Abstract
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.
Highlights
Water management is often concerned with preventing or mitigating extreme conditions
The overall objective of this paper is to develop a stochastic evapotranspiration model that generates evapotranspiration time series that are in agreement with accompanying rainfall time series, such that it can be used in hydrological impact analysis
In order to assess extreme statistics of the discharge for water management planning and decision making, extremely long time series of precipitation and evapotranspiration may be required as inputs to hydrological models
Summary
Water management is often concerned with preventing or mitigating extreme conditions Hydraulic structures, such as flood control reservoirs, are often constructed on rivers in order to prevent floods or to mitigate their consequences. It is of major importance to accurately dimension these structures such that they can cope with a hazard, being a flood or a drought event, of a given magnitude, duration and frequency of occurrence or its return period This can be accomplished by the use of design storms with given statistical properties (Wheater 2002; Willems 2013) or the use of long-term rainfall records in order to obtain a continuous discharge series from a rainfall-runoff model, from which flood or low flow events are extracted (Verhoest et al 2010; Willems 2014).
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