The propagation of errors in long‐term measurements of land‐atmosphere fluxes of carbon and water

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Abstract
For surface fluxes of carbon dioxide, the net daily flux is the sum of daytime and nighttime fluxes of approximately the same magnitude and opposite direction. The net flux is therefore significantly smaller than the individual flux measurements and error assessment is critical in determining whether a surface is a net source or sink of carbon dioxide. For carbon dioxide flux measurements, it is an occasional misconception that the net flux is measured as the difference between the net upward and downward fluxes (i.e. a small difference between large terms). This is not the case. The net flux is the sum of individual (half‐hourly or hourly) flux measurements, each with an associated error term. The question of errors and uncertainties in long‐term flux measurements of carbon and water is addressed by first considering the potential for errors in flux measuring systems in general and thus errors which are relevant to a wide range of timescales of measurement. We also focus exclusively on flux measurements made by the micrometeorological method of eddy covariance. Errors can loosely be divided into random errors and systematic errors, although in reality any particular error may be a combination of both types. Systematic errors can be fully systematic errors (errors that apply on all of the daily cycle) or selectively systematic errors (errors that apply to only part of the daily cycle), which have very different effects. Random errors may also be full or selective, but these do not differ substantially in their properties. We describe an error analysis in which these three different types of error are applied to a long‐term dataset to discover how errors may propagate through long‐term data and which can be used to estimate the range of uncertainty in the reported sink strength of the particular ecosystem studied.