This study proposes a general method for testing for self-correlation (also known as spurious or induced correlation) in comparisons where there is a common variable, e.g. the comparison of the fluvial flux of a component with water yield. We considered the case of the fluvial flux of nitrate from 153 catchments from across the UK for which there were at least 10 years of data. The results show that 66% of records (102 catchments) could be rejected as significantly self-correlated (P < 95%). Amongst the 51 catchments, which proved to be significantly different from the spurious, or self-correlated result, the response was variable with linear, convex, s-curve and mixed results proving the best description. There was no spatial pattern across the UK for the results that were and were not rejected as spurious; the most important predictor of not being self-correlated was the length of record rather than any catchment characteristic. The study shows that biogeochemical stationarity cannot be assumed and that caution should be applied when examining fluvial flux data.
Worrall, F., Burt, T., & Howden, N. (2015). The problem of self-correlation in fluvial flux data - the case of nitrate flux from UK rivers. Journal of Hydrology, 530, 328-335. https://doi.org/10.1016/j.jhydrol.2015.09.068