An Investigation of the conditional sampling method used to estimate fluxes of active, reactive, and passive scalars

An investigation of the conditional sampling method used to estimate fluxes of active, reactive, and passive scalars

Abstract: The conditional sampling flux measurement technique was evaluated for four scalars (temperature, water vapor, ozone, and carbon dioxide) by comparison with direct eddy correlation measurements at two sites. The empirical constant beta relating the turbulent flux to the accumulated concentration difference between updrafts and downdrafts was computed from 10 Hz turbulence measurements. Comparison between the simulated relaxed eddy accumulation flux formulation and the eddy correlation measurements allowed the direct determination of beta for all four scalars. The beta models previously proposed overpredicted the measured beta by about 8-10%. It was found that a mean beta=0.58 reproduced the eddy correlation measurements dependent of the scalar type being analyzed, roughness and atmospheric stability conditions, in agreement with previous studies. The role of energy-containing eddy motion in the deviations between the measured and predicted beta is considered using orthonormal wavelet expansion in conjunction with a wavelet shrinkage approach. It was demonstrated that the energy-containing large eddy motion contributed to a reduction in beta when compared to the predicted beta. Finally, the deadband vertical velocity effects were also considered and found to reduce beta exponentially, in agreement with other studies.

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

Abstract: Eddy-correlation measurements above an uneven aged forest, uniform-irrigated bare soil field, and within a grass-covered forest clearing were used to investigate the usefulness of the flux-variance 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 latent heat flux at all three sites. The flux-variance method systematically over estimated 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.

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

Abstract: 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 13 m 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 orthononormal 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 vapor 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 vapor fluxes using the flux-variance approach is the similarity between heat and water vapor transport by the turbulent air flow. This assumption is also investigated for this uniform forest terrain.

Estimation of momentum and heat fluxes using dissipation and flux-variance methods in the unstable surface layer

Abstract: Dissipation and flux-variance methods, derived from the turbulent kinetic energy and temperature variance budget equations in conjunction with Monin-Obukov similarity theory, were used to estimate surface fluxes of momentum and sensible heat. To examine the performance of these two methods, direct eddy-correlation measurements were carried out above a non-uniform grass-covered forest clearing in Durham, North Carolina. The dissipation method sensible heat flux predictions were in good agreement with the eddy-correlation measurements. Also, the flux-variance method reproduced the measured sensible heat flux well following an adjustment to the similarity constant. However, the momentum flux (or friction velocity) estimated by the dissipation and flux-variance methods were both inferior to those for sensible heat flux. The data from this experiment indicated that the above two methods are sensitive to the dimensionless wind shear and temperature standard deviation functions. Based on dimensional analysis and the temperature variance budget equation a new dissipation approach for estimating sensible heat flux was derived. The similarity constant for this new approach was shown to be around 1.6 for uniform surfaces and from the data for this experiment.

A Lagrangian dispersion model for predicting CO2 sources, sinks, and fluxes in a uniform Loblolly pine (Pinus taeda L.) stand

Abstract: A canopy Lagrangian turbulent scalar transport model for predicting scalar fluxes, sources, and sinks within a forested canopy was tested using CO2 concentration and flux measurements. The model formulation is based on the Localized Near Field theory (LNF) proposed by Raupach (1989 a,b). Using the measured mean CO2 concentration profile, the vertical velocity variance profile, and the Lagrangian integral time scale profile within and above a forested canopy, the proposed model predicted the CO2 flux and source (or sink) profiles. The model testing was carried out using eddy correlation measurements at 9 m in a uniform 13 m tall Pinus taeda L. loblolly pine stand at the Blackwood division of the Duke Forest near Durham, North Carolina. The tree height and spacing are relatively uniform throughout. The measured vertical profile leaf area index (LAI) was characterized by three peaks, with a maximum LAI occurring at 6.5 m in qualitative agreement with the LNF source-sink predicted profile. The LNF CO2 flux predictions were in better agreement with eddy correlation measurements (coefficient of determination =0.58; and standard error of estimate = 0.16 mg/Kg m/s) than K-Theory. The model reproduced the mean diurnal CO2 flux suggesting better performance over longer averaging time periods. Two key simplifications to the LNF formulation were considered, namely, the near Gaussian approximation to the vertical velocity, and the absence of longitudinal advection. It was found that both of these assumptions were violated throughout the day, but the resulting CO2 flux error at 9 m was not strongly related to these approximations. In contrast to the forward LNF approach utilized by other studies, this investigation demonstrated that the inverse LNF approach is sensitive to near-field corrections.

Soil water depletion by oak trees and the influence of root water uptake on the soil moisture content spatial statistics

Abstract: The space-time statistical structure of soil water uptake by oak trees was investigated in a 3.1 m diameter closed top chamber using a three dimensional measurement grid of soil moisture and pressure, and measurements of tree transpiration. Using the Time Domain Reflectometery (TDR) measured moisture content, resistance block measured soil water pressure, and a compact constant head permeameter measured saturated hydraulic conductivity, the soil hydraulic properties for the chamber were first estimated. Then, dimensionless statistical measures that utilize the soil water pressure were proposed and used to assess the relative importance of lateral to vertical flow. Based on the measured statistical properties of the soil-water pressure, it was found that the vertical flow is at least an order of magnitude larger than the lateral flow, and thus, a one-dimensional flow approximation to continuity was utilized. Using continuity and a first-order Taylor series expansion of the Buckingham-Darcy vertical flux about the spatial mean moisture content state, an approximate relation for the time variation of the spatial mean moisture content was derived and tested with the TDR measurements. Despite a large spatial coefficient of variation in the TDR measured moisture content (which was also shown to be comparable to reported values from larger scale field experiments), good agreement between mean moisture content predictions and measurements were found for two separate drying cycles. The approximate Taylor series flux expansion was utilized for deriving an analogous relation for the time variation of the spatial moisture content variance. The resultant variance budget was used to assess the role of root water uptake on the spatial variability of moisture content. It was found that the root uptake component, which resulted from a covariance between the root water uptake and moisture content spatial perturbations, is comparable to the contribution from soil hydraulic properties and soil water redistribution. One of the main findings in this study is that root water uptake is central to the moisture content spatial variance dissipation especially for dry soil moisture conditions. These results were further investigated using Monte-Carlo simulations.

The lagrangian stochastic model for fetch and latent heat flux estimation above uniform and non-uniform terrain

Abstract: A Lagrangian stochastic model was used to estimate the fetch and latent heat flux above a non-uniform grass-covered forest clearing site at the Duke Forest in Durham, North Carolina and an irrigated bare soil patch at the University of California in Davis. The latent heat flux predictions by the Lagrangian model compared well with eddy correlation flux measurements. In order to apply the Lagrangian model to a non-uniform grass-covered forest clearing, the surface was treated as an imaginary "equivalent" uniform terrain subjected to identical surface roughness and turbulence statistics (i.e., mean, variance, covariance) of velocities and scalars as those measured above the non-uniform terrain. At the irrigated bare soil site, the equilibrium distance of the air from dry to wet was well defined and its influence on the water vapor flux internal boundary layer was considered. In the Lagrangian model, five different schemes to account for inhomogeneous turbulent flows were compared in terms of estimating scalar fluxes. Our comparisons demonstrate that the five different schemes produce similar scalar fluxes despite the fact that some of them do not satisfy the well-mixed criterion. Also, the analytical solution to the advection-diffusion equation was used to predict the fetch and latent heat flux under neutral conditions and compared to the Lagrangian model.

Time constant for water transport in loblolly pine trees estimated from time series of evaporative demand and stem sapflow

Abstract: The use of stem flow data to estimate diurnal whole-tree transporation and canopy stomatal conductance dependents critically upon knowledge of the time lag between transpiration and water flux through the stem. In this study, the time constant for water movement in stems of 12-years-old Pinus taeda L. individuals was estimated from analysis of time series data of stem water flux and evaporative demand derived from vapor pressure deficit and solar radiation data. Water uptake through stems was measured using a constant-heat sapflow probe. Canopy evaporative demand was correlated to stem uptake using a resistance-capacitance equation that incorporates a time constant parameter. A least-squares auto-regression determined the parameters of the resistance-capacitance equation. The time constants for ten loblolly pine trees averaged 48 min and the time lag for the diurnal frequency averaged 47 min. A direct cross-correlation analysis between the canopy evaporative demand and stem flux time series showed maximum correlation at an approximately 30 minute lag. Residuals (model-predicts minus actual stem flow data) increased with increasing soil moisture depletion. While the time constants did not vary significantly within the range of tree sizes studied, hydraulic resistance and capacitance terms were individually dependent on stem cross-sectional area: capacitance increased and resistance decreased with stem volume. This result may indicate an inverse adjustment of resistance and capacitance to maintain a similar time constant over the range of tree sizes studied.

Radial patterns of xylem sap flow in non-,diffuse-and ring-porous tree species

Abstract:

We investigated radial patterns of sap flux and wood properties in the sapwood of young loblolly pine (Pinus taeda L.), mature white oak (Quercus alba L.) and sweetgu, (Liquidambar styraciflua L.), which represent three major classes of wood anatonmy: non-porous (coniferous), ring-porous and diffuse-porous. Radial measurements of xylem sap flux density were made in sections of xylem extending to 20 mm and 20-40 mm from the cambium. These measurements were compared with measurements of the relative water content (R_s) and sapwood specific gravity (sg) of corresponding radial sections. In pine, a 59% reduction in daily sapflux density from outer to inner sapwood was found. This could not be accounted for by a 3% drop in R_s;rather, an accompanying 9% reduction in sg indicated a transition between depth intervals from mature to juvenile sapwood, and is the probable cause of the lower flux rate in the ineer xylem of pine.

Leaf and canopy responses to FACE

Leaf and canopy responses to elevated CO2 in a pine forest under free-air CO2 enrichment

Abstract:

Physiological responses to elevated CO₂ at the leaf and canopy-level were studied in an intact pine (Pinus taeda) forest ecosystem exposed to elevated CO₂ using a free-air CO₂ enrichment (FACE) technique. Normalized canopy water-use of trees exposed to elevated CO₂ over an 8-day exposure period was similar to that of trees exposed to current ambient CO₂ under sunny conditions. During a portion of the exposure period when sky conditions were cloudy, CO₂ -exposed trees showed minor (< 7%) but significant reductions in relative sap flux density compared to trees under ambient CO₂ conditions. Short-term (minutes) direct stomatal responses to elevated CO₂ were also relatively weak (~ 5% reduction in stomatal aperture in response to high CO₂ concentrations). We observed no evidence of adjustment in stomatal conductance in foliage grown under elevated CO₂ for nearly 80 days compared to foliage grown under current ambient CO₂, so intrinsic leaf water-use efficiency at elevated CO₂ was enhanced primarily by direct responses of photosynthesis to CO₂.

We did not detect statistical differences in parameters from photosynthetic responses to intercellular CO₂ ('Anet-ci' curves) for Pinus taeda foliage grown under elevated CO₂ (550 umol mol^-1) for 50-80 days compared to those for foliage grown under current ambient CO₂ from similar-sized reference trees nearby. In both cases, leaf net photosynthetic rate at 550 umol mol^-1 CO₂ was enhanced by approximately 65% compared to the rate at ambient CO₂ (350 umol mol^-1). A similar level of enhancement under elevated CO₂ was observed for daily photosynthesis under field conditions on a sunny day. While enhancement of photosynthesis by elevated CO₂ during the study period appears to be primarily attributable to direct photosynthetic responses to CO₂ in the pine forest, longer-term CO₂ responses and feedbacks remain to be evaluated.