Stochastic analysis of hourly to monthly potential evapotranspiration with a focus on the long-range dependence and application with reanalysis and ground-station data

The stochastic structures of potential evaporation and evapotranspiration (PEV and PET or ETo) are analyzed using the ERA5 hourly reanalysis data and the Penman–Monteith model applied to the well-known CIMIS network. The latter includes high-quality ground meteorological samples with long lengths and simultaneous measurements of monthly incoming shortwave radiation, temperature, relative humidity, and wind speed. It is found that both the PEV and PET processes exhibit a moderate long-range dependence structure with a Hurst parameter of 0.64 and 0.69, respectively. Additionally, it is noted that their marginal structures are found to be light-tailed when estimated through the Pareto–Burr–Feller distribution function. Both results are consistent with the global-scale hydrological-cycle path, determined by all the above variables and rainfall, in terms of the marginal and dependence structures. Finally, it is discussed how the existence of, even moderate, long-range dependence can increase the variability and uncertainty of both processes and, thus, limit their predictability.