Evaluation of some equations for estimating evapotranspiration in the south of Iran

The Penman–Monteith (PM) equation is the most common method of estimating reference crop evapotranspiration (ET _o) for different climates of the world. This equation needs full weather data, however, few stations with complete weather data exist in Fars Province, in the south of Iran. Therefore, other equations based on more readily available weather data, such as temperature and rainfall, can be used instead of the PM equation in Fars Province. Four calibrated equations have been proposed in previous studies for Fars Province using weather data up to 2000. These equations were the Hargreaves equation (H), a new equation based on monthly temperature and rainfall (R), the Thornthwaite equation (T) and the Blaney–Criddle equation (B). Using weather data for 2001 to 2006 from 14 stations in Fars Province and outside the province, this study determined the best equations for estimating ET _o in each month and each station, rather than using the PM equation. The results revealed that equations H, R, T and B showed a good correlation to the PM equation, and can be used to estimate monthly ET _o in the study area. Also, the best equation for each location in Fars Province in each month of the year can be determined by using prepared distribution maps. Furthermore, the results showed that there was no specific relationship between the climate at the station and the best equation for estimating ET _o.     

Calibration of Hargreaves–Samani and Priestley–Taylor equations in estimating reference evapotranspiration in the Northwest of Iran

Accurate estimation of reference evapotranspiration (ET_o) is essential for water resources management and irrigation systems scheduling, especially in arid and semiarid regions such as Iran. In the present research, constant coefficients of Hargreaves–Samani (C_H–S) and Priestley–Taylor (C_P–T) equations were locally calibrated to estimate the ET_o based on the FAO–Penmen–Monteith (PM) method as standard method. For this purpose, meteorological data of eight synoptic stations located in the northwest of Iran were used during the period of 1997–2008. The outcomes showed that the values of C_H–S and C_P–T were 0.0026 (instead of 0.0023) and 1.68 (instead of 1.26), respectively. Also, at stations with high wind speed, the values of calibrated coefficients of C_H–S and C_P–T were maximum. Then, the estimated ET_o values using adjusted C_H–S and C_P–T coefficients were compared to the obtained actual ET_o values by PM method using root mean square error and mean bias error indices. The results indicated that the new calibrated H–S and P–T equations have good agreement with the PM method for estimation of the ET_o. Moreover, the equation of Ravazzani et al. was calibrated in the studied region. It was concluded that in general, the mentioned equation was shown better performance than original H–S equation.     

Proper methods and its calibration for estimating reference evapotranspiration using limited climatic data in Southwestern China

Proper methods for estimating reference evapotranspiration (ET₀) using limited climatic data are critical, if complete weather data are unavailable. Based on the weather data of 19 stations in Guizhou Province, China, several simple methods for ET₀ estimation, including the Hargreaves, Priestley–Taylor, Irmak–Allen, McCloud, Turk, and Valiantzas methods, were involved in comparison with the standard FAO-56 Penman–Monteith (PM) method. The Turk equation performs well for estimating ET₀ in humid locations. Both the Turk method and the Valiantzas method initially performed acceptably with mean root-mean-square difference (RMSD) of 0.1472 and 0.1282 mm d^?1, respectively, with only requiring parameters of temperature (T), relative humidity (RH), and sunshine duration (n). The corresponding calibration formulas to Turk and Valiantzas method were suggested as the most appropriate method for ET₀ estimation with the RMSD of 0.0098 and 0.0250 mm d^?1, respectively. The local calibrated Hargreaves–Samani method performed well and can be applied as the substitute of FAO-56 PM method under the condition that only the daily mean, maximum, and minimum temperatures were available, and local calibrated McCloud method was acceptable if only the mean temperature was available.     

Evaluation and calibration of simple methods for daily reference evapotranspiration estimation in humid East China

The current study aims to improve the performance of simple methods for the estimation of daily reference evapotranspiration (ET₀) in humid East China, namely Priestley–Taylor 1972 (P-T 1972), Hargreaves–Samani 1985 (H-S 1985) and Turc 1961 (TU 1961). These methods were evaluated and calibrated based on well-watered grass lysimeter experiments. The FAO-56 Penman–Monteith equation (FAO-56 PM) is the best method, and the radiation-based methods (TU 1961 and P-T 1972) perform much better than the temperature-based method (H-S 1985). In the simple methods, the coefficients are calibrated to: 1.34 for P-T 1972; 0.0186, 23.47 and 17.06 for TU 1961; and 0.0027 and 0.449 for H-S 1985. The locally calibrated TU 1961 and P-T 1972 perform much better than the original, with either the observed ET_0r or the ET_0c obtained by FAO-56 PM as standard. However, local calibration does not significantly improve the performance of the H-S 1985 method. In humid East China, FAO-56 PM is the best method for daily ET₀ calculation. TU 1961, especially if locally calibrated, is the optimal choice as a simple substitute for FAO-56 PM when solar radiation is available. Otherwise, serious local calibration is strongly recommended before applying H-S 1985 for daily ET₀ estimation.     

Forecasting daily reference evapotranspiration using the Blaney–Criddle model and temperature forecasts

Accurate daily reference evapotranspiration (ET_o) forecast is essential for real-time irrigation scheduling. An attempt was made to forecast ET_o using the Blaney–Criddle (BC) model and temperature forecasts in this study. Daily meteorological data for the period 2000–2014 at five stations in East China were collected to calibrate and validate the BC model against the FAO56 Penman–Monteith (FAO56-PM) model. Temperature forecasts up to 7 days’ lead time for 2012–2014 were input to the calibrated BC model to forecast ET_o. It is found that the performance of the BC model for ET_o forecast is further improved at all stations after monthly calibration. Average accuracy of forecasted ET_o (error within 1.5 mm d^?1) ranged from 82.7% to 89.3%, average values of mean absolute error (MAE) varied between 0.73 and 0.82 mm d^?1, average values of root mean square error (RMSE) ranged from 0.95 to 1.08 mm d^?1, and average values of the correlation coefficient (R) and concordance index (d) were more than 0.75 and 0.89, respectively. Furthermore, the error in ET_o forecast caused by error in temperature forecast is acceptable. The encouraging results indicate that the proposed method can be an alternative and effective solution for forecasting daily ET_o in East China.     

Calibration and validation of four common ET0 estimation equations by lysimeter data in a semi-arid environment

In this study, four different methods for reference crop evapotranspiration (ET₀) were calibrated and validated for estimation of daily to mean monthly ET₀ by weighing lysimeter data during 2005–2006 and 2004–2005, respectively, in a semi-arid region. The value of the constant in the Hargreaves–Samani method changed from 0.0023 to 0.0026 for daily to mean monthly ET₀, and can be used in stations with only air temperature data. The constant of the aerodynamic resistance equation in the FAO-56 Penman–Monteith method (208.0) changed to 85.0. The value of coefficient a in the FAO-24-Radiation method was between ?0.5 and ?0.67. Further, the empirical equations were modified to estimate the value of b in the FAO-24-Radiation method and C in the FAO-24 corrected Penman method. The results showed that the modified FAO-56, corrected Penman–Monteith and FAO-24-Radiation methods are the most appropriate for estimating daily to mean monthly ET₀. Furthermore, the modified FAO-24 corrected Penman method was ranked in fourth place and its accuracy was lower than that of the other methods. However, it is appropriate for estimating mean monthly ET₀. Smoothing the daily data decreased the fluctuation in measured daily weather data and ET₀ measured by lysimeter, and consequently resulted in a higher accuracy in the estimation of daily ET₀.     

Evaluation of pan coefficient equations for estimating reference crop evapotranspiration in the arid region

Reference evapotranspiration (ET₀) can be estimated on basis of pan evaporation data (E_pan), whose measurements have the advantage of low cost, simplicity of the measuring equipment, simple data interpretation and application as well as suitability for locations with limited availability of meteorological data. E_pan values were converted to ET₀ using the pan evaporation coefficient (K_pan). In this study, seven common K_pan equations were evaluated for prediction of ET₀ in the growing season (April to October) in arid region of Iran. The Cuenca approach was best suited compared to the standard FAO Penman–Monteith method (FAO-56 PM).     

Evaluation of wheat and maize evapotranspiration determination by direct use of the Penman–Monteith equation in a semi-arid region

The Penman–Monteith (PM) equation was introduced as one of the most reliable equations to determine crop ET_c, without using crop coefficient or ET_o values. In this study, the PM equation was evaluated using lysimeters in a semi-arid region for wheat and maize. Different equations for aerodynamic resistance (r _a) and canopy resistance (r _c) were tested in the PM equation and they were ranked using statistical analysis. It was shown that the combined method of r _a and r _c in FAO-56 does not lead to a good prediction of ET_c for wheat and maize in comparison with the lysimeter-measured data. The results indicated that a modified equation for r _c was the most accurate method for both wheat and maize. Using this equation, the suggested model of FAO-56 and another investigation for r _a led to the best results for wheat and maize, respectively. Furthermore, it was shown that the previously modified equation for r _c was newly modified as a function of vapor pressure deficit (VPD) and the results were as accurate as before. Therefore, an equation as a function of VPD can be used when solar radiation (R _n) is not available easily.     

Calibration of Hargreaves–Samani equation for estimating reference evapotranspiration in semiarid and arid regions

The Penman–Monteith (FAO-56 PM) equation is suggested as the standard method for estimating evapotranspiration (ET₀) by the International Irrigation and Drainage Committee and Food and Agriculture Organization (FAO). On the other hand, the Hargreaves–Samani (HS) equation is an alternative method compared with the FAO-56 PM equation. In the present study, the original coefficient C of the HS equation is calibrated based on the FAO-56 PM equation for estimating the reference ET₀ from 15 meteorological stations in central Iran (about 170,000 km²) under semiarid and arid conditions. After calibration, the new values for C are ranged from 0.0018 to 0.0037. The mean bias error (MBE), the root mean square error (RMSE), and the ratio of average estimations of ET₀ (R) values for all stations are ranged from 0.12 to 5.38, ?5.35 to 1.15 mm d^?1 and 0.64 to 1.28 for the HS equation and from 0.12 to 2.48, ?2.2 to 0.60 mm d^?1, and 1.00 to 1.05 for the calibrated Hargreaves–Samani equation (CHS), respectively. Results indicate that the average RMSE and MBE values are decreased by 40% and 66%, respectively. Relationships for calibrating the C coefficient on the basis of annual average of daily temperature range (ΔT) and wind speed (V) are proposed, calibrated, and validated. Hence, the CHS equation can be used for ET₀ estimates with acceptable accuracy instead of the FAO-56 PM method.     

Short-term forecasting of daily crop evapotranspiration using the ‘Kc-ETo’ approach and public weather forecasts

Short-term forecasting of daily crop evapotranspiration (ET_c) is essential for real-time irrigation management. This study proposed a methodology to forecast short-term daily ET_c using the ‘K_c-ET_o’ approach and public weather forecasts. Daily reference evapotranspiration (ET_o) forecasts were obtained using a locally calibrated version of the Hargreaves-Samani (HS) model and temperature forecasts, while the crop coefficient (K_c) was estimated from observed daily ET_o and ET_c. The methodology was evaluated by comparing the daily ET_c forecasts with measured ET_c values from a field irrigation experiment during 2012–2014 in Yongkang Irrigation Experimental Station, China. The overall average of the statistical indices was in the range of 0.96–1.27 mm d^?1 for the mean absolute error (MAE), 1.53–2.55 mm d^?1 for the mean square error (MSE), 1.77–2.30 mm d^?1 for the normalized mean square error (NMSE), 27.5–29.4% for the mean relative error (MRE), 0.71–0.44 for the correlation coefficient (R) and 0.46–0.05 for the mean square error skill score (MSESS). Sources of error werewere K_c estion, temperature forecasts and HS model that does not consider wind speed and humidity, and.the largesourceof error is K_c determination, which suggested that care should be taken when forecasting ET_c with estimated K_c values in the study area.     

Penman-Monteith与Penman修正式计算塔里木盆地参考作物潜在腾发量比较

利用1989~1996年阿克苏水平衡试验站的气象资料,对Penman-Monteith公式和Penman修正式计算的参考作物潜在腾发量进行了比较。Penman修正式计算的参考作物潜在腾发量年值略大于Penman-Monteith公式计算的年值,绝对偏差为42~128 mm,相对偏差为3.3~9.8%,且年际间变化不大。各月的参考作物潜在腾发量变化较大,绝对偏差可正可负,1、2、12月小于0,3~10月大于0,相对误差1、12月较大,2、11月较小,其它月份变化不大。导致计算偏差的原因在于两种公式采用了不同的辐射项和空气动力项计算公式和参数。两种公式计算的参考作物潜在腾发量具有显著的线性相关性。     

四种参考作物蒸散量综合法的比较

参考作物蒸散量(ET0)的估算是作物需水量计算的关键,诸多估算方法在不同地区具有不同的适应性。本文利用中国农业主产区6个代表站点的气象数据,以FAO 56 Penman-Monteith (PM)为标准,对常用的1963 Penman(Pen63)、FAO 1979 Penman(FAO 79)、FAO 24 Penman(FAO 24)及1996 Kimberly Penman(Kpen)共4种参考作物蒸散量综合方法进行比较评价。结果表明：（1）Pen63、FAO 79及Kpen的日估算值均比PM估算值偏高,FAO 24偏低,其平均偏差分别为0.28、0.52、0和-0.17mm×d-1,相对偏差为16.0%、25.2%、2.4%、-5.3%,相对均方根误差为12.1%、22.4%、14.2%和13.5%。（2）Pen63、FAO 79的月估算值显著高于PM值,在高估最大的5月份平均偏高12.5mm (10.8%)和28.2mm (22.6%)。FAO 24表现为低估,低估最大的月份平均偏低11.4mm (8.1%),但在南方站点多数月份的估算值与PM估算值无显著差异。Kpen月估算值与PM估算值相比,既有高估(5-10月),也有低估,高估最大的月份平均偏高19.7mm(14.5%),且在南方站点的秋冬季有近6个月与PM无显著差异。（3）Pen63和FAO 79的年值均显著大于PM年值,平均偏高103.8mm(11.8%)和191.5mm(21.3%)。FAO 24年平均低估PM值60.9mm (6.3%),Kpen则平均高估50.5mm (5.8%)。（4）时间尺度对评价结果具有一定影响,4种综合法依据日、年值的评价效果排序分别为Pen63＞FAO 24＞Kpen＞FAO 79和Kpen＞FAO 24＞Pen63＞FAO 79。在日尺度下4种方法更适于湿润气候,但年尺度下仅FAO 79和FAO 24较适于湿润气候。可见,4种综合法以Pen63普适性最好,FAO 79最低,因此使用FAO 79前对其进行适应性评价尤为重要。     

应用自适应神经模糊推理系统(ANFIS)的ET0预测

参照作物腾发量是计算作物需水量和进行灌溉预报的基础要素。该文利用自适应神经模糊推理系统(ANFIS)所具有的直接通过模糊推理实现输入层与输出层之间非线性映射能力，和神经网络的信息存储和学习能力，将其应用于参照作物腾发量预测中。根据相关分析，输入变量选择日照时数和日最高气温；用5年共1827个数据组对系统进行训练，建立了参照作物腾发量预测系统。利用该系统对近年213个数据组进行了实际预测，与Penman-Monteith方法计算结果进行比较，结果相关性良好。     

参考作物腾发量计算方法在新疆地区的适用性研究

新疆维吾尔族自治区地域辽阔，气候特征空间差异性显著。准确估算各地区的参考作物腾发量(ET₀)是新疆节水灌溉设计的基础。该文选用6种计算公式利用新疆4个典型气候区的气象资料计算了ET₀。并以Penman-Monteith方法作为标准，对其它方法进行评价。结果表明在新疆各气候区1948Penman法估算的ET₀值较FAO-24 Penman与FAO-24 Radiation方法更接近于P-M法的计算结果；在缺少资料的地区，Hargreaves方法或湿润区用Priestley-Taylor方法均可以得到与P-M法估值相当的结果；同时分析了P-M法计算的ET₀值和水面蒸发量之间的关系，为利用水面蒸发资料估算新疆地区ET₀值提供参考。     

Estimation of daily reference evapotranspiration by neuro computing techniques using limited data in a semi-arid environment

In this paper, the daily reference evapotranspiration (ET₀) for Bulawayo Goetz was estimated from climatic data using neuro computing techniques. The region lacks reliable weather data and experiences inconsistencies in the measuring process due to inadequate and obsolete measuring equipment. This paper aims to propose neuro computing techniques as an alternative methodology to estimating evapotranspiration. Firstly, ET₀ was calculated using FAO-56 Penman-Monteith (PM) equation from available climatic data. Data was divided into training, testing and validation for neuro computing purposes. The study also investigated the effect of different normalisation techniques on neuro computing ET₀ estimation accuracy. In another application, neuro-computing ET₀ estimates were compared against those obtained using empirical methods and their calibrated versions. The Z-score normalisation technique for all data sets gave best results with a Multi-layer perceptron (5–5-1) model having RMSE, MAE and R² values in the range 0.12–0.25 mm day^?1, 0.08–0.15 mm day^?1 and 0.94–0.99 respectively. There were no significant differences in ET₀ estimation accuracy by neuro computing techniques due to normalisation technique. The Neuro computing techniques were superior to empirical methods in ET₀ estimation for Bulawayo Goetz. The Neuro computing techniques are recommended for use in cases of limited climatic data at Bulawayo Goetz.     

纵向岭谷区参考作物腾发量变化的特点和趋势

以Penman Montieth方程分析了西南纵向岭谷区大理、元江、保山、昆明、景洪站46～48年的逐日ET₀及其余25个站1961～2000年逐月ET₀系列。研究结果表明：日最高温度是年内ET₀变化主导因素，年际变化主要受日照时数影响，个别站为最高气温或风速，短期ET₀变化与雾无直接关系。利用Mann-Kendall法对各站年际、年内分季节ET₀趋势检验，56.7%站点的年ET₀呈显著增加趋势，分布于澜沧江耿马-思茅-勐海一带以及横断山区维西、福贡等地。分季节逐日ET₀变化趋势为，昆明夏秋季显著下降，景洪冬春季显著增加，元江、保山、大理有增有减。降水量增加、气温升高，蒸发和日照时数减少，导致80%的站ET₀呈下降趋势，湿润指数普遍增加。     

石羊河流域气候变化对参考作物蒸发蒸腾量的影响

根据甘肃省气象局石羊河流域的6个气象站近50年的观测资料，应用1998年FAO最新推荐的Penman-Monteith公式计算了50年各月参考作物蒸发蒸腾量ET₀，分析了ET₀的月际变化和年际变化特征，除武威与肃南站ET₀呈逐年显著减少趋势外，其他各站的ET₀值均表现为逐年增加趋势，各个站ET₀ 20世纪90年代较80年代均有明显增加，说明气候变化对ET₀的影响较大；并分析了平均气温、平均最高气温、年日照时数、平均风速、平均相对湿度、年降水量、年蒸发量、海拔高度与ET₀的相关性，各站ET₀与平均相对湿度相关性最好；石羊河流域ET₀空间变化也较大，从山区到绿洲平原ET₀多年平均值呈递增趋势。     

Study of different climatic conditions to assess the role of solar radiation in reference crop evapotranspiration equations

This study aims to assess radiation-based models versus the FAO Penman–Monteith (FPM) model to determine the best model using linear regression under different weather conditions. The reference evapotranspiration was estimated using 22 radiation-based methods and was compared with the FPM. The results showed that the Stephens method estimates the reference evapotranspiration better than other methods in the most provinces of Iran (nine provinces). However, the values of R² were more than 0.9930 for 24 provinces of Iran. The radiation-based methods estimated the reference evapotranspiration near the Caspian Sea better than other regions. The most precise methods were the Berengena–Gavilan, Modified Priestley–Taylor, and Priestley–Taylor methods for the provinces ES (center of Iran), GI and GO (north of Iran) and the Stephens–Stewart method for IL (west of Iran). Finally, a list of the best performance of each method has been presented to use other regions and next research steps according to the values of mean, maximum, and minimum temperature, relative humidity, solar radiation, elevation, sunshine, and wind speed. The best weather conditions to use radiation-based equations are 23.6–24.6 MJ m^?2 day^?1, 12–20°C, 18–24°C, 5–13°C, and <180 hour month^?1 for solar radiation, mean, maximum, and minimum temperature, and sunshine, respectively.     

中国参考作物腾发量时空变化特性分析

分析参考作物腾发量的时空变化特征，有助于了解中国农业及生态需水的分布与演变规律。基于全国范围200多个气象站测站逐日气象观测资料，应用FAO-Penman-Monteith公式，计算得出各站历年逐日参照作物腾发量ET₀。利用GIS的空间分析功能，采用反距离空间插值方法得到全国参考腾发量的分布图，统计分析了不同分区不同时段ET₀的变化情况。结果表明：西北河西走廊地区和南方岭南地区的参考作物腾发量较大，最大值超过1500 mm。而东北黑龙江一带和四川盆地附近，参考作物腾发量较小，在600～700 mm之间。此外，夏季ET₀的分布特征决定了全年ET₀的分布特征。选取4个代表气象站，对其ET₀的历年变化及其与气象因素的关系进行了分析。分析表明，受风速减小和气温增加的共同影响，干旱地区、半干旱地区和半湿润地区的参考作物腾发量呈现减少趋势，湿润地区则相对稳定。     

基于GEP和地理位置信息的湘鄂地区月参考作物腾发量模拟计算

参考作物腾发量(ET0)是计算植被蒸散发的关键因子,准确估算ET0对水资源管理、灌溉制度设计等具有重要意义。本研究利用湘鄂地区46个气象站点1955—2005年的逐月气象数据,包括月最高气温、最低气温、平均风速、日照时数以及相对湿度,用FAO-56 Penman-Monteith法计算各站的逐月ET0值。然后结合基因表达式编程(GEP)算法挖掘公式的能力,以各站点的地理位置信息(纬度、经度、海拔)及月序数为输入,以多年逐月平均ET0值为输出,建立基于地理位置信息的月ET0模型,并与传统ET0模型的计算结果进行比较。结果表明,所建立的模型具有足够的精度,校正、检验阶段的决定系数(R2)和均方根误差(RMSE)分别为0.934、0.951和10.050 mm、8.628 mm;与Hargreaves和Priestley-Taylor法相比,基于地理位置信息建立的GEP模型的结果均方根误差最小,变化范围为8.628~9.967 mm。本研究所建立的月ET0模型具有明确的表达式,简单易用,在湘鄂地区仅利用地理位置信息计算逐月ET0是可行的,可以利用该模型进行月尺度的灌溉制度设计和植被蒸散发的估算。