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1.
We have carried out a theoretical study of the simplest possible, second-order, chemical destruction process in the atmospheric surface layer. The model describes the destruction of two gases emanating from the surface with the same molecular flux. Although this situation seems artificial with no counterpart in the real atmosphere, the results shed light on some fundamental problems. For example, it is possible to specify boundary conditions, with the concentrations and the fluxes at a given height away from the surface, which lead to unrealistic solutions with infinite surface fluxes. A method to describe and separate the consistent solutions for this process was developed. It is in general of particular interest from an experimental point of view since it is not possible to measure fluxes right at the surface: if a measurement of flux and concentration in a given height requires infinite surface fluxes there is something wrong with the data. We expect that such problems will be inherent in more complex reactions schemes, such as the NO-NO2-O3 triad. Just as in first-order destruction processes, the Damköhler ratio will enter the turbulent diffusivity, but where this ratio is concentration independent for first-order processes, the present second-order model implies that the Damköhler ratio is proportional to the concentration. In the study of first-order processes it was found that the Damköhler correction to the turbulent diffusivity is of minor importance from an experimental point of view. We arrive at the same conclusion in this particularly simple study of second-order destruction. In other words, this work may be considered a further development of a previous study of the first-order destruction of a passive scalar. The model and the method we develop to solve the corresponding nonlinear differential equations are considered a preliminary study for developing tools to deal with more complicated atmospheric processes. Also, the results obtained may serve as a “calibration case” for more elaborate simulations.  相似文献   

2.
We study the interactions of chemistry and turbulent mixing of tracersin the convective boundary layer with a second-order closure model,including higher order chemistry terms. In order to limit the number of predictive equations we prescribe the profiles for ¯w¯, ¯w¯ ¯ and the lengthscale l. However, for model validation we treat temperature and humidity asinert tracers, and compare the results with profiles observed during theAir Mass Transformation Experiment, and with similarity expressions for thesurface layer. We find good agreement of the mean profiles, but the (co-)variances are slightly underpredicted. Furthermore, the model usesdiagnostic equations expressing third moments of concentration in terms ofsecond moments and their vertical derivatives. They are compared withlarge-eddy model results, showing good agreement and, therefore, thesimplifications are justified. The model is applied to the transport of two gases subject to one bimolecular reaction. The importance of concentration correlations on themean transformation rate is studied. For two gases diffusing in oppositedirections we find for moderate and fast chemistry a 50% and90% decreased transformation rate due to the negatively correlatedconcentrations. These values are similar to large-eddy results of Schumannand Sykes et al. For two bottom-up tracers we find that the covariance ofboth reactive species is either positive or negative, increasing or reducingthe effective transformation rate depending on the Damköhler number (the ratio of the turbulent and the chemistry timescale). A significantdirect influence of chemistry on the flux divergence is found in bothcases. According to the model the effective transport to mid-levels of theboundary layer is increased when two reactive tracers diffuse in oppositedirections, and decreased in the case of two bottom-up tracers.  相似文献   

3.
Modelling the transfer of heat, water vapour, and CO2 between the biosphere and the atmosphere is made difficult by the complex two-way interaction between leaves and their immediate microclimate. When simulating scalar sources and sinks inside canopies on seasonal, inter-annual, or forest development time scales, the so-called well-mixed assumption (WMA) of mean concentration (i.e. vertically constant inside the canopy but dynamically evolving in time) is often employed. The WMA eliminates the need to model how vegetation alters its immediate microclimate, which necessitates formulations that utilize turbulent transport theories. Here, two inter-related questions pertinent to the WMA for modelling scalar sources, sinks, and fluxes at seasonal to inter-annual time scales are explored: (1) if the WMA is to be replaced so as to resolve this two-way interaction, how detailed must the turbulent transport model be? And (2) what are the added predictive skills gained by resolving the two-way interaction vis-à-vis other uncertainties such as seasonal variations in physiological parameters. These two questions are addressed by simulating multi-year mean scalar concentration and eddy-covariance scalar flux measurements collected in a Loblolly pine (P. taeda L.) plantation near Durham, North Carolina, U.S.A. using turbulent transport models ranging from K-theory (or first-order closure) to third-order closure schemes. The multi-layer model calculations with these closure schemes were contrasted with model calculations employing the WMA. These comparisons suggested that (i) among the three scalars, sensible heat flux predictions are most biased with respect to eddy-covariance measurements when using the WMA, (ii) first-order closure schemes are sufficient to reproduce the seasonal to inter-annual variations in scalar fluxes provided the canonical length scale of turbulence is properly specified, (iii) second-order closure models best agree with measured mean scalar concentration (and temperature) profiles inside the canopy as well as scalar fluxes above the canopy, (iv) there are no clear gains in predictive skills when using third-order closure schemes over their second-order closure counterparts. At inter-annual time scales, biases in modelled scalar fluxes incurred by using the WMA exceed those incurred when correcting for the seasonal amplitude in the maximum carboxylation capacity (V cmax, 25) provided its mean value is unbiased. The role of local thermal stratification inside the canopy and possible computational simplifications in decoupling scalar transfer from the generation of the flow statistics are also discussed.
“The tree, tilting its leaves to capture bullets of light; inhaling, exhaling; its many thousand stomata breathing, creating the air”. Ruth Stone, 2002, In the Next Galaxy
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4.
To what degree the variability of surface features can be identified in the turbulent signals observed in the atmospheric boundary layer is still an unresolved problem. This was investigated by conducting an analytical experiment for a one-dimensional 'chessboard'-type surface-flux distribution on the basis of local free convection scaling. The results showed that, due to their nonlinear dependency on the surface fluxes, the dimensionless gradients of the mean quantities and the dimensionless standard deviations are altered by the surface-flux variability. Furthermore, passive scalars, such as humidity, are considerably more sensitive to surface variability than the main active scalar, temperature. However, the response of the gradients of the mean quantities is fairly negligible in the range of variability studied herein as compared to that of the standard deviations, which were found to be more sensitive to the surface-flux variability. In addition, the phase difference between the active and the passive scalar flux distribution strongly affects the passive scalar turbulence. This dissimilarity between passive and active scalars, or between passive scalars when their source distributions are different, brings into question the use of variance methods for the measurement of a scalar flux, such as evaporation, over variable surfaces. The classical Bowen ratio method, which depends on the validity of the Reynolds analogy for the vertical gradients of the mean quantities, was shown to be relatively more robust. However, under conditions of strong surface variability, it can also be expected to fail.  相似文献   

5.
We have developed a simple, steady-state, one-dimensional second-order closure model to obtain continuous profiles of turbulent fluxes and mean concentrations of non-conserved scalars in a convective boundary layer without shear. As a basic tool we first set up a model for conserved species with standard parameterizations. This leads to formulations for profiles of the turbulent diffusivity and the ratio of temperature-scalar covariance to the flux of the passive scalar. The model is then extended to solving, in terms of profiles of mean concentrations and fluxes, the NO x –O3 triad problem. The chemical reactions involve one first-order reaction, the destruction of NO2 with decay time τ, and one second-order reaction, the destruction of NO and O3 with the reaction constant k. Since the fluxes of the sum concentrations of NO x = NO + NO2 and O3 + NO2 turn out to be constant throughout the boundary layer, the problem reduces to solving two differential equations for the concentration and the flux of NO2. The boundary conditions are the three surface fluxes and the fluxes at the top of the boundary layer, the last obtained from the entrainment velocity, and the concentration differences between the free troposphere and the top of the boundary layer. The equations are solved in a dimensionless form by using 1/(kτ) as the concentration unit, the depth h of the boundary layer as the length unit, the convective velocity scale w * as the velocity unit, and the surface temperature flux divided by w * as the temperature unit. Special care has been devoted to the inclusion of the scalar–scalar covariance between the concentrations of O3 and NO. Sample calculations show that the fluxes of the reactive species deviate significantly from those of non-reactive species. Further, the diffusivities, defined by minus the flux divided by the concentration gradient may become negative for reactive species in contrast to those of non-reactive species, which in the present model are never negative.  相似文献   

6.
Summary Non-uniform mixing of gas-phase trace species may limit the accuracy of the predictions of Eulerian transport/transformation models if the chemical reactions are rapid enough to be diffusion limited. If a reaction is diffusion limited, its average reaction rate might not be accurately represented by those models that assume instantaneous uniform mixing. One possible consequence of this artificial dilution is the overprediction of ozone and hydroxyl radicals. We have determined which reactions in the Regional Acid Deposition Model Gas-Phase Chemical Mechanism (Stockwell et al., 1990) are diffusion limited for a typical atmospheric condition through the calculation of Damköhler numbers. Damköhler numbers are defined to be the ratio of the diffusion mixing time to the chemical reaction time for a given chemical reaction (McRae et al., 1982; Hill, 1976). The reactions of hydroxyl radicals and the reactions of peroxy radicals with NO are diffusion limited under typical atmospheric conditions. Both sets of reactions are especially significant because NOx and organic species strongly affect ozone and hydroxyl radical concentrations. It is suggested that Damköhler numbers could be used to help determine the placement of Eulerian model boundaries and to determine model grid structure.With 2 Figures  相似文献   

7.
Summary The role of turbulence in the dispersion of atmospheric pollutants that react with linear (decay) and nonlinear (second-order) chemical reactions is examined. The most relevant processes that drive the reactivity of species emitted in a surface area or released by a point source are studied by deriving the dimensionless scaling numbers from equations for the atmospheric turbulent reacting flow. The first number is the ratio of the time scale of turbulence to the time scale of the chemical reaction, namely the Damköhler number. The second number is the ratio of the concentrations of the species present in the chemical transformations. In this paper, model results and experimental studies of turbulent reacting flows in the atmospheric boundary layer are presented to show the modifications and control exerted by turbulence on the atmospheric chemistry as a function of these numbers and processes. We also discuss how the chemical transformation is affected when species are in a state of chemical equilibrium.By studying the plume dispersion of a reactant, that decays with a simple chemical reaction, one can analyse the dependence of concentration fluctuations on the Damköhler number. The study is extended to plumes that react nonlinearly. In such reacting systems, the large gradients and segregation of species result in a significant reduction in the reaction rates. Because of this modification, the chemistry of species related to NOx and HOx can be very different from the chemistry in conditions where the species are uniformly mixed. The lack of complete observational evidence is hampering our understanding of these processes and our evaluation of numerical modelling results. Finally, we discuss briefly how to represent, in the form of a parameterization, the effect that turbulence can have on the reactivity of species emitted by a point source or an area source.  相似文献   

8.
Large-eddy simulations (LES) of the continuously turbulent quasi-equilibrium stable boundary layer (SBL) are conducted with grid lengths in the range of 12.5 m to 2 m, in order to explore resolution sensitivity, and determine at what point grid convergence occurs. The structure of the mean potential temperature, winds, and turbulent fluxes varies significantly over this resolution range. The highest resolution simulations show a significant degree of convergence. The dimensionless momentum diffusivity asymptotes to a value of 0.06, corresponding to a limiting flux Richardson number of 0.15.Using the converged simulations, some scaling hypotheses underpinning first-order and second-order closure models are revisited. The effective Richardson number stability functions of the LES are compared with the forms often used in numerical weather prediction (NWP). The mixing implied by the LES is less than that used in NWP. The commonly used similarity profiles for heat and momentum fluxes, and the scalings for dissipation and pressure covariances are compared with the LES. This information could provide guidance for the next generation of SBL parametrization schemes.  相似文献   

9.
The empirical dependence of turbulence Prandtl number (Pr) on gradient Richardson number (Ri) is presented, derived so as to avoid the effects of self-correlation from common variables. Linear power relationships between the underlying variables that constitute both Pr and Ri are derived empirically from flux and profile observations. Pr and Ri are then reconstructed from these power laws, to indicate their interdependence whilst avoiding self-correlation. Data are selected according to the stability range prior to regression, and the process is iterated from neutral to higher stability until error analysis indicates the method is no longer valid. A Butterworth function is fitted to the resulting Pr −1(Ri) regression to give an empirical summary of the analysis. The form suggests that asymptotically Pr −1 decreases as Ri 3/2. Scatter in the data increases above Ri ~ 1, however, indicating additional constraints to Pr are not captured by Ri alone in this high stability regime. The Butterworth function is analytic for all Ri > 0, and may be included in suitable boundary-layer parameterisation schemes where the turbulent diffusivity for heat is derived from the turbulent diffusivity for momentum.  相似文献   

10.
Atmospheric activity concentrations of 212Pb and short-lived 222Rndaughters, together with meteorological elements, have been observed continuously atthree sites at Kamisaibara Village in Japan. In addition, atmospheric activity concentrationof 222Rn, equilibrium-equivalent concentration of 222Rn and conditionsof the lower atmosphere were observed for three intensive observation periods at Akawase,one of the three sites in Kamisaibara Village. The equilibrium-equivalent concentration of222Rn is almost the same as the atmospheric activity concentration of short-lived222Rn daughters.The activity concentrations of 212Pb and the short-lived 222Rn daughtersand their ratio were low in the daytime owing to convective mixing, and high at nightowing to the surface-based inversion during periods of no precipitation. Their variationshave several patterns corresponding to the scale of the drainage wind or weak mixing.Mechanical mixing due to strong winds through both day and night during the first andsecond observation periods made the atmospheric activity concentrations of 212Pb and the short-lived 222Rn daughters continuously low. However, their ratios werecontinuously high during the first period yet continuously low during the second period.This difference can be explained by the effect ofextraction of 220Rn and 222Rndue to strong winds and snow cover. There were also cases in which the ratio of theatmospheric activity concentration of 212Pb to that of the short-lived 222Rndaughters at night was equal to or less than the ratio in the daytime. Thisinverse trend, asin the periods of no precipitation mentioned above, is considered to be due to near-neutralconditions on these nights.We find a difference in the ratio of the equilibrium-equivalent concentration of222Rn (the activity concentration of short-lived 222Rn daughters) tothe activity concentration of 222Rn during the first observation period and thatduring the second. The difference can be explained by snow cover on the ground. Wealso find differences among the ratios of the activity concentration of the short-lived222Rn daughters to that of 222Rn during the three observation periods.These differences can be explained by the submergence of paddy fields.  相似文献   

11.
The two-scalar covariance budget is significant within the canopy sublayer (CSL) given its role in modelling scalar flux budgets using higher-order closure principles and in estimating the segregation ratio for chemically reactive species. Despite its importance, an explicit expression describing how the two-scalar covariance is modified by inhomogeneity in the flow statistics and in the vertical variation in scalar emission or uptake rates within the canopy volume remains elusive even for passive scalars. To progress on a narrower version of this problem, an analytical solution to the two-scalar covariance budget in the CSL is proposed for the most idealized flow conditions: a stationary and planar homogeneous flow inside a uniform and dense canopy with a constant leaf area density distribution. The foliage emission (or uptake) source strengths are assumed to vary exponentially with depth while the forest floor emission is represented as a scalar flux. The analytical solution is a superposition of a homogeneous part that describes how the two-scalar covariance at the canopy top is transported and dissipated within the canopy volume, and an inhomogeneous part governed by local production mechanisms of the two-scalar covariance. The homogeneous part is primarily described by the canopy adjustment length scale, and the attenuation coefficients of the turbulent kinetic energy and the mean velocity. Conditions for which the vertical variation of the two-scalar covariance is controlled by the rapid attenuation in the mean velocity and turbulent kinetic energy profiles, vis-à-vis the vertical variation of the scalar source strength, are explicitly established. This model also demonstrates how dissimilarity in the emissions from the ground, even for the extreme binary case with one scalar turned ‘on’ and the other scalar turned ‘off’, modifies the vertical variation of the two-scalar covariance within the CSL. To assess its applicability to field conditions, the analytical model predictions were compared with observations made at two different forest types—a sparse pine forest at the Hyytiälä SMEAR II-station (in Finland) and a dense alpine hardwood forest at Lavarone (in Italy). While the model assumptions do not represent the precise canopy morphology, attenuation properties of the turbulent kinetic energy and the mean velocity, observed mixing length, and scalar source attenuation properties for these two forest types, good agreement was found between measured and modelled two scalar covariances for multiple scalars and for the triple moments at the Hyytiälä site.  相似文献   

12.
A second-order modelling technique is used to investigate the influence of turbulence on chemical reactions. The covariance and variance equations for the NO-O3-NO2 system are developed as a function of the ratio of the timescale of turbulence ( t ) and the timescale of chemistry (Ch): the first Damköhler number ( t /Ch). Special attention is given to the calculation of the covariance between NO and O3 normalized by the product of their means, the so-called intensity of segregation (I S ). This parameter quantifies the state of mixing of two chemical species.The intensity of segregation is calculated as a function of the flux of NO and the first Damköhler number. The model results presented illustrate the importance of taking the effect of turbulence on chemical reactions into account for higher values of the NO flux, for values of the ratio O3/NO larger than 12.5 and for values of the ratio t /CH larger than 0.1. For such cases, the effective reaction rates are slower than if the chemical species are assumed to be uniformly mixed.  相似文献   

13.
A Simple Method of Estimating Scalar Fluxes Over Forests   总被引：1，自引：0，他引：1  
A simple aerodynamic-variance method is proposed to fill gaps in continuous CO2 flux measurements in rainy conditions, when open-path analysers do not function. The method requires turbulent conditions (friction velocity greater than 0.1 ms–1), and uses measurements of mean wind speed, and standard deviations of temperature and CO2 concentration fluctuations to complement, and at times replace, eddy-covariance measurements of friction velocity, sensible heat flux and CO2 flux. Friction velocity is estimated from the mean wind speed with a flux-gradient relationship modified for the roughness sublayer. Since normalised standard deviations do not follow Monin-Obukhov similarity theory in the roughness sublayer, a simple classification scheme according to the scalar turbulence scale was used. This scheme is shown to produce sensible heat and CO2 flux estimates that are well correlated with the measured values.  相似文献   

14.
Mean Flow Near Edges and Within Cavities Situated Inside Dense Canopies   总被引：3，自引：3，他引：0  
A streamfunction-vorticity formulation is used to explore the extent to which turbulent and turbulently inviscid solutions to the mean momentum balance explain the mean flow across forest edges and within cavities situated inside dense forested canopies. The turbulent solution is based on the mean momentum balance where first-order closure principles are used to model turbulent stresses. The turbulently inviscid solution retains all the key terms in the mean momentum balance but for the turbulent stress gradients. Both exit and entry versions of the forest edge problem are explored. The turbulent solution is found to describe sufficiently the bulk spatial patterns of the mean flow near the edge including signatures of different length scales reported in canopy transition studies. Next, the ‘clearing inside canopy’ or the so-called ‘cavity’ problem is solved for the inviscid and turbulent solutions and then compared against flume experiments. The inviscid solution describes the bulk flow dynamics in much of the zones within the cavity. In particular, the solution can capture the correct position of the bulk recirculation zone within the cavity, although with a weaker magnitude. The inviscid solution cannot capture the large vertical heterogeneity in the mean velocity above the canopy, as expected. These features are better captured via the first-order closure representation of the turbulent solution. Given the ability of this vorticity formulation to capture the mean pressure variations and the mean advective acceleration terms, it is ideal for exploring the distributions of scalars and roughness-induced flow adjustments on complex topography.  相似文献   

15.
Numerical simulations of scalar transport in neutral flow over forested ridges are performed using both a 1.5-order mixing-length closure scheme and a large-eddy simulation. Such scalar transport (particularly of CO2) has been a significant motivation for dynamical studies of forest canopy–atmosphere interactions. Results from the 1.5-order mixing-length simulations show that hills for which there is significant mean flow into and out of the canopy are more efficient at transporting scalars from the canopy to the boundary layer above. For the case with a source in the canopy this leads to lower mean concentrations of tracer within the canopy, although they can be very large horizontal variations over the hill. These variations are closed linked to flow separation and recirculation in the canopy and can lead to maximum concentrations near the separation point that exceed those over flat ground. Simple scaling arguments building on the analytical model of Finnigan and Belcher (Q J Roy Meteorol Soc 130:1–29, 2004) successfully predict the variations in scalar concentration near the canopy top over a range of hills. Interestingly this analysis suggests that variations in the components of the turbulent transport term, rather than advection, give rise to the leading order variations in scalar concentration. The scaling arguments provide a quantitative measure of the role of advection, and suggest that for smaller/steeper hills and deeper/sparser canopies advection will be more important. This agrees well with results from the numerical simulations. A large-eddy simulation is used to support the results from the mixing-length closure model and to allow more detailed investigation of the turbulent transport of scalars within and above the canopy. Scalar concentration profiles are very similar in both models, despite the fact that there are significant differences in the turbulent transport, highlighted by the strong variations in the turbulent Schmidt number both in the vertical and across the hill in the large-eddy simulation that are not represented in the mixing-length model.  相似文献   

16.
We investigate the scaling behaviour of a turbulent kinetic energy (TKE) closure model for stably stratified conditions. The mixing length scale for stable stratification is proportional to the ratio of the square root of the TKE and the local Brunt–Väisälä frequency, which is a commonly applied formulation. We analyze the scaling behaviour of our model in terms of traditional Monin–Obukov Similarity Theory and local scaling. From the model equations, we derive expressions for the stable limit behaviour of the flux–gradient relations and other scaling quantities. It turns out that the scaling behaviour depends on only a few model parameters and that the results obey local scaling theory. The analytical findings are illustrated with model simulations for the second GABLS intercomparison study. We also investigate solutions for the case in which an empirical correction function is used to express the eddy diffusivity for momentum as a function of the Richardson number (i.e. an increasing turbulent Prandtl number with stability). In this case, it seems that for certain parameter combinations the model cannot generate a steady-state solution. At the same time, its scaling behaviour becomes unrealistic. This shows that the inclusion of empirical correction functions may have large and undesired consequences for the model behaviour.  相似文献   

17.
Extensive eddy-correlation datasets are analyzed to examine the influence of nonstationarity of the mean flow on the flux–gradient relationship near the surface. This nonstationarity is due to wavelike motions, meandering of the wind vector, and numerous unidentified small-scale mesoscale motions. While the data do not reveal an obvious critical gradient Richardson number, the maximum downward heat flux increases approximately linearly with increasing friction velocity for significant stability. The largest of our datasets is chosen to more closely examine the influence of stability, nonstationarity, distortion of the mean wind profile and self-correlation on the flux-gradient relationship. Stability is expressed in terms of z/L, the gradient Richardson number or the bulk Richardson number over the tower layer. The efficiency of the momentum transport systematically increases with increasing nonstationarity and attendant distortion of the mean wind profile. Enhancement of the turbulent momentum flux associated with nonstationarity is examined in terms of the nondimensional shear, Prandtl number and the eddy diffusivity.  相似文献   

18.
Atmospheric air pollution turbulent fluxes can be assumed to be proportional to the mean concentration gradient. This assumption, along with the equation of continuity, leads to the advection–diffusion equation. Moreover, large eddies are able to mix scalar quantities in a manner that is counter to the local gradient. In this work we present a semi-analytical solution for the three-dimensional steady-state advection–diffusion equation, considering non-local turbulence closure using the Generalized Integral Advection Diffusion Multilayer Technique (GIADMT). We report some examples of applications of the new solution for two different datasets and for a water tank experiment.  相似文献   

19.
An integrated canopy micrometeorological model is described for calculating CO2, water vapor and sensible heat exchange rates and scalar concentration profiles over and within a crop canopy. The integrated model employs a Lagrangian random walk algorithm to calculate turbulent diffusion. The integrated model extends previous Lagrangian modelling efforts by employing biochemical, physiological and micrometeorological principles to evaluate vegetative sources and sinks. Model simulations of water vapor, CO2 and sensible heat flux densities are tested against measurements made over a soybean canopy, while calculations of scalar profiles are tested against measurements made above and within the canopy. The model simulates energy and mass fluxes and scalar profiles above the canopy successfully. On the other hand, model calculations of scalar profiles inside the canopy do not match measurements.The tested Lagrangian model is also used to evaluate simpler modelling schemes, as needed for regional and global applications. Simple, half-order closure modelling schemes (which assume a constant scalar profile in the canopy) do not yield large errors in the computation of latent heat (LE) and CO2 (F c ) flux densities. Small errors occur because the source-sink formulation of LE andF c are relatively insensitive to changes in scalar concentrations and the scalar gradients are small. On the other hand, complicated modelling frames may be needed to calculate sensible heat flux densities; the source-sink formulation of sensible heat is closely coupled to the within-canopy air temperature profile.  相似文献   

20.
A simple closure scheme for nocturnal stratocumulus is proposed. The scheme is formulated in conserved variables. Cloud fraction and cloud water amount are diagnosed assuming a top-hat distribution for total water. Conversion of cloud water into rain water is parameterized in terms of cloud water and the incoming rain flux. Turbulence transport in the cloud layer is accounted for by a first-order vertical diffusion scheme with a profile-type diffusivity. The length scale corresponds to the thickness of the cloud layer. The turbulent velocity scale is directly related to the long wave radiative flux divergence in the cloud. Entrainment at cloud top is implicitly treated by extending the in-cloud mixing profile slightly beyond cloud top. The excess height is derived from the buoyancy frequency at cloud top and a radiative–convective velocity scale. The scheme is capable of simulating realistic profiles of the conserved variables and cloud parameters for a case of nocturnal stratocumulus prepared on the basis of ASTEX data.  相似文献   

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