A numerical model study of the structure and similarity scaling of the nocturnal boundary layer (NBL)

A one-dimensional numerical model based on the equations of mean motion and turbulent kinetic energy (TKE), with Delage's (1974) mixing-length parameterization has been used to simulate the mean and turbulent structure of the evolving stably stratified nocturnal boundary layer (NBL). The model also includes a predictive equation for the surface temperature and longwave radiational cooling effects.In the absence of advective and gravity wave effects, it is found that the model-simulated structure, after a few hours of evolution, could be ordered fairly well by a similarity scaling (u _*0, _*0, L ₀, and h) based on surface fluxes and the NBL height. Simple expressions are suggested to describe the normalized profiles of momentum and heat fluxes, TKE, eddy-viscosity and energy dissipation. A good ordering of the same variables is also achieved by a local scaling (u _*0, _* and L) based on the height-dependent local fluxes. The normalized TKE, eddy viscosity and energy dissipation are unique functions of z/L and approach constant values as z/L , where L is the local Monin-Obukhov length. These constants are close to the values predicted for the surface layer as z/L , thus suggesting that the Monin-Obukhov similarity theory can be extended to the whole NBL, by using the local (height-dependent) scales in place of surface-layer scales. The observed NBL structure has been shown to follow local similarity (Nieuwstadt, 1984).     

Spectral characteristics of the annual rainfall series for Northeast Brazil

The rainfall series for Fortaleza (Ceará) is compared with similar series for several other locations in Northeast Brazil. It is shown that the correlations are high for distances up to about 600 km from Fortaleza. The Fortaleza series shows prominent periodicities at T = 2.1, 10.1, 12.9, 25.1, and 61.0 years, all significant at a 3 a priori level. Amongst these, T = 12.9 and 25.1 years are significant at a 4 a priori level. A master Curve (for 1912–1978 only), obtained by averaging rainfall data for 93 stations having good correlations with Fortaleza, shows very prominent periodicities at T = 5.6, 12.3 and 47.3 years, significant at a 3 a priori level. T = 12.3 is significant at a 4 a priori level. Predictions from both the Fortaleza series (1849–1976) and the Master Curve (1912–1978) indicated droughts during 1979–1983. This prediction seems to have come true. In the future, droughts during 1992–1994 and 2002–2006 are indicated.     

An alternative analysis of flux-gradient relationships at the 1976 ITCE

An extensive micrometeorological data set from the 1976 International Turbulence Comparison Experiment (ITCE) is analysed to determine flux-gradient relationships in an unstable atmosphere for momentum, sensible heat and water vapour transfers. The data are first analysed for internal consistency, resulting in the rejection of some data. Following a least-square fit to the remaining data in the form /k = (1 – z/L)^-/k, rounded-off values of k, , and are selected for each form of transfer consistent with the statistical accuracy of the measurements. The equations finally adopted are _M = (1 – 28z/L)^-1/4 and _{H, W} = (1 – 14z/L)^-1/2 with k _M = k_H = k_W = 0.40.These expressions fit the averaged observations to within a few per cent in the stability range of the experiment (-4 < z/L < -0.004).     

The Role of diabatic heating, torques and stabilities in forcing the radial- vertical circulation within cyclones part iii: case study of lee-side cyclones

１．ＩｎｔｒｏｄｕｃｔｉｏｎＡｎａｇｒｅｅｍｅｎｔｂｅｔｗｅｅｎｔｈｅｓｉｍｕｌａｔｅｄａｎｄ“ｏｂｓｅｒｖｅｄ”ａｚｉｍｕｔｈａｌｙ－ａｖｅｒａｇｅｄｍａｓ－ｗｅｉｇｈｔｅｄｒａｄｉａｌｍｏｔｉｏｎｓｈａｓｂｅｎｅｓｔａｂｌｉｓｈｅｄｆｏｒｔｈｅＯ...     

The effect of orchard crop structure on the integral length-scale of turbulence

The integral length-scalesL for the three orthogonal components of diffusivityK=L are derived from spectral analysis of velocity time series measurements. A 3-D sonic anemometer was used to make these velocity measurements at heights in the range 0.7–7.0 m in and above a 2 m orchard canopy with near-neutral atmospheric boundary-layer stability conditions. The integral length-scale is compared with another length-scale of diffusionL obtained by fitting an exponential model to the auto-correlation spectrumR _E (t) in the region 0.95<R _E (t)<0.5 for smallt. This length-scale is appropriate to a high frequency region of the energy spectrum where turbulent momentum transport becomes diffusion-like and the turbulent energy varies with the inverse square of frequence. This region has been shown by others to determine the magnitude of the dissipation rate of turbulent energy by the action of viscosity even though the dominant dynamics are inviscid. Within the crop, the ratio of the length-scalesL/L were found to be smaller than the values measured above the crop for vertical turbulence. This was attributed to the enhanced decay rate of turbulent energy due to the effect of the airflow interaction with the crop. It is unclear whether similar effects are present in the horizontal plane because of greater scatter in the data, resulting from the more variable nature of the wind direction in the horizontal plane.     

Theoretical objections against Pearson's rule of thumb on estimating the significance of a correlation-coefficient

Summary V. Conrad in a brief note on estimating the significance of a correlation-coefficient, pays attention toPearson's rule of thumb: The correlation-coefficientr is significant if it is, at least, six times its probable error. The present author studies the theoretical and mathematical background of the rule. The conclusion is that the rule is based weakly. Although it is possible to correct it in accordance with the modern statistical point of view, it is better (especially ifn<60) touse the exact correlation tables. A diagram and a numerical example illustrate the text.

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Zusammenfassung V. Conrad hat in einem kurzen Aufsatz Pearsons Faustregel besprochen, wonach ein Korrelationskoeffizient als signifikant anzusehen ist, wenn sein Wert mindestens sechsmal größer als sein wahrscheinlicher Fehler ist. Der Autor betrachtet den mathematischen Hintergrund der genannten Regel. Es zeigt sich, daß die Regel schwach fundiert ist. Obschon es möglich ist, sie etwas zu verbessern, ist es doch besser (insbesondere fürn<60),die exakten Korrelationstafeln zu verwenden. Die Ausführungen werden durch ein Diagramm und ein numerisches Beispiel erläutert.

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Résumé V. Conrad a commenté, dans une petite note, la règle approximative dePearson qui se formule comme suit: Le coéfficient de correlation est significatif si sa valeur est au moins six fois plus grande que son erreur probable. L'auteur étudie la base mathématique de cette règle et constate qu'elle est très faible. Bien qu'il soit possible de corriger la règle, il est recommandable de se servir de tables exactes de corrélation, spécialement pour les valeurs den<60. Les déductions sont illustrées par un diagramme et un exemple numérique.

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With 1 Figure     

Radiation balance in a tropical city — Delhi (India)

The impact of urbanization is assessed by comparing values of the radiation parameters at an urban location with those of a rural site. Urban Delhi was divided according to land-use and the effects of urbanization was studied on incoming short-wave (K), albedo, incoming longwave (L, outgoing longwave (L), and net radiation (Q ^*), were individually studied at four representative sites (Rural, Commercial, Residential and Industrial). MaximumK was observed in the rural and commercial areas whereas highL was observed in the commercial and industrial locations. High depletion ofK of the order of 13% was observed for the industrial location in the winter season. An increase ofL in, the industrial location is of the same order as that of the commercial location, i.e. 20%. The residential location shows quite moderate (4.6%) depletion ofK in comparison with other sites.Nomenclature U Urban - R Rural - K Incoming Short-wave radiation - L Incoming Long-wave radiation - L Outgoing Long-wave radiation - Q ^* Net Radiation - Albedo - K ^* Net Short-wave radiation - L ^* Net Long-wave radiation     

A barotropic model of the Ekman planetary boundary layer based on the geostrophic momentum approximation

A model of a stationary planetary boundary layer is proposed based on the equation of motion with the advective term retained. The latter is modeled by means of the so-called geostrophic momentum approximation in two versions — original and modified. New expressions for the vertical velocity W at the top of the boundary layer are derived and analyzed. They underestimate W compared to the classical expression.     

Stability functions correct at the free convection limit and consistent for for both the surface and Ekman layers

For the thermal stability function _h used to calculate heat and moisture fluxes in the surface layer, we choose a formulation which has the theoretically correct free convection limit % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaeikaiabgk% HiTGqaciaa-PhacaqGVaGaamitaiaabMcadaahaaWcbeqaaiabgkHi% TiaaigdacaGGVaGaaG4maaaaaaa!3DFE!\[{\rm{(}} - z{\rm{/}}L{\rm{)}}^{ - 1/3} \]. We then use the experimental result that z/L Ri to deduce a formulation with an exponent -1/6 for the momentum stability function _m. This formulation also resolves the matching problem at the interface between the surface and Ekman layers. The proposed functions are found to remain reasonably close to another formulation that is well supported by observations and has exponents -1/2 for _h and -1/4 for _m. The intent of the proposals is mainly to clarify and simplify the parameterization of the convective boundary layer in present day atmospheric models, without significantly altering the results.     

Black body temperature, orbital elements, the Milankovitch precession index, and the Seversmith psychroterms

Summary The temperature T of a black or gray body orbiting the Sun can be expressed in terms of spherical harmonics in latitude and longitude, its Keplerian orbital elements, and a variable describing rotation about its axis. Assuming that the Earth is a black or gray body without thermal inertia, the resulting equation for T exhibits previously unrecognized odd-degree zonal terms dubbed Seversmith psychroterms. They cause a hemispheric temperature difference which depends upon e sin _S, where e is the orbital eccentricity and _S is the Suns argument of perigee measured in an Earth-centered frame. The hemisphere containing perihelion is the cooler. For a gray body with the Earths average albedo of 0.3, an emissivity of unity, and an obliquity of 23.5°, the pole-to-pole temperature difference for the combined first and third degree spherical harmonic psychroterms can reach 3.4K for the present eccentricity of 0.016, and 12.9K for the maximum eccentricity of 0.06. While a thermally inertia-less black or gray body with boiling hot subsolar points and nights at absolute zero are poor models for the Earth, the Seversmith psychroterms will survive in more realistic models (although with smaller amplitudes) because the Earth radiates nonlinearly in T. The psychroterms acts in the direction opposite to the Milankovitch precession index, which also depends on e sin _S: by warming the cool northern summers, the psychroterms make it harder for the traditional Milankovitch mechanism to operate. The Seversmith psychroterms could in fact be responsible for the ice sheets that cycle with e sin _S, instead of the Milankovitch mechanism. By cooling the southern hemisphere for thousands of years when perihelion is in the south, the psychroterms may somehow cause the southern hemisphere to control the northern ice sheets associated with the 23kyr and 19kyr periods (kyr=10³ years), possibly through ice-albedo feedback in the sea ice surrounding Antarctica. Two other unexpected features besides the psychroterms are: while the average insolation increases with increasing e, the average temperature of the Earth paradoxically decreases; and the equator-to-pole temperature difference of 21K on a gray body with an albedo equal to 0.3 and an emissivity of unity is actually smaller than the observed difference of 28K on the real Earth.     

Statistics of atmospheric turbulence within and above a corn canopy

Two three-dimensional split-film anemometers were used to measure turbulence statistics within and above a corn canopy. Normalised profiles of mean windspeed, root-mean-square velocity, momentum flux, and heat flux were constructed from half-hourly averages by dividing within-canopy measurements by the simultaneous canopy-top measurement. With the exception of the heat flux, these profiles showed consistent shape from day to day. Time series of the three velocity components were recorded on magnetic tape and subsequently analysed to obtain Eulerian time and length scales and the power spectrum of each component at several heights. The timescale was found to have a local minimum value at the top of the canopy. However the length scale L _wformed from the timescale and the root-mean-square vertical velocity varied with height as L _w 0.1 z. The power-spectra were non-dimensionalised to facilitate comparison of spectra at different heights and times. All spectra had -5/3 regions spanning at least two decades in frequency.     

Flux determination over a smooth surface under strongly unstable conditions

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

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]     

Turbulence measurements during mistral winds with a 1-dimensional sonic anemometer

Fluctuations in the vertical wind velocity and air temperature were measured with a 1-dimensional sonic anemometer and fine thermocouple over a flat agricultural site in the Rhone Valley, France. Strong Mistral winds with speeds up to 20 m s^–1 kept atmospheric conditions very close to neutral and ensured stationarity. Friction velocities estimated both by eddy correlation (sonic plus Gill Bivane) and inertialdissipation (sonic only) methods agreed within 1 and 5 % respectively of traditional profile measurements over the measured range of 0.2 to 1.2 m s^–1. The coefficient of eddy transport for heat exceeded that of momentum by a factor of 1.38 (± 0.05), a result almost identical to that obtained in the Kansas experiment (Businger et al., 1971). For - 0.15 >= z/L >= 0.05, the ratio _w /u _* was 1.69 and 1.34 for unstable and stable conditions, respectively. For ¦z/L¦ >= 0.05, the ratio /T _* was 1.40 independent of whether neutrality was approached from either stable or unstable conditions.     

Free convection scaling over the ocean derived from buoy measurements during gate

The structure of atmospheric turbulence in the surface layer over the open ocean is examined under conditions of local free convection. The raw data consist of profile and fluctuation measurements of wind and temperature as obtained from a meteorological buoy. For near neutral conditions and for waves running approximately along the wind direction, wave-induced wind fluctuations can be described by a simplified linear theory based on Miles (1957). In this case, the spectrum of wind velocity is given as the sum of two parts; for the turbulent part, the parameterization as obtained by Kaimal et al. (1972) applies, while the wave-induced part is parameterized using a simplification of Miles' linear theory. For cases of local free convection, the measurements of the vertical component of the wind velocity are well described by similarity theory; as expected, _w /(-uw)^1/2 is proportional to (- z/L)^1/3. In order to scale the longitudinal wind velocity component, it seems to be reasonable to extend the list of relevant parameters by the height of the mixed layer z _i. We obtain _u /(- uw)^1/2 (z/z _i)^1/3(- z/L)^1/3 with only a poor correlation coefficient of r = 0.6. Overall, the results of local free convection scaling obtained from direct measurements show good agreement with those obtained from profile measurements. A comparison between direct and indirect determination of turbulent fluxes of momentum shows an unexplained difference of about 20%. This discrepancy is mainly due to a gap in the uw-cospectrum at the swell frequency.     

A study of convective elements in the atmospheric surface layer

A statistical model, based on a method of Vulf'son, is used to examine some of the plume-like temperature structures formed in the unstable boundary layer. The model assumes that the plume diameter changes slowly with height so that a cylindrical approximation may be made. Measurements of the vertical velocity and temperature were used to determine the temperature dependent portion of the vertical velocity field. Temperature data were collected from sensors on a tower and from aircraft; velocity data were collected only from the tower.Using this model for analysis of the data indicates that: (1) the average isotherm diameter and the population of isotherms are a function ofz/L; (2) the distribution of core temperatures is approximately a uniform distribution.Independent of the model, a convective velocity was determined and found to have approximately the same profile as the temperature; from this the average velocity of the plumes was found to be a linear function ofz/L, fromz/L - 0.1 toz/L - 1.0. As a consequence of this functional dependence, the entrainment into the plumes is approximately constant over this range. The cumulative temperature distribution function was found to be an asymmetric function ofz/L. A simple relation which is independent ofu _* is given to determine the heat flux.Contribution No. 269 Dept. of Atmospheric Sciences, University of Washington.     

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.     

E-ε modelling of turbulent air flow downwind of a model forest edge

A two-dimensional E- model, which included the effects of plant-atmosphere interaction, was used to simulate air flow downwind of forest edges for the purpose of predicting the microclimate in forest openings. A suitable set of wall functions was selected to consider the aerodynamic effects of the ground in the opening. The model with discretization and parameter schemes was validated using a set of data from a wind-tunnel experiment. The simulated wind speed and turbulence kinetic energy closely agreed with the measured values. After validation, the model was used to predict eddy diffusivity in the lee of the forest edge. The modelled spatial distribution of the eddy diffusivity agreed in general with that calculated using wind-tunnel measurements. The usefulness and limitations of the E- model are discussed.Presently with Intera Information Technologies Corporation, IMS Division, 2 Gurdwara Road, Nepean, Ontario, Canada K2E 1A2.Corresponding author, and presently with Canada Centre for Remote Sensing, 419-588 Booth Street, Ottawa, Ontario, Canada K1A 0Y7.     

Drag and heat transfer relations for the planetary boundary layer

A theory is offered for the drag and heat transfer relations in the statistically steady, horizontally homogeneous, diabatic, barotropic planetary boundary layer. The boundary layer is divided into three regionsR ₁,R ₂, andR ₃, in which the heights are of the order of magnitude ofz ₀,L, andh, respectively, wherez ₀ is the roughness length for either momentum or temperature,L is the Obukhov length, andh is the height of the planetary boundary layer. A matching procedure is used in the overlap zones of regionsR ₁ andR ₂ and of regionsR ₂ andR ₃, assuming thatz ₀ L h. The analysis yields the three similarity functionsA(),B(), andC() of the stability parameter, = u _*/fL, where is von Kármán's constant,u _* is the friction velocity at the ground andf is the Coriolis parameter. The results are in agreement with those previously found by Zilitinkevich (1975) for the unstable case, and differ from his results only by the addition of a universal constant for the stable case. Some recent data from atmospheric measurements lend support to the theory and permit the approximate evaluation of universal constants.     

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.