Abstract The choice of coordinate system to calculate eddy covariance fluxes becomes particularly relevant at complex measurement sites. The traditional way is to perform double rotation (DR) of the coordinate system i.e., to calculate turbulent fluxes in a coordinate system that is aligned with the flow streamlines within the flux averaging period (e.g., Kaimal and Finnigan, 1994 ). The second approach, the so-called planar-fitted (PF) coordinate system, averages the flow over a longer period of time, in practice a month or more. The PF method allows to derive an intercept coefficient of the vertical wind speed which can be attributed to the offset of the sonic anemometer or the average vertical flow related to meteorological conditions. We evaluated the variants of the PF methods using data from a variety of sites ranging from complex urban and forest sites to nearly ideal forest and peatland sites. At complex sites, we found that the intercept of the vertical wind speed derived from the PF method is a function of wind direction, time of day and/or stability. The sector-wise PF (SPF) method frequently led to insignificant statistical relationships. We tested a continuous PF (CPF) method where the relationship establishing the coordinate frame was represented as the continuous function in the form of Fourier series. The method enabled to obtain the PF with lower uncertainty as compared to the SPF method, by selecting necessary number of harmonics for each site based on confidence intervals of estimated parameters. Therefore, we recommend to use the CPF method in cases when the number of observations in some wind direction interval is low or the obtained SPF is insignificant due to large variance in measurements. We also showed that significant systematic difference can exist in cumulative turbulent fluxes between the DR and PF methods over a longer period of time. Derived vertical advection of carbon dioxide exhibited large variability with wind direction due to topography at complex sites and therefore, without considering horizontal advection, cannot be used to improve the net ecosystem exchange estimation during nocturnal, low turbulence conditions.

中文翻译：

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坐标旋转对复杂位点涡流协方差通量的影响

摘要 在复杂的测量地点，选择坐标系来计算涡流协方差通量变得尤为重要。传统的方法是执行坐标系的双旋转（DR），即在与通量平均周期内的流动流线对齐的坐标系中计算湍流通量（例如，Kaimal 和 Finnigan，1994）。第二种方法，即所谓的平面拟合 (PF) 坐标系，在更长的时间内平均流量，实际上是一个月或更长时间。PF 方法允许推导出垂直风速的截距系数，该系数可归因于声速计的偏移或与气象条件相关的平均垂直流。我们使用来自各种地点的数据评估了 PF 方法的变体，从复杂的城市和森林地点到近乎理想的森林和泥炭地地点。在复杂的地点，我们发现从 PF 方法得出的垂直风速的截距是风向、一天中的时间和/或稳定性的函数。按部门划分的 PF (SPF) 方法经常导致不显着的统计关系。我们测试了一种连续 PF (CPF) 方法，其中建立坐标系的关系以傅立叶级数的形式表示为连续函数。通过基于估计参数的置信区间为每个站点选择必要数量的谐波，该方法能够获得与 SPF 方法相比具有较低不确定性的 PF。所以，我们建议在某些风向区间的观测次数较少或由于测量值差异较大而获得的 SPF 不显着的情况下使用 CPF 方法。我们还表明，在较长时间内，DR 和 PF 方法之间的累积湍流通量可能存在显着的系统差异。由于复杂地点的地形，二氧化碳的衍生垂直平流随着风向表现出很大的变异性，因此，如果不考虑水平平流，则不能用于改善夜间低湍流条件下的净生态系统交换估计。我们还表明，在较长时间内，DR 和 PF 方法之间的累积湍流通量可能存在显着的系统差异。由于复杂地点的地形，二氧化碳的衍生垂直平流随着风向表现出很大的变异性，因此，如果不考虑水平平流，则不能用于改善夜间低湍流条件下的净生态系统交换估计。我们还表明，在较长时间内，DR 和 PF 方法之间的累积湍流通量可能存在显着的系统差异。由于复杂地点的地形，二氧化碳的衍生垂直平流随着风向表现出很大的变异性，因此，如果不考虑水平平流，则不能用于改善夜间低湍流条件下的净生态系统交换估计。