Humidity fluctuations in the marine boundary layer measured at a coastal site with an infrared humidity sensor

An extensive set of humidity turbulence data has been analyzed from 22-m height in the marine boundary layer. Fluctuations of humidity were measured by an OPHIR, an infrared humidity sensor with a 10 Hz scanning frequency and humidity spectra were produced. The shapes of the normalized spectra follow the established similarity functions. However the 10-min time averaged measurements underestimate the value of the absolute humidity. The importance of the humidity flux contribution in a marine environment in calculating the Obukhov stability length has been studied. Deviations from Monin-Obukhov similarity theory seem to be connected to a low correlation between humidity and temperature.     

Mellor-Yamada simplified second-order closure models: Analysis and application of the generalized von Karman local similarity hypothesis

Mellor-Yamada's superequilibrium Level 2 and Level 1 models are analyzed using the Monin-Obukhov theory framework. Yamada's (1975) analysis is supplemented by a discussion of the realizability requirements posed on model constants and by the inclusion of the master-length scale problem. The generalized von Kármán local similarity hypothesis (Laikhtman, 1979) is examined as an alternative closure hypothesis for second-order models. A systematic method of model examination is used. First, a family of models, consisting of Level 1 and Level 2 Reynolds-stress equation sets and different length-scale hypotheses (Prandtl's, generalized von Kármán's), is built. Next, asymptotic characteristics of individual models are investigated and compared with similarity predictions. Monin-Obukhov universal functions for turbulent energy, space scale and temperature variance, derived from the models, are compared with experimental surface-layer data. Generally, models employing the stability-dependent generalized von Karman hypothesis perform better than those that use the conventional Prandtl mixing-length concept. The choice amongst the von Kármán type models is still ambiguous. However, the Level 1 model with a stability-dependent generalized von Kármán length scale seems to be the best of those considered.     

Local similarity relationships in a horizontally inhomogeneous boundary layer

Local similarity theory, an analogy to the Monin-Obukhov similarity theory, is successfully applied to airborne observations in a coastal area of South Australia. The boundary layer over this highly non-uniform surface is characterized by extensive variations in its thermal stratification and turbulence characteristics. However, the behaviour of some statistical parameters of second- and higher moments seems to be determined mainly by local forcing, while horizontal advection plays a less important role. For these parameters, local scaling is effective. It is shown that the dimensionless variances of vertical velocity and potential temperature are functions of z/ only, where is the local Monin-Obukhov length and z is the height above ground. The dimensionless variance of horizontal velocity components is found to depend on h/, where h is the height of the oundary layer. Similarity relationships for some triple correlations are also discussed. The empirically determined local similarity relationships are found to agree with those obtained from surface-layer similarity. Finally, to illustrate the complexity of the local forcing, distributions of vertical energy and momentum fluxes, from which the local scaling parameters are derived, are shown.     

Quantifying the Influence of Random Errors in Turbulence Measurements on Scalar Similarity in the Atmospheric Surface Layer

The influence of random errors in turbulence measurements on scalar similarity for temperature, water vapour, \(\hbox {CO}_{2}\), and \(\hbox {NH}_{3}\) is investigated using two eddy-covariance datasets collected over a lake and a cattle feedlot. Three measures of scalar similarity, namely, the similarity constant in the flux–variance relationship, the correlation coefficient between two scalars and the relative transport efficiency, are examined. The uncertainty in the similarity constant \(C_{s}\) in the flux–variance relationship resulting from random errors in turbulence measurements is quantified based on error propagation analyses and a Monte-Carlo sampling method, which yields a distribution instead of a single value for \(C_{s}\). For different scalars, the distributions of \(C_{s}\) are found to significantly overlap, implying that scalars are transported similarly under strongly unstable conditions. The random errors in the correlation coefficients between scalars and the relative transport efficiencies are also quantified through error propagation analyses, and they increase as the atmosphere departs from neutral conditions. Furthermore, the correlation coefficients between three scalars (water vapour, \(\hbox {CO}_{2}\), and \(\hbox {NH}_{3}\)) are statistically different from unity while the relative transport efficiencies are not, which highlights the difference between these two measures of scalar similarity. The results suggest that uncertainties in these measures of scalar similarity need to be quantified when using them to diagnose the existence of dissimilarity among different scalars.     

A Study of Correlations of Scalar Quantities in the Atmospheric Surface Layer

Standard deviations for vertical velocity and scalar quantities, such as temperature, T, and specific humidity, q, were analyzed on the basis of Monin-Obukhov (M-O) similarity theory in the atmospheric surface layer. The correlation coefficient between scalar quantities T and q, R_Tq, was derived from the similarity functions and can be expressed as the ratio of B_T/B_q (B_T≤ B_q), where parameter B is the value of the normalized standard deviation of any scalar quantity at neutral conditions.     

Measurements of fluctuations of vertical wind velocity,temperature and radio-refractive index above the sea

Mean spectra of vertical wind velocity, temperature, and humidity and co-spectra of vertical turbulent heat and moisture fluxes are reported, normalized in terms of the similarity theory of Monin-Obukhov. The measurements were made in April 1967 at light-house Alte Weser at a height of 30 m above the German Bight. Ten spectra measured under conditions of moderate instability (z/L –0.08) have been used for the evaluation of a mean spectral curve. The humidity fluctuations have been determined from simultaneous turbulence measurements of temperature and radiorefractive-index, which were obtained by a microwave refractometer.Similar to the BOMEX measurements discussed by Phelps and Pond (1971) our results also show a dissimilarity between the fluctuations of temperature and humidity. Accordingly, in the range of lower and higher natural frequencies, significant differences were present between the co-spectra of the vertical heat and moisture fluxes, although the mean peak frequencies of both the fluxes nearly correspond to that of the mean vertical wind-velocity spectrum (f _m 0.35).     

Experimental micrometeorology in an era of turbulence simulation

Micrometeorologists have traditionally used the framework of the ensemble mean, fluctuating decomposition in studying turbulence spectra, Reynolds-flux budgets, surface-exchange relations, and the universal functions of Monin-Obukhov similarity within the constant-flux layer. More recently, the growth in supercomputers and computational fluid dynamics has stimulated micrometeorological applications of large-eddy simulation (LES). LES uses a different framework, one based on the resolvable, subgrid-scale decomposition. This framework shift seems to have weakened the vital and historically strong coupling between experimental and computational work in micrometeorology. A challenge for experimentalists today is to address problems posed in the language of the resolvable, subgrid-scale decomposition. We illustrate by discussing measurement strategies for resolvable-scale turbulence fields and for local surface-exchange coefficients.     

Turbulent characteristics and bulk transfer coefficients over the desert in the HEIFE area

Observations of surface-layer turbulence and turbulent fluxes were made over a desert in northwestern China as a part of HEIFE (HEIhe river Field Experiment). These show that the normalized variations of the vertical wind component and of the air temperature obey Monin-Obukhov similarity well, especially in free convective conditions. However, the variations of specific humidity do not obey Monin-Obukhov similarity.Mean bulk transfer coefficients of sensible heat and momentum flux are obtained as functions of stability over a wide stability range from the observed data of turbulent fluxes and mast profiles. However, the bulk transfer coefficient for water vapor could not be obtained because of the large scatter of the data. In free convective conditions, the sensible heat flux was found to be approximately proportional to the 1.4 power of temperature difference between the surface and 20m. The bulk transfer coefficient of sensible heat is also obtained as a function of the bulk Richardson number for practical convenience.     

On similarity in the atmospheric boundary layer

A similarity theory for the atmospheric boundary layer is presented. The Monin-Obukhov similarity theory for the surface layer is a particular case of this new theory, for the case of z 0. Universal functions which are in agreement with empirical data are obtained for the stable and convective regimes.On leave from Institute of Environmental Engineering, Warsaw Technical University, 00653 Warsaw, Poland. Present address, Department of Geological and Geophysical Sciences, University of Wisconsin, Milwaukee, WI 53201 U.S.A.     

边界层局地相似理论在草原下垫面的适用性检验

利用锡林浩特草原平坦下垫面塔层湍流资料,对常值通量层的高度进行了估计,检验了局地相似理论在均匀草原下垫面的适用性,对Monin-Obukhov相似理论和局地相似理论在常值通量层以上的大气边界层的适用性进行了比较。结果表明:(1)对于锡林浩特草原来说,常值通量层厚度在50m左右;(2)通过分析无量纲风速和温度梯度、无量纲风速方差、无量纲标量(温度T、水汽q、CO2浓度C)方差与稳定度z/L之间的关系,验证了局地相似理论在均匀草原下垫面70m以下大气边界层的适用性;(3)感热通量尺度与浮力长度尺度之间存在线性关系;(4)从经典Monin-Obukhov长度、局地Monin-Obukhov尺度和浮力长度尺度的对比分析来看,局地尺度更适用于50m以上的大气边界层,而浮力长度尺度不适用于50m以上的大气边界层。     

A verification of some methods to determine the fluxes of momentum,sensible heat,and water vapour using standard deviation and structure parameter of scalar meteorological quantities

A set of micro-meteorological data collected over a horizontal, uniform terrain (the plain of La Crau, France) in June 1987 is analysed. Conditions were predominantly sunny and arid, while due to the Mistral the wind speed could exceed 10 m/s. Verification of several methods to evaluate surface fluxes of heat, momentum and water vapour from the standard deviation of temperature, wind and specific humidity is presented. Also, a similar approach using the structure parameter of temperature is considered. These methods are all based on Monin-Obukhov (M-O) similarity theory. It is found that the standard deviation of temperature, vertical and horizontal wind speed as well as the structure parameter for temperature behave according to M-O similarity. It is shown that the sensible heat flux and friction velocity can be determined from a fast response thermometer and a cup anemometer. Also, it appears that the analytic solution of the set of governing equations as derived by the first author yields good results. M-O theory does not appear to work for the standard deviation of specific humidity. This may be due to the relative importance of large eddies.     

On the Temperature and Humidity Dissimilarity in the Marine Surface Layer

The dissimilarity of temperature and humidity transfer in the marine surface layer (MSL) is investigated through the relative transport efficiency and correlation coefficient of these two scalars. We examine their variability and relationship with mean values, as well as spectral characteristics. It is shown that the dissimilarity between these two scalars in the MSL is a function of stability, the boundary-layer depth, and flow steadiness. In general the temperature and humidity are less correlated in shallow marine boundary layers compared to deep marine boundary layers, due to the stronger impact of the boundary-layer scale in breaking the “same source, same sink” assumption for scalar similarity. This is supported by the combination of our spectral analysis of scalar fluxes and corresponding measured and modelled boundary-layer depth. This assumption is also broken in near-neutral conditions, when there is an efficient latent heat transfer but negligible sensible heat transfer. Our data suggest that parametrization of humidity fluxes via similarity theory could still be reliable when the correlation coefficient $>$ 0.5, and in near-neutral conditions the humidity flux can be estimated without use of the sensible heat flux.     

On the sensitivity of mesoscale models to surface-layer parameterization constants

The Colorado State University standard mesoscale model is used to evaluate the sensitivity of one-dimensional (1D) and two-dimensional (2D) fields to differences in surface-layer parameterization constants. Such differences reflect the range in the published values of the von Karman constant, Monin-Obukhov stability functions and the temperature roughness length at the surface. The sensitivity of 1D boundary-layer structure, and 2D sea-breeze intensity, is generally less than that found in published comparisons related to turbulence closure schemes generally.     

Turbulence above Lake Ontario: Velocity and scalar statistics

Measurements of the fluctuations of wind, temperature and humidity were made with an instrumented aircraft at altitudes from 30 to 300m above Lake Ontario. The variations of the standard deviations of these fluctuations are examined. By applying Monin-Obukhov similarity theory based on local fluxes, it is shown that the vertical velocity, temperature and humidity fluctuations scale with the local Monin-Obukhov length. In the limit of free convection, 1/3 and –1/3 power laws are approached with constants of 1.2, 1.2, and 0.8 for vertical velocity, temperature and humidity, respectively. The von Karman scale lengths increase with height but were much larger than those found by Taylor et al. (1970).     

A scheme for computing surface fluxes from mean flow observations

A computational scheme is developed for estimating turbulent surface stress, sensible heat flux and humidity flux from mean velocity, temperature and humidity at a single height in the atmospheric surface layer; conditions at this reference level are presumed known from observations or from a numerical atmospheric circulation model. The method is based on coupling a Monin-Obukhov similarity profile to a force-restore formulation for the evolution of surface soil temperature to yield the local values of shear stress, heat flux and surface temperature. A self-contained formulation is presented including parameterizations for solar and infrared radiant flux at the surface.In addition to reference-level mean flow properties, the parameters needed to implement the scheme are thermal heat capacity of the soil, surface aerodynamic roughness, latitude, solar declination, surface albedo, surface emissivity and atmospheric transmissivity.Sample calculations are presented for (a), constant atmospheric forcing at the reference level, and (b) variable atmospheric forcing corresponding to Kahle's (1977) measurements of windspeed, air temperature and radiometer soil surface temperature under dry vegetatively sparse conditions in the Mohave Desert in California. The latter case simulated the observed diurnal variations resonably well for the parameters used.Consultant, Atmospheric Sciences Division, Department of Energy and Environment, Brookhaven National Laboratory, Upton, N.Y., pc11973, U.S.A.     

The variations of the statistics of wind,temperature and humidity fluctuations with stability

Measurements of the turbulent fluctuations of wind, temperature and humidity were made in the atmospheric surface layer. The statistics of the fluctuations were investigated in both the time and frequency domains. The vertical wind, temperature and smaller-scale horizontal wind fluctuations appear to obey the Monin-Obukhov similarity hypothesis. The humidity fluctuations were found to be governed by a humidity flux stability parameter rather than the normal Monin-Obukhov length.     

Estimation of surface heat and momentum fluxes using the flux-variance method above uniform and non-uniform terrain

Eddy-correlation measurements above an uneven-aged forest, a uniform-irrigated bare soil field, and within a grass-covered forest clearing were used to investigate the usefulness of the fluxvariance method above uniform and non-uniform terrain. For this purpose, the Monin and Obukhov (1954) variance similarity functions were compared with direct measurements. Such comparisons were in close agreement for momentum and heat but not for water vapor. Deviations between measured and predicted similarity functions for water vapor were attributed to three factors: 1) the active role of temperature in surface-layer turbulence, 2) dissimilarity between sources and sinks of heat and water vapor at the ground surface, and 3) the non-uniformity in water vapor sources and sinks. It was demonstrated that the latter non-uniformity contributed to horizontal gradients that do not scale with the vertical flux. These three factors resulted in a turbulence regime that appeared more efficient in transporting heat than water vapor for the dynamic convective sublayer but not for the dynamic sublayer. The agreement between eddy-correlation measured and flux-variance predicted sensible heat flux was better than that for latent heat flux at all three sites. The flux-variance method systematically overestimated the latent heat flux when compared to eddy-correlation measurements. It was demonstrated that the non-uniformity in water vapor sources reduced the surface flux when compared to an equivalent uniform terrain subjected to identical shear stress, sensible heat flux, and atmospheric water vapor variance. Finally, the correlation between the temperature and water vapor fluctuations was related to the relative efficiency of surface-layer turbulence in removing heat and water vapor. These relations were used to assess critical assumptions in the derivation of the flux-variance formulation.     

Quasi-Wavelet Model of Von Kármán Spectrum of Turbulent Velocity Fluctuations

The von Kármán spectra of turbulent temperature andvelocity fluctuations have been widely used in the literature on turbulenceand electromagnetic, seismic, and acoustic wave propagation in random media.In this paper we provide a phenomenological motivation for the vonKármán velocity spectrum in terms of the quasi-wavelet model ofturbulence developed recently. In this model, turbulence is represented as asuperposition of self-similar localized eddies of many different scales. Wefind a functional form for these eddies that yields the von Kármán velocity spectrum exactly. We also show that other eddy functions producevelocity spectra that have the same general form as the von Kármán spectrum, and we consider possible quasi-wavelet representations of the`Kansas' spectrum and the `-1' spectrum. We also present asystematic determination, based on turbulence similarity theories, of theparameters of the von Kármán spectra of temperature and velocityfluctuations in an unstable atmospheric boundary layer.     

Estimation of the Monin-Obukhov similarity functions from a spectral model

From measured one-dimensional spectra of velocity and temperature variance, the universal functions of the Monin-Obukhov similarity theory are calculated for the range –2 z/L + 2. The calculations show good agreement with observations with the exception of a range –1 z/L 0 in which the function _m , i.e., the nondimensional mean shear, is overestimated. This overestimation is shown to be caused by neglecting the spectral divergence of a vertical transport of turbulent kinetic energy. The integral of the spectral divergence over the entire wave number space is suggested to be negligibly small in comparison with production and dissipation of turbulent kinetic energy.Notation a,b,c contants (see Equations (–4)) - C_i constants i=u, v, w, (see Equation (5) - k_me,k_mT peak wave numbers of 3-d moel spectra of turbulent kinetic energy and of temperature variance, respectively - k_mi peak wave numbers of 1-d spectra of velocity components i=u, v, w and of temperature fluctuations i= - k_sb, k_c characteristics wave numbers of energy-feeding by mechanical effects being modified by mean buoyancy, and of convective energy feeding, respectively - L Monin-Obukhov length - % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiiYdd9qrFfea0dXdf9vqai-hEir8Ve% ea0de9qq-hbrpepeea0db9q8as0-LqLs-Jirpepeea0-as0Fb9pgea% 0lrP0xe9Fve9Fve9qapdbaqaaeGacaGaaiaabeqaamaabaabcaGcba% Gabeivayaaraaaaa!3C5B!\[{\rm{\bar T}}\] difference of mean temperature and mean potential temperature - T* Monin-Obukhov temperature scale - velocity of mean flow in positive x-direction - u* friction velocity - u, v, w components of velocity fluctuations - z height above ground - von Kármanán constant - temperature fluctuation - _m nondimensional mean shear - _H nondimensional mean temperature gradient - nondimensional rate of lolecular dissipation of turbulent kinetic energy - _D nondimensional divergence of vertical transports of turbulent linetic energy     

Radiative Effects on Temperature in the Stable Surface Layer

The interaction between longwave radiation and temperature fluctuations plays a role in the dissipation of temperature variance. This interaction is most easily described by spectral models of atmospheric turbulence and a spectral radiative dissipation function which gives the intensity of the damping at each radiative wavelength and wavenumber k. We have used a Corrsin–Pao closure for the spectral budgets of turbulent kinetic energy and temperature to study the coupling of radiation to turbulence. The spectral radiative dissipation function and a related integral have been fitted by analytical approximations with the correct asymptotic behavior. This resulted in a simple analytical formula for the dimensionless temperature spectrum as a function of Monin-Obukhov stability, and a new dimensionless parameter describing the relative importance of radiation in the temperature spectral budget. The radiative effects both on the temperature spectrum and on the dimensionless temperature variance can then be calculated. Based on typical values of the radiative dimensionless parameters for the surface layer, we conclude that radiative dissipation is probably negligible there.