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- Author or Editor: Jordi Vilà-Guerau de Arellano x

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## Abstract

The influence of the different scales of turbulent motion on plume dispersion in the atmospheric convective boundary layer (CBL) is studied by means of a large-eddy simulation (LES). In particular, the large-scale (meandering) and small-scale (relative diffusion) contributions are separated by analyzing dispersion in two reference systems: the absolute (fixed) coordinate system and the coordinate system relative to the plume’s instantaneous center of mass. In the relative coordinate system, the (vertically) inhomogeneous meandering motion is removed, and only the small-scale, homogeneous turbulent motion contributes to the dispersion process.

First, mean plume position, dispersion parameters (variance), and skewness of the plume position are discussed. The analysis of the third-order moments shows how the structure and the symmetry of scalar distribution are affected with respect to the turbulent characteristics of the CBL (inhomogeneity of the large-scale vertical motion) and the presence of the boundary conditions (surface and top of the CBL). In fact, the reflection of the plume by the CBL boundaries generates the presence of nonlinear cross-correlation terms in the balance equation for the third-order moments of the plume position. As a result, the third-order moment of the absolute position is not balanced by the sum of the third-order moments of the meandering and relative plume position.

Second, mean concentration and concentration fluctuations are calculated and discussed in both coordinate systems. The intensity of relative concentration fluctuation *i _{cr}*, which quantifies the internal (in plume) mixing, is explicitly calculated. Based on these results, a parameterization for the probability distribution function (PDF) of the relative concentration is proposed, showing very good agreement with the LES results. Finally, the validity of Gifford’s formula, which relates the absolute concentration’s high-order moments to the relative concentration and the PDF of the plume centerline, is studied. It is found that due to the presence of the CBL boundaries, Gifford’s formula is not able to reproduce correctly the value of the absolute mean concentration near the ground. This result is analyzed by showing that, when the plume is reflected by the CBL boundaries, the instantaneous relative plume width

*z*′

^{2}

_{r}(

*t*) departs from its mean value

*σ*

^{2}

_{r}. By introducing the skewness of the relative plume position into a parameterization for the relative mean concentration, the results for the calculated mean concentration are improved.

## Abstract

The influence of the different scales of turbulent motion on plume dispersion in the atmospheric convective boundary layer (CBL) is studied by means of a large-eddy simulation (LES). In particular, the large-scale (meandering) and small-scale (relative diffusion) contributions are separated by analyzing dispersion in two reference systems: the absolute (fixed) coordinate system and the coordinate system relative to the plume’s instantaneous center of mass. In the relative coordinate system, the (vertically) inhomogeneous meandering motion is removed, and only the small-scale, homogeneous turbulent motion contributes to the dispersion process.

First, mean plume position, dispersion parameters (variance), and skewness of the plume position are discussed. The analysis of the third-order moments shows how the structure and the symmetry of scalar distribution are affected with respect to the turbulent characteristics of the CBL (inhomogeneity of the large-scale vertical motion) and the presence of the boundary conditions (surface and top of the CBL). In fact, the reflection of the plume by the CBL boundaries generates the presence of nonlinear cross-correlation terms in the balance equation for the third-order moments of the plume position. As a result, the third-order moment of the absolute position is not balanced by the sum of the third-order moments of the meandering and relative plume position.

Second, mean concentration and concentration fluctuations are calculated and discussed in both coordinate systems. The intensity of relative concentration fluctuation *i _{cr}*, which quantifies the internal (in plume) mixing, is explicitly calculated. Based on these results, a parameterization for the probability distribution function (PDF) of the relative concentration is proposed, showing very good agreement with the LES results. Finally, the validity of Gifford’s formula, which relates the absolute concentration’s high-order moments to the relative concentration and the PDF of the plume centerline, is studied. It is found that due to the presence of the CBL boundaries, Gifford’s formula is not able to reproduce correctly the value of the absolute mean concentration near the ground. This result is analyzed by showing that, when the plume is reflected by the CBL boundaries, the instantaneous relative plume width

*z*′

^{2}

_{r}(

*t*) departs from its mean value

*σ*

^{2}

_{r}. By introducing the skewness of the relative plume position into a parameterization for the relative mean concentration, the results for the calculated mean concentration are improved.

## Abstract

The combined effect of ultraviolet radiation and turbulent mixing on chemistry in a cloud-topped boundary layer is investigated. The authors study a flow driven by longwave radiative cooling at cloud top. They consider a chemical cycle that is composed of a first-order reaction whose photodissociation rate depends on the cloud properties and time and a second-order chemical reaction between an abundant entrained reactant and a species with an initial concentration in the boundary layer. This turbulent reacting flow is represented numerically by means of a large eddy simulation. The simulation does not take evaporative cooling and aqueous-phase chemistry into account; that is, the authors simulate a dry smoke cloud.

The vertical concentration profiles of the reactants not in excess clearly show the appearance of gradients due to the chemical sources and sinks in the cloud. Moreover, the vertical-flux profiles depart from a linear profile. Fluxes that, in the absence of chemistry, are directed upward could change direction due to the different chemical reaction rate constants inside and below the cloud and because of the dominant downward motions generated by radiative cooling. The flux-budget analysis shows the relevance of the chemical term for the nonabundant species inside of the cloud. The exchange flux between the free troposphere and the boundary layer also depends on the chemical transformation above and in the cloud. An expression for the exchange velocity of reactive species is proposed in terms of an in-cloud flux, the production–depletion chemical rates, and the concentration jump at the inversion height. The calculated exchange velocity values for the smoke and the reactants differ considerably.

## Abstract

The combined effect of ultraviolet radiation and turbulent mixing on chemistry in a cloud-topped boundary layer is investigated. The authors study a flow driven by longwave radiative cooling at cloud top. They consider a chemical cycle that is composed of a first-order reaction whose photodissociation rate depends on the cloud properties and time and a second-order chemical reaction between an abundant entrained reactant and a species with an initial concentration in the boundary layer. This turbulent reacting flow is represented numerically by means of a large eddy simulation. The simulation does not take evaporative cooling and aqueous-phase chemistry into account; that is, the authors simulate a dry smoke cloud.

The vertical concentration profiles of the reactants not in excess clearly show the appearance of gradients due to the chemical sources and sinks in the cloud. Moreover, the vertical-flux profiles depart from a linear profile. Fluxes that, in the absence of chemistry, are directed upward could change direction due to the different chemical reaction rate constants inside and below the cloud and because of the dominant downward motions generated by radiative cooling. The flux-budget analysis shows the relevance of the chemical term for the nonabundant species inside of the cloud. The exchange flux between the free troposphere and the boundary layer also depends on the chemical transformation above and in the cloud. An expression for the exchange velocity of reactive species is proposed in terms of an in-cloud flux, the production–depletion chemical rates, and the concentration jump at the inversion height. The calculated exchange velocity values for the smoke and the reactants differ considerably.

## Abstract

The role of shear in the development and maintenance of a convective boundary layer is studied by means of observations and large eddy simulations (LESs). Particular emphasis is given to the growth of the boundary layer and to the way in which this growth is affected by surface fluxes of heat and moisture and entrainment fluxes. This paper analyzes the processes that drive the latter mechanism, which accounts for approximately 30% of the growth of the mixing layer. Typically, it is found that under pure convective conditions, without shear, the entrainment buoyancy flux at the inversion is about −20% of the surface buoyancy flux. This value is widely used for entrainment rate closures in general circulation models.

The data collected during the Atmospheric Radiation Measurement campaign allow one to introduce realistic vertical profiles and surface fluxes into the LES runs and to compare the simulation results with the observed evolution of the boundary layer height during a convective situation with high entrainment rates and high geostrophic winds. The analysis of the turbulent kinetic energy (TKE) budget shows that the inclusion of geostrophic winds, which produce shear at the surface and in the entrainment zone, modifies the vertical profile of the various terms in the TKE budget. As a consequence, the entrainment flux is enhanced, resulting in increased growth of the boundary layer. The numerical experiments and the observations enable one to validate the efficiency of earlier representations, based on the TKE equation, which describe the evolution of the ratio between entrainment and surface buoyancy fluxes. The proposed parameterization for the entrainment and surface buoyancy flux ratio (*β*), which includes the main buoyancy and shear contributions, is in good agreement with the LES results. Some aspects of the parameterization of *β,* for instance, the absence of entrainment flux and its behavior during the transition between convective to neutral conditions, are discussed.

## Abstract

The role of shear in the development and maintenance of a convective boundary layer is studied by means of observations and large eddy simulations (LESs). Particular emphasis is given to the growth of the boundary layer and to the way in which this growth is affected by surface fluxes of heat and moisture and entrainment fluxes. This paper analyzes the processes that drive the latter mechanism, which accounts for approximately 30% of the growth of the mixing layer. Typically, it is found that under pure convective conditions, without shear, the entrainment buoyancy flux at the inversion is about −20% of the surface buoyancy flux. This value is widely used for entrainment rate closures in general circulation models.

The data collected during the Atmospheric Radiation Measurement campaign allow one to introduce realistic vertical profiles and surface fluxes into the LES runs and to compare the simulation results with the observed evolution of the boundary layer height during a convective situation with high entrainment rates and high geostrophic winds. The analysis of the turbulent kinetic energy (TKE) budget shows that the inclusion of geostrophic winds, which produce shear at the surface and in the entrainment zone, modifies the vertical profile of the various terms in the TKE budget. As a consequence, the entrainment flux is enhanced, resulting in increased growth of the boundary layer. The numerical experiments and the observations enable one to validate the efficiency of earlier representations, based on the TKE equation, which describe the evolution of the ratio between entrainment and surface buoyancy fluxes. The proposed parameterization for the entrainment and surface buoyancy flux ratio (*β*), which includes the main buoyancy and shear contributions, is in good agreement with the LES results. Some aspects of the parameterization of *β,* for instance, the absence of entrainment flux and its behavior during the transition between convective to neutral conditions, are discussed.

## Abstract

The influence of convective turbulence on chemical reactions in the atmospheric boundary layer is studied by means of direct numerical simulation (DNS). An archetype of turbulent reacting flows is used to study the reaction zones and to obtain a description of the turbulent control of chemical reactions. Several simulations are carried out and classified using a turbulent Damköhler number and a Kolmogorov Damköhler number. Using a classification based on these numbers, it is shown that it is possible to represent and to solve adequately all relevant scales of turbulence and chemistry by means of DNS. The simulations show clearly that the reaction zones are located near the boundaries where the species are introduced. At the lower boundary of the convective boundary layer, the reaction takes place predominantly in the core of the updrafts, whereas in the upper part of the domain the chemical reaction is greatest in the center of the downdrafts. In the bulk of the boundary layer the chemical reaction proceeds very slowly, due to the almost complete segregation of the chemical species. From the point of view of chemistry, the mixing across the interface between updrafts and downdrafts in the bulk of the convective boundary layer plays only a minor role.

The amount of chemical reaction in relation to the degree of turbulence is quantified by the introduction of an effective Damköhler number. This dimensionless number explicitly takes into account the reduction of the reaction rate due to the segregation of the chemical species. It is shown that the number approaches an asymptotic value that is *O*(1) for increasingly fast reaction rates. This shows explicitly that the timescale of the chemical reactions is limited by the integral turbulent timescale. It is suggested how a parameterization could be used to include this effect into one-dimensional atmospheric models.

## Abstract

The influence of convective turbulence on chemical reactions in the atmospheric boundary layer is studied by means of direct numerical simulation (DNS). An archetype of turbulent reacting flows is used to study the reaction zones and to obtain a description of the turbulent control of chemical reactions. Several simulations are carried out and classified using a turbulent Damköhler number and a Kolmogorov Damköhler number. Using a classification based on these numbers, it is shown that it is possible to represent and to solve adequately all relevant scales of turbulence and chemistry by means of DNS. The simulations show clearly that the reaction zones are located near the boundaries where the species are introduced. At the lower boundary of the convective boundary layer, the reaction takes place predominantly in the core of the updrafts, whereas in the upper part of the domain the chemical reaction is greatest in the center of the downdrafts. In the bulk of the boundary layer the chemical reaction proceeds very slowly, due to the almost complete segregation of the chemical species. From the point of view of chemistry, the mixing across the interface between updrafts and downdrafts in the bulk of the convective boundary layer plays only a minor role.

The amount of chemical reaction in relation to the degree of turbulence is quantified by the introduction of an effective Damköhler number. This dimensionless number explicitly takes into account the reduction of the reaction rate due to the segregation of the chemical species. It is shown that the number approaches an asymptotic value that is *O*(1) for increasingly fast reaction rates. This shows explicitly that the timescale of the chemical reactions is limited by the integral turbulent timescale. It is suggested how a parameterization could be used to include this effect into one-dimensional atmospheric models.

## Abstract

The influence of land surface heterogeneity on potential cloud formation is investigated using relative humidity as an indicator. This is done by performing numerical experiments using a large-eddy simulation model (LES). The land surface in the model was divided into two patches that had the same sum of latent and sensible heat flux but different Bowen ratios to simulate heterogeneous land surfaces. For heterogeneity in the meso-*γ* scale (2–20 km), sensitivity analyses were carried out on the heterogeneity amplitude (Bowen ratio difference between contrasting areas) and the inversion strength of potential temperature and specific humidity. The competition between absolute temperature decrease by ABL growth and dry air entrainment in heterogeneous conditions is analyzed using the LES results. First, it is shown that entrainment is located and enhanced over patches with higher Bowen ratios (warm patches) than their surroundings (cold patches). The heterogeneity-induced strong thermals can further penetrate the inversion at the ABL top, thereby reaching lower absolute temperatures than in homogeneous conditions. Second, because of the heterogeneity-induced circulations the moisture is located over the warm patch, and higher time-averaged RH values at the ABL top (RH_{zi}) than over the cold patches are found here, even for dry atmospheres. These RH_{zi} exceed values found over homogeneous land surfaces and are an indication that surface heterogeneity may facilitate cloud formation. In vertical profiles of RH, few differences are found between the homogeneous and heterogeneous cases, but the essential heterogeneity-induced modifications are within the domain variability.

## Abstract

The influence of land surface heterogeneity on potential cloud formation is investigated using relative humidity as an indicator. This is done by performing numerical experiments using a large-eddy simulation model (LES). The land surface in the model was divided into two patches that had the same sum of latent and sensible heat flux but different Bowen ratios to simulate heterogeneous land surfaces. For heterogeneity in the meso-*γ* scale (2–20 km), sensitivity analyses were carried out on the heterogeneity amplitude (Bowen ratio difference between contrasting areas) and the inversion strength of potential temperature and specific humidity. The competition between absolute temperature decrease by ABL growth and dry air entrainment in heterogeneous conditions is analyzed using the LES results. First, it is shown that entrainment is located and enhanced over patches with higher Bowen ratios (warm patches) than their surroundings (cold patches). The heterogeneity-induced strong thermals can further penetrate the inversion at the ABL top, thereby reaching lower absolute temperatures than in homogeneous conditions. Second, because of the heterogeneity-induced circulations the moisture is located over the warm patch, and higher time-averaged RH values at the ABL top (RH_{zi}) than over the cold patches are found here, even for dry atmospheres. These RH_{zi} exceed values found over homogeneous land surfaces and are an indication that surface heterogeneity may facilitate cloud formation. In vertical profiles of RH, few differences are found between the homogeneous and heterogeneous cases, but the essential heterogeneity-induced modifications are within the domain variability.

## Abstract

Eulerian and Lagrangian statistics in the atmospheric convective boundary layer (CBL) are studied by means of large eddy simulation (LES). Spectra analysis is performed in both the Eulerian and Lagrangian frameworks, autocorrelations are calculated, and the integral length and time scales are derived. Eulerian statistics are calculated by means of spatial and temporal analysis in order to derive characteristic length and time scales. Taylor’s hypothesis of frozen turbulence is investigated, and it is found to be satisfied in the simulated flow.

Lagrangian statistics are derived by tracking the trajectories of numerous particles released at different heights in the turbulent flow. The relationship between Lagrangian properties (autocorrelation functions) and dispersion characteristics (particles’ displacement) is studied through Taylor’s diffusion relationship, with special emphasis on the difference between horizontal and vertical motion. Results show that for the horizontal motion, Taylor’s relationship is satisfied. The vertical motion, however, is influenced by the inhomogeneity of the flow and limited by the ground and the capping inversion at the top of the CBL. The Lagrangian autocorrelation function, therefore, does not have an exponential shape, and consequently, the integral time scale is zero. If distinction is made between free and bounded motion, a better agreement between Taylor’s relationship and the particles’ vertical displacement is found.

Relationships between Eulerian and Lagrangian frameworks are analyzed by calculating the ratio *β* between Lagrangian and Eulerian time scales. Results show that the integral time scales are mainly constant with height for *z*/*z _{i}* < 0.7. In the upper part of the CBL, the capping inversion transforms vertical motion into horizontal motion. As a result, the horizontal time scale increases with height, whereas the vertical one is reduced. Current parameterizations for the ratio between the Eulerian and Lagrangian time scales have been tested against the LES results showing satisfactory agreement at heights

*z*/

*z*< 0.7.

_{i}## Abstract

Eulerian and Lagrangian statistics in the atmospheric convective boundary layer (CBL) are studied by means of large eddy simulation (LES). Spectra analysis is performed in both the Eulerian and Lagrangian frameworks, autocorrelations are calculated, and the integral length and time scales are derived. Eulerian statistics are calculated by means of spatial and temporal analysis in order to derive characteristic length and time scales. Taylor’s hypothesis of frozen turbulence is investigated, and it is found to be satisfied in the simulated flow.

Lagrangian statistics are derived by tracking the trajectories of numerous particles released at different heights in the turbulent flow. The relationship between Lagrangian properties (autocorrelation functions) and dispersion characteristics (particles’ displacement) is studied through Taylor’s diffusion relationship, with special emphasis on the difference between horizontal and vertical motion. Results show that for the horizontal motion, Taylor’s relationship is satisfied. The vertical motion, however, is influenced by the inhomogeneity of the flow and limited by the ground and the capping inversion at the top of the CBL. The Lagrangian autocorrelation function, therefore, does not have an exponential shape, and consequently, the integral time scale is zero. If distinction is made between free and bounded motion, a better agreement between Taylor’s relationship and the particles’ vertical displacement is found.

Relationships between Eulerian and Lagrangian frameworks are analyzed by calculating the ratio *β* between Lagrangian and Eulerian time scales. Results show that the integral time scales are mainly constant with height for *z*/*z _{i}* < 0.7. In the upper part of the CBL, the capping inversion transforms vertical motion into horizontal motion. As a result, the horizontal time scale increases with height, whereas the vertical one is reduced. Current parameterizations for the ratio between the Eulerian and Lagrangian time scales have been tested against the LES results showing satisfactory agreement at heights

*z*/

*z*< 0.7.

_{i}## Abstract

In this paper variance spectra of chemically active species in a dry convective boundary layer are studied by means of large-eddy simulations (LESs). The aim is to quantify the impact of chemistry on the spatial fluctuations in the concentration fields. The computational domain has a large aspect ratio (width/height = 16) in order to encompass all relevant scales (mesoscale to microscale). Variance spectra are used to calculate a characteristic length scale of the species' concentration variability. By locating the peak in the spectrum, a “variance dominating length scale” is derived.

For a simple first-order reaction, this length scale demonstrates a clear dependence on the reaction rate: an increase in the reaction rate leads to a significant decrease of the length scale of the species.

For a chemical cycle composed of a second-order reaction and first-order backreaction, the length scales turn out to depend much less on the reaction rate. The value of the length scales of the species involved appears to lie well in the mesoscale range, rather than the microscale range, demonstrating that concentration fluctuations are driven predominantly by scales much larger than the depth of the boundary layer.

External perturbation of the chemical balance can have a direct impact on the variance spectra. For the case where a (hypothetical) passing cloud switches off the chemical backreaction for a while, a dramatic drop in the length scale of the nonabundant species is observed. Once the feedback has been restored, a rapid increase of the length scale is observed.

To better understand these results, a spectral model is developed that incorporates turbulent production and dissipation of variance, chemistry, and spectral transfer. The model gives valuable insight into the relative importance of these processes at each scale separately, and enables one to predict the value of the variance dominating length scale in the limiting cases of very slow and very fast chemistry.

## Abstract

In this paper variance spectra of chemically active species in a dry convective boundary layer are studied by means of large-eddy simulations (LESs). The aim is to quantify the impact of chemistry on the spatial fluctuations in the concentration fields. The computational domain has a large aspect ratio (width/height = 16) in order to encompass all relevant scales (mesoscale to microscale). Variance spectra are used to calculate a characteristic length scale of the species' concentration variability. By locating the peak in the spectrum, a “variance dominating length scale” is derived.

For a simple first-order reaction, this length scale demonstrates a clear dependence on the reaction rate: an increase in the reaction rate leads to a significant decrease of the length scale of the species.

For a chemical cycle composed of a second-order reaction and first-order backreaction, the length scales turn out to depend much less on the reaction rate. The value of the length scales of the species involved appears to lie well in the mesoscale range, rather than the microscale range, demonstrating that concentration fluctuations are driven predominantly by scales much larger than the depth of the boundary layer.

External perturbation of the chemical balance can have a direct impact on the variance spectra. For the case where a (hypothetical) passing cloud switches off the chemical backreaction for a while, a dramatic drop in the length scale of the nonabundant species is observed. Once the feedback has been restored, a rapid increase of the length scale is observed.

To better understand these results, a spectral model is developed that incorporates turbulent production and dissipation of variance, chemistry, and spectral transfer. The model gives valuable insight into the relative importance of these processes at each scale separately, and enables one to predict the value of the variance dominating length scale in the limiting cases of very slow and very fast chemistry.

## Abstract

The processes and feedbacks associated with the mass flux of shallow cumulus clouds over land are studied by analyzing the results from large-eddy simulations and a mixed-layer model. The primary focus is to study the development of the (well mixed) subcloud layer and understand the four primary feedbacks between the subcloud-layer dynamics and cumulus mass flux. Guided by numerical experiments in large-eddy simulations that show the transition from clear to cloudy boundary layers at midlatitudes over land, the feedbacks introduced by shallow cumuli are first conceptually described. To study the complex interplay between the subcloud and cloud layer, a mixed-layer model is proposed and validated with large-eddy simulations for the Atmospheric Radiation Measurement Southern Great Plains case. The mixed-layer model is shown to identify and reproduce the most relevant feedbacks in the transition from clear to cloudy boundary layers: a reduced mixed-layer growth and drying of the subcloud layer by enhanced entrainment and mass flux transport of moisture to the cloud layer. To complete the study, the strength of the different feedbacks is further quantified by an analysis of the individual contributions to the tendency of the relative humidity at the top of the mixed layer.

## Abstract

The processes and feedbacks associated with the mass flux of shallow cumulus clouds over land are studied by analyzing the results from large-eddy simulations and a mixed-layer model. The primary focus is to study the development of the (well mixed) subcloud layer and understand the four primary feedbacks between the subcloud-layer dynamics and cumulus mass flux. Guided by numerical experiments in large-eddy simulations that show the transition from clear to cloudy boundary layers at midlatitudes over land, the feedbacks introduced by shallow cumuli are first conceptually described. To study the complex interplay between the subcloud and cloud layer, a mixed-layer model is proposed and validated with large-eddy simulations for the Atmospheric Radiation Measurement Southern Great Plains case. The mixed-layer model is shown to identify and reproduce the most relevant feedbacks in the transition from clear to cloudy boundary layers: a reduced mixed-layer growth and drying of the subcloud layer by enhanced entrainment and mass flux transport of moisture to the cloud layer. To complete the study, the strength of the different feedbacks is further quantified by an analysis of the individual contributions to the tendency of the relative humidity at the top of the mixed layer.