doi:10.1007/s00376-016-5209-9

Ball F. K., 1960: Control of inversion height by surface heating. Quart. J. Roy. Meteor. Soc., 86, 483- 494.10.1002/qj.49708637005

7e07d96576d465f8440da8406fac3186

http%3A%2F%2Fonlinelibrary.wiley.com%2Fdoi%2F10.1002%2Fqj.49708637005%2Ffull

http://onlinelibrary.wiley.com/doi/10.1002/qj.49708637005/fullABSTRACT Viscous dissipation is inadequate to account for the destruction of all the thermal turbulence generated by upward transfer of heat in a deep convection layer. It is suggested that the surplus turbulent kinetic energy is destroyed by buoyancy forces in a region of downward transfer of heat in the upper part of the convection layer. This process is associated with mass transfer downwards through the convection (or subsidence) inversion and also with an upward movement of the inversion, though the latter may be overcome by sufficiently strong subsidence. A simple theory of the process is developed and the results deduced thereby agree well with observations of the diurnal variation of inversion height in Central Australia.

Breuer H., F. Ács, Á. Horváth, P. Németh, and K. Rajkai, 2014: Diurnal course analysis of the WRF-simulated and observation-based planetary boundary layer height. Adv. Sci. Res., 11, 83- 88.10.5194/asr-11-83-2014

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http%3A%2F%2Fadsabs.harvard.edu%2Fabs%2F2014AdSR...11...83B

http://adsabs.harvard.edu/abs/2014AdSR...11...83BWeather Research and Forecasting (WRF) single-column model simulations were performed in the late summer of 2012 in order to analyse the diurnal changes of the planetary boundary layer (PBL). Five PBL schemes were tested with the WRF. From the radiometer and wind-profiler measurements at one station, derived PBL heights were also compared to the simulations. The weather conditions during the measurement period proved to be dry; the soil moisture was below wilting point 85 percent of the time. Results show that (1) simulation-based PBL heights are overestimated by about 500-1000 m with respect to the observation-based PBL heights, and (2) PBL height deviations between different observation-based methods (around 700 m in the midday) are comparable with PBL height deviations between different model schemes used in the WRF single-column model. The causes of the deviations are also discussed. It is shown that in the estimation of the PBL height the relevance of the atmospheric profiles could be as important as the relevance of the estimation principles.

Canut G., M. Lothon, F. Sad, and F. Lohou, 2010: Observation of entrainment at the interface between monsoon flow and the Saharan Air Layer. Quart. J. Roy. Meteor. Soc., 136, 34- 46.10.1002/qj.471

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http%3A%2F%2Fonlinelibrary.wiley.com%2Fdoi%2F10.1002%2Fqj.471%2Fpdf

http://onlinelibrary.wiley.com/doi/10.1002/qj.471/pdfNot Available

Conzemius R., E. Fedorovich, 2007: Bulk models of the sheared convective boundary layer: Evaluation through large eddy simulations. J. Atmos. Sci., 64, 786- 807.10.1175/JAS3870.1

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http%3A%2F%2Fadsabs.harvard.edu%2Fabs%2F2007JAtS...64..786C

http://adsabs.harvard.edu/abs/2007JAtS...64..786CAbstract A set of first-order model (FOM) equations, describing the sheared convective boundary layer (CBL) evolution, is derived. The model output is compared with predictions of the zero-order bulk model (ZOM) for the same CBL type. Large eddy simulation (LES) data are employed to test both models. The results show an advantage of the FOM over the ZOM in the prediction of entrainment, but in many CBL cases, the predictions by the two models are fairly close. Despite its relative simplicity, the ZOM is able to quantify the effects of shear production and dissipation in an integral senses long as the constants describing the integral dissipation of shear- and buoyancy-produced turbulence kinetic energy (TKE) are prescribed appropriately and the shear is weak enough that the denominator of the ZOM entrainment equation does not approach zero, causing a numerical instability in the solutions. Overall, the FOM better predicts the entrainment rate due to its ability to avoid this instability. Also, the FOM in a more physically consistent manner reproduces the sheared CBL entrainment zone, whose depth is controlled by a balance among shear generation, buoyancy consumption, and dissipation of TKE. Such balance is manifested by nearly constant values of Richardson numbers observed in the entrainment zone of simulated sheared CBLs. Conducted model tests support the conclusion that the surface shear generation of TKE and its corresponding dissipation, as well as the nonstationary terms, can be omitted from the integral TKE balance equation.

Conzemius R. J., E. Fedorovich, 2006: Dynamics of sheared convective boundary layer entrainment. Part II: Evaluation of bulk model predictions of entrainment flux. J. Atmos. Sci., 63, 1179- 1199.10.1175/JAS3696.1

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http://www.ams.org/mathscinet-getitem?mr=2216928Abstract Several bulk model–based entrainment parameterizations for the atmospheric convective boundary layer (CBL) with wind shear are reviewed and tested against large-eddy simulation (LES) data to evaluate their ability to model one of the basic integral parameters of convective entrainment—the entrainment flux ratio. Test results indicate that many of these parameterizations fail to correctly reproduce entrainment flux in the presence of strong shear because they underestimate the dissipation of turbulence kinetic energy (TKE) produced by shear in the entrainment zone. It is also found that surface shear generation of TKE may be neglected in the entrainment parameterization because it is largely balanced by dissipation. However, the surface friction has an indirect effect on the entrainment through the modification of momentum distribution in the mixed layer and regulation of shear across the entrainment zone. Because of this effect, parameterizations that take into account the surface friction veloci...

Deardorff J. W., 1979: Prediction of convective mixed-layer entrainment for realistic capping inversion structure. J. Atmos. Sci., 36, 424- 436.10.1175/1520-0469(1979)0362.0.CO;2

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http%3A%2F%2Fonlinelibrary.wiley.com%2Fresolve%2Freference%2FADS%3Fid%3D1979JAtS...36..424D

http://onlinelibrary.wiley.com/resolve/reference/ADS?id=1979JAtS...36..424DThe first-order jump model for the potential temperature or buoyancy variable at the capping inversion atop a convectively mixed layer is reexamined and found to imply existence of an entrainment rate equation which is unreliable. The model is therefore extended here to allow all the negative buoyancy flux of entrainment to occur within the interfacial layer of thickness Δand to allow realistic thermal structure within the layer. The new model yields a well behaved entrainment rate equation requiring scarcely any closure assumption in the cases of steady-state entrainment with large-scale subsidence, and pseudo-encroachment. For nonsteady entrainment the closure assumption need only be made on (Δ)/in order to obtain the entrainment rates at both the outer and inner edges of the interfacial layer. A particular closure assumption for (Δ)/is tested against five laboratory experiments and found to yield favorable results for both Δand the mixed-layer thickness if the initial value of Δis known. It is also compared against predictions from two zero-order jump models which do not attempt prediction of Δand one first-order jump model.

Fedorovich E., 1995: Modeling the atmospheric convective boundary layer within a zero-order jump approach: An extended theoretical framework. J. Appl. Meteor., 34, 1916- 1928.10.1175/1520-0450(1995)0342.0.CO;2

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http%3A%2F%2Fadsabs.harvard.edu%2Fabs%2F1995JApMe..34.1916F

http://adsabs.harvard.edu/abs/1995JApMe..34.1916FThe paper presents an extended theoretical background for applied modeling of the atmospheric convective boundary layer within the so-called zero-order jump approach, which implies vertical homogeneity of meteorological fields in the bulk of convective boundary layer (CBL) and zero-order discontinuities of variables at the interface of the layer.The zero-order jump model equations for the most typical cases of CBL are derived. The models of nonsteady, horizontally homogeneous CBL with and without shear, extensively studied in the past with the aid of zero-order jump models, are shown to be particular cases of the general zero-order jump theoretical framework. The integral budgets of momentum and heat are considered for different types of dry CBL. The profiles of vertical turbulent fluxes are presented and analyzed. The general version of the equation of CBL depth growth rate (entrainment rate equation) is obtained by the integration of the turbulence kinetic energy balance equation, invoking basic assumptions of the zero-order parameterizations of the CBL vertical structure. The problems of parameterizing the turbulence vertical structure and closure of the entrainment rate equation for specific cases of CBL are discussed. A parameterization scheme for the horizontal turbulent exchange in zero-order jump models of CBL is proposed. The developed theory is generalized for the case of CBL over irregular terrain.

Fedorovich E., R. Conzemius, and D. Mironov, 2004: Convective entrainment into a shear-free, linearly stratified atmosphere: Bulk models reevaluated through large eddy simulations. J. Atmos. Sci., 61, 281- 295.10.1175/1520-0469(2004)0612.0.CO;2

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http%3A%2F%2Fadsabs.harvard.edu%2Fabs%2F2004JAtS...61..281F

http://adsabs.harvard.edu/abs/2004JAtS...61..281FRelationships between parameters of convective entrainment into a shear-free, linearly stratified atmosphere predicted by the zero-order jump and general-structure bulk models of entrainment are reexamined using data from large eddy simulations (LESs). Relevant data from other numerical simulations, water tank experiments, and atmospheric measurements are also incorporated in the analysis. Simulations have been performed for 10 values of the buoyancy gradient in the free atmosphere covering a typical atmospheric stability range. The entrainment parameters derived from LES and relationships between them are found to be sensitive to the model framework employed for their interpretation. Methods of determining bulk model entrainment parameters from the LES output are proposed and discussed. Within the range of investigated free-atmosphere stratifications, the LES predictions of the inversion height and buoyancy increment across the inversion are found to be close to the analytical solutions for the equilibrium entrainment regime, which is realized when the rate of time change of the CBL-mean turbulence kinetic energy and the energy drain from the CBL top are both negligibly small. The zero-order model entrainment ratio of about 0.2 for this regime is generally supported by the LES data. However, the zero-order parameterization of the entrainment layer thickness is found insufficient. A set of relationships between the general-structure entrainment parameters for typical atmospheric stability conditions is retrieved from the LES. Dimensionless constants in these relationships are estimated from the LES and laboratory data. Power-law approximations for relationships between the entrainment parameters in the zero-order jump and general-structure bulk models are evaluated based on the conducted LES. In the regime of equilibrium entrainment, the stratification parameter of the entrainment layer, which is the ratio of the buoyancy gradient in the free atmosphere to the overall buoyancy gradient across the entrainment layer, appears to be a constant of about 1.2.

Gentine P., G. Bellon, and C. C. Van Heerwaarden, 2015: A closer look at boundary layer inversion in large-eddy simulations and bulk models: Buoyancy-driven case. J. Atmos. Sci., 72, 728- 749.10.1175/JAS-D-13-0377.1

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http%3A%2F%2Fadsabs.harvard.edu%2Fabs%2F2015JAtS...72..728G

http://adsabs.harvard.edu/abs/2015JAtS...72..728GNot Available

Hong S.-Y., Y. Noh, and J. Dudhia, 2006: A new vertical diffusion package with an explicit treatment of entrainment processes. Mon. Wea. Rev., 134, 2318- 2341.10.1175/MWR3199.1

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http%3A%2F%2Fadsabs.harvard.edu%2Fabs%2F2006MWRv..134.2318H

http://adsabs.harvard.edu/abs/2006MWRv..134.2318HThis paper proposes a revised vertical diffusion package with a nonlocal turbulent mixing coefficient in the planetary boundary layer (PBL). Based on the study of Noh et al. and accumulated results of the behavior of the Hong and Pan algorithm, a revised vertical diffusion algorithm that is suitable for weather forecasting and climate prediction models is developed. The major ingredient of the revision is the inclusion of an explicit treatment of entrainment processes at the top of the PBL. The new diffusion package is called the Yonsei University PBL (YSU PBL). In a one-dimensional offline test framework, the revised scheme is found to improve several features compared with the Hong and Pan implementation. The YSU PBL increases boundary layer mixing in the thermally induced free convection regime and decreases it in the mechanically induced forced convection regime, which alleviates the well-known problems in the Medium-Range Forecast (MRF) PBL. Excessive mixing in the mixed layer in the presence of strong winds is resolved. Overly rapid growth of the PBL in the case of the Hong and Pan is also rectified. The scheme has been successfully implemented in the Weather Research and Forecast model producing a more realistic structure of the PBL and its development. In a case study of a frontal tornado outbreak, it is found that some systematic biases of the large-scale features such as an afternoon cold bias at 850 hPa in the MRF PBL are resolved. Consequently, the new scheme does a better job in reproducing the convective inhibition. Because the convective inhibition is accurately predicted, widespread light precipitation ahead of a front, in the case of the MRF PBL, is reduced. In the frontal region, the YSU PBL scheme improves some characteristics, such as a double line of intense convection. This is because the boundary layer from the YSU PBL scheme remains less diluted by entrainment leaving more fuel for severe convection when the front triggers it.

Jonker H. J. J., M. Van Reeuwijk, P. P. Sullivan, and E. G. Patton, 2013: On the scaling of shear-driven entrainment: A DNS study. J. Fluid Mech., 732, 150- 165.10.1017/jfm.2013.394

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http%3A%2F%2Fjournals.cambridge.org%2Farticle_S0022112013003947

http://journals.cambridge.org/article_S0022112013003947The deepening of a shear-driven turbulent layer penetrating into a stably stratified quiescent layer is studied using direct numerical simulation (DNS). The simulation design mimics the classical laboratory experiments by Kato & Phillips (J. Fluid Mech., vol.0237, 1969, pp.02643–655) in that it starts with linear stratification and applies a constant shear stress at the lower boundary, but avoids sidewall and rotation effects inherent in the original experiment. It is found that the layers universally deepen as a function of the square root of time, independent of the initial stratification and the Reynolds number of the simulations, provided that the Reynolds number is large enough. Consistent with this finding, the dimensionless entrainment velocity varies with the bulk Richardson number as \$R{i}^{- 1/ 2} \$. In addition, it is observed that all cases evolve in a self-similar fashion. A self-similarity analysis of the conservation equations shows that only a square root growth law is consistent with self-similar behaviour.

Kim S.-W., S.-U. Park, and C.-H. Moeng, 2003: Entrainment processes in the convective boundary layer with varying wind shear. Bound.-Layer Meteor., 108, 221- 245.10.1023/A:1024170229293

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http%3A%2F%2Fwww.ingentaconnect.com%2Fcontent%2Fklu%2Fboun%2F2003%2F00000108%2F00000002%2F05111563

http://www.ingentaconnect.com/content/klu/boun/2003/00000108/00000002/05111563Large-eddy simulations (LES) are performed to investigate the entrainment and the structure of the inversion layer of the convective boundary layer (CBL) with varying wind shears. Three CBLs are generated with the constant surface kinematic heat flux of 0.05 K m sand varying geostrophic wind speeds from 5 to 15 m s. Heat flux profiles show that the maximum entrainment heat flux as a fraction of the surface heat flux increases from 0.13 to 0.30 in magnitude with increasing wind shear. The thickness of the entrainment layer, relative to the depth of the well-mixed layer, increases substantially from 0.36 to 0.73 with increasing wind shear. The identification of vortices and extensive flow visualizations near the entrainment layer show that concentrated vortices perpendicular to the mean boundary-layer wind direction are identified in the capping inversion layer for the case of strong wind shear. These vortices are found to develop along the mean wind directions over strong updrafts, which are generated by convective rolls and to appear as large-scale wavy motions similar to billows generated by the Kelvin Helmholtz instability. Quadrant analysis of the heat flux shows that in the case of strong wind shear, large fluctuations of temperature and vertical velocity generated by large amplitude wavy motions result in greater heat flux at each quadrant than that in the weak wind shear case.

Kim S.-W., S.-U. Park, D. Pino, and J. V.-G. De Arellano, 2006: Parameterization of Entrainment in a sheared convective boundary layer using a first-order jump model. Bound.-Layer Meteor., 120, 455- 475.10.1007/s10546-006-9067-3

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http%3A%2F%2Fwww.ingentaconnect.com%2Fcontent%2Fklu%2Fboun%2F2006%2F00000120%2F00000003%2F00009067

http://www.ingentaconnect.com/content/klu/boun/2006/00000120/00000003/00009067Basic entrainment equations applicable to the sheared convective boundary layer (CBL) are derived by assuming an inversion layer with a finite depth, i.e., the first-order jump model. Large-eddy simulation data are used to determine the constants involved in the parameterizations of the entrainment equations. Based on the integrated turbulent kinetic energy budget from surface to the top of the CBL, the resulting entrainment heat flux normalized by surface heat flux is a function of the inversion layer depth, the velocity jumps across the inversion layer, the friction velocity, and the convection velocity. The developed first-order jump model is tested against large-eddy simulation data of two independent cases with different inversion strengths. In both cases, the model reproduces quite reasonably the evolution of the CBL height, virtual potential temperature, and velocity components in the mixed layer and in the inversion layer.

Lewellen D. C., W. S. Lewellen, 1998: Large-eddy boundary layer entrainment. J. Atmos. Sci., 55, 2645- 2665.10.1175/1520-0469(1998)0552.0.CO;2

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http%3A%2F%2Fadsabs.harvard.edu%2Fabs%2F1998JAtS...55.2645L

http://adsabs.harvard.edu/abs/1998JAtS...55.2645LA series of large-eddy simulations have been performed to explore boundary layer entrainment under conditions of a strongly capped inversion layer with the boundary layer dynamics driven dominantly by buoyant forcing. Different conditions explored include cloud-top cooling versus surface heating, smoke clouds versus water clouds, variations in cooling height and optical depth of longwave radiation, degree of cloud-top evaporative instability, and modest wind shear. Boundary layer entrainment involves transport and mixing over a full range of length scales, as warm fluid from the region of the capping inversion is first transported into the boundary layer and then mixed throughout. While entrainment is often viewed as the small-scale process of capturing warm fluid from the inversion into the top of the boundary layer, this need not be the physics that ultimately determines the entrainment rate. In these simulations the authors find instead that the entrainment rate is often limited by the boundary layercale eddy transport and is therefore surprisingly insensitive to the smaller scales of mixing near the inversion. The fraction of buoyant energy production available to drive large eddies that is lost to entrainment rather than dissipation was found to be nearly constant over a wide range of simulation conditions, with no apparent fundamental difference between top- versus bottom-driven or cloudy versus clear boundary layers. In addition, it is found that for quasi-steady boundary layers with dynamics driven by cloud-top cooling there is an effective upper limit on the entrainment rate for which the boundary layer dynamics just remains coupled, which is often approached when the cloud top is evaporatively unstable.

Lilly D. K., 1968: Models of cloud-topped mixed layers under a strong inversion. Quart. J. Roy. Meteor. Soc., 94, 292- 309.10.1002/qj.49709440106

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http%3A%2F%2Fonlinelibrary.wiley.com%2Fdoi%2F10.1002%2Fqj.49709440106%2Fabstract

http://onlinelibrary.wiley.com/doi/10.1002/qj.49709440106/abstractAbstract Theoretical models are constructed with the aim of relating, explaining and predicting features of a radiatively active turbulent cloud layer over the sea and under a strong subsidence inversion. Both dry aerosol clouds (no phase change) and wet clouds (with a phase change and latent heat exchanges) are considered. For the wet cloud case an important element of the theory is the requirement that the wet-bulb potential temperature must increase upwards in the inversion. For both cases entrainment of the upper warm air is hypothesized to lie between upper and lower limits determined from the turbulent energy budget. The dry cloud case is solved for both steady state and transient results, with only the transient behaviour depending on the entrainment hypothesis. Only steady state solutions are presented for the more complex wet cloud case and these differ somewhat for the maximum and minimum entrainment limits. Observational data from Oakland, California are used for comparison with those steady state solutions, with results indicating the essential validity of the approach. Detailed comparisons, especially for determination of the most correct entrainment rate, are hampered both by inadequate measurement of the inversion properties and by uncertainties in the net radiation flux leaving the cloud top. Computations of the latter suggest that several presently used radiation models are still in serious disagreement, at least for application to downward flux under an inversion. It is suggested that the present theory provides a partial explanation of the origin of the trade wind inversion.

Liu P., J. Sun, and L. Shen, 2016: Parameterization of sheared entrainment in the well-developed convective boundary layer. Part I: Evaluation of the scheme through large-eddy simulations. Adv. Atmos. Sci.,10.1007/s00376-016-5208-x.a4480e655d303e9ee34b28695cc3be93

http%3A%2F%2F159.226.119.58%2Faas%2FEN%2F10.1007%2Fs00376-016-5208-x

http://159.226.119.58/aas/EN/10.1007/s00376-016-5208-x

Moeng C.-H., P. P. Sullivan, 1994: A comparison of shear- and buoyancy-driven planetary boundary layer flows. J. Atmos. Sci., 51, 999- 1022.10.1175/1520-0469(1994)051<0999:ACOSAB>2.0.CO;2

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http%3A%2F%2Fadsabs.harvard.edu%2Fabs%2F1994JAtS...51..999M

http://adsabs.harvard.edu/abs/1994JAtS...51..999MPlanetary boundary layer (PBL) flows are known to exhibit fundamental differences depending on the relative combination of wind shear and buoyancy forces. These differences are not unexpected in that shear instabilities occur locally, while buoyancy force sets up vigorous thermals, which result in nonlocal transport of heat and momentum. At the same time, these two forces can act together to modify the flow field. In this study, four large-eddy simulations (LESs) spanning the shear and buoyancy flow regimes were generated; two correspond to the extreme cases of shear and buoyancy-driven PBLs, while the other two represent intermediate PBLs where both forces are important. The extreme cases are used to highlight and quantify the basic differences between shear and convective PBLs in 1) flow structures, 2) overall statistics, and 3) turbulent kinetic energy (TKE) budget distributions. Results from the two intermediate LES cases are used to develop and verify a velocity scaling and a TKE budget model, which are proposed for the intermediate PBL. The velocity variances and the variance fluxes (i.e., third moments) normalized by this velocity scaling are shown to become quantities on the order of one, and to lie mostly between those of the two extreme PBL cases. The proposed TKE budget model is shown to adequately reproduce the profiles of the TKE budget terms and the TKE.

Pino D., J. V.-G. De Arellano, 2008: Effects of shear in the convective boundary layer: Analysis of the turbulent kinetic energy budget. Acta Geophysica, 56, 167- 193.10.2478/s11600-007-0037-z

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http%3A%2F%2Fadsabs.harvard.edu%2Fabs%2F2008AcGeo..56..167P

http://adsabs.harvard.edu/abs/2008AcGeo..56..167PEffects of convective and mechanical turbulence at the entrainment zone are studied through the use of systematic Large-Eddy Simulation (LES) experiments. Five LES experiments with different shear characteristics in the quasi-steady barotropic boundary layer were conducted by increasing the value of the constant geostrophic wind by 5 m s-1 until the geostrophic wind was equal to 20 m s-1. The main result of this sensitivity analysis is that the convective boundary layer deepens with increasing wind speed due to the enhancement of the entrainment heat flux by the presence of shear. Regarding the evolution of the turbulence kinetic energy (TKE) budget for the studied cases, the following conclusions are drawn: (i) dissipation increases with shear, (ii) the transport and pressure terms decrease with increasing shear and can become a destruction term at the entrainment zone, and (iii) the time tendency of TKE remains small in all analyzed cases. Convective and local scaling arguments are applied to parameterize the TKE budget terms. Depending on the physical properties of each TKE budget contribution, two types of scaling parameters have been identified. For the processes influenced by mixed-layer properties, boundary layer depth and convective velocity have been used as scaling variables. On the contrary, if the physical processes are restricted to the entrainment zone, the inversion layer depth, the modulus of the horizontal velocity jump and the momentum fluxes at the inversion appear to be the natural choices for scaling these processes. A good fit of the TKE budget terms is obtained with the scaling, especially for shear contribution.

Pino D., J. V.-G. De Arellano, and S.-W. Kim, 2006: Representing sheared convective boundary layer by zeroth- and first-order-jump mixed-layer models: Large-eddy simulation verification. J. Appl. Meteor. Climatol., 45, 1224- 1243.10.1175/JAM2396.1

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http%3A%2F%2Fadsabs.harvard.edu%2Fabs%2F2006JApMC..45.1224P

http://adsabs.harvard.edu/abs/2006JApMC..45.1224PDry convective boundary layers characterized by a significant wind shear on the surface and at the inversion are studied by means of the mixed-layer theory. Two different representations of the entrainment zone, each of which has a different closure of the entrainment heat flux, are considered. The simpler of the two is based on a sharp discontinuity at the inversion (zeroth-order jump), whereas the second one prescribes a finite depth of the inversion zone (first-order jump). Large-eddy simulation data are used to provide the initial conditions for the mixed-layer models, and to verify their results. Two different atmospheric boundary layers with different stratification in the free atmosphere are analyzed. It is shown that, despite the simplicity of the zeroth-order-jump model, it provides similar results to the first-order-jump model and can reproduce the evolution of the mixed-layer variables obtained by the large-eddy simulations in sheared convective boundary layers. The mixed-layer model with both closures compares better with the large-eddy simulation results in the atmospheric boundary layer characterized by a moderate wind shear and a weak temperature inversion. These results can be used to represent the flux of momentum, heat, and other scalars at the entrainment zone in general circulation or chemistry transport models.

Shin H., S.-Y. Hong, 2011: Intercomparison of planetary boundary-layer parametrizations in the WRF model for a single day from CASES-99. Bound.-Layer Meteor., 139, 261- 281.10.1007/s10546-010-9583-z

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http%3A%2F%2Fonlinelibrary.wiley.com%2Fresolve%2Freference%2FADS%3Fid%3D2011BoLMe.139..261S

http://onlinelibrary.wiley.com/resolve/reference/ADS?id=2011BoLMe.139..261SThis study compares five planetary boundary-layer (PBL) parametrizations in the Weather Research and Forecasting (WRF) numerical model for a single day from the Cooperative Atmosphere-Surface Exchange Study (CASES-99) field program. The five schemes include two first-order closure schemes—the Yonsei University (YSU) PBL and Asymmetric Convective Model version 2 (ACM2), and three turbulent kinetic energy (TKE) closure schemes—the Mellor–Yamada–Janji04 (MYJ), quasi-normal scale elimination (QNSE), and Bougeault–Lacarrére (BouLac) PBL. The comparison results reveal that discrepancies among thermodynamic surface variables from different schemes are large at daytime, while the variables converge at nighttime with large deviations from those observed. On the other hand, wind components are more divergent at nighttime with significant biases. Regarding PBL structures, a non-local scheme with the entrainment flux proportional to the surface flux is favourable in unstable conditions. In stable conditions, the local TKE closure schemes show better performance. The sensitivity of simulated variables to surface-layer parametrizations is also investigated to assess relative contributions of the surface-layer parametrizations to typical features of each PBL scheme. In the surface layer, temperature and moisture are more strongly influenced by surface-layer formulations than by PBL mixing algorithms in both convective and stable regimes, while wind speed depends on vertical diffusion formulations in the convective regime. Regarding PBL structures, surface-layer formulations only contribute to near-surface variability and then PBL mean properties, whereas shapes of the profiles are determined by PBL mixing algorithms.

Skamarock W.C., Coauthors, 2008: A description of the advanced research WRF version 3. NCAR Tech. Note TN-475+STR, 77 pp.

Sühring M., B. Maronga, F. Herbort, S. Raasch, 2014: On the effect of surface heat-flux heterogeneities on the mixed-layer-top entrainment. Bound.-Layer Meteor., 151, 531- 556.10.1007/s10546-014-9913-7

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http%3A%2F%2Fadsabs.harvard.edu%2Fabs%2F2014BoLMe.151..531S

http://adsabs.harvard.edu/abs/2014BoLMe.151..531SWe used a set of large-eddy simulations to investigate the effect of one-dimensional stripe-like surface heat-flux heterogeneities on mixed-layer top entrainment. The profiles of sensible heat flux and the temporal evolution of the boundary-layer depth revealed decreased entrainment for small heat-flux amplitudes and increased entrainment for large heat-flux amplitudes, compared to the homogeneously-heated mixed layer. For large heat-flux amplitudes the largest entrainment was observed for patch sizes in the order of the boundary-layer depth, while for significantly smaller or larger patch sizes entrainment was similar as in the homogeneous case. In order to understand the underlying physics of this impact, a new approach was developed to infer local information on entrainment by means of the local flux divergence. We found an entrainment maximum over the centre of the stronger heated surface patch, where thermal energy is accumulated by the secondary circulation (SC) that was induced by the surface heterogeneity. Furthermore, we observed an entrainment maximum over the less heated patch as well, which we suppose is to be linked to the SC-induced horizontal flow convergence at the top of the convective boundary layer (CBL). For small heat-flux amplitudes a counteracting effect dominates that decreases entrainment, which we suppose is the horizontal advection of cold air in the lower, and warm air in the upper, CBL by the SC, stabilizing the CBL and thus weakening thermal convection. Moreover, we found that a mean wind can reduce the heterogeneity-induced impact on entrainment. If the flow is aligned perpendicular to the border between the differentially-heated patches, the SC and thus its impact on entrainment vanishes due to increased horizontal mixing, even for moderate wind speeds. However, if the flow is directed parallel to the border between the differentially-heated patches, the SC and thus its impact on entrainment persists.

Sullivan P. P., C.-H. Moeng, B. Stevens, D.H. Lenschow, and S.D. Mayor, 1998: Structure of the entrainment zone capping the convective atmospheric boundary layer. J. Atmos. Sci., 55, 3042- 3064.10.1175/1520-0469(1998)0552.0.CO;2

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http%3A%2F%2Fadsabs.harvard.edu%2Fabs%2F1998JAtS...55.3042S

http://adsabs.harvard.edu/abs/1998JAtS...55.3042SAbstract The authors use large-eddy simulation (LES) to investigate entrainment and structure of the inversion layer of a clear convectively driven planetary boundary layer (PBL) over a range of bulk Richardson numbers, Ri. The LES code uses a nested grid technique to achieve fine resolution in all three directions in the inversion layer. Extensive flow visualization is used to examine the structure of the inversion layer and to illustrate the temporal and spatial interaction of a thermal plume and the overlying inversion. It is found that coherent structures in the convective PBL, that is, thermal plumes, are primary instigators of entrainment in the Ri range 13.6 81 Ri 81 43.8. At Ri = 13.6, strong horizontal and downward velocities are generated near the inversion layer because of the plume–interface interaction. This leads to folding of the interface and hence entrainment of warm inversion air at the plume’s edge. At Ri = 34.5, the inversion’s strong stability prevents folding of the interface but stron...

Sun J. N., Y. Wang, 2008: Effect of the entrainment flux ratio on the relationship between entrainment rate and convective Richardson number. Bound.-Layer Meteor., 126, 237- 247.10.1007/s10546-007-9231-4

d93eceb40e9fe4602180137214e7aab4

http%3A%2F%2Fadsabs.harvard.edu%2Fabs%2F2008BoLMe.126..237S

http://adsabs.harvard.edu/abs/2008BoLMe.126..237SThe parameterization of the dimensionless entrainment rate ( w / w ) versus the convective Richardson number ( Ri ) is discussed in the framework of a first-order jump model (FOM). A theoretical estimation for the proportionality coefficient in this parameterization, namely, the total entrainment flux ratio, is derived. This states that the total entrainment flux ratio in FOM can be estimated as the ratio of the entrainment zone thickness to the mixed-layer depth, a relationship that is supported by earlier tank experiments, and suggesting that the total entrainment flux ratio should be treated as a variable. Analyses show that the variability of the total entrainment flux ratio is actually the effect of stratification in the free atmosphere on the entrainment process, which should be taken into account in the parameterization. Further examination of data from tank experiments and large-eddy simulations demonstrate that the different power laws for w / w versus Ri can be interpreted as the variability of the total entrainment flux ratio. These results indicate that the dimensionless entrainment rate depends not only on the convective Richardson number but also upon the total entrainment flux ratio.

Sun J. N., Q. J. Xu, 2009: Parameterization of sheared convective entrainment in the first-order jump model: Evaluation through large-eddy simulation. Bound.-Layer Meteor., 132, 279- 288.10.1007/s10546-009-9394-2

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http%3A%2F%2Fadsabs.harvard.edu%2Fabs%2F2009BoLMe.132..279S

http://adsabs.harvard.edu/abs/2009BoLMe.132..279SIn this note, two different approaches are used to estimate the entrainment-flux to surface-flux ratio for a sheared convective boundary layer (CBL); both are derived under the framework of the first-order jump model (FOM). That suggested by Sun and Wang (SW approach) has the advantage that there is no empirical constant included, though the dynamics are described in an implicit manner. The second, which was proposed by Kim et al. and Pino et al. (KP approach), explicitly characterizes the dynamics of the sheared entrainment, but uncertainties are induced through the empirical constants. Their performances in parameterizing the CBL growth rate are compared and discussed, and a new value of the parameter A in the KP approach is suggested. Large-eddy simulation (LES) data are employed to test both approaches: simulations are conducted for the CBL growing under varying conditions of surface roughness, free-atmospheric stratification, and wind shear, and data used when the turbulence is in steady state. The predicted entrainment rates in each case are tested against the LES data. The results show that the SW approach describes the evolution of the sheared CBL quite well, and the KP approach also reproduces the growth of the CBL reasonably, so long as the value of A is modified to 0.6.

vanZanten, M. C., P. G. Duynkerke, J. W. M. Cuijpers, 1999: Entrainment parameterization in convective boundary layers. J. Atmos. Sci., 56, 813- 828.10.1175/1520-0469(1999)0562.0.CO;2

fe9cc0b716154193f79ef27ea1304a58

http%3A%2F%2Fadsabs.harvard.edu%2Fabs%2F1999JAtS...56..813V

http://adsabs.harvard.edu/abs/1999JAtS...56..813VVarious runs were performed with a large eddy simulation (LES) model to evaluate different types of entrainment parametrizations. For this evaluation, three types of boundary layers were simulated: a clear convective boundary layer (CBL), a boundary layer containing a smoke concentration, and a cloud-topped boundary layer. It is shown that the assumption that the entrainment flux equals the product of the entrainment rate and the jump over a discontinuous inversion is not valid in CBLs simulated by an LES model. A finite inversion thickness (i.e., a first-order jump model) is needed to define an entrainment flux for which this approximation of the flux is valid. This entrainment flux includes not only the buoyancy flux at the inversion, but also the surface heat flux. The parameterization of the buoyancy flux at the inversion is evaluated for different closures, as suggested in the literature (i.e., Eulerian partitioning, process partitioning, and a closure developed by Deardorff), and where needed is extended for use in a first-order jump model. The closure based on process partitioning is found to yield consistent results in all types of convective boundary layers and shows the best agreement with the limit found in LES results if the longwave radiative flux divergence takes place in a much shallower layer than the mixed layer.

Xie B., J. C. H. Fung, A. Chan, and A. Lau, 2012: Evaluation of nonlocal and local planetary boundary layer schemes in the WRF model. J. Geophys. Res., 117, D12103.10.1029/2011JD017080

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http%3A%2F%2Fonlinelibrary.wiley.com%2Fdoi%2F10.1029%2F2011JD017080%2Ffull

http://onlinelibrary.wiley.com/doi/10.1029/2011JD017080/fullAbstract Top of page Abstract 1.Introduction 2.Model Setup and Configurations 3.Brief Descriptions of PBL Schemes and Surface Layer Schemes 4.Results and Discussions 5.Conclusions Acknowledgments References Supporting Information [1] A realistic reproduction of planetary boundary layer (PBL) structure and its evolution is critical to numerical simulation of regional meteorology and air quality. Conversely, insufficient realism in the simulated physical properties often leads to degraded meteorological and air quality prognostic skills. This study employed the Weather Research and Forecasting model (WRF) to evaluate model performance and to quantify meteorological prediction differences produced by four widely used PBL schemes. Evaluated were two nonlocal PBL schemes, YSU and ACM2, and two local PBL schemes, MYJ and Boulac. The model grid comprised four nested domains at horizontal resolutions of 27km, 9km, 3km and 1km respectively. Simulated surface variables 2m temperature and 10m wind at 1km resolution were compared to measurements collected in Hong Kong. A detailed analysis of land-atmosphere energy balance explicates heat flux and temperature variability among the PBL schemes. Differences in vertical profiles of horizontal velocity, potential temperature, bulk Richardson number and water vapor mixing ratio were examined. Diagnosed PBL heights, estimated by scheme specific formulations, exhibited the large intrascheme variance. To eliminate formulation dependence in PBL height estimation, lidar measurements and a unified diagnosis were jointly used to reanalyze PBL heights. The diagnosis showed that local PBL schemes produced shallower PBL heights than those of nonlocal PBL schemes. It is reasonable to infer that WRF, coupled with the ACM2 PBL physics option can be a viable producer of meteorological forcing to regional air quality modeling in the Pearl River Delta (PRD) Region.