Anomalies in Flux-Gradient Relationships Over Forest

Simultaneous profile and eddy correlation flux data gathered over Thetford Forest, U.K., have been analysed to find values of the vertical turbulent diffusivities K _M, K _H and K _E (for momentum, heat and water vapour transfer, respectively) at a reference height z _R, nine roughness lengths above the zero-plane displacement d. The results show: (i), that values of K _M over the forest are not significantly different from these predicted by semiempirical diabatic influence functions appropriate to much smoother surfaces such as short grass; and (ii), that K _H and K _E exceed their values predicted from the semiempirical functions by an average factor of 2 or more in unstable, near neutral and slightly stable conditions. These conclusions are strongly dependent on the assumed behaviour of d, here taken as 0.76 tree heights, independent of both property and stability. Consideration is given to an alternative analysis procedure, in which values of the zero-plane displacements d _H and d _E for heat and water vapour respectively, are obtained from the data by assuming K _H and K _E to be given by semiempirical diabatic influence functions; this procedure is shown to be unacceptable on both practical and physical grounds. To account for the anomalies in K _H and K _E, a mechanism is proposed in which the horizontally inhomogeneous temperature structure of the canopy causes free convection to be maintained by discrete; localized heat sources and/or sinks, effectively enhancing turbulent transport processes even in near neutral conditions.     

Inequality of eddy transfer coefficients for vertical transport of sensible and latent heats during advective inversions

Similarity of transport of water vapour and sensible heat was investigated within an advective inversion layer by measuring eddy fluxes together with gradients of temperature and humidity. The experimental site was a field of rice, grown under flood irrigation, which was situated in a semi-arid region. The fetch was about 300 m and local stabilities (z/L) over the rice ranged from 0 to 0.1. Results were expressed as the ratio of eddy transfer coefficients for sensible heat (K _H) and water vapour (K _w). Near neutral stability, K _H/K_W approached 1, but the ratio decreased to about 0.65 with increasing stability. Existing theory predicts the result qualitatively but accounts for only about one fifth of the decrease in K _H/K_W with stability.     

Positive and negative turbulent heat diffusivity observed on a 325-m meteorological tower in Beijing 基于北京325米气象塔观测的正, 负湍流热扩散系数

Turbulent diffusion efficiently transports momentum, heat, and matter and affects their transfers between the atmosphere and the surface. As a key parameter in describing turbulent diffusion, the turbulent heat diffusivity K_H has rarely been studied in the context of frequent urban pollution in recent years. In this study, K_H under urban pollution conditions was directly calculated based on K-theory. The authors found an obvious diurnal variation in K_H, with variations also in the vertical distributions between each case and over time. Interestingly, the height corresponding to the high occurrence frequency of negative K_H rises gradually after sunrise, peaks at noon, falls near sunset, and concentrates around 140 m during most of the night. The K_H magnitude and fluctuation are smaller in the pollutant accumulation stage (CS) at all levels than in the pollutant transport stage and pollutant removal stage. Turbulent diffusion may greatly affect PM_2.5 concentrations at the CS because of the negative correlation between PM_2.5 concentrations and the absolute value of K_H at the CS accompanied by weak wind speeds. The applicability of K-theory is not very good during either day or at night. These problems are inherent in K-theory when characterizing complex systems, such as turbulent diffusion, and require new frameworks or parameterization schemes. These findings may provide valuable insight for establishing a new turbulence diffusion parameterization scheme for K_H and promote the study of turbulent diffusion, air quality forecasting, and weather and climate modeling.摘要本文基于K理论和北京325m铁塔湍流观测资料直接计算了城市污染条件下的湍流热扩散系数K_H.K_H具有明显的日变化特征, 其垂直分布随个例和时间而变化.负K_H较高发生频率对应高度在日出后逐渐升高, 在中午达到峰值, 在日落附近下降, 而在夜间大部分时间集中在140 m左右.和传输和清除阶段相比, 污染物累积阶段的K_H大小和波动程度均较小.此阶段PM_2.5浓度与K_H绝对值之间的负相关关系表明湍流扩散可能会极大地影响PM_2.5浓度.这些发现可能为建立新湍流扩散参数化方案提供有价值的启示.     

Surface-layer fog considered using a modified Monin-Obukhov theory

The Prandtl-layer concept, assuming constant turbulent fluxes in the lowest meters or decameters of the atmosphere under horizontal homogeneous and steady-state conditions, is widely used; and it is also one of the fundamentals of Monin-Obukhov similarity theory. Thus, surface-layer condensation processes-essentially formation of shallow fog layers-implying convergence and divergence of turbulent fluxes of water vapour, liquid water content and sensible heat, cannot be treated within this concept. This paper tries to overcome this restriction by a modified Monin-Obukhov theory, which deals with constant fluxes of total water content and moist static energy (instead of water vapour and sensible heat). It shows that surface-layer fog situations (under steady-state and horizontally homogeneous conditions and neglecting radiational effects) can be treated by this modified theory, which yields turbulent vertical fluxes of sensible heat, water vapour and liquid water content and their divergences.The paper also derives a simple formula for the divergence of the turbulent flux of water vapour (E/z) under saturation conditions, which elucidates convergence ofE very close to the ground and divergence ofE higher up independent of whether the stratification is stable or unstable, i.e., whether there is fog over cold or warm ground. Model computations with the modified Monin-Obukhov theory are in full accordance with this formula. Thus a steam-fog case can be given as a demonstration of vertical profiles of turbulent fluxes of sensible heat, water vapour and liquid water content and their divergences.     

Calculation of basin-scale surface fluxes by combining remotely sensed data and atmospheric properties in a semiarid landscape

Optical remote sensing data collected during the Monsoon '90 experiment in the Walnut Gulch Experimental Watershed in southern Arizona were used to estimate basin-scale surface temperature, net radiation (R _n) and soil heat flux (G). These were combined with several atmospheric boundary-layer (ABL) models to allow computation of basin-scale surface fluxes of sensible (H) and latent heat (LE). The calculated fluxes were compared to averages from a network of surface flux stations. One ABL model calculatedH using a bulk similarity approach for wind and temperature with remotely sensed surface temperature as the lower boundary condition. With basin-scale estimates ofR _n andG, LE was solved as a residual. The other ABL model applied atmospheric profiles from a series of soundings in the conservation equations of temperature and humidity in the mixed layer to computeH andLE directly. By combining theseH values withR _n andG, calculation ofLE by residual also was performed. The ABL-derivedH values differed from the averages from the surface network by roughly 20 and 30% for the bulk similarity and conservation approaches, respectively. ForLE, these same differences were around 10 and 70%. The disparity was reduced to nearly 30% for the conservation approach whenLE was solved as a residual. Days with significant spatial variation in surface soil moisture and/or cloud cover were associated with most of the disagreement between the ABL-derived and surface-based values. This was particularly true for conservation estimates ofLE. The bulk similarity method appeared less sensitive non-ideal environmental conditions. This may in part be due to the use of remotely sensed information, which provided a lower boundary value of surface temperature and estimates ofR _n andG over the study area, thereby allowing for residual calculations ofLE. Such information clearly has utility for assessing the surface energy and water balance at basin scale.     

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).     

Determination des echanges verticaux moyens dans la couche limite planetaire a partir des donnees statistiques obtenues par les radiosondages de temperature

We have studied the vertical structure of the planetary boundary layer (PBL) as well as the vertical exchanges between this layer and the free atmosphere, using average macroscopic temperature data obtained from radiosondes. For this study we have used, for seven months in 1972, twice-daily radiosondes (00 and 12 H) from Trappes (Paris area) and PointK (Atlantic Ocean). The vertical structure of the PBL is given in the first part of the present work in terms of monthly average statistical parameters (vertical temperature gradient, frequency and level of inversion layers, frequency and thickness of mixing layers). We have thus demonstrated for the continental station, the influence of the daily cycle on the vertical temperature gradient; we have determined the monthlyH _M level above which the daily variation is not noticed. However, for the oceanic station, the absence of a daily cycle makes the temperature gradients at 00 and 12 H identical. The study of temperature inversion layers clearly indicates a high probability of their existence between 1500 and 2000 m; this probability is more than 80% both in summer at PointK, and in winter at Trappes. Similarly, we have demonstrated the annual evolution of the level of these elevated inversions at the two stations. An identical process has been performed in the case of the mixing layers. In the second part of our study, we have used a relationship between the vertical temperature gradient and the coefficients of matter exchange (K _z ), obtained from natural radioactive tracers (Guedaliaet al., 1974). Statistics have thus been obtained on the values ofK _z in the various layers above the two stations. These statistics prove that for the two stations and above 1500 m, values of the coefficients between 1 and 5 m² s^?1 are the most frequent; on the other hand, below 1500 m, the distribution of the coefficientsK _z offers different characteristics according to the month and to the station considered. Finally, we have used the concept of ‘equivalent coefficient’ -K _e - to characterize the exchanges between two levels considered as a whole. We have made a comparison of the values ofK _e when in the 0–1000 m layer and when in the 0–2000 m layer. The equivalent coefficientK _e allows us to compare the average exchanges above the two areas; thus, in summer, between the 0 and 1000 m level, the exchanges are more important above Trappes than they are above Point K. On the other hand, whatever may be the vertical structure of the PBL below, the value ofK _e in the 0–2000 m-layer is always between 1 and 5 m² s^?1. A generalisation of such a study applied to better chosen continental and oceanic sites would allow a comprehensive view of the structure of the PBL as well as of the turbulent exchanges between the PBL and the free atmosphere.     

Area-Averaged Sensible Heat Flux and a New Method to Determine Zero-Plane Displacement Length over an Urban Surface using Scintillometry

Field observations of area-averagedturbulence characteristics were conducted in a densely built-up residential neighbourhood in Tokyo, Japan. In addition to eddy-correlation (EC) sensors a scintillometer was used for the first time in a city. Significant results include: (1) Scintillometer-derived sensible heat fluxes, Q_H, obtained at a height 3.5 times the building height agree well with those using the EC technique; (2) source areas for the scintillometer fluxes are larger than for the EC sensors, so that at low heights over inhomogeneous terrain scintillometry offers advantages; (3) new similarity relationships for dissipation rates are proposed for urban areas; (4) a new technique that uses simultaneous scintillation measurements at two heights to directly estimate area-averaged zero-plane displacement height, z_d, is proposed. z_d estimated in this way depends slightly on atmospheric stability (lower z_d under more unstable conditions).     

Available energy and energy balance closure at four coniferous forest sites across Europe

The available energy (AE), driving the turbulent fluxes of sensible heat and latent heat at the earth surface, was estimated at four partly complex coniferous forest sites across Europe (Tharandt, Germany; Ritten/Renon, Italy; Wetzstein, Germany; Norunda, Sweden). Existing data of net radiation were used as well as storage change rates calculated from temperature and humidity measurements to finally calculate the AE of all forest sites with uncertainty bounds. Data of the advection experiments MORE II (Tharandt) and ADVEX (Renon, Wetzstein, Norunda) served as the main basis. On-site data for referencing and cross-checking of the available energy were limited. Applied cross checks for net radiation (modelling, referencing to nearby stations and ratio of net radiation to global radiation) did not reveal relevant uncertainties. Heat storage of sensible heat J _H, latent heat J _E, heat storage of biomass J _veg and heat storage due to photosynthesis J _C were of minor importance during day but of some importance during night, where J _veg turned out to be the most important one. Comparisons of calculated storage terms (J _E, J _H) at different towers of one site showed good agreement indicating that storage change calculated at a single point is representative for the whole canopy at sites with moderate heterogeneity. The uncertainty in AE was assessed on the basis of literature values and the results of the applied cross checks for net radiation. The absolute mean uncertainty of AE was estimated to be between 41 and 52 W m^?2 (10–11 W m^?2 for the sum of the storage terms J and soil heat flux G) during mid-day (approximately 12% of AE). At night, the absolute mean uncertainty of AE varied from 20 to about 30 W m^?2 (approximately 6 W m^?2 for J plus G) resulting in large relative uncertainties as AE itself is small. An inspection of the energy balance showed an improvement of closure when storage terms were included and that the imbalance cannot be attributed to the uncertainties in AE alone.     

Determination of zero-plane displacement and roughness length of a forest canopy using profiles of limited height

Flux parameters, zero-plane displancement height and roughness length of a forest canopy are determined taking into consideration a transition layer and atmospheric diabatic influences. The present study, unlike previous studies by DeBruin and Moore (1985) and Lo (1990) that accounted for the velocity profile alone, make use of information from both wind and temperature profiles in formulating the governing equations. However, only the top level measurement is assumed to be within the logarithmic regime. In addition to the mass conservation principle (e.g., Lo, 1990; DeBruin and Moore, 1985), an analytic relationship between the Monin-Obukhov length and the bulk Richardson number is employed as the closure equation for the governing system.The present method is applied to profile measurements taken at Camp Borden (den Hartog and Neumann, 1984) in and above a forest canopy with mean crown height of about 18.5 m. Profile data under neutral or near-neutral conditions yieldedd=12.69 m andz ₀=0.97 m, which are realistic values. In general,z ₀ increases slightly with increasing wind yet remains relatively constant with respect to small variation of stabilities. On the other hand, increases of wind speed reduced values of displacement height,d, by as much as 50%. The influence, if any, of stability ond, however, is not clear from the results of the present study. The validity of using profile data of limited height is also carefully examined. At least for neutral or near-neutral stabilities, the present method can yield realistic results even though the profile heights are substantially below the transition layer height suggested by Garratt (1978).     

A determination of the Dalton and Stanton numbers over a saturated barley field

In order to determine the values of the Dalton and the Stanton numbers, an observational study was made over a saturated barley field in the Hachirogata. flat reclaimed land located in the northern part of Japan. The mean height of the barley was about 11 cm; the roughness height for momentum was determined from the mean wind profiles as 4.24 ± 0.18 cm and the zero-plane displacement height as 0 cm. Under neutral stratification and a saturated surface, the reciprocals of the Dalton and Stanton numbers, Da^-1 and St^-1, were estimated. The results show that the mean value of St^-1 is 12.1, and the ratio of the bulk transfer coefficient for heat to that for momentum. C _H/C_M, is 0.53, which are not entirely incompatible with the few results available from past observations. The mean value of Da^- is 38.2. This value is larger than St^-1, and fits reasonably well with the semi-empirical equation proposed by Brutsaert (1975a,b).     

A comparison of airborne eddy correlation and bulk aerodynamic methods for ocean-air turbulent fluxes during cold-air outbreaks

Four bulk schemes (LKB, FG, D and DB), with the flux-profile relationships of Liuet al. (1979), Francey and Garratt (1981), Dyer (1974), and Dyer and Bradley (1982), are derived from the viscous interfacial-sublayer model of Liuet al. These schemes, with stability-dependent transfer coefficients, are then tested against the eddy-correlation fluxes measured at the 50 m flight level above the western Atlantic Ocean during cold-air outbreaks. The bulk fluxes of momentum (), sensible heat (H), and latent heat (E) are found to increase with various von Kármán constants (k _M for k _H forH, andk _E forE). Except that the LKB scheme overestimates by 28% (46Wm^–2), on the average, the fluxes estimated by the four bulk schemes appear to be in fairly good agreement with those of the eddy correlation method (magnitudes of biases within 10% for , 17% forH, and 13% forE). The results suggest that the overall fluxes and surface-layer scaling parameters are best estimated by FG and thatk _H <k _E . On the average, the FG scheme underestimates by 10% (0.032N m^–2) andE by 4% (12Wm^–2), and overestimatesH by 0.3% (0.5W m^–2). The equivalent neutral transfer coefficients at 10 m height of the FG scheme compare well with some schemes of those tested by Blanc (1985).The relative importance of various von Kármán constants, dimensionless gradients and roughness lengths to the oceanic transfer coefficients is assessed. The dependence of transfer coefficients on wind speeds and roughness lengths is discussed. The transfer coefficients for andE agree excellently between LKB and FG. However, the ratio of the coefficient forH of LKB to that of FG, increasing with decreasing stability, is very sensitive to stability at low winds, but approaches the neutral value of 1.25 at high winds.     

A Theoretical and Experimental Investigation of Energy-Containing Scales in the Dynamic Sublayer of Boundary-Layer Flows

The existence of universal power laws at low wavenumbers (K) in the energy spectrum (E_u) of the turbulent longitudinal velocity (u) is examined theoretically and experimentally for the near-neutral atmospheric surface layer. Newly derived power-law solutions to Tchen's approximate integral spectral budget equation are tested for strong- and weak-interaction cases between the mean flow and turbulent vorticity fields. To verify whether these solutions reproduce the measured E_u at low wavenumbers, velocity measurements were collected in the dynamic sublayer of the atmosphere at three sites and in the inner region of a laboratory open channel. The atmospheric surface layer measurements were carried out using triaxial sonic anemometers over tall corn, short grass, and smooth desert-like sandy soil. The open channel measurements were performed using a two-dimensional boundary-layer probe above a smooth stainless steel bed. Comparisons between the proposed analytical solution for E_u, the dimensional analysis by Kader and Yaglom, and the measured Haar wavelet E_u spectra are presented. It is shown that when strong interaction between the mean flow and turbulent vorticity field occurs, wavelet spectra measurements, predictions by the analytical solution, and predictions by the dimensional analysis of Kader-Yaglom (KY) are all in good agreement and confirm the existence of a -1 power law in E_u(= C_uuu² _* K^-1, where C_uu is a constant and u_* is the friction velocity). The normalized upper wavenumber limit of the -1 power law (Kz = 1, where z is the height above the zero-plane displacement) is estimated using two separate approaches and compared to the open channel and atmospheric surface-layer measurements. It is demonstrated that the measured upper wavenumber limit is consistent with Tchen's budget but not with the KY assumptions. The constraints as to whether the mean flow and turbulent vorticity strongly interact are considered using a proposed analysis by Panchev. It is demonstrated that the arguments by Panchev cannot be consistent with surface-layer turbulence. Using dimensional analysis and Heisenberg's turbulent viscosity model, new constraints are proposed. The new constraints agree with the open channel and atmospheric surface-layer measurements, Townsend's inactive eddy motion hypothesis, and the Perry et al. analysis.     

Heat transport coefficients for constant energy flux models of broad leaves

Experimental determinations of the local heat transfer by forced convection from model leaves heated by a constant energy flux were made in the laboratory under laminar and turbulent flow conditions.The results are expressed in a logarithmic dimensionless plot of the local Nusselt number, Nu _d , against the local Reynolds number, Re _d . For the laminar case, Nu _d was only a linear function of Re _d ^1/2 downwind from the leading edge regions, although this relationship departed from that predicted theoretically due to the finite size and thickness of the model. For the turbulent case, a simple relationship between Nu _d and Re _d was found over a wide range of Reynolds numbers. The enhancement of heat transfer in the turbulent case depends primarily on the scale of turbulence rather than on the turbulent intensity.Past workers have discussed their results in relation to a factor , defined as the ratio between the heat transfer predicted by the Polhausen equation, and that measured. The results suggest that is not a unique parameter and may not be useful in describing the overall turbulent transfer process.     

A coupled model on land-atmosphere interactions — Simulating the characteristics of the PBL over a heterogeneous surface

An attempt is made to construct a model, coupling land surface and atmospheric processes in the planetary boundary layer (PBL). A grassland strip in a semi-desert (hereinafter called desert) is presupposed, so as to simulate the case of heterogeneous vegetation cover.Modeling results indicate that every term in the equation of the surface energy balance changes as the air flows over the grassland. The striking contrast of water and energy conditions between the grassland and the desert means that the air over the grassland is cooler and wetter than that over the desert. Consequently, in the heating and dynamic forcing of the air by the underlying surface, heterogeneities arise and are then transferred upward by the turbulent motions. Horizontal differences thus develop in the PBL, resulting in a local circulation. Meanwhile, the horizontal differences affect the free atmosphere through vertical motion at the top of the PBL.List of symbols d ₁,d ₂,d ₃ depths of surface, middle and lower layers of soil - T _c ,T ₁,T ₂,T ₃ temperatures of canopy, surface, middle and lower layers of soil - R _nc net radiation of canopy layer - _c shielding factor of vegetation - Ew, Etc evaporation from wet fraction of foliage and transpiration from dry fraction of foliage - Et ₁,Et ₂ transpiration of foliage water absorbed by the root in the upper and lower soil, respectively - H _c sensible heat of canopy - P _c ,D _c precipitation rate and drainage of canopy - C _s ,C _c ,C _w heat capacity of soil, canopy and water - _w , _s density of water and air near the surface - D hydraulic permeability of soil - _s saturated value of the ratio of volumetric soil moisture - S _g , _g solar radiation and surface reflection - H _g ,R _{L g} turbulent heat flux and long wave radiation of surface - P _g ,E _g precipitation rate and evaporation of soil surface - K _s soil thermal diffusivity - K ^(m),K ^(H),K ^(q) eddy coefficients of momentum, heat and moisture - u, v, w components of wind speed in three directions - air potential temperature - e turbulent kinetic energy - p atmospheric pressure - C _p specific heat of air under constant pressure - R _d gas constant - u _* friction velocity - _* feature temperature - h height of the PBL - f Coriolis parameter - L ₀ Monin-Obukhov length - latent heat of vaporization - q specific humidity - M _c ,M _cm interception water storage of canopy and its maximum - ₀ Exner number of largescale background field - perturbation Exner number - u _g ,v _g components of the geostrophic wind speed Sponsored by the National Natural Science Foundation of China.     

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.     

Flux determination over a smooth surface under strongly unstable conditions

Careful micrometeorological measurements on an empty parking lot allowed determination of the surface fluxes of sensible heatH and of momentum by applying profile equations derived from Monin-Obukhov similarity theory with two sets of the stability correction function for momentum _m and sensible heat _h . These fluxes were compared with reference values ofH independently determined by means of an eddy correlation technique. In general, better agreement was found betweenH values derived from profiles with the stability functions of Brutsaert (1992) and referenceH values, than when the Businger-Dyer functions were used to deriveH. The disagreement in the latter comparison was especially serious under strongly unstable conditions, with the value ofy=–z/L (wherez is the height andL is the Obukhov length) larger than 10. A closer look at the procedure for calculatingH from the profiles revealed that the large differences between theH values derived with these two different versions of the stability correction functions were caused by the small differences of the _h values, and not by the larger differences of the _m values. This result stems from the strong sensitivity of the resultingH values on the choice of _h .     

Single and dual crop coefficients and crop evapotranspiration for wheat and maize in a semi-arid region

In this study, weighing lysimeters were used to investigate the daily crop coefficient and evapotranspiration of wheat and maize in the Fars province, Iran. The locally calibrated Food and Agriculture Organization (FAO) Penman–Monteith equation was used to calculate the reference crop evapotranspiration (ET_o). Micro-lysimetry was used to measure soil evaporation (E). Transpiration (T) was estimated by the difference between crop evapotranspiration (ET_c) and E. The single crop coefficient (K _c) was calculated by the ratio of ET_c to ET_o. Furthermore, the dual crop coefficient is composed of the soil evaporation coefficient (K _e) and the basal crop coefficients (K _cb) calculated from the ratio of E and T to ET_o, respectively. The maximum measured evapotranspiration rate for wheat was 9.9 mm?day^?1 and for maize was 10 mm?day^?1. The total evaporation from the soil surface was about 30 % of the total wheat ET_c and 29.8 % of total maize ET_c. The single crop coefficient (K _c) values for the initial, mid-, and end-season growth stages of maize were 0.48, 1.40, and 0.31 and those of wheat were 0.77, 1.35, and 0.26, respectively. The measured K _c values for the initial and mid-season stages were different from the FAO recommended values. Therefore, the FAO standard equation for K _c-_mid was calibrated locally for wheat and maize. The K _cb values for the initial, mid-, and end-season growth stages were 0.23, 1.14, and 0.13 for wheat and 0.10, 1.07, and 0.06 for maize, respectively. Furthermore, the FAO procedure for single crop coefficient showed better predictions on a daily basis, although the dual crop coefficient method was more accurate on seasonal scale.     

Characteristic heat transfer coefficients near the ground at night during strong winds

Based on theoretical radiative cooling values and observed temperature changes with time near the surface during the night, the bulk heat transfer coefficient C _H is estimated from standard meteorological observations obtained from stations representative of open rural, small town and large urban areas, for nights with clear skies and relatively strong winds. It is shown that C _H is smaller than the drag coefficient C _M, and that C _H/C _M over urban areas is smaller than that over open countryside.     

Local and Global Similarity in Turbulent Transfer of Heat, Water Vapour, And CO 2 in the Dynamic Convective Sublayer Over a Suburban Area

We investigated the ‘local’ and ‘global’ similarity of vertical turbulent transfer of heat, water vapour, and CO₂ within an urban surface layer. The results were derived from field measurements in a residential area of Tokyo, Japan during midday on fair-weather days in July 2001. In this study, correlation coefficients and quadrant analysis were used for the evaluation of ‘global’ similarity and wavelet analysis was employed for investigating ‘local’ similarity. The correlation coefficients indicated that the transfer efficiencies of water vapour and CO₂ were generally smaller than that of heat. Using wavelet analysis, we found that heat is always efficiently transferred by thermal and organized motions. In contrast, water vapour and CO₂, which are passive quantities, were not transferred as efficiently as heat. The quadrant analyses showed that the heat transfer by ejection exceeded that by sweep, and the ratios of ejection to sweep for water vapour and CO₂ transfer were less than that for heat. This indicated that heat is more efficiently transferred by upward motions and supported the findings from wavelet analysis. The differences of turbulent transfer between heat and both CO₂ and water vapour were probably caused both by the active role of temperature and the heterogeneity in the source distribution of scalars