Monin-Obukhov Similarity Functions Research Articles

Symmetry Analysis of Mean Velocity Distribution in Stratified Atmospheric Surface Layers

The mean velocity distributions of unstably and stably stratified atmospheric surface layers (ASLs) are investigated here using the symmetry approach. Symmetry groups for the mean momentum and the Reynolds stress equations of ASL are searched under random dilation transformations, which, with different leading order balances in different flow regions, lead to a set of specific scalings for the characteristic length ℓ13 (defined by Reynolds shear stress and mean shear). In particular, symmetry analysis shows that in the shear-dominated region, ℓ13 scales linearly with the surface height z, which corresponds to the classical log law of mean velocity. In the buoyancy-dominated region, ℓ13/L∼z/L4/3 for unstably stratified ASL and ℓ13/L∼const for stably stratified ASL, where L is the Obukhov length. The specific formula of the celebrated Monin–Obukhov similarity function is obtained, and hence an algebraic model of mean velocity profiles in ASL is derived, showing good agreement with the datum from the QingTu Lake observation array (QLOA) in China.

Variable antennas positions solution to reduce pointing errors due to wind speed and temperature coupled effects during free space optical link using matrix Rician pointing error model

Pointing errors (PE) during free space optical (FSO) transmission can be caused by laser beam wander due to thermal and wind dynamic instability. The aim of this work is to study the coupled effects of temperature and wind speed on PE using matrix Rician pointing error (MRPE) model; then show how variable antennas height can reduce PE due to wind speed and temperature coupled effects. To achieve this purposes, average PE expression was established using MRPE model. Then considering a Gaussian beam wave and Monin–Obukhov similarity functions for the structure parameters of temperature, explicit relationship was established between average PE, temperature and wind speed. It comes out of this study that under dynamic turbulence, one can appropriately modify temperature to reduce PE due to dynamic instability and reciprocally. Depending on turbulence large cells or frozen turbulence eddies distribution, PE can be reduced by appropriately modified antennas height or the distance between transmitter and receiver. That is why this work suggests to install variable or dynamic antennas (rather than fixed ones) which could intelligently modify its positions according to laser beam wander created by atmospheric turbulence.

Refinements and Analysis of the Optical-Microwave Scintillometry Method Applied to Measurements over a Vineyard in Chile

Evapotranspiration (ET) is a critical component of the hydrological cycle, and it links water and energy budgets in the form of latent heat (LvE) released into the atmosphere. However, ET is difficult to measure and is not always well described in arid regions. Thus, novel techniques are required for its accurate measurement. Scintillometers are an interesting alternative for traditional methods, such as Eddy Covariance systems (EC). Scintillometer studies have reported good results, but their signals can present unwanted contributions that result in incorrect heat fluxes. In this study, scintillometer data showed unrealistic heat flux values, and thus, the data were reprocessed through spectral analysis to eliminate unwanted contributions from electronic noise, absorption, and tripod vibrations using a new proposed data cleaning method. After performing the spectral cleaning method, scintillometer-based heat fluxes were calculated using several methods: (i) the standalone LAS method, (ii) Hill model, (iii) Lüdi et al. model, and (iv) a hybrid model between Hill and Lüdi et al. Furthermore, a Monin–Obukhov similarity theory (MOST) analysis was performed to evaluate the fluxes’ sensitivity to the choice of the similarity functions. Corrected sensible heat flux (H) estimations agreed well with those obtained with an EC system. However, considerable differences were found for LvE (and, consequently, ET). The Lüdi et al. model LvE estimates were closer to those obtained with the EC system, overestimating it by 14%, with a correlation slope of 1.07, R2 = 0.91, and a Nash-Sutcliffe efficiency of 0.90. Furthermore, it was found that using different Monin–Obukhov similarity functions resulted in more than ±12% of difference on the estimated LvE. For future works, it is strongly recommended to apply the proposed spectral cleaning method as it greatly improves scintillometer data.

Analytic derivation of Monin-Obukhov similarity function for open atmospheric surface layer

The Monin-Obukhov (MO) similarity function φm of the atmospheric surface layer (ASL) describing the deviation from the log law of the canonical turbulent boundary layer because of thermal stratification has been traditionally determined empirically. This study presents a unified analytic expression derived from a symmetry-based theory of wall turbulence, called structural ensemble dynamics (SED), which postulates a generalized dilation symmetry principle expressing the effect of the wall on turbulence, leading to an analytic multi-regimes expression for the mixing length. For ASL in unstable and stable conditions (i.e., UC and SC), a unified two-regime formula of the mixing length is proposed, leading to a φm, similar to the Businger-Dyer (BD) formula; with a simplified model energy balance equation, φm is completely specified with no free parameter. Furthermore, the theory allows the study of the open ASL’s underlying additional physical processes such as bottom-up or top-down flux due to pressure variations Tp. Assuming that Tp is decomposed into shear-like and buoyancy-like components, we propose new explanations for two important features of typical ASL: a significantly smaller Karman constant of 0.36 and a varying φm for SC mean speed profiles. The theory is validated by the data obtained at Kansas and also at Qingtu Lake Observation Array in Northern China for a variety of heat flux conditions. In conclusion, due to pressure variations, we assert that ASL is intrinsically open and that the current theory offers a new basis for its quantification.

On the Formulation and Universality of Monin–Obukhov Similarity Functions for Mean Gradients and Standard Deviations in the Unstable Surface Layer: Results from Surface-Layer-Resolving Large-Eddy Simulations

Abstract Surface-layer-resolving large-eddy simulations (LESs) of free-convective to near-neutral boundary layers are used to study Monin–Obukhov similarity theory (MOST) functions. The LES dataset, previously used for the analysis of MOST relationships for structure parameters, is extended for the mean vertical gradients and standard deviations of potential temperature, specific humidity, and wind. Also, local-free-convection (LFC) similarity is studied. The LES data suggest that the MOST functions for mean gradients are universal and unique. The data for the mean gradient of the horizontal wind display significant scatter, while the gradients of temperature and humidity vary considerably less. The LES results suggest that this scatter is mostly related to a transition from MOST to LFC scaling when approaching free-convective conditions and that it is associated with a change of the slope of the similarity functions toward the expected value from LFC scaling. Overall, the data show slightly, but consistent, steeper slopes of the similarity functions than suggested in literature. The MOST functions for standard deviations appear to be unique and universal when the entrainment from the free atmosphere into the boundary layer is sufficiently small. If entrainment becomes significant, however, we find that the standard deviation of humidity no longer follows MOST. Under free-convective conditions, the similarity functions should reduce to universal constants (LFC scaling). This is supported by the LES data, showing only little scatter, but displaying a systematic height dependence of these constants. Like for MOST, the LFC similarity constant for the standard deviation of specific humidity becomes nonuniversal when the entrainment of dry air reaches significant levels.

Quantifying the parameters that control turbulent land–atmosphere energy exchange over the Dunhuang Gobi land surface, northwest China

Land–atmosphere interactions in the northwest arid and semi-arid areas of China are important because of their influence on energy exchange at both regional and global scales. In this paper, regular meteorological observations, as well as flux eddy covariance methods, are used to measure land–atmosphere energy exchange. Experiments were conducted over the Dunhuang Gobi, a typical arid region of northwest China, during the summer of 2008. Surface fluxes were measured directly using an eddy-correlation system, while the vertical gradients of wind and temperature were also observed at four levels using a meteorological tower. Based on the observation data, the integral mean of surface albedo over the Gobi was found to be 0.238. In addition, the mean values of momentum, heat roughness lengths, and soil thermal conductivity were, 0.045, 0.005 cm, 0.199 and 0.201 W (m K)−1, respectively. The Monin–Obukhov similarity functions for momentum and heat were analyzed and new empirical formulae were developed.

Methodical assessment of the differences between the QNSE and MYJ PBL schemes for stable conditions

The increasing number of physics parametrization schemes adopted in numerical weather forecasting models has resulted in a proliferation of intercomparison studies in recent years. Many of these studies concentrated on determining which parametrization yields results closest to observations rather than analyzing the reasons underlying the differences. In this work, we study the performance of two 1.5‐order boundary layer parameterizations, the quasi‐normal scale elimination (QNSE) and Mellor–Yamada–Janjić (MYJ) schemes, in the weather research and forecasting model. Our objectives are to isolate the effect of stability functions on the near‐surface values and vertical profiles of virtual temperature, mixing ratio and wind speed. The results demonstrate that the QNSE stability functions yield better error statistics for 2 m virtual temperature but higher up the errors related to QNSE are slightly larger for virtual temperature and mixing ratio. A surprising finding is the sensitivity of the model results to the choice of the turbulent Prandtl number for neutral stratification (Prt0): in the Monin–Obukhov similarity function for heat, the choice of Prt0 is sometimes more important than the functional form of the similarity function itself. There is a stability‐related dependence to this sensitivity: with increasing near‐surface stability, the relative importance of the functional form increases. In near‐neutral conditions, QNSE exhibits too strong vertical mixing attributed to the applied turbulent kinetic energy subroutine and the stability functions, including the effect of Prt0.

Similarity Relations for $$C_{T}^2 $$ C T 2 in the Unstable Atmospheric Surface Layer: Dependence on Regression Approach, Observation Height and Stability Range

A great variety of similarity functions for the structure parameter of temperature ( $$C_{T}^2$$ ) have been proposed in the literature. They differ in the way they were derived from the data and in the characteristics of the dataset used for their derivation (surface type, observation level, stability range). In this study, we use one single dataset (CASES-99 experiment) and investigate the impact on the similarity functions of applying various regression approaches, and measuring at different heights and within different stability ranges. We limit ourselves to similarity functions under unstable conditions, and evaluate only the most common shape that describes the relation with two coefficients ( $$f\left( z/L\right) =c_{1} \left( 1-c_{2} {z}/{L}\right) ^{-2/3}$$ , where $$z$$ is the height, and $$L$$ is the Obukhov length and a measure of the stability, and $$c_{1}$$ and $$c_{2}$$ are the regression coefficients). The results show that applying various regression approaches has an impact on the regression coefficients $$c_{1}$$ and $$c_{2}$$ . Thus studies should always specify the regression approach when presenting similarity relations. We suggest use of an orthogonal distance regression method such that uncertainties in $$-z/L$$ are also taken into account, to apply this to the logarithmic transformation of both dimensionless groups, and to use a weighted dataset such that unreliable data points have a smaller influence on the fit. Dividing the dataset into eight height ( $$z$$ ) and eight stability ( $$-{1/L}$$ classes) classes, we show that the observation height and the stability range has an impact on the coefficients too. This implies that variations in $$c_{1}$$ and $$c_{2}$$ found in the literature may result from variations in the height and stability ranges among the datasets. Furthermore, application of the coefficients on a dataset obtained at a different height or within a different stability range has to be made with care. Finally, the variation in the coefficients between the classes indicates that the Monin–Obukhov similarity function for $$C_{T}^2$$ is not sufficiently described by the two-coefficient function used here.

Monin–Obukhov Similarity Functions for the Structure Parameters of Temperature and Humidity in the Unstable Surface Layer: Results from High-Resolution Large-Eddy Simulations

Abstract Large-eddy simulations (LESs) of free-convective to near-neutral boundary layers are used to investigate the surface-layer turbulence. The article focuses on the Monin–Obukhov similarity theory (MOST) relationships that relate the structure parameters of temperature and humidity to the surface fluxes of sensible and latent heat, respectively. Moreover, the applicability of local free convection (LFC) similarity scaling is studied. The LES data suggest that the MOST function for is universal. It is shown to be within the range of the functions proposed from measurement data. It is found that follows MOST if entrainment of dry air from the free atmosphere is sufficiently small. In this case the similarity functions for and are identical. If entrainment is significant, dissimilarity between the transport of sensible heat and moisture is observed and no longer follows MOST. In the free-convection limit the LFC similarity functions should collapse to universal constants. The LES data suggest values around 2.7, which is in agreement with the value proposed in the literature. As for MOST, the LFC similarity constant for becomes nonuniversal if entrainment of dry air is significant. It is shown that LFC scaling is applicable even if shear production of turbulence is moderately high.

A mathematical and physical model study on the 20 cm pan evaporation

Based on the energy conservation principle and the boundary layer gradient transport theory, this paper built a single layer 20 cm evaporation pan model. In this model, both sensible and latent heat fluxes of the evaporation pan were calculated by Monin-Obukhov similarity function. Meanwhile, the heat transport of the lateral wall was parameterized. Following that, the model was verified by the continuous 14-day hourly measurements from the Gulang Heterogeneous Underlying Surface Layer Experiment. Analysis results showed that the model could reflect the non-uniformity between water surface and land surface. In addition, the results indicated that day performance of the model was good with a root-mean-square error (RMSE) of 0.44(mm.d(-1)), a mean relative error ratio (MRER) of 3.7% and a correlation coefficient of 0.998.

Bulk transfer coefficients of momentum and sensible heat over semiarid grassland surface and their parameterization scheme

The momentum and heat transfer coefficients used in the atmospheric numerical models usually are taken as constants. In fact, the bulk transfer coefficients change not only with atmospheric stabilities, but also with the air motion and thermodynamic properties of the surface boundary layer. In this paper, the bulk transfer coefficients of momentum and sensible heat are determined by using the data observed by the eddy correlation system and those of the average wind velocity and temperature gradients over the Xilin Guole semiarid grassland in May, 2008. The relations between the bulk transfer coefficients and the gradients in Richardson numbers are analyzed, and the relationship between the bulk transfer coefficients and atmospheric stabilities is also studied. Finally, the changes of momentum bulk transfer coefficients with wind speed and the relations between sensible heat transfer coefficients and temperature are determined. Comparison with the eddy correlation method for observing transfer coefficients, there is a great difference between the computational values of typical Businger-Dyer similarity functions. The revised Monin-Obukhov similarity functions could significantly improve the accuracy of the transfer coefficients. Under the near neutral stratification, there was an obvious interaction between the land surface and the flow condition over semiarid regions. The momentum bulk transfer coefficient varies with the mean wind speed at 10 m according to the quadratic curve laws. Under the low wind velocity condition, the influence of the air flow on the roughness was not significant and the momentum transfer coefficient will increase with increasing wind velocity. While at the high wind speed, the momentum transfer coefficient will decrease with increasing wind velocity, for the air flow changes the roughness height of surface boundary layer. Under the near neutral stratification, there was a quadratic curve law between the temperature and the sensible heat transfer coefficient, which provides a useful parameterization scheme for sensible heat transfer coefficient. The new schemes could parameterize the turbulent fluxes with average wind velocity and temperature gradients data, and does not need to compute the roughness.

The characteristics of turbulent momentum and heat similarity function and bulk transfer coefficient over grassland surface

The turbulent momentum and sensible heat transfer over land surface have a notable influence on the change of global climate and atmospheric circulation, and Monin-Obukhov similarity function is a most important method to calculate the turbulent momentum and sensible heat flux near the surface, and ascertaining the right bulk transfer coefficient is a most effective way of improving the atmospheric model simulation capabilities. The characteristic of Monin-Obukhov similarity function is analyzed and the empirical formula is fitted, and the changes of bulk transfer coefficients of momentum and sensible heat over grassland with mean wind speed at 10 m high are discussed by using the data of the flux observations over Xilin Gol grassland in Spring 2008. Comparison with the observation values by eddy correlation method shows that the revised Monin-Obukhov similarity function underestimates the momentum flux by 10.8% and over estimates the sensible heat flux by 6.5%, but the typical Businger-Dyer similarity function underestimates the momentum flux by 37.0% and over estimates the sensible heat flux by 16.1%. Under unstable stratification, the bulk transfer coefficients of momentum (CD) and sensible heat (CH) vary with mean wind speed at 10 m high (U) according to the power law, which take the forms CD=0.009U-0.322 and CH=0.184U-1.978 respectively. Under stable stratification, the bulk transfer coefficients are found to increase in the manner of the logarithm law over grassland surface and tend to neutral or nearly neutral values with wind speed increasing. The revised Monin-Obukhov similarity function can significantly improve the accuracy of turbulent momentum and sensible heat flux computed by average gradient data, and the relations between bulk transfer coefficients and wind speed at 10 m high provide the useful parameterization schemes for accurately expressing the transportation characteristics of near surface turbulence.

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.

A Study of the Stable Boundary Layer Based on a Single-Column K-Theory Model

We document numerical experiments with a single-column, high-resolution model of the stable boundary layer. The model resolves the logarithmic layer, and does not require inverting the Monin–Obukhov similarity functions in order to calculate the surface fluxes. The turbulence closure is based on the K-theory approach, with a new form of stability functions of the Richardson number, evaluated by using the Surface Heat Budget of the Arctic Ocean (SHEBA) and the Cooperative Atmosphere-Surface Exchange Study (CASES-99) data. A comparison with two, high-resolution large-eddy simulation models shows very good agreement. The reported numerical experiments test the effects of shear, surface cooling, the Coriolis parameter, subsidence, and baroclinicity. The time evolution of the drag coefficient, the heat-transfer coefficient, and the cross-isobar angle is also evaluated.

Reply to the Comments by J. C. Bergmann on the Paper: “Local Similarity in the Stable Boundary Layer and Mixing Length Approaches: Consistency of Concepts”

In his comment J. C. Bergmann discusses the analysis of Van de Wiel et al. (2008; VDW08), acknowledges the conceptual merits of the work related to the introduced “apparent wall concept”, but identifies a factor of two error in the potential energy calculation. As a consequence (see Bergmann 2011; B11), the derived value (equal to 6.25) of the numerical constant (slope) in the Monin–Obukhov similarity function, respectively in its local-scaling equivalent (Nieuwstadt 1984), is reduced to half its value. The present authors fully agree with this re-analysis by B11, but wish to emphasise that the “apparent wall concept” is used to anticipate a plausible order of magnitude of the abovementioned constant, rather than predicting an exact value. In the following, we briefly reanalyse the comment of B11. Consider a linear density profile (the very stable limit considered in VDW08). On average, parcels at a reference level z′ = 0 with density ρ0 will reach their ‘maximum’ displacement zB when all their vertical kinetic energy is converted into potential energy (see Fig. 1). B11 refers to zB “as the root-mean-square displacement”. Thus we can find this length scale by computing the maximum work (in the mean sense: B11) that can be done by parcels, given their mean initial vertical kinetic energy (1/2)ρσ 2 w (per volume):

Monin–Obukhov Similarity Functions of the Structure Parameter of Temperature and Turbulent Kinetic Energy Dissipation Rate in the Stable Boundary Layer

The Monin–Obukhov similarity theory (MOST) functions fe and f T , of the dissipation rate of turbulent kinetic energy (TKE). e, and the structure parameter of temperature, C 2 , were determined for the stable atmospheric surface layer using data gathered in the context of CASES-99. These data cover a relatively wide stability range, i.e. ζ=z/L of up to 10, where z is the height and L the Obukhov length. The best fits were given by fe = 0.8 + 2.5ζ and f T = 4.7[ 1+1.6(ζ)2/3], which differ somewhat from previously published functions. e was obtained from spectra of the longitudinal wind velocity using a time series model (ARMA) method instead of the traditional Fourier transform. The neutral limit fe =0.8 implies that there is an imbalance between TKE production and dissipation in the simplified TKE budget equation. Similarly, we found a production-dissipation imbalance for the temperature fluctuation budget equation. Correcting for the production-dissipation imbalance, the ‘standard’ MOST functions for dimensionless wind speed and temperature gradients (φ m and φ m ) were determined from fe and f T and compared with the φ m and φ h formulations of Businger and others. We found good agreement with the Beljaars and Holtslag [J. Appl. Meteorol. 30, 327–341 (1991)] relations. Lastly, the flux and gradient Richardson numbers are discussed also in terms of fe and f T .

Turbulence flux measurement above the overstory of a subtropical Pinus plantation over the hilly region in southeastern China

Continuous turbulence flux measurement using the eddy covariance (EC) technique was made from January 1 to December 31 in 2003 at two and three canopy heights of a subtropical Pinus plantation on the red earth hilly region in southeastern China. To be able to make sure that the measured turbulence flux will equal the net ecosystem/atmosphere exchange, the quality of the data has to be assessed. Three criteria were investigated here, including the power spectra and cospectra analyses, flux variance similarity (integral turbulence test) and energy balance closure. The spectral analyses suggested that above-canopy power spectral slopes for all velocity components and scalars such as CO2, H2O and air temperature followed the expected -2/3 power law in the inertial subrange, and their cospectral slopes were close to -4/3 power law in the inertial subrange. The important contribution of large-scale motions to energy and mass transfer above the canopy at higher measurement level was also confirmed by the spectral analyses. The eddy covariance systems have the ability to resolve fluctuations associated with small-scale eddies and did not induce an obvious underestimation of the measured turbulence flux. The Monin-Obukhov similarity functions for the normalized standard deviation of vertical wind speed and air temperature were well-defined functions of atmospheric stability at two heights above the forest canopy, which indicated that turbulence flux measurements made at two heights were within the surface layer. Nocturnal flux underestimation and departures of this normalized standard deviation of vertical wind speed similarity function from that expected from Monin-Obukhov theory were a function of friction velocity. Thus, an optimal criterion of friction velocity was determined to be greater than 0.2-0.3 m s-1 for nocturnal fluxes so that the eddy covariance flux measurement was under high turbulent mixing conditions. Energy balance closure reached about 72%-81% at the studied site, which was comparable to the 10%-30% of energy imbalance reported in the literature. However, the energy balance closure could be only used as a useful reference criterion.

A Parameterization Scheme of Surface Turbulent Momentum and Sensible Heat over the Gobi Underlying Surface

The parameterization of surface turbulent fluxes over the Gobi Desert in arid regions is studied by using rationally screened observational data. First, the characteristics of Monin-Obukhov similarity functions are analyzed and their empirical formulae are fitted. The results show that fitted curves of changes of similarity functions of wind speed and temperature with stability parameter differ little from the typical empirical curves and are within the ranges of scatter of the empirical curves, but their values in the neutral condition arc different from the typical values to some extent. Furthermore, average values of momentum and scalar (sensible heat) roughness lengths as well as changes of scalar roughness length with friction velocity are determined by utilizing the data. It is found that the average values of scalar roughness length are about one order smaller than that of the momentum roughness length and decrease with increasing friction velocity, but they are evidently larger than their theoretically forecasted values.

Large-Eddy Simulations of the Atmospheric Boundary Layer Using a New Subgrid-Scale Model – II. Weakly and moderately stable cases

A series of simulations under weakly to moderately stable boundary layers (SBLs) have been performed using the proposed subgrid-scale (SGS) model implemented into the Terminal Area Simulation System (TASS). The proposed SGS model incorporates some aspects of the two-part eddy viscosity SGS model of Sullivan et al. (1994) and further refinements which include the dependence of SGS mixing length on stratification, two-part separation of the SGS eddy diffusivity of heat, and more realistic empirical forms of Monin–Obukhov similarity functions. The potential temperature profiles from simulations clearly show a three-layer structure: a stable surface layer of strong gradients, a middle layer of small gradients, and an inversion layer on the top. The wind speed profiles show the formation of low level jet (LLJ). However, the sub-layer structures under moderately SBLs differ from those under weakly SBLs. Both the momentum and heat fluxes decrease almost linearly in the lower part of the SBL. The near surface values of the normalized turbulent kinetic energy (TKE/u*2) in all simulations are about 4 which is much less than the typical value of 5.5 under the neutral condition. The decay of turbulence first occurs in the area with large values of Richardson number (Ri<0.2). Generally, instantaneous values of the TKE and Ri at the various grid points are negatively correlated, but there is not a unique relationship between the two parameters.

Estimation of Scalar Source/Sink Distributions in Plant Canopies Using Lagrangian Dispersion Analysis: Corrections for Atmospheric Stability and Comparison with a Multilayer Canopy Model

Source/sink distributions of heat, water vapour and CO 2 within a rice canopy were inferred using an inverse Lagrangian dispersion analysis and measured mean profiles of temperature, specific humidity and CO 2 mixing ratio. Monin-Obukhov similarity theory was used to account for the effects of atmospheric stability on σ w (z). the standard deviation of vertical velocity and τ L (z), the Lagrangian time scale of the turbulence. Classical surface layer scaling was applied in the inertial sublayer (z > z ruf ) using the similarity parameter ζ = (z - d)/L, where z is height above ground, d is the zero plane displacement height for momentum, L is the Obukhov length, and z ruf 2.3h c , where h c is canopy height. A single length scale h c , was used for the stability parameter 3 = h c /L in the height range 0.25 < z/ h c < 2.5. This choice is justified by mixing layer theory, which shows that within the roughness sublayer there is one dominant turbulence length scale determined by the degree of inflection in the wind profile at the canopy top. In the absence of theoretical or experimental evidence for guidance, standard Monin-Obukhov similarity functions, with ζ = h c /L, were used to calculate the stability dependence of σ w (z) and τ L (z) in the roughness sublayer. For z/h c < 0.25 the turbulence length and time scales are influenced by the presence of the lower surface, and stability effects are minimal. With these assumptions there was excellent agreement between eddy covariance flux measurements and deductions from the inverse Lagrangian analysis. Stability corrections were particularly necessary for night time fluxes when the atmosphere was stably stratified. The inverse Lagrangian analysis provides a useful tool for testing and refining multilayer canopy models used to predict radiation absorption, energy partitioning and CO 2 exchanges within the canopy and at the soil surface. Comparison of model predictions with source strengths deduced from the inverse analysis gave good results. Observed discrepancies may be due to incorrect specification of the turbulent time scales and vertical velocity fluctuations close to the ground. Further investigation of turbulence characteristics within plant canopies is required to resolve these issues.