Effect of land management on ecosystem carbon fluxes at a subalpine grassland site in the Swiss Alps

Summary The influence of agricultural management on the CO₂ budget of a typical subalpine grassland was investigated at the Swiss CARBOMONT site at Rigi-Seebodenalp (1025m a.s.l.) in Central Switzerland. Eddy covariance flux measurements obtained during the first growing season from the mid of spring until the first snow fall (17 Mai to 25 September 2002) are reported. With respect to the 10-year average 1992–2001, we found that this growing season had started 10 days earlier than normal, but was close to average temperature with above-normal precipitation (100–255% depending on month). Using a footprint model we found that a simple approach using wind direction sectors was adequate to classify our CO₂ fluxes as being controlled by either meadow or pasture. Two significantly different light response curves could be determined: one for periods with external interventions (grass cutting, cattle grazing) and the other for periods without external interventions. Other than this, meadow and pasture were similar, with a net carbon gain of –128±17g Cm^–2 on the undisturbed meadow, and a net carbon loss of 79±17g Cm^–2 on the managed meadow, and 270±24g Cm^–2 on the pasture during 131 days of the growing season, respectively. The grass cut in June reduced the gross CO₂ uptake of the meadow by 50±2% until regrowth of the vegetation. Cattle grazing reduced gross uptake over the whole vegetation period (37±2%), but left respiration at a similar level as observed in the meadow.     

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     

The budget of carbon dioxide variance in the surface layer over vegetated fields

The budget equation for carbon dioxide variance can be represented by production, dissipation and flux divergence terms. Each term is measured under near neutral to moderately unstable conditions over vegetated fields. The flux divergence term is about an order of magnitude smaller than production and dissipation terms, though it shows a loss for 0.006 < _v < 1 and a gain for 1 < - _v < 10. Here, _v is the Monin-Obukhov stability parameter including humidity effect. As expected from a closure of the budget, the nondimensional production and dissipation terms are basically identical and represented by the same functional form: (1–16 _v )^–1/2.     

Stability Effects on Heat and Moisture Fluxes at Sea

During the 1996 ASGAMAGE experiment we measured windspeed, air temperature T_a, watertemperature T_s, humidity and the momentum,heat and moisture fluxes at a research platform offthe Dutch coast. For each quantity we used several(sets of) instruments simultaneously. This allowed usto make an extensive assessment of the quality of themeasurements and to find optimal values for thevarious quantities for each run. From these values wecalculated C_H and C_E, theStanton and Dalton numbers, and reduced them to 10-mheight and neutral conditions. For this reductionwe made a separate analysis for the effect ofinclusion or non-inclusion of the assumption that theroughness length for heat or moisture is the same forthe neutral and non-neutral cases. Differences inthe reduced data due to this assumption turned out tobe well within the measurement error.For C_H we distinguished three separategroups of data: stable (A), unstable with_{a s} (B) and unstablewith thetas;_a > _s (C), with indicating the potential temperature.The stable data separate into two groups, depending onwater temperature and/or the wave field. The data ofgroup B showed a relation with wave age. The data ofgroup C consistently gave negative values forC_H, a result that might indicate conversion oflatent heat into sensible heat through condensation ofwater vapour just above the water surface. An attemptto re-analyse the data in terms of density fluxes,combining the effects of heat and moisture, still gavenegative transfer coefficients for group C.For the moisture flux we found the more conventionalresult of a separation in stable and unstable values;these categories showed a clear difference, but notrends with, for example, wind speed.We conclude that standard Monin-Obukhov similaritytheory cannot explain our data.     

Application of an infrared carbon dioxide and humidity instrument to studies of turbulent transport

A calibration equation and some results of the field performance of an infrared instrument, which is designed to measure simultaneous fluctuations of atmospheric carbon dioxide and water vapor, are described. Field observations show that the instrument is suitable for simultaneous measurement of turbulent fluxes of carbon dioxide and water vapor in conjunction with a sonic anemometer. Measured values of carbon dioxide and water vapor fluxes show diurnal variations characterized by crop activity with respect to assimilation, respiration and evapotranspiration. Carbon dioxide is transferred downward during the daytime and upward at night, while latent heat and sensible heat are transferred in the opposite sense. The non-dimensional gradient of carbon dioxide is expressed in the following form under weak unstable conditions: _c = (1 – 16 _v )^-1/2. Here, _v is the Monin-Obukhov stability parameter including the humidity effect. This relation was originally proposed for temperature and humidity. Thus, the results indicate that the turbulent mechanisms of carbon dioxide fluctuations are similar to those of other scalar entities. This is strongly supported by the high correlation coefficient found between fluctuations of carbon dioxide and temperature or humidity in the air layer over crop fields.     

Prediction of the abiotic degradability of organic compounds in the troposphere

A statistically relevant correlation between the reaction rate coefficient, k _OH, for the OH radical reaction with 161 organic compounds in the gas phase at 300 K, and the corresponding vertical ionisation energies E _i,v, reveals two classes of compounds: aromatics where –log(k _OH/cm³s^-1)3/2E _i,v(eV)–2 and aliphatics where –log(k _OH/cm³s^-1)4/5E _i,v(eV)+3. The prediction of the rate coefficient, k _OH, for the reaction of OH with organic molecules from the above equations has a probability of about 90%. Assuming a global diurnal mean of the OH radical concentration of 5×10⁵ cm³, the upper limit of the tropospheric half-life of organic compounds and their persistence can be estimated.     

On the temperature coefficient of PCO 2 in seawater

The commonly reported temperature coefficient of P. the equilibrium partial pressure of CO₂, is (P/T) _A,C ,which is about 15 ppm/°C, or 5% of the atmospheric partial pressure of CO₂. This coefficient, however, applies only to deep water, not to surface water which can exchange CO₂ with the atmosphere. The coefficient (P/T) _A,C ,, where designates constancy of the sum of atmospheric and surface-ocean CO₂, is the appropriate value for air-sea exchange. Numerical values are mass-dependent because the depth of the exchanging ocean layer must be specified. For a 100-m surface layer, the value is ca. 1.5 ppm/°C, or 0.5% of ambient CO₂. Editor's Note:In view of the interdisciplinary importance of the carbon dioxide-climate problem, this note on seawater chemistry should be of interest to specialists beyond the discipline of ocean chemistry.     

Kritische Bemerkung zur Frage der Temperatur-abhängigkeit der Ozonverteilung

Zusammenfassung A. undE. Vassy haben in der Frage der Temperatur-abhängigkeit des Ozongehalts der Atmosphäre aus der Gleichung loge _n –logJ _n logK(T _n ) geschlossen, daß auch die Gleichung loge _n logJ _n +logK(T _n ) gültig sei. Es wird hier nun gezeigt, daß die bei der ersten Gleichung erlaubten Vernachlässigungen bei der zweiten zu großen Fehlern führen können und daß daher von A. undE. Vassy kein Beweis für die Richtigkeit der Beziehunge=J.K(T) erbracht ist.

---

Summary In the question of temperature dependence of ozone content of the atmosphere A. andE. Vassy have concluded from the equation loge _n –logJ _n logK(T _n ) that also the formula loge _n logJ _n +logK(T _n ) must be valid. In this paper it is proved that the neglections which may be admitted for the first equation, can conduct to great errors. Therefore A. andE. Vassy have not produced a proof for the correctness of the equatione=J.K(T).

---

Résumé A. etE. Vassy en étuidant le problème de la teneur de l'ozone atmosphérique en relation avec la température ont admis que l'équation loge _n –logJ _n logK(T _n ) entraînait aussi la relation loge _n logJ _n +logK(T _n ). On montre ici que les simplifications admises pour la première équation conduisent pour l'application de la seconde à de fortes erreurs, et que par conséquent ces auteurs n'ont pas fourni de preuve de la justesse de la relatione=J.K(T).

     

The Kolmogorov constant for carbon dioxide in the atmospheric surface layer over a paddy field

From measurements in the atmospheric surface layer over a paddy field, the Kolmogorov constants for CO₂ and longitudinal wind velocity were obtained. In this study, the nondimensional dissipation rate _nc = (1–16 _v )^-1/2 for CO₂ variance and = (1–16 _v )^-1/4 – _v for turbulent energy were used, assuming the equality of the local production term and the local dissipation term, and neglecting the divergence flux term in the budget equation. The value of the constant for CO₂ was consistent with recent determinations for temperature and humidity. The constant for longitudinal wind velocity showed good agreement with other recent observations.     

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     

Effect of finite sampling on atmospheric spectra

The effect of a finite averaging time on variances is well known, but its effect on power spectra is less clearly understood. We present numerical solutions for the spectral distortion arising from sampling over a finite time interval T and show that the commonly used filter function (1 – sinc²f T), valid for variances, is a reasonable approximation for power spectra only when T 10 _m , where f is the cyclic frequency, and _m is the dominant time scale of the process. Our results exhibit an increasingly steeper low-frequency roll-off as T decreases relative to _m , indicating that the measured spectrum is subject to a greater suppression of the lower frequencies (f > 1/T) than predicted by (1 – sinc²f T). This suppression is, in a sense, compensated by an overestimation of spectral estimates in the frequency range f 1/T.     

Similarity scaling applied to sodar observations of the convective boundary layer above an irregular hill

Nine profiles of the temperature structure parameter C _T ² and the standard deviation of vertical velocity fluctuations ( _w) in the convective boundary layer (CBL) were obtained with a monostatic Doppler sodar during the second intensive field campaign of the First ISLSCP Field Experiment in 1987. The results were analyzed by using local similarity theory. Local similarity curves depend on four parameters: the height of the mixed layer (z _i ), the depth of the interfacial layer (), and the temperature fluxes at the top of the mixed layer (Q _i ) and the surface (Q _o). Values of these parameters were inferred from sodar data by using the similarity curve for C _T ² and observations at three points in its profile. The effects of entrainment processes on the profiles of C _T ² and _wnear the top of the CBL appeared to be described well by local similarity theory. Inferred estimates of surface temperature flux, however, were underestimated in comparison to fluxes measured by eddy correlation. The measured values of _wappeared to be slightly smaller than estimates based on available parmeterizations. These discrepancies might have been caused by experimental error or, more likely, by the distortion of turbulence structure above the site by flow over the nonuniform terrain at the observation site.     

Equatorial disturbances,monsoons, and 1982–1983 ENSO

Summary Interannual modes are described in terms of three-month running mean anomaly winds (u,v), outgoing longwave radiation (OLR), and sea surface temperature (T _* ). Normal atmospheric monsoon circulations are defined by long-term average winds (u _n,v _n) computed every month from January to December. Daily winds are grouped into three frequency bands, i.e., 30–60 day filtered winds (u _L,v _L); 7–20 day filtered winds (u _M,v _M); and 2–6 day filtered winds (u _S,v _S). Three-month running mean anomaly kinetic energy (signified asK _L , K _M , andK _S , respectively) is then introduced as a measure of interannual variation of equatorial disturbance activity. Interestingly, all of theseK _L , K _M , andK _S perturbations propagate slowly eastward with same phase speed (0.3 ms^–1) as ENSO modes. Associated with this eastward propagation is a positive (negative) correlation between interannual disturbance activity (K _L , K _M , K _S ) and interannualu (OLR) modes. Namely, (K _L , K _M , K _S ) becomes more pronounced than usual nearly simultaneously with the arrival of westerlyu and negativeOLR (above normal convection) perturbutions. In these disturbed areas with (K _L , K _M , K _S >0), upper ocean mixing tends to increase, resulting in decreased sea surface temperature, i.e.T _* 0. Thus, groups (not individual) of equatorial disturbances appear to play an important role in determiningT _* variations on interannual time scales. HighestT _* occurs about 3 months prior to the lowestOLR (convection) due primarily to radiational effects. This favors the eastward propagation of ENSO modes. The interannualT _* variations are also controlled by the prevailing monsoonal zonal windsu _n, as well as the zonal advection of sea surface temperature on interannual time scales. Over the central Pacific, all of the above mentioned physical processes contribute to the intensification of eastward propagating ENSO modes. Over the Indian Ocean, on the other hand, some of the physical processes become insignificant, or even compensated for by other processes. This results in less pronounced ENSO modes over the Indian Ocean.With 10 FiguresContribution No. 89-6, Department of Meteorology, University of Hawaii, Honolulu, Hawaii.     

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.     

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.     

Surface-layer scintillation measurements of daytime sensible heat and momentum fluxes

Line-averaged measurements of the structure parameter of refractive index (C _n ² ) were made using a semiconductor laser diode scintillometer above two markedly different surfaces during hours of positive net radiation. The underlying vegetation comprised in the first instance a horizontally homogeneous, pasture sward well-supplied with water, and in the second experiment, a sparse thyme canopy in a semi-arid environment. Atmospheric stability ranged between near neutral and strongly unstable (–20). The temperature structure parameterC _T ² computed from the optical measurements over four decades from 0.001 to 2 K² m^–2/3 agreed to within 5% of those determined from temperature spectra in the inertial sub-range of frequencies. Spectra were obtained from a single fine thermocouple sensor positioned near the midway position of the 100m optical path and at the beam propagation height (1.5m).With the inclusion of cup anemometer measurements, rule-of-thumb assumptions about surface roughness, and Monin-Obukhov similarity theory, path-averaged optical scintillations allow calculation of surface fluxes of sensible heat and momentum via a simple iterative procedure. Excellent agreement was obtained between these fluxes and those measured directly by eddy correlation. For sensible heat, agreement was on average close to perfect over a measured range of 0 to 500 W m^–2 with a residual standard deviation of 30 W m^–2. Friction velocities agreed within 2% over the range 0–0.9 m s^–1 (residual standard deviation of 0.06 m s^–1). The results markedly increase the range of validation obtained in previous field experiments. The potential of this scintillation technique and its theoretical foundation are briefly discussed.     

Intercepted flux and the horizontal component of solar radiation

Summary For the first time a method is presented to actually measure the radiative flux intercepted by cylindrical and conical objects in radiation fields of any unknown angular distribution.The horizontal component of solar radiationH is a newly introduced parameter expressed in Wm^–2 and defined as specific radiative flux intercepted by the lateral surface of a vertical cylinder. The horizontal componentH can be measured and must be considered complementary to the vertical component of solar radiationG which is conventionally measured as Global radiation.Radiative fluxes intercepted by cylindrical and conical objects are expressed as simple analytic functions ofG andH in any irregular radiation field. Before the introduction of the H-concept, when onlyG was measured, intercepted fluxes had to be approximated on the basis of assumed angular distributions of the radiation field.The climatological characteristics ofH andG are different: under clear skies in the open field the H-climatology is more temperate than the G-climatology all over the world and in all seasons. In the radiative environment of elongate vertical bodies H is generally a more significant parameter thanG. With 4 Figures     

The use of σ T as a temperature scale in the atmospheric surface layer

The standard deviation of temperature _T is proposed as a temperature scale and as a velocity scale to describe the behaviour of turbulent flows in the Atmospheric Surface Layer (ASL), instead of _* andu _* of the Monin—Obukhov similarity theory, and ofT _f andU _f used for free convection stability conditions. On the basis of experimental evidence reported in the literature, it is shown that _T T _f andv _* U _f in the free convection region, and _{T *} andv _* U _* in nearneutral and stable conditions. This implies that the proposed scales can be applied for all stabilities. Furthermore, a new length scale is proposed and its relation with Obukhov length is given. Also, a simple semi-empirical expression is presented with which _T andv _* can be evaluated in a rather simple way. Some examples of practical applications are given, e.g., a stability classification for unstable conditions.     

The stably stratified internal boundary layer for steady and diurnally varying offshore flow

A two-dimensional numerical mesoscale model is used to investigate the internal structure and growth of the stably stratified internal boundary layer (IBL) beneath warm, continental air flowing over a cooler sea. Two situations are studied — steady-state and diurnally varying offshore flow. In the steady-state case, vertical profiles of mean quantities and eddy diffusion coefficients (K) within the IBL show small, but significant, changes with increasing distance from the coast. The top of the IBL is well defined, with large vertical gradients within the layer and a maximum in the coast-normal wind component near the top. Well away from the coast, turbulence, identified by non-zero K, decreases to insignificant levels near the top of the IBL; the IBL itself is characterised by a critical value of the layer-flux Richardson number equal to 0.18. The overall behaviour of the mean profiles is similar to that found in the horizontally homogeneous stable boundary layer over land.A simple physical model is used to relate the depth of the layer h to several relevant physical parameters viz., x, the distance from the coast and U, the large-scale wind (both normal to the coastline) and g/, being the temperature difference between continental mixed-layer air and sea surface, is the mean potential temperature and g is the acceleration due to gravity. Excellent agreement with the numerical results is found, with h = 0.014x ^1/2 U (g/)^–1/2.In the diurnally varying case, the mean profiles within the IBL show only small differences from the steady-state case, although diurnal variations, particularly in the wind maximum, are evident within a few hundred kilometres of the coast. A mesoscale circulation normal to the coast, and superimposed upon the mean offshore flow, develops seawards of the coastline with maximum vertical velocities about sunset, of depth about 2 km and horizontal scale 500 km. The circulation is related to the advection, and subsequent decay, of daytime convective turbulence over the sea.     

The response of a propeller anemometer to turbulent flow with the mean wind vector perpendicular to the axis of rotation

The system transfer function ¦H(v)¦² at frequencyv (units of Hz) for a vertical velocity propeller anemometer in a statistically stationary and horizontally homogeneous turbulent flow is determined from: (1) experimental estimates of propeller velocity spectra; and (2) estimates of Eulerian vertical velocity spectra based on the hypothesis that degradation of the input vertical velocity Fourier components occurs in the inertial subrange. The experimental estimates of ¦H(v)¦² were adequately summarized with the mathematical expression for the system transfer function of a first-order system with parameterT which has units of time and is analogous to the time constant of a horizontal velocity propeller anemometer. Dimensional analysis techniques and the Monin-Obukhov similarity hypothesis were used to construct a model for the system parameterT which yielded the result that _w /D ₁ ( _w /)^1/3, where _w , andD ₁ denote the standard deviation of the input vertical velocity fluctuations, the horizontal mean wind speed, and the diameter of the propeller, respectively. The system parameterT is interpreted in terms of the time required for the propeller velocity statistics to become asymptotically independent of time upon being released from rest in a statistically stationary turbulent flow.Currently on leave of absence from the Indian Institute of Technology, New Delhi, India.