Impact of Heterogeneity on Scalar Flux Variance Relations Across Diverse Ecosystems

TL;DR

This work probes how three forms of heterogeneity—spatial heterogeneity of scalar sources, turbulence anisotropy in Reynolds stresses, and temporal non-stationarity—alter Monin-Obukhov Similarity Theory (MOST) based flux-variance relations for heat, water vapor, and carbon dioxide across 47 NEON sites. By combining high-resolution 1 m airborne heterogeneity metrics, NEON turbulence data, and anisotropy-informed curve fitting, the authors show substantial deviations from traditional MOST, especially for CO$_2$, and demonstrate that incorporating anisotropy via $y_b$-dependent scalings significantly improves fit quality. Spatial heterogeneity and site-specific bioactivity modulate the scaling, with strong anisotropy effects observed in one-component or highly structured turbulence; non-stationarity further amplifies deviations, particularly for moisture and carbon at near-neutral stability. The findings offer anisotropy-generalized scalings and site-aware parameterizations that can enhance surface layer schemes in large-scale atmospheric models and improve interpretation of flux-variance measurements.

Abstract

Monin-Obukhov Similarity Theory (MOST), the traditional surface layer theory used to understand the behavior, scaling and exchange of heat, water vapor and carbon dioxide between the land surface and atmosphere relies on a number of commonly broken assumptions. In particular, traditional theory breaks down under three different forms of heterogeneity highlighted in this work: spatial heterogeneity in the sources of the scalars, heterogeneity in the Reynolds stress tensor (turbulence anisotropy), and temporal heterogeneity (non-stationarity). The work explores the relationship between the idealized flux-variance relations and these three forms of heterogeneity across a diverse network of 47 flux towers representing a broad range of ecosystems including forests, agricultural land, grasslands, tundra, tropical and arid: the National Ecological Observation Network (NEON). Results use high resolution spatial data (1 meter resolution) to show a direct relationship between spatial heterogeneity and deviation from traditional scaling relations. The study indicates an interplay between stationarity and anisotropy, with the non-dimensionalized scalar variance scaling more strongly with anisotropy under more non-stationary turbulence conditions. Updated flux-variance relations that leverage turbulence anisotropy for the scaling of heat are introduced, as are novel anisotropy-generalized scalings for water vapor and carbon dioxide. The work also explores in detail how the scaling relations, and their relationship with heterogeneity, vary across the diverse sites in the NEON network. Deviations from traditional theory in carbon dioxide scaling in particular are well correlated with the bioactivity of the site. Results have important implications for development of improved surface layer parameterizations in large scale atmospheric models and flux-variance based flux measurements.

Figures (13)

• Figure 1: Table and bar plot illustrating key environmental characteristics of the NEON sites. Sites are grouped, ordered and colored according to the dominant NLCD land cover type in a 2km box around the tower. From left to right, measurement height for the 3D sonic anemometer, mean growing season Leaf Area Index (LAI), and the standard deviation of the Digital Surface Model (DSM), a measure of complexity, are shown. The blue bar indicates the median daytime dewpoint temperature, and the red bar indicates median daytime air temperature. Three sites have NLCD land cover that may not be representative of the tower area: YELL, SJER and SOAP are all relatively sparse canopies, that produce a scrub/grass landcover type despite significant treecover.
• Figure 2: Observed scaling for the square root of the variance of, from top to bottom, non-dimensionalized potential temperature $\Phi_{\theta}$, water vapor $\Phi_q$ and carbon dioxide $\Phi_c$. The full lines show the median values of $\Phi$ across logarithmically spaced bins of $\zeta$. The shaded areas show binned deciles; the outer area shades between the 10th and 90th percentile, then 20th to 80th, and so on.
• Figure 3: Correlations between five variables ($\zeta$, the magnitude of the surface flux $\left|\overline{w's'}\right|$ ,$\alpha_{solar}$, stationarity metric $\xi_s$ and $y_b$) and the Median Absolute Deviation (MAD) of the data to traditional MOST for the three scalars $s$. $\Phi_{\theta}$ (left), $\Phi_q$ (middle) and $\Phi_c$ (right). The first row shows the magnitude of the spearman correlation coefficient for unstable conditions, and the second row for stable conditions. Slanted lines inside the color are used to indicate inverse (negative) correlations.
• Figure 4: Ratio of the lengthscale of heterogeneity to the turbulent lengthscale ($\ell_{het}/L_t$) compared to the MAD (log scaled) for $\Phi_{\theta}$ (top), $\Phi_q$ (middle) and $\Phi_c$ (bottom) under unstable (left) and stable (right) stratification. $\ell_{het}$ is determined from spatial patterns of albedo for $\theta$, NDWI for $q$ and LAI for $c$. The ratio is plotted in log scale, with 100 binned medians plotted in white, and the filled area representing the interquartile range.
• Figure 5: Observed scaling for the square root of the variance of, from top to bottom, non-dimensionalized potential temperature $\Phi_{\theta}$, water vapor $\Phi_q$ and carbon dioxide $\Phi_w$. The full lines, colored according to $y_b$ (with red being anisotropic and blue being isotropic), show the median values of $\Phi$ across linearly spaced bins of anisotropy and logarithmically spaced bins of $\zeta$. The area between the 1st and 3rd quartile is shaded. Black dashed lines show a traditional MOST scaling for these non-dimensionalized quantities.