Long-range persistence in climatological and hydrological time series: analysis, modeling and application to drought hazard assessment

We present power spectra of time-series data for tree ring width chronologies, atmospheric temperatures, river discharges and precipitation averaged over hundreds of stations worldwide. The average power spectrum S for each of these phenomena is found to have a power-law dependence on frequency with exponent -l/2: S(f) xf-‘/‘. An advection-diffusion model of the vertical transport of heat and water vapor in the atmosphere is presented as a first-order model of climatic and hydrological variability. The model generates variability with the observed spectrum. The model is validated with a correlation anaiysis of temperature and water vapor concentration measurements from the TIROS operational vertical sounder (TO%). Drought frequency analyses based on synthetic lognormal streamflows with the above power spectrum are presented. We show that the presence of long memory as implied by the power-law power spectrum has a significant effect on the likelihood of extended droughts compared with the drought hazard implied from standard autoregressive models with short memory.