Why we need to estimate sampling error in eddy covariance measurement?

Since early 1990s, eddy covariance (EC) measurement have steadily taken place as the method to observe the exchanges of heat, water vapor and carbon dioxide between biosphere and the atmosphere, and in recent over 650 sites have been operating to monitor the exchange across the globe. This flourish have substantially contributed to not only understanding characteristics of the exchanges upon various ecosystems under the global climate change, but also validating satellite analyses and model estimates for the spatiotemporal distribution of the exchanges. Basically, EC measurement is fulfilled over the hypotheses of stationarity in ergodicity, so that in practical world an ensemble average can be replaced by a time average under the existence of time scale and its integrability as turbulence characteristics of boundary inertial layer. However, spatiotemporal condition would be incomplete to ensure the specified confidence level in practical EC measurement because of the variability according to the synoptic change in various atmospheric conditions and the spatial heterogeneity over diverse land surface. Therefore, the sampling error of EC measurement coming from an averaging problem is inherently inevitable and conditionally variable on account of the length of averaging time being finite and fixed. We therefore should pay attention to the investigations using the exchanges measured by EC method to specify vegetation responses in climate change and to integrate regional or global values of the exchange, as well as to validate model performance or satellite analysis and to synthesis the spatiotemporal values by data assimilation. Nevertheless, it is difficult to say that those current analyses of the exchanges have meditated the sampling error in terms of the quantification. This presentation shows that 1) the characteristics of the sampling error in terms of a random error and its fractional value against the exchange, namely relative sampling error, 2) the relationship of the relative sampling error to the integral turbulence characteristic, and 3) the advantage of the weighed average by the relative sampling error in EC measurement.