Abstract. Detrended Cross-Correlation Analysis (DCCA) revealed an emergent transition in non-periodic (deseasonalized) atmospheric variability at time-scales ~1-year. At multi-year time-scales (i) ρSST,Tland ~ 0.6 (i.e. the correlation been global-averaged sea surface temperature, SST, and 2-meter air temperature averaged over global-land, Tland); (ii) Clausius-Clapeyron relationship becomes the dominant control of global-averaged precipitable water vapor (W), with ρW,T2m ≈ ρW,SST ~ 0.9; (iii) atmospheric radiative fluxes, specifically the surface downwelling longwave radiative flux (DLR), become a key constraint for global-mean precipitation (P) variability (ρP,Ratm ≈ ρP,DLR ~ −0.8); (iv) cloud effects are negligible in (iii), and clear-sky DLR becomes a dominant P constraint; and (v) ρP,T2m and ρP,SST displayed significant multi-year correlations, although with large spread amongst different datasets (~ 0.4 to ~ 0.7). Result (v) provides a new perspective into the well-known uncertainties climate models associated with the dynamical component of precipitation. At sub-yearly time-scales all correlations underlying these five results decrease abruptly towards negligible values. The relevance and validity of this multi-scale structure is demonstrated by three reconstructed P time-series at 2-year resolution, two relying on clear-sky DLR constraints and one based on P-SST correlation. These simple models, particularly one based on clear-sky DLR, were able to reproduce observed P anomaly time-series with similar accuracy to a (uncoupled) atmospheric model (ERA-20CM) and two climate reanalysis (ERA-20C and 20CR). The idealized models aren't applicable at sub-yearly time-scales, where the underlying correlations become negligible. However, monthly P probability density functions (PDFs) were derived by stochastic downscaling of reconstructed P, leveraging on scale-invariant properties, outperforming the statistics simulated by ERA-20C, 20CR and ERA-20CM.