L. Mahrt

Surface Heterogeneity and Vertical Structure of the Boundary Layer

The concepts of vertical structure of the boundary layer over homogeneous surfaces are discussed, including the roughness sublayer, surface layer (inertial layer) and outer layer. As an interpretive literature survey, the vertical depth of the influence of surface heterogeneity, relative to such vertical structure, is examined in terms of blending height theory, convective boundary-layer scaling and internal boundary-layer theory.These concepts are examined with data over different surface types. The rich variety of types of surface heterogeneity and background flow preclude description of their influence on the boundary layer by one single approach. Nonetheless, new scaling arguments offer promise for convective conditions.Internal boundary layers are found to form only in certain situationsand even then may exhibit more diffuse vertical structure comparedto the textbook internal boundary layer. New scaling arguments aredeveloped to describe the potential for internal boundary-layerdevelopment in flow of warm air over a cooler surface. These argumentsexplain some aspects of the observations but remain incomplete.

An observational study of the structure of the nocturnal boundary layer

In an effort to describe the basic vertical structure of the nocturnal boundary layer, observations from four experiments are analyzed. During the night, the depth of significant cooling appears to increase with time while the depth of the turbulence and height of the low level wind maximum tend to remain constant or decrease with time. Since the inversion layer extends above the low level wind maximum and shear is small in the region of the low level jet, the Richardson number reaches a maximum at the jet level and then decreases again with height. As a result, turbulence is observed to be a minimum at the height of the low level wind maximum and then increases again above this height.

Observations of Fluxes and Inland Breezes over a Heterogeneous Surface

Abstract Repeated aircraft runs at about 33 m over heterogeneous terrain are analyzed to study the spatial variability of the mesoscale flow and turbulent fluxes. An irrigated area, about 12 km across, generates a relatively cool moist inland breeze. As this air flows out over the warmer, drier surrounding land surface, an internal boundary layer develops within the inland breeze, which then terminates at a well-defined inland breeze front located about 1½ km downstream from the change of surface conditions. This front is defined by horizontal convergence, rising motion, and sharp spatial change of moisture, carbon dioxide, and ozone. Both a scale analysis and the observations suggest that the overall vertical motion associated with the inland breeze is weak. However, the observations indicate that this vertical motion and attendant vertical transport are important in the immediate vicinity of the front, and the inland breeze does lead to significant modification of the turbulent flux. In the inland breez...

Observations of fluxes over heterogeneous surfaces

This study analyzes data collected from repeated aircraft runs 30 m over alternating regions of irrigated and dry nonirrigated surfaces, each region on the order of 10 km across, during the California Ozone Deposition Experiment (CODE). After studying the scale dependence of the flow, the variables and their fluxes are decomposed into means for sublegs defined in terms of irrigated and nonirrigated regions and deviations from such subleg means. Since the repeated runs were flown over the same track, compositing the eight flight legs for each of the two days allows partial isolation of the influences of surface heterogeneity and transient mesoscale motions.A variance analysis is carried out to quantify the relative importance of surface heterogeneity and transient mesoscale motions on the variability of the turbulence fluxes. The momentum and ozone fluxes are more influenced by transient mesoscale motions while fluxes of heat, moisture and carbon dioxide are more influenced by surface heterogeneity. The momentum field is also influenced by a quasi-stationary mesoscale front and larger scale velocity gradients.For the present case, the mesoscale modulation of the turbulent flux is numerically more important than the direct mesoscale flux. This spatial modulation of the turbulent fluxes leads to extra Reynolds terms which act to reduce the area-averaged turbulent momentum flux and enhance the area-averaged turbulent heat flux.

Flux decomposition into coherent structures

This study examines the intermittency of the momentum flux near the surface and the relation of such intermittency to coherent structures. Toward this goal, variances and covariances are decomposed into coherent structures and less coherent activity. The sampled structures are identified using the Haar transform and then decomposed into eigenvectors of the lagged covariance matrix.The methodology is applied to the momentum flux for a relatively stationary 50-h period of strong winds measured from a 45 m tower in the Lammefjord Experiment. Events of sinking motion with strong horizontal momentum account for the majority of the flux. Such sweeping motions arrive as gust microfronts. The large momentum flux is associated with strong coherent fluctuations of the longitudinal wind component and high correlation with relatively modest fluctuations of vertical motion. In the heated case (HAPEX), a phase lag between the vertical and horizontal velocity fluctuations leads to less efficient momentum transport by the main coherent structures.The event nature of the flux is used to formulate an expression for the flux error due to sampling problems. Estimation of the momentum flux requires a significantly longer record than for the heat flux. Modulation of the flux by mesoscale variations also affects the sampling strategy.

Determination of the surface drag coefficient

This study examines the dependence of the surface drag coefficienton stability, wind speed, mesoscale modulation of the turbulent flux and method of calculation of the drag coefficient. Data sets over grassland, sparse grass, heather and two forest sites are analyzed. For significantly unstable conditions, the drag coefficient does not depend systematically on z/L but decreases with wind speed for fixed intervals of z/L, where L is the Obukhov length. Even though the drag coefficient for weak wind conditions is sensitive to the exact method of calculation and choice of averaging time, the decrease of the drag coefficient with wind speed occurs for all of the calculation methods. A classification of flux calculation methods is constructed, which unifies the most common previous approaches.The roughness length corresponding to the usual Monin–Obukhovstability functions decreases with increasing wind speed. This dependence on wind speed cannot be eliminated by adjusting the stability functions. If physical, the decrease of the roughness length with increasing wind speed might be due to the decreasing role of viscous effectsand streamlining of the vegetation, although these effects cannot be isolated from existing atmospheric data.For weak winds, both the mean flow and the stress vector often meander significantly in response to mesoscale motions. The relationship between meandering of the stress and wind vectors is examined. For weak winds, the drag coefficient can be sensitive to the method of calculation, partly due to meandering of the stress vector.

Relationship of surface heat flux to microscale temperature variations: Application to boreas

The surface heat flux is normally parameterized in terms of the difference between the air temperature and the surface radiative temperature, or equivalently, the temperature computed from the surface energy balance. In this note, the relationship between the heat flux and the air-surface temperature difference is shown to be sensitive to the microscale variability of the surface radiation temperature caused by differences between the well-ventilated tree tops and less ventilated ground surface. This conclusion is based on surface and aircraft data collected during the Boreal Ecosystem-Atmosphere Study (BOREAS). For this case, the heat flux cannot be predicted by adjusting the thermal roughness height. As an alternative, the aerodynamic temperature can be related to a weighted average of the surface radtation temperature analogous to application of a simple canopy model. Here, the total heat flux is the sum of the heat fluxes from each individual surface type weighted by the area-fractional coverage.

Formulation of Turbulent Fluxes in the Stable Boundary Layer

Abstract The mixing lengths for heat and momentum are computed from seven levels of eddy correlation data during the Cooperative Atmosphere–Surface Exchange Study-1999 (CASES-99). A number of formulations of the mixing length are evaluated, including surface layer similarity theory, several hybrid similarity theories, a formulation based on the Richardson number, and a formulation based on the local shear. A formulation of the mixing length is examined, which approaches z-less similarity for large z and surface layer similarity close to the ground surface. A generalized version includes a dependence on boundary layer depth, which approaches the usual boundary layer height dependence for neutral conditions. However, for many of the observational cases, a boundary layer did not exist in the usual sense, in that turbulence was generated primarily above the surface inversion layer and occasionally extended downward toward the surface. For these cases, inclusion of z-less turbulence is crucial.

Spatial variations of surface moisture flux from aircraft data

Abstract This study surveys the existing conceptual views of the influence of surface heterogeneity on spatial variability of fluxes into the atmosphere, and constructs an approach for using low-level aircraft to measure spatial variations of the surface moisture flux. This approach is applied to Canadian Twin Otter aircraft data collected during the Southern Great Plains Experiment. The response of turbulent moisture fluxes to surface heterogeneity is reduced by horizontal mixing by the turbulent eddies. During the evolution of the daytime convective boundary layer, the eddy size increases and the spatial variation of the moisture flux into the atmosphere is confined to larger horizontal scales. The influence of the surface heterogeneity on moisture fluxes into the atmosphere is framed here in terms of a horizontal blending scale, which can be used as guidance for partitioning the aircraft track. Problems with the estimation of the spatial variability of surface moisture fluxes from aircraft eddy correlation data are examined. Obtaining an adequate sample size of the moisture fluxes over heterogeneous surfaces is considerably more difficult than over homogeneous surfaces. Sampling requirements determine the maximum spatial resolution of the measured surface fluxes. The time-dependence of the spatial variation of the surface moisture flux is even more difficult to estimate since simple compositing of different aircraft passes would eliminate the time-dependence. A new scheme for estimating the time–space dependence of surface fluxes is developed. As an application example, this method is used to show that the evaporative fraction varies only slowly from morning to afternoon for the surface types examined here.

Heat Flux in the Coastal Zone

Various difficulties with application of Monin–Obukhov similarity theory are surveyed including the influence of growing waves, advection and internal boundary-layer development. These complications are normally important with offshore flow. The transfer coefficient for heat is computed from eddy correlation data taken at a mast two kilometres off the Danish coast in RASEX. For these coastal zone data, the thermal roughness length shows no well-defined relation to the momentum roughness length or roughness Reynolds number, in contrast to previous theories. The variation of the momentum roughness length is dominated by wave state. In contrast, the thermal roughness length shows significant dependence on wave state only for small values of wave age where the mixing is apparently enhanced by wave breaking. The development of thin internal boundary layers with offshore flow substantially reduces the heat transfer and thermal roughness length but has no obvious influence on momentum roughness length. A new formulation of the thermal roughness length based on the internal boundary-layer depth is calibrated to the RASEX data. For the very stable case, the turbulence is mainly detached from the surface and existing formulations do not apply.As an alternative to adjusting the thermal roughness length, the transfer coefficient is related directly to the stability and the internal boundary-layer depth. This avoids specification of roughness lengths resulting from the usual integration of the non-dimensional temperature function. The resulting stability function is simpler than previous ones and satisfies free convection similarity theory without introduction of the gustiness factor. The internal boundary layer also influences the moisture transfer coefficient.