Short-term forecasting of daily reference evapotranspiration using the Hargreaves–Samani model and temperature forecasts
Introduction
Accurate estimation of reference evapotranspiration (ET0) is essential for irrigation management (Allen et al., 1998). ET0 is usually estimated using observed weather data (Stockle et al., 2004, Jabloun and Sahli, 2008, Trajkovic and Kolakovic, 2009, Luo et al., 2012, Todorovic et al., 2013). Snyder et al. (2009) noted that the California Irrigation Management Information System provided excellent information on near-real-time ET0 but did not provide forecast ET0, which is useful for planning irrigation, especially for high-frequency irrigation systems and shallow-rooted vegetation.
Monthly or weekly ET0 forecasts, which are helpful for planning middle- to long-term irrigation planning, can be produced well using time series methods (including the artificial neural network method, as it uses historic weather data to train the network), due to the obvious periodicity in ET0. The autoregressive integrated moving average (ARIMA) model, for example, has typically been used to forecast weekly or monthly ET0 values. Marino et al. (1993) developed seasonal ARIMA models to forecast ET0 on a monthly basis and they were believed to perform 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 ET0 on a weekly basis and Arca et al. (2006) believed that for hourly ET0 forecast time series models (ARIMA and ANN models) performed less well than the method based on weather forecast.
In fact, daily ET0 forecasts are more useful in short-term irrigation management. As the daily ET0 is primarily dominated by weather conditions, time series methods may not be applicable; thus, Mao (1994) proposed a daily average modification method in which the average daily ET0 of each day in a year was calculated from historical weather data and the forecast ET0 was obtained from the average daily ET0 multiplied by an empirical coefficient corresponding to the forecasted weather conditions.
Although numerical weather forecast data have been employed to estimate or forecast ET0 and are believed to provide sufficient accuracy (e.g., Duce et al., 2000, Arca et al., 2006, Silva et al., 2010, Tian and Martinez, 2012), public weather forecasts are easier to access and more intuitive. Cai et al. (2007) used the Penman–Monteith equation (PM) (Allen et al., 1998) and daily weather forecasts to estimate ET0. In fact, daily weather forecasts can be used for ET0 forecasting, and there have been some attempts to use daily weather forecasts for this purpose. Guo et al. (2011) used a least-squares support vector machine model to forecast ET0 with public weather forecasts, but data for only 61 days with a forecast horizon of 1 day were collected to test the performance of their method. There are many similar studies (Xu et al., 2006, Chi et al., 2008, Zhang et al., 2010, Torres et al., 2011); however, in these studies, so-called weather forecast data generated from historical weather data were used. The National Weather Service (NWS)’s Weather Forecast Offices (WFO) recently began to produce “experimental” daily ET0 forecasts for farmer and water management agencies. These forecasts use daily NWS forecast data (cloud cover, maximum and minimum temperature, mean dew point temperature, and mean wind speed) and the American society of civil engineers–environmental water resources institute's standardized ET0 method (Allen et al., 2006) to compute ET0 for up to 7 days (the current date plus a 6-day forecast) (Snyder et al., 2009, Palmer et al., 2012, Palmer and Osborne, 2013). Ballesteros et al. (2012) developed a computer program, FORETo, for reference evapotranspiration forecasting. In FORETo, daily ET0 forecasts for a 6-day period are obtained from an artificial neural network, forecasted maximum and minimum temperature, and calculated extraterrestrial radiation. The results showed that the error in the forecasts increased as the number of forecasting days increases. The PM has been selected as the standard method for estimating ET0. This method requires daily maximum and minimum temperature, relative humidity, solar radiation and wind speed. Public weather forecasts usually only include weather conditions, maximum and minimum temperatures, wind scale and direction. Reference evapotranspiration depends on several interacting meteorological factors, such as radiation, air temperature, humidity and wind speed; however, the temperature is the most important influencing factor. The Hargreaves–Samani (HS) model only requires daily maximum and minimum air temperatures, and these data are relatively easy to obtain.
The objectives of this work include: (1) to propose a method for short-term forecasting of ET0 using a locally calibrated HS model and temperature forecasts; (2) to validate the proposed method by comparisons between the forecasted ET0 and the calculated ET0 from observed meteorological data and the PM model and; (3) to identify the sources of errors from two aspects, the model drawbacks and errors in input data.
Section snippets
Materials and methods
In this work, we proposed a method for short-term ET0 forecast using the locally calibrated HS model and temperature forecasts. Daily meteorological data from four stations in China for the period 2001–2013 were collected from the China Meteorological Data Sharing Service System (http://cdc.cma.gov.cn), and the temperature forecasts for a 7-day horizon in 2012–2013 from Weather China (http://www.weather.com.cn). The observed meteorological data for 2001–2011 and 2012–2012 were used to locally
The evaluation of temperature forecasts
The respective statistical index values of the forecast accuracy for the locations considered are shown in Table 2. For all locations, the average accuracy of the 7-day minimum temperature forecasts ranged from 60.48% to 76.29% and the average values of MAE and RMSE ranged from 1.37 to 2.43 °C and from 1.77 to 2.69 °C, respectively. The average accuracy of the 7-day maximum temperature forecasts ranged from 50.18% to 62.94% and the average values of MAE and RMSE ranged from 2.17 to 2.43 °C and
Conclusions
This study describes a method to forecast ET0 for a 7-day horizon based on weather forecast temperature data and the HS model. The forecasted ET0 values were evaluated by comparison to values calculated from observed weather data and the PM model for four stations at locations in China with different climates. The main conclusions are as follows.
- (1)
The accuracy of temperature forecasts based on public weather forecasts is high overall, and the error in minimum temperature forecasts is less than
Acknowledgements
We are grateful for research grants from the National Natural Science Foundation of China (NSFC 51179048) and the Ministry of Science and Technology of China under the National Scientific and Technological Support Project (2011BAD25B07 and 2012BAD08B04). The observed meteorological data obtained from the China Meteorological Data Sharing Service System (http://cdc.cma.gov.cn) and weather forecast data from Weather China (http://www.weather.com.cn) are gratefully acknowledged. The comments made
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These authors contributed equally to the work.