Stochastic simulation of precipitation-consistent daily reference evapotranspiration using vine copulas

Evapotranspiration is an important process in the water cycle that represents a considerable amount of moisture lost to the atmosphere through evaporation from the soil and wet surfaces, and transpiration from plants. Therefore, several water management methods, such as irrigation scheduling and hydrological impact analysis, rely on an accurate estimation of evapotranspiration rates. Often, daily reference evapotranspiration is modelled based on the Penman, Priestley-Taylor or Hargraeves equation. However, each of these models requires extensive input data, such as daily mean temperature, wind speed, relative humidity and solar radiation. Yet, in design studies, such data may be unavailable and therefore, another approach may be needed that is based on stochastically generated time series. More specifically, when rainfall-runoff models are used, these evapotranspiration data need to be consistent with the accompanying (stochastically generated) precipitation time series data. In this paper, such an approach is presented in which the statistical dependence between evapotranspiration, precipitation and temperature is described by three-and four-dimensional vine copulas. Based on a case study of 72 years of evapotranspiration, temperature and precipitation data, observed in Uccle, Belgium, it is shown that canonical vine copulas (C-vines) perform very well in preserving the dependences between variables.