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Short-term forecasting of daily reference evapotranspiration using the Penman-Monteith model and public weather forecasts
Agricultural Water Management 177 (2016) 329–339
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Agricultural Water Management journal homepage: www.elsevier.com/locate/agwat
Short-term forecasting of daily reference evapotranspiration using the Penman-Monteith model and public weather forecasts Yang Yang a,1 , Yuanlai Cui a , Yufeng Luo a,∗,1 , Xinwei Lyu b,c , Seydou Traore d , Shahbaz Khan e , Weiguang Wang f a
State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University, Wuhan, Hubei 430072, China School of Software Engineering, University of Science and Technology of China, Hefei, Anhui 230026, China c Wuhan Zhirun Water Technologies Co., Ltd., Wuhan, Hubei 430030, China d Department of Biological and Agricultural Engineering, Texas A&M University, College Station, TX 77843, USA e Regional Science Bureau for Asia and the Pacific UNESCO, DKI Jakarta 12110, Indonesia f State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering, Hohai University, Nanjing, Jiangsu 210098, China b
a r t i c l e
i n f o
Article history: Received 5 January 2016 Received in revised form 29 June 2016 Accepted 20 August 2016 Keywords: Reference evapotranspiration Irrigation demand forecast Public weather forecast Weather variables Penman-Monteith model
a b s t r a c t Short-term daily reference evapotranspiration (ETo) forecasts are required to facilitate real-time irrigation decision making. We forecasted daily 7-day-ahead ETo using the Penman–Monteith (PM) model and public weather forecasts. Public weather forecast data, including daily maximum and minimum temperatures, weather types and wind scales, for six stations located in a wide range of climate zones of China were collected. Weather types and wind scales were converted to sunshine duration and wind speed to forecast ETo. Meanwhile, daily meteorological data for the same period and locations were collected to calculate ETo, which served as reference standard for evaluating forecasting performance. The results showed that the forecasting performance for the minimum temperature was the best, followed by maximum temperature, sunshine duration and wind speed. Also, it was found that using public weather forecasts and the PM model improved the forecasting performance of daily ETo compared to those obtained when using the HS model with temperature forecasts as the only input data, and this improvement was because the weather type and wind scale forecasts also have positive influence on ETo forecasting. Further, the greatest impact on ETo forecasting error was found to be caused by the errors in sunshine duration and wind speed, followed by maximum and minimum temperature forecasts. © 2016 Elsevier B.V. All rights reserved.
1. Introduction The process of water loss from soil and crop surfaces to the atmosphere is called evapotranspiration (ET), which is a major component of the hydrological cycle and which impacts crop water resource management, farm irrigation scheduling and environmental assessment (Kisi and Zonemat-Kermani, 2014). Although crop ET can be directly measured, it is laborious, time consuming and costly; therefore, under most conditions, crop water requirements can be computed using reference crop evapotranspiration (ETo) from a standard surface and using an appropriate crop coefficient (KC ) (Eslamian et al., 2012; Rahimikhoob and Hosseinzadeh,
∗ Corresponding author. E-mail address: yfl[email protected] (Y. Luo). 1 These authors contributed equally to the work. http://dx.doi.org/10.1016/j.agwat.2016.08.020 0378-3774/© 2016 Elsevier B.V. All rights reserved.
2014). ETo plays an important role in real-time irrigation scheduling and in the management of irrigation systems. Therefore, some attempts have been made to estimate or predict ETo through observed weather data (Allen et al., 1989, 2005; Droogers and Allen, 2002; Khoob, 2008; Silva et al., 2010). Previous studies have placed particular emphasis on ETo estimation, and ETo forecasts have demonstrated greater utility in real-time irrigation management, as reported in the studies by Snyder et al. (2009), Luo et al. (2014), Lorite et al. (2015), Gavilán et al. (2015) and Traore et al. (2015). Based on the methodology and the input data, the ETo forecasting procedures can be divided into direct and indirect methods (Perera et al., 2014). In direct methods, two primary and typical procedures, namely, the time series method and artificial neural networks (ANNs), are utilized to forecast medium- or long-term ETo using historical weather data. For the time series method, Tracy et al. (1992) forecasted yearly ETo using an autoregressive integrated moving average (ARIMA) model, and Marino et al. (1993)
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proposed a seasonal ARIMA mode based on the ARIMA model and obtained accurate monthly ETo forecasts. Further, investigators have turned to forecasting daily and weekly ETo, which are more capable of assisting in medium- and short-term irrigation decision making. Mao (1994) analyzed the variation regularity of ETo over a year for North and Southwestern China and presented a modified daily mean model to forecast daily ETo. As the time series method, ANNs were applied for medium- and long-range forecasting and provide high accuracy in the past (Fernando and Jayawardena, 1998; Kumar et al., 2002; Trajkovic et al., 2003; Landeras et al., 2009), then turned to short-term forecasting in recent years (Luo et al., 2015; Ballesteros et al., 2016). Direct methods usually perform well in forecasting medium- or long-term ETo; however, forecasting daily ETo has become a trend because daily ETo forecasts are more useful in short-term irrigation scheduling. Daily ETo forecasts are restricted by weather conditions to a great extent, and direct methods using historical weather data are not applicable under most circumstances (Xiong et al., 2015). Therefore, indirect methods based on weather forecast data are widely adopted to forecast daily ETo. Recently, numerical weather forecast data have been utilized to forecast daily ETo, and several studies reported that numerical weather prediction models might be more accurate than statistical and time series models if the weather data are accurate (Duce et al., 1999; Arca et al., 2004; Ishak et al., 2010). Arca et al. (2004) forecasted ETo through PM models and weather data from the Agrometeorological Service of Sardinia, Italy, and produced better results in comparison to those obtained by the ARIMA and ANN models. Perera et al. (2014) forecasted daily ETo for lead times of up to 9 days using the PM model and numerical weather prediction (NWP) outputs, and the largest error source of ETo was found to be solar radiation. Although certain studies demonstrated that the utilization of NWP outputs in ETo forecasting could obtain sufficient accuracy (Duce et al., 1999; Perera et al., 2014), complete NWP outputs are still unavailable for the public in China that farmers and irrigation system operators cannot gain these data for practical agricultural production. Currently, public weather forecasts can be obtained freely from public channels in China, which released by China Meteorological Administration (CMA) through Weather China (http://www. weather.com.cn/). The public weather forecast data are based on a model called Global and Regional Assimilation and Prediction System (GRAPES), which is the new generation NWP system in China established by CMA, and these weather forecast data are also modified by weather forecasters in order to minimize the forecast error from NWP system error (Xue, 2005). Additionally, public weather forecasts contained enough parameters for daily ETo forecasting, including maximum and minimum temperature, weather type and wind scale. In this context, previous studies confirmed that the public weather forecasts were reasonable for ETo forecasting (Cai et al., 2007; Guo et al., 2011; Luo et al., 2014). Guo et al. (2011) proposed the Least squares support vector machine (LSSVM) model using public weather forecasts to forecast ETo, and the forecasted values exhibited a good fit with values calculated from meteorological data; however, this model lacked a physical basis. Although public weather forecast data include temperature, weather type and wind scale forecasts, temperature is the most influential and accurately forecasted variable; hence, several studies have used temperature-based models for forecasting ETo. Luo et al. (2014) proposed a method for short-term 7-day-ahead ETo forecasting using the Hargreaves-Samani (HS) model and temperature forecasts. Similarly, the Blaney-Criddle HS and ANN models and forecasted temperature data were adopted to forecast daily ETo in East China (Xiong et al., 2015; Ballesteros et al., 2016). All the models obtained ideal results and also showed that the major error in ETo forecasts resulted from the fact that the wind speed and humidity were not considered in the relevant method. Regard-
ing the above studies, although the temperature-based models can provide reasonable results, weather type and wind scale are also contained in public weather forecasts. Weather type and wind scale forecasts are original forecast data that cannot be directly applied as inputs to the PM model and they are also unable to be evaluated in a quantitative manner; however, through the analytical method (AM) proposed by Cai et al. (2007), weather type and wind scale can be respectively converted into sunshine duration and wind speed, which needed in ETo calculations and their forecasting performance can be measured through quantitative method. If the weather type and wind scale are accurately forecasted, considering these two variables might improve the forecasting performance of ETo because of the comprehensive consideration; however, if the errors of these two variables are high, a larger error can be introduced and lead to decreased ETo forecasting performance. Thus, the objectives of this work are twofold: (1) to verify whether the forecasting performance of ETo will improve when weather type and wind scale forecasts are adopted as the input weather variables and (2) to quantify the impact on ETo forecasting accuracy by each weather variable, including daily maximum and minimum temperature, sunshine duration and wind speed. 2. Materials and methods 2.1. Study area and data collection Public weather forecast data with a 7-day lead time for the period of 2012–2014 collected at six stations in China were obtained from Weather China (http://www.weather.com.cn), and daily observed meteorological data for the same period and stations were gathered from the China Meteorological Data Sharing Service System (http://data.cma.gov.cn). Forecasting performance of daily ETo and weather variables vary spatially with the change of climate to a certain extent (Perera et al., 2014). Therefore, the stations used in this study fall in typical climates, including humid, sub-humid and sub-arid regions, which distribute in a wide range of China according to different latitudes and longitudes. The characteristic of these six stations are shown in Fig. 1 and are described in Table 1. The meteorological data and public weather forecast data collected at these stations were obtained for the same period (May 24, 2012–May 24, 2014). Mean air pressure, daily minimum and maximum temperature, average temperature, average wind speed, sunshine duration and mean relative humidity were included in the observed daily meteorological data. Moreover, the corresponding public weather forecast data set for 7-day-ahead forecasting included daily minimum and maximum temperatures, weather type and wind scale. 2.2. Penman-Monteith model The FAO recommended the PM method (Allen et al., 1998) as the universal standard for ETo calculation; thus, we used the ETo calculated from the PM model to evaluate the forecasted ETo. The FAO-PM model (Allen et al., 1998) is ETo,PM =
0.408(Rn − G) + [900/(T + 273)]u2 (es − ea ) + (1 + 0.34u2 )
(1)
where ETo,PM is the daily ETo calculated from the PM model, in mm day −1 ; Rn is the net radiation at the crop surface, in MJ m−2 day−1 ; G is the soil heat flux density, in MJ m−2 day−1 ; T is the air temperature at a height of 2 m, in ◦ C; u2 is the wind speed at a height of 2 m, in m s −1 ; es is the vapor pressure of the air at saturation, in kPa; ea is the actual vapor pressure, in kPa; is the slope of the vapor pressure curve, in kPa ◦ C−1 ; and is the psychrometric constant, in kPa ◦ C−1 .
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Fig. 1. Locations of the weather stations used in this study.
2.3. ETo forecasts using PM model and public weather forecasts Weather type and wind scale forecasts from weather forecast information cannot be directly applied as inputs to the PM model, which also unable to be evaluated by a quantitative manner; Through the analytical method (AM) proposed by Cai et al. (2007), weather type and wind scale can be respectively transformed into sunshine duration and wind speed, which are available for PM model and their forecasting performance can be measured through quantitative method. Previous studies have reported that solar radiation (Rs ) had the largest effect on ETo among all the meteorological variables (Liu and Pereira, 2001) and played an important role in ETo forecasting (Arca et al., 2004). In addition, Rs has the largest impact on the accuracy of the ETo forecast (Perera et al., 2014); therefore, the first trial was conducted to estimate Rs . Solar radiation was estimated from sunshine duration (n), which, under each weather type, are in equal increments between 0 and N (Cai et al., 2007).
The sunshine duration can be calculated from the forecast descriptions as follows: n = aN
(2)
where n is the forecasted sunshine duration (hour); a is the adjustment coefficient; the five forecasting weather types, namely, clear, clear to partially cloudy, cloudy, overcast and rainy, correspond to the values of 0.9, 0.7, 0.5, 0.3 and 0.1, respectively; and N is the daylight duration or maximum sunshine duration (hours). Based on the standards of meteorological observations (CMA, 2003), the wind scales can be converted into wind speeds at a height of 10 m (u10 ), as displayed in Table 2. Furthermore, wind speeds at a height of 2 m (u2 ) are needed in the PM model. Thus, we transformed u10 into u2 using the following model (Allen et al., 1998): u2 = uz
4.87 ln (67.8z − 5.42)
(3)
Table 1 Characteristics of the weather stations used in this study. WMO Number
Station
Latitude
Longitude
Elevation (m)
Climate zone
58040 57957 57091 53614 50953 57494
Ganyu (GY) Guilin (GL) Kaifeng (KF) Yinchuan (YC) Harbin (HB) Wuhan (WH)
39◦ 49 48 N 25◦ 19 12 N 34◦ 46 12 N 38◦ 28 48 N 45◦ 45 30 N 30◦ 37 12 N
119◦ 07 12 E 110◦ 17 59 E 114◦ 22 48 E 106◦ 13 12 E 126◦ 47 12 E 114◦ 07 48 E
3.3 164.4 73.7 1111.4 142.3 23.1
Humid Humid Humid Sub-arid Sub-humid Humid
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Table 2 Conversion relationship between wind scales and wind speeds at a height of 10 m. Wind scale
0 1 2 3 4 5 6 7 8 9 10 11 12
Designation
Calm Light Slight Gentle Moderate Fresh Strong wind High wind Gale Strong gale Whole gale Storm Hurricane
result of ETo performance (Cai et al., 2007; Luo et al., 2014; Perera et al., 2014; Traore et al., 2015) and are calculated as follows:
u10 (m s−1 )
n
Range
Average
0.0–0.2 0.3–1.5 1.6–3.3 3.4–5.4 5.5–7.9 8.0–10.7 10.8–13.8 13.9–17.1 17.2–20.7 20.8–24.4 24.5–28.4 28.5–32.6 32.7–36.9
0.1 1.0 2.0 4.0 7.0 9.0 12.0 16.0 19.0 23.0 26.0 31.0 35.0
MAE =
(4)
n
n 2 (Fi − Oi ) i=1
RMSE =
n
R=
(5)
n Fi − F
Oi − O
i=1 n 2 2 n Fi − F Oi − O i=1
where u2 is the 2-m-height wind speed (m s−1 ), uz is the average value of the measured wind speed at height z (m s−1 ), and z is the height of the measurements above the ground surface (m). Based on the above calculations with the AM approach, the parameters needed by the FAO-PM model were prepared; thus, the public weather forecasts with a 7-day lead time can be used to forecast ETo (ETo,WF ) for lead times of up to 7 days. The daily weather forecast description and observed daily meteorological data were entered into the PM for ETo calculation. Then, forecasted ETo was compared with ETo calculated using observed daily meteorological data for the same stations and period.
|Fi − Oi |
i=1
(6)
i=1
where n is the number of observations; Fi and Oi are the ith ¯ are the observed and forecasted values, respectively; and F¯ and O mean of Fi and Oi for the observation period. 3. Results and discussion The accuracy of weather variables, specifically, the maximum and minimum temperature (Tmax and Tmin ), sunshine duration and wind speed, strongly impacts daily ETo. Any deviation produces errors in ETo forecasts (Perera et al., 2014); therefore, we first evaluated the forecasting performance of these variables for lead times of 1–7 days at all stations. Then, the ETo forecasting performance was quantified for the same period and locations. Finally, we roughly assessed the impacts on daily ETo by each weather variable.
2.4. Statistical analysis
3.1. Forecasting performance for weather variables
Several parameters were utilized to evaluate the forecasting performance for daily ETo and weather forecast variables for each lead time (daily maximum and minimum temperature, daily weather types and daily wind scales). The accuracy of the forecast weather variable was defined as the percentage of days where accurate forecasts were obtained for all the days of the observation period. When the absolute error of the forecasted weather datum was within ± 2 ◦ C (or m s−1 or h) compared to the equivalent observed meteorological information, we regarded the forecast variable as accurate, as suggested by Thornes (1996) and CMA (2005). Similarly, the accuracy of the forecasted ETo was defined as the percentage of days with accurate forecasts being obtained for all days of the observation period. When the forecasted ETo was within ±1.5 mm day−1 in terms of absolute error, we regarded the ETo forecast was accurate (Luo et al., 2014; Xiong et al., 2015). The accuracy provided clear evaluation that the values range from 0 to 100% according to the proportion of accurate forecasts and are hoped to be close to 100%. Other statistical indices, including the mean absolute error (MAE), the root mean square error (RMSE), and the correlation coefficient (R), are also employed to quantify forecasting performance of daily ETo and weather variables. The MAE offered a range of error between the forecast and actual as represented by observations. The RMSE measured the level of agreement between the forecast and observed values (Perera et al., 2014). Both the MAE and RMSE are desirably as small as possible that good forecasting performance could be gained. The R was used to quantify the variance of the forecasts with the variance of the observations, and forecast values showed goodness of fitting with observed values when R was close to 1.0 (Traore et al., 2015). In previous works, the mentioned statistical indices have been adopted to quantify the
3.1.1. Temperature Daily Tmax and Tmin were essential to computing the slope of the curve of the vapor pressure versus saturation vapor pressure and outgoing net longwave radiation. In humid, sub-humid and subarid climates, Tmin was assumed to be a good estimator of the dew point temperature (Tdew ) to calculate the actual vapor pressure, while it may happen that Tmin > Tdew under extreme aridity climates and lead to less good estimation (Allen, 1996; Cai et al., 2007). Each weather stations in this study was located in the range of humid, sub-humid or sub-arid climates, thus the assumption Tmin = Tdew was generally acceptable. The respective performance indicators are shown in Fig. 2. For all stations, the average accuracy of Tmin ranged between 56.82% and 73.12%, and the average MAE and RMSE ranged from 1.56 to 2.73 ◦ C and 2.09–4.55 ◦ C, respectively. For Tmax , the average accuracy ranged from 46.30% to 51.54%, and the average MAE and RMSE ranged from 2.45 to 3.33 ◦ C and 3.20–5.04 ◦ C, respectively. R for both Tmax and Tmin was greater than 0.92, i.e., strong linear relationships between forecasted and observed values were obtained. The above results indicated that the forecasting performance of Tmin was higher than that of Tmax , in contrast to NWP outputs in Australia (Perera et al., 2014), and was in agreement with previous work in China (Luo et al., 2014; Luo et al., 2015; Xiong et al., 2015). For all locations, trends were found for both Tmax and Tmin wherein the forecasting performance followed a decreasing trend with increasing lead time but continued to perform well in forecasting ETo. 3.1.2. Sunshine duration The comparisons between observed sunshine duration values and those calculated using the forecasted weather type at six sta-
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Fig. 2. Statistical indices for daily minimum temperature forecasting performance ((a) Accuracy, (b) MAE, (c) RMSE, and (d) R) and daily maximum temperature forecasting performance ((e) Accuracy, (f) MAE, (g) RMSE, and (h) R) at 6 stations.
tions are given in Fig. 3. For the 1-7-day lead time, comparatively weaker statistical indicators were found: the average accuracy varied between 30.02% and 43.11%; the MAE and RMSE varied from 2.96 to 4.08 h and 3.65–5.06 h, respectively; and R ranged from 0.25 to 0.46. The forecasting performance of sunshine duration decreased with increasing forecast lead time, and there was no significant scatter among these six locations. The lower performance might be caused by the poor forecasting performance and the calculation method, which translates the weather type forecast into sunshine duration. Thus, a better outcome can be expected with the
improvement in weather type forecasts and amelioration in calculation method. These results suggested that the sunshine duration forecasting performance was acceptable, although all the statistical indices of sunshine duration were worse than those of the temperature variables.
3.1.3. Wind speed Fig. 4 summarizes the comparison between u10 calculated from wind scale forecasts and those computed based on the observed data. For the 7-day lead times at six stations, the accuracy ranged
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Fig. 3. Forecasting performance of sunshine duration as manifested by (a) Accuracy, (b) MAE, (c) RMSE, and (d) R at 6 stations.
from 10.31% to 64.24%; the MAE and RMSE ranged from 1.72 to 3.57 m s−1 and 1.95–3.80 m s−1 , respectively; and R ranged from 0.06 to 0.27. The forecasted wind speed yielded the lowest correlation coefficient among all the weather variables, which indicated that the linear relationship between forecast and observed data was weak. Moreover, forecasted wind speeds were almost always over-predicted compared to the observed values and led to the over-prediction of the ETo. The annual forecasted wind speeds were higher than those observed, from 24.48% to 108.43% for six locations. There were no significant differences in the forecasting performance of each weather variable among the 6 stations, excluding wind speed, which exhibited a large fluctuation between stations. The Ganyu and Kaifeng stations are located in the same climate region and have similar latitude and longitude but not elevation. There was a large gap between their corresponding forecasting performances, with accuracies of 10.31% and 64.24% for Ganyu and Kaifeng, respectively. This result suggests further investigation on the climate zone and geographical elements experienced by the weather stations, especially the elevation. Considering the above fact, it can be concluded that the wind speed forecasts presented the worst performance of all the weather variables considered. 3.2. Forecasting performance of ETo from weather forecast data Fig. 5 presents comparison charts of forecasted ETo,WF against ETo,PM calculated using full meteorological data (for clarity, only 1-, 4-, and 7-day lead times are shown) for the period at all stations. As shown in the figure, the smaller and larger absolute error were respectively found during winter and summer for all lead times, and one of the reason for the seasonal different relates to
the variation amplitude of weather, which change slightly in a day during winter while change greatly during summer. For all stations, the over-prediction of the values mainly appeared from September to March, whereas slight under-predictions were obtained from April to August. This may be because wind speed strongly impacts ETo during autumn to spring and because wind scale forecasts were over-predicted most of the year, thereby leading to the overprediction of ETo. There were a number of cases, and we took a typical example: For January 14, 2013, at Ganyu, the forecasted temperature was accurate compared to the observed values (errors within ±2 ◦ C), and the forecasted ETo and forecasted wind speed were 1.33 mm day−1 and 4.11 m s−1 , respectively. The ETo computed from observed metrological data and the observed wind speed were 0.66 mm day−1 and 0.90 m s−1 , respectively. During summer, ETo is greatly influenced by the duration of sunshine, and the poor forecasting performance of weather types may result in the slight under-prediction of ETo. Although over-predicted and under-predicted values were obtained, these charts also show that ETo,WF is in good agreement with ETo,PM , and the changes in the period for ETo,WF and ETo,PM exhibit the same patterns, therein suggesting that the forecasted values can reflect the seasonal variation process of ETo. Analogous relationships were found among these six stations; therefore, Kaifeng station was selected as an example, and the ratio of the absolute errors for different forecast lead times for daily ETo in 2012–2014 are shown in Fig. 6 (for clarity, only 1-, 3-, 5- and 7day lead times are shown). More than half of the ETo results were slightly over-predicted in comparison to the observed values; the proportions of over-predicted values were 56.62%, 54.39%, 54.61% and 55.04% for lead times of 1 day, 3 days, 5 days and 7 days, respectively. Similarly, ETo forecasts were over-predicted using numerical
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Fig. 4. Four statistical indices for forecasting performance of wind speeds at height of 10 m for 6 stations: (a) Accuracy, (b) MAE, (c) RMSE, and (d) R.
Table 3 Average statistical measures for ETo forecasts and those computed with observed data.
Table 4 Statistical indices of the forecasted ETo and ETo calculated from observed data at Guilin station for 1- to 7-day lead times.
Location
Accuracy (%)
MAE (mm day−1 )
RMSE (mm day−1 )
R
Lead time (day)
Accuracy (%)
MAE (mm day−1 )
RMSE (mm day−1 )
R
GY GL KF YC HB WH
87.12 87.58 85.62 91.14 84.69 84.70
0.76 0.75 0.76Z 0.63 0.75 0.84
0.98 0.95 1.00 0.65 1.08 1.06
0.82 0.78 0.83 0.89 0.83 0.83
1 2 3 4 5 6 7
91.79 89.14 89.12 88.41 86.43 85.15 83.03
0.64 0.72 0.71 0.74 0.78 0.81 0.85
0.82 0.91 0.90 0.93 1.00 1.02 1.09
0.83 0.81 0.81 0.79 0.75 0.75 0.71
weather prediction (NWP) outputs because of the over-predicted weather variables (Perera et al., 2014). On average, the proportion of smallest errors (errors of ±0.3 mm day−1 ) corresponded to the highest percentage of all lead times and decreased with increasing lead time, while the largest errors (errors greater than ±1.5 mm day−1 ) exhibited an opposite tendency with increasing lead times. In addition, other parts of the errors (errors within 0.3–1.5 and −0.3 to −1.5) did not show obvious changing rules with lead times. To quantify the forecasting performance, the forecasted ETo,WF were compared with the values calculated from the PM model and observed meteorological data, and Table 3 presents average statistical measures for ETo,WF and ETo,PM computed using observed data. For all stations and for all lead times, the average accuracy ranged between 84.69% and 91.14%, and the MAE and RMSE values ranged from 0.63 to 0.84 mm day−1 and from 0.65 to 1.08 mm day−1 , respectively. The value of R between the forecasted and observed data was high, ranging from 0.78 to 0.89, which suggested that ETo,WF agreed well with the observed values. Because similar rules were found among all the stations, Guilin station was
selected as a typical example, as shown in Table 4. The accuracy and R decreased with increased lead time from 91.79% (1 day lead time) to 83.03% (7 day lead time) and from 0.83 to 0.71, respectively, and the MAE and RMSE exhibited opposite variation trends from 0.64 to 0.85 mm day−1 and 0.82–1.09 mm day−1 for 1- to 7-day lead times, respectively. Analogous to the input weather variables, the forecasted ETo,WF exhibited the same regulation whereby the forecasting performance slightly decreased with increasing lead time. The decreasing forecasting performance of the daily ETo was directly caused by the decreasing forecasting performance of the input weather variables, for instance, solar radiation and wind speed (Chiew et al., 1995; Perera et al., 2014). In a previous study, daily ETo was forecasted using the Hargreaves-Samani model based only on temperature forecasts (Luo et al., 2014), and the statistical indices of accuracy, MAE, RMSE and R ranged from 77.43% to 90.81%, 0.64–1.02 mm day−1 , 0.87–1.36 mm day−1 and 0.64–0.86, respectively. In addition, for the same stations in this study, the accuracy, MAE, RMSE and R ranged from 85.62% to 91.14%, 0.63–0.76 mm day−1 ,
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0.65–1.00 mm day−1 and 0.83–0.89, respectively. By contrast, all the statistical indices in the proposed study were worse than those in this study. This may be because the HS model does not consider the sunshine duration and wind speed, which also influence the ETo forecasts, although the forecasting performance of these two factors were relatively low compared with the temperature forecasts. Other authors, such as Ballesteros et al. (2016), similarly concluded that sunshine duration and wind speed have a strong effect on ETo computations, whereas HS does not consider these factors. In another previous study on ETo forecasting using NWP outputs (Perera et al., 2014), the average RMSEs of forecasted ETo were 0.73 (1-day lead time) and 1.10 mm day−1 (5-day lead time) for all locations; in this work, the average RMSEs were 0.91 (1-day lead time) and 0.96 mm day−1 (5-day lead time). The above indicates that the ETo forecast using public weather forecasts have similar performance with those using NWP outputs. Also, it was found that the forecasting performance of ETo using NWP outputs declined faster than those in this study with increasing lead time, and this may be because the forecasting performance of input weather variables from NWP outputs declined faster than did those of public weather forecasts with increasing lead time. All the weather variables were used in ETo forecasts to obtain greater accuracy, and because of the comprehensive consideration, as expected, good results were obtained. In conclusion, better outcomes were obtained with the use of public weather forecasts and the PM model compared to those obtained with the HS model using temperature forecasts as the only input data. This is because weather type and wind scale forecasts also have positive influence on ETo forecasts. Although the forecasting performance was good, the accuracies of the weather type and wind scale forecasts were both relatively low compared to the temperature forecasts; therefore, it is necessary to detect the influence degree on the error in ETo forecasts by each weather variable, as discussed in the next section.
3.3. Impact of weather variable forecasts on ETo forecasts
Fig. 5. Variation tendency of ETo (2012–2014) calculated from public weather forecasts and full observed data: (a) Ganyu, (b) Guilin, (c) Kaifeng, (d) Yinchuan, (e) Harbin, and (f) Wuhan.
To investigate the impact of each forecast weather variable on the ETo forecasting performance, four ETo forecasts were produced by replacing one observed climatic variable (maximum and minimum air temperature, sunshine duration and wind speed) at a time with the equivalent forecast weather variable. Note that the larger the decreased obtained using the corresponding weather variable, the more a significant error in that variable contributes to the error in the ETo forecasts. The statistical indices are shown in Fig. 7. When observed temperature data were replaced by corresponding forecast data, the errors in ETo were minimal, and the ETo forecasting performance was extremely high for both Tmin and Tmax ; the average accuracy was greater than 99.42% and 98.98% for all stations and for all lead times. For Tmin , the average MAE and RMSE were less than 0.10 mm day−1 and 0.22 mm day−1 , respectively, and for Tmax , the average MAE and RMSE were less than 0.17 mm day−1 and 0.35 mm day−1 , respectively. In addition, R for both Tmin and Tmax was greater than 0.98 for all lead times. For lead times of up to 2 days, the largest reduction in accuracy was obtained by substituting the forecasted wind speed; then, the forecasted sunshine duration produced the largest reduction for lead times of 3–7 days. Concerning the correlation coefficient, sunshine duration provided the largest reduction. Concerning the MAE, the largest decrease was caused by using wind speed. In addition, for the RMSE, wind speed engendered the largest reduction for lead times of up to 5 days; for lead times of 6–7 days, sunshine duration provided the largest reduction. For all stations except for Yinchuan, when the observed sunshine duration and wind speed were replaced by corresponding
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Fig. 6. Errors in ETo forecasts (2012–2014) at Kaifeng station for different lead times: (a) 1 day, (b) 3 days, (c) 5 days, and (d) 7 days.
Fig. 7. Average statistical indices of ETo forecasts when replacing equivalent forecasted weather variables one at a time for 7-day lead times at all stations: (a) Accuracy, (b) MAE, (c) RMSE, (d) R.
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forecast variables, the average accuracy of the ETo forecast ranged from 97.64% (1-day lead time) to 95.37% (7-day lead time) and from 99.14% to 98.99%, respectively. Other statistical indices also indicated that the largest reduction in ETo was provided by sunshine duration, followed by wind speed. Similar results have been reported wherein the solar radiation (calculated using the sunshine duration) from NWP outputs leads to the greatest decrease in forecasted ETo because the greatest amount of energy for ET is provided by solar radiation (Perera et al., 2014). In addition, ETo values are most sensitive to errors in sunshine duration (Liu and Pereira, 2001; Popova et al., 2006). However, at Yinchuan, the error in the ETo forecast was mainly produced by errors in wind speed, and the accuracy of the ETo forecast greatly decreased, ranging from 84.17% to 82.35% for 1- to 7-day lead times, when using forecasted wind speed. In addition, the reduction provided by the sunshine duration was quite low compared to those obtained from using wind speed, where the accuracy varied from 98.89% to 97.20%. Therefore, for all stations, the highest MAEs and RMSEs of the wind speed were mainly influenced by the data obtained at Yinchuan station. As pointed out by Cai et al. (2007), estimating the wind speed from wind scale forecasts shows acceptable but estimation errors are larger for arid sites. Only the Yinchuan station locates in subarid region while the other stations locate in humid or sub-humid regions, thus we infer that wind speed calculated by forecasted wind scale lead to the greatest errors in ETo forecasts for arid or sub-arid climate zones. These results indicated that the greatest reduction in the ETo forecast was provided by sunshine duration, followed by wind speed, Tmax and Tmin under most circumstances. Moreover, due to the climate zone where the weather station located, such as arid and sub-arid regions, the largest error source might be wind speed instead of sunshine duration. When wind speed represents the greatest error source in these climate zones, this can lead to larger declines in ETo forecasts compared to those areas being most influence by sunshine duration. George et al. (1985) concluded that ETo forecasts would be of limited benefit when using forecasted wind velocity, which is one of the most difficult variables to accurately forecast. Thus, we suggest that wind scale forecasts should be used with caution when weather stations in arid or sub-arid regions in order to minimize forecast errors. To enhance the capability of accurately forecasting ETo, a high-priority task is to ameliorate the calculated model and improve the accuracy of weather type forecasting, which has the largest direct influence on ETo forecasts.
4. Conclusions This paper quantified the forecasting performance of weather variables derived from public weather forecasts as well as forecasted ETo for a 7-day lead time at six stations in China. In addition, this paper verified whether the forecasting performance of ETo will be improved when weather type and wind scale forecasts were adopted as the input weather variables. Moreover, we also measured the impacts of each weather variable on ETo forecasts. The main conclusions are as follows. The accuracies of ETo forecasts based on this method were relatively high and results suggested that using public weather forecasts and the PM model improved the forecasting performance of daily ETo compared to those obtained when using the HS model with temperature forecasts as the only input data. On average, the RMSE declined 17.57% for the same station and for all lead time. This improvement was because the weather type and wind scale forecasts also have positive influence on ETo forecasting. The forecasting performance of Tmin was the highest of all the considered weather variables, followed by Tmax , sunshine duration and wind speed. Furthermore, there were no significant differences
in the forecasting performance of each weather variable among the six stations, excluding wind speed, which exhibited large fluctuations between stations. This calls for further investigation on the climate zone and geographical elements experienced by the weather stations, especially elevation. Moreover, it was found that the greatest reduction in the ETo forecasts was provided by sunshine duration, followed by wind speed, Tmax and Tmin under most circumstances; however, due to the climate zones where the weather station located, such as arid and sub-arid regions, the largest error source might be wind speed. The forecasting performance of weather type and wind scale are not good as those of temperature, therefore, further research is required to detect that these two factors which contributes most to errors in ETo forecasts on the basis of the climate zone and whether they should be both or alternative used can obtain greatest ETo forecasts based on different climate area. From a practical viewpoint, the irrigation system operators could obtain complete public weather forecasts data easily and freely from public channel, and using PM equation with weather forecast message to gain accurate daily ETo forecasts for lead time up to 7days, which are of significant use in real-time irrigation scheduling and irrigation water management.
Acknowledgements This work was financially supported by the National Natural Science Foundation of China (NSFC 51179048 and 51579184) and the Water Resources Department of Jiangxi Province (KT201427 and KJ201409). The observed meteorological data obtained from the China Meteorological Data Sharing Service System (http:// data.cma.gov.cn) and weather forecast data from Weather China (http://www.weather.com.cn) are gratefully acknowledged. The comments made by two anonymous reviewers are also highly appreciated.
References Allen, R.G., Jensen, M.E., Wright, J.L., Burman, R.D., 1989. Operation estimates of reference evapotranspiration. J. Agron. 81, 650–662. Allen, R.G., Pereira, L.S., Raes, D., Smith, M., 1998. Crop evapotranspiration: guidelines for computing crop water requirements. In: FAO Irrigation and Drainage Paper No. 56. FAO, Rome, Italy. Allen, R.G., Clemments, A.J., Burt, C.M., Solomon, K., O’Halloran, T., 2005. Prediction accuracy for project wide evpotranspiration using crop coefficients and reference evapotranspiration. J. Irrig. Drain. Eng. 131 (1), 24–36. Allen, R.G., 1996. Assessing integrity of weather data for reference evapotranspiration estimation. J. Irri. Drain. Eng. 122 (2), 97–106. Arca, B., Duce, P., Snyder, R.L., Spano, D., Fiori, M., 2004. Use of numerical weather forecast and time series models for predicting reference evapotranspiration. Acta Hortic. 664, 39–46. Ballesteros, R., Ortega, J.F., Moreno, M.A., 2016. FORETo: new software for reference evapotranspiration forecasting. J. Arid Environ. 124 (1), 128–141. Blaney, H.F., Criddle, W.D., 1962. Determining Consumptive Use and Irrigation Water Requirements. USDA ARS Tech Bull, Washington (DC). CMA, 2003. Surface Meteorological Observation Criterion. China Meteorological Administration, Beijing, China (In Chinese). CMA, 2005. Quality Inspection of Medium-short-term Weather Forecast. China Meteorological Administration, Beijing China (In Chinese). Cai, J.B., Liu, Y., Lei, T., Pereira, L.S., 2007. Estimating reference evapotranspiration with the FAO Penman–Monteith equation using daily weather forecast messages. Agric. For. Meteorol. 145 (1), 22–35. Chiew, F.H.S., Kamladasa, N.N., Malano, H.M., McMahon, T.A., 1995. Penman-Monteith, FAO-24 reference crop evapotranspiration and class-A pan data in Australia. Agric. Water Manag. 28 (1), 9–21. Droogers, P., Allen, R.G., 2002. Estimating reference evapotranspiration under inaccurate data conditions. J. Irrig. Drain. Eng. 16, 33–45. Duce, P., Snyder, R.L., Spano, D., 1999. Forecasting reference evapotranspiration, III. Int. Soc. Hortic. Sci. (ISHS) 537 (1), 135–141. Eslamian, S.S., Gohari, S.A., Zareian, M.J., Firoozfar, A., 2012. Estimating penman-Monteith reference evapotranspiration using artificial neural networks and genetic algorithm: a case study. Arab. J. Sci. Eng. 37 (4), 935–944. Fernando, D.A., Jayawardena, A.W., 1998. Runoff forecasting using RBF networks with OLS algorithm. J. Hydrol. Eng. 3 (3), 203–209.
Y. Yang et al. / Agricultural Water Management 177 (2016) 329–339 Gavilán, P., Ruiz, N., Lozano, D., 2015. Daily forecasting of reference and strawberry crop evapotranspiration in greenhouses in a Mediterranean climate based on solar radiation estimates. Agric. Water Manag. 159, 307–317. George, W., Pruitt, W.O., Dong, A., 1985. Evapotranspiration modelling In: CIMIS final report 10013-A. Land Air Water Res. Paper Ser. B 53812, 3.36–3.61. Guo, X., Sun, X., Ma, J., 2011. Prediction of daily crop reference evapotranspiration (ETo) values through a least-squares support vector machine model. Hydrol. Res. 42 (4), 268–274. Hargreaves, G.H., Samani, Z.A., 1985. Reference crop evapotranspiration from temperature. Appl. Eng. Agric. 1, 96–99. Ishak, A.M., Bray, M., Remesanm, R., Han, D., 2010. Estimating reference and Irrigation using numerical weather modeling. Hydrol. Process. 24 (24), 3490–3509. Khoob, A.R., 2008. Comparative study of Hargreaves’s and artificial neural network’s methodologies in estimating reference evapotranspiration in a semiarid environment. Irrig. Sci. 26 (3), 253–259. Kisi, O., Zonemat-Kermani, 2014. Comparison of two different adaptive neuro-Fuzzy inference systems in modlling daily reference evapotranspiration. Water Resour. Manag. 28 (9), 2655–2675. Kumar, M., Raghuwanshi, N.S., Singh, R., Wallender, W.W., Pruitt, W.O., 2002. Estimating evapotranspiration using artificial neural network. J. Irrig. Drain. Eng. 128 (4), 224. Landeras, G., Ortiz-Barredo, A., Lopez, J.J., 2009. Comparison of artificial neural network models and empirical and semi-empirical equations for daily reference evapotranspiration estimation in the Basque Country (Northern Spain). Liu, Y., Pereira, L.S., 2001. Calculation methods for reference evapotranspiration with limited weather data. J. Hydraul. Eng. 32 (3), 11–17 (In Chinese with English abstract). Lorite, I.J., Ramírez-Cuesta, J.M., Cruz-Blanco, M., Santos, C., 2015. Using weather forecast data for irrigation scheduling under semi-arid conditions. Irrig. Sci. 33 (6), 411–427. Luo, Y., Chang, X., Peng, S., Khan, S., Wang, W., Zheng, Q., Cai, X., 2014. Short-term forecasting of daily reference evapotranspiration using the Hargreaves–Samani model and temperature forecasts. Agric. Water Manag. 136, 42–51. Luo, Y., Traore, S., Lyu, X., Wang, W., Wang, Y., Xie, Y., Jiao, X., Fipps, G., 2015. Medium range daily reference evapotranspiration forecasting by using ANN and public weather forecasts. Water Resour. Manag. 29, 3863–3876.
339
Mao, Z., 1994. Forecast of crop evapotranspiration. ICID Bull. 43 (1), 23–36. Marino, M.A., Tracy, J.C., Taghavi, S.A., 1993. Forecasting of reference crop evapotranspiration. Agric. Water Manag. 24, 163–187. Perera, K.C., Western, A.W., Nawarathna, B., George, B., 2014. Forecasting daily reference evapotranspiration for Australia using numerical weather prediction outputs. Agric. Forest Meteor. 194 (2014), 50–63. Popova, Z., Kercheva, M., Pereira, L.S., 2006. Validation of the FAO methodology for computing ETo with missing climatic data application to South Bulgaria. Irrig. Drain. 55, 201–215. Rahimikhoob, A., Hosseinzadeh, M., 2014. Assessment of Blaney-Criddle Equation for Calculating Reference Evapotranspiration with NOAA/AVHRR Data. Water Resour. Manag. 28 (10), 3365–3375. Silva, D., Meza, F.J., Varas, E., 2010. Estimating reference evapotranspiration (ETo) using numerical weather forecast data in central Chile. J. Hydrol. 382 (1–4), 64–71. Snyder, R.L., Palmer, C., Orang, M., Anderson, M., 2009. National weather service reference evapotranspiration forecast. Crop Water Use. 4, 1–6. Thornes, J.E., 1996. The quality and accuracy of a sample of public and commercial weather forecasts in the UK. Meteorol. Appl. 3 (1), 63–74. Tracy, J.C., Marino, M.A., Taghavi, S.A., 1992. Predicting water demand in agricultural regions using time series forecasts of reference crop evapotranspiration. Proceedings of the Water Resources Sessions at Water Forum, 50–55. Trajkovic, S., Todorovic, B., Stankovic, M., 2003. Forecasting of reference evapotranspiration by artificial neural networks. J. Irrig. Drain. Eng. 129, 454–457. Traore, S., et al., 2015. Deployment of artificial neural network for short-term forecasting of evapotranspiration using public weather forecast restricted messages. Agric. Water Manag., http://dx.doi.org/10.1016/j.agwat.2015.10.009. Xiong, Y., Luo, Y., Wang, Y., Traore, S., Xu, J., Jiao, X., Fipps, G., 2015. Forecasting daily reference evapotranspiration using the Blaney-Criddle model and temperature forecasts. Arch. Agron. Soil, http://dx.doi.org/10.1080/03650340. 2015.1083983. Xue, J., 2005. Progresses of researches on numerical weather prediction in China: 1999–2002. Adv. Atmos. Sci. 21 (3), 467–474.
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Agricultural Water Management journal homepage: www.elsevier.com/locate/agwat
Short-term forecasting of daily reference evapotranspiration using the Penman-Monteith model and public weather forecasts Yang Yang a,1 , Yuanlai Cui a , Yufeng Luo a,∗,1 , Xinwei Lyu b,c , Seydou Traore d , Shahbaz Khan e , Weiguang Wang f a
State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University, Wuhan, Hubei 430072, China School of Software Engineering, University of Science and Technology of China, Hefei, Anhui 230026, China c Wuhan Zhirun Water Technologies Co., Ltd., Wuhan, Hubei 430030, China d Department of Biological and Agricultural Engineering, Texas A&M University, College Station, TX 77843, USA e Regional Science Bureau for Asia and the Pacific UNESCO, DKI Jakarta 12110, Indonesia f State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering, Hohai University, Nanjing, Jiangsu 210098, China b
a r t i c l e
i n f o
Article history: Received 5 January 2016 Received in revised form 29 June 2016 Accepted 20 August 2016 Keywords: Reference evapotranspiration Irrigation demand forecast Public weather forecast Weather variables Penman-Monteith model
a b s t r a c t Short-term daily reference evapotranspiration (ETo) forecasts are required to facilitate real-time irrigation decision making. We forecasted daily 7-day-ahead ETo using the Penman–Monteith (PM) model and public weather forecasts. Public weather forecast data, including daily maximum and minimum temperatures, weather types and wind scales, for six stations located in a wide range of climate zones of China were collected. Weather types and wind scales were converted to sunshine duration and wind speed to forecast ETo. Meanwhile, daily meteorological data for the same period and locations were collected to calculate ETo, which served as reference standard for evaluating forecasting performance. The results showed that the forecasting performance for the minimum temperature was the best, followed by maximum temperature, sunshine duration and wind speed. Also, it was found that using public weather forecasts and the PM model improved the forecasting performance of daily ETo compared to those obtained when using the HS model with temperature forecasts as the only input data, and this improvement was because the weather type and wind scale forecasts also have positive influence on ETo forecasting. Further, the greatest impact on ETo forecasting error was found to be caused by the errors in sunshine duration and wind speed, followed by maximum and minimum temperature forecasts. © 2016 Elsevier B.V. All rights reserved.
1. Introduction The process of water loss from soil and crop surfaces to the atmosphere is called evapotranspiration (ET), which is a major component of the hydrological cycle and which impacts crop water resource management, farm irrigation scheduling and environmental assessment (Kisi and Zonemat-Kermani, 2014). Although crop ET can be directly measured, it is laborious, time consuming and costly; therefore, under most conditions, crop water requirements can be computed using reference crop evapotranspiration (ETo) from a standard surface and using an appropriate crop coefficient (KC ) (Eslamian et al., 2012; Rahimikhoob and Hosseinzadeh,
∗ Corresponding author. E-mail address: yfl[email protected] (Y. Luo). 1 These authors contributed equally to the work. http://dx.doi.org/10.1016/j.agwat.2016.08.020 0378-3774/© 2016 Elsevier B.V. All rights reserved.
2014). ETo plays an important role in real-time irrigation scheduling and in the management of irrigation systems. Therefore, some attempts have been made to estimate or predict ETo through observed weather data (Allen et al., 1989, 2005; Droogers and Allen, 2002; Khoob, 2008; Silva et al., 2010). Previous studies have placed particular emphasis on ETo estimation, and ETo forecasts have demonstrated greater utility in real-time irrigation management, as reported in the studies by Snyder et al. (2009), Luo et al. (2014), Lorite et al. (2015), Gavilán et al. (2015) and Traore et al. (2015). Based on the methodology and the input data, the ETo forecasting procedures can be divided into direct and indirect methods (Perera et al., 2014). In direct methods, two primary and typical procedures, namely, the time series method and artificial neural networks (ANNs), are utilized to forecast medium- or long-term ETo using historical weather data. For the time series method, Tracy et al. (1992) forecasted yearly ETo using an autoregressive integrated moving average (ARIMA) model, and Marino et al. (1993)
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proposed a seasonal ARIMA mode based on the ARIMA model and obtained accurate monthly ETo forecasts. Further, investigators have turned to forecasting daily and weekly ETo, which are more capable of assisting in medium- and short-term irrigation decision making. Mao (1994) analyzed the variation regularity of ETo over a year for North and Southwestern China and presented a modified daily mean model to forecast daily ETo. As the time series method, ANNs were applied for medium- and long-range forecasting and provide high accuracy in the past (Fernando and Jayawardena, 1998; Kumar et al., 2002; Trajkovic et al., 2003; Landeras et al., 2009), then turned to short-term forecasting in recent years (Luo et al., 2015; Ballesteros et al., 2016). Direct methods usually perform well in forecasting medium- or long-term ETo; however, forecasting daily ETo has become a trend because daily ETo forecasts are more useful in short-term irrigation scheduling. Daily ETo forecasts are restricted by weather conditions to a great extent, and direct methods using historical weather data are not applicable under most circumstances (Xiong et al., 2015). Therefore, indirect methods based on weather forecast data are widely adopted to forecast daily ETo. Recently, numerical weather forecast data have been utilized to forecast daily ETo, and several studies reported that numerical weather prediction models might be more accurate than statistical and time series models if the weather data are accurate (Duce et al., 1999; Arca et al., 2004; Ishak et al., 2010). Arca et al. (2004) forecasted ETo through PM models and weather data from the Agrometeorological Service of Sardinia, Italy, and produced better results in comparison to those obtained by the ARIMA and ANN models. Perera et al. (2014) forecasted daily ETo for lead times of up to 9 days using the PM model and numerical weather prediction (NWP) outputs, and the largest error source of ETo was found to be solar radiation. Although certain studies demonstrated that the utilization of NWP outputs in ETo forecasting could obtain sufficient accuracy (Duce et al., 1999; Perera et al., 2014), complete NWP outputs are still unavailable for the public in China that farmers and irrigation system operators cannot gain these data for practical agricultural production. Currently, public weather forecasts can be obtained freely from public channels in China, which released by China Meteorological Administration (CMA) through Weather China (http://www. weather.com.cn/). The public weather forecast data are based on a model called Global and Regional Assimilation and Prediction System (GRAPES), which is the new generation NWP system in China established by CMA, and these weather forecast data are also modified by weather forecasters in order to minimize the forecast error from NWP system error (Xue, 2005). Additionally, public weather forecasts contained enough parameters for daily ETo forecasting, including maximum and minimum temperature, weather type and wind scale. In this context, previous studies confirmed that the public weather forecasts were reasonable for ETo forecasting (Cai et al., 2007; Guo et al., 2011; Luo et al., 2014). Guo et al. (2011) proposed the Least squares support vector machine (LSSVM) model using public weather forecasts to forecast ETo, and the forecasted values exhibited a good fit with values calculated from meteorological data; however, this model lacked a physical basis. Although public weather forecast data include temperature, weather type and wind scale forecasts, temperature is the most influential and accurately forecasted variable; hence, several studies have used temperature-based models for forecasting ETo. Luo et al. (2014) proposed a method for short-term 7-day-ahead ETo forecasting using the Hargreaves-Samani (HS) model and temperature forecasts. Similarly, the Blaney-Criddle HS and ANN models and forecasted temperature data were adopted to forecast daily ETo in East China (Xiong et al., 2015; Ballesteros et al., 2016). All the models obtained ideal results and also showed that the major error in ETo forecasts resulted from the fact that the wind speed and humidity were not considered in the relevant method. Regard-
ing the above studies, although the temperature-based models can provide reasonable results, weather type and wind scale are also contained in public weather forecasts. Weather type and wind scale forecasts are original forecast data that cannot be directly applied as inputs to the PM model and they are also unable to be evaluated in a quantitative manner; however, through the analytical method (AM) proposed by Cai et al. (2007), weather type and wind scale can be respectively converted into sunshine duration and wind speed, which needed in ETo calculations and their forecasting performance can be measured through quantitative method. If the weather type and wind scale are accurately forecasted, considering these two variables might improve the forecasting performance of ETo because of the comprehensive consideration; however, if the errors of these two variables are high, a larger error can be introduced and lead to decreased ETo forecasting performance. Thus, the objectives of this work are twofold: (1) to verify whether the forecasting performance of ETo will improve when weather type and wind scale forecasts are adopted as the input weather variables and (2) to quantify the impact on ETo forecasting accuracy by each weather variable, including daily maximum and minimum temperature, sunshine duration and wind speed. 2. Materials and methods 2.1. Study area and data collection Public weather forecast data with a 7-day lead time for the period of 2012–2014 collected at six stations in China were obtained from Weather China (http://www.weather.com.cn), and daily observed meteorological data for the same period and stations were gathered from the China Meteorological Data Sharing Service System (http://data.cma.gov.cn). Forecasting performance of daily ETo and weather variables vary spatially with the change of climate to a certain extent (Perera et al., 2014). Therefore, the stations used in this study fall in typical climates, including humid, sub-humid and sub-arid regions, which distribute in a wide range of China according to different latitudes and longitudes. The characteristic of these six stations are shown in Fig. 1 and are described in Table 1. The meteorological data and public weather forecast data collected at these stations were obtained for the same period (May 24, 2012–May 24, 2014). Mean air pressure, daily minimum and maximum temperature, average temperature, average wind speed, sunshine duration and mean relative humidity were included in the observed daily meteorological data. Moreover, the corresponding public weather forecast data set for 7-day-ahead forecasting included daily minimum and maximum temperatures, weather type and wind scale. 2.2. Penman-Monteith model The FAO recommended the PM method (Allen et al., 1998) as the universal standard for ETo calculation; thus, we used the ETo calculated from the PM model to evaluate the forecasted ETo. The FAO-PM model (Allen et al., 1998) is ETo,PM =
0.408(Rn − G) + [900/(T + 273)]u2 (es − ea ) + (1 + 0.34u2 )
(1)
where ETo,PM is the daily ETo calculated from the PM model, in mm day −1 ; Rn is the net radiation at the crop surface, in MJ m−2 day−1 ; G is the soil heat flux density, in MJ m−2 day−1 ; T is the air temperature at a height of 2 m, in ◦ C; u2 is the wind speed at a height of 2 m, in m s −1 ; es is the vapor pressure of the air at saturation, in kPa; ea is the actual vapor pressure, in kPa; is the slope of the vapor pressure curve, in kPa ◦ C−1 ; and is the psychrometric constant, in kPa ◦ C−1 .
Y. Yang et al. / Agricultural Water Management 177 (2016) 329–339
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Fig. 1. Locations of the weather stations used in this study.
2.3. ETo forecasts using PM model and public weather forecasts Weather type and wind scale forecasts from weather forecast information cannot be directly applied as inputs to the PM model, which also unable to be evaluated by a quantitative manner; Through the analytical method (AM) proposed by Cai et al. (2007), weather type and wind scale can be respectively transformed into sunshine duration and wind speed, which are available for PM model and their forecasting performance can be measured through quantitative method. Previous studies have reported that solar radiation (Rs ) had the largest effect on ETo among all the meteorological variables (Liu and Pereira, 2001) and played an important role in ETo forecasting (Arca et al., 2004). In addition, Rs has the largest impact on the accuracy of the ETo forecast (Perera et al., 2014); therefore, the first trial was conducted to estimate Rs . Solar radiation was estimated from sunshine duration (n), which, under each weather type, are in equal increments between 0 and N (Cai et al., 2007).
The sunshine duration can be calculated from the forecast descriptions as follows: n = aN
(2)
where n is the forecasted sunshine duration (hour); a is the adjustment coefficient; the five forecasting weather types, namely, clear, clear to partially cloudy, cloudy, overcast and rainy, correspond to the values of 0.9, 0.7, 0.5, 0.3 and 0.1, respectively; and N is the daylight duration or maximum sunshine duration (hours). Based on the standards of meteorological observations (CMA, 2003), the wind scales can be converted into wind speeds at a height of 10 m (u10 ), as displayed in Table 2. Furthermore, wind speeds at a height of 2 m (u2 ) are needed in the PM model. Thus, we transformed u10 into u2 using the following model (Allen et al., 1998): u2 = uz
4.87 ln (67.8z − 5.42)
(3)
Table 1 Characteristics of the weather stations used in this study. WMO Number
Station
Latitude
Longitude
Elevation (m)
Climate zone
58040 57957 57091 53614 50953 57494
Ganyu (GY) Guilin (GL) Kaifeng (KF) Yinchuan (YC) Harbin (HB) Wuhan (WH)
39◦ 49 48 N 25◦ 19 12 N 34◦ 46 12 N 38◦ 28 48 N 45◦ 45 30 N 30◦ 37 12 N
119◦ 07 12 E 110◦ 17 59 E 114◦ 22 48 E 106◦ 13 12 E 126◦ 47 12 E 114◦ 07 48 E
3.3 164.4 73.7 1111.4 142.3 23.1
Humid Humid Humid Sub-arid Sub-humid Humid
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Table 2 Conversion relationship between wind scales and wind speeds at a height of 10 m. Wind scale
0 1 2 3 4 5 6 7 8 9 10 11 12
Designation
Calm Light Slight Gentle Moderate Fresh Strong wind High wind Gale Strong gale Whole gale Storm Hurricane
result of ETo performance (Cai et al., 2007; Luo et al., 2014; Perera et al., 2014; Traore et al., 2015) and are calculated as follows:
u10 (m s−1 )
n
Range
Average
0.0–0.2 0.3–1.5 1.6–3.3 3.4–5.4 5.5–7.9 8.0–10.7 10.8–13.8 13.9–17.1 17.2–20.7 20.8–24.4 24.5–28.4 28.5–32.6 32.7–36.9
0.1 1.0 2.0 4.0 7.0 9.0 12.0 16.0 19.0 23.0 26.0 31.0 35.0
MAE =
(4)
n
n 2 (Fi − Oi ) i=1
RMSE =
n
R=
(5)
n Fi − F
Oi − O
i=1 n 2 2 n Fi − F Oi − O i=1
where u2 is the 2-m-height wind speed (m s−1 ), uz is the average value of the measured wind speed at height z (m s−1 ), and z is the height of the measurements above the ground surface (m). Based on the above calculations with the AM approach, the parameters needed by the FAO-PM model were prepared; thus, the public weather forecasts with a 7-day lead time can be used to forecast ETo (ETo,WF ) for lead times of up to 7 days. The daily weather forecast description and observed daily meteorological data were entered into the PM for ETo calculation. Then, forecasted ETo was compared with ETo calculated using observed daily meteorological data for the same stations and period.
|Fi − Oi |
i=1
(6)
i=1
where n is the number of observations; Fi and Oi are the ith ¯ are the observed and forecasted values, respectively; and F¯ and O mean of Fi and Oi for the observation period. 3. Results and discussion The accuracy of weather variables, specifically, the maximum and minimum temperature (Tmax and Tmin ), sunshine duration and wind speed, strongly impacts daily ETo. Any deviation produces errors in ETo forecasts (Perera et al., 2014); therefore, we first evaluated the forecasting performance of these variables for lead times of 1–7 days at all stations. Then, the ETo forecasting performance was quantified for the same period and locations. Finally, we roughly assessed the impacts on daily ETo by each weather variable.
2.4. Statistical analysis
3.1. Forecasting performance for weather variables
Several parameters were utilized to evaluate the forecasting performance for daily ETo and weather forecast variables for each lead time (daily maximum and minimum temperature, daily weather types and daily wind scales). The accuracy of the forecast weather variable was defined as the percentage of days where accurate forecasts were obtained for all the days of the observation period. When the absolute error of the forecasted weather datum was within ± 2 ◦ C (or m s−1 or h) compared to the equivalent observed meteorological information, we regarded the forecast variable as accurate, as suggested by Thornes (1996) and CMA (2005). Similarly, the accuracy of the forecasted ETo was defined as the percentage of days with accurate forecasts being obtained for all days of the observation period. When the forecasted ETo was within ±1.5 mm day−1 in terms of absolute error, we regarded the ETo forecast was accurate (Luo et al., 2014; Xiong et al., 2015). The accuracy provided clear evaluation that the values range from 0 to 100% according to the proportion of accurate forecasts and are hoped to be close to 100%. Other statistical indices, including the mean absolute error (MAE), the root mean square error (RMSE), and the correlation coefficient (R), are also employed to quantify forecasting performance of daily ETo and weather variables. The MAE offered a range of error between the forecast and actual as represented by observations. The RMSE measured the level of agreement between the forecast and observed values (Perera et al., 2014). Both the MAE and RMSE are desirably as small as possible that good forecasting performance could be gained. The R was used to quantify the variance of the forecasts with the variance of the observations, and forecast values showed goodness of fitting with observed values when R was close to 1.0 (Traore et al., 2015). In previous works, the mentioned statistical indices have been adopted to quantify the
3.1.1. Temperature Daily Tmax and Tmin were essential to computing the slope of the curve of the vapor pressure versus saturation vapor pressure and outgoing net longwave radiation. In humid, sub-humid and subarid climates, Tmin was assumed to be a good estimator of the dew point temperature (Tdew ) to calculate the actual vapor pressure, while it may happen that Tmin > Tdew under extreme aridity climates and lead to less good estimation (Allen, 1996; Cai et al., 2007). Each weather stations in this study was located in the range of humid, sub-humid or sub-arid climates, thus the assumption Tmin = Tdew was generally acceptable. The respective performance indicators are shown in Fig. 2. For all stations, the average accuracy of Tmin ranged between 56.82% and 73.12%, and the average MAE and RMSE ranged from 1.56 to 2.73 ◦ C and 2.09–4.55 ◦ C, respectively. For Tmax , the average accuracy ranged from 46.30% to 51.54%, and the average MAE and RMSE ranged from 2.45 to 3.33 ◦ C and 3.20–5.04 ◦ C, respectively. R for both Tmax and Tmin was greater than 0.92, i.e., strong linear relationships between forecasted and observed values were obtained. The above results indicated that the forecasting performance of Tmin was higher than that of Tmax , in contrast to NWP outputs in Australia (Perera et al., 2014), and was in agreement with previous work in China (Luo et al., 2014; Luo et al., 2015; Xiong et al., 2015). For all locations, trends were found for both Tmax and Tmin wherein the forecasting performance followed a decreasing trend with increasing lead time but continued to perform well in forecasting ETo. 3.1.2. Sunshine duration The comparisons between observed sunshine duration values and those calculated using the forecasted weather type at six sta-
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Fig. 2. Statistical indices for daily minimum temperature forecasting performance ((a) Accuracy, (b) MAE, (c) RMSE, and (d) R) and daily maximum temperature forecasting performance ((e) Accuracy, (f) MAE, (g) RMSE, and (h) R) at 6 stations.
tions are given in Fig. 3. For the 1-7-day lead time, comparatively weaker statistical indicators were found: the average accuracy varied between 30.02% and 43.11%; the MAE and RMSE varied from 2.96 to 4.08 h and 3.65–5.06 h, respectively; and R ranged from 0.25 to 0.46. The forecasting performance of sunshine duration decreased with increasing forecast lead time, and there was no significant scatter among these six locations. The lower performance might be caused by the poor forecasting performance and the calculation method, which translates the weather type forecast into sunshine duration. Thus, a better outcome can be expected with the
improvement in weather type forecasts and amelioration in calculation method. These results suggested that the sunshine duration forecasting performance was acceptable, although all the statistical indices of sunshine duration were worse than those of the temperature variables.
3.1.3. Wind speed Fig. 4 summarizes the comparison between u10 calculated from wind scale forecasts and those computed based on the observed data. For the 7-day lead times at six stations, the accuracy ranged
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Fig. 3. Forecasting performance of sunshine duration as manifested by (a) Accuracy, (b) MAE, (c) RMSE, and (d) R at 6 stations.
from 10.31% to 64.24%; the MAE and RMSE ranged from 1.72 to 3.57 m s−1 and 1.95–3.80 m s−1 , respectively; and R ranged from 0.06 to 0.27. The forecasted wind speed yielded the lowest correlation coefficient among all the weather variables, which indicated that the linear relationship between forecast and observed data was weak. Moreover, forecasted wind speeds were almost always over-predicted compared to the observed values and led to the over-prediction of the ETo. The annual forecasted wind speeds were higher than those observed, from 24.48% to 108.43% for six locations. There were no significant differences in the forecasting performance of each weather variable among the 6 stations, excluding wind speed, which exhibited a large fluctuation between stations. The Ganyu and Kaifeng stations are located in the same climate region and have similar latitude and longitude but not elevation. There was a large gap between their corresponding forecasting performances, with accuracies of 10.31% and 64.24% for Ganyu and Kaifeng, respectively. This result suggests further investigation on the climate zone and geographical elements experienced by the weather stations, especially the elevation. Considering the above fact, it can be concluded that the wind speed forecasts presented the worst performance of all the weather variables considered. 3.2. Forecasting performance of ETo from weather forecast data Fig. 5 presents comparison charts of forecasted ETo,WF against ETo,PM calculated using full meteorological data (for clarity, only 1-, 4-, and 7-day lead times are shown) for the period at all stations. As shown in the figure, the smaller and larger absolute error were respectively found during winter and summer for all lead times, and one of the reason for the seasonal different relates to
the variation amplitude of weather, which change slightly in a day during winter while change greatly during summer. For all stations, the over-prediction of the values mainly appeared from September to March, whereas slight under-predictions were obtained from April to August. This may be because wind speed strongly impacts ETo during autumn to spring and because wind scale forecasts were over-predicted most of the year, thereby leading to the overprediction of ETo. There were a number of cases, and we took a typical example: For January 14, 2013, at Ganyu, the forecasted temperature was accurate compared to the observed values (errors within ±2 ◦ C), and the forecasted ETo and forecasted wind speed were 1.33 mm day−1 and 4.11 m s−1 , respectively. The ETo computed from observed metrological data and the observed wind speed were 0.66 mm day−1 and 0.90 m s−1 , respectively. During summer, ETo is greatly influenced by the duration of sunshine, and the poor forecasting performance of weather types may result in the slight under-prediction of ETo. Although over-predicted and under-predicted values were obtained, these charts also show that ETo,WF is in good agreement with ETo,PM , and the changes in the period for ETo,WF and ETo,PM exhibit the same patterns, therein suggesting that the forecasted values can reflect the seasonal variation process of ETo. Analogous relationships were found among these six stations; therefore, Kaifeng station was selected as an example, and the ratio of the absolute errors for different forecast lead times for daily ETo in 2012–2014 are shown in Fig. 6 (for clarity, only 1-, 3-, 5- and 7day lead times are shown). More than half of the ETo results were slightly over-predicted in comparison to the observed values; the proportions of over-predicted values were 56.62%, 54.39%, 54.61% and 55.04% for lead times of 1 day, 3 days, 5 days and 7 days, respectively. Similarly, ETo forecasts were over-predicted using numerical
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Fig. 4. Four statistical indices for forecasting performance of wind speeds at height of 10 m for 6 stations: (a) Accuracy, (b) MAE, (c) RMSE, and (d) R.
Table 3 Average statistical measures for ETo forecasts and those computed with observed data.
Table 4 Statistical indices of the forecasted ETo and ETo calculated from observed data at Guilin station for 1- to 7-day lead times.
Location
Accuracy (%)
MAE (mm day−1 )
RMSE (mm day−1 )
R
Lead time (day)
Accuracy (%)
MAE (mm day−1 )
RMSE (mm day−1 )
R
GY GL KF YC HB WH
87.12 87.58 85.62 91.14 84.69 84.70
0.76 0.75 0.76Z 0.63 0.75 0.84
0.98 0.95 1.00 0.65 1.08 1.06
0.82 0.78 0.83 0.89 0.83 0.83
1 2 3 4 5 6 7
91.79 89.14 89.12 88.41 86.43 85.15 83.03
0.64 0.72 0.71 0.74 0.78 0.81 0.85
0.82 0.91 0.90 0.93 1.00 1.02 1.09
0.83 0.81 0.81 0.79 0.75 0.75 0.71
weather prediction (NWP) outputs because of the over-predicted weather variables (Perera et al., 2014). On average, the proportion of smallest errors (errors of ±0.3 mm day−1 ) corresponded to the highest percentage of all lead times and decreased with increasing lead time, while the largest errors (errors greater than ±1.5 mm day−1 ) exhibited an opposite tendency with increasing lead times. In addition, other parts of the errors (errors within 0.3–1.5 and −0.3 to −1.5) did not show obvious changing rules with lead times. To quantify the forecasting performance, the forecasted ETo,WF were compared with the values calculated from the PM model and observed meteorological data, and Table 3 presents average statistical measures for ETo,WF and ETo,PM computed using observed data. For all stations and for all lead times, the average accuracy ranged between 84.69% and 91.14%, and the MAE and RMSE values ranged from 0.63 to 0.84 mm day−1 and from 0.65 to 1.08 mm day−1 , respectively. The value of R between the forecasted and observed data was high, ranging from 0.78 to 0.89, which suggested that ETo,WF agreed well with the observed values. Because similar rules were found among all the stations, Guilin station was
selected as a typical example, as shown in Table 4. The accuracy and R decreased with increased lead time from 91.79% (1 day lead time) to 83.03% (7 day lead time) and from 0.83 to 0.71, respectively, and the MAE and RMSE exhibited opposite variation trends from 0.64 to 0.85 mm day−1 and 0.82–1.09 mm day−1 for 1- to 7-day lead times, respectively. Analogous to the input weather variables, the forecasted ETo,WF exhibited the same regulation whereby the forecasting performance slightly decreased with increasing lead time. The decreasing forecasting performance of the daily ETo was directly caused by the decreasing forecasting performance of the input weather variables, for instance, solar radiation and wind speed (Chiew et al., 1995; Perera et al., 2014). In a previous study, daily ETo was forecasted using the Hargreaves-Samani model based only on temperature forecasts (Luo et al., 2014), and the statistical indices of accuracy, MAE, RMSE and R ranged from 77.43% to 90.81%, 0.64–1.02 mm day−1 , 0.87–1.36 mm day−1 and 0.64–0.86, respectively. In addition, for the same stations in this study, the accuracy, MAE, RMSE and R ranged from 85.62% to 91.14%, 0.63–0.76 mm day−1 ,
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0.65–1.00 mm day−1 and 0.83–0.89, respectively. By contrast, all the statistical indices in the proposed study were worse than those in this study. This may be because the HS model does not consider the sunshine duration and wind speed, which also influence the ETo forecasts, although the forecasting performance of these two factors were relatively low compared with the temperature forecasts. Other authors, such as Ballesteros et al. (2016), similarly concluded that sunshine duration and wind speed have a strong effect on ETo computations, whereas HS does not consider these factors. In another previous study on ETo forecasting using NWP outputs (Perera et al., 2014), the average RMSEs of forecasted ETo were 0.73 (1-day lead time) and 1.10 mm day−1 (5-day lead time) for all locations; in this work, the average RMSEs were 0.91 (1-day lead time) and 0.96 mm day−1 (5-day lead time). The above indicates that the ETo forecast using public weather forecasts have similar performance with those using NWP outputs. Also, it was found that the forecasting performance of ETo using NWP outputs declined faster than those in this study with increasing lead time, and this may be because the forecasting performance of input weather variables from NWP outputs declined faster than did those of public weather forecasts with increasing lead time. All the weather variables were used in ETo forecasts to obtain greater accuracy, and because of the comprehensive consideration, as expected, good results were obtained. In conclusion, better outcomes were obtained with the use of public weather forecasts and the PM model compared to those obtained with the HS model using temperature forecasts as the only input data. This is because weather type and wind scale forecasts also have positive influence on ETo forecasts. Although the forecasting performance was good, the accuracies of the weather type and wind scale forecasts were both relatively low compared to the temperature forecasts; therefore, it is necessary to detect the influence degree on the error in ETo forecasts by each weather variable, as discussed in the next section.
3.3. Impact of weather variable forecasts on ETo forecasts
Fig. 5. Variation tendency of ETo (2012–2014) calculated from public weather forecasts and full observed data: (a) Ganyu, (b) Guilin, (c) Kaifeng, (d) Yinchuan, (e) Harbin, and (f) Wuhan.
To investigate the impact of each forecast weather variable on the ETo forecasting performance, four ETo forecasts were produced by replacing one observed climatic variable (maximum and minimum air temperature, sunshine duration and wind speed) at a time with the equivalent forecast weather variable. Note that the larger the decreased obtained using the corresponding weather variable, the more a significant error in that variable contributes to the error in the ETo forecasts. The statistical indices are shown in Fig. 7. When observed temperature data were replaced by corresponding forecast data, the errors in ETo were minimal, and the ETo forecasting performance was extremely high for both Tmin and Tmax ; the average accuracy was greater than 99.42% and 98.98% for all stations and for all lead times. For Tmin , the average MAE and RMSE were less than 0.10 mm day−1 and 0.22 mm day−1 , respectively, and for Tmax , the average MAE and RMSE were less than 0.17 mm day−1 and 0.35 mm day−1 , respectively. In addition, R for both Tmin and Tmax was greater than 0.98 for all lead times. For lead times of up to 2 days, the largest reduction in accuracy was obtained by substituting the forecasted wind speed; then, the forecasted sunshine duration produced the largest reduction for lead times of 3–7 days. Concerning the correlation coefficient, sunshine duration provided the largest reduction. Concerning the MAE, the largest decrease was caused by using wind speed. In addition, for the RMSE, wind speed engendered the largest reduction for lead times of up to 5 days; for lead times of 6–7 days, sunshine duration provided the largest reduction. For all stations except for Yinchuan, when the observed sunshine duration and wind speed were replaced by corresponding
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Fig. 6. Errors in ETo forecasts (2012–2014) at Kaifeng station for different lead times: (a) 1 day, (b) 3 days, (c) 5 days, and (d) 7 days.
Fig. 7. Average statistical indices of ETo forecasts when replacing equivalent forecasted weather variables one at a time for 7-day lead times at all stations: (a) Accuracy, (b) MAE, (c) RMSE, (d) R.
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forecast variables, the average accuracy of the ETo forecast ranged from 97.64% (1-day lead time) to 95.37% (7-day lead time) and from 99.14% to 98.99%, respectively. Other statistical indices also indicated that the largest reduction in ETo was provided by sunshine duration, followed by wind speed. Similar results have been reported wherein the solar radiation (calculated using the sunshine duration) from NWP outputs leads to the greatest decrease in forecasted ETo because the greatest amount of energy for ET is provided by solar radiation (Perera et al., 2014). In addition, ETo values are most sensitive to errors in sunshine duration (Liu and Pereira, 2001; Popova et al., 2006). However, at Yinchuan, the error in the ETo forecast was mainly produced by errors in wind speed, and the accuracy of the ETo forecast greatly decreased, ranging from 84.17% to 82.35% for 1- to 7-day lead times, when using forecasted wind speed. In addition, the reduction provided by the sunshine duration was quite low compared to those obtained from using wind speed, where the accuracy varied from 98.89% to 97.20%. Therefore, for all stations, the highest MAEs and RMSEs of the wind speed were mainly influenced by the data obtained at Yinchuan station. As pointed out by Cai et al. (2007), estimating the wind speed from wind scale forecasts shows acceptable but estimation errors are larger for arid sites. Only the Yinchuan station locates in subarid region while the other stations locate in humid or sub-humid regions, thus we infer that wind speed calculated by forecasted wind scale lead to the greatest errors in ETo forecasts for arid or sub-arid climate zones. These results indicated that the greatest reduction in the ETo forecast was provided by sunshine duration, followed by wind speed, Tmax and Tmin under most circumstances. Moreover, due to the climate zone where the weather station located, such as arid and sub-arid regions, the largest error source might be wind speed instead of sunshine duration. When wind speed represents the greatest error source in these climate zones, this can lead to larger declines in ETo forecasts compared to those areas being most influence by sunshine duration. George et al. (1985) concluded that ETo forecasts would be of limited benefit when using forecasted wind velocity, which is one of the most difficult variables to accurately forecast. Thus, we suggest that wind scale forecasts should be used with caution when weather stations in arid or sub-arid regions in order to minimize forecast errors. To enhance the capability of accurately forecasting ETo, a high-priority task is to ameliorate the calculated model and improve the accuracy of weather type forecasting, which has the largest direct influence on ETo forecasts.
4. Conclusions This paper quantified the forecasting performance of weather variables derived from public weather forecasts as well as forecasted ETo for a 7-day lead time at six stations in China. In addition, this paper verified whether the forecasting performance of ETo will be improved when weather type and wind scale forecasts were adopted as the input weather variables. Moreover, we also measured the impacts of each weather variable on ETo forecasts. The main conclusions are as follows. The accuracies of ETo forecasts based on this method were relatively high and results suggested that using public weather forecasts and the PM model improved the forecasting performance of daily ETo compared to those obtained when using the HS model with temperature forecasts as the only input data. On average, the RMSE declined 17.57% for the same station and for all lead time. This improvement was because the weather type and wind scale forecasts also have positive influence on ETo forecasting. The forecasting performance of Tmin was the highest of all the considered weather variables, followed by Tmax , sunshine duration and wind speed. Furthermore, there were no significant differences
in the forecasting performance of each weather variable among the six stations, excluding wind speed, which exhibited large fluctuations between stations. This calls for further investigation on the climate zone and geographical elements experienced by the weather stations, especially elevation. Moreover, it was found that the greatest reduction in the ETo forecasts was provided by sunshine duration, followed by wind speed, Tmax and Tmin under most circumstances; however, due to the climate zones where the weather station located, such as arid and sub-arid regions, the largest error source might be wind speed. The forecasting performance of weather type and wind scale are not good as those of temperature, therefore, further research is required to detect that these two factors which contributes most to errors in ETo forecasts on the basis of the climate zone and whether they should be both or alternative used can obtain greatest ETo forecasts based on different climate area. From a practical viewpoint, the irrigation system operators could obtain complete public weather forecasts data easily and freely from public channel, and using PM equation with weather forecast message to gain accurate daily ETo forecasts for lead time up to 7days, which are of significant use in real-time irrigation scheduling and irrigation water management.
Acknowledgements This work was financially supported by the National Natural Science Foundation of China (NSFC 51179048 and 51579184) and the Water Resources Department of Jiangxi Province (KT201427 and KJ201409). The observed meteorological data obtained from the China Meteorological Data Sharing Service System (http:// data.cma.gov.cn) and weather forecast data from Weather China (http://www.weather.com.cn) are gratefully acknowledged. The comments made by two anonymous reviewers are also highly appreciated.
References Allen, R.G., Jensen, M.E., Wright, J.L., Burman, R.D., 1989. Operation estimates of reference evapotranspiration. J. Agron. 81, 650–662. Allen, R.G., Pereira, L.S., Raes, D., Smith, M., 1998. Crop evapotranspiration: guidelines for computing crop water requirements. In: FAO Irrigation and Drainage Paper No. 56. FAO, Rome, Italy. Allen, R.G., Clemments, A.J., Burt, C.M., Solomon, K., O’Halloran, T., 2005. Prediction accuracy for project wide evpotranspiration using crop coefficients and reference evapotranspiration. J. Irrig. Drain. Eng. 131 (1), 24–36. Allen, R.G., 1996. Assessing integrity of weather data for reference evapotranspiration estimation. J. Irri. Drain. Eng. 122 (2), 97–106. Arca, B., Duce, P., Snyder, R.L., Spano, D., Fiori, M., 2004. Use of numerical weather forecast and time series models for predicting reference evapotranspiration. Acta Hortic. 664, 39–46. Ballesteros, R., Ortega, J.F., Moreno, M.A., 2016. FORETo: new software for reference evapotranspiration forecasting. J. Arid Environ. 124 (1), 128–141. Blaney, H.F., Criddle, W.D., 1962. Determining Consumptive Use and Irrigation Water Requirements. USDA ARS Tech Bull, Washington (DC). CMA, 2003. Surface Meteorological Observation Criterion. China Meteorological Administration, Beijing, China (In Chinese). CMA, 2005. Quality Inspection of Medium-short-term Weather Forecast. China Meteorological Administration, Beijing China (In Chinese). Cai, J.B., Liu, Y., Lei, T., Pereira, L.S., 2007. Estimating reference evapotranspiration with the FAO Penman–Monteith equation using daily weather forecast messages. Agric. For. Meteorol. 145 (1), 22–35. Chiew, F.H.S., Kamladasa, N.N., Malano, H.M., McMahon, T.A., 1995. Penman-Monteith, FAO-24 reference crop evapotranspiration and class-A pan data in Australia. Agric. Water Manag. 28 (1), 9–21. Droogers, P., Allen, R.G., 2002. Estimating reference evapotranspiration under inaccurate data conditions. J. Irrig. Drain. Eng. 16, 33–45. Duce, P., Snyder, R.L., Spano, D., 1999. Forecasting reference evapotranspiration, III. Int. Soc. Hortic. Sci. (ISHS) 537 (1), 135–141. Eslamian, S.S., Gohari, S.A., Zareian, M.J., Firoozfar, A., 2012. Estimating penman-Monteith reference evapotranspiration using artificial neural networks and genetic algorithm: a case study. Arab. J. Sci. Eng. 37 (4), 935–944. Fernando, D.A., Jayawardena, A.W., 1998. Runoff forecasting using RBF networks with OLS algorithm. J. Hydrol. Eng. 3 (3), 203–209.
Y. Yang et al. / Agricultural Water Management 177 (2016) 329–339 Gavilán, P., Ruiz, N., Lozano, D., 2015. Daily forecasting of reference and strawberry crop evapotranspiration in greenhouses in a Mediterranean climate based on solar radiation estimates. Agric. Water Manag. 159, 307–317. George, W., Pruitt, W.O., Dong, A., 1985. Evapotranspiration modelling In: CIMIS final report 10013-A. Land Air Water Res. Paper Ser. B 53812, 3.36–3.61. Guo, X., Sun, X., Ma, J., 2011. Prediction of daily crop reference evapotranspiration (ETo) values through a least-squares support vector machine model. Hydrol. Res. 42 (4), 268–274. Hargreaves, G.H., Samani, Z.A., 1985. Reference crop evapotranspiration from temperature. Appl. Eng. Agric. 1, 96–99. Ishak, A.M., Bray, M., Remesanm, R., Han, D., 2010. Estimating reference and Irrigation using numerical weather modeling. Hydrol. Process. 24 (24), 3490–3509. Khoob, A.R., 2008. Comparative study of Hargreaves’s and artificial neural network’s methodologies in estimating reference evapotranspiration in a semiarid environment. Irrig. Sci. 26 (3), 253–259. Kisi, O., Zonemat-Kermani, 2014. Comparison of two different adaptive neuro-Fuzzy inference systems in modlling daily reference evapotranspiration. Water Resour. Manag. 28 (9), 2655–2675. Kumar, M., Raghuwanshi, N.S., Singh, R., Wallender, W.W., Pruitt, W.O., 2002. Estimating evapotranspiration using artificial neural network. J. Irrig. Drain. Eng. 128 (4), 224. Landeras, G., Ortiz-Barredo, A., Lopez, J.J., 2009. Comparison of artificial neural network models and empirical and semi-empirical equations for daily reference evapotranspiration estimation in the Basque Country (Northern Spain). Liu, Y., Pereira, L.S., 2001. Calculation methods for reference evapotranspiration with limited weather data. J. Hydraul. Eng. 32 (3), 11–17 (In Chinese with English abstract). Lorite, I.J., Ramírez-Cuesta, J.M., Cruz-Blanco, M., Santos, C., 2015. Using weather forecast data for irrigation scheduling under semi-arid conditions. Irrig. Sci. 33 (6), 411–427. Luo, Y., Chang, X., Peng, S., Khan, S., Wang, W., Zheng, Q., Cai, X., 2014. Short-term forecasting of daily reference evapotranspiration using the Hargreaves–Samani model and temperature forecasts. Agric. Water Manag. 136, 42–51. Luo, Y., Traore, S., Lyu, X., Wang, W., Wang, Y., Xie, Y., Jiao, X., Fipps, G., 2015. Medium range daily reference evapotranspiration forecasting by using ANN and public weather forecasts. Water Resour. Manag. 29, 3863–3876.
339
Mao, Z., 1994. Forecast of crop evapotranspiration. ICID Bull. 43 (1), 23–36. Marino, M.A., Tracy, J.C., Taghavi, S.A., 1993. Forecasting of reference crop evapotranspiration. Agric. Water Manag. 24, 163–187. Perera, K.C., Western, A.W., Nawarathna, B., George, B., 2014. Forecasting daily reference evapotranspiration for Australia using numerical weather prediction outputs. Agric. Forest Meteor. 194 (2014), 50–63. Popova, Z., Kercheva, M., Pereira, L.S., 2006. Validation of the FAO methodology for computing ETo with missing climatic data application to South Bulgaria. Irrig. Drain. 55, 201–215. Rahimikhoob, A., Hosseinzadeh, M., 2014. Assessment of Blaney-Criddle Equation for Calculating Reference Evapotranspiration with NOAA/AVHRR Data. Water Resour. Manag. 28 (10), 3365–3375. Silva, D., Meza, F.J., Varas, E., 2010. Estimating reference evapotranspiration (ETo) using numerical weather forecast data in central Chile. J. Hydrol. 382 (1–4), 64–71. Snyder, R.L., Palmer, C., Orang, M., Anderson, M., 2009. National weather service reference evapotranspiration forecast. Crop Water Use. 4, 1–6. Thornes, J.E., 1996. The quality and accuracy of a sample of public and commercial weather forecasts in the UK. Meteorol. Appl. 3 (1), 63–74. Tracy, J.C., Marino, M.A., Taghavi, S.A., 1992. Predicting water demand in agricultural regions using time series forecasts of reference crop evapotranspiration. Proceedings of the Water Resources Sessions at Water Forum, 50–55. Trajkovic, S., Todorovic, B., Stankovic, M., 2003. Forecasting of reference evapotranspiration by artificial neural networks. J. Irrig. Drain. Eng. 129, 454–457. Traore, S., et al., 2015. Deployment of artificial neural network for short-term forecasting of evapotranspiration using public weather forecast restricted messages. Agric. Water Manag., http://dx.doi.org/10.1016/j.agwat.2015.10.009. Xiong, Y., Luo, Y., Wang, Y., Traore, S., Xu, J., Jiao, X., Fipps, G., 2015. Forecasting daily reference evapotranspiration using the Blaney-Criddle model and temperature forecasts. Arch. Agron. Soil, http://dx.doi.org/10.1080/03650340. 2015.1083983. Xue, J., 2005. Progresses of researches on numerical weather prediction in China: 1999–2002. Adv. Atmos. Sci. 21 (3), 467–474.