A simple model of the atmospheric boundary layer; sensitivity to surface evaporation

A simple formulation of the boundary layer is developed for use in large-scale models and other situations where simplicity is required. The formulation is suited for use in models where some resolution is possible within the boundary layer, but where the resolution is insufficient for resolving the detailed boundary-layer structure and overlying capping inversion. Surface fluxes are represented in terms of similarity theory while turbulent diffusivities above the surface layer are formulated in terms of bulk similarity considerations and matching conditions at the top of the surface layer. The boundary-layer depth is expressed in terms of a bulk Richardson number which is modified to include the influence of thermals. Attention is devoted to the interrelationship between predicted boundary-layer growth, the turbulent diffusivity profile, countergradient heat flux and truncation errors.The model predicts growth of the convectively mixed layer reasonably well and is well-behaved in cases of weak surface heat flux and transitions between stable and unstable cases. The evolution of the modelled boundary layer is studied for different ratios of surface evaporation to potential evaporation. Typical variations of surface evaporation result in a much greater variation in boundary-layer depth than that caused by the choice of the boundary-layer depth formulation.     

Boundary-Layer Adjustment Over Small-Scale Changes of Surface Heat Flux

Four months of eddy correlation data collected over a grass field and a nearby sage brush community are analyzed to examine the adjustment of the boundary-layer structure as it flows from the heated brush to the snow-covered grass. The grass site includes a 34-m tower with seven levels of eddy correlation data. The midday heat flux over the snow-covered grass and bare ground surfaces is often downward particularly with melting conditions, while the corresponding heat flux over the brush is almost always upward. For most of these cases, a stable internal boundary layer over the snow is well defined in terms of vertical profiles of the buoyancy flux over the snow-covered grass. The stable internal boundary layer is generally embedded within a deeper layer of flux divergence corresponding to increasing upward heat flux with height above the internal boundary layer. With thin snow cover, the surface heat flux over the grass is weak upward due to heating of grass protruding above the snow so that the flow adjusts to a decrease of the upward surface heat flux in the downwind direction. This common case of an adjusting boundary layer contrasts with the formation of an internal boundary layer due to a change of sign of the surface heat in flux the downwind direction. The adjustment of the boundary layer to the decrease of the surface heat flux leads to vertical divergence of the upward heat flux in contrast to the usual heated boundary layer over homogeneous surfaces. The consequences of the cooling due to the vertical divergence of the heat flux are discussed in terms of the heat budget of the adjusting and internal boundary layers.     

Surface energy balance,parameterizations of boundary-layer heights and the application of resistance laws near an Antarctic Ice Shelf front

A study of the surface energy balance with turbulent fluxes obtained by the Monin-Obukhov similarity theory and a comparison with results for resistance laws are presented for the strong baroclinic conditions in the vicinity of the Filchner/Ronne Ice Shelf front. The data are taken from a field experiment in the Antarctic summer season 1983/84. For the first time in the coastal Antarctic region, this data set comprises synchronous energy balance measurements over the polynya and the ice shelf together with soundings of the boundary layer, yielding vertical profiles of the wind velocity and temperature over the ice shelf, at the ice shelf front and over the polynya.Over the ice shelf, the radiation balance is the largest component of the energy fluxes and is mainly compensated by the subsurface energy flux and the turbulent heat flux in the daily mean. Over the polynya, turbulent fluxes of sensible and latent heat lead to large energy losses of the water surface in the night-time and in situations of very low air temperatures.Different parameterizations for boundary-layer height are compared using tethered sonde and energy balance measurements. With the height of the inversion base over the polynya and the height of the critical bulk Richardson number over the ice shelf, external parameters for the application of resistance laws were determined. The comparison of turbulent surface fluxes obtained by the energy balance measurements and by the resistance laws shows good agreement for the convective conditions over the polynya. For the stably stratified boundary layer over the ice shelf with small amounts of the turbulent heat flux, the deviation is large for the case of a cold air outflow with a superposed inertial oscillation.     

Mean Profiles of Moisture Fluxes in Snow-Filled Boundary Layers

Profiles of moisture fluxes have been examined for convective boundary layers containing clouds and snow, using data derived from aircraft measurements taken on four dates during the 1983/1984 University of Chicago lake-effect snow project. Flux profiles were derived from vertical stacks of aircraft cross-wind flight legs taken at various heights over Lake Michigan near the downwind shore. It was found that, if ice processes are taken into account, profiles of potential temperature and water content were very similar to those presented in past studies of convective boundary layers strongly heated from below. Profiles of total water content and equivalent potential temperature adjusted for ice were nearly invariant with height, except very near the top of the boundary layer, suggesting that internal boundary-layer mixing processes were rapid relative to the rates at which heat and vapour were transported into the boundary layer through entrainment and surface fluxes. Ice was found to play a significant, measurable role in boundary-layer moisture fluxes. It was estimated that 40 to 57% of the upward vapour flux was returned to the surface in the form of snow, converting about 45 to 64% of the surface latent heat flux into sensible heat in the snow-producing process. Assuming advective fluxes are relatively small (thought to be appropriate after the first few tens of km over the lake as suggested by past studies), the boundary layer was found to warm at a rate faster than could be explained by surface heat fluxes and latent heat releases alone, the remainder of the heating presumably coming from radiational processes and entrainment. Discussions of moisture phase change processes throughout the boundary layer and estimates of errors of these flux measurements are presented.     

Boundary-layer modification in wintertime cold-air outbreaks from the Arctic sea ice

During the field experiment ARKTIS 1993 ten cases of boundary-layer modification in wintertime cold-air outbreaks from the Arctic sea ice in the Spitsbergen region were observed by aircraft over a distance ranging from about 50 km over the ice to about 300 km over the water. The modification depends decisively on the initial conditions over the ice, the boundary conditions at the bottom and top of the boundary layer and on the conditions of the large-scale flow. The modification of the bulk boundary-layer characteristics in relation to these conditions is presented.Besides the air-sea temperature contrast, the most important role for the boundary-layer modification is played by the stability on top of the boundary layer and by the divergence of the large-scale flow. According to the high variability of these conditions the observed boundary-layer modifications were very variable ranging from 100 to 300 m thick boundary layers with air temperatures between -32 and -22 °C over the ice to thicknesses between 900 and 2200 m and air temperatures between -15 and -5 °C after 300 km fetch over the open water. In most cases the large-scale flow was anticyclonic and divergent over the ice and changed to cyclonic and convergent over the water and an ice-sea breeze was superimposed on it.The sensible and latent heat fluxes are the dominant terms in the surface energy budget over the open water and ranged between 200 and 700 W m^-2 whereas the net longwave radiation is the dominating term over the ice with the heat fluxes only about 10 W m^-2.     

On the Temperature and Humidity Dissimilarity in the Marine Surface Layer

The dissimilarity of temperature and humidity transfer in the marine surface layer (MSL) is investigated through the relative transport efficiency and correlation coefficient of these two scalars. We examine their variability and relationship with mean values, as well as spectral characteristics. It is shown that the dissimilarity between these two scalars in the MSL is a function of stability, the boundary-layer depth, and flow steadiness. In general the temperature and humidity are less correlated in shallow marine boundary layers compared to deep marine boundary layers, due to the stronger impact of the boundary-layer scale in breaking the “same source, same sink” assumption for scalar similarity. This is supported by the combination of our spectral analysis of scalar fluxes and corresponding measured and modelled boundary-layer depth. This assumption is also broken in near-neutral conditions, when there is an efficient latent heat transfer but negligible sensible heat transfer. Our data suggest that parametrization of humidity fluxes via similarity theory could still be reliable when the correlation coefficient $>$ 0.5, and in near-neutral conditions the humidity flux can be estimated without use of the sensible heat flux.     

Airborne Measurements in the Stable Boundary Layer over the Larsen Ice Shelf,Antarctica

We present aircraft measurements of boundary-layer structure and surface turbulent fluxes from a flight over the Larsen Ice Shelf, Antarctica. Warm advection, associated with föhn flow, led to the formation of a stable boundary layer over the ice shelf, with a well-defined low-level jet at the top of the surface inversion. The strong shear associated with the jet kept the gradient Richardson number small and maintained a turbulent boundary layer over a depth of at least 600 m. The net surface energy balance amounted to 52 Wm^?2, equivalent to a melt rate of 13 mm water per day, with net radiation (48 Wm^?2) making the largest contribution to melt. The contribution from the sensible heat flux (13 Wm^?2) was largely balanced by an upwards latent heat flux (?9 Wm^?2). These measurements provide insight into the processes that control surface melt rates in an area that has experienced recent rapid warming and deglaciation.     

On the Effect of Surface Heat-Flux Heterogeneities on the Mixed-Layer-Top Entrainment

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

The temperature structure in a stably stratified internal boundary layer over a cold sea

Data from the Öresund experiment are used to investigate the structure of the stably stratified internal boundary layer (SIBL) which develops when warm air is advected from a heated land surface over a cooler sea. The present study is based on a theory developed by Stull (1983a, b, c). He proposed that the turbulence and the mean structure of the nocturnal boundary layer is controlled by the time-integrated value of surface heat flux and that the instantaneous heat flux is of less importance.Dimensional arguments are used to define simple, physically consistent, temperature, velocity and length scales. The dimensionless surface heat flux has a high value immediately downwind of the shoreline and it decreases rapidly in magnitude with increasing distance from the coast. Farther away, it is essentially constant. The dimensionless potential temperature change exhibits an exponential profile. It is estimated that turbulence accounts for 71% of boundary-layer cooling while clear-air radiational cooling is responsible for the remaining 29%.Finally it is found that theoretical predictions for the height of the SIBL are in a good agreement with observations.     

Wind-Tunnel Simulation of Weakly and Moderately Stable Atmospheric Boundary Layers

The simulation of horizontally homogeneous boundary layers that have characteristics of weakly and moderately stable atmospheric flow is investigated, where the well-established wind engineering practice of using ‘flow generators’ to provide a deep boundary layer is employed. Primary attention is given to the flow above the surface layer, in the absence of an overlying inversion, as assessed from first- and second-order moments of velocity and temperature. A uniform inlet temperature profile ahead of a deep layer, allowing initially neutral flow, results in the upper part of the boundary layer remaining neutral. A non-uniform inlet temperature profile is required but needs careful specification if odd characteristics are to be avoided, attributed to long-lasting effects inherent of stability, and to a reduced level of turbulent mixing. The first part of the wind-tunnel floor must not be cooled if turbulence quantities are to vary smoothly with height. Closely horizontally homogeneous flow is demonstrated, where profiles are comparable or closely comparable with atmospheric data in terms of local similarity and functions of normalized height. The ratio of boundary-layer height to surface Obukhov length, and the surface heat flux, are functions of the bulk Richardson number, independent of horizontal homogeneity. Surface heat flux rises to a maximum and then decreases.     

A Numerical Study of Sea-Fog Formation over Cold Sea Surface Using a One-Dimensional Turbulence Model Coupled with the Weather Research and Forecasting Model

The formation mechanism of a cold sea-fog case observed over the Yellow Sea near the western coastal area of the Korean Peninsula is investigated using numerical simulation with a one-dimensional turbulence model coupled with a three-dimensional regional model. The simulation was carried out using both Eulerian and Lagrangian approaches; both approaches produced sea fog in a manner consistent with observation. For the selected cold sea-fog case, the model results suggested the following: as warm and moist air flows over a cold sea surface, the lower part of the air column is modified by the turbulent exchange of heat and moisture and the diurnal variation in radiation. The modified boundary-layer structure represents a typical stable thermally internal boundary layer. Within the stable thermally internal boundary layer, the air temperature is decreased by radiative cooling and turbulent heat exchange but the moisture loss due to the downward vapour flux in the lowest part of the air column is compensated by moisture advection and therefore the dewpoint temperature does not decrease as rapidly as does the air temperature. Eventually water vapour saturation is achieved and the cold sea fog forms in the thermal internal boundary layer.     

Large-eddy simulations of thermally forced circulations in the convective boundary layer. Part I: A small-scale circulation with zero wind

We have conducted large-eddy simulations (LES) of the atmospheric boundary layer with surface heat flux variations on a spatial scale comparable to the boundary layer depth.We first ran a simulation with a horizontally homogeneous heat flux. In general the results are similar to those of previous large-eddy simulations. The model simulates a field of convective eddies having approximately the correct velocity and spatial scales, and with the crucial property that kinetic energy is transported vigorously upwards through the middle levels. However, the resolved temperature variance is only about half what is observed in the laboratory or the atmosphere. This deficiency — which is shared by many other large-eddy simulations — has dynamic implications, particularly in the pressure/temperature interaction terms of the heat flux budget. Recent simulations by other workers at much higher resolution than ours appear to be more realistic in this respect.The surface heat flux perturbations were one-dimensional and sinusoidal with a wavelength equal to 1.3 times the boundary-layer depth. The mean wind was zero. Results were averaged over several simulations and over time. There is a mean circulation, with ascent over the heat flux maxima (vertical velocity ~0.1w _*) and descent over the heat flux minima. Turbulence is consistently stronger over the heat flux maxima. The horizontal velocity variance components (calculated with respect to the horizontal average) become unequal, implying that convective eddies are elongated parallel to the surface heat flux perturbations.A consideration of the budgets for temperature and velocity suggests several simplifying concepts.The research reported in this paper was conducted while the first author was on study leave at Colorado State University.     

A Sensitivity Study of Arctic Ice-Ocean Heat Exchange to the Three-Equation Boundary Condition Parametrization in CICE6

In this study, we perform a stand-alone sensitivity study using the Los Alamos Sea ice model version 6 (CICE6) to investigate the model sensitivity to two Ice-Ocean (IO) boundary condition approaches. One is the two-equation approach that treats the freezing temperature as a function of the ocean mixed layer (ML) salinity, using two equations to parametrize the IO heat exchanges. Another approach uses the salinity of the IO interface to define the actual freezing temperature, so an equation describing the salt flux at the IO interface is added to the two-equation approach, forming the so-called three-equation approach. We focus on the impact of the three-equation boundary condition on the IO heat exchange and associated basal melt/growth of the sea ice in the Arctic Ocean. Compared with the two-equation simulation, our three-equation simulation shows a reduced oceanic turbulent heat flux, weakened basal melt, increased ice thickness, and reduced sea surface temperature (SST) in the Arctic. These impacts occur mainly at the ice edge regions and manifest themselves in summer. Furthermore, in August, we observed a downward turbulent heat flux from the ice to the ocean ML in two of our three-equation sensitivity runs with a constant heat transfer coefficient (0.006), which caused heat divergence and congelation at the ice bottom. Additionally, the influence of different combinations of heat/salt transfer coefficients and thermal conductivity in the three-equation approach on the model simulated results is assessed. The results presented in this study can provide insight into sea ice model sensitivity to the three-equation IO boundary condition for coupling the CICE6 to climate models.     

Large-eddy simulations of thermally forced circulations in the convective boundary layer. Part II: The effect of changes in wavelength and wind speed

This paper extends previous large-eddy simulations of the convective boundary layer over a surface with a spatially varying sensible heat flux. The heat flux variations are sinusoidal and one-dimensional. The wavelength is 1500 or 4500 m (corresponding to 1.3 and 3.8 times the boundary-layer depth, respectively) and the wind speed is 0, 1 or 2 m s^-1.In every case the heat flux variation drives a mean circulation. As expected, with zero wind there is ascent over the heat flux maxima. The strength of the circulation increases substantially with an increase in the wavelength of the perturbation. A light wind weakens the circulation drastically and moves it downwind. The circulation has a significant effect on the average concentration field from a simulated, elevated source.The heat flux variation modulates turbulence in the boundary layer. Turbulence is stronger (in several senses) above or downwind of the heat flux maxima than it is above or downwind of the heat flux minima. The effect remains significant even when the mean circulation is very weak. There are effects too on profiles of horizontal-average turbulence statistics. In most cases the effects would be undetectable in the atmosphere.We consider how the surface heat flux variations penetrate into the lower and middle boundary layer and propose that to a first approximation the process resembles passive scalar diffusion.The research reported in this paper was conducted while the first author was on study leave at Colorado State University.     

Estimation of the average surface heat flux over an inhomogeneous terrain from the vertical velocity variance

An indirect method of estimating the surface heat flux from observations of vertical velocity variance at the lower mid-levels of the convective atmospheric boundary layer is described. Comparison of surface heat flux estimates with those from boundary-layer heating rates is good, and this method seems to be especially suitable for inhomogeneous terrain for which the surface-layer profile method cannot be used.     

Analysis of Vertical Turbulent Heat Flux Limit in Stable Conditions with a Local Equilibrium, Turbulence Closure Model

Assuming that the vertical turbulent heat flux vanishes at extremely stable conditions, one should expect its maximal absolute value to occur somewhere at moderate stability, between a neutral and extremely stable equilibrium. Consequently, in some situations duality of solutions may be encountered (e.g. two different values of temperature difference associated with the same values of heat flux and wind speed). A quantitative analysis of this feature with a local equilibrium Reynolds-stress model is presented. The fixed-wind / fixed-shear maximum has been identified both in the bulk and in single-point flux–gradient relationships (that is, in the vertical temperature gradient and wind-shear parameter domain). The value of the Richardson number corresponding to this maximum is derived from the model equations. To study the possible feedback in strongly stable conditions, weak and intense cooling scenarios have been simulated with a one-dimensional numerical, high-resolution atmospheric boundary-layer model. Despite the rapid cooling, flow decoupling at the surface has not been observed; instead, a stability-limited heat flux is maintained, with a gradual increase of the Richardson number towards the top of the turbulent layer, with some signs of oscillatory behaviour at intermediate heights. Vertical changes of wind shear and the Brunt–Väisälä frequency display a remarkably non-monotonic character, with some signs of a gradually developing instability.     

On the Structure and Adjustment of Inversion-Capped Neutral Atmospheric Boundary-Layer Flows: Large-Eddy Simulation Study

A range of large-eddy simulations, with differing free atmosphere stratification and zero or slightly positive surface heat flux, is investigated to improve understanding of the neutral and near-neutral, inversion-capped, horizontally homogeneous, barotropic atmospheric boundary layer with emphasis on the upper region. We find that an adjustment time of at least 16 h is needed for the simulated flow to reach a quasi-steady state. The boundary layer continues to grow, but at a slow rate that changes little after 8 h of simulation time. A common feature of the neutral simulations is the development of a super-geostrophic jet near the top of the boundary layer. The analytical wind-shear models included do not account for such a jet, and the best agreement with simulated wind shear is seen in cases with weak stratification above the boundary layer. Increasing the surface heat flux decreases the magnitude and vertical extent of the jet and leads to better agreement between analytical and simulated wind-speed profiles. Over a range of different inversion strengths and surface heat fluxes, we also find good agreement between the performed simulations and models of the equilibrium boundary-layer height, and of the budget of turbulent kinetic energy integrated across the boundary layer.     

Mesoscale moisture variability and its impact on energy transfer through the boundary layer

The impact of mesoscale moisture variability on the vertical energy transfer through a pre-frontal boundary layer is studied with NOPEX aircraft data. The moisture variability relates to a cold front that passed the area 2 1/2 hours after the observations. We find a density front ahead of the cold front. The large vertical divergence of the turbulent moisture flux in the surface layer is partly related to this moisture variability. Large scale horizontal advection contributes to the observed vertical turbulent flux divergence. The estimated horizontal mesoscale advection term in the budget of sensible heat and moisture is on average small but locally it can be large. This term acts to re-distribute moisture in the boundary layer and leads to sub-grid variations of relative humidity, which is an important quantity for boundary-layer cloud models. The distinct spatial variations of specific humidity are mainly related to synoptic forcing and not to heterogeneity in the surface energy balance.     

A moving grid finite-element model of the bulk properties of the atmospheric boundary layer

A moving-grid finite-element model has been developed to model numerically the vertically integrated properties of the atmospheric boundary layer (ABL) in one dimension. The model equations for mean wind velocity and potential temperature are combined with a surface energy budget and predictive equations for boundary-layer height to simulate both stable and unstable ABLs. The nodal position defining the top of the boundary layer is one of the model unknowns and is determined by boundary-layer dynamics. The finite-element method, being an integral method, has advantages of accurate representation of both bulk values and their vertical derivatives, the latter being essential properties of the nocturnal boundary layer. Compared with observations and results of other models, the present model predicts bulk properties very well while retaining a simple and economical form.Journal Paper No. J-12996 of the Iowa Agriculture and Home Economics Experiment Station, Ames, Iowa, Project No. 2779.     

The influence of convergence movement on turbulent transportation in the atmospheric boundary layer

Classical turbulent K closure theory of the atmospheric boundary layer assumes that the vertical turbulent transport flux of any macroscopic quantity is equivalent to that quantity‘s vertical gradient transport flux. But a cross coupling between the thermodynamic processes and the dynamic processes in the atmospheric system is demonstrated based on the Curier-Prigogine principle of cross coupling of linear thermodynamics. The vertical turbulent transportation of energy and substance in the atmospheric boundary layer is related not only to their macroscopic gradient but also to the convergence and the di-vergence movement. The transportation of the convergence or divergence movement is important for the atmospheric boundary layer of the heterogeneous underlying surface and the convection boundary layer.Based on this, the turbulent transportation in the atmospheric boundary layer, the energy budget of the heterogeneous underlying surface and the convection boundary layer, and the boundary layer parameteri-zation of land surface processes over the heterogeneous underlying surface are studied. This research offers clues not only for establishing the atmospheric boundary layer theory about the heterogeneous underlying surface, but also for overcoming the difficulties encountered recently in the application of the atmospheric boundary layer theory.