Data length requirements for observational estimates of land-atmosphere coupling strength

Multiple metrics have been developed in recent years to characterize the strength of land-atmosphere coupling in regional and global climate models. Evaluation of these metrics against observations has proven challenging because of limited observations and/or metric definitions based on model experimental designs that are not replicable with observations. Additionally, because observations are limited in time, with only a single realization of the earth's climate available, metrics of land-atmosphere coupling strength typically assume stationarity and ergodicity, so that an observed time series (or set of time series) can be used in place of an ensemble mean of multiple realizations. The present study evaluates the observational data requirements necessary for robust quantification of a suite of land-atmosphere coupling metrics previously described in the literature. It is demonstrated that the amount of data required to obtain robust estimates of metrics assessing relationships between variables is greater than that necessary to constrain means of directly measured observables. Moreover, while the addition of unbiased noise does not significantly alter the mean of a directly observable quantity, inclusion of such noise degrades metrics based on connections between variables, yielding a unidirectional and negative impact on metric strength estimates. This analysis suggests that longer records of surface observations are required to correctly estimate land-atmosphere coupling strength than are required to estimate mean values of the observed quantities.