the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Field assessments on the impact of CO_{2} concentration fluctuations along with complexterrain flows on the estimation of the net ecosystem exchange of temperate forests
Dexiong Teng
Jiaojun Zhu
Fengyuan Yu
Yuan Zhu
Xinhua Zhou
Bai Yang
CO_{2} storage (F_{s}) is the cumulation or depletion in CO_{2} amount over a period in an ecosystem. Along with the eddy covariance flux and windstream advection of CO_{2}, it is a major term in the net ecosystem CO_{2} exchange (NEE) equation. The CO_{2} storage dominates the NEE equation under a stable atmospheric stratification when the equation is used for forest ecosystems over complex terrains. However, estimating F_{s} remains challenging due to the frequent gusts and random fluctuations in boundarylayer flows that lead to tremendous difficulties in capturing the true trend of CO_{2} changes for use in storage estimation from eddy covariance along with atmospheric profile techniques. Using measurements from Qingyuan Ker Towers equipped with NEE instrument systems separately covering mixed broadleaved, oak, and larch forest towers in a mountain watershed, this study investigates gust periods and CO_{2} fluctuation magnitudes and examines their impact on F_{s} estimation in relation to the terrain complexity index (TCI). The gusts induce CO_{2} fluctuations for numerous periods of 1 to 10 min over 2 h. Diurnal, seasonal, and spatial differences (P < 0.01) in the maximum amplitude of CO_{2} fluctuations (A_{m}) range from 1.6 to 136.7 ppm, and these differences range from 140 to 170 s in a period (P_{m}) at the same significance level. A_{m} and P_{m} are significantly correlated to the magnitude of and random error in F_{s} with diurnal and seasonal differences. These correlations decrease as CO_{2} averaging time windows become longer. To minimize the uncertainties in F_{s}, a constant [CO_{2}] averaging time window for the F_{s} estimates is not ideal. Dynamic averaging time windows and a decisionlevel fusion model can reduce the potential underestimation of F_{s} by 29 %–33 % for temperate forests in complex terrain. In our study, the relative contribution of F_{s} to the 30 min NEE observations ranged from 17 % to 82 % depending on turbulent mixing and the TCI. The study's approach is notable as it incorporates the TCI and utilizes three flux towers for replication, making the findings relevant to similar regions with a single tower.
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The accurate estimation of the net ecosystem exchange (NEE) of carbon dioxide (CO_{2}) in forest ecosystems is crucial for a comprehensive understanding of the global carbon cycle. The eddy covariance (EC) technique has been widely used in forest ecosystems due to its capacity to directly measure the NEE with measurement conditions satisfying the underlying theory. The EC technique is based on a simplified mass conservation equation (after Reynolds averaging), given by
where V_{m} is the volume of dry air in the control volume; c is the CO_{2} mixing ratio; t is the time; h is the measurement height; u, v, and w denote the velocity components in the x, y, and z directions, respectively; and an overbar denotes Reynolds averaging. This equation conceptualizes the NEE within a control volume from the ground to the measurement height (h) while ignoring the horizontal turbulence term divergence (Feigenwinter et al., 2004). In this equation, term I is the CO_{2} storage (F_{s}) representing the change in the average CO_{2} concentration (hereafter [CO_{2}]). Terms II, IIIa, IIIb, and IV represent the vertical turbulent flux (F_{c}); the vertical advection; the interface vertical mass advection, such as the evaporation process (Webb et al., 1980); and the horizontal advection, respectively.
Most flux measurements typically lack solutions for terms III and IV and can only estimate the NEE by summing F_{c} and F_{s}, and a significant number of sites even ignore F_{s}. F_{s} in the vertical gas column within a canopy can be substantial, requiring attention in NEE estimates (Aubinet et al., 2000). F_{s} contributes ∼ 60 % to nocturnal turbulent flux underestimation in forest ecosystems with “ideal” topography (McHugh et al., 2017). During atmospherically stable periods such as the early morning, sunset, and nighttime transitions, F_{s} has an especially significant impact on the NEE. For 30 min ecosystem carbon flux measurements, ignoring F_{s} would cause the NEE to be underestimated (Zhang et al., 2010). The F_{s} value typically ranges from −2 to −5 µmol m^{−2} s^{−1} in the early morning, and it is about 1–3 µmol m^{−2} s^{−1} after sunset for temperate forests. The effect of F_{s} on the NEE of forest ecosystems decreases with an increase in the timescale (Li et al., 2020). However, neglecting the F_{s} value can lead to misunderstanding the CO_{2} exchange processes, such as ecosystem respiration and photosynthesis, and their relationship with key control factors such as solar radiation, temperature, and moisture (McHugh et al., 2017). Therefore, it is imperative not to overlook F_{s} to ensure more precise NEE estimates of forest ecosystems, particularly in complex terrain.
Despite the challenges inherent in monitoring forest conditions, understanding the carbon flux of forest ecosystems in complex terrain or with heterogeneous underlying surfaces remains an area of great interest. Topography complexity plays a complex role in the transportation of momentum, energy, and mass in the atmospheric boundary layer, with direct impacts on airflow patterns, spatiotemporal characteristics, and gas concentration fluctuations (Sha et al., 2021; Finnigan et al., 2020). Differences in airflow along a slope, lateral CO_{2} discharge downhill, and spatiotemporal variations in soil respiration result in the CO_{2} outflow from slopes and valleys lagging behind the flat tops of mountains (de Araújo et al., 2010). At night, under stable atmospheric stratification, cold air moves from the valley forest canopy to the ground and then flows to lowlying areas, causing a “carbon pooling” effect. The gradient of [CO_{2}] below the EC sensors fluctuates significantly, and the coldair discharge above the canopy reduces CO_{2} storage, leading to an underestimation of forest ecosystem respiration (Yao et al., 2011; de Araújo et al., 2008, 2010).
According to the theoretical definition, F_{s} estimates are derived by averaging the [CO_{2}] of the control volume at the beginning and the end of the EC averaging period (30 min or 1 h) and dividing this by the EC averaging period (Finnigan, 2006). The estimation of F_{s} at numerous sites frequently employs a vertical profile system. This approach operates under the assumption that F_{s} represents the integration of the time derivative of the vertically determined columnaveraged [CO_{2}]. It is noteworthy that the columnaveraged [CO_{2}] may not accurately represent the average [CO_{2}] of the control volume in cases of inadequate air mixing, leading to insufficient sampling. A previous study showed that relying solely on towertop measurements can lead to the underestimation of F_{s} by up to 34 % compared to using an eightlevel profile approach (Gu et al., 2012). The NEE magnitude with F_{s} based on a 2 min [CO_{2}] averaging time window (instantaneousconcentration approach) was found to be 5 % higher than that with F_{s} based on a 30 min window (averagingconcentration approach), particularly during the nighttime in the growing season (Wang et al., 2016). A proper measuring system that improves horizontal representativeness can reduce the bias in F_{s} to 2 %–10 % (Nicolini et al., 2018). Most research has examined how the vertical and horizontal gas concentration sampling point distribution affects the uncertainty in F_{s} estimation (Bjorkegren et al., 2015; Wang et al., 2016; Yang et al., 2007, 1999), with a small number of studies examining the effect of [CO_{2}] sampling frequency on F_{s} (Finnigan, 2006; Heinesch et al., 2007). Certain studies have experimentally validated new concepts, such as correlating the gas sampling point concentration with the horizontal distribution (Nicolini et al., 2018). Some studies have approached the true value theoretically, such as through defining the control volume represented by flux measurements (Metzger, 2018; Xu et al., 2019). However, the number of complete column samples required to describe the columnaveraged [CO_{2}] of each 30 min or 1 h F_{s} estimate is still undetermined.
Previous studies have emphasized the significance of F_{s} to the NEE and the influence of [CO_{2}] dynamics on F_{s} estimates in complex terrain. To overcome any disparities between sensors and obtain precise changes in the [CO_{2}] gradient above and below the forest canopy, individual gas analyzers are extensively utilized to measure [CO_{2}] levels vertically (Siebicke et al., 2011). However, a single gas analyzer introduces time delays when monitoring multipoint [CO_{2}] curves. Accurately determining the F_{s} estimates can be challenging due to the spatial and temporal resolution of [CO_{2}] measurements (Wang et al., 2016). The random error in the F_{s} estimates using one complete column sample is considerably high due to shortterm [CO_{2}] fluctuations (Nicolini et al., 2018). The calculation of F_{s} using timeaveraged [CO_{2}] profiling leads to significant information loss at a high frequency, resulting in a substantial underestimation bias. Furthermore, timeaveraged [CO_{2}] profiling is employed to represent the [CO_{2}] average within the control volume due to resource constraints. This leads to the systematic bias and random error in F_{s} estimates being irreconcilable. This issue necessitates further efforts to characterize [CO_{2}] fluctuations across different sites and to demonstrate the mechanisms influencing F_{s} magnitudes, F_{s} uncertainties, and their contributions to NEE observations in complex terrain. Thus, this study aims to bridge this gap by introducing a statistical method to estimate F_{s} values and their uncertainties.
This paper employs an innovative EC experimental setup with three flux towers (Qingyuan Ker Towers) to monitor three typical types of temperate forest stands located in complex terrain in northeastern China. This study introduces a decisionlevel fusion model based on weighting the underestimation bias and random error in F_{s} to obtain more accurate results. The objectives of this study were to (1) compare diurnal, seasonal, and spatial differences in [CO_{2}] fluctuations, F_{s}, and its uncertainty; (2) examine the variation in F_{s} uncertainty with different [CO_{2}] averaging time windows; and (3) investigate the response of F_{s} and its uncertainty to [CO_{2}] fluctuations, wind above the canopy, and terrain complexity, quantifying the impact of F_{s} on the NEE estimates under these conditions.
2.1 Study site and instrumental setup
This study was conducted in temperate forests in a watershed based on Qingyuan Ker Towers (Zhu et al., 2021; Gao et al., 2020), situated in northeast China (41°50^{′} N, 124°56^{′} E). The region experiences a temperate continental monsoon climate, with an average annual temperature of 4.3 °C and annual rainfall of 758 mm from 2010 to 2021 (Li et al., 2023). Qingyuan Ker Towers consist of three 50 m high EC towers (Fig. 1) that observe a mixed broadleaved forest (MBF), a Mongolian oak forest (MOF), and a larch plantation forest (LPF).
Basic information regarding Qingyuan Ker Towers in this study is presented in Table 1. The CPEC310 integrated system from Campbell Scientific, comprising an EC155 closedpath infrared gas analyzer (IRGA) and a CSAT3A sonic anemometer, was employed to monitor the threedimensional wind speed and CO_{2} and H_{2}O concentrations (10 Hz). An atmospheric profiling system (AP200, Campbell Scientific, Inc., Logan, UT, USA) was utilized to measure the CO_{2} and H_{2}O concentrations with eight height levels. Each level was measured for 15 s (with 10 s for the flushing of the manifold and 5 s for logging the average), leading to a measurement cycle of 2 min. Due to calibration, filter changes, and rugged weather, 10 % of CPEC310 data and 3 % of AP200 data were missed in our study period.
2.2 Calculation of storage flux
Averaging [CO_{2}] in a time window was utilized to calculate the F_{s} values, in addition to data on the air pressure, CO_{2} and H_{2}O molar fractions, and air temperature at different heights above the ground surface (Finnigan, 2006; Montagnani et al., 2018; Xu et al., 2019). The molar mixing ratio and mass mixing ratio are quantities conserved with the variation in air temperature, air pressure, and water vapor concentration, whereas the molar fraction is not. This study determined F_{s} using the molar mixing ratio obtained from CO_{2} and H_{2}O molar fraction observations, applying the ideal gas law and Dalton's partial pressure law (Montagnani et al., 2009). The water vapor molar mixing ratio (χ_{v}) in mmol mol^{−1} is given by
where c_{v} is the water vapor molar fraction in mmol mol^{−1}. The CO_{2} molar mixing ratio (χ_{c}) in µmol mol^{−1} is given by
where c_{c} is the CO_{2} molar fraction in µmol mol^{−1}.
The dry air density (${\stackrel{\mathrm{\u203e}}{\mathit{\rho}}}_{\mathrm{d}}$) in mol m^{−3} is calculated as follows:
where R^{∗} is the air gas constant (8.31441 Pa m^{3} K^{−1} mol^{−1}), $\stackrel{\mathrm{\u203e}}{P}$ is the air pressure in pascals, and $\stackrel{\mathrm{\u203e}}{T}$ is the average air temperature in degrees Celsius. M_{d} and M_{v} are the dry air and water vapor molar mass (18.015 g mol^{−1}), respectively. M_{d} is calculated from the CO_{2} molar mixing ratio (Khélifa et al., 2007):
where M_{c} is the carbon molar mass (12.011 g mol^{−1}).
The F_{s} values estimated from eightlevel profiles are calculated as follows:
where ${\stackrel{\mathrm{\u203e}}{\mathit{\chi}}}_{\mathrm{c}}$ is the average CO_{2} molar mixing ratio and Δh_{i} is the height represented by each level.
When measuring F_{s} by sampling CO_{2} at several levels using a single analyzer, synchronous observations of the CO_{2} profile are impractical. Consequently, discrete temporal sampling and time averaging become necessary. To ensure the temporal alignment of F_{s} with F_{c}, the average [CO_{2}] measurements within the control volume at the beginning and end (t) of an averaging period (30 min) are calculated by averaging over a time window (τ min) as follows:
where τ = 4, 8, …, 28 min. Theoretically, the time window should be kept as short as possible in comparison to the turbulence flux averaging period to comply with the principle of Reynolds decomposition. We use large windows here for CO_{2} averaging in an attempt to demonstrate the effects of different window sizes on the accuracy of storage flux estimates.
2.3 Data analysis
To evaluate the impact of [CO_{2}] fluctuations on F_{s} measurements and corresponding uncertainty, empirical modal decomposition (EMD) and Fourier spectrum analysis (FSA) were used to extract the period and amplitude of fluctuations in the highfrequency [CO_{2}] time series (10 Hz). EMD was used to decompose the [CO_{2}] time series into intrinsic mode functions based on local signal properties (Huang and Wu, 2008), which yielded instantaneous frequencies as functions of time and allowed for the identification of embedded structures of eddies. EMD is applicable to nonlinear and nonstationary processes (Huang et al., 1998). The period and amplitude of [CO_{2}] fluctuations above the forest canopies reflected the eddy size. Subsequently, the maximum period and amplitude of [CO_{2}] fluctuations in the short term (2 h) were indicative of large eddies under the influence of gusts.
Due to the diurnal and seasonal variability in flux measurements, this study defined the transition period and growing season. The solar elevation angle was used to define the transition period as 1 h before sunrise (sunset) to 2 h after sunrise (sunset). The growing degree days (GDDs) were calculated using the base temperature (T_{base}) to determine the beginning and end of the growing season, and the formula for this was as follows (McMaster and Wilhelm, 1997):
where T_{base} is 6 °C. Considering the persistent need for temperature levels to support vegetation growth, the fourth day of the first GDD greater than zero (less than zero) over a span of 5 consecutive days was defined as the starting (ending) time of the growing season.
The main data processing and analysis steps are outlined below:

EMD and Fourier spectrum analysis of [CO_{2}] highfrequency time series were used to extract the maximum amplitude (A_{m}) and corresponding period (P_{m}) of [CO_{2}] fluctuations every 2 h. The data were divided into two subsets based on P_{m}, with a cutoff of 150 s.

CO_{2} storage fluxes were calculated for different [CO_{2}] averaging time windows (τ), ranging from 4 to 28 min in increments of 4 min.

The standardized major axis (SMA) regression model (Warton et al., 2012) was used to compare the slope differences (bias) between F_{s_τ} and F_{s_28} for different P_{m} values and the forest stands. The SMA model offers routines for comparing parameters a and b among groups for symmetric problems.

The normalized root mean square error (NRMSE) and slope were used to evaluate the relative error and bias between F_{s_τ} and F_{s_28}. The NRMSE is calculated as
$$\begin{array}{}\text{(9)}& \text{NRMSE}=\mathrm{100}\times \sqrt{{\displaystyle \frac{{\sum}_{i=\mathrm{1}}^{N}{\left({F}_{\mathrm{s}\mathit{\_}\mathit{\tau}}^{\left(i\right)}{F}_{\mathrm{s}\mathrm{\_}\mathrm{28}}^{\left(i\right)}\right)}^{\mathrm{2}}}{{\sum}_{i=\mathrm{1}}^{N}{\left({F}_{\mathrm{s}\mathrm{\_}\mathrm{28}}^{\left(i\right)}\stackrel{\mathrm{\u203e}}{{F}_{\mathrm{s}\mathrm{\_}\mathrm{28}}}\right)}^{\mathrm{2}}}}},\end{array}$$where i indicates the ith observation.

The normalized weighting coefficient (w) of F_{s_τ} was estimated based on the NRMSE and slope (Wang et al., 2020). Details are shown in Appendix A1. Then, using the decisionlevel fusion model, F_{s_comb} was calculated as
$$\begin{array}{}\text{(10)}& {F}_{\mathrm{s}\mathrm{\_}\mathrm{comb}}={w}_{\mathrm{1}}^{\ast}\cdot {F}_{\mathrm{s}\mathrm{\_}\mathrm{4}}+{w}_{\mathrm{2}}^{\ast}\cdot {F}_{\mathrm{s}\mathrm{\_}\mathrm{8}}+\mathrm{\dots}+{w}_{\mathrm{7}}^{\ast}\cdot {F}_{\mathrm{s}\mathrm{\_}\mathrm{28}}.\end{array}$$
The decisionlevel fusion model automatically assigned weights to F_{s} based on different [CO_{2}] averaging time windows. Its purpose in this study was to balance the relative error and bias in F_{s} estimates caused by [CO_{2}] sampling. The analysis was performed using the EMD and smatr R packages (Warton et al., 2012; Huang et al., 1998).
2.4 Uncertainty analysis
To improve the accuracy of estimating the uncertainty in F_{s} using an individual tower, this work has made modifications to the 24 h difference method by extending the sampling time windows and applying meteorologicalcondition constraints (Hollinger and Richardson, 2005). This method trades time for space to estimate the uncertainty in F_{s}. To determine the uncertainty in F_{s}, expressed as σ(ε_{s}), in this case, we compared the observations at moment i within a day to the average of several observations during a similar period and with similar meteorological conditions. The specific computations were as follows:
where Ω is the moment interval (i−0.5 h, i+0.5 h) within a certain time window (15 d); I is the indicator function; the set represented by Λ consisted of elements that meet similar meteorological conditions, including u_{∗}, air temperature (T_{a}), and sensible heat flux (H); ${\mathit{\sigma}}_{{u}_{\ast}}$, ${\mathit{\sigma}}_{{T}_{\mathrm{a}}}$, and σ_{H} are the standard deviation of u_{∗}, T_{a}, and H, respectively; δ is the threshold of Euclidean distance; and ε_{s} is the random error in F_{s}.
After estimating the uncertainty in F_{s}, this study extended the work conducted by Richardson et al. (2008) to analyze its relationship with the magnitude of flux measurements ($\left{F}_{\mathrm{s}}\right$), [CO_{2}] fluctuations (A_{m} and P_{m}), u_{∗}, and the terrain complexity index (TCI). A comprehensive description of the TCI can be found in Appendix A2. This relationship can be approximated using the following equation:
where the nonzero intercept term β_{0} indicates the size of the random uncertainty as x_{i} approaches 0, which varies with the observation site, with larger values of β_{0} indicating greater uncertainty. The slope term β_{i} indicates the sensitivity of the size of the random uncertainty in x_{i}, with smaller β_{i} values indicating a probability distribution of uncertainty closer to white noise.
3.1 Characterization of [CO_{2}] fluctuation and F_{s} variations
The highfrequency [CO_{2}] time series above the forest canopies were decomposed using EMD, and this was followed by spectral analysis to extract the fluctuation period and amplitude of [CO_{2}] on different timescales. As depicted in Fig. 2, it became evident that the [CO_{2}] above the canopies displayed shortterm fluctuations with periods ranging from 1 to 10 min, and the amplitude of these fluctuations showed an increasing trend with longer periods. This observation strongly suggests the presence of large eddies influenced by gusts above the canopies, and these eddies were responsible for the increasing amplitude of [CO_{2}] fluctuations as their size increased.
^{1} DT represents daytime. ^{2} NT represents nighttime. ^{3} TP represents the transition period. ^{4} A_{m} represents the maximum amplitude of shortterm CO_{2} concentration fluctuations. ^{5} P_{m} represents the corresponding period of maximum amplitude. ^{6} MBF represents mixed broadleaved forest. ^{7} MOF represents Mongolian oak forest. ^{8} LPF represents larch plantation forest.
To examine the spatiotemporal variations in large eddies, this study compared the A_{m} and P_{m} values above canopies across different forest stands. The analysis utilized data from daytime, nighttime, and transition periods in both the growing and the dormant seasons. The averages of A_{m} and P_{m} for the abovecanopy [CO_{2}] in the three forest stands ranged from 1.588 to 136.667 ppm and from 2.313 to 2.784 min, respectively (Table 2). Figure 3 demonstrates significant seasonal and diurnal differences (P < 0.01) in P_{m}, with higher values during the daytime in the growing season and lower values during the daytime in the dormant season. Moreover, P_{m} was significantly different (P < 0.01) among different forest stands during the same time period, with the MBF stand having the highest values, followed by MOF and then LPF with the lowest values. During the growing season, the A_{m} values were significantly higher than those during the dormant season, with both daytime and nighttime values also exhibiting significant differences (P < 0.01) among different forest stands. This observation provides evidence of significant spatiotemporal variability in the large eddies influenced by gusts.
To estimate the uncertainty in F_{s} using an individual tower, a comprehensive analysis of the diurnal and seasonal dynamics, as well as the functional relationship between F_{s} and u_{∗}, was necessary. Significant diurnal variations and seasonal differences in F_{s} were observed across the three forest stands, as shown in Fig. 4. During the growing season, the median diurnal variation in F_{s} for the three forest stands ranged from −2.960 to 2.647 µmol m^{−2} s^{−1}, whereas during the dormant season, it ranged from −1.306 to 1.012 µmol m^{−2} s^{−1}. Comparing the extent of F_{s} diurnal variation among the three forest stands, MBF exhibited the largest extent during the growing season, while the extents of the three forest stands were similar during the dormant season. Notably, it was observed that the amplitudes for higher P_{m} values were greater than those for lower P_{m} values. This observation indicates that the larger the eddies, the greater the magnitude of F_{s}.
Furthermore, a u_{∗} threshold value was identified for the variation in F_{s} with u_{∗} during the daytime in both the dormant and the growing seasons (Fig. 5). When u_{∗} fell below the u_{∗} threshold, the magnitude of F_{s} ($\left{F}_{\mathrm{s}}\right$) decreased with increasing u_{∗}. Conversely, when u_{∗} exceeded the u_{∗} threshold, $\left{F}_{\mathrm{s}}\right$ tended to remain relatively constant. Notably, a maximum point for $\left{F}_{\mathrm{s}}\right$ was observed when u_{∗} was less than 0.5 m s^{−1} during the growing season, whereas this was not the case during the dormant season. This phenomenon was particularly evident during the nighttime and transition periods of the growing season, when $\left{F}_{\mathrm{s}}\right$ exhibited an initial increase followed by a subsequent decrease with u_{∗}. These observations strongly indicate that the effect of the turbulent mixing strength on $\left{F}_{\mathrm{s}}\right$ over complex terrain is nonlinear and exhibits diurnal and seasonal differences.
3.2 Effect of [CO_{2}] fluctuations on F_{s} and its uncertainty
To investigate the influence of the [CO_{2}] fluctuation periods on the error in F_{s} measurement, this study computed the diurnal average of the standard deviation σ(ε_{s}) of the 30 min F_{s} uncertainty (ε_{s}) separately for different P_{m} values and the seasons. The overall distribution of ε_{s} showed a nonnormal distribution with a high peak (kurtosis > 2 and P < 0.05; results presented in Tables S1–S4 in the Supplement). The daily variation curves of σ(ε_{s}) in various [CO_{2}] averaging time windows are presented in Fig. 6. It was observed that the diurnalvariation range of σ(ε_{s}) was higher during the growing season compared to the dormant season, regardless of the P_{m} lengths, indicating a seasonal difference independent of P_{m}. Additionally, during the growing season, both MBF and MOF demonstrated evident diurnal variation in σ(ε_{s}), with the peak occurring at night and the trough during the daytime. The diurnalvariation range of σ(ε_{s}) varied across the three forest stands, with MBF exhibiting the largest amplitude.
Furthermore, a significantly positive correlation was observed between σ(ε_{s}) and $\left{F}_{\mathrm{s}}\right$ (P < 0.01), with site, seasonal, and diurnal differences (Fig. 7). The relationship between σ(ε_{s}) and $\left{F}_{\mathrm{s}}\right$ was characterized by intercepts and slopes ranging from 1.99 to 2.82 µmol m^{−2} s^{−1} and from 0.24 to 0.28, respectively (results presented in Tables S5–S6). Both decreased as the [CO_{2}] averaging time window increased, with the growing season exhibiting larger values compared to the dormant season (results shown in Tables S5 and S6). These findings suggest that increasing the [CO_{2}] averaging time window results in a reduction in the random error in F_{s} and the correlation coefficient between σ(ε_{s}) and $\left{F}_{\mathrm{s}}\right$. This indicates a decrease in variability in σ(ε_{s}) and behavior similar to white noise.
To assess the impact of [CO_{2}] fluctuations on the error and bias in F_{s} measurement, this study compared the NRMSE and slopes of F_{s} based on different [CO_{2}] averaging time windows, with reference to the baseline F_{s_28}, across various P_{m} values, time periods, and sites. As shown in Fig. 8, the NRMSE decreased and approached convergence as the [CO_{2}] averaging time windows increased. During both the daytime and the nighttime in the growing season, the NRMSE corresponding to higher P_{m} was greater than that corresponding to lower P_{m}, while the opposite trend was observed during the dormant season. Additionally, the longer the [CO_{2}] averaging time window, the greater the relative underestimation of F_{s}.
A comparison of slopes between F_{s_4} and F_{s_28} in the three forest stands revealed interesting patterns, as depicted in Fig. 9. During the growing season, the slopes corresponding to the lower P_{m} of [CO_{2}] fluctuations were consistently lower than those for the higher P_{m}, indicating that the effect of P_{m} on F_{s} uncertainty decreased with increasing [CO_{2}] averaging time windows. However, for the MBF stand (Fig. 9d and g), the slopes corresponding to the lower P_{m} of [CO_{2}] fluctuations during the dormantseason nighttime were actually greater than those for the higher P_{m}, primarily due to diurnal variations in the daily dynamics of F_{s}. Overall, the influence of P_{m} on F_{s} uncertainty decreased with increasing [CO_{2}] averaging time windows. This suggests that averaging [CO_{2}] reduced the effect of gusts on the random uncertainty in estimating F_{s} but led to a systematic underestimation of F_{s}.
To analyze the effect of [CO_{2}] fluctuations on $\left{F}_{\mathrm{s}}\right$ in complex terrain, this study developed a multiple linear regression model, considering the interaction effects of turbulent mixing and terrain complexity on $\left{F}_{\mathrm{s}}\right$, as shown in Fig. 10. A_{m} exhibited a significant positive correlation with $\left{F}_{\mathrm{s}}\right$ in all time periods (P < 0.05). Conversely, P_{m} showed a significant negative correlation with $\left{F}_{\mathrm{s}}\right$ during the dormantseason daytime, the growingseason daytime, and the transition periods (P < 0.05). Additionally, their correlation coefficient decreased with increasing τ. In Fig. 10d and e, a u_{∗} threshold is observed during the growingseason nighttime. When u_{∗} was below the threshold, higher TCI values resulted in smaller $\left{F}_{\mathrm{s}}\right$ values, whereas when u_{∗} was above the threshold, higher TCI values led to larger $\left{F}_{\mathrm{s}}\right$ values. During the growingseason nighttime and transition periods, u_{∗} showed a significant negative correlation (P < 0.05) with $\left{F}_{\mathrm{s}}\right$, and the correlation coefficient decreased with increasing TCI values. These observations suggest that the effect of turbulent mixing on the $\left{F}_{\mathrm{s}}\right$ uncertainty is regulated by terrain complexity.
A multiple linear regression model was used to analyze the effect of [CO_{2}] fluctuations on the random uncertainty in F_{s}, σ(ε_{s}), in complex terrain. This model considered the interaction effects of [CO_{2}] fluctuations and terrain complexity on σ(ε_{s}), as shown in Fig. 11. As evident from Fig. 11a and e, A_{m} exhibited a significant positive correlation (P < 0.05) with σ(ε_{s}) during both the dormant season's nighttime and the growing season. Throughout the transition period of the growing season, P_{m} displayed a significant negative correlation with σ(ε_{s}) (P < 0.05). The magnitude of these correlation coefficients decreased with the increasing [CO_{2}] averaging time windows. During the transition period of the dormant season, a TCI threshold was observed, with P_{m} showing a significant positive correlation (P < 0.05) with σ(ε_{s}) when the TCI was below the threshold and a significantly negative correlation (P < 0.05) with σ(ε_{s}) when the TCI exceeded the threshold (Fig. 11b and f). The u_{∗} value showed a significantly negative correlation with σ(ε_{s}) during the daytime and transition periods of the growing season (P < 0.05), while in other time periods, u_{∗} was significantly positively correlated with σ(ε_{s}) (P < 0.05). $\left{F}_{\mathrm{s}}\right$ demonstrated a significant positive correlation with σ(ε_{s}) (P < 0.05) in all time periods, with its correlation coefficient being greater during the growing season than during the dormant season. These observations suggest that the relationship between the random uncertainty in F_{s} and [CO_{2}] fluctuations is moderated by topographic complexity. Increasing the [CO_{2}] averaging time window reduces the effect of [CO_{2}] fluctuations on the random uncertainty in F_{s}.
3.3 Effect of CO_{2} storage flux uncertainty in NEE observations
The 30 min F_{s_comb} was obtained by weighting the bias and random error in F_{s} using different [CO_{2}] averaging time windows and P_{m} values. This study then focused on the magnitude of F_{s_comb} in relation to the F_{c} magnitude and its diurnal, seasonal, and site variations. To assess the significance of F_{s} in NEE observations, the relative contribution ratio of F_{s_comb} magnitude ($\left{F}_{\mathrm{s}\mathrm{\_}\mathrm{comb}}\right/\left(\right{F}_{\mathrm{c}}+{F}_{\mathrm{s}\mathrm{\_}\mathrm{comb}}\left\right)$) was employed. $\left{F}_{\mathrm{s}\mathrm{\_}\mathrm{comb}}\right/\left(\right{F}_{\mathrm{c}}+{F}_{\mathrm{s}\mathrm{\_}\mathrm{comb}}\left\right)$ showed a decreasing trend towards convergence with increasing u_{∗} (Fig. 12). On average, $\left{F}_{\mathrm{s}\mathrm{\_}\mathrm{comb}}\right/\left(\right{F}_{\mathrm{c}}+{F}_{\mathrm{s}\mathrm{\_}\mathrm{comb}}\left\right)$ ranged from 17.2 % to 82.0 %, with a higher value during the dormant season compared to the growing season. This indicated that as turbulence intensity increased, the contribution of F_{s} to the NEE in forests decreased to a constant value. Nevertheless, even under strong turbulence intensity, F_{s} still played a significant role in the NEE observations of forests in complex terrain.
^{a} GD represents the growing season's daytime. ^{b} GN represents the growing season's nighttime. ^{c} GT represents the growing season's transition period. ^{d} DD represents the dormant season's daytime. ^{e} DN represents the dormant season's nighttime. ^{f} DT represents the dormant season's transition period. ^{g} P_{m} represents the corresponding period of maximum amplitude. ^{h} A_{m} represents maximum amplitude. ^{i} u_{∗} represents friction velocity. ^{j} TCI denotes the terrain complexity index.
${}^{\ast \ast \ast}$ P < 0.001. ${}^{\ast \ast}$ P < 0.01. ^{∗} P < 0.05.
As indicated in Table 3, both P_{m} and the TCI exhibited a significant positive correlation with $\left{F}_{\mathrm{s}\mathrm{\_}\mathrm{comb}}\right/\left(\right{F}_{\mathrm{c}}+{F}_{\mathrm{s}\mathrm{\_}\mathrm{comb}}\left\right)$ (P < 0.05), while both A_{m} and u_{∗} showed a significant negative correlation with $\left{F}_{\mathrm{s}\mathrm{\_}\mathrm{comb}}\right/\left(\right{F}_{\mathrm{c}}+{F}_{\mathrm{s}\mathrm{\_}\mathrm{comb}}\left\right)$ (P < 0.05). Notably, seasonal variations in correlation coefficients were observed. The correlation between u_{∗} and $\left{F}_{\mathrm{s}\mathrm{\_}\mathrm{comb}}\right/\left(\right{F}_{\mathrm{c}}+{F}_{\mathrm{s}\mathrm{\_}\mathrm{comb}}\left\right)$ was more pronounced during both the dormant season's transition period and the growing season, and it decreased with increasing TCI values during the dormant season's daytime and nighttime.
To evaluate the impact of F_{s_comb} on NEE_{obs} (F_{c}+F_{s}), we further evaluated the slope (with intercept terms forced to zero) and NRMSE of F_{c}+F_{s_comb} compared to F_{c}+F_{s_28}, as presented in Tables S7 and S8. F_{s_28} in the three forest stands was underestimated by 28.6 %–33.3 % compared to F_{s_comb}, and the NRMSE of F_{s_comb} versus F_{s_28} ranged from 59.2 % to 67.2 %. NEE_{obs} with F_{s_28} was underestimated by 1.9 %–4.3 % compared to NEE_{obs} with F_{s_comb}. The NRMSE of NEE_{obs} with F_{s_comb} versus F_{s_28} in the three forest stands ranged from 16.0 % to 25.4 %. The analysis suggested that combining the F_{s} values based on different averaging [CO_{2}] time windows in the decisionlevel fusion model could successfully weight potential underestimation bias and random uncertainties.
The influences of F_{s} on the relationship between NEE observations and meteorological drivers indicated the effect of uncertainty in F_{s} estimates on NEE observations. Our analysis showed that the correlations between NEE observations derived from F_{c}+F_{s} and both photosynthetic photon flux density (PPFD) and air temperature are lower compared to those obtained from F_{c} alone (Figs. S1 and S2 in the Supplement). Additionally, the estimated lightsaturated net CO_{2} assimilation (A_{max}) is greater when NEE observations are estimated by F_{s}+F_{c}, as opposed to when the NEE is estimated solely by F_{c}. This suggests that F_{s} significantly affects the daytime NEE and can correct the estimation of A_{max} and related parameters. The relationship between NEE observations and PPFD is influenced by the size of the averaging time window the F_{s} measurement. A larger averaging window results in less random uncertainty in the F_{s} estimation, thereby increasing the correlation between NEE observations and meteorological drivers, including PPFD and T_{a}.
4.1 Shortterm [CO_{2}] fluctuations above the forest canopy and F_{s} estimates in complex terrain
Compared to flat and uniform underlying surfaces, complex terrain and heterogeneous canopies modify the trajectory, speed distribution, and direction of the airflow. Increased wind speeds and shifting wind directions also increase turbulent activity above the canopy, facilitating the mixing and dispersion of CO_{2}. This study found that shortterm fluctuations in [CO_{2}] above the canopy exhibited a range of 1 to 10 min (Fig. 2). These fluctuations were characterized by an average P_{m} ranging from 2.313 to 2.784 min (Table 2). Our results are in line with previous research using wavelet analysis, which reported fluctuation periods of [CO_{2}] within and above the forest canopy to be between 14 and 116 s (Cava et al., 2004). These previous observations of the canopy waves during periods of extreme atmospheric stability (when $z/L\gg \mathrm{1}$) exhibited a dominant period of 1–2 min, which is consistent with our findings. The period of [CO_{2}] fluctuations was found to be predominantly influenced by turbulent fluxes and the residence time of CO_{2} within the canopy. This indicated a potential correlation between P_{m} and the residence time of CO_{2} within the canopy. Fuentes et al. (2006) employed a Lagrangian model and calculated the residence time of air parcels released near the ground and in the canopy, finding values ranging from 3 to 10 min and from 1 to 10 min, respectively. Similarly, Edburg et al. (2011) used the standard deviation of [CO_{2}] averages to determine the CO_{2} residence time at different locations, including at the ground, within the canopy, and in their gas mixtures, yielding values of 8.6, 3.6, and 5.6 min, respectively. The results of these simulation experiments are consistent with our study, further supporting the association between [CO_{2}] fluctuations above the forest canopy and CO_{2} residence time.
Tree density and canopy structure also play a role in influencing the air parcel residence time; on flat terrain, the air parcel residence time correlates with u_{∗} (Gerken et al., 2017), and an increase in the vegetation leaf area leads to longer residence times when turbulence is not fully penetrative. During the growing season, forests in our study site exhibit a higher leaf area index and greater canopy densities than during the dormant season (Li et al., 2023), resulting in higher P_{m} values of shortterm [CO_{2}] fluctuations above the canopy (Fig. 3). Additionally, at night, stable atmospheric conditions lead to longer residence times due to suppressed turbulent mixing, resulting in relatively high nighttime P_{m} values compared to daytime and transition periods (Fig. 3).
Complex terrain introduces complex changes into airflow structures, including gravityinduced waves, drainage, and nonlinear waves induced by single gusts, leading to dramatic [CO_{2}] fluctuations. These dynamics contribute to uncertainties in estimating F_{s}. At night, the difference between incoming and outgoing longwave radiation over the valley soil surface and vegetation canopy gives rise to radiative cooling. Subsequently, the air near the soil surface experiences a gravityinduced downslope acceleration, potentially causing katabatic flow. As inertiadriven upslope winds are halted by katabatic acceleration, a local shallow drainage flow is established, reaching a quasiequilibrium state approximately 1.5 h after sunset (Nadeau et al., 2013). Under stable atmospheric conditions, even gentle slopes (around 1°) can generate strong gravitydriven waves (Belušić and Mahrt, 2012). Consequently, advection may complicate the interpretation of nighttime EC measurements at certain relatively gentle sites, but this complexity is not evident during daytime measurements (Leuning et al., 2008). Advection plays a role in depleting the CO_{2} accumulated within the canopy, resulting in lower F_{s} fluxes and establishing an inverse relationship between storage and advection (van Gorsel et al., 2011). The occurrence of larger F_{s} values for high P_{m} values suggests weaker advection compared to low P_{m} values (Fig. 4). In our study, we observed that the F_{s} magnitude was relatively large during nighttime and transition periods, while it was smaller during the daytime (Fig. 4), which is consistent with the findings reported by Wang et al. (2016).
The terrain unevenness and the complexity of canopy structure significantly affect the airflow divergence in the atmospheric boundary layer. This results in weakened air circulation within the canopy and spatial variation in the patterns and extent of airflow separation (Grant et al., 2015). During nighttime and transition periods in a closed canopy, the turbulent coupling state above and below the canopy gradually decouples, eventually reaching complete decoupling as u_{∗} decreases (Fig. 5). However, this decoupling does not lead to stable stratification within the canopy. Despite the occurrence of decoupling and advection in the closed canopy, waves are unlikely to exist within the canopy itself (van Gorsel et al., 2011). As a result, a consistent trend in the variation in F_{s} with τ is observed across the three forest stands during the growing season, independent of P_{m} (Fig. 9). Conversely, in an open canopy where waves are present, the observations of F_{s} become more complex. This complexity could be the primary reason for the variation in F_{s} with [CO_{2}] averaging time windows differing between the three forest stands for low P_{m} values during the dormantseason daytime (Fig. 9). The presence of waves introduces additional variability into the measurements, leading to differences in F_{s} estimates based on different [CO_{2}] averaging time windows in these particular conditions.
4.2 Uncertainty in forest ecosystem F_{s} measurement in complex terrain
The random uncertainty in F_{s} shares similarities with NEE estimation. For example, the magnitude of F_{s} measurements is positively correlated with the standard deviation of random uncertainty in F_{s}. Additionally, the overall distribution of F_{s} measurements exhibits a nonGaussian distribution with a high peak, aligning with the statistical properties of NEE uncertainty (Richardson et al., 2006, 2008). The uncertainty in the storage term depends a great deal on the setup used, together with the biological activity of the ecosystem and the height of the control volume. In addition, various factors contribute to the uncertainty in F_{s} estimates, including the flux measurement footprint variations, sampling frequency, the spatial sampling resolution of CO_{2} and H_{2}O concentrations, and instrumental measurement accuracy. The accuracy and precision requested for the CO_{2} and H_{2}O concentration measurements are ±1 µmol mol^{−1} and ±1 mmol mol^{−1}, respectively (Montagnani et al., 2018). The uncertainty arising from variations in the flux measurement footprint is considerable, typically on the order of tens of percent, which is an order of magnitude higher than typical sensor errors (Metzger, 2018). AP200 adopts buffer volumes to mix the gas. The LI850 analyzer integrated within AP200 exhibits a sensitivity to water vapor of less than 0.1 µmol CO_{2} per mmol mol^{−1} H_{2}O and a sensitivity to CO_{2} of less than 0.0001 mmol mol^{−1} H_{2}O per µmol CO_{2}. Efforts to reduce random errors in [CO_{2}] originating from pressure fluctuations include adding buffer volumes before IRGA pumping tests (Marcolla et al., 2014). The buffer volumes are fully mixed during gas extraction, and a weighted average of [CO_{2}] instantaneous measurements is obtained to minimize the sampling error for each level's [CO_{2}] measurement (Cescatti et al., 2016).
The F_{s} estimates can be influenced by singular eddies that penetrate the canopy (Finnigan, 2006). Accurate calculation of F_{s} requires considering the period of [CO_{2}] fluctuations with the eddy coherence structure. The spectral energy of the F_{s} time series is primarily concentrated between 0.001 and 0.2 Hz (500 and 5 s, respectively). However, even with sampling frequencies of 2 Hz and below, significantly lower F_{s} values are obtained (Bjorkegren et al., 2015). The Nyquist–Shannon sampling theorem dictates that accurate measurements of [CO_{2}] require a sampling period that is no longer than half the period of [CO_{2}] fluctuations. Consequently, to monitor shortterm changes in [CO_{2}], measurements must be taken over a period that is no longer than half of the period corresponding to the maximum amplitude (or major energy) of [CO_{2}] fluctuations. In this study, the average P_{m} for [CO_{2}] fluctuations fell within the range of 2.313–2.784 min (Table 2). Therefore, it is crucial to ensure that the sampling period for [CO_{2}] does not exceed 1.256 to 1.392 min, which corresponds to half the average P_{m} range. Monitoring fluctuations in P_{m} for less than 4 min during a 2 min monitoring period of [CO_{2}] presents a significant challenge. This is a primary reason for the systematic bias and random error in the F_{s} estimate with a singleprofile system being irreconcilable (Wang et al., 2016). Shortterm [CO_{2}] fluctuations are mainly influenced by boundarylayer turbulence, and sampling errors in incomplete fluctuation cycles are superimposed with the real advection flux (anisotropy) dispersion in complex terrain (van Gorsel et al., 2011). This substantially increases the random uncertainty in F_{s} based on shorter [CO_{2}] averaging time windows (Figs. 6 and 8). As a result, the deviation of NEE estimates from the actual value expands.
Fluxes in heterogeneous regions are significantly higher than in uniform regions. The energy transfer from the ground surface to large eddies occurs primarily in areas with pronounced heterogeneity, and this energy distribution is uneven across the region (Aubinet et al., 2012). Once largescale eddies acquire energy, their cascading of energy to smallerscale eddies is influenced by topographic features, leading to variations in these smallerscale eddies along different flow streams (Chen et al., 2023). In complex terrain, the bidirectional airflow within forests along slopes can cause the decoupling of soil CO_{2} fluxes from EC measurements above the forest canopy (Feigenwinter et al., 2008; Aubinet et al., 2003), leading to significant errors in CO_{2} flux measurements. Forest soil serves as the primary source of CO_{2} gas, and regions of high flux over complex terrain act like chimneys, transporting air parcels from the soil surface within forests (Chen et al., 2019). By increasing the number of gas concentration sampling points near the ground, the horizontal representativeness can be enhanced, thereby reducing the bias in the estimation of F_{s} (Nicolini et al., 2018). In situations where turbulence is not well developed and CO_{2} mixing is inadequate, the trend of F_{s} with turbulence intensity aligns with that of advective fluxes, which is the opposite to that of turbulent fluxes (McHugh et al., 2017). The temporal dynamics and amplitudes of F_{s} changes are influenced by topography complexity and wind conditions above the forest canopy (Fig. 10). Locations with more complex and sloping topography at the flux tower are more likely to generate advective fluxes that may not be easily observed at a single point.
Estimating landscape CO_{2} fluxes in complex terrain solely based on measurements from a single flux tower can introduce significant errors and biases that are not acceptable. The magnitude of these errors in F_{s} estimates is dependent on the height of the forest canopy and the endogenous source/sink (Chen et al., 2020). To mitigate errors and biases associated with estimating F_{s} in complex terrain, we employed a regression modeling approach using the decisionlevel fusion model. This method involves computing a weighted average of F_{s} based on different [CO_{2}] averaging time windows, effectively reducing errors and biases in the estimation of F_{s} (see Table 5). In fact, from the definition of storage flux, it can be seen that weighting the storage flux essentially means weighting the [CO_{2}] in the averaging time window, which in turn means replacing spatial sequences with temporal sequences for weighting. The weighting coefficients used to construct the model were based on the relative errors and biases in F_{s} estimation, with the weighting coefficient decreasing as the represented moment's length increased. To obtain more accurate estimates of forest ecosystem F_{s} in complex terrain, further research should focus on understanding the spatiotemporal patterns and dynamics of [CO_{2}].
This study investigated the impact of shortterm [CO_{2}] fluctuations on the estimation of F_{s} in temperate forest ecosystems within complex terrain. Additionally, it examined the F_{s} uncertainty and the contribution of F_{s} to the NEE using data from three flux towers. To enhance F_{s} uncertainty estimation, statistical sampling techniques were applied based on an individualtower approach.
The results highlighted the significance of considering multiple time windows for averaging [CO_{2}] when estimating F_{s}, as [CO_{2}] above the forest canopies exhibited fluctuations with periods ranging from 1 to 10 min. Diurnal, seasonal, and spatial variations were observed in the amplitude and periodicity of [CO_{2}] fluctuations, highlighting the need for thoughtful sampling strategies. The use of individual gas analyzers to sample the CO_{2} in the control volume was inadequate, leading to systematic biases and random errors in the F_{s} estimates. Increasing [CO_{2}] averaging time windows mitigated the effect of [CO_{2}] fluctuations on F_{s} estimates, reducing both their magnitude and their uncertainty.
The study also revealed that the uncertainty in F_{s} followed a nonnormal distribution, with its standard deviation positively correlated with F_{s} magnitude, which has important implications for quality control. To improve F_{s} estimation, a decisionlevel fusion model was introduced, integrating F_{s} estimates from multiple [CO_{2}] averaging time windows, effectively reducing the impact of shortterm [CO_{2}] fluctuations while considering underestimation bias and random errors. The contribution of F_{s} to the NEE exhibited diurnal, seasonal, and spatial variations associated with u_{∗}, contributing to the NEE observations at rates ranging from 17.2 % to 82.0 % depending on the turbulent mixing and terrain complexity. The influence of terrain complexity on the relationship between [CO_{2}] fluctuations, turbulent mixing, and the contribution of F_{s} to the NEE was also evident. The findings from the three flux towers allowed for the generalization of these results beyond the study site. These insights provide crucial scientific support for the practical application of the eddy covariance technique and advance our understanding of accurately estimating the NEE in forest ecosystems in complex terrain.
A1 The weight parameters of the decisionlevel fusion model
For each 30 min CO_{2} storage flux (F_{s}) estimate based on the CO_{2} concentration ([CO_{2}]) averaging time window (τ), the weight in the decisionlevel fusion model can be obtained by weighting the random uncertainty and bias in F_{s_τ}.
The weight of the random uncertainty for F_{s_τ} is expressed as follows:
where σ(ε_{τ}) is the random uncertainty in F_{s_τ}, qualified as the standard deviation.
The weight of the bias for F_{s_τ} is expressed as follows:
where K_{τ} is the slope between F_{s_τ} and F_{s_28}.
Ultimately, the weight of F_{s_τ} in the decisionlevel fusion model can be calculated using the following equation:
where r represents the proportion of the weight of random uncertainty.
A2 Complexterrain index
This study employed a novel descriptor called the terrain complexity index (TCI) to quantify the complexity of the threedimensional terrain. For a given unit area, the TCI equation can be expressed as follows:
where P_{d} represents the volume of terrain above the lowest elevation of an area unit (V_{u}) divided by the product of its largest vertically projected area (S_{v}) and the edge length of the side of the area unit (d), expressed as ${P}_{\mathrm{d}}=\frac{{V}_{\mathrm{u}}}{{S}_{\mathrm{v}}d}$; P_{d} is defined as 1 when S_{v} is 0. Given V_{u}, an increase in S_{v} correlates with a higher degree of terrain complexity. Notably, P_{d} is defined as 1 when the terrain volume is 0 or when the terrain surface of the area unit is parallel to the horizontal plane and is smooth and homogeneous. α_{d} indicates the slope of the area unit. Z_{d} denotes the terrain roughness, which is defined as the ratio of the terrain surface area to the projected horizontal plane (Loke and Chisholm, 2022). The value of Z_{d} was in the range of [1, +∞). The larger the Z_{d}, the more complex the terrain. D_{f} is the fractal dimension of the terrain surface area, which ranged from 2 to 3 and describes the complexity in the spatially selfsimilar structure of the local surface within the area unit and the area unit surface (Mandelbrot, 1967; Taud and Parrot, 2005). Employing the terrain surface area, the boxcounting method was used to estimate the fractal dimension of the unit area. H represents the Shannon–Wiener index and is expressed as $H=\sum _{i=\mathrm{1}}^{n}{P}_{i}\mathrm{ln}\left({P}_{i}\right)$, capturing the uniformity of the spatial distribution of the pixel aspects within the area unit (Brown, 1997). When the aspect of each pixel is divided into 30° segments, P_{i} denotes the proportion of the ith type of pixel aspects within the area unit and n is the total number of pixel aspect types within the area unit. A larger H indicates a more complex terrain. When the number of pixel aspect types in the area unit is kept constant, it is essential to recognize that greater uniformity in the distribution of all pixel aspects in the area unit results in a larger H. Similarly, when the uniformity of the distribution of pixel aspects in the area unit is kept constant, a larger H is achieved with an increase in the observation of the number of pixel aspect types.
To quantify the terrain complexity of the underlying surface around the flux towers, we computed the quartiles of the TCI for all area units within a sector (divided by 30°) with a radius of 380 m. A weighted geometric mean was employed to construct TCI_{s}, which describes the statistical distribution of the TCI of the sector. TCI_{s} represents the topographic complexity of the sector and is calculated using the following equation:
where TCI_{5}, TCI_{25}, TCI_{50}, TCI_{75}, and TCI_{95} are the quartiles of 5 %, 25 %, 50 %, 75 %, and 95 %, respectively. The TCI_{s} values range from 0 to 1, with higher values indicating greater terrain complexity.
Data used in this paper are available at the Science Data Bank (https://www.scidb.cn/en/s/7ZfQZv, Teng et al., 2023) or upon request to the corresponding author.
The supplement related to this article is available online at: https://doi.org/10.5194/amt1755812024supplement.
DT developed the manuscript; JZ was responsible for conceptualizing the idea and designing the research study; TG substantially structured the manuscript; FY contributed to the data collection process; YZ helped in the design and preparation of the figures and tables; XZ and BY revised the manuscript.
The contact author has declared that none of the authors has any competing interests.
Publisher’s note: Copernicus Publications remains neutral with regard to jurisdictional claims made in the text, published maps, institutional affiliations, or any other geographical representation in this paper. While Copernicus Publications makes every effort to include appropriate place names, the final responsibility lies with the authors.
We are grateful to Qingyuan Forest CERN, Chinese Academy of Sciences–Qingyuan Forest, National Observation and Research Station, Liaoning Province, China, for providing forest sites, instrument systems, and logistical support.
This research was financially supported by the National Natural Science Foundation of China (grant no. 32192435), the China Postdoctoral Science Foundation (grant no. 2023M733672), the Key R&D Program of Liaoning Province (2023JH2/101800043), and the Postdoctoral Research Startup Foundation of Liaoning Province of China (grant no. 2022BS022).
This paper was edited by Luca Mortarini and reviewed by Leonardo Montagnani and Ivan Mauricio Cely Toro.
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