The space-time evolution of instabilities manifested in the daily fields of Precipitable Water (PW) from a 16-year long GCM (Global Climate Model) simulation was analyzed using finite-size comoving Lyapunov exponents (CMLE), a generalization of the finite-size Lyapunov exponent (a measure of the rate of growth of local perturbations, Tao and Barros 2008) to a moving reference frame. In this work, we focus on the analysis of zonal CMLE fields of PW perturbations at a 14-day timescale. Visual inspection shows that the bi-weekly march of CMLE fields maps global sources of instabilities and their propagation from low to high latitude and along land-ocean contrast lines. Specifically, the meridional extent of the space-time patterns of instability appears contained and organized by the North and South Annular Modes roughly at 65oN and 65oS, whereas zonal propagation is controlled by major orographic barriers, specifically the Western Cordillera of North America, the Andes and the Central Asia Highlands. The results suggest that the space-time distribution of the GCM Precipitable Water CMLE provides a thermodynamics tag to the space-time evolution of the storm tracks, including both the midlatitude and subtropical jet streams, and can capture most of the seasonal and some of the inter-annual variability of the morphology and intensity of macroscale features associated with the Aleutian and Icelandic Lows and the Siberian High. At the sub-seasonal scale, it is hypothesized that the spatial variability of the CMLE fields at subseasonal scale may be linked to shortwaves and jet streaks. Wavelet analysis of the low-frequency behavior of CMLE local maxima over the 16-year simulation shows evidence of non-stationarity up to 2-4 and 8- year time-scales consistent with ENSO and with basin-scale oscillations such as the PDO (Pacific Decadal Oscillation) and the NAO (North Atlantic Oscillation) in the Northern Hemisphere. Nevertheless, the signal does not meet the 95% significance level at time-scales beyond the annual cycle, and even then is mostly concentrated at the sub-seasonal and seasonal time-scales.