Random errors in carbon and water vapor fluxes assessed with Gaussian Processes

The flow of carbon between terrestrial ecosystems and the atmosphere is mainly driven by nonlinear, complex and time-lagged processes. Understanding the associated ecosystem responses is a key challenge regarding climate change questions such as the future development of the terrestrial carbon sink. However, high temporal resolution measurements of ecosystem variables (with the eddy covariance method) are subject to random error, that needs to be accounted for in model-data fusion, multi-site syntheses and up-scaling efforts. Gaussian Processes (GPs), a nonparametric regression method, have recently been shown to capture relationships in high-dimensional, nonlinear and noisy data. Heteroscedastic Gaussian Processes (HGPs) are a specialized GP method for data with inhomogeneous noise variance, such as eddy covariance measurements. Here, it is demonstrated that the HGP model captures measurement noise variances well, outperforming the model residual method and providing reasonable flux predictions at the same time. Based on meteorological drivers and temporal information, uncertainties of annual sums of carbon flux and water vapor flux at six different tower sites in Europe and North America are estimated. Similar noise patterns with different magnitudes were found across sites. Random uncertainties in annual sums of carbon fluxes were between 9.80 and 31.57 g C m−2 yr−1 (or 4–9% of the annual flux), and were between 2.54 and 8.13 mm yr−1 (or 1–2% of the annual flux) for water vapor fluxes. The empirical HGP model offers a general method to estimate random errors at half-hourly resolution based on entire annual records of measurements. It is introduced as a new tool for random uncertainty assessment widely throughout the FLUXNET network.