Monin–Obukhov Similarity Functions for the Structure Parameters of Temperature and Humidity

Monin–Obukhov similarity functions for the structure parameters of temperature and humidity are needed to derive surface heat and water vapour fluxes from scintillometer measurements and it is often assumed that the two functions are identical in the atmospheric surface layer. Nevertheless, this assumption has not yet been verified experimentally. This study investigates the dissimilarity between the turbulent transport of sensible heat and water vapour, with a specific focus on the difference between the Monin–Obukhov similarity functions for the structure parameters. Using two datasets collected over homogeneous surfaces where the surface sources of sensible heat and water vapour are well correlated, we observe that under stable and very unstable conditions, the two functions are similar. This similarity however breaks down under weakly unstable conditions; in that regime, the absolute values of the correlations between temperature and humidity are also observed to be low, most likely due to large-scale eddies that transport unsteadiness, advection or entrainment effects from the outer layer. We analyze and demonstrate how this reduction in the correlation leads to dissimilarity between the turbulent transport of these two scalars and the corresponding Monin–Obukhov similarity functions for their structure parameters. A model to derive sensible and latent heat fluxes from structure parameters without measuring the friction velocity is tested and found to work very well under moderately to strongly unstable conditions (−z/L > 0.5). Finally, we discuss the modelling of the cross-structure parameter over wet surfaces, which is crucial for correcting water vapour effects on optical scintillometer measurements and also for obtaining surface sensible and latent heat fluxes from the two-wavelength scintillometry.     

On Monin–Obukhov Similarity In The Stable Atmospheric Boundary Layer

Atmospheric measurements from several field experiments have been combined to develop a better understanding of the turbulence structure of the stable atmospheric boundary layer. Fast response wind velocity and temperature data have been recorded using 3-dimensional sonic anemometers, placed at severalheights (1 m to 4.3 m) above the ground. The measurements wereused to calculate the standard deviations of the three components of the windvelocity, temperature, turbulent kinetic energy (TKE) dissipation andtemperature variance dissipation. These data were normalized and plottedaccording to Monin–Obukhov similarity theory. The non-dimensional turbulencestatistics have been computed, in part, to investigate the generalapplicability of the concept of z-less stratification for stable conditions. From the analysis of a data set covering almost five orders ofmagnitude in the stability parameter = z/L (from near-neutral tovery stable atmospheric stability), it was found that this concept does nothold in general. It was only for the non-dimensional standard deviation oftemperature and the average dissipation rate of turbulent kinetic energythat z-less behaviour has been found. The other variables studied here(non-dimensional standard deviations of u, v, and w velocity components and dissipation of temperature variance) did not follow the concept of z-less stratification for the very stable atmospheric boundary layer. An imbalance between production and dissipation of TKE was found for the near-neutral limit approached from the stable regime, which matches with previous results for near-neutral stability approached from the unstable regime.     

Moving Beyond Monin–Obukhov Similarity Theory in Modelling Wind-Speed Profiles in the Lower Atmospheric Boundary Layer under Stable Stratification

Monin–Obukhov similarity theory (MOST) is commonly used to model the wind-speed profile at altitudes relevant to wind-power production (e.g. 10–200 m). Though reasonably accurate for unstable to weakly stable stratification, this approach becomes less accurate under increasingly stable stratification, largely due to the constant-flux surface layer assumed by MOST becoming shallower than the altitude range of interest. Furthermore, above the surface layer, the Coriolis force has a considerable influence on the wind-speed profile (in particular in the formation of low-level jets) that cannot be modelled using similarity theory. Our goal is to compare the accuracy of alternative extrapolation models that are more physically appropriate above the surface layer. Using data from the 213-m Cabauw meteorological tower in the Netherlands between July 2007 and June 2008, it is shown that MOST is accurate only at low altitudes and low stability, and breaks down at high altitudes and high stability. Local similarity is generally more accurate than MOST across all altitudes and stabilities, though the model requires turbulent flux data at multiple altitudes that is generally impractical. In contrast, a two-layer MOST–Ekman model is found to be comparable to the other models at low stability ranges and considerably more accurate in the high stability range, while requiring only a measure of surface stability and the geostrophic wind.     

An Analytical Formulation of the Monin–Obukhov Stability Parameter in the Atmospheric Surface Layer Under Unstable Conditions

A non-iterative analytical scheme is developed for unstable stratification that parametrizes the Monin–Obukhov stability parameter \(\zeta \) (\({=}z{/}L\), where z is the height above the ground and L is the Obukhov length) in terms of bulk Richardson number (\(Ri_B\)) within the framework of Businger–Dyer type similarity functions. The proposed scheme is valid for a wide range of roughness lengths of heat and momentum. The absolute relative error in the transfer coefficients of heat and momentum is found to be less than 1.5% as compared to those obtained from an iterative scheme for Businger–Dyer type similarity functions. An attempt has been made to extend this scheme to incorporate the similarity functions having a theoretically consistent free convection limit. Further, the performance of the scheme is evaluated using observational data from two different sites. The proposed scheme is simple, non-iterative and relatively more accurate compared to the schemes reported in the literature and can be used as a potential alternative to iterative schemes used in numerical models of the atmosphere.     

Nondimensionalization of the Atmospheric Boundary-Layer System: Obukhov Length and Monin–Obukhov Similarity Theory

Boundary-Layer Meteorology - The Obukhov length, although often adopted as a characteristic scale of the atmospheric boundary layer, has been introduced purely based on a dimensional argument...     

An Evaluation of the Flux–Gradient Relationship in the Stable Boundary Layer

Data collected during the SHEBA and CASES-99 field programs are employed to examine the flux–gradient relationship for wind speed and temperature in the stably stratified boundary layer. The gradient-based and flux-based similarity functions are assessed in terms of the Richardson number Ri and the stability parameter z/Λ_*, z being height and Λ_* the local Obukhov length. The resulting functions are expressed in an analytical form, which is essentially unaffected by self-correlation, when thermal stratification is strong. Turbulence within the stably stratified boundary layer is classified into four regimes: “nearly-neutral” (0 < z/Λ_* < 0.02), “weakly-stable” (0.02 < z/Λ_* < 0.6), “very-stable” (0.6 < z/Λ_* < 50), and “extremely-stable” (z/Λ_* > 50). The flux-based similarity functions for gradients are constant in “nearly-neutral” conditions. In the “very-stable” regime, the dimensionless gradients are exponential, and proportional to (z/Λ_*)^3/5. The existence of scaling laws in “extremely-stable” conditions is doubtful. The Prandtl number Pr decreases from 0.9 in nearly-neutral conditions and to about 0.7 in the very-stable regime. The necessary condition for the presence of steady-state turbulence is Ri < 0.7.     

Detection of Entrainment Influences on Surface-Layer Measurements and Extension of Monin–Obukhov Similarity Theory

We present a method to detect influences of boundary-layer processes on surface-layer measurements, using statistics and spectra of surface-layer variables only. We validated our detection method with boundary-layer measurements. Furthermore, we confirm that Monin–Obukhov similarity functions fit well to temperature-variance data obtained at two different homogeneous surfaces. However, we found that humidity variance measurements deviate from the universal functions above one of the two studied surfaces for days on which entrained air reached the surface layer. These results confirm that Monin–Obukhov similarity theory should be used with care in the analysis of surface-layer data. Finally, we propose the use of an extra term in flux-variance relations that depends on the entrainment ratio for humidity and on the boundary-layer height. If boundary-layer measurements are not available, we show how the entrainment ratio for humidity can be approximated from the skewness of the humidity distribution.     

A Cautionary Note on the Use of Monin–Obukhov Similarity Theory in Very High-Resolution Large-Eddy Simulations

In several recent large-eddy simulation studies, the lowest grid level was located well within the roughness sublayer. Monin–Obukhov similarity-based boundary conditions cannot be used under this scenario, and in this note we elaborate on this fundamental problem and suggest potential solutions.     

On Monin–Obukhov Scaling in and Above the Atmospheric Surface Layer: The Complexities of Elevated Scintillometer Measurements

In scintillometry Monin–Obukhov similarity theory (MOST) is used to calculate the surface sensible heat flux from the structure parameter of temperature (C_T²){(C_{T^2})} . In order to prevent saturation a scintillometer can be installed at an elevated level. However, in that case the observation level might be located outside the atmospheric surface layer (ASL) and thus the validity of MOST questioned. Therefore, we examine two concepts to determine the turbulent surface sensible heat flux from the structure parameter at elevated levels with data obtained at 60-m height on the Cabauw tower (the Netherlands). In the first concept (MOSTs) C_T²{C_{T^2}} is still scaled with the surface flux, whereas in the second (MOSTl) C_T²{C_{T^2}} is scaled with the local sensible heat flux. The C_T²{C_{T^2}} obtained from both concepts is compared with direct observations of C_T²{C_{T^2}} using a sonic anemometer/thermometer. In the afternoon (when the measurement height is located within the ASL) both concepts give results that are comparable to the directly observed values of C_T²{C_{T^2}} . In the morning (data outside the ASL), our data do not unequivocally support either of the two concepts. First, the peak in C_T²{C_{T^2}} that occurs when the measurement height is located in the entrainment zone disqualifies the use of MOST. Second, during the morning transition, local scaling shows the correct pattern (zero flux and a minimum in C_T²{C_{T^2}}) but underestimates C_T²{C_{T^2}} by a factor of ten. Third, from the best linear fit a we found that the slope of MOSTl gave better results, whereas the offset is closer to zero for MOSTs. Further, the correlation between the direct observations and MOST-scaled results is low and similar for the two concepts. In the end, we conclude that MOST is not applicable for the morning hours when the observation level is above the ASL.     

Discrepancy and Applicability of Various Similarity Functions in Flux Calculations Under Stable Conditions

Based on data obtained during the Hualhe River Basin Experiment （HUBEX） in 1999, this study intends to detect the quantitative discrepancies in the momentum （τ0）, sensible heat （H0） and latent heat （E0） fluxes among six sets of similarity functions with the aerodynamic method. It also aims to clarify the applicability of the functions under stable conditions. The relative discrepancy was studied with the normalized transfer coefficients for τ0, H0 and E0, namely CD, CH and CQ, respectively. Except for one set of functions that adopted a rather small von Kármán＇s constant （0.365）, the relative discrepancy in τ0 among the other functions was less than 10%, while that in H0（E0） sometimes reached 25% when the bulk Richardson number （R/B） was less than 0.07. The absolute discrepancy in the fluxes was studied with statistical computations. Among the six sets of functions, the discrepancy in τ0, H0 and E0 sometimes reached 0.03 kg m^-1 s^-2, 4 W m^-2 and 10 W m^-2, respectively, and the discrepancy in the energy balance ratio sometimes exceeded 0.1. Furthermore, when RiB exceeded the critical value （Ric） for a specific set of functions, no fluxes could be derived with the functions. It is therefore suggested that RiB be compared with Ric before computing the fluxes if RiB is less than Ric. Finally, two sets of nonlinear similarity functions are recommended, due to their unlimited applicability in terms of RiB.     

A Numerical Study of Second-Order Turbulent Moments in the Stably Stratified Nocturnal Boundary Layer

The structures and the vertical profiles of turbulent variance and covariance of the stably stratified boundary layer (SBL) are simulated with a second-order closure turbulence model. The results confirm that the vertical profiles of the dimensionless turbulence variance and covariance can be well represented by the form F = A(1 - Z / h)x. Here h is the height of SBL. and both exponent a and coefficient A are the functions of terrain, baroclinicity, radiation cooling and the state of temporal development of SBL. Comparing with Minnesota and Cabauw experiment data, we have analysed the value of a and expounded the main reasons that great difference in a exists among different literatures.     

An Analysis of the Turbulent Structure in the Unstable Surface Layer nearby a Shelter Belt

An analysis was performed of the turbulent data obtained from Yucheng experimental station in the Shandong Province in 1984. [t is shown that at variant wind speed, the spectra of streamwise velocity remain similar and the intensity of wind fluctuations is proportional to wind speed in the downwind area of shelter belt. Therefore, we may decide the similarity of wind fluctuations by a speed scale and a length scale which is not correlated with stability, σu /V0 = F(X / H). The -5/3 power range of temperature spectra extends to lower frequency. The variation of ratio σ0 /T. with stability becomes σ0 / T . = C(X / H)( - Z / L)-1/3 . There is not such an extension of -5 / 3 power range in the humidity spectra.     

A Method for Increasing the Turbulent Kinetic Energy in the Mellor–Yamada–Janjić Boundary-Layer Parametrization

A method for enhancing the calculation of turbulent kinetic energy in the Mellor–Yamada–Janjić planetary boundary-layer parametrization in the Weather Research and Forecasting numerical model is presented. This requires some unconventional selections for the closure constants and an additional stability dependent surface length scale. Single column model and three-dimensional model simulations are presented showing a similar performance with the existing boundary-layer parametrization, but with a more realistic magnitude of turbulence intensity closer to the surface with respect to observations. The intended application is an enhanced calculation of turbulence intensity for the purposes of a more accurate wind-energy forecast.     

Can Water Vapour Raman Lidar Resolve Profiles of Turbulent Variables in the Convective Boundary Layer?

High-resolution water vapour measurements made by the Atmospheric Radiation Measurement (ARM) Raman lidar operated at the Southern Great Plains Climate Research Facility site near Lamont, Oklahoma, U.S.A. are presented. Using a 2-h measurement period for the convective boundary layer (CBL) on 13 September 2005, with temporal and spatial resolutions of 10 s and 75 m, respectively, spectral and autocovariance analyses of water vapour mixing ratio time series are performed. It is demonstrated that the major part of the inertial subrange was detected and that the integral scale was significantly larger than the time resolution. Consequently, the major part of the turbulent fluctuations was resolved. Different methods to retrieve noise error profiles yield consistent results and compare well with noise profiles estimated using Poisson statistics of the Raman lidar signals. Integral scale, mixing-ratio variance, skewness, and kurtosis profiles were determined including error bars with respect to statistical and sampling errors. The integral scale ranges between 70 and 130 s at the top of the CBL. Within the CBL, up to the third order, noise errors are significantly smaller than sampling errors and the absolute values of turbulent variables, respectively. The mixing-ratio variance profile rises monotonically from ≈0.07 to ≈3.7 g² kg⁻² in the entrainment zone. The skewness is nearly zero up to 0.6 z/z _i , becomes −1 around 0.7–0.8 z/z _i , crosses zero at about 0.95 z/z _i , and reaches about 1.7 at 1.1 z/z _i (here, z is the height and z _i is the CBL depth). The noise errors are too large to derive fourth-order moments with sufficient accuracy. Consequently, to the best of our knowledge, the ARM Raman lidar is the first water vapour Raman lidar with demonstrated capability to retrieve profiles of turbulent variables up to the third order during daytime throughout the atmospheric CBL.     

Summary of the Lövånger International Workshop on Turbulence and Diffusion in the Stable Planetary Boundary Layer

A workshop on the stable planetary boundary layer (PBL) was held on 21–24 October, 1997 at Lövånger, a small town about 80 km north of Umeå, Sweden. Thirty-five scientists representing eight countries participated in the meeting, which was arranged by the U.S. Army Research Office, the Swedish Defence Research Establishment, the U.S. National Oceanic and Atmospheric Administration's Air Resources Laboratory, and the Meteorology Department of Uppsala University. Topics addressed included the very stable boundary layer, gravity wave/turbulence interactions, modeling the stable boundary layer, future observations and new measurement techniques, the role of condensation (fog) and radiative flux divergence, and atmospheric diffusion. Invited papers appear in this special issue. Workshop discussions, informal presentations, and specific recommendations are summarized. Workshop participants and organizers are presented in Appendix A.     

Diurnal Variations of Air Pollution and Atmospheric Boundary Layer Structure in Beijing During Winter 2000／2001

The diurnal variations of gaseous pollutants and the dynamical and thermodynamic structures of the atmospheric boundary layer (ABE) in the Beijing area from January to March 2001 are analyzed in this study using data from the Beijing City Air Pollution Observation Field Experiment (BECAPEX). A heavy pollution day (22 February) and a good air quality day (24 February) are selected and individually analyzed and compared to reveal the relationships between gaseous pollutants and the diurnal variations of the ABL. The results show that gaseous pollutant concentrations exhibit a double-peak-double-valley-type diurnal variation and have similar trends but with different magnitudes at different sites in Beijing. The diurnal variation of the gaseous pollutant concentrations is closely related to (with a 1-2 hour delay of) changes in the atmospheric stability and the mean kinetic energy in the ABL.     

Air–Sea Interaction in the Southern Ocean: Exploring the Height of the Wave Boundary Layer at the Air–Sea Interface

We investigate the momentum and energy exchange across the wave boundary layer (WBL). Directly at the air–sea interface, we test three wave-growth parametrizations by comparing estimates of the wave-induced momentum flux derived from wave spectra with direct covariance estimates of the momentum flux. An exponential decay is used to describe the vertical structure of the wave-induced momentum in the atmospheric WBL through use of a decay rate, a function of the dimensionless decay rate and wavenumber (A?=?α k). The decay rate is varied to minimize the difference between the energy extracted from the WBL and the energy flux computed from wave spectra using our preferred wave-growth parametrization. For wave ages (i.e. the peak phase speed to atmospheric friction velocity ratio) in the range \( 15 < c_{p}/u_{*} < 35 \) we are able to balance these two estimates to within 10%. The decay rate is used to approximate the WBL height as the height to which the wave-induced flux is 0.1 of its surface value and the WBL height determined this way is found to be between 1–3 m. Finally, we define an effective phase speed with which to parametrize the energy flux for comparison with earlier work, which we ultimately attempt to parametrize as a function of wind forcing.     

On the Seasonal Transition and the Interannual Variability in Global Kinetic Energy at 500 hPa, Accompanied withAnomalies of Energy during the 1982 / 83 ENSO

Utilizing the material of monthly means of the three primary kinetic energy modes over the whote globe at 500 hPa during the nine years of 1980-1988, both the rapid seasonal changes and the interannual variability in tie general circulation in terms of the energy modes have been investigated, with special attention paid to the unusual year 1983, Two main results are obtained. One, there are remarkable seasonal rapid changes over the Northern Hemisphere, occurring ganerally in April and October. The other, among the nine years of 1980-1988, 1983 is the only one with unusual energy modes and remarkably abnormal seasonal changes.