Identifying the timescales of model error: NACP inter-comparison wavelet analysis

Ecosystem models serve as one of our most important tools for diagnosing the carbon cycle and projecting across space and time. Most assessments of model performance occur in the time domain, however ecosystem dynamics respond to drivers at multiple timescales. Spectral methods, such as wavelet analyses, present an alternative that allows the identification of the dominant timescales of model error. The goal of this project is to use wavelet analyses to synthesize the results about the performance of 21 models at nine eddy-covariance towers as part of the North American Carbon Program's site-level inter-comparison. Full wavelet spectra were calculated for the normalized model-data residuals of every model x site combination. Furthermore, we developed a novel Monte Carlo approach to incorporating the spectra of flux tower observation error to assess the significance of model error. To distill the key trends we evaluated the site-average spectra and the model-average global power spectra. Averaging spectra by site reveal a consistent annual and diurnal signals as well as event-driven errors at the intermediate scales. Averaging by model reveals most power in the error spectra is at the annual and 20-120 day scales, a clear peak at the diurnal scale, and large model-to-model variability in the ability to capture the 2-20 day scales. Breaking the global power spectra into discrete bands, ANOVA suggests there was a significant model by band effect but a non-significant model by site effect which together suggest that individual models may be consistent in their error patterns. There are also consistent site and site by band effects but not a clear biome or spatial pattern to the cross-site variability. Overall we produce a clear set of recommendations for diagnosing and resolving model error in terms of three ranked priorities: 1) Resolve errors in the annual cycle; 2) Resolve errors in the growing-season diurnal cycle; and 3) Diagnose and resolve the causes of event-driven errors at intermediate time scales.