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

Gerrity, Joseph P.; Black, Thomas L.; Treadon, Russell E.

doi:10.1175/1520-0493(1994)122<1640:tnsotm>2.0.co;2

Cited by 29 publications

(16 citation statements)

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“…A discussion of the basic differences between the two schemes is found in Gallus (1999) and Jankov and Gallus (2004a). Vertical turbulent exchange in the Eta analyses is calculated based on the Mellor-Yamada level 2.5 model (Mellor andYamada 1974, 1982) with some recent modifications (Łobocki 1993;Gerrity et al 1994). …”

Section: Methodsmentioning

confidence: 99%

The 4 June 1999 Derecho Event: A Particularly Difficult Challenge for Numerical Weather Prediction

Gallus

Correia

Jankov

2005

Weather and Forecasting

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Warm season convective system rainfall forecasts remain a particularly difficult forecast challenge. For these events, it is possible that ensemble forecasts would provide helpful information unavailable in a single deterministic forecast. In this study, an intense derecho event accompanied by a well-organized band of heavy rainfall is used to show that for some situations, the predictability of rainfall even within a 12-24-h period is so low that a wide range of simulations using different models, different physical parameterizations, and different initial conditions all fail to provide even a small signal that the event will occur. The failure of a wide range of models and parameterizations to depict the event might suggest inadequate representation of the initial conditions. However, a range of different initial conditions also failed to lead to a well-simulated event, suggesting that some events are unlikely to be predictable with the current observational network, and ensemble guidance for such cases may provide limited additional information useful to a forecaster. KeywordsAgronomy, atmospheric thermodynamics, climate change, climatology, heat convection, mathermatical models, rain, numerical weather prediction, rainfall forecasts, warm season convective system, weather forecasting, ensemble forecasting, parameterization ABSTRACT Warm season convective system rainfall forecasts remain a particularly difficult forecast challenge. For these events, it is possible that ensemble forecasts would provide helpful information unavailable in a single deterministic forecast. In this study, an intense derecho event accompanied by a well-organized band of heavy rainfall is used to show that for some situations, the predictability of rainfall even within a 12-24-h period is so low that a wide range of simulations using different models, different physical parameterizations, and different initial conditions all fail to provide even a small signal that the event will occur. The failure of a wide range of models and parameterizations to depict the event might suggest inadequate representation of the initial conditions. However, a range of different initial conditions also failed to lead to a well-simulated event, suggesting that some events are unlikely to be predictable with the current observational network, and ensemble guidance for such cases may provide limited additional information useful to a forecaster.

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Section: Methodsmentioning

confidence: 99%

The 4 June 1999 Derecho Event: A Particularly Difficult Challenge for Numerical Weather Prediction

Gallus

Correia

Jankov

2005

Weather and Forecasting

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“…Because the Level-2 model is non-singular, such a singularity is found to occur when G H (q 2 ) is larger (smaller) than that in the Level-2 model, i.e., in the case of growing turbulence. To prevent this, a number of previous studies imposed restrictions on G H , q 2 , and L (e.g., MY82; Gerrity et al, 1994;Janjić, 2001). The function α introduced by HL88 also substantially corresponds to a restriction on q 2 and assures the positiveness of the above quantities.…”

Section: Unstable Stratificationmentioning

confidence: 99%

“…The principal cause for this is that these models do not always satisfy realizability conditions: e.g., a constraint that velocity variances remain non-negative. To ensure the realizability for the M-Y Level-2.5 model, many researchers have suggested inclusion of various restrictions and modifications on parameters involving velocity and temperature gradients and on the turbulent kinetic energy (TKE) and length scale (e.g., Mellor and Yamada, 1982, hereafter MY82;Galperin et al, 1988;Helfand and Labraga, 1988, hereafter HL88;Gerrity et al, 1994;Janjić, 2001). Our improved M-Y Level-3 model is incorporated with the modification by HL88, which appears to be physically most plausible.…”

Section: Introductionmentioning

confidence: 99%

An Improved Mellor–Yamada Level-3 Model: Its Numerical Stability and Application to a Regional Prediction of Advection Fog

Nakanishi

Niino

2006

Boundary-Layer Meteorol

1,135

573

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This note describes a numerically stable version of the improved Mellor-Yamada (M-Y) Level-3 model proposed by Nakanishi and Niino [Nakanishi, M. and Niino, H.: 2004, Boundary-Layer Meteorol. 112, 1-31] and demonstrates its application to a regional prediction of advection fog. In order to ensure the realizability for the improved M-Y Level-3 model and its numerical stability, restrictions are imposed on computing stability functions, on L/q, the temperature and water-content variances, and their covariance, where L is the master length scale and q 2 /2 the turbulent kinetic energy per unit mass. The model with these restrictions predicts vertical profiles of mean quantities such as temperature that are in good agreement with those obtained from large-eddy simulation of a radiation fog. In a regional prediction, it also reasonably reproduces the satellite-observed horizontal distribution of an advection fog.

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“…Although most of the previous e¤orts to improve the MY model focused on excluding singular solutions (e.g., Mellor and Yamada 1982;Galperin et al 1988;Helfand and Labraga 1988;Gerrity et al 1994;Janjić 2002), several authors did attempt to improve the problems described above (e.g., Gambo 1978;Sun and Ogura 1980;Kantha and Clayson 1994;Cheng et al 2002). Using a database of a large-eddy simulation (LES) for dry ABLs under di¤erent stratifications, Nakanishi (2001, hereafter N01) recently proposed an improved MY model in which a newly-proposed diagnostic equation for the turbulent length scale and reevaluated model constants are incorporated.…”

Section: Introductionmentioning

confidence: 99%

Development of an Improved Turbulence Closure Model for the Atmospheric Boundary Layer

Nakanishi

Niino

2009

Journal of the Meteorological Society of Japan

806

447

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An improved Mellor-Yamada (MY) turbulence closure model (MYNN model: Mellor-YamadaNakanishi-Niino model) that we have developed is summarized and its performance is demonstrated against a large-eddy simulation (LES) of a convective boundary layer. Unlike the original MY model, the MYNN model considers e¤ects of buoyancy on pressure covariances and e¤ects of stability on the turbulent length scale, with model constants determined from a LES database. One-dimensional simulations of Day 33 of the Wangara field experiment, which was conducted in a flat area of southeastern Australia in 1967, are made by the MY and MYNN models and the results are compared with horizontal-average statistics obtained from a threedimensional LES. The MYNN model improves several weak points of the MY model such as an insu‰cient growth of the convective boundary layer, and underestimates of the turbulent kinetic energy and the turbulent length scale; it reproduces fairly well the results of the LES including the vertical distributions of the mean and turbulent quantities. The improved performance of the MYNN model relies mainly on the new formulation of the turbulent length scale that realistically increases with decreasing stability, and partly on the parameterization of the pressure covariances and the expression for stability functions for third-order turbulent fluxes.

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

Cited by 29 publications

References 0 publications

The 4 June 1999 Derecho Event: A Particularly Difficult Challenge for Numerical Weather Prediction

The 4 June 1999 Derecho Event: A Particularly Difficult Challenge for Numerical Weather Prediction

An Improved Mellor–Yamada Level-3 Model: Its Numerical Stability and Application to a Regional Prediction of Advection Fog

Development of an Improved Turbulence Closure Model for the Atmospheric Boundary Layer

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