Using measured variances to compute surface fluxes and dry deposition velocities: A comparison with measurements from three surface types

Abstract

Fluxes of temperature, water vapour, O₃, SO₂ and CO₂ were estimated from the measurement of their variances, taken over a wetland region in northern Ontario (Canada) during the summer of 1990 and over a deciduous forest when it was fully leafed during the summer of 1988 and when it was leafless during the winter of 1990. A set of flux‐variance relations was employed, including empirical forms of universal functions that could be adjusted with some constants. Results from the present study show that these constants needed to be adjusted with site‐specific data in order to achieve a closer agreement between estimated and observed fluxes. Best estimates were obtained for the fluxes of temperature and water vapour and it was found that the flux estimates of O₃, SO₂ and CO₂ correlated better with water vapour than with temperature. For these trace gases the flux‐variance method yielded estimates of dry deposition velocities that were either comparable with or larger than those obtained from a resistance analogue model. Both methods yielded values that overestimated the observed dry deposition velocities. The employment of the flux‐variance method in an operational network would require the use of fast‐response sensors and a practical method for reducing the noise level of the measured variances.     

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.     

基于通量方差法对青藏高原东侧高寒草甸地表通量的估算

利用位于青藏高原东侧理塘大气综合观测站2008年观测资料,分析了高寒草甸下垫面上地表通量的时间变化特征,确定了温度、水汽和CO₂的归一化标准差在不稳定情况下随稳定度变化的通量方差关系,应用通量方差法对感热、潜热和CO₂通量进行了计算,并与涡旋相关系统的观测结果进行了比较。结果表明：地表通量月平均日变化呈较为规则的日循环特征,季节变化特征也很明显,雨季（5-9月）潜热大于感热,干季则以感热为主,CO₂通量以6-9月值最大。在不稳定条件下,温度、水汽和CO₂的归一化标准差随稳定度的变化均满足-1/3规律,其通量方差相似性常数分别为1.2,1.4和0.9。通量方差法估算出的通量值与涡旋相关观测得到的通量值有较好的一致性,但感热通量的效果优于潜热通量和CO₂通量。该方法高估了感热通量尤其是潜热通量,而低估了CO₂通量。采用直接观测的感热通量值计算潜热通量和CO₂通量可改善计算结果。     

Surface and Mixed-Layer Variance Methods to Estimate Regional Sensible Heat Flux at the Surface

Turbulence measurements in the lower half of the convective boundary layer (CBL), which includes both mixed layer and surface layer, were carried out with five sonic anemometers mounted on a 213-m tower over a complex flat suburban area with patches of forest, agricultural land, houses and buildings. Also made were radiosoundings of temperature, humidity and wind speed, to determine the CBL height. The sonic anemometer data of wind speed and temperature were processed to derive the second-moment turbulent statistics and were analyzed to investigate the applicability of variance methods to estimate regional surface fluxes of sensible heat. It was found that the temperature variances in the lower mixed layer, coupled with universal functions, produced sensible heat fluxes H over the area with an rms error of the order of 40 Wm^-2 when compared with H values derived from the eddy correlation method. The variance of the vertical wind speed did not produce as good a result. In contrast, the surface-layer temperature variances yielded H values with rms error of the order of 20 Wm^-2, even though the underlying surface was non-uniform and highly non-isothermal, above which enhanced temperature variances could be suspected.     

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.     

Mean Profiles of Moisture Fluxes in Snow-Filled Boundary Layers

Profiles of moisture fluxes have been examined for convective boundary layers containing clouds and snow, using data derived from aircraft measurements taken on four dates during the 1983/1984 University of Chicago lake-effect snow project. Flux profiles were derived from vertical stacks of aircraft cross-wind flight legs taken at various heights over Lake Michigan near the downwind shore. It was found that, if ice processes are taken into account, profiles of potential temperature and water content were very similar to those presented in past studies of convective boundary layers strongly heated from below. Profiles of total water content and equivalent potential temperature adjusted for ice were nearly invariant with height, except very near the top of the boundary layer, suggesting that internal boundary-layer mixing processes were rapid relative to the rates at which heat and vapour were transported into the boundary layer through entrainment and surface fluxes. Ice was found to play a significant, measurable role in boundary-layer moisture fluxes. It was estimated that 40 to 57% of the upward vapour flux was returned to the surface in the form of snow, converting about 45 to 64% of the surface latent heat flux into sensible heat in the snow-producing process. Assuming advective fluxes are relatively small (thought to be appropriate after the first few tens of km over the lake as suggested by past studies), the boundary layer was found to warm at a rate faster than could be explained by surface heat fluxes and latent heat releases alone, the remainder of the heating presumably coming from radiational processes and entrainment. Discussions of moisture phase change processes throughout the boundary layer and estimates of errors of these flux measurements are presented.     

Scalar Similarity for Relaxed Eddy Accumulation Methods

The relaxed eddy accumulation (REA) method allows the measurement of trace gas fluxes when no fast sensors are available for eddy covariance measurements. The flux parameterisation used in REA is based on the assumption of scalar similarity, i.e., similarity of the turbulent exchange of two scalar quantities. In this study changes in scalar similarity between carbon dioxide, sonic temperature and water vapour were assessed using scalar correlation coefficients and spectral analysis. The influence on REA measurements was assessed by simulation. The evaluation is based on observations over grassland, irrigated cotton plantation and spruce forest.Scalar similarity between carbon dioxide, sonic temperature and water vapour showed a distinct diurnal pattern and change within the day. Poor scalar similarity was found to be linked to dissimilarities in the energy contained in the low frequency part of the turbulent spectra ( < 0.01 Hz).The simulations of REA showed significant change in b-factors throughout the diurnal course. The b-factor is part of the REA parameterisation scheme and describes a relation between the concentration difference and the vertical flux of a trace gas. The diurnal course of b-factors for carbon dioxide, sonic temperature and water vapour matched well. Relative flux errors induced in REA by varying scalar similarity were generally below ± 10%. Systematic underestimation of the flux of up to − 40% was found for the use of REA applying a hyperbolic deadband (HREA). This underestimation was related to poor scalar similarity between the scalar of interest and the scalar used as proxy for the deadband definition.     

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.     

Heat and water vapour fluxes and scalar roughness lengths over an Antarctic ice shelf

We present eddy-correlation measurements of heat and water vapour fluxes made during the Antarctic winter. The surface layer was stably stratified throughout the period of observation and sensible heat fluxes were always directed downwards. However, both upward and downward water vapour fluxes were observed. Their magnitude was generally small and the latent heat flux was not a significant fraction of the surface energy budget. The variation of heat and water vapour fluxes with stability is well described by Monin-Obukhov similarity theory but the scalar roughness lengths for heat and water vapour appear to be much larger than the momentum roughness length. Possible explanations of this effect are discussed.     

On the Anomalous Behaviour of Scalar Flux–Variance Similarity Functions Within the Canopy Sub-layer of a Dense Alpine Forest

Within the canopy sub-layer (CSL), variability in scalar sources and sinks are known to affect flux–variance (FV) similarity relationships for water vapour (q) and carbon dioxide (C) concentrations, yet large-scale processes may continue to play a significant role. High frequency time series data for temperature (T), q and C, collected within the CSL of an uneven-aged mixed coniferous forest in Lavarone, Italy, are used to investigate these processes within the context of FV similarity. This dataset suggests that MOST scaling describes the FV similarity function of T even though the observations are collected in the CSL, consistent with other studies. However, the measured FV similarity functions for q and C appear to have higher values than their temperature counterpart. Two hypotheses are proposed to explain the measured anomalous behaviour in the FV similarity functions for q and C when referenced to T. Respired CO₂ from the forest floor leads to large positive excursions in the C time series at the canopy top thereby contributing significantly to both C variance increase and C vertical flux decrease—both leading to an anomalous increase in the FV similarity function. For q, transport of dry air from the outer-layer significantly increases both the variance and the water vapour flux. However, the expected flux increase is much smaller than the variance increase so that the net effect remains an increase in the measured FV similarity function for water vapour above its T counterpart. The hypothesis here is that identifying these events in the temporal and/or in the frequency domain and filtering them from the C and q time series partially recovers a scalar flow field that appears to follow FV similarity theory scaling. Methods for identifying both types of events in the time and frequency domains and their subsequent effects on the FV similarity functions and corollary flow variables, such as the relative transport efficiencies, are also explored.     

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.     

Testing of the bandpass eddy covariance method for a long-term measurement of water vapour flux over a forest

The bandpass eddy covariance method has been used to measure the turbulent flux of scalar quantities using a slow-responsescalar sensor. The method issimilar in principle to the traditional eddy correlation method but includes the estimation of high-frequency components of the flux on the basis of cospectral similarity in the atmospheric surface layer. In order to investigate the performance of the method, measurements of the water vapour flux over a forest with the bandpass eddy covariance method and the direct eddy correlation method were compared. The flux obtained by the bandpass eddy covariance method agreed with that by the eddy correlation method within ±20% for most cases, in spite of a rather slow sensor-response of the adopted hygrometer. This result supports its relevance to a long-term continuous operation, since a stable, low-maintenance,general-purpose sensor canbe utilized for scalar quantities. Oneweak point of the method isits difficulty in principle to measure the correct flux when the magnitude of the sensible heat flux is very small, because the method uses the sensible heat flux as a standard reference for the prediction of undetectable high-frequency components of the scalar flux. An advanced method is then presented to increase its robustness. In the new method, output signals from a slow-response sensor are corrected using empirical frequency-responsefunctions for the sensor,thereby extending the width of the bandpass frequency region where components of the flux are directly measured (not predicted). The advanced method produced correct fluxes for all cases including the cases of small sensible heat flux. The advanced bandpass eddy covariance method is thus appropriate for along-term measurement of the scalar fluxes.     

Regional Fluxes Of Momentum And Sensible Heat Over A Sub-Arctic Landscape During Late Winter

Based on measurements at Sodankylä Meteorological Observatory the regional (aggregated) momentum and sensible heat fluxes are estimated for two days over a site in Finnish Lapland during late winter. The forest covers 49% of the area. The study shows that the forest dominates and controls the regional fluxes of momentum and sensible heat in different ways. The regional momentum flux is found to be 10–20% smaller than the measured momentum flux over the forest, and the regional sensible heat flux is estimated to be 30–50% of the values measured over a coniferous forest.The regional momentum flux is determined in two ways, both based on blending height theory. One is a parameterised method, the other represents a numerical solution of an aggregation model. The regional sensible heat flux is determined from the theory of mixed-layer growth. At near neutral conditions the regional momentum flux can be determined independently of the regional sensible heat flux. At unstable conditions the two models become coupled.The information that is needed by the parameterised blending height method and by the mixed-layer evolution method in order to derive the regional fluxes of momentum and sensible heat can be obtained from radiosonde profiles of wind speed and temperature.     

Attenuation Correction Procedures for Water Vapour Fluxes from Closed-Path Eddy-Covariance Systems

Evapotranspiration is a source of water vapour to the atmosphere, and as a crucial indicator of landscape behaviour its accurate measurement has widespread implications. Here we investigate errors that are prevalent and systematic in the closed-path eddy-covariance measurement of latent heat flux: the attenuation of fluxes through dampened cospectral power at high frequencies. This process is especially pronounced during periods of high relative humidity through the adsorption and desorption of water vapour along the tube walls. These effects are additionally amplified during lower air temperature conditions. Here, we quantify the underestimation of evapotranspiration by a closed-path system by comparing its flux estimate to simultaneous and adjacent measurements from an open-path sensor. We apply models relating flux loss to relative humidity itself, to the lag time of the cross-correlation peak between the water vapour and vertical wind velocity signals, and to models of cospectral attenuation relative to the cospectral power of simultaneous sensible heat-flux measurements. We find that including the role of temperature in modifying the attenuation–humidity relationship is essential for unbiased flux correction, and that physically based cospectral attenuation methods are effective characterizers of closed-path instrument signal loss relative to the unattenuated flux value.     

Area-Averaged Surface Fluxes Over the Litfass Region Based on Eddy-Covariance Measurements

Micrometeorological measurements (including eddy-covariance measurements of the surface fluxes of sensible and latent heat) were performed during the LITFASS-2003 experiment at 13 field sites over different types of land use (forest, lake, grassland, various agricultural crops) in a 20 × 20 km² area around the Meteorological Observatory Lindenberg (MOL) of the German Meteorological Service (Deutscher Wetterdienst, DWD). Significant differences in the energy fluxes could be found between the major land surface types (forest, farmland, water), but also between the different agricultural crops (cereals, rape, maize). Flux ratios between the different surfaces changed during the course of the experiment as a result of increased water temperature of the lake, changing soil moisture, and of the vegetation development at the farmland sites. The measurements over grass performed at the boundary-layer field site Falkenberg of the MOL were shown to be quite representative for the farmland part of the area. Measurements from the 13 sites were composed into a time series of the area-averaged surface flux by taking into account the data quality of the single flux values from the different sites and the relative occurrence of each surface type in the area. Such composite fluxes could be determined for about 80% of the whole measurement time during the LITFASS-2003 experiment. Comparison of these aggregated surface fluxes with area-averaged fluxes from long-range scintillometer measurements and from airborne measurements showed good agreement.     

Stability dependence of the temperature structure parameter

Experimental data of C _T ², determined during various experiments in the surface layer, are compared with several functions giving the stability dependence of the temperature structure parameter. The universal function of the dimensionless temperature gradient by Skeib (1980) follows very well the experimental data and the empirical function by Wyngaard et al. (1971). This function can be used in an inertial-dissipation method.     

Energy partitioning at treeline forest and tundra sites and its sensitivity to climate change

Abstract

Summertime energy budgets of contiguous wetland tundra and forest near Churchill, Manitoba along the coast of Hudson Bay were measured over a five year period, 1989–1993. An examination of differences in energy budgets between the two sites showed that net radiation was similar in all years. Soil heat flux was greater at the tundra site in most, but not all, years. However, sensible heat flux was always larger at the forest site and latent heat flux was always greater at the tundra site. Mean daily Bowen ratios at both sites were less than unity in all years. Average Bowen ratios for the five years were 0.45 for tundra and 0.66 for forest. Wind direction is used as an analogue for changing climatic conditions where onshore winds are cooler and moister than offshore winds. Sensible and latent heat fluxes at both sites varied significantly between onshore and offshore wind regimes. However, differences between onshore and offshore fluxes at the tundra site were larger than for the forest. Thus, Bowen ratios also varied more at the tundra site. We have plotted the ratio of tundra‐to‐forest Bowen ratios as a measure of the relative sensitivity of energy partitioning to climatic change. The ratio decreases with increasing vapour pressure deficit (and increasing air temperature). We interpret these results as suggesting that energy partitioning over the wetland tundra is more sensitive to changes in climate than the treeline forest environment. Thus, as the climate warms and becomes drier, more additional energy goes into evaporation of water from the wetland tundra than from the forest.     

The Turbulent Lagrangian Time Scale in Forest Canopies Constrained by Fluxes,Concentrations and Source Distributions

One-dimensional Lagrangian dispersion models, frequently used to relate in-canopy source/sink distributions of energy, water and trace gases to vertical concentration profiles, require estimates of the standard deviation of the vertical wind speed, which can be measured, and the Lagrangian time scale, T _L , which cannot. In this work we use non-linear parameter estimation to determine the vertical profile of the Lagrangian time scale that simultaneously optimises agreement between modelled and measured vertical profiles of temperature, water vapour and carbon dioxide concentrations within a 40-m tall temperate Eucalyptus forest in south-eastern Australia. Modelled temperature and concentration profiles are generated using Lagrangian dispersion theory combined with source/sink distributions of sensible heat, water vapour and CO₂. These distributions are derived from a multilayer Soil-Vegetation-Atmospheric-Transfer model subject to multiple constraints: (1) daytime eddy flux measurements of sensible heat, latent heat, and CO₂ above the canopy, (2) in-canopy lidar measurements of leaf area density distribution, and (3) chamber measurements of CO₂ ground fluxes. The resulting estimate of Lagrangian time scale within the canopy under near-neutral conditions is about 1.7 times higher than previous estimates and decreases towards zero at the ground. It represents an advance over previous estimates of T _L , which are largely unconstrained by measurements.     

Atmospheric turbulence within and above a douglas-fir stand. Part II: Eddy fluxes of sensible heat and water vapour

This is the second paper describing a study of the turbulence regimes and exchange processes within and above an extensive Douglas-fir stand. The experiment was conducted on Vancouver Island during a two-week rainless period in July and August 1990. Two eddy correlation units were operated in the daytime to measure the fluxes of sensible heat and water vapour and other turbulence statistics at various heights within and above the stand. Net radiation was measured above the overstory using a stationary net radiometer and beneath the overstory using a tram system. Supplementary measurements included soil heat flux, humidity above and beneath the overstory, profiles of wind speed and air temperature, and the spatial variation of sensible heat flux near the forest floor.The sum of sensible and latent heat fluxes above the stand accounted for, on average, 83% of the available energy flux. On some days, energy budget closure was far better than on others. The average value of the Bowen ratio was 2.1 above the stand and 1.4 beneath the overstory. The mid-morning value of the canopy resistance was 150–450 s/m during the experiment and mid-day value of the Omega factor was about 0.20. The daytime mean canopy resistance showed a strong dependence on the mean saturation deficit during the two-week experimental period.The sum of sensible and latent heat fluxes beneath the overstory accounted for 74% of the available energy flux beneath the overstory. One of the reasons for this energy imbalance was that the small number of soil heat flux plates and the short pathway of the radiometer tram system was unable to account for the large horizontal heterogeneity in the available energy flux beneath the overstory. On the other hand, good agreement was obtained among the measurements of sensible heat flux made near the forest floor at four positions 15 m apart.There was a constant flux layer in the trunk space, a large flux divergence in the canopy layer, and a constant flux layer above the stand. Counter-gradient flux of sensible heat constantly occurred at the base of the canopy.The transfer of sensible heat and water vapour was dominated by intermittent cool downdraft and warm updraft events and dry downdraft and moist updraft events, respectively, at all levels. For sensible heat flux, the ratio of the contribution of cool downdrafts to that of warm updrafts was greater than one in the canopy layer and less than one above the stand and near the forest floor.     

Flux Footprint Simulation Downwind of a Forest Edge

Surface fluxes, originating from forest patches, are commonly calculated from atmospheric flux measurements at some height above that patch using a correction for flux arising from upwind surfaces. Footprint models have been developed to calculate such a correction. These models commonly assume homogeneous turbulence, resulting in a simulated atmospheric flux equal to the average surface flux in the footprint area. However, atmospheric scalar fluxes downwind of a forest edge have been observed to exceed surface fluxes in the footprint area. Variations in atmospheric turbulence downwind of the forest edge, as simulated with an E – model, can explain enhanced atmospheric scalar fluxes. This E – model is used to calculate the footprint of atmospheric measurements downwind of a forest edge. Atmospheric fluxes appear mainly enhanced as a result of a stronger sensitivity to fluxes from the upwind surface. A sensitivity analysis shows that the fetch over forest, necessary to reach equilibrium between atmospheric fluxes and surface fluxes, tends to be longer for scalar fluxes as compared to momentum fluxes. With increasing forest density, atmospheric fluxes deviate even more strongly from surface fluxes, but over shorter fetches. It is concluded that scalar fluxes over forests are commonly affected by inhomogeneous turbulence over large fetches downwind of an edge. It is recommended to take horizontal variations in turbulence into account when the footprint is calculated for atmospheric flux measurements downwind of a forest edge. The spatially integrated footprint is recommended to describe the ratio between the atmospheric flux and the average surface flux in the footprint.