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.     

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.     

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.     

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).     

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。     

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.     

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。     

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。     

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.     

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。     

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.     

Comparison of artificial neural networks and prediction models for reference evapotranspiration estimation in a semi-arid region

Estimation of reference evapotranspiration (ET_o) is essential for determination of crop water requirements. In this research, Penman–FAO (P-FAO) and Penman–Monteith (PM) equations were calibrated and validated by lysimeter-measured ET_o with six and four weather parameters. Furthermore, two input structures (six and four weather parameters) to artificial neural networks (ANNs) were investigated. Results showed that the accuracy of the PM equation is greater than that of the P-FAO equation. An empirical equation was developed to estimate daily ET_o using mean daily temperature and relative humidity, and sunshine hours. The accuracy of the equation to estimate daily ET_o using smooth weather data is greater than that of an equation using original data. Furthermore, ANNs were able to estimate ET_o properly. The accuracy of ANNs with six inputs is higher than that obtained using the P-FAO equation and is similar to that determined using the PM equation. A decrease in number of inputs to ANNs generally decreased the accuracy of estimation, however, ANNs were able to estimate ET_o properly when wind speed and solar radiation were unavailable. Furthermore, the accuracy of ANNs, with four input parameters is greater than that obtained using the PM equation and is similar to that obtained with P–FAO and the developed empirical equations.     

甘肃地区参考作物蒸散量时空变化研究

区域水土平衡模型的建立通常需要确定计算参考作物蒸散量的模型,这一模型的精确与否,直接影响整体预测模型的最终预报精度.运用FAO-24 Blaney-Criddle法、FAO-24 Radiation法、FAO PPP-17 Penman法及FAO Penman-Monteith(98) 4种方法,对甘肃省1981～2000年33个站点的月参考作物蒸散量进行了计算.对比分析结果表明,AO Penman-Monteith(98)模型的精度与灵敏度均显示了较强的优越性.运用该模型对甘肃省参考作物蒸散量的时空分布特征进行研究表明:甘肃省参考作物蒸散量年内逐月演变曲线呈单峰状;年际蒸散量变化与夏季年际波动变化存在较高一致性;全年参考作物蒸散量分布具有从东南向西北递增的趋势.     

Estimation of reference evapotranspiration and crop coefficient in wheat under semi-arid environment in India

Abstract

The comparison of six standard reference evapotranspiration (ETo) estimate models was carried out with measured lysimeter evapotranspiration (ETc) in wheat crop in a semi-arid environment at Rahuri, India. The globally accepted reference evapotranspiration model of FAO 56 Penman Monteith underestimated the references ETo by 19.2% (420.5 mm) over lysimeter ET (520.7 mm). Out of the remaining five models, the Hargreaves model ranked first and was overestimated by 6.5% followed by the Blaney Criddle model (underestimated by ?5.6%). The references ETo by pan evaporation model underestimated the reference ETo to the extent of ?28.8%. The influence of statistical indicators like RMSE, MBE which was computed by considering Lysimeter ETc as standard, was quite low in the Hargreaves model compared to the rest of the models and hence, the Hargreaves method is quite acceptable for ETo estimates as this method requires much less climatic parameters (temperature and extraterrestrial radiation) than Penman Monteith (FAO56) and Modified Penman of FAO 24 as these models require aerodynamic and radiation terms, besides additional physical terms in former models of ETo estimates. The seasonal crop coefficients were 1.24, 1.13, 0.94, 0.85, 1.06 and 1.40 in Penman Monteith, Modified Penman, Hargreaves, Radiation balance, Blaney Criddle and Pan Evaporation models, respectively.     

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.     

小流域水文循环过程中蒸散发量模拟方法评价

蒸散发(ET)在农业灌溉和水资源管理中起着重要作用。ET可通过FAO-Penman-Monteith方法(ET_(FPM))进行准确估算,ET_(FPM)方法是ET估算的标准参考方法,此方法需要提供更为详实的气象数据。对于ET的估算,需要寻找使用较少的输入数据,而不会影响预测准确性的替代方法。研究运用5个基于辐射的模型,包括Makkink(ET_(MAK))、Priestley和Taylor(ET_(PT))、Abtew(ET_(ABT))、Jensen-Haise(ET_(JH))、McGuinness和Bordne(ET_(MB)),3个基于温度的模型,包括Hargreaves and Samani(ET_(HS))、Hamon(ET_(HAM))和Linacre(ET_(LIN)),以及1个基于空气动力学的模型Penman(ET_(PEN)),通过使用韩仓河流域周边6个气象水文站的长期数据,将选取的模型与ET_(FPM)模型在月尺度和生长季节尺度上进行比较评价。结果表明,ET_(JH)、ET_(HAM)分别是67%,33%研究区域每月ET的最佳预测方法。在研究区域中,基于辐射的方法优于基于温度的方法。植被生长季节ET累积值表明,Jensen-Haise和Hamon方法在暖季和秋冬季生长期表现最佳,而春季生长期最佳预测方法仅包括Jensen-Haise方法。最佳替代方法和ET_(FPM)方法之间的差异表明,最佳替代方法在某些地区的估算可信度不高,因此在使用之前应考虑ET模型可预测性能的时空变化。     

Prediction of daily reference evapotranspiration by a multiple regression method based on weather forecast data

Prediction of daily reference evapotranspiration (ET ₀) is the basis of real-time irrigation scheduling. A multiple regression method for ET ₀ prediction based on its seasonal variation pattern and public weather forecast data was presented for application in East China. The forecasted maximum temperature (T _max), minimum temperature (T _min) and weather condition index (WCI) were adopted to calculate the correction coefficient by multilinear regression under five time-division regimes (10 days, monthly, seasonal, semi-annual and annual). The multiple regression method was tested for its feasibility for ET ₀ prediction using forecasted weather data as the input, and the monthly regime was selected as the most suitable. Average absolute error (AAE) and root mean square error (RMSE) were 0.395 and 0.522 mm d^?1, respectively. ET ₀ prediction errors increased linearly with the increase in temperature prediction error. A temperature error within 3 K is likely to result in acceptable ET ₀ predictions, with AAE and average absolute relative error (AARE) <0.142 mm d^?1 and 5.8%, respectively. However, one rank error in WCI results in a much larger error in ET ₀ prediction due to the high sensitivity of the correction coefficient to WCI and the large relative error in WCI caused by one rank deviation. Improving the accuracy of weather forecasts, especially for WCI prediction, is helpful in obtaining better estimations of ET ₀ based on public weather data.     

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.     

湛江地区适宜参考作物蒸发蒸腾量计算模型分析

用湛江市日平均、旬平均、月平均气象资料,以6种方法计算参考作物蒸发蒸腾量,并以FAO56 Penman-Monteith公式计算结果为标准,评价其他方法在湛江的适用性.结果表明:Hargreaves-Samani方法的年平均参考作物蒸发蒸腾量与FAO56 Penman-Monteith没有显著差异;月平均参考作物蒸发蒸腾量,除个别月份外,其他5种方法与FAO56 Penman-Monteith方法都有显著差异;不同方法计算结果与FAO56 Penman-Monteith法的均方偏差不同的时间尺度表现不同,日值计算,1948 Penman方法最小,Irmark-Allen次之;旬值计算,1948 Penman方法最小,Hargreaves-Samani、Irmark-Allen次之;月值计算Hargreaves-Samani最小,1948 Penman次之.1948 Penman、FAO24 Penman与FAO56 Penman-Monteith法的相关系数较大,Priestley-Taylor、Irmark-Allen次之,Hargreaves-Samani法的较小.     

喀斯特与非喀斯特地区参考作物蒸散量时空变化分析——以广西壮族自治区为例

参考作物蒸散量(ET_0)是确定植被生态系统需水量的关键因子,其时空分布特征及主要影响因素分析对于制定植被恢复策略与区域水资源配置方案具有重要意义。本文基于FAO-56 Penman-Monteith公式和广西地区25个气象站点1960—2010年的逐日资料,计算了各站点的ET_0,在此基础上采用GIS的克里金插值、Spearman秩次相关法和通径分析方法分析了广西喀斯特与非喀斯特地区ET_0的时空变化特征及其影响因子。结果表明,51年来广西各站点多年平均ET_0为1 138 mm×a~(-1);空间分布呈由南向北、由低纬度向高纬度递减的特征,高值区主要分布在非喀斯特地区,低值区主要分布在喀斯特地区。喀斯特与非喀斯特地区年ET_0累积距平曲线均呈"N"型分布;20世纪70年代最高,90年代最低,21世纪以来年ET_0有所回升,但仍低于51年平均值。此外,喀斯特地区ET_0年际变化小于非喀斯特地区。日照时数、风速和平均温度是影响非喀斯特地区年ET_0变化的主要气象因子,而相对湿度则通过与其他气象因子的相互作用间接对喀斯特地区年ET_0的变化产生较大影响。在季节尺度上,日照时数和平均气温在各季节都是ET_0最主要的影响因子,与ET_0呈正相关关系;风速在喀斯特地区冬、春两季对ET_0的间接作用系数为负,在非喀斯特地区并未发现这一现象。了解不同地区ET_0的变化趋势是植被生态需水定额计算的必要措施。