Flux-variance Method Research Articles

Estimation of Sensible and Latent Heat Fluxes Using Flux Variance Method under Unstable Conditions: A Case Study of Tea Plants

Evapotranspiration is essential for precise irrigation and water resource management. Previous literature suggested that eddy covariance (EC) systems could directly measure evapotranspiration in agricultural fields. However, the eddy covariance method remains difficult for routine use, due to its high cost, operational complexity, and relatively multifaceted raw data processing. An alternative method is the flux variance (FV) method, which can estimate the sensible heat flux using high-frequency air temperature measurements by fine-wire thermocouples, at relatively low-cost and with less complexity. Additional measurements of the net radiation and soil heat flux permit the extraction of latent heat flux through the energy balance closure equation. This study examined the performance of the FV method and the results were compared against direct eddy covariance measurements. Data were collected from November 2018 to July 2019, covering seasonal variations. Due to the method’s limitation, only the data under unstable conditions were used for the analysis and days with rainfall were omitted. The results showed that the FV-estimated sensible heat flux was in good agreement with that of eddy covariance in the seasons of winter 2018 and summer 2019. The best agreement between the estimated and measured sensible heat fluxes was observed in the summer, with R2 = 0.83, RMSE = 34.97 Wm−2 and RE = 8.20%. The FV extracted latent heat flux was in good agreement with that measured by EC for both seasons. The best result was obtained in the summer, with R2 = 0.92, RMSE = 23.12 Wm−2, and RE = 6.37%. Overall estimations of sensible and latent heat fluxes by the FV method were in close relation with the eddy covariance data.

Physical mechanism of vertical gradient of pressure flux and its impact on turbulent flux estimation

• Flux-variance method is an effective way to indirectly obtain pressure flux. • Pressure flux convergence/divergence is partially related to larger-scale eddies. • Ejection and sweep events lead to opposite vertical gradient of pressure flux. • There's a quadratic relation between pressure flux gradient and friction velocity. • Taking pressure transport into account refines estimation of turbulent flux in CBL. Using multi-layer pressure fluctuations and other conventional turbulence observational data over a nearly flat and homogeneous dune underlying surface, the temporal and spatial characteristics of pressure flux and its profile were analyzed to illustrate the physical mechanism of pressure flux convergence/divergence and the impact of pressure transport terms on the estimation of turbulent fluxes in this study. The flux-variance (FV) method is an effective approach to indirectly obtain pressure flux through momentum flux when no fast-response observations of pressure fluctuations are available. The fitted functions are w ′ p ′ ¯ = 0.16 · ( − F Z ( z ) · u ′ w ′ ¯ σ p σ u ) and u ′ p ′ ¯ = 0.55 · ( F X ( z ) · u ′ w ′ ¯ σ p σ w ) , where F Z ( z ) and F X ( z ) are the height normalized functions for vertical and horizontal directions. Under the circumstance of pressure flux divergence (FD), the transport efficiency of pressure and contribution of larger-scale eddies to pressure flux at higher levels are greater than those at lower levels, and flows in the atmospheric surface layer (ASL) are mainly dominated by the sweep events; while the pressure flux convergence (FC) cases are exactly the opposite situations. A good quadratic function relationship was found between the vertical gradient of pressure flux and friction velocity under different atmospheric stabilities: ∂ w ′ p ′ ¯ ∂ z = 0.01 u * ( 16 u * − 1 ) . Turbulence kinetic energy (TKE) and its vertical transport are greater in the FD cases than those in the FC cases. The momentum and sensible heat fluxes in the convective boundary layer (CBL) were overestimated by their common second-order diagnostic equations and Rotta model (pressure redistribution term parameterization) which neglect the diffusion terms. After adding the contribution of pressure transport terms into the diagnostic equations and Rotta model and modifying the original Rotta constants, the overestimations were well corrected and the estimated turbulent fluxes were more consistent with the observations. This work provides a novel direction and idea for the future improvement of the planetary boundary layer (PBL) parameterization schemes in many numerical weather and climate models.

Fetch Effect on Flux-Variance Estimations of Sensible and Latent Heat Fluxes of Camellia Sinensis

Precise estimation of surface-atmosphere exchange is a major challenge in micrometeorology. Previous literature presented the eddy covariance (EC) as the most reliable method for the measurements of such fluxes. Nevertheless, the EC technique is quite expensive and complex, hence other simpler methods are sought. One of these methods is Flux-Variance (FV). The FV method estimates sensible heat flux (H) using high frequency (~10Hz) air temperature measurements by a fine wire thermocouple. Additional measurements of net radiation (Rn) and soil heat flux (G) allow the derivation of latent heat flux (LE) as the residual of the energy balance equation. In this study, the Flux Variance method was investigated, and the results were compared against eddy covariance measurements. The specific goal of the present study was to assess the performance of the FV method for the estimation of surface fluxes along a variable fetch. Experiment was carried out in a tea garden; an EC system measured latent and sensible heat fluxes and five fine-wire thermocouples were installed towards the wind dominant direction at different distances (fetch) of TC1 = 170 m, TC2 = 165 m, TC3 = 160 m, TC4 = 155 m and TC5 = 150 m from the field edge. Footprint analysis was employed to examine the effect of temperature measurement position on the ratio between 90% footprint and measurement height. Results showed a good agreement between FV and EC measurements of sensible heat flux, with all regression coefficients (R2) larger than 0.6; the sensor at 170 m (TC1), nearest to the EC system, had highest R2 = 0.86 and lowest root mean square error (RMSE = 25 Wm−2). The estimation of LE at TC1 was also in best agreement with eddy covariance, with the highest R2 = 0.90. The FV similarity constant varied along the fetch within the range 2.2–2.4.

Measuring H2O and CO2 fluxes at field scales with scintillometry: Part II – Validation and application of 1-min flux estimates

This paper evaluates four methods to obtain accurate averaged flux estimates under conditions of non-stationary turbulence. In Part I (Van Kesteren et al., 2012), we introduced and evaluated these four combined methods for 30-min averaging intervals, notably the flux-variance method, the Bowen-variance method, the structure-parameter method, and the energy-balance method. The aim of this paper, Part II, is to validate the accuracy of the 1-min flux estimates of the CO2 flux, FCO2, and the evapotranspiration/latent-heat flux, LvE. Furthermore, we use the 1-min fluxes to investigate flux and vegetation responses under conditions of non-stationary turbulence. Using several validation methods, we show that both the eddy-covariance method and the energy-balance method are unsuitable for estimating fluxes over 1-min averaging intervals. The three other combined methods are more successful in determining 1-min fluxes. The random error is approximately half that of the eddy-covariance method, but still some issues limit the success. The Bowen-variance method has a +0.09 systematic error and moreover, 30% of the data had to be omitted, because the method requires more stringent conditions. Furthermore, the flux-variance method has a −0.15 systematic error. The structure-parameter method performs best of all methods and accurately resolves 1-min fluxes. With this method, we do a final validation with a different data set and show that also under dry conditions the method accurately resolves FCO2, although LvE was more difficult to resolve. In the last part, the structure-parameter method is successfully applied under conditions of non-stationary turbulence. We show that LvE and FCO2 have a different step response upon abrupt changes in solar radiation, because different processes drive these fluxes. Also, we observe a 2-min time lag between solar radiation and 1-min fluxes and show the relevance of taking this into account for determining light–response curves of the plants for both 1-min and 30-min averaging intervals. Furthermore, we show the relevance of 1-min fluxes for studying the light–response curves of plants for conditions with different temperature and humidity. Finally, we show that accurate estimates of 1-min averaged canopy resistances can be determined via the resistance expressions for sensible heat and LvE. As such, we show that vegetation can indeed modify its canopy resistance significantly within several minutes.

Estimation of turbulent fluxes using the flux-variance method over an alpine meadow surface in the eastern Tibetan Plateau

The flux-variance similarity relation and the vertical transfer of scalars exhibit dissimilarity over different types of surfaces, resulting in different parameterization approaches of relative transport efficiency among scalars to estimate turbulent fluxes using the flux-variance method. We investigated these issues using eddycovariance measurements over an open, homogeneous and flat grassland in the eastern Tibetan Plateau in summer under intermediate hydrological conditions during rainy season. In unstable conditions, the temperature, water vapor, and CO2 followed the flux-variance similarity relation, but did not show in precisely the same way due to different roles (active or passive) of these scalars. Similarity constants of temperature, water vapor and CO2 were found to be 1.12, 1.19 and 1.17, respectively. Heat transportation was more efficient than water vapor and CO2. Based on the estimated sensible heat flux, five parameterization methods of relative transport efficiency of heat to water vapor and CO2 were examined to estimate latent heat and CO2 fluxes. The strategy of local determination of flux-variance similarity relation is recommended for the estimation of latent heat and CO2 fluxes. This approach is better for representing the averaged relative transport efficiency, and technically easier to apply, compared to other more complex ones.

Measuring H2O and CO2 fluxes at field scales with scintillometry: Part I – Introduction and validation of four methods

This study introduces four methods for determining turbulent water vapour and carbon dioxide flux densities, the evapotranspiration and CO2 flux respectively. These methods combine scintillometer measurements with point-sampling measurements of scalar quantities and consequently have a faster statistical convergence than the eddy-covariance method. The scintillometer measures the friction velocity and stability averaged over space, allowing the time averaging to be a minute or less in homogenous conditions. This paper aims to thoroughly test the methods by analysing their sensitivity to the variables that go into the method and validate the methods with 30-min eddy-covariance data. Introduced are: the Bowen-variance method, the flux-variance method, the structure-parameter method, and the energy-balance method. Sensitivity analysis shows that each method is sensitive to the turbulence measurements of the scalar quantities that are specific to the method, as well as to the friction velocity. This demonstrates that the accuracy of the flux results from a correct representation of the turbulence variables used by the methods. Furthermore, a 30-min flux validation shows that the methods compare well to the independent eddy-covariance fluxes. We found that the structure-parameter method performs best – a low scatter (the correlation coefficient, r=0.99) and a 5% underestimation were observed. Also the other methods perform well, although the energy-balance did not close, because storage terms and CO2 flux were neglected. Furthermore, during the night the variance methods were influenced by non-stationarity in the measurement signal. Finally, we suggest using the correlation coefficients between temperature and scalar quantities to acquire the sign of the fluxes. Data for this study were gathered in May–June 2009 over a wheat field near Merken, Germany, in the framework of the TransRegio32 program.

A Comparison of Flux Variance and Surface Renewal Methods With Eddy Covariance

Sensible and latent heat fluxes are important parameters for understanding energy/mass interactions. At present, there are a number of methods available to estimate these fluxes, with varying degrees of difficulty and success. In the present study, we explore the use of the flux variance method and the surface renewal method to estimate the sensible and latent heat fluxes in two agricultural sites in China. The results of these two methods were compared to direct measurements using eddy covariance. The study sites, a wheat field in a semi-arid area and a rice paddy in a humid area provide an opportunity to examine two extreme conditions. In the arid conditions, both estimation methods provided similar sensible heat flux estimations but higher latent heat flux estimations with respect to the eddy covariance measurements. The sum of the estimated sensible and latent heat fluxes was in good agreement with measurements. In the rice paddy, sensible heat flux estimated by both methods showed similar results, whereas latent heat fluxes estimation were 1.2 times greater than eddy covariance measurements. The surface renewal method underestimated the Bowen ratio over the rice paddy, but overestimated it over the wheat field. In conclusion, both methods appear more appropriate for the estimation of sensible heat flux rather than for latent heat flux, in particular in humid environments.

Flux-Variance Method for Latent Heat and Carbon Dioxide Fluxes in Unstable Conditions

Applied previously to momentum and heat fluxes, the present study extends the flux-variance method to latent heat and CO2 fluxes in unstable conditions. Scalar similarity is also examined among temperature (θ), water vapour (q), and CO2 (c). Temperature is adopted as the reference scalar, leading to two feasible strategies to estimate latent heat and CO2 fluxes: the first one relies on flux-variance similarity relations for scalars, while the second is based on the parameterization of relative transport efficiency in terms of scalar correlation coefficient and a non-dimensional quantity. The relationship between the θ-to-q transport efficiency (λ θ q ) and θ-q correlation coefficient (R θ q ) is used to describe the intermediate hydrological conditions. We also parameterize the θ-to-c transport efficiency (λ θ c ) as a function of the θ-c correlation coefficient (R θ c ) by introducing a new non-dimensional ratio (α). The flux-variance method is a viable technique for flux gap-filling, when turbulence measurements of wind velocity are not available. It is worth noting that the extended method is not exempt from a correction for density effects when used for estimating water or carbon exchange.

Estimation of sensible heat, water vapor, and CO2 fluxes using the flux-variance method

This study investigated the flux-variance relationships of temperature, humidity, and CO(2), and examined the performance of using this method for predicting sensible heat (H), water vapor (LE), and CO(2) fluxes (F(CO2)) with eddy-covariance measured flux data at three different ecosystems: grassland, paddy rice field, and forest. The H and LE estimations were found to be in good agreement with the measurements over the three fields. The prediction accuracy of LE could be improved by around 15% if the predictions were obtained by the flux-variance method in conjunction with measured sensible heat fluxes. Moreover, the paddy rice field was found to be a special case where water vapor follows flux-variance relation better than heat does. However, the CO(2) flux predictions were found to vary from poor to fair among the three sites. This is attributed to the complicated CO(2) sources and sinks distribution. Our results also showed that heat and water vapor were transported with the same efficiency above the grassland and rice paddy. For the forest, heat was transported 20% more efficiently than evapotranspiration.

Low-frequency modulation of the atmospheric surface layer over Amazonian rain forest and its implication for similarity relationships

The application of Monin–Obukhov similarity theory (MOS) is based on empirical relationships derived over uniform surfaces in flat terrain. It is not clear to what extent these relationships hold for complex surfaces such as tropical forest or hilly terrain. This study investigates the influence of low-frequency motions in the structure of the atmospheric surface layer over Amazonian forest and its implication for the application of MOS theory. We test the estimation of heat fluxes by the flux-variance method, which is based on MOS theory, for measurements in unstable conditions in the K34 forest site in central Amazonia, north of Manaus, Brazil. It is found that the MOS relationships and the flux-variance method provide reasonable results only when the w − T correlation ( r w T ) is above 0.5. Examining the scale dependence of r w T and of u − w correlation ( r u w ) revealed that w variations tend to be not well correlated with fluctuations in u or T at low frequencies. In this sense, a greater influence of low-frequency processes tends to cause r w T and r u w to decrease, and in these conditions the surface layer cannot be characterized by the ‘textbook’ descriptions of the surface layer observed over uniform terrain. As an alternative to the conventional MOS scaling, we test the use of the ‘dissipation velocity’ u ɛ = ( kzɛ) 1/3, proposed by McNaughton [McNaughton, K.G., 2006. On the kinetic energy budget of the unstable atmospheric surface layer. Boundary-Layer Meteorol. 118, 83–107], to scale the standard deviations and parameterize the modulation of low-frequency motions. The systematic variation with stability is taken out by the use of the new parameters, and the scaled variables become independent of the MOS stability parameter ζ. This result is consistent with the self-organizing nature of the turbulent structure in the modulated surface layer. The results highlight the complexities of the surface layer above vegetation such as Amazonian forest. Estimations of the parameter υ */ u *, which represent the modulation of the outer-layer motions on the surface layer, indicate that during roughly 20% of the time the unstable surface layer above the forest deviates from the ‘classical’ description.

Turbulent variance characteristics of temperature and humidity over a non-uniform land surface for an agricultural ecosystem in China

This paper describes the application of the variance method for flux estimation over a mixed agricultural region in China. Eddy covariance and flux variance measurements were conducted in a near-surface layer over a non-uniform land surface in the central plain of China from 7 June to 20 July 2002. During this period, the mean canopy height was about 0.50 m. The study site consisted of grass (10% of area), beans (15%), corn (15%) and rice (60%). Under unstable conditions, the standard deviations of temperature and water vapor density (normalized by appropriate scaling parameters), observed by a single instrument, followed the Monin-Obukhov similarity theory. The similarity constants for heat (CT) and water vapor (Cq) were 1.09 and 1.49, respectively. In comparison with direct measurements using eddy covariance techniques, the flux variance method, on average, underestimated sensible heat flux by 21% and latent heat flux by 24%, which may be attributed to the fact that the observed slight deviations (20% or 30% at most) of the similarity “constants” may be within the expected range of variation of a single instrument from the generally-valid relations.

Temperature–Humidity Dissimilarity and Heat-to-water-vapour Transport Efficiency Above and Within a Pine Forest Canopy: the Role of the Bowen Ratio

Over the past 15 years atmospheric surface-layer experiments over heterogeneous canopies have shown that the vertical transfer of sensible heat and water vapour exhibit a strong dissimilarity. In particular, the sensible-heat-to-water-vapour transport efficiencies generally exceed unity. One of the main consequences is that evaporation (latent heat flux) computed by the flux-variance method is overestimated, as persistently demonstrated by comparisons with evaporation obtained with the eddy-correlation method. Various authors proposed to take into account the temperature–humidity dissimilarity to extend the applicability of the flux-variance method in order to compute evaporation from non-uniform surfaces. They attempted to connect the sensible-heat-to-water-vapour transport efficiency (λ) to the correlation coefficient between temperature and humidity turbulent fluctuations (R Tq ). This approach was found to be successful over ‘wet’ surfaces for which λ can be approximated by R Tq and ‘dry’ surfaces for which λ can be approximated by 1/R Tq . However, no solution has been proposed until now for intermediate hydrological conditions. We investigated this question using eddy-correlation measurements above and inside a pine forest canopy. For both levels, our data present a strong likeness with previously published results over heterogeneous surfaces. In particular, they confirm that λ is R Tq in wet conditions and 1/R Tq in dry conditions. Moreover, we defined the range of the Bowen ratio (Bo) values for which those two approximations are valid (below 0.1 and greater than 1, respectively) and established a relationship between λ, R Tq and Bo for the intermediate range of Bo. We are confident that this new parameterization will enlarge the applicability of the flux-variance method to all kinds of heterogeneous surfaces in various hydrological conditions

Estimating sensible heat flux using surface renewal analysis and the flux variance method: A case study over olive trees at Sástago (NE of Spain)

The eddy covariance technique for measuring surface fluxes is often not affordable outside experimental research institutes. Therefore knowledge of the performance of alternative methods for determining surface fluxes is valuable. The performance of surface renewal (SR) analysis and the flux variance (FV) method for estimating sensible heat flux has been evaluated in an experiment carried out over a heterogeneous canopy (olive orchard, 50% ground cover) at a semiarid climate in a windy area. Measurements were made at a single level close to the canopy top. SR analysis was accurate under both stable and unstable conditions. The FV method also showed a good performance under unstable conditions, but it was uncertain near neutral conditions and was not applicable under stable conditions.

An Application of the Variational Method to Computation of Sensible Heat Flux over a Deciduous Forest

Abstract A variational method is employed to compute surface sensible heat fluxes over a deciduous forest using observed temperature, temperature variance, and wind. Because the variational approach is able to take into account comprehensive observational meteorological conditions over a heterogeneous surface, it is applicable to the computations of sensible heat flux over a forest canopy in which the conventional flux-variance method is difficult to use. Verifications using the direct eddy-correlation measurements over a deciduous forest during the fully leafed summer of 1988 and the leafless winter of 1990 show that the variational method yields very good agreements between the computed and the measured sensible heat fluxes. It is also shown that the variational method is much more accurate than the flux-variance method in computations of sensible heat flux over a forest canopy.

Turbulent exchange of heat, water vapor, and momentum over a Tibetan prairie by eddy covariance and flux variance measurements

Land‐atmosphere interactions on the Tibetan Plateau are important because of their influence on energy and water cycles on both regional and global scales. Flux variance and eddy covariance methods were used to measure turbulent fluxes of heat, water vapor, and momentum over a Tibetan shortgrass prairie during the Global Energy and Water Cycle Experiment (GEWEX) Asian Monsoon Experiment (GAME) in 1998. Under unstable conditions during the monsoon period (July–September), the observed standard deviations of temperature and specific humidity (normalized by appropriate scaling parameters) followed the Monin‐Obukhov theory. The similarity constants for heat CT and water vapor Cq in their dimensionless functions of stability under a free convection limit were both 1.1, unlike the differences (i.e., CT ≤ Cq) reported in other studies. While the transfer efficiency of heat and water vapor exchange generally agreed with the prediction from the Monin‐Obukhov theory, momentum exchange was less efficient than predicted. In comparison with the eddy covariance data, the flux variance method (with CT = Cq = 1.1) underestimated both heat and water vapor fluxes by <5%. When the eddy covariance data were absent, the flux variance method was used for gap filling the seasonal flux database. To estimate latent heat flux during the premonsoon period in June, CT/Cq was approximated as rTq (where rTq is a correlation coefficient for the fluctuations of temperature and water vapor) because of the sensitivity of Cq to changes in soil moisture conditions. The dramatic changes in the Bowen ratio from 9.0 to 0.4 indicate the shift of energy sources for atmospheric heating over the plateau, which, in turn, resulted in the shift of turbulent exchange mechanisms for heat and water vapor.

Combining surface renewal analysis and similarity theory: A new approach for estimating sensible heat flux

Castellví et al. [2002] proposed a new approach for estimating sensible heat flux that combined surface renewal analysis and similarity theory. The approach used a calibration parameter (here referred as β) which was introduced by scaling the mean local gradient of air temperature with the ramp amplitude of air temperature over the mean volume of air parcel renewed per unit ground area, traditionally denoted as (αz), with z as the measurement height. Parameter β is explained and determined for half‐hourly samples. It is shown that (kβ) ∼ 0.1 is appropriate under unstable conditions over a variety of canopies, with k as the von Kármán constant. This value is rather robust with regard to height and when measuring in both the roughness and inertial sublayers. This understanding of parameter β allowed a better understanding of parameter α and permitted the derivation of a modified approach for estimating sensible heat flux. In practice, it was possible to consider the new approach exempt from calibration. It was attractive for field applications and showed excellent performance under both stable and unstable conditions. A test was carried out for canopies where fetch requirements and full surface cover were not adequate. It was also shown that the flux variance method required calibration and did not perform as well as the proposed approach under such field conditions.

Sensible heat flux estimation by flux variance and half‐order time derivative methods

This study is the first to contrast two similarity theory methods, the flux variance and the half‐order time derivative, over a wide range of atmospheric stability and surface roughness conditions. These two methods were selected because they require only single‐level temperature measurement to estimate sensible heat flux. The data used were collected over bare soil, a grass‐covered forest clearing, and an even‐aged pine forest. For all three sites the flux variance method estimated the sensible heat flux relatively well for unstable atmospheric conditions. The half‐order time derivative method was found to be sensitive to the parameterization of the eddy diffusivity, especially for the grass and bare soil field sites. Overall, the flux variance method was able to reproduce the measured sensible heat flux with greater accuracy than the half‐order time derivative methods for the three experiment sites.

A Note on the Flux-Variance Similarity Relationships for Heat and Water Vapour in the Unstable Atmospheric Surface Layer

Atmospheric surface layer (ASL) experiments over the past 10 years demonstrate that the flux-variance similarity functions for water vapour are consistently larger in magnitude than their temperature counterpart. In addition, latent heat flux calculations using the flux-variance method do not compare as favorably to eddy- correlation measurements when compared to their sensible heat counterpart. These two findings, in concert with measured heat to water vapour transport efficiencies in excess of unity, are commonly used as evidence of dissimilarity between heat and water vapour transport in the unstable atmospheric surface layer. In this note, it is demonstrated that even if near equality in flux-profile similarity functions for heat and water vapour is satisfied, the flux-variance similarity functions for water vapour are larger in magnitude than temperature for a planar, homogeneous, unstably-stratified turbulent boundary-layer flow.

Latent and sensible heat flux predictions from a uniform pine forest using surface renewal and flux variance methods

A surface renewal model that links organized eddy motion to the latent and sensible heat fluxes is tested with eddy correlation measurements carried out in a 13m tall uniform Loblolly pine plantation in Duke Forest, Durham, North Carolina. The surface renewal model is based on the occurance of ramp-like patterns in the scalar concentration measurements. To extract such ramp-like patterns from Eulerian scalar concentration measurements, a newly proposed time-frequency filtering scheme is developed and tested. The time-domain filtering is carried out using compactly-supported orthonormal wavelets in conjunction with the “Universal Wavelet Thresholding” approach of Donoho and Johnstone, while the frequency filtering is carried out by a band-pass sine filter centered around the ramp-occurrence frequency as proposed by other studies. The method was separately tested for heat and water vapour with good agreement between eddy correlation flux measurements and model predictions. The usefulness of the flux-variance method to predict sensible and latent heat fluxes is also considered. Our measurements suggest that the simple flux-variance method reproduces the measured heat and momentum fluxes despite the fact that the variances were measured within the roughness sublayer and not in the surface layer. Central to the predictions of water vapour fluxes using the flux-variance approach is the similarity between heat and water vapour transport by the turbulent air flow. This assumption is also investigated for this uniform forest terrain.

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.