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Abstract
The interactions surrounding the coupling between surface energy balance and a boundary layer with shallow cumuli are investigated using the National Center for Atmospheric Research’s large-eddy simulation code coupled to the Noah land surface model. The simulated cloudy boundary layer is based on the already well-documented and previously simulated 21 June 1997 case at the Atmospheric Radiation Measurement Southern Great Plains central facility. The surface energy balance response to cloud shading is highly nonlinear, leading to different partitioning between sensible and latent heat flux compared to the surface not impacted by cloud. The evaporative fraction increases by about 2%–3% in the presence of shallow cumuli at the regional scale but can increase by up to 30% at any individual location. As expected, the cloud’s reduction of solar irradiance largely controls the surface’s response. However, the turbulence and secondary circulations associated with the cloud dynamics increases the surface flux variability. Even though they are less than 1 km in horizontal scale, the cloud-induced surface heterogeneities impact the vertical flux of heat and moisture up to approximately 20% of the height of the subcloud layer z sl, higher than the surface layer’s typical extent. Above 0.2z sl, the cloud root tends to amplify the drying and the cooling of the subcloud layer. Near the entrainment zone, the cloud-induced latent heat flux increase and sensible heat flux decrease compensate each other with respect to total buoyancy and therefore do not significantly modify the subcloud-layer entrainment rate over large time scales.
Abstract
The interactions surrounding the coupling between surface energy balance and a boundary layer with shallow cumuli are investigated using the National Center for Atmospheric Research’s large-eddy simulation code coupled to the Noah land surface model. The simulated cloudy boundary layer is based on the already well-documented and previously simulated 21 June 1997 case at the Atmospheric Radiation Measurement Southern Great Plains central facility. The surface energy balance response to cloud shading is highly nonlinear, leading to different partitioning between sensible and latent heat flux compared to the surface not impacted by cloud. The evaporative fraction increases by about 2%–3% in the presence of shallow cumuli at the regional scale but can increase by up to 30% at any individual location. As expected, the cloud’s reduction of solar irradiance largely controls the surface’s response. However, the turbulence and secondary circulations associated with the cloud dynamics increases the surface flux variability. Even though they are less than 1 km in horizontal scale, the cloud-induced surface heterogeneities impact the vertical flux of heat and moisture up to approximately 20% of the height of the subcloud layer z sl, higher than the surface layer’s typical extent. Above 0.2z sl, the cloud root tends to amplify the drying and the cooling of the subcloud layer. Near the entrainment zone, the cloud-induced latent heat flux increase and sensible heat flux decrease compensate each other with respect to total buoyancy and therefore do not significantly modify the subcloud-layer entrainment rate over large time scales.
Determining Stationary Periods across Multiple Sensors: An Application to Observed Canopy Turbulence Response to Atmospheric StabilityAbstract
A recently proposed multisensor stationarity analysis technique (MSATv1) is improved to eliminate the initial interrogation of time-averaged wind directions, a redundant and potentially biasing procedure for a technique capable of detecting changes in mean wind directions. The new technique, MSATv2, satisfies two basic expectations that are not guaranteed in MSATv1: 1) a nonstationary event should not belong to any stationary interval identified with a given stringency, and 2) nonstationary events identified with an arbitrary stringency should continue to be identified as nonstationary with increasing stringency. These expectations are confirmed by applying MSATv2 to two long periods, during the defoliated phase of the Canopy Horizontal Array Turbulence Study (CHATS), whose durations are determined solely by data availability. MSATv2 successfully determines visually trivial and nontrivial nonstationary transitions, uncovering details of the time evolution of dynamic processes. MSATv2 yields ensemble-average estimates of mean wind speeds and directions with well-controlled and quantifiable uncertainties for atmospheric stability conditions ranging from near neutral to free convection. These results enable interrogation of the observed canopy turbulence response to atmospheric stability in isolation from contamination by spatial variation with position relative to canopy elements. MSATv2 results also reveal the connection between the presence of organized convective structures and variability in mean shear, showing the role of organized convective structures in the observed relationship between the bulk drag coefficient and atmospheric instability.
Abstract
A recently proposed multisensor stationarity analysis technique (MSATv1) is improved to eliminate the initial interrogation of time-averaged wind directions, a redundant and potentially biasing procedure for a technique capable of detecting changes in mean wind directions. The new technique, MSATv2, satisfies two basic expectations that are not guaranteed in MSATv1: 1) a nonstationary event should not belong to any stationary interval identified with a given stringency, and 2) nonstationary events identified with an arbitrary stringency should continue to be identified as nonstationary with increasing stringency. These expectations are confirmed by applying MSATv2 to two long periods, during the defoliated phase of the Canopy Horizontal Array Turbulence Study (CHATS), whose durations are determined solely by data availability. MSATv2 successfully determines visually trivial and nontrivial nonstationary transitions, uncovering details of the time evolution of dynamic processes. MSATv2 yields ensemble-average estimates of mean wind speeds and directions with well-controlled and quantifiable uncertainties for atmospheric stability conditions ranging from near neutral to free convection. These results enable interrogation of the observed canopy turbulence response to atmospheric stability in isolation from contamination by spatial variation with position relative to canopy elements. MSATv2 results also reveal the connection between the presence of organized convective structures and variability in mean shear, showing the role of organized convective structures in the observed relationship between the bulk drag coefficient and atmospheric instability.
Abstract
This study demonstrates that a pulsed wind lidar is a reliable instrument for measuring angles between horizontal vectors of significance in the atmospheric boundary layer. Three different angles are considered: the wind turning, the angle between the stress vector and the mean wind direction, and the angle between the stress vector and the vertical gradient of the mean velocity vector. The latter is assumed to be zero by the often applied turbulent-viscosity hypothesis, so that the stress vector can be described through the vertical gradient of velocity. In the atmospheric surface layer, where the Coriolis force is negligible, this is supposedly a good approximation. High-resolution large-eddy simulation data show that this is indeed the case even beyond the surface layer. In contrast, through analysis of WindCube lidar measurements supported by sonic measurements, the study shows that it is only valid very close to the surface. The deviation may be significant even at 100 m. This behavior is attributed to mesoscale effects.
Abstract
This study demonstrates that a pulsed wind lidar is a reliable instrument for measuring angles between horizontal vectors of significance in the atmospheric boundary layer. Three different angles are considered: the wind turning, the angle between the stress vector and the mean wind direction, and the angle between the stress vector and the vertical gradient of the mean velocity vector. The latter is assumed to be zero by the often applied turbulent-viscosity hypothesis, so that the stress vector can be described through the vertical gradient of velocity. In the atmospheric surface layer, where the Coriolis force is negligible, this is supposedly a good approximation. High-resolution large-eddy simulation data show that this is indeed the case even beyond the surface layer. In contrast, through analysis of WindCube lidar measurements supported by sonic measurements, the study shows that it is only valid very close to the surface. The deviation may be significant even at 100 m. This behavior is attributed to mesoscale effects.
On Determining Stationary Periods within Time SeriesAbstract
A novel approach is constructed for determining both the occurrence and the duration of stationary periods within time series. After reviewing four statistical techniques that provide stationarity measures invariant to applying a constant offset to the variable of interest, the reverse arrangement test is selected as the basic statistical operation to construct the approach. The probability distributions of the starting and ending points of stationary intervals are used to determine the nonstationary location at which a period should be split into two subperiods and nonstationary samples that should be discarded from analysis of time-averaged statistics. The approach provides efficient analysis of long-term datasets and is capable of relating data sampled at multiple locations. Applying the approach to data obtained within a walnut orchard canopy during the defoliated phase of the Canopy Horizontal Array Turbulence Study (CHATS) yields periods with stationary within-canopy velocities required by analysis of the bulk drag–wind relationship. The uncertainties in empirical estimates of the bulk drag–wind relationship associated with nonstationarity and finite duration of time series are evaluated. An integral view of various stationarity measures is presented, with a highlight of their links to physical processes.
Abstract
A novel approach is constructed for determining both the occurrence and the duration of stationary periods within time series. After reviewing four statistical techniques that provide stationarity measures invariant to applying a constant offset to the variable of interest, the reverse arrangement test is selected as the basic statistical operation to construct the approach. The probability distributions of the starting and ending points of stationary intervals are used to determine the nonstationary location at which a period should be split into two subperiods and nonstationary samples that should be discarded from analysis of time-averaged statistics. The approach provides efficient analysis of long-term datasets and is capable of relating data sampled at multiple locations. Applying the approach to data obtained within a walnut orchard canopy during the defoliated phase of the Canopy Horizontal Array Turbulence Study (CHATS) yields periods with stationary within-canopy velocities required by analysis of the bulk drag–wind relationship. The uncertainties in empirical estimates of the bulk drag–wind relationship associated with nonstationarity and finite duration of time series are evaluated. An integral view of various stationarity measures is presented, with a highlight of their links to physical processes.
Abstract
A massively parallel large-eddy simulation (LES) code for planetary boundary layers (PBLs) that utilizes pseudospectral differencing in horizontal planes and solves an elliptic pressure equation is described. As an application, this code is used to examine the numerical convergence of the three-dimensional time-dependent simulations of a weakly sheared daytime convective PBL on meshes varying from 323 to 10243 grid points. Based on the variation of the second-order statistics, energy spectra, and entrainment statistics, LES solutions converge provided there is adequate separation between the energy-containing eddies and those near the filter cutoff scale. For the convective PBL studied, the majority of the low-order moment statistics (means, variances, and fluxes) become grid independent when the ratio zi /(Cs Δ f ) > 310, where zi is the boundary layer height, Δ f is the filter cutoff scale, and Cs is the Smagorinsky constant. In this regime, the spectra show clear Kolmogorov inertial subrange scaling. The bulk entrainment rate determined from the time variation of the boundary layer height we = dzi /dt is a sensitive measure of the LES solution convergence; we becomes grid independent when the vertical grid resolution is able to capture both the mean structure of the overlying inversion and the turbulence. For all mesh resolutions used, the vertical temperature flux profile varies linearly over the interior of the boundary layer and the minimum temperature flux is approximately −0.2 of the surface heat flux. Thus, these metrics are inadequate measures of solution convergence. The variation of the vertical velocity skewness and third-order moments expose the LES’s sensitivity to grid resolution.
Abstract
A massively parallel large-eddy simulation (LES) code for planetary boundary layers (PBLs) that utilizes pseudospectral differencing in horizontal planes and solves an elliptic pressure equation is described. As an application, this code is used to examine the numerical convergence of the three-dimensional time-dependent simulations of a weakly sheared daytime convective PBL on meshes varying from 323 to 10243 grid points. Based on the variation of the second-order statistics, energy spectra, and entrainment statistics, LES solutions converge provided there is adequate separation between the energy-containing eddies and those near the filter cutoff scale. For the convective PBL studied, the majority of the low-order moment statistics (means, variances, and fluxes) become grid independent when the ratio zi /(Cs Δ f ) > 310, where zi is the boundary layer height, Δ f is the filter cutoff scale, and Cs is the Smagorinsky constant. In this regime, the spectra show clear Kolmogorov inertial subrange scaling. The bulk entrainment rate determined from the time variation of the boundary layer height we = dzi /dt is a sensitive measure of the LES solution convergence; we becomes grid independent when the vertical grid resolution is able to capture both the mean structure of the overlying inversion and the turbulence. For all mesh resolutions used, the vertical temperature flux profile varies linearly over the interior of the boundary layer and the minimum temperature flux is approximately −0.2 of the surface heat flux. Thus, these metrics are inadequate measures of solution convergence. The variation of the vertical velocity skewness and third-order moments expose the LES’s sensitivity to grid resolution.
Abstract
Observations from the Southern Ocean Flux Station provide a wide range of wind, buoyancy, and wave (Stokes) forcing for large-eddy simulation (LES) of deep Southern Ocean boundary layers. Almost everywhere there is a nonzero angle Ω between the shear and the stress vectors. Also, with unstable forcing there is usually a depth where there is stable stratification, but zero buoyancy flux and often a number of depths above where there is positive flux, but neutral stratification. These features allow nonlocal transports of buoyancy and of momentum to be diagnosed, using either the Eulerian or Lagrangian shear. The resulting profiles of nonlocal diffusivity and viscosity are quite similar when scaled according to Monin–Obukhov similarity theory in the surface layer, provided the Eulerian shear is used. Therefore, a composite shape function is constructed that may be generally applicable. In contrast, the deeper boundary layer appears to be too decoupled from the Stokes component of the Lagrangian shear. The nonlocal transports can be dominant. The diagnosed across-shear momentum flux is entirely nonlocal and is highly negatively correlated with the across-shear component of the wind stress, just as nonlocal and surface buoyancy fluxes are related. Furthermore, in the convective limit the scaling coefficients become essentially identical, with some consistency with atmospheric experience. The nonlocal contribution to the along-shear momentum flux is proportional to (1 − cosΩ) and is always countergradient, but is unrelated to the aligned wind stress component.
Abstract
Observations from the Southern Ocean Flux Station provide a wide range of wind, buoyancy, and wave (Stokes) forcing for large-eddy simulation (LES) of deep Southern Ocean boundary layers. Almost everywhere there is a nonzero angle Ω between the shear and the stress vectors. Also, with unstable forcing there is usually a depth where there is stable stratification, but zero buoyancy flux and often a number of depths above where there is positive flux, but neutral stratification. These features allow nonlocal transports of buoyancy and of momentum to be diagnosed, using either the Eulerian or Lagrangian shear. The resulting profiles of nonlocal diffusivity and viscosity are quite similar when scaled according to Monin–Obukhov similarity theory in the surface layer, provided the Eulerian shear is used. Therefore, a composite shape function is constructed that may be generally applicable. In contrast, the deeper boundary layer appears to be too decoupled from the Stokes component of the Lagrangian shear. The nonlocal transports can be dominant. The diagnosed across-shear momentum flux is entirely nonlocal and is highly negatively correlated with the across-shear component of the wind stress, just as nonlocal and surface buoyancy fluxes are related. Furthermore, in the convective limit the scaling coefficients become essentially identical, with some consistency with atmospheric experience. The nonlocal contribution to the along-shear momentum flux is proportional to (1 − cosΩ) and is always countergradient, but is unrelated to the aligned wind stress component.
Abstract
Empirical rules for both entrainment and detrainment are developed from LES of the Southern Ocean boundary layer when the turbulence, stratification, and shear cannot be assumed to be in equilibrium with diurnal variability in surface flux and wave (Stokes drift) forcing. A major consequence is the failure of downgradient eddy viscosity, which becomes more serious with Stokes drift and is overcome by relating the angle between the stress and shear vectors to the orientations of Lagrangian shear to the surface and of local Eulerian shear over 5 m. Thus, the momentum flux can be parameterized as a stress magnitude and this empirical direction. In addition, the response of a deep boundary layer to sufficiently strong diurnal heating includes boundary layer collapse and the subsequent growth of a morning boundary layer, whose depth is empirically related to the time history of the forcing, as are both morning detrainment and afternoon entrainment into weak diurnal stratification. Below the boundary layer, detrainment rules give the maximum buoyancy flux and its depth, as well a specific stress direction. Another rule relates both afternoon and nighttime entrainment depth and buoyancy flux to surface layer turbulent kinetic energy production integrals. These empirical relationships are combined with rules for boundary layer transport to formulate two parameterizations; one based on eddy diffusivity and viscosity profiles and another on flux profiles of buoyancy and of stress magnitude. Evaluations against LES fluxes show the flux profiles to be more representative of the diurnal cycle, especially with Stokes drift.
Abstract
Empirical rules for both entrainment and detrainment are developed from LES of the Southern Ocean boundary layer when the turbulence, stratification, and shear cannot be assumed to be in equilibrium with diurnal variability in surface flux and wave (Stokes drift) forcing. A major consequence is the failure of downgradient eddy viscosity, which becomes more serious with Stokes drift and is overcome by relating the angle between the stress and shear vectors to the orientations of Lagrangian shear to the surface and of local Eulerian shear over 5 m. Thus, the momentum flux can be parameterized as a stress magnitude and this empirical direction. In addition, the response of a deep boundary layer to sufficiently strong diurnal heating includes boundary layer collapse and the subsequent growth of a morning boundary layer, whose depth is empirically related to the time history of the forcing, as are both morning detrainment and afternoon entrainment into weak diurnal stratification. Below the boundary layer, detrainment rules give the maximum buoyancy flux and its depth, as well a specific stress direction. Another rule relates both afternoon and nighttime entrainment depth and buoyancy flux to surface layer turbulent kinetic energy production integrals. These empirical relationships are combined with rules for boundary layer transport to formulate two parameterizations; one based on eddy diffusivity and viscosity profiles and another on flux profiles of buoyancy and of stress magnitude. Evaluations against LES fluxes show the flux profiles to be more representative of the diurnal cycle, especially with Stokes drift.
Abstract
Momentum and scalar transport in the marine atmospheric boundary layer (MABL) is driven by a turbulent mix of winds, buoyancy, and surface gravity waves. To investigate the interaction between these processes, a large-eddy simulation (LES) model is developed with the capability to impose a broadband spectrum of time-varying finite-amplitude surface waves at its lower boundary. The LES model adopts a Boussinesq flow model and integrates the governing equations on a time-varying, surface-fitted, nonorthogonal mesh using cell-centered variables with special attention paid to the solution of the pressure Poisson equation near the wavy boundary. Weakly unstable MABLs are simulated with geostrophic winds increasing from 5 to 25 m s−1 and wave age varying from swell-dominated to wind-wave equilibrium. The simulations illustrate cross-scale coupling as wave-impacted near-surface turbulence transitions into shear-convective rolls with increasing distance from the water. In a regime with swell, low winds, and weak heating, wave-induced vertical velocity and pressure signals are readily observed well above the standard reference height ζ a = 10 m. At wind-wave equilibrium, the small-scale wave-induced signals are detectable only near the water surface. Below ζ a , a nearly-constant-flux layer is observed where the momentum flux carried by turbulence, form stress, and subgrid-scale motions shifts with varying wave age and distance above the water. The spectral content of the surface form stress is wave-age dependent, especially at low wavenumbers. The LES wind profiles deviate from Monin–Obukhov similarity theory in nonequilibrium wind-wave conditions, and entrainment is greatly enhanced by shear-induced engulfment events.
Abstract
Momentum and scalar transport in the marine atmospheric boundary layer (MABL) is driven by a turbulent mix of winds, buoyancy, and surface gravity waves. To investigate the interaction between these processes, a large-eddy simulation (LES) model is developed with the capability to impose a broadband spectrum of time-varying finite-amplitude surface waves at its lower boundary. The LES model adopts a Boussinesq flow model and integrates the governing equations on a time-varying, surface-fitted, nonorthogonal mesh using cell-centered variables with special attention paid to the solution of the pressure Poisson equation near the wavy boundary. Weakly unstable MABLs are simulated with geostrophic winds increasing from 5 to 25 m s−1 and wave age varying from swell-dominated to wind-wave equilibrium. The simulations illustrate cross-scale coupling as wave-impacted near-surface turbulence transitions into shear-convective rolls with increasing distance from the water. In a regime with swell, low winds, and weak heating, wave-induced vertical velocity and pressure signals are readily observed well above the standard reference height ζ a = 10 m. At wind-wave equilibrium, the small-scale wave-induced signals are detectable only near the water surface. Below ζ a , a nearly-constant-flux layer is observed where the momentum flux carried by turbulence, form stress, and subgrid-scale motions shifts with varying wave age and distance above the water. The spectral content of the surface form stress is wave-age dependent, especially at low wavenumbers. The LES wind profiles deviate from Monin–Obukhov similarity theory in nonequilibrium wind-wave conditions, and entrainment is greatly enhanced by shear-induced engulfment events.
Abstract
This manuscript describes numerical experiments investigating the influence of 2–30-km striplike heterogeneity on wet and dry convective boundary layers coupled to the land surface. The striplike heterogeneity is shown to dramatically alter the structure of the convective boundary layer by inducing significant organized circulations that modify turbulent statistics. The impact, strength, and extent of the organized motions depend critically on the scale of the heterogeneity λ relative to the boundary layer height zi . The coupling with the land surface modifies the surface fluxes and hence the circulations resulting in some differences compared to previous studies using fixed surface forcing. Because of the coupling, surface fluxes in the middle of the patches are small compared to the patch edges. At large heterogeneity scales (λ/zi ∼18) horizontal surface-flux gradients within each patch are strong enough to counter the surface-flux gradients between wet and dry patches allowing the formation of small cells within the patch coexisting with the large-scale patch-induced circulations. The strongest patch-induced motions occur in cases with 4 < λ/zi < 9 because of strong horizontal pressure gradients across the wet and dry patches. Total boundary layer turbulence kinetic energy increases significantly for surface heterogeneity at scales between λ/zi = 4 and 9; however, entrainment rates for all cases are largely unaffected by the striplike heterogeneity.
Velocity and scalar fields respond differently to variations of heterogeneity scale. The patch-induced motions have little influence on total vertical scalar flux, but the relative contribution to the flux from organized motions compared to background turbulence varies with heterogeneity scale. Patch-induced motions are shown to dramatically impact point measurements in a free-convective boundary layer. The magnitude and sign of this impact depends on the location of the measurement within the region of heterogeneity.
Abstract
This manuscript describes numerical experiments investigating the influence of 2–30-km striplike heterogeneity on wet and dry convective boundary layers coupled to the land surface. The striplike heterogeneity is shown to dramatically alter the structure of the convective boundary layer by inducing significant organized circulations that modify turbulent statistics. The impact, strength, and extent of the organized motions depend critically on the scale of the heterogeneity λ relative to the boundary layer height zi . The coupling with the land surface modifies the surface fluxes and hence the circulations resulting in some differences compared to previous studies using fixed surface forcing. Because of the coupling, surface fluxes in the middle of the patches are small compared to the patch edges. At large heterogeneity scales (λ/zi ∼18) horizontal surface-flux gradients within each patch are strong enough to counter the surface-flux gradients between wet and dry patches allowing the formation of small cells within the patch coexisting with the large-scale patch-induced circulations. The strongest patch-induced motions occur in cases with 4 < λ/zi < 9 because of strong horizontal pressure gradients across the wet and dry patches. Total boundary layer turbulence kinetic energy increases significantly for surface heterogeneity at scales between λ/zi = 4 and 9; however, entrainment rates for all cases are largely unaffected by the striplike heterogeneity.
Velocity and scalar fields respond differently to variations of heterogeneity scale. The patch-induced motions have little influence on total vertical scalar flux, but the relative contribution to the flux from organized motions compared to background turbulence varies with heterogeneity scale. Patch-induced motions are shown to dramatically impact point measurements in a free-convective boundary layer. The magnitude and sign of this impact depends on the location of the measurement within the region of heterogeneity.
