Evaluating the agreement between measurements and models of net ecosystem exchange at different times and timescales using wavelet coherence: an example using data from the North American Carbon Program Site-Level Interim Synthesis
Authors: Stoy P. C. , Dietze M. C. , Richardson A. D. , Vargas R. , Barr A. G. , Anderson R. S. , Arain M. A. , Baker I. T. , Black T. A. , Chen J. M. , Cook R. B. , Gough C. M. , Grant R. F. , Hollinger D. Y. , Izaurralde R. C. , Kucharik C. J. , Lafleur P. , Law B. E. , Liu S. , Lokupitiya E. , Luo Y. , Munger J. W. , Peng C. , Poulter B. , Price D. T. , Ricciuto D. M. , Riley W. J. , Sahoo A. K. , Schaefer K. , Schwalm C. R. , Tian H. , Verbeeck H. , Weng E. 
Published: November 2013

Abstract. Earth system processes exhibit complex patterns across time, as do the models that seek to replicate these processes. Model output may or may not be significantly related to observations at different times and on different frequencies. Conventional model diagnostics provide an aggregate view of model–data agreement, but usually do not identify the time and frequency patterns of model–data disagreement, leaving unclear the steps required to improve model response to environmental drivers that vary on characteristic frequencies. Wavelet coherence can quantify the times and timescales at which two time series, for example time series of models and measurements, are significantly different. We applied wavelet coherence to interpret the predictions of 20 ecosystem models from the North American Carbon Program (NACP) Site-Level Interim Synthesis when confronted with eddy-covariance-measured net ecosystem exchange (NEE) from 10 ecosystems with multiple years of available data. Models were grouped into classes with similar approaches for incorporating phenology, the calculation of NEE, the inclusion of foliar nitrogen (N), and the use of model–data fusion. Models with prescribed, rather than prognostic, phenology often fit NEE observations better on annual to interannual timescales in grassland, wetland and agricultural ecosystems. Models that calculated NEE as net primary productivity (NPP) minus heterotrophic respiration (HR) rather than gross ecosystem productivity (GPP) minus ecosystem respiration (ER) fit better on annual timescales in grassland and wetland ecosystems, but models that calculated NEE as GPP minus ER were superior on monthly to seasonal timescales in two coniferous forests. Models that incorporated foliar nitrogen (N) data were successful at capturing NEE variability on interannual (multiple year) timescales at Howland Forest, Maine. The model that employed a model–data fusion approach often, but not always, resulted in improved fit to data, suggesting that improving model parameterization is important but not the only step for improving model performance. Combined with previous findings, our results suggest that the mechanisms driving daily and annual NEE variability tend to be correctly simulated, but the magnitude of these fluxes is often erroneous, suggesting that model parameterization must be improved. Few NACP models correctly predicted fluxes on seasonal and interannual timescales where spectral energy in NEE observations tends to be low, but where phenological events, multi-year oscillations in climatological drivers, and ecosystem succession are known to be important for determining ecosystem function. Mechanistic improvements to models must be made to replicate observed NEE variability on seasonal and interannual timescales.