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.     

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.     

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.     

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.     

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.     

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.     

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。     

西南区域单季稻生长季干湿演变及影响因素分析

结合作物生产开展区域干湿演变及其影响因素研究,对农业可持续发展和粮食安全具有重要的科学意义。本文基于西南水稻种植区316个气象站点1961—2015年的观测资料,利用降水量与参考作物蒸散量(ET_0)的比值计算湿润指数,分析近55年西南区域单季稻生长季干湿演变特征;探讨ET_0对主要气候要素的敏感性及主要气候要素对ET_0的贡献率,对西南区域单季稻生长季干湿演变的影响因素展开研究。结果表明:西南区域单季稻生长季的半湿润区主要分布在四川攀西地区南部、云南中部和东北部,其余地区属湿润区。与1961—1990年相比,1991—2015年研究区域内的半湿润区面积增加、湿润区面积减小。近55年来,单季稻生长季内西南区域有40.8%的站点气候变湿,其余地区气候变干。四川盆地东北部、云南东北部由于降水量的增加和ET_0的减少,气候变湿;四川攀西地区由于降水量增加对湿润指数的正效应大于ET_0增加对湿润指数的负效应,气候变湿;重庆南部、贵州北部和西部由于降水量减少对湿润指数的负效应小于ET_0减少对湿润指数的正效应,气候变湿;云南大部由于降水量的减少和ET_0的增加,气候变干;西南其他区域由于降水量减少对湿润指数的负效应大于ET_0减少对湿润指数的正效应,气候变干。西南区域单季稻生长季ET_0随平均气温和相对湿度的增加而减小,而随日照时数和风速的增加而增加,日照时数和风速的显著下降是ET_0减小的主要原因。研究为气候变化背景下降低西南区域单季稻生长季可能的气候风险提供了科学依据。     

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.     

利用温度资料和广义回归神经网络模拟参考作物蒸散量

参考作物蒸散量(reference evapotranspiration,ET0)精确模拟对水资源高效利用和灌溉制度制定具有重要意义,该文以四川盆地19个气象站点1961-1990年逐日最高、最低温度和大气顶层辐射作为输入参数,FAO-56 Penman-Monteith(PM)模型计算的ET0为标准值,建立基于广义回归神经网络(generalized regression neural network,GRNN)的ET0模拟模型,基于1991-2014年资料进行模型验证,将GRNN模型同Hargreaves(HS1)和改进Hargreaves(HS2)等简化模型的模拟结果进行比较,分析只有温度资料情况下不同模型模拟ET0误差的时空变异性。结果表明:GRNN、HS1和HS2模型均方根误差(root mean square error,RMSE)分别为0.41、1.16和0.70 mm/d,模型效率系数(Ens)分别为0.88、0.13和0.67。3种模型RMSE在时空上均呈现HS1HS2GRNN、Ens均呈现GRNNHS2HS1趋势;与PM模型模拟结果相比,GRNN、HS1和HS2模型模拟结果分别偏大0.8%、45.1%和17.3%。在时空尺度上的误差分析均表明利用温度资料建立的GRNN模型能够较为准确地模拟四川盆地ET0,因此可以作为资料缺失情况下ET0模拟的推荐模型。该研究可为四川盆地作物需水精确预测提供科学依据。     

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.     

不同ET0计算方法在川中丘陵地区的比较及改进

为了获取川中丘陵地区参考作物蒸散量(ET0)在气象资料短缺条件下不同类型的简化计算方法,选用FAO-56Penman-Monteith(PM)法、Hargreaves法、Hargreaves校正法、Priestley-Taylor法和Irmark-Alleen拟合法计算简阳站1999-2005年逐日的ET0。以PM公式为标准,对其他4种方法进行评价及改进。结果表明,Hargreaves校正法计算误差最小,Irmark-Alleen拟合法和Hargreaves法次之,Priestley-Taylor法计算误差最大。通过灵敏度分析,得出川中丘陵地区影响ET0的主要气象因子是相对湿度,因此该文对在湿润气候条件下应用的Priestley-Taylor法和Irmark-Alleen拟合法的参数进行逐月修正,改进后的计算方法精度得到明显提高。Hargreaves校正法、该文提出的Priestley-Taylor修正法和Irmark-Alleen拟合改进法可以作为川中丘陵地区气象资料短缺条件下ET0的简化计算方法。     

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。     

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。     

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。     

秦淮河流域五种参考作物蒸散量估算方法的比较及改进

基于秦淮河流域内部及周边共7个气象站2000-2013年的逐日气象资料,使用FAO-56 Penman- Monteith、Irmak-Allen、Makkink、Turc、Jensen-Haise和Hargreaves共6种方法估算各站点逐日参考作物蒸散量（ET0）。以FAO-56 Penman-Monteith结果为标准,修正其余5种方法估算公式的原始经验系数,并通过平均绝对误差、平均相对误差、相关系数等精度评价指标和Wilcoxon非参数检验法,分别从年、月尺度对比分析5种方法修正前后的估算结果,旨在获得一种适于秦淮河流域的数据要求低,估算过程简单,精度较高的ET0估算方法。分别以5种方法的ET0日值为自变量,P-M法ET0日值为因变量,建立逐月线性回归方程,寻找经验系数的修正倍数,对5种方法经验系数进行逐月修正。结果表明,使用原始经验系数时,年尺度上,Irmak-Allen、Makkink、Turc法存在较大误差,Hargreaves法相关性较差,均不适于秦淮河流域;月尺度上,Irmak-Allen法在5-8月,Turc在9-11月,Hargreaves法在4月及9-11月适用性较好,其余月份误差较大,Makkink和J-H法分别在1-12月和3-11月存在显著差异,故5种方法均不能代替P-M法在年内12个月使用。使用修正后经验系数,年尺度上Makkink法适用性最好,平均绝对误差和平均相对误差分别为14.9mm·a-1和1.4%,相关系数为0.89,无显著差异,其次为Turc法,I-A法估算结果仍存在显著差异,Hargreaves法相关性仍较差;月尺度上,从估算精度考虑,Turc和Makkink法搭配使用,4-10月推荐使用Turc法,其平均绝对误差为2.1～6.1mm·mon-1,平均相对误差为2.9%～4.3%,无显著差异,月平均相对误差波动较小,稳定性好,1-3月和11-12月推荐使用Makkink法,其平均绝对误差为1.2～2.4mm·mon-1,平均相对误差为3.2%～5.7%,无显著差异,月平均相对误差波动较小,稳定性好,从时间连续性考虑,推荐使用Hargreaves法,其平均绝对误差为1.9～10.4mm·mon-1,平均相对误差为3.9%～9.2%,无显著差异,月平均相对误差波动较小,稳定性好。     

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。