent transport process modulated by the subgrid-scale cloud strongly controls not only the low-cloud amount but also mid- and high-cloud amounts. This indicates that parameterization of unresolvable subgrid-scale clouds remains an important component of cloud behavior in GCRMs.

E − ε − 〈θ 2〉 turbulence closure model for an atmospheric boundary layer including the urban canopy

A modified three-parameter model of turbulence for a thermally stratified atmospheric boundary layer (ABL) is presented. The model is based on tensor-invariant parameterizations for the pressure–strain and pressure–temperature correlations that are more complete than the parameterizations used in the Mellor–Yamada model of level 3.0. The turbulent momentum and heat fluxes are calculated with explicit algebraic models obtained with the aid of symbol algebra from the transport equations for momentum and heat fluxes in the approximation of weakly equilibrium turbulence. The turbulent transport of heat and momentum fluxes is assumed to be negligibly small in this approximation. The three-parameter $$E - \varepsilon - {\left\langle {\theta ^{2} } \right\rangle }$$ model of thermally stratified turbulence is employed to obtain closed-form algebraic expressions for the fluxes. A computational test of a 24-h ABL evolution is implemented for an idealized two-dimensional region. Comparison of the computed results with the available observational data and other numerical models shows that the proposed model is able to reproduce both the most important structural features of the turbulence in an urban canopy layer near the urbanized ABL surface and the effect of urban roughness on a global structure of the fields of wind and temperature over a city. The results of the computational test for the new model indicate that the motion of air in the urban canopy layer is strongly influenced by mechanical factors (buildings) and thermal stratification.

Modelling the tidal mixing fronts and seasonal stratification of the Northwest European Continental shelf

We investigate mixing processes under stratified conditions on the Northwest European Continental shelf using a numerical model (POLCOMS). Our results indicate that convection induced by vertical shearing of horizontal density gradients (‘shear-induced convection’) is a regularly occurring feature in the bottom and surface boundary layers in this open shelf-sea situation. Two types of turbulence models are investigated to study their capability for reproducing the observed location of tidal mixing fronts, and the physical processes occurring in seasonally stratified waters. The first model is a one-equation variant of the Mellor–Yamada model, whereas the second model combines a more recent second-momentum closure with a two-equation model. It is found that generally mean frontal positions (as estimated from ICES data) are predicted more accurately by the two-equation model. The one-equation model reproduces the mean frontal locations to 18.1km (<3 grid spacings) and the two-equation model to 17.1km; although in the Celtic Sea the accuracy is ∼33 and ∼12km, respectively. Comparison with historical tide gauges, current metres, CTD stations, and thermistor chain data from the North Sea Project all show an improvement in accuracy when the two-equation model is used. This is particularly apparent in the model's ability to reproduce the spring–neap variability during stratification. We find that in the presence of shear-induced convection the routinely applied clipping of the turbulent length-scale, previously thought to be a minor ingredient in a turbulence model, has a dramatic effect on the results: if the length-scale clipping is not applied, substantial over-mixing is observed to occur. The causes and possible remedies of this effect are investigated. Overall our results demonstrate a sensitivity to the details of the turbulence model that is significantly greater than previously thought.

Three-parameter model of turbulence for the atmospheric boundary layer over an urbanized surface

A modified three-parameter model of turbulence for a thermally stratified atmospheric boundary layer (ABL) is presented. The model is based on tensor-invariant parametrizations for the pressure-strain and pressure-temperature correlations that are more complete than the parametrizations used in the Mellor-Yamada model of level 3.0. The turbulent momentum and heat fluxes are calculated with explicit algebraic models obtained with the aid of symbol algebra from the transport equations for momentum and heat fluxes in the approximation of weakly equilibrium turbulence. The turbulent transport of heat and momentum fluxes is assumed to be negligibly small in this approximation. The three-parameter E − e − model of thermally stratified turbulence is employed to obtain closed-form algebraic expressions for the fluxes. A computational test of a 24-h ABL evolution is implemented for an idealized two-dimensional region. Comparison of the computed results with the available observational data and other numerical models shows that the proposed model is able to reproduce both the most important structural features of the turbulence in an urban canopy layer near the urbanized ABL surface and the effect of urban roughness on a global structure of the fields of wind and temperature over a city. The results of the computational test for the new model indicate that the motion of air in the urban canopy layer is strongly influenced by mechanical factors (buildings) and thermal stratification.

A generic length-scale equation for geophysical turbulence models

A generalization of a class of differential length-scale equations typically used in second-order turbulence models for oceanic flows is suggested. Commonly used models, like the κ-e model and the Mellor-Yamada model, can be recovered as special cases of this generic model, and thus can be rationally compared. In addition, a method is proposed that yields a generalized framework for the calibration of the most frequently used class of differential length-scale equations. The generic model, calibrated with this method, exhibits a greater range of applicability than any of the traditional models. Stratified flows, plane mixing layers, and turbulence introduced by breaking surface waves are considered besides some classical test cases.

Extending the k– ω turbulence model towards oceanic applications

Four different two-equation turbulence models for geophysical flows are compared: The k– ϵ model, two new versions of the k– ω model, and the Mellor–Yamada model. An extension of the k– ω model for buoyancy affected and rotating flows is suggested. Model performance is evaluated for a few typical oceanic flows. First, new analytical solutions of the models for the surface layer affected by breaking surface waves are discussed. The deficiencies of earlier attempts are high-lighted, and it is demonstrated why the Mellor–Yamada model and the k– ϵ model fail. It is illustrated that only one version of the k– ω model computes correct decay rates for turbulent quantities under breaking waves. Second, it is demonstrated that all models predict almost identical mixed layer depths and profiles for the turbulent kinetic energy in a classical stratified shear-entrainment experiment if the buoyancy term in the second equation is appropriately weighted. Third, the accuracy and numerical robustness of the new k– ω model in realistic oceanic situations is confirmed by comparison with the data-set of the Ocean Weather Ship ‘Papa’.

数値モデルによる計算結果と観測データを併用した都市スケールの気候解析

Regional climate in Kinki district is analyzed by numerical prediction tool based on Mellor-Yamada model. In order to clarify the characteristics of the overall regional climate, the method of using and compensating the calculation result and the observation result together is examined. Since the nesting technique is used, in the target area, the calculation result and the observation result are adjusted. By considering the distribution of air temperature and wind vector obtained by the calculation and by the observation, the recommendation to urban and building planning can be proposed.

The Numerical Solution of the Mellor-Yamada Level 2.5 Turbulent Kinetic Energy Equation in the Eta Model

Abstract A new method is presented for obtaining the numerical solution of the production-dissipation component of the turbulent kinetic energy equation that arises in the Mellor-Yamada level 2.5 turbulent closure model. The development of this new method was motivated by the occasional appearance of large temporal oscillations in the solution provided by a previously used method. Analysis of the equation revealed that the solution should tend toward a stationary asymptotic value, which is the equilibrium value of turbulent kinetic energy for the level 2, Mellor-Yamada model. Failure to identify the correct asymptotic value in the formalism underlying the numerical solution of the equation allows the solution to overshoot the equilibrium. Repeated overshooting gives rise to an oscillation in the solution from one time step to the next. The new method prevents this from happening. Idealized cases are used to demonstrate the performance of the new method. It has been incorporated into the eta coordinate, nu...