Air-sea bulk transfer coefficients in diabatic conditions

On the basis of recent data for the roughness Reynolds number of the sea surface, and using the Owen-Thomson theory on the transfers of heat and mass between a rough surface and the flow above it, the bulk transfer coefficients of the sea surface have been estimated. For a reference height of 10 m, the neutral-lapse transfer coefficient for water vapor is larger by only a few percent than that for sensible heat. When the wind speed at the 10-m height is u ₁₀>3 m s^–1, the coefficient for sensible heat C _H is larger by about 10% than that for momentum C _D . For u ₁₀<5 m s^–1, however, the value of C _D exceeds the value of C _H , and for u ₁₀=15 m s^–1 it is shown that C _H 0.8C _D . It may be also proposed that 10³ C _D =1.11 to 1.70, 10³ C _E =1.18 to 1.30, and 10³ C _H =1.15 to 1.26 for a range of u ₁₀=4 to 20 m s^–1. A plot of diabatic transfer coefficients versus wind speed is obtained by using a parameter of the sea-air temperature difference. For practical purposes, the coefficients are approximated by empirical formulae.     

A theory for the scalar roughness and the scalar transfer coefficients over snow and sea ice

Although the bulk aerodynamic transfer coefficients for sensible (C _H ) and latent (C _E ) heat over snow and sea ice surfaces are necessary for accurately modeling the surface energy budget, they have been measured rarely. This paper, therefore, presents a theoretical model that predicts neutral-stability values of C _H and C _E as functions of the wind speed and a surface roughness parameter. The crux of the model is establishing the interfacial sublayer profiles of the scalars, temperature and water vapor, over aerodynamically smooth and rough surfaces on the basis of a surface-renewal model in which turbulent eddies continually scour the surface, transferring scalar contaminants across the interface by molecular diffusion. Matching these interfacial sublayer profiles with the semi-logarithmic inertial sublayer profiles yields the roughness lengths for temperature and water vapor. When coupled with a model for the drag coefficient over snow and sea ice based on actual measurements, these roughness lengths lead to the transfer coefficients. C _E is always a few percent larger than CH. Both decrease monotonically with increasing wind speed for speeds above 1 m s^–1, and both increase at all wind speeds as the surface gets rougher. Both, nevertheless, are almost always between 1.0 × 10^–3 and 1.5 × 10^–3.     

Momentum and sensible heat fluxes calculated by the dissipation technique during the Ocean Storms Project

High frequency measurements of wind velocity and temperature were made during the Ocean Storms Project in November 1987. The dissipation method was applied to the resulting time series in order to determine friction velocities,u _*, and the characteristic temperature scale,t _*, at 1-min intervals. These values were then compared to the 1-min mean wind speed and air-sea temperature differences to determine relationships for the drag coefficient (C _d ) and Stanton number (C _h ). The drag coefficient was comparable to other values reported in the literature, although the variation with wind speed was greater than reported by other investigators. An examination of the residual time series indicated a systematic low frequency periodicity of about 2-hr duration which was attributed to a fluctuating wind interacting with the surface gravity wave field. The temperature fluctuations did not produce meaningful estimates ofC _h for stable conditions. For unstable conditions, a value of 1.09±0.02×10^–3 was found.     

Estimating the Monin-Obukhov length in the stable boundary layer for dispersion calculations

Analysis of data collected during the Prairie Grass, Kansas and Minnesota experiments reveals the following empirical relationship between the Monin-Obukhov length L and the friction velocity u _*: L = Au _* ², A = 1.1 × 10³s²m^-1. This result combined with the formulation for the height of the stable boundary layer h suggested by Zilitinkevich (1972) leads to h u _* ^3/2 f–^1/2 where f is the Coriolis parameter. Data from the Minnesota study (Caughey et al., 1979) provide ample support for this expression.These empirical equations for L and h are useful for routine dispersion estimates during stable conditions.     

Stability dependence of the drag and bulk transfer coefficients over a coastal sea surface

Bulk transfer coefficients were evaluated from eddy correlation flux measurements on a fixed pier during onshore winds. The mean values are C _D = 1.69 × 10^-3, C _H = 2.58 × 10^-3 and C _E = 1.51 × 10^-3. The drag coefficient, C _D, gradually increases with wind speed but C _H and C _E are independent of wind speed. According to theory and empirical formulas based on experimental results over flat grassland, the transfer coefficients should gradually increase with increasing instability. This is confirmed experimentally in the stable region in our case. However, the drag coefficient appears to decrease with increasing instability, which is against the theoretical result. A stability dependence is not clearly observed for C _H or C _E.     

Numerical study on the bulk heat transfer coefficient for a variety of vegetation types and densities

The relationship between the geometrical structure of a canopy layer and the bulk transfer coefficient was investigated using a numerical canopy model. The following results were obtained:

1. The bulk transfer coefficients for momentum and heat, C _M and C _H , change with non-dimensional canopy density C _* each has a maximum.
2. The value of C _M is always larger than the value of C _H for a canopy with c _m > c _h , c _m and c _h being the drag coefficient and the heat transfer coefficient of an individual canopy element, respectively.
3. The value of C _* at which C _H has its maximum value is larger than the value of C _* at which C _M has its maximum. Therefore, the reciprocal of the sublayer Stanton number b _h ^?1 ranges between 50 and 65 for C _* around 0.1 while it ranges between 0 and 30 for C _* < 10^?2 and C _* > 2 (when c _m = 0.5).
4. The value of B _H ^?1 in the present study is consistent with most available observations, except for canopies of medium density (when C _* is around 0.1) for which no observational value has been obtained.

     

The prediction of dust erosion by wind: An interactive model

We have devised a partial differential equation for the prediction of dust concentration in a thin layer near the ground. In this equation, erosion (detachment), transport, deposition and source are parameterised in terms of known quantities. The interaction between a wind prediction model in the boundary layer and this equation affects the evolution of the dust concentration at the top of the surface layer. Numerical integrations are carried out for various values of source strength, ambient wind and particle size. Comparison with available data shows that the results appear very reasonable and that the model should be subjected to further development and testing.Notation (x, y, z, t) space co-ordinates and time (cm,t) - u, v components of horizontal wind speed (cm s^–1) - u _g, v_g components of the geostrophic wind (cm s^–1) - V=(u²+v²)^1/2 (cm s^–1) - (û v)= 1/(h – k) _k ^h(u, v)dz(cm s^–1) - V _* friction velocity (cm s^–1) - z ₀ roughness length (cm) - k ₁ von Karman constant =0.4 - V _d deposition velocity (cm s^–1) - V _g gravitational settling velocity (cm s^–1) - h height of inversion (cm) - k height of surface layer (cm) - potential temperature (°K) - _gr potential temperature at ground (°K) - _K potential temperature at top of surface layer (°K) - P pressure (mb) - P ₀ sfc pressure (mb) - C _p/C_v - (t)= /z lapse rate of potential temperature (°K cm^–1) - A(z) variation of wind with height in transition layer - B(z) variation of wind with height in transition layer - Cd drag coefficient - C _HO transfer coefficient for sensible heat - C dust concentration (g m^–3) - C _K dust concentration at top of surface layer (g m^–3) - D(z) variation with height of dust concentration - u, v, w turbulent fluctuations of the three velocity components (cm s^–1) - A ₁ constant coefficient of proportionality for heat flux =0.2 - Ri Richardson number - g gravitational acceleration =980 cm s^–2 - Re Reynolds number = - D _s thickness of laminar sub-layer (cm) - v molecular kinematic viscosity of air - coefficient of proportionality in source term - dummy variable - t time step (sec) - n time index in numerical equations On sabbatical leave at University of Aberdeen, Department of Engineering, September 1989–February 1990.     

The Fallacy of Drifting Snow

A common parametrization over snow-covered surfaces that are undergoing saltation is that the aerodynamic roughness length for wind speed (z ₀) scales as au_*²/g{\alpha u_\ast^2/g}, where u _* is the friction velocity, g is the acceleration of gravity, and α is an empirical constant. Data analyses seem to support this scaling: many published plots of z ₀ measured over snow demonstrate proportionality to u_*²{u_\ast^2 }. In fact, I show similar plots here that are based on two large eddy-covariance datasets: one collected over snow-covered Arctic sea ice; another collected over snow-covered Antarctic sea ice. But in these and in most such plots from the literature, the independent variable, u _*, was used to compute z ₀ in the first place; the plots thus suffer from fictitious correlation that causes z ₀ to unavoidably increase with u _* without any intervening physics. For these two datasets, when I plot z ₀ against u _* derived from a bulk flux algorithm—and thus minimize the fictitious correlation—z ₀ is independent of u _* in the drifting snow region, u _* ≥ 0.30 ms⁻¹. I conclude that the relation z₀ = au_*²/g{z_0 = \alpha u_\ast^2/g} when snow is drifting is a fallacy fostered by analyses that suffer from fictitious correlation.     

Transfer coefficients of sensible heat on a snowmelt surface

Summary Field observations were carried out in order to determine the transfer coefficeient of sensible heat flux above a melting snow surface at the Moshiri experimental site. The coefficient is calculated as the ratio of the sensible heat flux determined by the eddy correlation method using a sonic anemometer to the product of the wind speed and the temperature difference between the air and snow surface. The sensible heat fluxes are also compared with the result of the precise heat balance observations. The nondimensional transfer coefficienth shows a good correlation with the atmospheric stability,Ri. The value ofh=2.3×10^–3 is obtained in the range of 0<Ri<0.1, however, it is smaller and scattered under stronger stable condition (Ri>0.1). The dimensional transfer coefficent for sensible heat flux is calculated, and a linear relationship is obtained as a function of the logarithm of atmospheric stability.With 11 Figures     

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     

Henry's law and the behavior of weak acids and bases in fog and cloud

Experimental data from two field experiments on ground based clouds were used to study the distribution of formic acid, acetic acid, ammonia and S(IV) species between liquid and gas phase. The ratio of the concentrations of these compounds between the phases during concurrent measurements was compared to ratios expected according to Henry's law (considering the pH influence). Large discrepancies of several orders of magnitude were seen. Three hypotheses have been investigated to explain the observed discrepancies: The existence of a microscale equilibrium which does not persist in a bulk sample, a thermodynamic shift of the equilibrium due to competing reactions, and nonequilibrium conditions due to mass transfer limitations. Approximate quantitative calculations show that none of these hypotheses is sufficient to explain all of the discrepancies, so a combination of different effects seems to be responsible for this observation. The same theoretical considerations also suggest that mass transfer limitation may be an important factor for highly soluble compounds. The data presented here indicates that it is not possible to simply extrapolate interstitial gas phase composition from measured bulk liquid phase concentrations of a fog or cloud.Notation [r _max] liquid phase molar uptake rate (mol l^–1 s^–1) - [A _g ] concentration ofA in gas phase (atm) - [A _l ] concentration ofA in liquid phase (mol l^–1) - [A _g , 0] concentration ofA in gas phase (atm) at time 0 - LWC liquid water content (g m^–3) - R universal gas constant (0.082 l atm mol^–1 K^–1 - D _g diffusivity (for all gases 0.1 cm² s^–1 was used) - K _H ^* effective Henry's law coefficient (mol l^–1 atm^–1) - t _f lifetime of fog droplet (s) - a droplet radius (cm) - accommodation coefficient - R factor of discrepancy - T temperature (K) - v mean molecular speed (cm s^–1) formic acid: 35 000 acetic acid: 31 000 ammonia: 58 000     

Etude experimentale d'une relation entre le coefficient de frottement et le facteur de rafales en regime de vent faible et au-dessus d'une surface d'eau

In usual aerodynamic bulk formulas, the drag coefficient C _d has been best estimated in the 5 to 16 m s^–1 range of mean wind velocity; a value of 1.3 × 10^–3 is often considered for operational use. However, in the 0 to 5 m s^–1 range of mean wind velocity, corresponding to meteorological conditions of very light wind, experimental results have not resulted in any convincing agreement between various authors (Hicks et al., 1974; Wu, 1969; Kondo and Fujinawa, 1972; Mitsuta, 1973; Brocks and Krugermeyer, 1970).In the present paper, the drag coefficient is experimentally determined in conditions of very light wind and limited fetch (about 250 m). Due to this limited fetch, we have to be cautious in the extrapolation of our results to other sites. Nevertheless, some of experimental results are worth describing, considering the paucity of data in light wind conditions.Mean value and standard deviation (respectively 1.84 × 10^–3 and 1.24 × 10^–3) are obtained from 70 runs of 10-min duration. Mean wind velocities observed at 2 m above water surface are found to lie between 1.2 and 3.6 m s^–1. Whereas this mean value is in fair agreement with C _{d 10} = 1.3 × 10^–3, usually given for the 5 to 16 m s^–1 range (Kraus, 1972), the above value for the standard deviation seems too large to be left without further analysis.A more exhaustive analysis of the 70 values obtained for C _d shows that it depends on a parameter characteristic of longitudinal fluctuations of the wind velocity. A similar idea was put forward earlier by Kraus (1972). Relations between the drag coefficient and wind fluctuations may be tentatively given by: % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4qamaaBa% aaleaacaWGKbGaaGOmaaqabaGccqGH9aqpdaqadaqaaiabgkHiTiaa% igdacaGGUaGaaGimaiaaiEdacqGHRaWkcaaIXaGaaGinaiaac6caca% aIZaGaaGinamaalaaabaGaeq4Wdm3aaSbaaSqaaiaadwhacaGGNaaa% beaaaOqaaaaaaiaawIcacaGLPaaaruqqYLwySbacfaGaa8hEaiaa-b% cacaaIXaGaaGimamaaCaaaleqabaGaeyOeI0IaaG4maaaakiaabcca% caqGGaGaaeiiaiaabccacaqGXaGaaeOlaiaabAdacaqGGaGaaeyBai% aabccacaqGZbWaaWbaaSqabeaacaqGTaGaaeymaaaakiabgsMiJkqa% dwhagaqeamaaBaaaleaacaaIYaaabeaakiabgsMiJkaaiodacaGGUa% GaaGOnaiaab2gacaqGGaGaae4CamaaCaaaleqabaGaaeylaiaabgda% aaaaaa!634E!\[C_{d2} = \left( { - 1.07 + 14.34\frac{{\sigma _{u'} }}{{}}} \right)x 10^{ - 3} {\text{ 1}}{\text{.6 m s}}^{{\text{ - 1}}} \leqslant \bar u_2 \leqslant 3.6{\text{m s}}^{{\text{ - 1}}} \] and % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4qamaaBa% aaleaacaWGKbGaaGOmaaqabaGccqGH9aqpdaqadaqaaiabgkHiTiaa% iodacaGGUaGaaGioaiaaiAdacqGHRaWkcaaIZaGaaiOlaiaaiodaca% aI2aGaam4raaGaayjkaiaawMcaaerbbjxAHXgaiuaacaWF4bGaa8hi% aiaaigdacaaIWaWaaWbaaSqabeaacqGHsislcaaIZaaaaOGaaeilaa% aa!4B42!\[C_{d2} = \left( { - 3.86 + 3.36G} \right)x 10^{ - 3} {\text{,}}\] where _u/\-u ₂ and G, respectively, represent the standard deviation of u normalized with \-u ₂ and the longitudinal gust factor quoted in Smith (1974).We have established a relationship between these fluctuation parameters and the stability as given by a bulk layer Richardson number (between 0 and 2 m). These relations are given by: % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaacq% aHdpWCdaWgaaWcbaGaamyDaiaacEcaaeqaaaGcbaGabmyDayaaraWa% aSbaaSqaaiaaikdaaeqaaaaakiabg2da9iaaicdacaGGUaGaaGymai% aaikdacqGHRaWkcaaIZaGaaiOlaiaaiIdacaaI1aGaaeiiaiaabkfa% caqGPbWaaSbaaSqaaiaabcdacaqGTaGaaeOmaaqabaaaaa!4802!\[\frac{{\sigma _{u'} }}{{\bar u_2 }} = 0.12 + 3.85{\text{ Ri}}_{{\text{0 - 2}}} \] and G=1.35+14.56 Ri_0–2. The increase in gustiness with stability is in qualitative agreement with Goptarev (1957)'s experimental results.In spite of the high-level correlation between C _d and _u/\-u ₂(G) on the one hand and between _u/\-u ₂(G) and Ri_0–2on the other hand, we found a poor relationship between C _d and Ri_0–2. It is worth noting too that the trend observed here for C _d to increase with stability is in complete disagreement with the usual theoretical expectation for C _d to decrease with increasing layer stability above water.

---

---

E.R.A. du C.N.R.S. n 259.     

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]     

Three-dimensional modeling of synthetic cold fronts approaching the Alps

Summary A numerical model was used to study the behaviour of prototype cold fronts as they approach the Alps. Two fronts with different orientations relative to the Alpine range have been considered. One front approaches from west, a second one from northwest. The first front is connected with southwesterly large-scale air-flow producing pre-frontal foehn, whereas the second front is associated with westerly largescale flow leading to weak blocking north of the Alps.Model simulations with fully represented orography and parameterized water phase conversions have been compared with control runs where either the orography was cut off or the phase conversions were omitted. The results show a strong orographic influence in case of pre-frontal foehn which warms the pre-frontal air and increases the cross-frontal temperature contrast leading to an acceleration of the front along the northern Alpine rim. The latent heat effect was found to depend much on the position of precipitation relative to the surface front line. In case of pre-frontal foehn precipitation only falls behind the surface front line into the intruding cold air where it partly evaporates. In contrary, precipitation already appears ahead of the front in the case of blocking. Thus, the cooling effect of evaporating rain increases the cross-frontal temperature difference only in the first case causing an additional acceleration of the front.List of symbols C _pd specific heat capacity of dry air at constant pressure (C _pd =1004.71 J kg^–1 K^–1) - C _pv specific heat capacity of water vapour at constant pressure (C _pv =1845.96 J kg^–1 K^–1) - C _f propagation speed of a front - x, y horizontal grid spacing (cartesian system) - , horizontal grid spacing (geographic system) - t time step - E turbulent kinetic energy - f Coriolis parameter - g gravity acceleration (g=9.81 ms^–1) - h terrain elevation - H height of model lid (H=9000 m) - k Karman constant (k=0.4) - K _Mh horizontal exchange coefficient of momentum - K _Hh horizontal exchange coefficient of heat and moisture - K _Mz vertical exchange coefficient of momentum - K _Hz vertical exchange coefficient of heat and moisture - l mixing length - l _c specific condensation heat (l _c =2500.61 kJ kg^–1) - l _f specific freezing heat (l _f =333.56 kJ kg^–1) - l _s specific sublimation heat (l _s =2834.17 kJ kg^–1) - longitude - m ₁,m ₂,m ₃ metric coefficients - p pressure - Exner function - Pr Prandtl number - latitude - _M profile function - q _v specific humidity - q _c specific content of cloud droplets - q _i specific content of cloud ice particles - q _R specific content of rain drops - q _S specific content of snow - R _d gas constant of dry air (R _d =287.06 J kg^–1 K^–1) - R _v gas constant of water vapour (R _v =461.51 J kg^–1 K^–1) - r _E radius of earth (r _E =6371 km) - Ri _F flux Richardson number - density of dry air - t time - T temperature - _dia period of diastrophy - potential temperature - _v virtual potential temperature - _e equivalent potential temperature - U relative humidity - u, v, w cartesian wind components - u _F ,v _F front-normal and front-parallel wind components - x, y, z cartesian coordinates - w ^* transformed vertical wind component - W _R speed of falling rain - W _S speed of falling snow - z ^* transformed vertical coordinate Abbreviations GND (above) ground level - MSL (above) mean sea level With 12 Figures     

A laboratory study of the mechanism of the oxygen airglow

Further laboratory studies of emission by O(¹ S) and by O₂ A ³ _u ⁺ ,A³ _u andc ¹ _u ^– in the oxygen afterglow lead to the conclusion that Barth's mechanism for the excitation of the auroral green line O ₂ ^* +O(³P=O₂+O(¹S)–(1) is correct and that levelsv=6 and 7 of O₂ A ³ _u ⁺ are Barth precursors. The value ofk ₁=7×10^–11 cm³ s^–1 deduced for these levels is shown to be in fair agreement with atmospheric measurements.     

Measurements of the turbulent heat flux over the sea

The turbulent heat flux was measured with two instruments simultaneously over the Baltic Sea by means of the eddy-correlation method. In one observational period, a small but noticeable divergence in heat flux was found, which may be explained by the advection of colder air. The parameterization of heat flux by the bulk method leads to a value for C _Hof 1 × 10^–3.     

Tilt errors and precipitation effects in trivane measurements of turbulent fluxes over open water

For 390 ten-minute samples of turbulent flux, made with a trivane above a lake, the vertical alignment is determined within 0.1 ° through azimuth-dependent averaging. One degree of instrumental misalignment is found to produce an average tilt error of 9 ± 4% for momentum flux, and 4 ± 2% for heat flux. The tilt error in the vertical momentum flux depends mainly ons _u/u_*, and cannot be much diminished with impunity by high-pass pre-filtering of the turbulence signals. The effects of rain on trivane measurements of vertical velocity are shown to be negligible at high wind speeds, and adaptable to correction in any case.The normalized vertical velocity variance,s _w/u_*, appears to be proportional to the square root ofz/L for unstable stratification. For a wind speed range of 2 to 15 m s^–1, the eddy correlation stresses measured at 4- and 8-m heights can be reasonably well estimated by using a constant drag coefficientC _d=1.3 X 10^-3, while cup anemometer profile measurements give an overestimate of eddy stress at high wind speeds. A good stress estimate is also obtained from the elevation variance; it is suggested that trivane measurement of this variance might be made from a mobile platform, e.g., a moderately stabilized spar buoy.     

Measurements of the humidity structure function parameters,C q 2and C Tq,over the ocean

Atmospheric turbulence measurements, including temperature and humidity fluctuations, were made from the R/V Acania off the coast of California in June, 1979. The purpose of the experiment was to investigate the scaling properties of the humidity structure function parameter (C _q ²) and temperaturehumidity cospectrum structure parameter (C _Tq) in the marine surface layer. The bulk parameterization method was used to obtain Monin-Obukhov Similarity (MOS) scaling parameters u _*, T _*, q _*and L. Assuming a neutral stability humidity drag coefficient c _qn = 1.3 × 10^-3the dimensionless humidity structure function parameter C _q ²Z^2/3/q_* ²was found to be 18% lower than the corresponding temperature function obtained by Wyngaard et al. (1971). Furthermore, the measurements indicate that the temperature-humidity fluctuations are highly coherent well into the inertial subrange. The results have direct application to turbulent scattering of waves propagating in the atmosphere (particularly microwaves) and methods of estimating air-sea surface fluxes.     

Estimates of water vapor flux and canopy conductance of Scots pine at the tree level utilizing different xylem sap flow methods

Summary During the Hartheim Experiment (HartX) 1992 conducted in the upper Rhine Valley, Germany, three different methods were used to measure sap flow in Scots pine trees via heating of water transported in the xylem: (1) constant heating applied radially in the sapwood (Granier-system-G), (2) constant heating of a stem segment (ermák-system-C), and (3) regulated variable heating of a stem segment that locally maintains a constant temperature gradient in the trunk (ermák/Schulze-system-CS). While the constant heating methods utilize changes in the induced temperature gradient to quantify sap flux, the CS-system estimates water flow from the variable power requirement to maintain a 2 or 3 degree Kelvin temperature gradient over a short distance between inserted electrodes and reference point. The C- and CS-systems assume that all transported water is encompassed and equally heated by the electrodes. In this case, flux rate is determined from temperature difference or energy input and the heat capacity of water. Active sapwood area need not be determined exactly. In contrast, the G-system requires an empirical calibration of the sensors that allows conversion of temperature difference into sap flow density. Estimates of sapwood area are used to calculate the total flux. All three methods assume that the natural fluctuation in temperature of the trunk near the point of insertion of heating and sensing elements is the same as that where reference thermocouples are inserted.Using all three systems, 24 trees were simultaneously monitored during the HartX campaign. Tree size within the stand ranged between 18 and 61 cm circumference at breast height, while sample trees ranged between 24 and 55 cm circumference. The smallest trees could only be measured by utilizing the G-system. Sap flow rates of individual trees measured at breast height increased rapidly in the morning along with increases in irradiance and vapor pressure deficit (D), decreased slowly during the course of the afternoon with continued increase inD, and decreased more slowly during the night.Ignoring potential effects introduced by the different methods, maximum flow rates of individual trees ranged between 0.5 and 2.5 kg H₂O h^–1 tree^–1 or 0.3 and 0.6 mm h^–1 related to projected crown area of trees and daily sums of sap flow for individual trees varied between 4.4 and 24 kg H₂O tree^–1 d^–1 or 1.1 and 6.0 mm d^–1. Maximum sap flow rates per sapwood area of trees varied least for the G-system (11–17 g cm^–2 h^–1) and was of similar magnitude as the C- (8–21 g cm^–2 h^–1) and CS-system (4–14 g cm^–2 h^–1).Regressions of total tree conductance (g _t ) derived from sap flow estimates demonstrated the same linear increase of conductance with increasing irradiance, however decrease of conductance with increasingD under non-limiting light conditions was different for the three systems with strongest reduction ofg _t measured with the CS-system followed by the C- and G-system. This led to different estimates of daily sap flow rates especially during the second part of the measurement period.Variation in sap flow rates is explained on the basis of variation in leaf area index of individual trees, heterogeneity in soil conditions, and methodological differences in sap flow measurements. Despite the highly uniform plantation forest at the scale of hectares, the heterogeneity in tree size and soil depth at the scale of square meters still make it difficult to appropriately and efficiently select sample trees and to scale-up water flux from individual trees to the stand level.With 5 Figures     

Estimation of the Exchange Coefficient of Heat During Low Wind Convective Conditions

For the first time, the exchange coefficient of heat C_H has been estimated from eddy correlation of velocity and virtual temperature fluctuations using sonic anemometer measurements made at low wind speeds over the monsoon land atJodhpur (26°18' N, 73°04' E), a semi arid station. It shows strong dependence on wind speed, increasing rapidly with decreasing wind speed, and scales according to a power law C_H = 0.025U₁₀ ^-0.7 (where U₁₀ is the mean wind speed at 10-m height). A similar but more rapid increase in the drag coefficient C_Dhas already been reported in an earlier study. Low winds (<4 m s^-1) are associated with both near neutral and strong unstable situations. It is noted that C_H increases with increasing instability. The present observations best describe a low wind convective regime as revealed in the scaling behaviour of drag, sensible heat flux and the non-dimensional temperature gradient. Neutral drag and heat cofficients,corrected using Monin–Obukhov (M–O) theory, show a more uniform behaviour at low wind speeds in convective conditions, when compared with the observed coefficients discussed in a coming paper.At low wind convective conditions, M-O theory is unable to capture the observed linear dependence of drag on wind speed, unlike during forced convections. The non-dimensional shear inferred from the present data shows noticeable deviations from Businger's formulation, a forced convection similarity. Heat flux is insensitive to drag associated with weak winds superposed on true free convection. With heat flux as the primary variable, definition of new velocity scales leads to a new drag parameterization scheme at low wind speeds during convective conditionsdiscussed in a coming paper.