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Exchange coefficients (K) are key factors for gradient method fluxes. Different methods of determining K result in different exchange coefficients. Figure 1 shows the mean diurnal variations of the transfer coefficients calculated by the three methods. Overall, the variation trends in the three K types are the same, presenting an obvious diurnal variation pattern. With the increase in radiation and temperature, the air turbulence becomes strong, and the three K types are increased. Around noon, the maximum K appears with smooth changes. It starts to decrease in the later afternoon. However, large differences exist in the three K values. The K value determined by the AG method (KAG) is the largest, and the K calculated with the MBR method (KMBR) is the smallest.
The KAGEC value is between those of KMBR and KAG, and the variables for calculating KAGEC are measured by the EC technique. It can therefore be considered the most appropriate, as validated by comparing its results with those of the EC O3 flux (see section 3.3). The 30-min averaged KAG and KMBR are compared with KAGEC in Fig. 2. Based on the scatterplot, coefficient of determination (R2), and significance level, it is clear that the correlation between KMBR and KAGEC is better than that between KAG and KAGEC. Based on the linear regression equations, KMBR is approximately 0.08 m s−1 lower than the KAGEC in value, while the KAG is larger than the KAGEC overall. The difference becomes small when K is large. The mean values of KAGEC, KMBR, and KAG are 0.20, 0.12, and 0.25, respectively. KMBR is 40% lower and KAG is 25% higher than KAGEC.
The differences in the exchange coefficients are affected by their calculation equations and the accuracy of each variable measurement. The large differences in the K values show that there were systematic errors in determining K with the different methods (see Fig.2). For KMBR, the error sources include the H and temperature gradient measurements. Wilson et al. (2002) evaluated the energy balance closure of 22 sites in FLUXNET and concluded that a general lack of closure existed at most sites, with a mean imbalance in the order of 20% in most conditions. The sum of the measured H and LE (latent heat flux) with the EC method, (H + LE)EC, is smaller than the difference in net radiation (Rn) and soil heat flux (G) (Rn−G). This may imply that the H measured with EC might be underestimated, leading to the underestimation of KMBR. Additionally, the error in the temperature gradient is dependent on the sensors’ performance. Although the best precision that the temperature sensors can reach is ±0.055°C, as the two temperature sensors were not exchanged periodically, a radiation shield could also result in a certain systematic bias in the temperature at the two levels (Loubet et al., 2013). To eliminate the systematic error of two temperature sensors, using thermocouples rather than the routine temperature sensors may be a good choice. It would be better if two temperature sensors could be exchanged regularly.
The sources of error and uncertainty in KAG come from the wind speed measurements, estimations of d, parameters of stability correction functions, etc. Wind speeds were measured with two new 2D sonic anemometers. The precision is ±0.1 m s−1 or 2% of the readings, and the initial wind speed is 0.01 m s−1 (according to the manual). We can consider the accuracy to be sufficiently high and the random error to be very limited. These assumptions would ensure that the wind speed gradient is reliable. Improper stability correction functions in Eq. (2) might also be error sources. The commonly used universal models and parameters of the functions are usually based on previous literature that utilized empirical equations obtained at a specific site and in a specific condition. Different researchers have presented different stability correction models and parameters (Foken, 2006; Song et al., 2010).
The error and uncertainty of zero-plane displacement (d) are dependent on the estimation method and parameters (Loubet et al., 2013). The commonly used method is simply estimated by the plant height (hc) being multiplied by a constant (usually in the range of 0.6–0.8). The second method is inversely derived from the flux–gradient relationships, and the scalar flux can utilize the EC measurements. The third method is estimated by linearly fitting the wind speed profiles U(z) and ln(z–d), making the root-mean-square error of the wind speed minimal in neutral conditions or making some corrections under non-neutral conditions. In this study, it was calculated as d = 0.67hc. To validate whether this is suitable, we compared the u* calculated by the third method (
$u^*_{\rm AG} $ ) and the u* measured with the EC technique ($u^*_{\rm EC} $ ), respectively. As seen in Fig. 3, the correlation is very good, with a slope of 0.99 and an R2 of 0.8, indicating that the estimated d has no systematic bias. -
Figure 4 shows the frequency distribution of the O3 gradient in the daytime during the observation period. Most gradients are distributed in the range between −6 μg m−3 and 0 μg m−3, and the median of the gradient is −3 μg m−3. As the two-level O3 concentrations were measured with the same analyzer, the systematic error caused by the analyzers can be ignored. However, the random error must still be considered. The uncertainty or relative error of the gradient depends on the magnitude of the real gradient that can be estimated by the ratio of the sampling errors (
$\delta_{\Delta{\rm C_O}_{_3}} $ ) to the gradient Δ${\rm C}_{\rm O_3} $ (Wolff et al., 2010). According to the manual, its precision and accuracy are greater than 1.0 ppb (approximately 1.9 μg m−3) or 2% of the reading, and its resolution is 0.1 ppb. This allows the small O3 gradient to be detected, but it is difficult to quantitatively determine the uncertainty in the O3 gradient. Nevertheless, a zero-gradient test could be used to roughly evaluate the precision and accuracy of the flux-gradient system. The larger the gradient (absolute value) is, the smaller the uncertainty of the gradient.Figure 5 shows the mean diurnal variations of the O3 concentration (average of two levels) and gradient during the entire observation period. The analyzer is a new product, and its precision can guarantee that the O3 concentration is reliable. Compared to the ambient absolute concentration, the vertical O3 gradient is very small within the ranges of several ppb. In the morning, the gradient shows increasingly larger trends. It is less than 2 μg m−3 in the early morning (before 0900 LST), implying that there may be large uncertainty during this period. The change in the mean gradient is relatively stable in the afternoon, with a mean gradient of 3.6 μg m−3, starting to decrease after 1900 LST.
Figure 5. Mean diurnal variations of the O3 concentration (average of two levels) and gradients during the entire observation period.
In general, the negative effects of O3 on crops happen in the daytime and during high concentration conditions (Pleijel et al., 2007; Feng et al., 2015). This can be reflected by O3 concentration–based assessing indexes (Dingenen et al., 2009), such as M7 [the 7-h (0900–1600 LST) mean O3 concentration] and AOT40 (the accumulated hourly O3 concentration above a 40 ppbV threshold). The mean gradient was more than 2.4 μg m−3 in the later morning and afternoon at high O3 concentrations (Fig. 5), implying that the uncertainty of the gradient is relatively small during the times that O3 is affecting the ecosystem.
The accuracy of the O3 gradient is a key variable for the O3 flux measured with gradient methods. It depends on not only the analyzer’s performance but also the measurement and calculation methods. For example, the number of measuring heights is a source of uncertainty for the gradient. According to AG theory, the flux is proportional to the concentration changes with height. For only the two-level measurements, a few random errors in the O3 concentration could result in a large bias in the O3 gradient. Hence, measuring the concentration profiles at more heights would filter or smooth out the random error, and the gradient would be more stable.
Besides the number of measuring heights, it is noteworthy that the proper calculation method is very important for reducing bias in the O3 gradient. In this study, the two-level O3 concentrations were measured alternately (in 5-min intervals) with one analyzer, in which there exists a measuring order issue (i.e., which 5-min O3 concentration level is measured first during a 30-min period). A simple average of each of the O3 concentration levels might produce certain errors without considering the measuring order. Table 1 presents an example of 30-min averaged O3 mix ratio gradients with two calculation methods. In method I, the upper and lower 30-min O3 concentrations are the simple re-average of three 5-min measurements. As shown in Table 1, the upper concentrations were measured during 1000–1005 LST, 1010–1015 LST, and 1020–1025 LST on 21 August 2017. The lower concentration measurements were taken during 1005–1010 LST, 1015–1020 LST, and 1025–1030 LST on 21 August 2017. In method II, the gaps were first filled with the averages before and after the 5-min measured O3 concentrations, and there were six 5-min data points for each height, including three measured and three gap-filled data points. The gradient was then calculated as the difference between the two-height O3 concentrations.
Start Time (LST) 1000 1005 1010 1015 1020 1025 1030 ${\rm C_O}_{_3} $_upper (5 min, ppb) 58.66* 61.78 63.83* 65.87 65.99* 66.10 66.19* ${\rm C_O}_{_3} $_lower (5 min, ppb) 57.77 60.78* 63.79 64.54* 65.28 65.21* 65.14 Mean1_upper (30 min) 64.58** − − 64.58*** − − − Mean1_lower (30 min) 62.28** − − 64.74*** − − − Mean2_upper (30 min) 63.70** − − 64.96*** − − − Mean2_lower (30 min) 62.89** − − 64.12*** − − − ΔC1 (Lower − upper) −2.30** − − 0.15*** − − − ΔC2 (Lower − upper) −0.81** − − −0.84*** − − − Notes: *no measurements, filled with the average of the measurements before and after 5 min; **averages of 1000–1030 LST; ***averages of 1005–1035 LST. Mean1 (Method I) is the average of real measurements during a 30-min period with three data points; Mean2 (Method II) is the average of measurements and gap-filled data during a 30-min period with six data points. ΔC1 and ΔC2 are the differences in the lower and upper O3 concentrations that are calculated with Mean1 and Mean2. Table 1. An example of a comparison of different O3 mix ratio gradient calculation methods.
It is clear that there are large differences in the O3 gradients determined with the two methods (see ΔC1 and ΔC2 in Table 1). To demonstrate that method II is better than method I, we calculated the gradient of an offset of 5 min (i.e., 1005–1035 LST), in which the measuring order is changed. With method I, the O3 gradients of 1000–1030 LST (−2.30 ppb) and 1005–1035 LST (0.15 ppb) are largely variable and even result in a change of sign. However, the variation in the gradients of 1000–1030 LST and 1005–1035 LST calculated with method II is very small (−0.81 ppb and −0.84 ppb).
Figure 6 shows the diurnal variations of O3 gradients calculated with two methods and time ranges on 15 August 2017. In method I, the difference of two 30-min averaged O3 gradients during different time ranges (5-min offset) is very large sometimes (see the two solid lines in Fig. 6). However, the difference with method II is obviously small (see the two dashed lines in Fig. 6). Even so, the difference means that there was still some uncertainty in the O3 gradient calculated with method II.
Figure 6. Diurnal variations of 30-min averaged O3 gradients calculated with two methods and time ranges on 15 August 2017. M1A: Method I and start times are on the hour or half-hour; M1B: Method I but start times are 5-min delayed; M2A: Method II and start times are on the hour or half-hour; M2B: Method II but start times are 5-min delayed.
The main reason for this phenomenon is that the concentration changes in 5 min, and the O3 gradient is on the same order of magnitude (maximum several ppb). If the measuring time is not synchronous, the gradient would be affected by the changing trend of the O3 concentration. To ensure that both the upper and lower intakes measure the same air eddy, setting a quick switching time (e.g. ~1 min) may eliminate the phenomenon and improve the performance of the gradient system. Of course, if possible, the use of two analyzers and periodically exchanging the sample position to measure the O3 concentrations at two heights is better than using one analyzer to cyclically measure them (Meyers et al., 1996). This not only removes the systematic bias from the two analyzers but can also eliminate the errors caused by asynchronous sampling.
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Figure 7 presents the mean diurnal variations of the O3 fluxes with different methods. The disparities in the O3 fluxes with different methods were small in the morning and large in the afternoon. This is primarily because the gradient was relatively large in the afternoon (see Fig. 5). As the analyzer's random error is relatively small and stable, its effect on the O3 flux will decrease at a large gradient. Relatively, the O3 flux calculated by the AGEC method (
$F_{\rm O_3\_{\rm AGEC}} $ ) is closest to$F_{\rm O_3\_{\rm EC}} $ . The MBR O3 flux ($F_{\rm O_3\_{\rm MBR}} $ ) is lower than$F_{{\rm O_3}\_{\rm EC}} $ , and the AG O3 flux ($F_{\rm O_3\_{\rm AG}} $ ) in the afternoon is about twice as large as$F_{\rm O_3\_{\rm EC}} $ .Figure 7. Mean diurnal variations of the O3 fluxes estimated by different methods. The top and bottom of the vertical lines represent the mean ± std.
Figure 8 shows comparisons of daytime O3 fluxes calculated by the EC method (
$F_{\rm O_3\_{\rm EC}} $ ) and the$F_{\rm O_3} $ calculated by different gradient methods. Overall, the correlations between$F_{\rm O_3\_{\rm EC}} $ and O3 fluxes with different gradient methods are not good. To analyze the relationships between$F_{\rm O_3\_{\rm EC}} $ and the fluxes from different gradient methods, two types of linear regression equations were calculated. Type 1 is the general linear regression equation, and type 2 is the linear equation with the intercept phased to zero, reflecting the relationships between the two mean fluxes. Relatively, the gradient method’s O3 flux with AGEC is the best, with the largest R2 (0.1845), and the slope of the type 2 linear regression curve is closest to the 1:1 line (Fig. 8b). The low correlations show that the gradient O3 fluxes were not very reliable.Figure 8. Comparisons of 30-min O3 fluxes estimated by different gradient methods and the EC method’s flux.
A few previous studies compared the gradient O3 flux with that of the EC technique and found that the results varied. Muller et al. (2009) found that the O3 flux determined by the gradient method was larger than that of the EC technique at a grassland area. The transfer coefficient was derived by the wind speed gradient and EC momentum flux. It also showed a very large comparison scatterplot, with a slope of 1.19 and a poor R2 (0.15). The O3 flux with the AGEC method was similar to the results presented by Muller et al. (2009). Loubet et al. (2013) compared the O3 fluxes and deposition velocities (Vd) with AG methods and the EC technique over a maize field and showed that the AG method had a roughly 40% larger Vd than the EC technique. In this study, the AG O3 flux was calculated from the product of u* (calculated by the wind speed gradient with a stability correction) by a concentration scaling parameter
$C^*_{\rm O_3} $ (determined by the O3 concentration gradient with a stability correction). The$F_{\rm O_3} $ calculated with the AG method is close to these results. Keronen et al. (2003) found that the Vd values determined by the AG method and EC technique generally agreed well in a Nordic pine forest, as did Stella et al. (2012) over bare soil in Paris. Droppo (1985) found that the Vd determined with the MBR method was close to that of the EC method at a Northeastern U.S. grassland site. Although the O3 flux with the AGEC method approaches that of the EC method in these results, the agreement is not very good.The errors of the gradient method’s fluxes come from the joint effects of the exchange coefficient and gradient. The theoretical basis of the gradient method is MOST, but it is limited to the homogeneous surface layer (or constant-flux layer) above the roughness sub-layer, and a range of |z/L|≤1~2 (Foken, 2006). The large discrepancy among the O3 fluxes with different methods may be related to the non-ideal conditions. For example, the sensors’ heights were not elevated enough, and the turbulent intensity was not always strong enough. Rinne et al. (2000) summarized the sources of uncertainty with AG methods for hydrocarbon flux measurements and presented the error estimate of gradient measurements, turbulent exchange coefficients, and parameterizations. The uncertainty caused by the gradient measurement was the largest. Loubet et al. (2013) also analyzed the potential errors in the AG method. They included the non-stationarity of the concentration changes, temperature errors caused by shields, roughness sub-layer correction issues, uncertainty in the displacement height estimation, etc. Based on this error source analysis, the most important error source was determined to be the gradient measurement. Decreasing the uncertainty in the O3 gradient is the key to more accurately estimating the O3 flux for gradient methods. Increasing the number of analyzers and measuring levels might reduce the errors in the O3 gradient. The gradient calculated using only the two-level O3 concentrations can easily produce random errors.