Characteristics of turbulent fluxes of sensible heat and momentum in the surface boundary layer during the Indian summer monsoon

Turbulent fluctuations of wind and temperature were measured using a three-component sonic anemometer at 8 m on a 30 m micro-meteorological tower erected at the Indian Institute of Technology (IIT) Kharagpur (22.3° N, 87.2° E), India, as part of the Monsoon Trough Boundary Layer Experiment (MONTBLEX). Diurnal and nocturnal variations of fluxes of sensible heat and momentum were estimated by the eddy correlation technique from 42 observations, each of 10 min duration during 6–8 July in the monsoon season of 1989. The estimated heat flux shows a diurnal trend while the momentum flux shows variability but no particular trend. The nocturnal heat flux changes sign intermittently.Fluctuations of vertical wind velocity _wand temperature when normalised with the respective scaling parameters u _*and _* are found to scale with Z/L in accordance with the Monin-Obukhov similarity hypothesis: % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqOXdy2aaS% baaSqaaiaadEhaaeqaaOGaamiEaiaacIcacaWGAbGaai4laiaadYea% caGGPaWaaWbaaSqabeaacaaIXaGaai4laiaaiodaaaaaaa!3FE8!\[\phi _w x(Z/L)^{1/3} \], % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqOXdy2aaS% baaSqaaiabeI7aXbqabaGccaWG4bGaaiikaiaadQfacaGGVaGaamit% aiaacMcadaahaaWcbeqaaiaaigdacaGGVaGaaG4maaaaaaa!40A2!\[\phi _\theta x(Z/L)^{1/3} \] during unstable conditions and % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqOXdy2aaS% baaSqaaiaadEhaaeqaaOGaamiEaiaacIcacaWGAbGaai4laiaadYea% caGGPaaaaa!3D90!\[\phi _w x(Z/L)\], % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqOXdy2aaS% baaSqaaiabeI7aXbqabaGccaWG4bGaaiikaiaadQfacaGGVaGaamit% aiaacMcadaahaaWcbeqaaiabgkHiTiaaigdaaaaaaa!401F!\[\phi _\theta x(Z/L)^{ - 1} \] during stable conditions. Correlation coefficients for heat and momentum flux % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4SdC2aaS% baaSqaaiaadEhacqaH4oqCaeqaaaaa!3A71!\[\gamma _{w\theta } \] and _uwshow stability dependence. For unstable conditions, % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4SdC2aaS% baaSqaaiaadEhacqaH4oqCaeqaaaaa!3A71!\[\gamma _{w\theta } \] increases with increasing ¦Z/L¦ whereas _uwdecreases. During stable conditions, % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4SdC2aaS% baaSqaaiaadEhacqaH4oqCaeqaaaaa!3A71!\[\gamma _{w\theta } \] decreases with increasing Z/L while _uwdecreases very slowly from a value -0.36 to -0.37.     

The transport of momentum, sensible heat, potential energy and moisture over the western Himalayas during the winter season

Summary The western Himalayas receive higher precipitation than the eastern Himalayas during the winter season (December–March). This differential pattern of winter precipitation over the Himalayas can be attributed to topography and to a higher frequency of disturbances over the western Himalayas, which result in variations in the circulation features. These circulation features, in turn, result in variations in the meridional transport of heat, momentum, potential energy, and moisture across the Himalayas due to mean and eddy motion. Significant meridional transport due to mean motion takes place in the upper troposphere at 300 hPa and 200 hPa. Transport east of 100° E dominates the transport over the western Himalayas. The eddy transport of heat, momentum, and potential energy is considerably smaller than that due to mean motion. Eddy transport magnitudes are smaller up to 500 hPa and increase rapidly aloft to 300 hPa and 200 hPa. Eddy transport over the western Himalayas is greater than over the eastern Himalayas.     

A note on the analogy between momentum transfer across a rough solid surface and the air-sea interface

The aerodynamic classification of the resistance laws above solid surfaces is based on the use of a so-called Reynolds roughness number Re _s =h _s u _*/, whereh _s is the effective roughness height, -viscosity,u _*-friction velocity. The recent experimental studies reported by Toba and Ebuchi (1991), demonstrated that the observed variability of the sea roughness cannot be explained only on the basis of the classification of aerodynamic conditions of the sea surface proposed by Kitaigorodskii and Volkov (1965) and Kitaigorodskii (1968) even though the latter approach gains some support from recent experimental studies (see for example Geernaertet al. 1986). In this paper, an attempt is made to explain some of the recently observed features of the variability of surface roughness (Toba and Ebuchi, 1991; Donelanet al., 1993). The fluctuating regime of the sea surface roughness is also described. It is shown that the contribution from the dissipation subrange to the variability of the sea surface can be very important and by itself can explain Charnock's (1955) regime.     

On momentum flux and velocity spectra over waves

Data from a research tower in Lake Ontario are used to study the validity of Monin--Obukhov scaling in the marine atmospheric boundary layer under various wave conditions. It is found that over pure wind seas, the velocity spectra and cospectra follow established universal scaling laws. However, in the presence of swells outrunning weak winds, velocity spectra and cospectra no longer satisfy universal spectral shapes. Here, Monin–Obukhov similarity theory, and the classical logarithmic boundary layers, are no longer valid. It is further shown that, in the presence of such swells, the momentum flux can be significantly modified in comparison to pure wind sea values. The implications of these findings for bulk flux estimations and on the inertial dissipation method for calculating fluxes are discussed.     

Surface renewal analysis for sensible and latent heat flux density

High frequency temperature measurements were recorded at five heights and surface renewal (SR) analysis was used to estimate sensible heat flux density (H) over 0.1 m tall grass. Traces of the temperature data showed ramp-like structures, and the mean amplitude and duration of these ramps were used to calculate H using structure functions. Data were compared with H values measured with a sonic anemometer. Latent heat flux density (E) was calculated using an energy balance and the results were compared with E computed from the sonic anemometer data. SR analysis provided good estimates of H for data recorded at all heights but the canopy top and at the highest measurement level, which was above the fully adjusted boundary layer.     

干旱区热力学粗糙度特征及对感热通量估算的影响

利用ＨＥＩＦＥ的实测资料估算了黑河实验区几个沙漠戈壁表面上的热力学粗糙度（以附加阻尼ｋＢ＾－１的形式）,发现在任一测站ｋＢ＾－１值的变化范围较大,同时分析了附加阻尼项在估算感热通量时的作用,而忽略该附加阻尼将会导致对感热通量的明显高估,提出在利用阻尼型公式计算感热通量时,不能采用简单的ｚ０ｍ＝ｚ０ｈ的假设,否则会带来较大误差。     

Regional differences in surface sensible and latent heat fluxes in China

This study documents the variability of surface sensible and latent heat fluxes in five regions of China (Northwest China, the Tibetan Plateau, Northeast China, North China, and Southeast China) using the ERA-40 reanalysis for the years 1960–2000. The surface sensible and latent heat flux variations are remarkably different in Northwest and Southeast China. The seasonal variation of the surface sensible heat fluxes is largest in Northwest China and smallest in Southeast China. In contrast, the seasonal variation in latent heat flux is largest in Southeast China and smallest in Northwest China. The interdecadal variation of surface sensible and surface latent heat fluxes strongly depends on both the region and season. The trends in surface sensible and latent heat fluxes in all four seasons are mainly caused by variations in both the land–air temperature difference and in the specific humidity. There is also a limited contribution of wind speed in some regions, depending on the season.     

Comparison of three schemes for predicting surface sensible heat flux

This paper compares three schemes which use standard meteorological observations to estimate values of the surface sensible heat flux. All three schemes have been designed to be applicable to mid-latitude, grass covered surfaces. The estimates are compared with heat flux data measured by a sonic anemometer situated at Cardington in the UK. Consideration is also given to the problem of predicting the surface sensible heat flux when could information is not available, as is the case for automatic weather stations. Provided incoming solar radiation is available, the predictions are not substantially worse.     

A verification of some methods to determine the fluxes of momentum,sensible heat,and water vapour using standard deviation and structure parameter of scalar meteorological quantities

A set of micro-meteorological data collected over a horizontal, uniform terrain (the plain of La Crau, France) in June 1987 is analysed. Conditions were predominantly sunny and arid, while due to the Mistral the wind speed could exceed 10 m/s. Verification of several methods to evaluate surface fluxes of heat, momentum and water vapour from the standard deviation of temperature, wind and specific humidity is presented. Also, a similar approach using the structure parameter of temperature is considered. These methods are all based on Monin-Obukhov (M-O) similarity theory. It is found that the standard deviation of temperature, vertical and horizontal wind speed as well as the structure parameter for temperature behave according to M-O similarity. It is shown that the sensible heat flux and friction velocity can be determined from a fast response thermometer and a cup anemometer. Also, it appears that the analytic solution of the set of governing equations as derived by the first author yields good results. M-O theory does not appear to work for the standard deviation of specific humidity. This may be due to the relative importance of large eddies.     

Nearly steady convection and the boundary-layer budgets of water vapor and sensible heat

The budgets of water vapor and sensible heat in the convective atmospheric boundary (mixed) layer are analyzed by means of a simple slab approach adapted to steady large-scale advective conditions with radiation and cloud activity. The entrainment flux for sensible heat is assumed to be a linear function of the surface flux. The flux of water vapor at the top of the mixed layer is parameterized by extending the first-order Betts-Deardorff approach, i.e., by adopting linear changes for both the specific humidity and the flux across the mixed layer and across the inversion layer of finite thickness. In this way the dissimilarity of sensible heat and water vapor transport in the mixed layer can be taken into account. The experimental data were obtained from the Air Mass Transformation Experiment (AMTEX). The entrainment constant for sensible heat at the top of the mixed layer was found to have values similar to those observed in other weakly convective situations, i.e., around 0.4 to 0.6. This appears to indicate that the effect of mechanical turbulence was not negligible; however, the inclusion of this effect in the formulation did not improve the correlation. In contrast to the first-order approach, the zero-order approach, i. e., the jump equation commonly used for the flux of a scalar at the inversion, (ovwc ) _h = w_e c (where w _e is the entrainment velocity and c the concentration jump across the inversion), was found to be invalid and incapable of describing the data.     

The influence of stratification on heat and momentum turbulent transfer in antarctica

Data from the Antarctic winter at Halley Base have been used in order to evaluate qualitatively and quantitatively how the stratification in the low atmosphere (evaluated with the gradient Richardson number, Ri) influences the eddy transfers of heat and momentum. Vertical profiles of wind and temperature up to 32 m, and turbulent fluxes ( , and ) measured from three ultrasonic thermo-anemometers installed at 5, 17 and 32 m are employed to calculate Ri, the friction velocity (u _*) and the eddy diffusivities for heat (K _h ) and momentum (K _m ). The results show a big dependence of stability onK _m ,K _h andu _*, with a sharp decrease of these turbulent parameters with increasing stability. The ratio of eddy diffusivities (K _h /K _m ) is also analyzed and presents a decreasing tendency as Ri increases, reaching values even less than 1, i.e., there were situations where the turbulent transfer of momentum was greater than that of heat. Possible mechanisms of turbulent mixing are discussed.     

Determination of turbulent momentum and heat fluxes by spectral methods

Methods are studied which permit one to evaluate turbulent fluxes from the results of spectral measurements in turbulent laboratory flows and an unstable atmospheric surface layer. The well known dissipation method of flux measurements, which uses spectral data related to the inertial range, is reanalyzed. New theoretical ideas and the latest experimental data are used to specify this method in cases of moderately and very strongly unstable thermal stratifications.Moreover, it is also explained how to estimate momentum and heat fluxes from data in the low frequency parts of the velocity and temperature spectra in the low frequency ranges beyond the lower limit of the inertial range. This permits one to estimate fluxes using rather simple and cheap instruments (e.g., Pilot-tubes and thermocouples in laboratory flows or cup anemometers and crude resistance thermometers in meteorological studies). The equations for flux determination are based in such cases on the recent models by Kader (1987, 1988) and Kader and Yaglom (1990, 1991) of spectral shapes at mesoscale wave numbers; these models agree quite satisfactorily with many (though not all) data of direct spectral measurements. It is shown that estimated momentum and heat fluxes in the laboratory and in an unstably stratified atmospheric surface layer obtained by the method suggested in this paper agree satisfactorily with direct flux measurements.     

An evaluation of aircraft flux measurements of CO2, water vapor and sensible heat

Ground-based flux measurements of carbon dioxide and water vapor integrate physiological processes taking place on a field scale. Aircraft flux measurements have recently been undertaken to attempt to widen the scope of applicability of such measurements. However, because of the intermittency of turbulent transfer, flux measurements must be averaged over long periods of time or long distances to give reproducible results. This requirement makes it difficult to relate aircraft flux measurements to local surface processes. Flux measurements of CO₂, latent and sensible heat obtained from repeated passes in four directions and at three elevations over a homogeneous wheat-growing area are compared with ground-based measurements. Averages based on four runs of 4 km in length gave results consistent with ground-based measurements. The largest percentage differences were in the sensible heat flux. Cospectral analyses showed no significant high frequency losses for the data from flight levels of 25 and 50 m, but an underestimation of approximately 10% resulted at 10 m. Flight direction with respect to wind direction was relatively unimportant at 10 and 25 m but some effects were observed at 50 m. It was also shown that at 25 m, over a relatively smooth and homogeneous surface, the means of either three or four runs 4 km in length were similar to the means of 12–16 km runs. This confirms that at this altitude, most of the flux contribution is contained at wavelengths less than 4 km and that the mean of 3 to 4 passes accounts for most of the intermittency of turbulent transfer.     

Estimation of sensible heat flux by a hybrid method of temperature profile and light-beam deflection

A new method of sensible heat flux estimation by a hybrid use of temperature profile and light-beam deflection is proposed and tested over an asphalt pavement on fine days.A helium-neon gas laser with wavelength 0.6328 m was used as a light-beam source. Temperature gradient near the surface was measured by the deflection of a light-beam propagated nearly horizontally at a distance of 25 m. Measurement of the air temperature profile in the upper part of the surface layer was made by means of a copper-constantan thermocouple thermometer. The sensible heat flux was estimated from the temperature profile using profile-flux relationships.The surface temperature of the asphalt pavement rose to as high as 63 °C in the daytime and never decreased below the air temperature even in the morning in summer. The maximum value of heat flux obtained from this observation attained 365 W m^-2, which was about 48% of incoming solar radiation.     

Simulated changes of the Southern Ocean air-sea heat flux feedback in a warmer climate

Climate Dynamics - In this paper, we have evaluated the Southern Ocean (SO) heat flux feedback in a fully coupled model and for the first time examined how this feedback evolves in response to...     

The effect of changes in surface resistance on temperature and humidity fields and fluxes of sensible and latent heat

In this paper we consider temperature (% MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGafuiMdeLbae% baaaa!377B!\[\bar \Theta \]) and specific humidity (% MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGabmyuayaara% aaaa!36DA!\[\bar Q\]) fields in the lower part of the planetary boundary layer and present a method for calculating the way these variables and their fluxes vary over changes in available surface moisture expressed as a surface resistance. Near the surface, the turbulence is close to equilibrium and an eddy diffusivity model enables the changes in (% MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGafuiMdeLbae% baaaa!377B!\[\bar \Theta \]), % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGabmyuayaara% aaaa!36DA!\[\bar Q\], sensible heat flux (% MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGabmOrayaara% WaaSbaaSqaaiaadIeaaeqaaaaa!37C8!\[\bar F_H \]), and latent heat flux (% MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGabmOrayaara% WaaSbaaSqaaiaadweaaeqaaaaa!37C5!\[\bar F_E \]) to be determined in terms of the assumed mean wind, turbulence profiles and upwind profiles of temperature and humidity. An important advantage of this method is that it is possible to consider arbitrary changes in surface properties.     

Net radiation,sensible and latent heat flux densities on slopes computed by the energy balance method

Energy balance components obtained over five grass-covered sloping surfaces near Manhattan, KS, using the Bowen ratio energy balance technique with the instruments mounted horizontally were compared with calculated values when the instruments were mounted parallel to the surfaces. Hourly values of the components changed when the instruments were parallel to the surfaces. The changes were larger at low solar angles (spring and fall) and on steeper slopes. An area average of daylight totals, assuming that all aspects were equally represented, changed only 0.1% on June 6 and 2.3% on October 11. The calculations, extended to steeper slopes, indicated small changes in the daylight totals for slopes of less than 10 deg.Supported in part by a grant from NASA NAG 5-901.     

Impact of surface variations on the momentum flux above the urban canopy

Based on the momentum flux–wind profile relationship of the Monin–Obukhov Similarity (MOS) theory, the observational data from the urban boundary layer field campaign in Nanjing are used to calculate the friction velocity ( $ {u_*} $ ) at the top of the urban canopy and the calculated results are evaluated. The urban surface roughness parameters (the roughness length z ₀ and zero-plane displacement height z _d) are estimated with the Ba method (Bottema’s morphological method). Two different regimes are employed for the calculations. In the homogeneous approach, z ₀ and z _d are averagely derived from the surface elements in the whole study area; while in the heterogeneous approach, z ₀ and z _d are locally derived from the surface elements in the corresponding upwind fetches (or source areas). The calculated friction velocities are compared to the measurement data. The results show that the calculated friction velocities from the heterogeneous approach are in better agreement with the observed values than those from the homogeneous approach are. This study implies that the local roughness parameters can properly represent the dynamical heterogeneity of urban surface, and its application can significantly improve the performance of parameterizations based on the MOS theory in the urban roughness sublayer.     

A quantitative method for estimating Pasquill stability class from windspeed and sensible heat flux density

A simple exponential expression, based upon a form of the Kazanski-Monin stability parameter, modified to account explicitly for effects of surface roughness, and semi-empirically derived from both qualitative and quantitative observations, is presented that relates windspeed and sensible heat flux density to Pasquill stability class. The method, though simple in mathematical form, gives results consistent with physical intuition and reproduces, quantitatively, the essential features of previously published nomograms with an added capability for treating all stability classes and any surface roughness from 0.10 to 100 cm. For the stable classes, a new expression for the wind profile stability factor, predicted by similarity theory, is introduced that produces results more consistent than the more common linear form.