Short-term forecasting of reference evapotranspiration using limited area models and time series techniques

Reference evapotranspiration (ETo) forecasts can be obtained using analytical models (Penman-Monteith, Penman, etc.) and meteorological data from numerical weather forecasts. The use of both ETo equations and weather forecasts makes possible to obtain ETo forecast on hourly base, usually for up to 72 hours, and with different spatial resolution. Data spatial resolution is a key factor for many applications in regions with high variable landscape characteristics, in particular in case of complex terrain. Evapotranspiration forecast can be also based on time series analysis of ETo and meteorological variables related to evapotranspiration process. For example, regional ETo maps for budgeting irrigation water needs have been developed using past information on ETo rates (Pruitt, 1984) and then time series analysis has been extensively used to predict weekly, monthly or seasonal ETo rates (Mariño et al., 1993; Mohan and Arumugam, 1995). In earlier research, the discrepancy between calculated ETo and predicted ETo using weather forecasts resulted from inaccuracy of the forecast weather variables such as wind speed, water vapor pressure or solar irradiance (Meyer et al., 1988). Time series analysis is a major statistical prediction tool and it is based on the collection and analysis of past observations of a variable to develop a model for future trends. Time series models do not assume knowledge of the structural relationships between variables involved in the studied process, for example the relations between evapotranspiration rates and weather variables. Since an observed time series is an actual realization of a stochastic process, time series models are simply stochastic models. The most common time series models are the autoregressive integrated moving average (ARIMA) models (Box et al., 1994) where the forecast of a variable is described as a linear (additive) combination of the previous states of the variable (pure autoregressive component) and the previous forecast errors (pure moving average component). The term “integrated” refers to the adjustment of the time series removing seasonal or periodic components (detrending or differencing). The major limitation of ARIMA models is the linear correlation structure that is assumed among the time series values (Zhang, 2003), while the linearity is only an approximation of the real world. Therefore, ARIMA models are not able to capture non linear patterns, which can coexist with linear patterns in real-world time series. ARIMA models have generally been used to provide weekly or monthly forecasted ETo values. Mariño et al. (1993) developed seasonal ARIMA models to forecast ETo on a monthly basis. ARIMA models performed better than other statistical methods in two distinct climatic areas of California. Mohan and Arumugam (1995) used both Winter’s exponential smoothing and ARIMA models to forecast ETo on a weekly basis, and concluded that their use could improve irrigation scheduling and management of irrigation systems. The aim of this study is to analyze and compare the performances of the above-mentioned techniques in short-term prediction of hourly and daily ETo.