The net ecosystem exchange of CO₂ (NEE) varies at time scales from seconds to years and longer via the response of its components, gross ecosystem productivity (GEP) and ecosystem respiration (RE), to physical and biological drivers. Quantifying the relationship between flux and climate at multiple time scales is necessary for a comprehensive understanding of the role of climate in the terrestrial carbon cycle. Orthonormal wavelet transformation (OWT) can quantify the strength of the interactions between gappy eddy covariance flux and micrometeorological measurements at multiple frequencies while expressing time series variance in few energetic wavelet coefficients, offering a low-dimensional view of the response of terrestrial carbon flux to climatic variability. The variability of NEE, GEP and RE, and their co-variability with dominant climatic drivers, are explored with nearly one thousand site-years of data from the FLUXNET global dataset consisting of 253 eddy covariance research sites. The NEE and GEP wavelet spectra were similar among plant functional types (PFT) at weekly and shorter time scales, but significant divergence appeared among PFT at the biweekly and longer time scales, at which NEE and GEP were relatively less variable than climate. The RE spectra rarely differed among PFT across time scales as expected. On average, RE spectra had greater low frequency (monthly to interannual) variability than NEE, GEP and climate. CANOAK ecosystem model simulations demonstrate that "multi-annual" spectral peaks in flux may emerge at low (4+ years) time scales. Biological responses to climate and other internal system dynamics, rather than direct ecosystem response to climate, provide the likely explanation for observed multi-annual variability, but data records must be lengthened and measurements of ecosystem state must be made, and made available, to disentangle the mechanisms responsible for low frequency patterns in ecosystem CO₂ exchange.