Linear and global space-time dependence and Taylor hypotheses for rainfall in the tropical Andes

The space-time linear and global dependence of tropical rainfall in an intra-Andean valley of Colombia is estimated using 15 min of resolution data, recorded by 18 raingauges, through correlation (rho) and mutual information (MI) analysis of the entire record (1998-2006) and at seasonal and interannual (ENSO) timescales. Spatial dependence analyses are developed for increasing (1) time aggregation intervals T = 15 min to T = 24 hours, and (2) time lags tau = 15 min to tau = 120 min. Results for (1) indicate that both spatial MI and rho decay as I(lambda, T) = A(T)lambda(-alpha(T)), but also that A(T) = aT(mu) and alpha(T) = bT(-omega). Maps of MI and rho for increasing values of T are discussed in terms of geographical and few known meteorological features. Regarding (2), exponential functions fit better the spatial decay rates of both MI and rho, such that I(lambda, tau) = F(tau)exp[-phi(tau)lambda], with F(tau) = exp[-d tau], and phi(tau) = j-k tau. Maps of MI and rho for increasing values of tau suggest that MI may be better suited than rho to capture highly localized singularities of tropical mountain rainfall. Estimated power laws are highly dependent on both the seasonal cycle and ENSO phases, consistently with temporal dynamics of rainfall at both timescales. We tested the validity of Taylor hypothesis rho(0, tau) = rho(U tau, 0) and found it rejected in 11 of 18 raingauges, which prompted us to introduce a global Taylor hypothesis using the space-time MIs as I(0, tau) = I(U tau, 0). Results indicate that power laws characterize the decay of both the temporal I(0, tau) and the space-transformed I(lambda, 0) with respect to tau. A rigorous statistical test indicates that the global Taylor hypothesis is valid in 14 of 18 raingauges within the 20-180 min time range.