Taylors hypothesis and its impact on flux measurements in a forest clearcut

TL;DR

This study tests the validity of Taylor's hypothesis for translating temporal turbulence observations into spatial information over a heterogeneous forest clearcut, using high-resolution Distributed Temperature Sensing and Eddy Covariance datasets. By extracting scale-dependent convective speeds $U_C(\kappa z)$ from space-time correlations and pairing them with EC flux statistics, the work reveals that convective speeds can exceed the mean wind and follow a power-law with $\kappa z$, leading to non-linear frequency-to-wavenumber transformations that modify inertial-range spectra. A key finding is a slope enhancement in the inertial subrange (approximately -1.13 for $\alpha=0.8$ when $\beta=5/3$) and a defined critical frequency $f_{\rm cr}\approx0.3$ Hz beyond which flux estimates become unreliable due to instrumental scale limitations. The results highlight the impact of heterogeneous surface roughness and sweeping on TH applicability and EC measurements, offering a framework for adjusting turbulence statistics in field analyses and motivating further multi-height and LES studies. $U_C$, $U_e$, and $V$ are central quantities linking space-time structure, twist in advection, and sweeping, all of which influence flux accuracy in complex landscapes.

Abstract

Taylors hypothesis is the backbone to convert observations done over time to spatial information of the flow while carrying out turbulence measurements on a micrometeorological tower. To address its validity over a highly heterogeneous forest clearcut surface, we utilize an extensive Distributed Temperature Sensing (DTS) and Eddy Covariance (EC) datasets. The DTS measured space-time correlation curves of temperature fluctuations are used to compute the bulk convective speeds of temperature structures in buoyant conditions at a height of 3.1 m above the clearing. These convective speeds are compared with the mean wind speed and turbulent intensities of streamwise velocities obtained from the EC system at the middle of the clearcut. Depending on if is parallel or perpendicular to the forest edge, the relationships between and are significantly different. However, irrespective of the wind direction, the convective speeds of temperature structures at inertial subrange scales behave in a power-law fashion with increasing wavenumbers. The exponent of this power-law differs from a homogeneous atmospheric surface layer flow, thereby pointing towards the effects of heterogeneity. The scale-dependent convective speeds non-linearly transform the temporal frequencies to streamwise wavenumbers, which, eventually, impacts the properties of turbulence (co) spectra. More importantly, this non-linear transformation yields a critical frequency limit, beyond which the eddy length scales derived from frequencies are smaller than the physical dimension of the sonic anemometers, and therefore, cannot be faithfully resolved. This critical limit questions the EC flux estimates beyond this frequency.

Figures (12)

• Figure 1: (a) Image and a (b) map of the study site. The image was taken towards South-West on June 28 2024 at the location of the white triangle in (b). Different DTS cable sections are highlighted with red lines. In (b) the black contours show the topography with 2-m increments based on the National Land Survey of Finland Topographic Database (data retrieved: 10/2023). The canopy height map was derived from a drone flight conducted during September 27 2022 and complemented with canopy height model of Finnish Forest Center (data retrieved: 12/2024). Note that the canopy height shown in the map does not fully reflect the conditions at the clearing during the study period due to the rapidly developing vegetation cover.
• Figure 2: (a) The space-time contour plot of temperature fluctuations ($T^{\prime}$) is shown from the DTS measurements of a specific section (Section-1) for a particular 30-min period between 10:30-11:00 UTC on 18 May 2024. The spatial locations along the cable section are denoted by $X$ and the temperature fluctuations are obtained by linearly detrending the temperature signals measured along time. The white horizontal strips indicate the regions where the DTS cable was fastened to masts and the temperature values were omitted from those locations. (b) The space-time correlation curves of temperature fluctuations ($R_{TT}(\tau,r)$) are shown for the same 30-min period obtained from Section-1. The temporal lags or leads are denoted as $\tau$ while the colors indicate different values of spatial separations along $X$, $r$. The blue squares denote the peaks of the correlation curves ($\tau_p$) for each value of $r$. (c) A scatter plot between $r$ and $\tau_p$ is shown. The thick black color denotes the best fit line to compute the convective speed of the temperature structures, denoted as $U_C$.
• Figure 3: (a) Contrary to Fig. \ref{['fig:2']}b, the space-time correlation curves of temperature fluctuations ($R_{TT}(r,\tau)$) are shown where the $x$-axis represents the lags or leads in the spatial domain ($r$) while the colors indicate different values of temporal separations, $\tau$. The blue squares denote the peaks of the correlation curves ($r_p$) for each value of $\tau$. (b) A scatter plot between $r_p$ and $\tau$ is shown. The thick black color denotes the best fit line to compute the convective speed of the temperature structures, denoted as $U_e$.
• Figure 4: (a) The scatter plot between the convection speed estimated from the DTS measurements ($U_C$) and the mean wind speed from EC system ($U$) at the clearcut. The dash-dotted black line show the 1:1 relationship while the blue dash-dotted line is the best fit line. (b)--(c) The ratios $U_C/U$ are plotted against the turbulence intensities $\sigma_u/U$ for the cases when the direction of the mean wind was either along or perpendicular to the forest edge. For the perpendicular case, the wind directions are further subdivided when the wind was approaching directly from the forest or from the clearcut. (d) The scatter plot between $U_e$ and $U$ is shown, where $U_e$ is obtained from the $r_p$-$\tau$ relationship. The black dash dotted line indicates the 1:1 relationship. (e) The relationship between the square of the sweeping speed ($V^2$) and turbulence kinetic energy (TKE) is shown for the DTS cable sections 1--5 (along-wind conditions). The TKE is obtained from the EC system in the middle of the clearcut. The black, magenta, and red dash-dotted lines indicate the relationships $V^2 \approx \rm TKE$, $V^2 \approx \rm 2.16 \ TKE$, and $V^2 \approx \rm 2.25 \ TKE$, respectively. The latter two are obtained from everard2021sweeping for flows over a vineyard canopy.
• Figure 5: (a) The scale-dependent convection speeds ($U_C(\kappa z)$) are plotted against the streamwise wavenumbers ($\kappa$) computed directly from the DTS spatial information. The wavenumbers are normalized by the measurement height ($\kappa z$) while $U_C(\kappa z)$ values are scaled by the convection speed $U_e$. The gray- and red-colored lines denote the along- and perpendicular-wind cases, respectively. The error bars indicate the spread, computed as one standard deviation from the ensemble mean. (b) Same as in (a), but the $U_C(\kappa z)$ values are scaled by $U_C$. The various fits to the scale-dependent convection speeds are shown by the dash-dotted lines (see the legend).