Flux-profile Relationships for Wind Speed and Temperature in the Stable Atmospheric Boundary Layer

Wind and temperature profiles in the stable boundary layer were analyzed in the context of MoninObukhov similarity. The measurements were made on a 60-m tower in Kansas during October 1999 (CASES-99). Fluxprofile relationships, obtained from these measurements in their integral forms, were established for wind speed and temperature. Use of the integral forms eliminates the uncertainty and accuracy issues resulting from gradient computations. The corresponding stability functions, which were nearly the same for momentum and virtual sensible heat, were found to exhibit different features under weakly stable conditions compared to those under strongly stable conditions. The gradient stability functions were found to be linear, namely _m = 1+ 5.8 and _h = 1 + 5.4 up to a limit of the MoninObukhov stability parameter = 0.8; this is consistent with earlier findings. However, for stronger stabilities beyond a transition range, both functions were observed gradually to approach a constant, with a value of approximately 7. To link these two distinct regimes, a general but pliable functional form with only two parameters is proposed for the stability functions, covering the entire stability range from neutral to very stable conditions.     

Convective Profile Constants Revisited

This paper examines the interpolation betweenBusinger–Dyer (Kansas-type) formulae,_u = (1 -1 6 )^-1/4 and_t = (1 - 16 )^-1/2, and free convection forms. Based on matching constraints, the constants, a_u and a_t, in the convective flux-gradient relations, _u = (1 - a_u )^-1/3 and _t = (1 - a_t )^-1/3, are determined. It isshown that a_u and a_t cannot be completely independent if convective forms are blended with theKansas formulae. In other words, these relationships already carryinformation about a_u and a_t. This follows because the Kansas relations cover a wide stability range (up to = - 2), which includes a lower part of the convective sublayer (about 0.1 < - < 2). Thus, there is a subrange where both Kansas and convective formulae are valid. Matching Kansas formulae and free convection relations within thesubrange 0.1 < - < 2 and independently smoothing ofthe blending function are used to determine a_u and a_t. The values a_u = 10 for velocity and a_t = 34for scalars (temperature and humidity) give a good fit. This new approacheliminates the need for additional independent model constants and yields a`smooth' blending between Kansas and free-convection profileforms in the COARE bulk algorithm.     

Interpolation between Businger–Dyer Formulae and Free Convection Forms: A Revised Approach

In this study, profile functions for flux calculations during unstable conditions are proposed and examined. These functions are based on a direct interpolation for the dimensionless wind speed and temperature gradients between the standard Businger–Dyer formulae, , , and free convection forms, , being the Monin–Obukhov stability parameter. A previously presented interpolation between the corresponding profile relationships, in attempting to provide a general relationship for the whole unstable regime, leads to serious restrictions for the values of in the free convection forms. These restrictions rendered available experimental data almost inapplicable, since the behaviour of the formulae in the near-neutral range controls the values of those parameters. The proposed interpolation provides functions that, firstly, fit the standard Businger–Dyer forms for near-neutral conditions and, secondly, satisfy the asymptotic behaviour as , permitting wider ranges of possible values. This step is very important, taking into account the large spread of the experimental data. Thus, as further and more accurate observations at strong instability become available, this approach could prove very efficient in fitting these data while retaining correct near-neutral behaviour.     

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.     

On the Determination of the Neutral Drag Coefficient in the Convective Boundary Layer

Based on the idea that free convection can be considered as a particular case of forced convection, where the gusts driven by the large-scale eddies are scaled with the Deardorff convective velocity scale, a new formulation for the neutral drag coefficient, C_Dn, in the convective boundary layer (CBL) is derived. It is shown that (i) a concept of C_Dn can still be used under strongly unstable conditions including a pure free-convection regime even when no logarithmic portion in the velocity profile exists; (ii) gustiness corrections must be applied for rational calculations of C_Dn; and (iii) the stratification function used in the derivation of C_Dn should satisfy the theoretical free-convection limit. The new formulation is compared with the traditional relationship for C_Dn, and data collected over the sea (during the Tropical Ocean-Global Atmosphere Coupled Ocean-Atmosphere Response Experiment (TOGA COARE) and the San Clemente Ocean Probing Experiment (SCOPE)) and over land (during the BOREX-95 experiment) are used to illustrate the difference between the new and traditional formulations. Compared to the new approach, the traditional formulation strongly overestimates C_Dn and z_o in the CBL for mean wind speed less than about 2 m s^-1. The new approach also clarifies several contradictory results from earlier works. Some aspects related to an alternate definition of the neutral drag coefficient and the wind speed and the stress averaging procedure are considered.     

Heat and Water Vapour Diffusivities Near the Base of a Disturbed Stable Internal Boundary Layer

We present results from an experiment that wasdesigned to investigate turbulent transportrelationships in a nearly homogeneous boundary layerdisturbed by unsteady wind swings, as found at thebase of an advective inversion with a convectiveboundary layer overhead. In such a situation wemeasured vertical gradients and eddy fluxes of temperature andhumidity at two heights. From these, the turbulentdiffusivities of heat and water vapour are obtained,and compared to the predictions of Monin–Obukhovsimilarity theory and those of a numericalsecond-order closure model. It is found that themeasured diffusivities exceed both predictions. Thisis interpreted as a consequence of the unsteadyconditions. It is also found that the diffusivity forheat is roughly 10% larger than that for watervapour. This is in agreement with a theoreticaltreatment of the unsteadiness effects that wedeveloped in an earlier publication. This result isnot reproduced by the numerical model because themodel has no provision for unsteady conditions. Ourresult disagrees with that from an earlier, verysimilar, field experiment, which may be due to asystematic underestimation of sensible heat flux inthe older experiment.     

Sensitivity Tests of an Energy Balance Model to Choice of Stability Functions and Measurement Accuracy

Sensible (H) and latent (L_vE) heat fluxes are obtained by a combined energy budget – similarity model applied to observations from Melle in Belgium and Cabauw in The Netherlands. The sensitivity to both the stability functions and the accuracy of input data is investigated. In a first step, fluxes are calculated for a selection of stability functions and compared to values obtained with pre-defined (reference) functions. For the diurnal fluxes higher than 10 W m⁻² in 1996 at Melle, the root-mean-square rmsreaches 9 W m⁻² for H and 6 W m⁻² for L_vE, depending on the chosen functions. A lesser sensitivity is obtained at Cabauw and can be explained by lower absolute values of the stability parameter ζ (L involving the Obukhov length) mainly induced by higher mean wind speeds. Different stability bins are also considered. It is concluded that a more accurate assessment of the stability functions is already desirable for absolute values of L above a few metres. These values are not so scarce at Melle and should be captured in the future by an increasing number of new developing long-term measurement stations. In a second step, a statistical approach is proposed with errors depicted by both systematic biases and random fluctuations represented by means of Gaussian distributions. The results show that very accurate measurements are needed in order to maintain the mean annual value of the bias and rms below 5–10 W m⁻², and thus to allow the discrimination between the sensitivity to errors on input data and to the stability functions selection.     

Structure of the atmospheric surface layer over an industrialized equatorial area

This paper is written to report observations of the structure of the atmospheric surface layer over a coastal industrialized equatorial area. The observations were recorded at Prai Industrial Park, Penang (5° 22′ N, 100° 23′ E) a relatively simple terrain area during the south-west monsoon season in the period of three months using slow response systems. The limitations of the instruments used and its effects on the results are discussed. Wind turbulence and temperature were measured on a 10 m tower and analyzed using eddy correlation method and Monin–Obukhov similarity relations to obtain the normalized standard deviation of longitudinal (σ_u/u), lateral (σ_v/u) and vertical wind velocity fluctuations (σ_w/u) with respect to stability parameter z/L. From the results of the analysis, we found that most of turbulence is generated by shear or mechanical force. It was found that the average neutral value of σ_u/u is 2.35, 1.98 for σ_v/u and 1.47 for σ_w/u with a significantly lower than the proportionality to the power of 1/3 during unstable atmospheric conditions, and thus do not obey Monin–Obukhov similarity theory. It was observed that σ_u/u and σ_v/u values increase linearly in the range of 0 < z/L < 2 and fairly well correlated while σ_w/u does not.     

Bulk Formulation of the Surface Heat Flux

An interpretive literature survey examines different approachesfor applying the bulk aerodynamic formulato predict the surface heat flux. The surface heat flux is often predicted in terms of the surface radiation temperature, which is also used to predict the upward longwave radiation and the heat flux into the soil. In models, the thermal roughness length based on the surface radiation temperature (radiometric roughness length) is often specified to be smaller than the roughness length for momentum for a number of distinct reasons. The definition of the radiometric roughness length depends on the way that the surface temperature is measured, the choice of stability functions and displacement height and inclusion of any additional resistances.Using airborne eddy correlation data collected over eight different sites including bare soil, crops and grassland and several types of forests, the radiometric roughness length is found to vary by orders of magnitude in a manner that is difficult to formulate. Alternatively, we evaluate the approach where the thermal roughness length is equated with the better behaved roughness length for momentum and the corresponding aerodynamic surface temperature is modelled in terms of the surface radiation temperature, solar radiation, and vegetation index. The influence of wind speed and soil moisture on the difference between the aerodynamic and surface radiation temperatures is also examined.     

Power Spectra and Cospectra for Wind and Scalars in a Disturbed Surface Layer at the Base of an Advective Inversion

This paper reports power spectra and cospectra of windspeed and several scalars measured at two heights nearthe base of an advective inversion. The inversion hadformed over a paddy field downwind of an extensive dryregion. Winds over the paddy field were variable instrength and direction, as a result of convectivemotions in the atmospheric boundary layer passing overfrom the dry region upwind. Fetch over the rice waslarge enough that advective effects on the transportprocesses were small at the upper level and negligibleat the lower level. Results from the lower level areinterpreted in terms of a horizontally homogeneous,but disturbed, surface layer.Power spectra of longitudinal and lateral velocitywere substantially enhanced at low frequencies. Theresulting vertical motions added only a small amountto the spectrum of vertical velocity but this stronglyaffected scalar power spectra and cospectra. Thesewere all substantially enhanced over a range of lowfrequencies. We also found that differences in lowerboundary conditions cause differences among scalarspectra at low frequencies.Our analysis shows that the spectra and cospectra havethree components, characterized by different scalingregimes. We call these the ILS (inner-layer scaling),OLS (outer-layer scaling) and CS (combined scaling)components. Of these, the CS component had notpreviously been identified. We identify CS componentsof spectra by their independence of height andfrequency. Spectra with these characteristics had beenpredicted by Kader and Yaglom for a layer of theatmosphere where spectral matching between ILS and OLSwas proposed. However, we find that the velocity andscalar scales used by Kader and Yaglom do not fit ourresults and that their concept of a matching layer isincompatible with our application. An alternativebasis for this behaviour and alternative scales areproposed.We compare our decomposition of spectra into ILS, CSand OLS components with an extended form of Townsend'shypothesis, in which wind and scalar fluctuations aredivided into active and inactive components. Wefind the schemes are compatible if we identify all OLSspectral components as inactive, and all CS and ILScomponents as active.By extending the implications of our results toordinary unstable daytime conditions,we predict that classical Monin–Obukhovsimilarity theory should be modified. We find that theheight of the convective boundary layer is animportant parameter when describing transportprocesses near the ground, and that the scalar scalein the ILS part of the spectrum, which includes theinertial subrange, is proportional to observationheight times the local mean scalar gradient, and notthe Monin–Obukhov scalar scale parameter. The formerdepends on two stability parameters: the Monin–Obukhovstability parameter and the ratio of the inner-layerand outer-layer velocity scales. The outer-layer scalecan reflect disturbances by topographically-inducededdying as well as by convective motions.