Temporal Error Correlations in a Terrestrial Carbon Cycle Model Derived by Comparison to Carbon Dioxide Eddy Covariance Flux Tower Measurements

Atmospheric CO₂ flux inversions require as input an estimate of spatial and temporal correlations of errors in their estimate of the prior mean. Some previous studies have used the differences in CO₂ daily average flux estimates produced by terrestrial carbon cycle models and eddy covariance measurements to constrain the flux error correlations. Since inversions are starting to resolve the daily cycle, we set out to examine the correlations at sub-daily time scales, as well as the correlations across years. To this end, we examine the autocorrelations in the difference between net ecosystem-atmosphere exchange measurements from 75 AmeriFlux towers and temporally downscaled high-spatial-resolution flux estimates from the Carnegie-Ames-Stanford Approach (CASA) terrestrial carbon cycle model. We find that the daily cycle is prominent in these hourly autocorrelations and that these autocorrelations persist across years. We propose a family of functions to model these temporal correlations in atmospheric inversions, and use cross validation to determine which of the correlation functions best fits autocorrelation data from towers not in the training set. Correlation functions with a component that attempts to model the daily cycle in the differences match correlations from other towers better than those without. Those models that reproduce the same correlation structures at 1-year intervals while modulating the amplitudes of the correlations between those intervals improve the fit still further.