Bulk Transfer Relations for the Roughness Sublayer

In the roughness sublayer (RSL), Monin–Obukhov surface layer similarity theory fails. This is problematic for atmospheric modelling applications over domains that include rough terrain such as forests or cities, since in these situations numerical models often have the lowest model level located within the RSL. Based on empirical RSL profile functions for momentum and scalar quantities, and scaling the height with the RSL height z _*, we derive a simple bulk transfer relation that accounts for RSL effects. To verify the validity of our approach, these relations are employed together with wind speed and temperature profiles measured over boreal forest during the BOREAS experimental campaign to estimate momentum and heat fluxes. It is demonstrated that, when compared with observed flux values, the inclusion of RSL effects in the transfer relations yields a considerable improvement in the estimated fluxes.     

Spatial Variability of Turbulent Fluxes in the Roughness Sublayer of an Even-Aged Pine Forest

The spatial variability of turbulent flow statistics in the roughness sublayer (RSL) of a uniform even-aged 14 m (= h) tall loblolly pine forest was investigated experimentally. Using seven existing walkup towers at this stand, high frequency velocity, temperature, water vapour and carbon dioxide concentrations were measured at 15.5 m above the ground surface from October 6 to 10 in 1997. These seven towers were separated by at least 100m from each other. The objective of this study was to examine whether single tower turbulence statistics measurements represent the flow properties of RSL turbulence above a uniform even-aged managed loblolly pine forest as a best-case scenario for natural forested ecosystems. From the intensive space-time series measurements, it was demonstrated that standard deviations of longitudinal and vertical velocities (_u, _w) and temperature (_T) are more planar homogeneous than their vertical flux of momentum (u_* ²) and sensible heat (H) counterparts. Also, the measured H is more horizontally homogeneous when compared to fluxes of other scalar entities such as CO₂ and water vapour. While the spatial variability in fluxes was significant (>15 %), this unique data set confirmed that single tower measurements represent the canonical structure of single-point RSL turbulence statistics, especially flux-variance relationships. Implications to extending the moving-equilibrium hypothesis for RSL flows are discussed. The spatial variability in all RSL flow variables was not constant in time and varied strongly with spatially averaged friction velocity u_*, especially when u_* was small. It is shown that flow properties derived from two-point temporal statistics such as correlation functions are more sensitive to local variability in leaf area density when compared to single point flow statistics. Specifically, that the local relationship between the reciprocal of the vertical velocity integral time scale (I_w) and the arrival frequency of organized structures (/h) predicted from a mixing-layer theory exhibited dependence on the local leaf area index. The broader implications of these findings to the measurement and modelling of RSL flows are also discussed.     

Methodological Considerations Regarding the Measurement of Turbulent Fluxes in the Urban Roughness Sublayer: The Role of Scintillometery

We address some of the methodological challenges associated with the measurement of turbulence and use of scintillometers in the urban roughness sublayer (RSL). Two small-aperture scintillometers were located near the roof interface in a densely urbanized part of Basel, Switzerland, as part of the Basel Urban Boundary-Layer Experiment (BUBBLE) in the summer of 2002. Eddy correlation instruments were co-located near the mid-point of each scintillometer path for data verification purposes. The study presents the first values of the inner length scale of turbulence (l ₀) and the refractive index structure parameter of air for a city and demonstrates the influence of mechanical driven turbulence on dissipation. Comparison of dissipation values determined from the two approaches show large scatter that is possibly due to the spatial inhomogeneity of the turbulence statistics within the RSL. Velocity and temperature spectra display a −2/3 slope in the inertial subrange, although the spectral ratio is less than the theoretical prediction of 4/3 expected for isotropy. Conventional Monin–Obukhov equations used to calculate fluxes from the scintillometer were replaced with urban forms of the equations. The results suggest that the scintillometer may be an appropriate tool for the measurement of sensible heat flux (Q _H ) above the rooftops given a suitable determination of the effective measurement height.     

Buoyancy and The Sensible Heat Flux Budget Within Dense Canopies

In contrast to atmospheric surface-layer (ASL) turbulence, a linear relationship between turbulent heat fluxes (F_T) and vertical gradients of mean air temperature within canopies is frustrated by numerous factors, including local variation in heat sources and sinks and large-scale eddy motion whose signature is often linked with the ejection-sweep cycle. Furthermore, how atmospheric stability modifies such a relationship remains poorly understood, especially in stable canopy flows. To date, no explicit model exists for relating F_T to the mean air temperature gradient, buoyancy, and the statistical properties of the ejection-sweep cycle within the canopy volume. Using third-order cumulant expansion methods (CEM) and the heat flux budget equation, a “diagnostic” analytical relationship that links ejections and sweeps and the sensible heat flux for a wide range of atmospheric stability classes is derived. Closure model assumptions that relate scalar dissipation rates with sensible heat flux, and the validity of CEM in linking ejections and sweeps with the triple scalar-velocity correlations, were tested for a mixed hardwood forest in Lavarone, Italy. We showed that when the heat sources (S_T) and F_T have the same sign (i.e. the canopy is heating and sensible heat flux is positive), sweeps dominate the sensible heat flux. Conversely, if S_T and F_T are opposite in sign, standard gradient-diffusion closure model predict that ejections must dominate the sensible heat flux.     

Roughness length for heat over an urban canopy

The roughness length for heat z_T was evaluated over an urban canopy, using the measured sensible heat flux and radiometric temperature. To overcome thermal heterogeneity in the urban area, the measured radiometric temperature was transformed into the equivalent temperature of an upward longwave radiation flux. The equivalent temperature was found to provide an effective parameterization of the radiometric temperature. The daytime average of the resulting ln(z_T/z₀) was 10, where z₀ is the aerodynamic roughness length. This result generally agrees with previous studies; however, the anthropogenic heat is a large uncertainty, which could cause an error at least 240% in z_T.     

Estimation of the sensible heat flux of a semi-arid area using surface radiative temperature measurements

In the framework of an international field program for the study of semi-arid areas, observations were done in the region called La Crau in southern France. In this paper, the use of the surface radiative temperature for the determination of the sensible heat flux is addressed. We found that, once proper values of the roughness length of momentum (z ₀) and heat (z ₀h) are set, the sensible heat flux can be reliably predicted with a one-layer resistance model using standard observations of wind speed and air temperature, together with the surface temperature. The latter quantity has to be known with a precision better than ±2°C. From our observations, the value of the parameterB ^–1k ^–1 In (z ₀ z ₀h) was found to be 9.2, which falls between values quoted by Brutsaert (1982) for grass and bluff bodies.     

Effects of Wall Heating on Flow Characteristics in a Street Canyon

We develop a large-eddy simulation (LES) model based on a meteorological numerical model for a real scale street-canyon flow with rough building facets heated by a given temperature. The model is applied to a canyon with the aspect ratio of unity for two idealized heating scenarios: (1) the roof and the entire upstream wall are heated, named as ‘assisting cases’, and (2) the roof and the entire downstream wall are heated, named as ‘opposing cases’. These facets were heated up to 15 K above the air temperature. A wall function for temperature is proposed for a rough facet with an assumption that the thermal roughness length, z _0T, is much smaller than the aerodynamic roughness length, z ₀. It is demonstrated that the sensible heat flux and canyon-air temperature are significantly influenced by the near-facet process that is parametrized by z _0T as the primary factor; other processes such as in-canyon mixing and roof-level exchange are secondary. This new finding strongly suggests that it is vital to choose an appropriate value of z _0T in a numerical simulation of street-canyon flows with the facet-air exchange processes of heat or any scalar. The finding also raises an awareness of the demand for carefully designed laboratory or field experiments of quantifying z _0T values for various urban surfaces. For the opposing cases, an unsteady penetrating narrow updraft zone appears occasionally along the heated wall and this feature is consistent field observations. The unique result indicates the superior capability of LES. The results of this study can be used to guide the parametrization of turbulent processes inside the urban canopy layer.     

On Monin–Obukhov Scaling in and Above the Atmospheric Surface Layer: The Complexities of Elevated Scintillometer Measurements

In scintillometry Monin–Obukhov similarity theory (MOST) is used to calculate the surface sensible heat flux from the structure parameter of temperature (C_T²){(C_{T^2})} . In order to prevent saturation a scintillometer can be installed at an elevated level. However, in that case the observation level might be located outside the atmospheric surface layer (ASL) and thus the validity of MOST questioned. Therefore, we examine two concepts to determine the turbulent surface sensible heat flux from the structure parameter at elevated levels with data obtained at 60-m height on the Cabauw tower (the Netherlands). In the first concept (MOSTs) C_T²{C_{T^2}} is still scaled with the surface flux, whereas in the second (MOSTl) C_T²{C_{T^2}} is scaled with the local sensible heat flux. The C_T²{C_{T^2}} obtained from both concepts is compared with direct observations of C_T²{C_{T^2}} using a sonic anemometer/thermometer. In the afternoon (when the measurement height is located within the ASL) both concepts give results that are comparable to the directly observed values of C_T²{C_{T^2}} . In the morning (data outside the ASL), our data do not unequivocally support either of the two concepts. First, the peak in C_T²{C_{T^2}} that occurs when the measurement height is located in the entrainment zone disqualifies the use of MOST. Second, during the morning transition, local scaling shows the correct pattern (zero flux and a minimum in C_T²{C_{T^2}}) but underestimates C_T²{C_{T^2}} by a factor of ten. Third, from the best linear fit a we found that the slope of MOSTl gave better results, whereas the offset is closer to zero for MOSTs. Further, the correlation between the direct observations and MOST-scaled results is low and similar for the two concepts. In the end, we conclude that MOST is not applicable for the morning hours when the observation level is above the ASL.     

The scintillation method tested over a dry vineyard area

Measurements of a scintillometer device mounted at 4 m above a dry vineyard area in La Mancha, Spain, are used to obtain an average sensible heat flux densityH. Averaging is over a rectangular area determined by the distance between the scintillometer light source and receptor (875 m) and some upwind distance governed by the horizontal wind speed perpendicular to that line. Using similarity relations obtained from La Crau, a good correspondence betweenH measured with the scintillometer and an eddy-correlation device in the centre of a vineyard is obtained. The friction velocityu _* was either measured directly using a sonic anemometer or obtained indirectly from two wind speeds and known values of the roughness length z_o and displacementd. The free convection formulation underestimates the sensible heat flux by about 30%. This is due to a significant contribution of mechanically generated turbulence to the total turbulent transport, which was caused by relatively strong winds and rough terrain.     

Heat flux parameterization for sparse and dense grasslands with the analytical land-atmosphere radiometer model (alarm)

The dependence of radiometric surface temperature (_s) on view angle and the unclear definition of the aerodynamic temperature, which is the temperature that gives the correct sensible heat flux estimate at a specified roughness length, bring about a challenge in estimating sensible heat flux from _s. An analytical-land-atmosphere-radiometer model (ALARM) has been developed to convert _s taken at any zenith view angle to a clearly defined equivalent isothermal surface temperature, _i, at a defined scalar roughness length. ALARM is an analytical model based on K-theory that links the foliage temperature profile to the radiometric surface temperature and the temperature felt by the turbulent lower atmosphere. ALARM has previously been applied with slightly different values of its parameters to several grassland sites of varying canopy density. Our objective in this study was to apply ALARM to these and to one additional dataset with a single parameterization. When compared to the reference (measured) values of sensible heat flux H, ALARM estimates of H had root mean square errors of about 35 W m^-2. These results were comparable to those from two other simple canopy models also tested with these datasets.     

Daily sensible heat flux estimation from a single measurement of surface temperature and maximum air temperature

Surface energy budget investigations of a range of agricultural surfaces in France and the African Sahel demonstrate consistent linear relationships between daily totals of sensible heat flux (H _d) and the difference between a once-a-day radiative measurement of surface temperature and the maximum air temperature at a height of 2 m. Surface temperature was measured with nadir-viewing radiothermometers near 1400 h (LST). The average residual standard error in the estimate ofH _d was 0.6 mm of equivalent evaporation.An equation for the daily sensible heat flux (H _d) having a form analogous to Dalton's evaporation formula was derived from surface energy budget considerations. This equation discriminates well between relatively homogeneous, low-cover surfaces where surface exchange characteristics can be assumed to be simple fractions of the height of the roughness elements. By contrast, data from two other crops with discontinuous plant cover suggest a much reduced sensitivity to canopy architecture. This result is not unreasonable if scalar transport were controlled by the thermal conductivity of a layer of still air close to ground level which is sheltered by the plant canopy. There is scope for further experimental and theoretical work on this matter.     

Spatio-temporal Variability of Surface-layer Turbulent Fluxes Over the Bay of Bengal and Arabian sea During the ICARB Field Experiment

We report the spatio-temporal variability of surface-layer turbulent fluxes of heat, moisture and momentum over the Bay of Bengal (BoB) and the Arabian Sea (AS) during the Integrated Campaign for Aerosols, gases Radiation Budget (ICARB) field experiment. The meteorological component of ICARB conducted during March – May 2006 onboard the oceanic research vessel Sagar Kanya forms the database for the present study. The bulk transfer coefficients and the surface-layer fluxes are estimated using a modified bulk aerodynamic method, and then the spatio-temporal variability of these air-sea interface fluxes is discussed in detail. It is observed that the sensible and latent heat fluxes over the AS are marginally higher than those over the BoB, which we attribute to differences in the prevailing meteorological conditions over the two oceanic regions. The values of the wind stress, sensible and latent heat fluxes are compared with those obtained for the Indian Ocean Experiment (INDOEX) period. The variation of drag coefficient (C _D ), exchange coefficients of sensible heat and moisture (C _H = C _E ) and neutral drag coefficient (C _DN ) with wind speed is also discussed.

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Validation of parametrisations for the meridional energy and moisture transport used in simple climate models

Parametrisations of meridional energy and moisture transport used in zonally averaged climate models are validated using reanalysis data and results from a doubling CO₂-experiment from a general circulation model. Global meridional fluxes of moisture and sensible heat are calculated by integrating surface and top-of-the-atmosphere vertical fluxes from one pole to the other. The parametrisations include an eddy-diffusion term, representing down-gradient transport of specific humidity and temperature due to the transient atmospheric eddies at mid- and high latitudes, and simple representations of the mean meridional circulation. Qualitative and quantitative agreement between the increased hydrological cycle in the 2×CO₂-run from the GCM and the parametrisation is found. The performance for the sensible heat flux shows larger differences to the GCM results, particularly at low latitudes. Seasonal variations of the moisture and sensible heat transport are well captured by parametrisations including the influence of the mean meridional circulation. Interannual variability cannot be simulated. An examination of the parametrisations on different spatial scales suggests that they should not be used for small scales. Furthermore, two closures for the zonal distribution of precipitation were examined. They are used in zonally averaged atmosphere models coupled to an ocean model with different ocean basins at one latitudinal belt. An assessment of both the reanalysis data and the GCM results shows that both closures exhibit very similar behaviour and are valid in the long-term mean and seasonal cycle. Interannual variability is not captured well. They become invalid for spatial scales smaller than 10^∘. Received: 30 November 1998 / Accepted: 4 July 1999     

Airborne measurements of turbulent fluxes during LITFASS-98: Comparison with ground measurements and remote sensing in a case study

Summary ?Simultaneous flight measurements with the research aircraft Do 128 and the helicopter-borne turbulence probe Helipod were performed on 18 June 1998 during the LITFASS-98 field experiment. The area-averaged turbulent vertical fluxes of momentum, sensible, and latent heat were determined on a 15 km × 15 km and a 10 km × 10 km flight pattern, respectively. The flights were carried out over heterogeneous terrain at different altitudes within a moderately convective boundary layer with Cumulus clouds. Co-spectra-analysis demonstrated that the small scale turbulent transport was completely sampled, while the comparatively small flight patterns were possibly of critical size regarding the large-scale turbulence. The phygoide of the airplane was identified as a significant peak in some co-spectra. The turbulent fluxes of momentum and sensible heat at 80 m above the ground showed systematic dependence on the location of the flight legs above the heterogeneous terrain. This was not observed for the latent heat flux, probably due to the vertical distribution of humidity in the boundary layer. Statistical error analysis of the fluxes F showed that the systematic statistical error ΔF was one order of magnitude smaller than the standard deviation σ _F . The difference between area-averaged fluxes derived from simultaneous Helipod and Do 128 measurements was much smaller than σ _F , indicating that the systematic statistical error was possibly over-estimated by the usual method. In the upper half of the boundary layer the airborne-measured sensible heat flux agreed well with windprofiler/RASS data. A linear fit was the best approximation for the height dependence of all three fluxes. The linear extrapolations of the latent and sensible heat fluxes to the ground were in good agreement with tower, scintillometer, and averaged ground-station measurements on various surface types. Systematic discrepancies between airborne and ground-based measurements were not found. Received June 18, 2001; revised December 21, 2001; accepted June 3, 2002     

Surface-layer profile evaluation using a generalization of Robinson's method for the determination ofd andz 0

The iteration scheme of Robinson (1962) for the determination ofz ₀ andd under neutral atmospheric stability has been generalized in a relatively simple manner. It now accounts for nonneutral conditions and permits simultaneous calculation ofd,z ₀, and flux densities of latent and sensible heat. Using profile data sets given in the literature, the generalized scheme yields results which agree quite well with those obtained by Kramm (1989).     

Measurement of the Sensible Eddy Heat Flux Based on Spatial Averaging of Continuous Ground-Based Observations

Using the standard eddy-covariance (EC) method to quantify mass and energy exchange at a single location usually results in an underestimation of vertical eddy fluxes at the surface. In order to better understand the reasons for this underestimation, an experimental set-up is presented that is based on spatial averaging of air temperature data from a network of ground-based sensors over agricultural land. For eight days during the 34-day observational period in May and June 2007, additional contributions to the sensible heat flux of more than 50Wm⁻² were measured in the lower surface layer by applying the spatial EC method as opposed to the standard temporal EC method. Smaller but still significant additional sensible heat fluxes were detected for four more days. The additional energy is probably transported in organised convective structures resulting in a mean vertical wind velocity unequal to zero at the tower location. The results show that convective transport contributes significantly to the surface energy budget for measurement heights as low as 2–3 m. Since these structures may be quasi-stationary, they can hardly be captured by a single-location measurement. The spatial EC set-up presented here is capable of quantifying contributions to the sensible heat flux from structures up to the scale of our spatial sensor network, which covered an area 3.5 × 3.5 km. For future experiments aiming at closing the energy balance, the spatial EC method should be employed to measure both the sensible and latent heat fluxes. Experimental determination of the horizontal advection of sensible and latent heat should also be considered, since such transport must occur due to convergence and divergence related to convection.     

Radiometrically determined skin temperature and scalar roughness to estimate surface heat flux part II: Performance of parameterized scalar roughness for the determination of sensible heat

Several formulations and proposals to determine the value of the radiometric scalar roughness for sensible heatz _0h,r are tested with respect to their performance in the estimation of the sensible heat flux by means of the profile equations derived from Monin-Obukhov similarity theory. The equations are applied to the data set of spatially averaged surface skin temperature and profiles of wind speed and temperature observed in a pasture field during a growing season. The use of a physical model developed for a dense canopy to estimate scalar roughness for sensible heatz _0h,r produced sensible heat fluxH with a correlation coefficientr=0.884, the ratio of means being H _s /H=1.19 in a comparison with reference values ofH _s . In comparison, a proposal for a fixed value ofz _0h yieldedr=0.887, H _s /H=0.879. In both cases, the validity ofz _0h =z _0h,r was assumed. All expressions derived to estimatez _0h,r from a multiple linear regression with such predictors as leaf area index, solar radiation and the ratio of solar radiation to extraterrestrial radiation, were found to produce a better result, withr better than 0.90 and H _s /H around 1.0. However, when the constantsc andf of a linear regression equationHs=cH+f are used to evaluate the equations, a marked difference in performance of each formulation appeared. In general, equations with smaller numbers of predictors tend to produce a biased result, i.e., an overestimation ofH at largeH _s . These values ofH are used in conjunction with the energy balance equation to derive values of the latent heat fluxLE, which are shown to be in good agreement with the reference valuesLE _s , withr greater than 0.97.     

A model of airflow above changes in surface heat flux,temperature and roughness for neutral and unstable conditions

A numerical model of airflow in the lowest 50–100 m of the atmosphere above changes in surface roughness and temperature or heat flux has been developed based on boundary layer approximations, the Businger-Dyer hypotheses for the non-dimensional wind shear and heat flux and a mixing length hypothesis.Results have been obtained for several situations, in particular, airflow with neutral upstream conditions encountering a step change in surface temperature or heat flux with no roughness change. In these cases large increases in shear stress at the outer edge of the internal boundary layer are predicted. The case of unstable upstream flow encountering a step change to zero heat flux is also considered.Two situations that may be encountered near the shores of the Great Lakes are considered.Notation B Businger-Dyer constant (= 16.0) in form for _M, _H - c _p Specific heat at constant pressure - g Acceleration due to gravity - H Upward vertical heat flux - H ₀ , H ₁ Surface heat fluxes for x < 0, x 0 - k von Kármán's constant ( = 0.4) - l Mixing length - L Monin-Obukhov length - L ₀ Upstream value of L - m Ratio of roughness lengths (= z ₁/z ₀) - RL ^* Non-dimensional parameter, see Equations (20, 22 and 24) - RL ₁ ^* Same as RL ^* but with z ₁ scaling (= mRL ^*) - T Scaled temperature - T ₀ (z) Upstream temperature profile - u ₀, u ₁(x) Surface friction velocities for x < 0, x 0 - U, W Horizontal and vertical mean velocities - U ₀ (z) Upstream velocity profile - x, z Horizontal and vertical coordinates - z _i Local roughness length     

Dissimilarity of Scalar Transport in the Convective Boundary Layer in Inhomogeneous Landscapes

A land-surface model (LSM) is coupled with a large-eddy simulation (LES) model to investigate the vegetation-atmosphere exchange of heat, water vapour, and carbon dioxide (CO₂) in heterogeneous landscapes. The dissimilarity of scalar transport in the lower convective boundary layer is quantified in several ways: eddy diffusivity, spatial structure of the scalar fields, and spatial and temporal variations in the surface fluxes of these scalars. The results show that eddy diffusivities differ among the three scalars, by up to 10–12%, in the surface layer; the difference is partly attributed to the influence of top-down diffusion. The turbulence-organized structures of CO₂ bear more resemblance to those of water vapour than those of the potential temperature. The surface fluxes when coupled with the flow aloft show large spatial variations even with perfectly homogeneous surface conditions and constant solar radiation forcing across the horizontal simulation domain. In general, the surface sensible heat flux shows the greatest spatial and temporal variations, and the CO₂ flux the least. Furthermore, our results show that the one-dimensional land-surface model scheme underestimates the surface heat flux by 3–8% and overestimates the water vapour and CO₂ fluxes by 2–8% and 1–9%, respectively, as compared to the flux simulated with the coupled LES-LSM.     

珠海凤凰山森林下垫面干季和湿季气象要素的对比分析与动量和感热交换系数的参数化研究

利用珠海凤凰山陆气相互作用观测塔站2014年11月至2016年5月的观测数据,对比分析了干湿季森林下垫面能量通量和气象要素的变化特征,分析了在不同稳定度下3个风向范围（315°～45°、45°～135°和135°～225°）的动量和感热交换系数随冠层表面风速的变化特征,并对动量和感热交换系数进行了参数化研究。结果表明:干季感热和潜热通量值相当,湿季潜热远大于感热。干季和湿季的夜晚都出现负感热现象,感热从大气向森林输送。相对湿度的变化幅度大,与该地气象状况密切相关,相对湿度的垂直梯度夜晚较大,白天较小。干季的气温垂直梯度比湿季的明显。风速在冬季变化平缓,夏季变化剧烈,低层风速随高度变化梯度明显,高层较紊乱。各高度风向差异不大。中性和近中性状态下,在风向为315°～45°、45°～135°和135°～225°时,动量交换系数C_dn分别为0.05、0.0055和0.022,感热交换系数C_hn分别为0.0055、0.003和0.004。在稳定和不稳定状态下,动量交换系数C_d、感热交换系数C_h随冠层表面风速v明显发生变化,稳定条件下,C_d、C_h随v的增大而增大;不稳定条件下,C_d、C_h随v的增大而减小。分不同风向对森林冠层C_d、C_h在稳定和不稳定条件下与v的关系进行了拟合,得到了参数化公式。