Effect of Coordinate Rotation Systems on Calculated Fluxes over a Forest in Complex Terrain: A Comprehensive Comparison

Abstract

Seven coordinate rotation systems were compared to determine a suitable system for a forest in complex terrain, using eddy-covariance data for a period of 40 days. The traditional double rotation was set as the standard of comparison with six other fixed coordinate systems, whose coefficients were carefully determined based on wind component data for a two-year period. Differences in total heat fluxes and daytime $\hbox {CO}_{2}$ fluxes calculated from all systems were small, except those from the sector-wise planar fit, which linearly and systematically underestimated the fluxes by about 5 %. The nighttime $\hbox {CO}_{2}$ flux was also underestimated by the sector-wise planar fit, but there was significant scatter in the plots, and the mean difference was 7 %. The standard deviations of the wind components and scalars normalized by the friction velocity and the dynamic parameters were calculated for each system, and the errors from the relationships obtained previously from flat and homogenous terrain were examined. The nighttime normalized standard deviation for scalars agreed better with the relationships after applying the sector-wise planar fit than those calculated by the other systems, although no remarkable difference was found in the daytime data. Therefore, the sector-wise planar fit was not the first choice for our site during daytime based on the energy imbalance, which was mainly caused by underestimating daytime heat fluxes. Double rotation or one of the four systems without the roll rotation process might be superior at our site. However, the offset error in the vertical wind component of the sonic anemometer induced errors of several percent in the fluxes in these systems, which was equivalent to the underestimation using the sector-wise planar fit. Meanwhile, the sector-wise planar fit system might still be the best system for calculating nighttime flux, considering the tendency of the nighttime normalized standard deviations.

Appendix

1.1 High Frequency Correction for the Closed-Path $\hbox {H}_{2}\hbox {O}$ Flux

Ibrom et al. (2007a) proposed that the closed-path $\hbox {H}_{2}\hbox {O}$ fluctuation has an attenuated signal in the high frequency region, which is unaccountable based on previous correction theories (e.g. Shimizu 2007). Furthermore, Ibrom et al. (2007b) showed that a signal delay occurs in the closed-path $\hbox {H}_{2}\hbox {O}$ data compared with that in the $\hbox {CO}_{2}$ data, although both were simultaneously taken from the sample mouth. We found a similar relationship between relative humidity or vapour pressure deficit (VPD) and the additional signal delay time in $\hbox {H}_{2}\hbox {O}$ to that in $\hbox {CO}_{2}$ as Ibrom et al. (2007b) using the class-1 quality control data obtained in June–August 2007 and January–February 2008. The additional delay time was estimated to be 9.5 s when VPD = 2.5 hPa (figure not shown). First, the class-1 data were used to calculate the $w_\mathrm{r}-\chi _\mathrm{H}$ cospectrum after correcting for sensor separation, the line averaging effect (both in Moore 1986), and the volume averaging effect of the closed-path IRGA (Massman 2004). Then, the cut-off frequencies ($f_\mathrm{c}$ [Hz]) at which the magnitude of the normalized $w_\mathrm{r}-\chi _\mathrm{H}$ cospectrum became $(1/2)^{0.5}$ to that of the normalized $w_\mathrm{r}-T$ cospectrum obtained simultaneously were compiled for four time ranges (14–16, 16–18, 18–22, and 22–30 s). The average $f_\mathrm{c}$ plotted against typical delay time is shown in Fig. 12; we obtained the relationship between delay time and $f_\mathrm{c}$ as,

$$\begin{aligned} f_\mathrm{c} = 0.0208 + 21.958\;\exp (-0.346 \,\text {d}t_\mathrm{H}), \end{aligned}$$

(10)

where $\text {d}t_\mathrm{H}$ is the delay time determined from the maximum correlation between $w_\mathrm{r}$ and closed-path $\chi _\mathrm{H}$. The $f_\mathrm{c}$ estimated from this equation was applied to the $\hbox {H}_{2}\hbox {O}$ tube flow correction, instead of the theoretical equation.

Fig. 12

Cut-off frequency $(f_\mathrm{c})$ calculated from the normalized cospectral ratio of closed-path water vapour flux to sensible heat flux. White circles are bin-averaged of $f_\mathrm{c}$ by four ranges of delay time estimated from the maximum correlation that occurred. The line represents Eq. 10 in the text