# Seasonal Dynamics of Flux Footprint for a Measuring Tower in Southern Taiga via Modeling and Experimental Data Analysis

^{*}

## Abstract

**:**

_{0}were used to estimate the footprint for canopy sources. The Lagrangian simulation (LS) approach driven by flow statistics from measurements and modeling was used to estimate the footprint for ground-located sources. The Flux Footprint Prediction (FFP) tool for assessing canopy flux footprint applied as the option in the EddyPro v.7 software was inspected against analytical and LS methods. For model comparisons, two parameters from estimated footprint functions were used: the upwind distance (fetch) of the peak contribution in the measured flux (X

_{max}) and the fetch that contributed to 80% of the total flux (CF

_{80}). The study shows that X

_{max}varies slightly with season but relies on wind direction and time of day. All methods yield different X

_{max}values but fall in the same range (60–130 m, around 2–5 h); thus, they can estimate the maximum influence distance with similar confidence. The CF

_{80}values provided by the FFP tool are significantly lower than the CF

_{80}values from other methods. For instance, the FFP tool estimates a CF

_{80}of about 200 m (7 h), whereas other methods estimate a range of 600–1100 m (25–40 h). The study emphasizes that estimating the ground source footprint requires either the LS method or more complex approaches based on Computational Fluid Dynamics (CFD) techniques. These findings have essential implications in interpreting eddy-flux measurements over the quasi-homogeneous forest.

## 1. Introduction

**r**′ is the separation between measurement and forcing, and $\Re $ is the integration domain. During the last decades, considerable progress has been made in developing mathematical tools that allow for estimating the actual “source area” affecting the sensor response. These include analytical methods [10,11,12], the use of Lagrangian stochastic (LS) models [13,14,15,16,17], and the employment of models based on numerical solutions of the Navier–Stokes equations [18,19]. Each class includes models with different levels of complexity and numerical demands. The advantages and disadvantages of existing models are given in detail in the following reviews on this subject [20,21,22,23].

## 2. Materials and Methods

#### 2.1. Research Area, Site Measurement Design, and Data Selection

_{2}/H

_{2}O gas analyzer LI-7200A (LI-COR Inc., Lincoln, NE, USA). Since April 2015, carbon dioxide, water vapor concentrations, and air temperature were measured along a vertical profile at eight heights (0.5, 1, 2, 7, 14.5, 19.5, 29.5, and 42.0 m) using the AP200 integrated CO

_{2}and H

_{2}O atmospheric profile system (Campbell Scientific, Logan, UT, USA). Also, at the same heights, wind velocity and wind direction were measured along a vertical profile using DS-2 sonic anemometers (Decagon Devices, Inc., Pullman, WA, USA).

_{2}fluxes using the 0–2 flag policy according to [30].

_{2}flux were chosen.

#### 2.2. Flux Footprint Estimation

_{m})). Throughout this text, the term “footprint” will be used for brevity to refer to the entire above definition. As a result, calculating the footprint for sources located within the forest canopy can be done analytically, requiring only basic knowledge of aerodynamic parameters of canopy flow, such as displacement height d and aerodynamic roughness z

_{0}. Two analytical models developed by Schuepp et al. (SP) [10] and Kormann and Meixner (KM) [12] are used for this purpose. These models have varying assumptions for the wind speed profile and eddy diffusivity within the surface boundary layer.

_{0}, to simplify and make comparisons among different footprint models. We also used LS techniques in forward mode to estimate the ground footprint, with sources near the soil surface at z = 0.1 m.

#### 2.3. Estimation of Aerodynamic Properties

^{−1}K

^{−1}), T

_{v}is the virtual temperature, g is the acceleration due to gravity (9.81 m s

^{−2}), and ${H}_{v}$ is the buoyancy (virtual heat) flux.

_{0}from Equation (2). The literature offers recursive methods that enable the calculation of both parameters using a single measuring point (e.g., [41]). Graf et al. [42] examined those methods and concluded that it is essential to compare the results of several methods rather than rely on a single one. They recommended using an ensemble average or median of the results to achieve more reliable estimates, potentially after eliminating methods that produce outliers. In addition, a shear or roughness layer may form at the canopy top, which can disrupt the logarithmic wind speed solution [43]. Recently, Cintolesi et al. [44] discovered that in a forest with equivalent geometric features and measurement methods as the Ru-Fyo site, the roughness layer extended to the highest point of measurement. As a result, a complex analytical solution was necessary to estimate d and z

_{0}.

_{0}, we apply wind speed measurement ${u}_{29.5}$ and ${u}_{42}$ from levels ${z}_{29.5}$ = 29.5 m and ${z}_{42}$ = 42.0 m, respectively, and dynamical velocity ${u}_{*}$ from 42 m. Assuming the log-law profiles above the forest and the fact that these two levels are above the forest top (see Section 2.1), d is estimated as

## 3. Results and Discussion

#### 3.1. Measurements

_{0}. The behavior of ${u}_{*}$ (Figure 2A) through three considered years is quite similar, with relatively small differences in absolute values associated with different weather conditions in different seasons. The behavior of dynamical velocity values has a clear day course, with the highest values in the afternoon and the lowest ones at night. In general, the dynamical, or friction, velocity depends on the atmospheric stability and background wind speed, and, as such, ${u}_{*}$ describes general airflow properties above the forest surrounding the tower. Concerning footprint, increasing ${u}_{*}$ usually results in gaining more information by a sensor from a shorter upwind distance. A decrease in ${u}_{*}$ results in the opposite.

_{0}data plotted in Figure 2A–C, respectively, show that parameters, calculated using whole-day observations, have small variability throughout the year, with mean values of ${u}_{*}$ = 0.45 ms

^{−1}, d = 22 m, and z

_{0}= 1.7 m. Such a result was expected, because the forest is mainly populated by mature coniferous trees. The data suggest that the mean aerodynamically active height of the forest is approximately 27 m (calculated using Equation (6)), which is slightly taller than the maximum height of trees near the tower (see Section 2.1). There was a noticeable difference in parameter values between daytime and nighttime observations, indicating daily changes in stability. The amplitude of parameter values was highest in spring and summer, whereas in winter, it tended to be lowest.

#### 3.2. Footprints

#### 3.2.1. Intermodel Comparison Test

_{2}) experiments in unstable conditions over an open field to evaluate three analytical footprint models (SP, KM, and Hsieh et al. (HS) [57]) and also the FFP model under variable source-receptor settings. The results indicate that the KM model is in good agreement with the EC measurements under ideal conditions compared to other analytical models and the FFP model. The KM model captured both the footprintmaximum and its location. Though results were derived for open field conditions, we can assume that the KM model will demonstrate a better performance than other models also for the forest surface, and it can be considered as a benchmark for comparison of the models used here.

_{0}but different below this level.

#### 3.2.2. Seasonal Dynamics of Footprints

_{max}) and (2) the fetch whose contribution to the measured signal or cumulative flux is 80% (CF

_{80}). The threshold of 80% is chosen for practical reasons to reduce the distance when particles are considered leaving the domain in LS and, as such, to speed up the calculation. Figure 5 shows the seasonal distribution of these two parameters, X

_{max}and CF

_{80}, for different upwind sectors.

_{max}and CF

_{80}for both the analytical models and the FFP. The distribution of X

_{max}and CF

_{80}is similar, and one parameter can be estimated from the other using a specific multiplicator. When using analytical models to estimate CF

_{80}from X

_{max}, a factor of approximately 9 should be used, whereas FFP requires a factor of about 2.5. This is expected, as all flow characteristics, when scaled on ${u}_{*}$, are the same. However, when it comes to LS simulations, the factors are direction-dependent and range from 10 to 15. This is because above the canopy height, the flow characteristics scaled on ${u}_{*}$ are equivalent to those in analytical models and follow the log-law relationship. In contrast, inside the canopy, they are unique in each direction.

_{max}and CF

_{80}confusing or even impossible. For more information, the reader can refer to [31,35]. To simplify things, we assume that the canopy photosynthesis is the primary signal contribution in the afternoon, which makes the canopy footprint a noon footprint of the tower. Similarly, we can assume that the ground footprint describes the night footprint of the tower sensor, considering steam and needle respiration to be minor.

_{80}for different sources are insignificant and vary by approximately one-and-a-half to two times depending on the direction. This is because the air parcel with information coming from the canopy source is transported not only in well-mixed and windy conditions in the upper part of the forest but also through the entire canopy, as is the case with the air parcel released on the ground surface.

_{max}to be further from the tower at night and closer to the tower during the day, although no straightforward stability effect was taken into account. The observed wind speed profiles and dynamical velocity scale exhibit the turbulence behavior of the day. The FFP method estimates X

_{max}differently, which may be due to the method’s sensitivity to stability parameters involved in the footprint estimation. This sensitivity is more direct, because the FFP method uses a prescribed d and z

_{0}.

_{max}and time of day. In spring, X

_{max}is higher at noon and night than during average daytime conditions, whereas the opposite is true in autumn. X

_{max}behaves similarly to that derived by the SP and KM models during the summer months. This is because, as previously mentioned, the LS method relies on flow statistics within the canopy, cf. wind speed at a height of 7 m, and even for canopy sources, flow parameters are not the same as in the analytical models. The behavior of these parameters can be different in different seasons and during other times of the day.

_{max}during winter for noon, night, and whole-day conditions. For ground sources, the daily and noon average X

_{max}estimated by the LS method have similar values, with slightly higher X

_{max}at night. The difference in X

_{max}for ground sources during winter is minimal for canopy sources. X

_{max}for ground sources reaches its minimum values during the winter season.

_{max}, the CF

_{80}seasonal patterns are similar for both the analytical and the FFP models. The SP and KM models do not show significant seasonal variation in their estimated CF

_{80}values. CF

_{80}is located further from the tower at night and closer during the day. The FFP method estimates CF

_{80}to be four times shorter than other methods, with minimal daily and no explicit seasonal dependency. Surprisingly, the LS method shows CF

_{80}patterns similar to analytical methods with direct time-of-day dependence. CF

_{80}estimated by the LS method for ground sources also displays seasonal and daily dependency, with maximum values in summer and at night.

_{max}estimates for the canopy source that are similar to those generated by the KM method and CF

_{80}values that are close to those produced by the SP method. Therefore, for the tower under investigation, the LS method can be replaced by the KM and SP methods, which are less time-consuming. However, the LS method is no substitute for estimating ground footprint. The results of analytical methods can be used to preliminarily determine X

_{max}values for ground sources. As a result, the X

_{max}for a ground source is approximately two-and-a-half to three times further upwind than the canopy source estimated by analytical methods. Similarly, the same can be applied for CF

_{80}using a factor of 1.1 for SP- and 1.3 for KM-estimated values.

_{max}and CF

_{80}derived by the LS method [35]. Additionally, we have simplified the analysis by not considering the turning of wind within the canopy, which causes the transport of air parcels to have a different direction at different levels. Therefore, carefully considering these factors may lead to a directional distribution of X

_{max}and CF

_{80}that differs significantly from what is presented in Figure 6B,D and Figure 7B,D. When analyzing the data, it is essential to consider these factors by utilizing simple analytical or LS models for homogeneous conditions.

## 4. Conclusions

_{0}and can be utilized for any measuring tower with multilevel observations. Using this technique, one can eliminate any subjective guesswork regarding the mean aerodynamic height of the forest surrounding a particular tower.

_{max}and CF

_{80}exist even when looking at seasonal average data.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A. Forward LS Footprint Model

## Appendix B. Kernel Function

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**Figure 1.**(

**A**) Geographical location, (

**B**) satellite image, and (

**C**) photo of the study area in forest stand in southern taiga, Tver region, Russia. Spatial distribution of (

**D**) heights of trees, H, (

**E**) LAI, and (

**F**) main forest types—coniferous (1) and broadleaves (2)—around the tower indicated by black triangle symbol.

**Figure 2.**Seasonal plot of monthly average (thin lines) values of (

**A**) dynamical velocity ${u}_{*}$, (

**B**) displacement height d, and (

**C**) roughness length ${z}_{0}$ for nighttime 0.00–4.00 a.m. (blue lines), noontime 0.00–4.00 pm (red lines), and a whole day (black lines) at the measuring tower for different years. Solid thick lines with circles are seasonal average values.

**Figure 3.**(

**A**) Summer wind speed profiles derived using analytical expressions (lines) and based on three-years observations (filled symbols) for noon (red) and nighttime (blue). The black line is the wind speed profile simulated by SCADIS applying the LAD profiles given in dots. Unfilled symbols are for the 2017 year, for which only wind speed measurements at the height of 19.5 were available. Whiskers are for standard deviation. (

**B**) Flow statistics used in the LS method for footprint estimation based on SCADIS simulations (black lines) and analytical expression (red lines) for noon time.

**Figure 4.**(

**A**) Flux footprints and (

**B**) cumulative fluxes (CF) for canopy- and ground-located sources for average flow conditions during afternoon of summer season. Footprints estimated by analytical methods and by LS model driven by flow statistics based on SCADIS model simulation (LS SCADIS) and provided from analytical expressions (LS analytic) (see Figure 3 and text for details). Smoothed lines for LS simulations are derived from simulated data using the Epanechnikov kernel function (see Appendix B). The dotted line in (

**B**) is for the threshold of CF

_{80}(see text for details).

**Figure 5.**Directional plot of seasonal average fetch of maximal influence (X

_{max}) (

**A**,

**C**,

**E**,

**G**) and fetch of 80% flux contribution (CF

_{80}) (

**B**,

**D**,

**F**,

**H**) of canopy-located sources on measuring tower derived by different methods. The scale of X

_{max}to CF

_{80}is 1:9.

**Figure 6.**Directional plot of seasonal average fetch of maximal influence (X

_{max}) (upper plot, (

**A**,

**B**)) and fetch of 80% flux contribution (CF80) (lower plot, (

**C**,

**D**)) of canopy-located sources (left, (

**A**,

**C**)) and ground-located sources (right, (

**B**,

**D**)) derived by LS method.

**Figure 7.**Seasonal plot of the distance of maximal influence (X

_{max}) (

**A**,

**B**) and the distance of cumulative flux of 80% (CF

_{80}) (

**C**,

**D**) at measuring tower derived by different models for canopy (

**A**,

**C**)- and ground (

**B**,

**D**)-located sources for different time moments. Note that plots for ground-located sources (

**B**,

**D**) have different scales for X

_{max}and CF

_{80}. Abbreviations W, S, Su, and F stand for winter, spring, summer, and fall, respectively.

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## Share and Cite

**MDPI and ACS Style**

Sogachev, A.; Varlagin, A.
Seasonal Dynamics of Flux Footprint for a Measuring Tower in Southern Taiga via Modeling and Experimental Data Analysis. *Forests* **2023**, *14*, 1968.
https://doi.org/10.3390/f14101968

**AMA Style**

Sogachev A, Varlagin A.
Seasonal Dynamics of Flux Footprint for a Measuring Tower in Southern Taiga via Modeling and Experimental Data Analysis. *Forests*. 2023; 14(10):1968.
https://doi.org/10.3390/f14101968

**Chicago/Turabian Style**

Sogachev, Andrey, and Andrej Varlagin.
2023. "Seasonal Dynamics of Flux Footprint for a Measuring Tower in Southern Taiga via Modeling and Experimental Data Analysis" *Forests* 14, no. 10: 1968.
https://doi.org/10.3390/f14101968