Airflow above changes in surface heat flux,temperature and roughness; an extension to include the stable case

A numerical model of airflow above changes in surface roughness and thermal conditions is extended to include cases with stable thermal stratification within the internal boundary-layer. The model uses a mixing-length approach with empirical forms for M and H.Results are presented for some basic cases and an attempt is then made to compare results given by the model with the experimental results of Rider, Philip and Bradley. Tolerable agreement is achieved. The importance of roughness change and thermal stability effects in the diffusion of heat and moisture near a leading edge is emphasised.Notation A Refers to Taylor (1970) - B Businger-Dyer constant (= 16.0) in forms for _M and _H - C Constant in form for in stable case - c _p Specific heat at constant pressure - E Scaled absolute humidity - g Acceleration due to gravity - H Upward vertical heat flux - H ₀, H ₁ Surface heat fluxes for x <0, x0 - H _E Upward latent heat flux - k Von Kármán's constant (= 0.4) - K _H K _W Eddy transfer coefficients for heat and water vapour - L Monin-Obukhov length - L _H Latent heat of evaporation for water - m Ratio of roughness lengths ( = z ₁/z ₀) - RPB Refers to Rider et al. (1964) - RL* Non-dimensional parameter (see Equations (9), (20a), (22a), (24a)) - R* Net radiation less ground heat flux (see Equations (15), (16)) - T Scaled temperature - T ₁ Downstream scaled surface temperature - u ₀ u ₁(x) Surface friction velocities for x <0, x0 - U, W Horizontal and vertical mean velocities - x, z Horizontal and vertical co-ordinates - Z _i Local roughness length - z ₀, z _i Roughness lengths for x < 0, x 0 - Temperature - ₀, ₁ Surface temperatures for x<0, x0 - _E Non-dimensional absolute humidity gradient - _H Non-dimensional temperature gradient of heat flux - _M Non-dimensional wind shear - = _M = _H = _E an assumption used in stable conditions - Air density - Absolute humidity - _w Density of water - Kinematic shear stress - Logarithmic height scale (= ln(z+z ₁)/z ₁)     

Momentum and heat transfers in the surface layer over a frozen sea

Wind and temperature profiles from a 10-m mast were measured over the frozen Baltic Sea. The Monin-Obukhov similarity theory applies well to runs carefully selected according to stationarity criteria. This provides relatively low-scattered results with the roughness length z ₀ 0.04 cm, the drag coefficient C _D 1.5 × 10^-3 and the Stanton number C _H 1.00 × 10^-3 under near-neutral conditions. The roughness length, however, behaves in a peculiar way under intense stratification conditions. The reasons proposed for this could lead to an extension of the theory. The mechanisms for momentum and heat transfers are also examined, revealing that there are two different regimes, the smooth and the rough, for the wall friction but not for the heat transfer. Further, the scatter of the data for momentum and heat transfer under the aerodynamically rough regime can be explained by the distinction between the type of thermal stability conditions.     

A study of the seasonal migration of ITCZ and the quasi-periodic oscillations in a simple monsoon system using an energy balance model

Summary A zonally averaged global energy balance model with feedback mechanisms was constructed to simulate (i) the poleward limits of ITCZ over the continent and over the ocean and (ii) a simple monsoon system as a result of differential heating between the continent and the ocean. Three numerical experiments were performed with lower boundary as (1) global continent, (2) global ocean and (3) continent-ocean, with freezing latitudes near the poles. Over the continent, midlatitude deserts were found and the ITCZ migrates 25° north and south with seasons. Over a global swamp ocean results do not show migration of ITCZ with time but once the ocean currents are introduced the ITCZ migrates 5° north and south with seasons. It was found that the seasonal migration of ITCZ strongly depends on the meridional distribution of the surface temperature. It was also found that continent influences the location of the oceanic ITCZ. In the tropics northward progression of quasi-periodic oscillations called events are found during the pre- and post-monsoon periods with a period of 8 to 15 days. This result is consistent with the observed quasi-periodic oscillations in the tropical region. Northward propagation of the surface temperature perturbation appears to cause changes in the sensible heat flux which in turn causes perturbations in vertical velocity and latent heat flux fields.List of Symbols vertical average - ₀ zonal average - vertical mean of the zonal average - _0s zonal average at the surface - _0a zonal average at 500 mb level - latitude We now define the various symbols used in the model rate of atmospheric heating due to convective cloud formation (K/sec) - dp/dt (N/m²/sec) - density - potential temperature (K) - rate of rotation of the earth (rad/sec) - empirical constant - humidity mixing ratio - ^* saturated humidity mixing ratio - opacity of the atmosphere - ₁,₂ factors for downward and upward effective black body long wave radiation from the atmosphere - Stefan-Boltzmann constant - emissivity of the surface - _D subsurface temperature (K) - a specific volume - _0xs ,_0ys eastward and northward components of surface frictional stress - ^* vertical velocity at the top of the boundary layer (N/m²/sec) - P Thickness of the boundary layer (mb) - nondimensional function of pressure - P pressure - P _a pressure of the model atmosphere (N/m²) - P _s pressure at the surface (N/m²) - t time (sec) - U eastward wind speed (m/sec) - V northward wind speed (m/sec) - surface water availability - T absolute temperature (K) - heat addition due to water phase changes - g acceleration due to gravity (m²/sec) - a radius of the earth (m) - R gas constant for dry air (J/Kg/K) - C _p specific heat of air at constant pressure (J/Kg/K) - k R/C _p - L latent heat of condensation (J/Kg) - f coriolis parameter (rad/sec) - H _s H _0s ⁽¹⁾ +H _0s ⁽²⁾ +H _0s ⁽³⁾ +H _0s ⁽⁴⁾ +H _0s ⁽⁵⁾ (J/m²/Sec)=sum of the rates of vertical heat fluxes per unit surface area, directed toward the surface - H _a H _0a ⁽¹⁾ +H _0a ⁽²⁾ +H _0a ⁽³⁾ +H _0a ⁽⁴⁾ (J/m²/Sec)=sum of the rates of heat additions to the atmospheric column per unit horizontal area by all processes - H _0s ⁽¹⁾ ,H _0a ⁽¹⁾ heat flux due to short wave radiation - H _0s ⁽²⁾ ,H _0a ⁽²⁾ heat flux due to long wave radiation - H _0s ⁽³⁾ ,H _0a ⁽³⁾ heat flux due to small scale convection - H _0s ⁽⁴⁾ heat flux due to evaporation - H _0a ⁽⁴⁾ heat flux due to condensation - H _0s ⁽⁵⁾ heat flux due to subsurface conduction and convection - e ^* saturation vapor pressure - R solar constant (W/m²) - r _a albedo of the atmosphere - r _s albedo of the surface - b ₂ empirical constant (J/m²/sec) - c ₂ empirical constant (J/m²/sec) - e ₂ nondimensional empirical constant - f ₂ empirical constant (J/m₂/sec) - factor proportional to the conductive capacity of the surface medium - a _s constant used in Sellers model - b _s positive constant of proportionality used in the Sellers model (kg m²/J/sec²) - K _HT coefficient for eddy diffusivity of heat (m²/sec) - K _HE exchange coefficient for water vapor (m²/sec) - h depth of the water column (m) - z height (m) - V _0ws meridional component of surface current (m/sec) - n cloud amount - G _0,n long wave radiation form the atmosphere for cloud amount n (W/m²) - B ₀ long wave radiation from the surface (W/m²) - S _0,n short wave radiation from the atmosphere for cloud amount n (W/m²) - A _n albedo factor for a cloud amount n - R _f1 large scale rainfall (mm/day) - R _f2 small scale rainfall (mm/day) With 22 Figures     

Temperature distribution and current system in a convectively mixed lake

During spring and autumn, many lakes in temperate latitudes experience intensive convective mixing in the vertical, which leads to almost isothermal conditions with depth. Thus the regime of turbulence appears to be similar with that characteristic of convective boundary layers in the atmosphere. In the present paper a simple analytical approach, based on boundary-layer theory, is applied to convective conditions in lakes. The aims of the paper are firstly to analyze in detail the temperature distribution during these periods, and secondly to investigate the current system, created by the horizontal temperature gradient and wind action. For these purposes, simple analytical solutions for the current velocities are derived under the assumption of depth-constant temperatures. The density-induced current velocities are shown to be small, in the order of a few mm/sec. The analytical model of wind-driven currents is compared with field data. The solution is in good qualitative agreement with observed current velocities under the condition that the wind field is steady for a relatively long time and that residual effects from former wind events are negligible.The effect of the current system on an approximately depth-constant temperature distribution is then checked by using the obtained current velocity fields in the heat transfer equation and deriving an analytical solution for the corrected temperature field. These temperature corrections are shown to be small, which indicates that it is reasonable to describe the temperature distribution with vertical isotherms.Notation T temperature - t time - x, y, z cartesian coordinates - molecular viscosity - _h , _v horizontal and vertical turbulent viscosity - K _h ,K _v horizontal and vertical turbulent conductivity - Q heat flux through the water surface - D depth - u, v, w average current velocity components inx, y andz directions - f Coriolis parameter - p pressure - density - g gravity acceleration - a constant in the freshwater state equation - h _s deviation from the average water surface elevation - L _*,H _* length and depth scale - U _*,W _* horizontal and vertical velocity scale - T temperature difference scale - bottom slope - u _* friction velocity at the water surface - von Karman constant - L Monin-Obukhov length scale - buoyancy parameter - l turbulence length scale - C ₁,C ₂,C ₃ dimensionless constants in the expressions for the vertical turbulent viscosity - , dimensionless vertical coordinate and dimensionless local depth - angle between surface stress direction andx-axis - T _bx ,T _by bottom stress components - c bottom drag coefficient     

Experiments On Buoyant Plume Dispersion In A Laboratory Convection Tank

Plume dispersion in the convective boundary layer (CBL) is investigated experimentally in a laboratory convection tank. The focusis on highly-buoyant plumes that loft near or become trapped in the CBL capping inversion and resistdownward mixing. Such plumes are defined by dimensionless buoyancy fluxes F_* 0.1, where F_* = F_b/(U w_* ² z_i), F_b is the stack buoyancy flux,U is the mean wind speed, w_* is the convective velocity scale, and z_i is the CBL depth. The aim is to obtain statistically-reliable mean (C) and root-mean-square (rms, _c) concentration fields as a function of F_* and the dimensionless distance X = w_*x/(U z_i), where x is the distance downstream of the source.The experiments reveal the following mainresults: (1) For 3 X 4and F_* 0.1, the crosswind-integrated concentration (CWIC) fields exhibit distinctly uniform profiles below z_i with a CWIC maximum aloft, in contrast to the nonuniform profiles obtained earlier by Willis and Deardorff. (2) The lateral dispersion (_y) variation with X is consistent with Taylor's theory for _* 0.1 and a buoyancy-enhanced dispersion, _y/z_i F_* ^1/3X^2/3, forF_* = 0.2 and 0.4. (3) The entrapment, the plume fraction above z_i, has a mean (E) that follows a systematic variationwith X and F_*, and a variability (_e/E) that is broad ( 0.3 to 2) near the source but subsides to 0.25 far downstream. (4) Vertical profiles of the concentration fluctuation intensity (c/C) are uniform for z < z_i and X > 1.5, but exhibit significant increases: (a) at the surface and close to the source (X 1.5), and(b) in the entrainment zone. (5) The cumulative distribution functions (CDFs) of the scaled concentration fluctuations (c/_c) separate into mixed-layer and entrainment-layer CDFs for X 2, with the mixed-layer group collapsing to a single distribution independent of z.These are the first experiments to obtain all components of the lateral and vertical dispersion parameters (rms meander, relative dispersion, total dispersion) for continuous buoyant releases in a convection tank. They also are the first tank experiments to demonstrate agreement with field observations of: (1) the scaled ground-level concentration along the plume centreline, and (2) the dimensionless lateral dispersion _y/z_i of buoyant plumes.     

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.     

Mixed-layer heat advection and entrainment during the sea breeze

A model is developed to simulate the potential temperature and the height of the mixed layer under advection conditions. It includes analytic expressions for the effects of mixed-layer conditions upwind of the interface between two different surfaces on the development of the mixed layer downwind from the interface. Model performance is evaluated against tethersonde data obtained on two summer days during sea breeze flow in Vancouver, Canada. It is found that the mixed-layer height and temperature over the ocean has a small but noticeable effect on the development of the mixed layer observed 10 km inland from the coast. For these two clear days, the subsidence velocity at the inversion base capping the mixed layer is estimated to be about 30 mm s^–1 from late morning to late afternoon. When the effects of subsidence are included in the model, the mixed-layer height is considerably underpredicted, while the prediction for the mean potential temperature in the mixed layer is considerably improved. Good predictions for both height and temperature can be obtained when values for the heat entrainment ratio,c, 0.44 and 0.68 for these two days respectively for the period from 1000 to 1300 LAT, were used. These values are estimated using an equation including the additional effects on heat entrainment due to the mechanical mixing caused by wind shear at the top of the mixed layer and surface friction. The contribution of wind shear to entrainment was equal to, or greater than, that from buoyant convection resulting from the surface heat flux. Strong wind shear occurred near the top of the mixed layer between the lower level inland flow and the return flow aloft in the sea breeze circulation.Symbols c entrainment parameter for sensible heat - c _p specific heat of air at constant pressure, 1010 J kg^–1 K^–1 - d ₁ the thickness of velocity shear at the mixed-layer top, m - Q _H surface sensible heat flux, W m^–2 - u _m mean mixed-layer wind speed, m s^–1 - u _* friction velocity at the surface, m s^–1 - w subsidence velocity, m s^–1 - W subsidence warming,^oC s^–1 - w _e entrainment velocity, m s^–1 - w _* convection velocity in the mixed layer, m s^–1 - x downwind horizontal distance from the water-land interface, m - y dummy variable forx, m - Z height above the surface, m - Z _i height of capping inversion, m - Z _m mixed-layer depth, i.e.,Z _i–Z_s, m - Z _s height of the surface layer, m - lapse rate of potential temperature aboveZ _i, K m^–1 - potential temperature step atZ _i, K - u _h velocity step change at the mixed-layer top - _m mean mixed-layer potential temperature, K     

A Field Study of the Mean Pressure About a Windbreak

To provide additional field data for assessingwindbreak flow models, mean ground-level pressurehas been measured upstream and downstream from along porous fence (height H = 1.25 m, resistancecoefficient k _r = 2.4). Measurements were madeduring periods of near-neutral stability and near-normallyincident flow, with the fence standing on bare soil(roughness length, z ₀ 0.8 cm;H/z ₀ 160), or within a plant canopy. The mean pressure field,measured far from the ends of the fence, was foundto be quite insensitive to mean wind direction( , zero for perpendicular flow), for| | less than about 25°.In the absence of a canopy, during each measurementperiod the minimum pressure occurred at the closestsampling location to leeward of the windbreak, thepressure-gradient in most cases beingmaximally-adverse in the immediate lee, and decayingwith increasing downwind distance (x). On one day ofmeasurements, however, the pressure gradient over2 x/H 6 (H = windbreak height) resembled theleeward plateau identified by Wang and Taklein their numerical studies. Perhaps thisoccasional feature was only due to instrumenterror. Nevertheless a plateau of sorts wasindicated in similar measurements by Judd andPrendergast (with H = 1.92 m, z ₀ 1.2 cm;H/z ₀ 160, k _r 3). Therefore,existence of a leeward pressure plateau behind athin fence cannot be definitely ruled out.When the windbreak was placed in a canopy, minimumsurface pressure was displaced downwind. Thisagrees with the wind-tunnel study of Judd, Raupach and Finnigan,and is consistent with a simple simulation reported here.     

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.     

Similarity forms for ground-source surface-layer diffusion

Past work on analyzing ground-source diffusion data in terms of surface-layer similarity theory is reviewed; these analyses assume that _z /L orh/L is a function of u ^* x/L (where h = Q/ dy). It is argued that an alternative scaling, h ^*/L versus x/L, is nearly as universal in that it is very weakly influenced by surface roughness, except for a modest influence in the free convective case (h ^* = Q/u ^* dy); the advantage of this scaling is that it eliminates the need to reassess as vertical diffusion progresses. The Prairie Grass data set is adjusted for the difference in source and sampling heights, and is plotted with this scaling. Simple analytic equations are suggested that fit the resultant data plots for stable and unstable conditions, and suggestions are made towards practical application of these results.On assignment from the National Oceanic and Atmospheric Administration, U.S. Department of Commerce.     

Momentum and scalar transfer coefficients over aerodynamically smooth antarctic surfaces

Vertical profiles of wind speed, temperature and humidity were used to estimate the roughness lengths for momentum (z ₀), heat (z _H ) and moisture (z _Q) over smooth ice and snow surfaces. The profile-measurements were performed in the vicinity of a blue ice field in Queen Maud Land, East Antarctica. The values ofz ₀ over ice (3·10^–6 m) seem to be the smallest ever obtained over permanent, natural surfaces. The settling of snow on the ice and the loss of momentum at saltating snow particles serve as momentum dissipating processes during snow-drift events, expressed as a strong dependence ofz ₀ on u_#.The scalar roughness lengths and surface temperature can be evaluated from the temperature and humidity profile measurements if the ratioz _H /z _Q is specified. This new method circumvents the difficult measurement of surface temperature. The scalar roughness lengths seem to be approximately equal toz0 for a large range of low roughness Reynolds numbers, despite the frequent occurrence of drifting snow. Possible reasons for this agreement with theory of non-saltating flow are discussed.     

A numerical modeling study of the marine boundary layer over the Gulf Stream during cold air advection

A two-dimensional mesoscale model has been developed to simulate the air flow over the Gulf Stream area where typically large gradients in surface temperature exist in the winter. Numerical simulations show that the magnitude and the maximum height of the mesoscale circulation that develops downwind of the Gulf Stream depends on both the initial geostrophic wind and the large-scale moisture. As expected, a highly convective Planetary Boundary Layer (PBL) develops over this area and it was found that the Gulf Stream plays an important role in generating the strong upward heat fluxes causing a farther seaward penetration as cold air advection takes place. Numerical results agree well with the observed surface fluxes of momentum and heat and the mesoscale variation of vertical velocities obtained using Doppler Radars for a typical cold air outbreak. Precipitation pattern predicted by the numerical model is also in agreement with the observations during the Genesis of Atlantic Lows Experiment (GALE).List of Symbols u east-west velocity [m s^–1] - v north-south velocity [m s^–1] - vertical velocity in coordinate [m s^–1] - w vertical velocity inz coordinate [m s^–1] - gq potential temperature [K] - q moisture [kg kg^–1] - scaled pressure [J kg^–1 K^–1] - U _g the east-south component of geostrophic wind [m s^–1] - V _g the north-south component of geostrophic wind [m s^–1] - vertical coordinate following terrain - x east-west spatial coordinate [m] - y north-south spatial coordinate [m] - z vertical spatial coordinate [m] - t time coordinate [s] - g gravity [m² s^–1] - E terrain height [m] - H total height considered in the model [m] - q _s saturated moisture [kg kg^–1] - p pressure [mb] - p ₀₀ reference pressure [mb] - P precipitation [kg m^–2] - vertical lapse rate for potential temperature [K km^–1] - L latent heat of condensation [J kg^–1] - C _p specific heat at constant pressure [J kg^–1 K^–1] - R gas constant for dry air [J kg^–1 K^–1] - R _v gas constant for water vapor [J kg^–1 K^–1] - f Coriolis parameter (2 sin ) [s^–1] - angular velocity of the earth [s^–1] - latitude [^o] - K _H horizontal eddy exchange coefficient [m² s^–1] - t integration time interval [s] - x grid interval distance inx coordinate [m] - y grid interval distance iny coordinate [m] - adjustable coefficient inK _H - subgrid momentum flux [m² s^–2] - subgrid potential temperature flux [m K s^–1] - subgrid moisture flux [m kg kg^–1 s^–1] - u _* friction velocity [m s^–1] - _* subgrid flux temperature [K] - q _* subgrid flux moisture [kg kg^–1] - w _* subgrid convective velocity [m s^–1] - z ₀ surface roughness [m] - L Monin stability length [m] - _s surface potential temperature [K] - k von Karman's constant (0.4) - v air kinematic viscosity coefficient [m² s^–1] - K _M subgrid vertical eddy exchange coefficient for momentum [m² s^–1] - K subgrid vertical eddy exchange coefficient for heat [m² s^–1] - K _q subgrid vertical eddy exchange coefficient for moisture [m² s^–1] - z _i the height of PBL [m] - h _s the height of surface layer [m]     

On the role of roughness lengths in flux parameterizations of boundary-layer models

Flux-profile relationships based on surface-layer similarity theory are used to derive relationships between the Monin-Obukhov stability parameter = z/L and the bulk Richardson number Ri _b . In contrast to previous studies, the roughness length for heat, z _0h ,is assumed unequal to the roughness length for momentum, z _0m .For the stable case, an analytic expression of in terms of Ri _b can be derived and in the unstable case, the solution is obtained through a simple iterative process.Errors introduced from the simplification of z _0h = z _0m are evaluated and are shown to be very significant in most cases. Thus, this error in many practical applications may invalidate the intended solution.     

Standard deviation of vertical two-point longitudinal velocity differences in the atmospheric boundary layer

The standard deviation of vertical two-point longitudinal velocity fluctuation differences is analyzed experimentally with eleven sets of turbulence measurements obtained at the NASA 150-m ground-winds tower site at Cape Kennedy, Florida. It is concluded that /u _*0 is proportional to (fz/u _*0)^0.22, where the coefficient of proportionality is a function of fz/u _*0 and u _*0/fL ₀. The quantities f and L₀ denote the Coriolis parameter and the surface Monin-Obukhov stability length, respectively; u _*0 is the surface friction velocity; z is the vertical distance between the two points over which the velocity difference is calculated; and zz is the mean height of the mid-point of the interval z above natural grade. The results of the analysis are valid for 20<-u _*0/fL ₀<2000.     

Energy flux partitioning over the Amazon forest

The present study involved determination of the experimental energy receipt partitioning over the tropical Amazon forest. Diurnal variation of net radiation (Q ^*), sensible heat flux (Q _H) and latent heat flux (Q _E) is presented. The daytimeQ _E is in phase withQ ^* and it is always an important term in the energy balance. The daily averagedQ _E is 59 to 100% of the dailyQ ^* whereasQ _H is 5 to 28% at the Amazon forest site (2° 57 S; 59° 57 W) for the sample periods. The results present evidence thatQ _E over the Amazon forest is greater thanQ ^* in the afternoon hours. The role of sensible heat advection in maintaining largeQ _E over the forest surface is discussed. Hourly Bowen ratio () values for two campaigns of the Amazon forest micrometeorological experiment are presented. During daylight hours, the differences in are not significant, and exhibit a systematic pattern. The only time that the variation in Bowen ratio increased significantly was at sunrise and sunset when the thermal structure of the air was changing from a strong inversion to lapse and vice versa. The diurnal values changed from –3.50 to 0.85. The mean hourly calculated from values from 07.00 to 16.00 h, varied from 0.05 to 0.85.Diese Studie beschäftigt sich mit der Aufteilung der empfangenen Energie über dem tropischen Amazonasurwald. Es wird der Tagesgang der Strahlungsbilanz (Q ^*), des fühlbaren (Q _H) und des latenten Wärmestromes (Q _E) vorgestellt. Während der Tagesstunden istQ _E in Phase mitQ ^* und ist immer ein wichtiger Term der Energiebilanz. Das Tagesmittel vonQ _E beträgt 59 bis 100%,Q _H 5 bis 28% des täglichenQ ^* an den Meßtagen bei der Amazonasurwaldstation (2° 57 S; 59° 57 W). Die Ergebnisse legen nahe, daß in den NachmittagsstundenQ _E über dem Amazonasurwald größer ist alsQ ^*. Die Rolle der Advektion von fühlbarer Wärme zur Aufrechterhaltung des großenQ _E über der Waldoberfläche wird diskutiert. Für zwei Meßkampagnen wurden die stündlichen Bowenverhältnisse () vorgestellt. Während der Tagesstunden ergaben sich keine signifikanten Änderungen von, während bei Sonnenaufgang und -untergang, wenn der thermische Aufbau der Luft von einer starken Inversion zu neutral und umgekehrt wechselt, die Unterschiede deutlich anstiegen. Die Tageswerte von lagen zwischen –3.50 und 0.85. Die Stundenmittel von 7.00 bis 16.00 Uhr schwankten zwischen 0.05 und 0.85.

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With 3 Figures     

Displaced-Beam Small Aperture Scintillometer Test. Part I: The Wintex Data-Set

The friction velocity (u_*) and the sensible heat flux density (H) determined with a displaced-beam small aperture scintillometer (DBSAS) and a hot-film eddy correlation system are compared. Random errors in the DBSAS are relatively small, compared to scatter found with two eddy-correlation systems. Assuming that the hot-film system yields the true fluxes, theDBSAS appears to overestimate u_* when u_* is less than 0.2 m s^-1 and to underestimate u_* at high wind speeds. This implies that the DBSAS measurements of theinner scale length of turbulence, l₀, a direct measure for the dissipation rate of kinetic turbulent energy, are biased. Possible causes for these results are discussedin detail. A correction procedure is presented to account for effects of random noise and of so-called inactive turbulence or sensor vibrations. The errors in u_* cause errors in the DBSAS measurements of the structure parameter of temperature C_T ². The derived H appears to be less sensitive to errors in l₀ and C_T ², because errors in these quantities tend to cancel out.     

Turbulence characteristics in a near neutrally stratified urban atmosphere

Turbulence measurements from the city of Uppsala, Sweden, are analysed. Measurements were taken at two sites: one in the central area, ca. 6 m above roof level, the average building height being ca. 15 m; the other at ca. 8 and 50 m above the ground on a tower situated 100 m downwind of a sharp discontinuity between the densely built-up urban area and flat grass-covered land. The average stability was close to neutral, the range being -0.2 < z/L < 0.2. The main emphasis of the study is on the non-dimensional standard deviations of the velocity components _i /u _*t and on the corresponding non-dimensional energy spectra, u _*t being a local velocity scale defined as _i /( _l is the local momentum flux). Comparison with results obtained from surface-layer measurements at ideal sites (with u _*, being the ordinary friction velocity) shows good general agreement. The most complete agreement is found for the tower 50 m measurements, a result which is notable as this measurement point is found to be within a distinctly transitional zone between the urban and post-urban boundary layers. The results from the central city measurement point are also fairly close to the ideal results, the deviations found being small in view of the fact that the site is probably inside the layer in which the roughness elements (the buildings) have direct influence. The measurements at the tower 8 m level show certain distinct deviations from ideal results: all three _i /u _*l , are higher by ca. 10%, the excessive energy being found at the low frequency end of the spectrum. Arguments are presented for this feature to be due to a spectral lag effect.     

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.     

Numerical studies of heat island circulations

A two dimensional model has been set up to investigate the circulation induced by an urban heat island in the absence of synoptic winds. The boundary conditions need to be formulated carefully and due to difficulties arising here, we restrict our attention to cases of initially stable thermal stratification. Heat island circulations are allowed to develop from rest and prior to the appearance of the final symmetric double cell pattern, a transitional multi-cell pattern is observed in some cases. The influence on the steady state circulation of various parameters is studied, among which are eddy transfer coefficients, the heat island intensity, the initial temperature stratification and the heat island size. Some results are presented for a case in which differential surface cooling beneath an initially stable atmosphere produces a circulation and an unstable layer capped by an elevated inversion over the city. It is hoped that this case is vaguely representative of the night-time heat island with no geostrophic wind.Notation c_p Specific heat at constant pressure - g Acceleration due to gravity - H Top of integration region - K_z Vertical eddy transfer coefficient - K_x, K_xH, K_xm Horizontal eddy transfer coefficients for heat and momentum - l ixing length - p Pressure - p₀ Reference surface pressure (1000 mb) - P_H (x, t) Pressure at z = H - R Specific gas constant for dry air - t Time - u, w Horizontal and vertical velocities - x, z Horizontal and vertical coordinates - x₁, x₂ Positions of discontinuities in surface temperature field (see Figure 2) - x_a Heat island half-width - x_b Boundary of integration region - Parameter in formula for eddy coefficients (variable-K case) = 18.0 - _s Intensity of heat island - Potential temperature field - Reference absolute temperature (variable-K case) - _r Reference temperature (° C) - _s Surface temperature - Q Air density     

A Richardson Number criterion for the air-sea interface

It is shown that the observationally determined roughness relation z ₀ = u _* ²/g in which g is the acceleration of gravity, u _*, is the friction velocity in air, and = 0.0185 (Wu, 1982) for the wind profile over the sea surface relative to the surface current, is consistent with the existence of a Richardson Number criterion at the air-sea interface in which the critical Richardson Number, Ri_c = 1, such that all the shear energy is converted into potential energy.