Self-correlation between assimilation and respiration resulting from flux partitioning of eddy-covariance CO2 fluxes

Self-correlation between estimates of assimilation and respiration of carbon is a consequence of the flux partitioning of eddy-covariance measurements, where the assimilation is computed as the difference between the measured net carbon dioxide flux (NEE) and an estimate of the respiration. The estimates of assimilation and respiration suffer from self-correlation because they share a common variable (the respiration). The issue of self-correlation has been treated before, however, published studies continue to report regression relationships without accounting for the problem. The self-correlation is defined here (for example) as the correlation between variables A and B, where A=x+y and B=x, and where x and y are random, uncorrelated variables (random permutations of the observations). In this case, any correlation found between A and B has no physical meaning and is entirely due to the self-correlation associated with the shared variable x. Estimates for the self-correlation are presented for a range of timescales using two different methods applied to a 6-yr dataset of eddy-covariance and soil chamber measurements from a ponderosa pine forest. Although the estimate of self-correlation is itself uncertain, it is not small compared to the observed correlation, and therefore it can reduce the strength of the relationship that can be demonstrated even though there is a strong apparent relationship in the observations and a strong causal relationship is expected based on tree physiology through coupling of photosynthesis and autotrophic respiration. We conclude that previous studies using eddy-covariance measurements and standard flux partitioning methods may have inadvertently overstated the real correlation between assimilation and respiration because they failed to account for self-correlation.