Least squares support vector machine for modeling daily reference evapotranspiration

The accuracy of a least square support vector machine (LSSVM) in modeling of reference evapotranspiration (ET₀) was examined in this study. The daily weather data, solar radiation, air temperature, relative humidity and wind speed of two stations, Glendale and Oxnard, in southern district of California, were used as inputs to the LSSVM models to estimate ET₀ obtained using the FAO-56 Penman–Monteith equation. In the first part of the study, LSSVM estimates were compared with those of the following empirical models: Priestley–Taylor, Hargreaves and Ritchie methods. The comparison results indicated that the LSSVM performed better than the empirical models. In the second part of the study, the LSSVM results were compared with those of the conventional feed-forward artificial neural networks (ANN). It was found that the LSSVM models were superior to the ANN in modeling ET₀ process.     

基于人工蜂群优化算法的SOFC耦合生物质综合能源系统 日前经济调度

综合能源系统在运行过程中会遇到多种类能源复杂转换，多类型设备互相耦合，多需求分配不均等一系列复杂的优化问题。在近些年以及未来我国实现“双碳”目标的过程中，生物质综合能源系统的优化调度是当前研究的热点问题。本文以最小化综合能源系统经济运行成本（包含了燃料、运行以及维护成本）为目标函数，以系统安全为约束，提出了基于人工蜂群算法的燃料电池（SOFC）耦合生物质冷热电三联供综合能源系统的运行调度方法，其中包含的设备有生物质锅炉以及对应的蒸汽轮机、沼气池、SOFC、储气罐等。运行调度结果表明，相较于传统的随机规划与动态规划算法的运行调度方法，本文所提出的改进型人工蜂群算法能够节省4.2%与3.1%的运行成本。     

Artificial neural network for modeling reference evapotranspiration complex process in Sudano-Sahelian zone

The major problem when dealing with modeling evapotranspiration process is its nonlinear dynamic high complexity. Researchers developed reference evapotranspiration (ET-ref) estimation models in rich and poor data situations. Thus, the well-known Penman-Monteith (PM) model always performs the highest accuracy results of ET-ref from a rich data situation. Its application in many areas particularly in developing countries such as Burkina Faso has been limited by the unavailability of the enormous climatic data required. In such circumstances, simple empirical Hargreaves (HARG) equation is often used despite of its non-universal suitability. The present study assesses the artificial neural network (ANN) performance in ET-ref modeling based on temperature data in Bobo-Dioulasso region, located in the Sudano-Sahelian zone of Burkina Faso. The models of feed forward backpropagation neural network (BPNN) algorithm type ANN and Hargreaves (HARG) were employed to study their performance by comparing with the true PM. From the statistical results, BPNN temperature-based models perform better than HARG. Beside, when wind speed is introduced into the neural network models, the coefficient of determination (r²) increases significantly up to 9.52%. While, sunshine duration and relative humidity might cause only 3.51 and 6.69% of difference, respectively. Wind is found to be the most effective variable extremely required for modeling with high accuracy the nonlinear complex process of ET-ref in the Sudano-Sahelian zone of Burkina Faso.     

Artificial neural networks approach in evapotranspiration modeling: a review

The use of artificial neural networks (ANNs) in estimation of evapotranspiration has received enormous interest in the present decade. Several methodologies have been reported in the literature to realize the ANN modeling of evapotranspiration process. The present review discusses these methodologies including ANN architecture development, selection of training algorithm, and performance criteria. The paper also discusses the future research needs in ANN modeling of evapotranspiration to establish this methodology as an alternative to the existing methods of evapotranspiration estimation.     

Comparison of artificial neural network models and empirical and semi-empirical equations for daily reference evapotranspiration estimation in the Basque Country (Northern Spain)

Reference evapotranspiration (ETo) determination is a key factor for water balance and irrigation scheduling. Evapotranspiration can be measured directly by high-cost micrometeorological techniques, or estimated by mathematical models. The combination equation of Penman–Monteith, modified by Allen et al. [Allen, R.G., Pereira, L.S., Raes, D., Smith, M., 1998. Crop evapotranspiration. Guidelines for computing crop water requirements. FAO Irrigation and Drainage, Paper no. 56. FAO, Rome] (PM56), is the reference equation for ETo estimation. This method is also appropriate for the calibration of other ETo estimation equations. The utilization of these calibrated ETo equations is recommended in the absence of data of any of the meteorological parameters necessary for the application of PM56. In addition to the use of classic ETo equations, the adoption of artificial neural network (ANN) models for the estimation of daily ETo has been evaluated in this study. ANNs are mathematical models, whose architecture has been inspired by biological neural networks. They are highly appropriate for the modelling of non-linear processes, which is the case of the evapotranspiration process. Seven ANNs (with different input combinations) have been implemented and compared with ten locally calibrated empirical and semi-empirical ETo equations and variants of these equations (with estimated meteorological parameters as inputs). The comparisons have been based on statistical error techniques, using PM56 daily ETo values as a reference. ANNs have obtained better results than the locally calibrated ETo equations in the three groups of evaluated methods: temperature and/or relative humidity-based methods (0.385 mm d⁻¹ of root mean square error (RMSE)), solar radiation-based methods (0.238 mm d⁻¹ of RMSE), and methods based on similar requirements to those of PM56 except for the estimation of solar radiation and/or relative humidity (0.285 mm d⁻¹ of RMSE).     

Estimating reference evapotranspiration with atmometers in a semiarid environment

Reference evapotranspiration (ET₀) estimations require accurate measurements of meteorological variables (solar radiation, air temperature, wind speed, and relative humidity) which are not available in many countries of the world. Alternative approaches are the use of Class A pan evaporimeters and atmometers, which have several advantages compared to meteorological stations: they are simple, inexpensive and provide a visual interpretation of ET₀. The objectives of the study were to compare the evaporation from atmometers (ET_gage) with the evapotranspiration estimated by the FAO-56 Penman-Monteith equation (ET_0PM) and to evaluate the variability between three modified atmometers of a commercial model. Comparison between daily ET_gage measured by the atmometer and ET_0PM showed a good correlation. However, ET_gage underestimated ET_0PM by approximately 9%. Differences between ET_gage and ET_0PM ranged from −2.4 to 2.2 mm d⁻¹ while the mean bias error was −0.41 mm d⁻¹. Underestimations occurred more frequently on days with low maximum temperatures and high wind speeds. On the contrary, atmometer overestimations occurred on days with high maximum temperatures and low wind speeds. Estimates of ET₀ using the atmometer appeared to be more accurate under non-windy conditions and moderate temperatures as well as under windy conditions and high temperatures. Atmometers 2 and 3 overestimated the evaporated water by atmometer 1 with a maximum variability of cumulative water losses of 4.5%. A temperature-based calibration was performed to improve the atmometer accuracy, using maximum temperature as an independent variable, with good results.     

Accuracy of canopy temperature energy balance for determining daily evapotranspiration

The application of a single-layer canopy temperature energy balance (CTEB) model for determining integrated daily ET rates was tested, with possible applications towards determining irrigation requirements (“how much to irrigate”) as a complement to crop water stress index (CWSI) measurements (“when to irrigate”), an irrigation scheduling tool which uses much of the same data. Evapotranspiration (ET) rates estimated using the CTEB model were compared to Bowen ratio energy balance (BREB) measurements made over substantial portions of the growing seasons of corn and potato crops. Canopy temperature, net radiation and soil heat flux data were collected and analyzed at 20-minute intervals, and ET for each interval was summed to obtain daily and multi-day estimations. Only full canopy conditions were examined. Two methods for atmospheric stability correction were applied to the aerodynamic resistance required by the CTEB model; an iterative procedure proposed by Campbell, and a second procedure proposed by Monteith which uses an adjustment coefficient. To reduce instrumentation requirements for combined CTEB/CWSI data collection, estimates of ET were also determined using net radiation and soil heat flux values estimated from solar radiation measurements. Results showed that uncorrected CTEB ET estimates agreed reasonably well with BREB measurements over corn and potato canopies (RMSE = 0.5 to 0.7 mm day⁻ for observed average ET ranging from 4.8 to 5.5 mm day⁻, with a trend toward seasonal overprediction with corn. Stability corrections usually lowered the daily RMSE 0.1 to 0.2 mm day⁻, with seasonal ET more in agreement with BREB ET. The Monteith-based adjustment gave slightly better results. CTEB ET model with estimated net radiation and soil heat flux terms produced similar average and total ET, but somewhat larger daily errors (RMSE=0.5 to 0.9 mm day⁻). Seasonal total ET by the uncorrected CTEB model generally overestimated within 10% (ranging from 1% to 10%) of the observed BREB total ET, an acceptable error for most irrigation practices. Stability corrections generally caused seasonal ET to be underestimated within 1% to 9%.     

蝙蝠算法优化极限学习机模拟参考作物蒸散量

为提高参考作物蒸散量模拟的准确性,提出蝙蝠算法优化极限学习机的参考作物蒸散量模拟模型.基于汕头站1966-2015年月值气象数据(包括逐月最高温度、最低温度、地表总辐射量、风速和相对湿度),建立参考作物蒸散量的极限学习机模型,并采用蝙蝠算法通过交叉验证方法对极限学习机的正则化系数和径向基函数的幅宽进行优化,最后对参考作物蒸散量模拟效果进行评估.结果表明:与传统调参方法和遗传算法优化后的模型相比,蝙蝠算法优化参数极限学习机模型建立了整体性能优异并且稳定的参考作物蒸散量模型,提高了参考作物蒸散量的模拟精度.     

New empirical formula for hourly estimations of reference evapotranspiration

A new empirical equation for estimating hourly reference evapotranspiration ET₀ is proposed. This equation requires data for three pertinent meteorological attributes, solar radiation R_s, air temperature T, and relative humidity RH. A routine surface polynomial regression analysis in three stages, is employed in order to estimate the factors c_i entering the empirical model ET₀=f(R_s, RH, T; c_i). For the calibration of the proposed model, data sets collected from Copais (Greece) were used. Verification of the validity of the model was obtained using independent data from Copais as well as data from CIMIS (Davis, Sacramento, CA). A comparative evaluation of the model was performed against some of the most widely used and strongly recommended models for estimating hourly ET₀. Among them are the recently proposed Penman–Monteith (FAO56-Penman–Monteith), CIMIS version of Penman (CIMIS-Penman), and the American Society of Civil Engineers version of Penman–Monteith (ASCE-PM). Statistics and scatterplots, using ASCE-PM as the standard model indicate that the new empirical equation (Copais) operates quite satisfactorily for both regions, therefore may provide the premises to become a tool, for routine hourly reference evapotranspiration calculations.     

4种人工智能模型在江西省参考作物蒸散量计算中的适用性

为了实现气象资料缺失下参考作物蒸散量ET₀的高精度预测,以江西南昌、吉安及龙南站1966-2015年每日最高气温T_max、最低气温T_min、日照时数n、相对湿度RH和2 m高风速u₂作为输入参数,以FAO-56 Penman-Monteith(P-M)公式的计算结果作为对照,建立了6种不同气象要素组合条件下的4种ET₀计算模型,并分别与输入相同数据的经验法计算结果进行了比较.结果表明,在3个站点中,多元自适应回归样条法MARS模型的精度最高,且计算简便,可作为江西省蒸散量模拟的推荐方法.当4种模型的输入数据完整时,模拟精度均达到最高,表明4种模型均可适用于对参考作物蒸散量的模拟;输入数据缺失条件下,各气象要素对智能模型模拟ET₀的影响由大到小按参数排序依次为T_max,T_min,n,RH,u₂.与传统经验公式相比,4种智能模型的ET₀计算结果精度均优于输入相同数据的经验法.     

Evaluation of pan coefficient for reference crop evapotranspiration for semi-arid region

Pan coefficient (K _pan) is the important factor for computation of reference evapotranspiration (ET _o ) from pan evaporation (E _pan). In this paper, the approaches proposed by Cuenca (Irrigation system design: an engineering approach. Prentice-Hall, Englewood Cliffs, 1989), Snyder (J Irrig Drain Eng 118(6):977–980, 1992), Orang (Potential accuracy of the popular non-linear regression equations for estimating pan coefficient values in the original and FAO-24 tables. Unpublished Report, Calif. Dept. of Water Resources, Sacramento, 1998), Raghuwanshi and Wallender (J Irrig Drain Eng 118 (6):977–980, 1998) and Pereira et al. (Agric Water Manage 76:75–82, 1995) were evaluated for a semi-arid region. By comparing with the FAO 56 Penman-Monteith (F-PM) method the Snyder (J Irrig Drain Eng 118(6):977–980, 1992, 1992) approach was best suited for the semi-arid region.     

Software for missing data error analysis of Penman-Monteith reference evapotranspiration

The most common approach for the estimation of crop water requirements is to pair a crop factor with the evaporation from a reference surface. In this study, a user-friendly computer tool was developed to facilitate the calculation of daily FAO (Food and Agricultural Organization of the United Nations, Rome, Italy) Penman-Monteith reference crop evaporation (ET₀), and to estimate errors that can arise if solar radiation, wind and vapour pressure data are not available. The ET₀ calculator imports comma, tab or space-delimited daily weather data files in any user-specified format. It displays graphically and processes statistically, ET₀ values calculated from full and incomplete weather data sets. The program is written in Delphi with a Paradox database and includes a comprehensive, context-sensitive help file. Sensitivity analyses were carried out for three locations as examples. The error in predicting ET₀ using estimated weather parameters was reduced by using 5-day averages of ET₀ rather than daily values. Although some error is incurred by estimating weather parameters, this is somewhat compensated for by the absence of any error that may have been associated with the measurements.     

Estimation of reference evapotranspiration for southern region of Saudi Arabia

The reference crop evapotranspiration (ET_r) for four areas in Saudi Arabia was estimated using five different methods: FAO-Penman, Jensen-Haise, Blaney & Criddle, pan evaporation, and calibrated FAO-Penman under local conditions (Penman_-SA). Comparison was also made between the estimated ET_r and the measured ET_r of alfalfa grown in lysimeters in the Riyadh area. Regression analysis revealed that estimated ET_r values were highly correlated with measured ET_r values. In addition, linear regression relationships between ET_r values estimated by the Penman_-SA method and other methods were determined. The results of this study indicated that the calibrated Penman_-SA method can be transferred successfully to other locations, and this method could be used for the estimation of ET_r values in all areas in the southern region of Saudi Arabia. Received: 16 January 1998     

Evaluation of estimated weather data for calculating Penman-Monteith reference crop evapotranspiration

Utilizing the weather generator ClimGen, daily solar radiation (R_s) and vapor pressure deficit (VPD) were estimated from temperature data and used to calculate evapotranspiration at five locations, representing tropical, temperate, semi-arid, and arid climates. ClimGen was calibrated for each location using the most recent 2 or 5 years of complete daily weather records. Actual and estimated values were compared on a daily and weekly (7-day running average) basis. Error indices were defined to indicate excellent to poor performance of the estimation methods. Overall in all locations, the ClimGen estimates for both daily R_s and VPD were poor to acceptable. The weekly analyses showed significant improvement in performance for both R_s and VPD estimations in arid and semi-arid locations. Daily reference crop evapotranspiration values using the FAO Penman-Monteith equation (PM ET_o) were calculated using complete daily weather records. These values were compared with (1) ET_o calculated with the PM model, actual temperature data, and ClimGen estimates of daily R_s, VPD, and generated wind speed (PM_Est ET_o), and (2) ET_o calculated solely from actual daily temperature data using a calibrated version of the Hargreaves method (HG_Adj ET_o). The daily PM_Est ET_o results were poor to acceptable in all locations, but analyses for weekly periods showed improved performance to acceptable and good levels for arid and semi-arid locations. The performance of the HG_Adj ET_o method was also poor to acceptable for daily ET estimates in all locations, while weekly analyses showed improvement. A non-calibrated version of the Hargreaves method did not work for either daily or weekly periods. The PM_Est ET_o and HG_adj ET_o methods appeared suitable for weekly periods in arid and semi-arid locations provided that at least 2 years of complete weather records were available to calibrate the parameters required. There was no advantage in using 5 years of weather records for calibration.Communicated by E. Fereres     

An evaluation of two hourly reference evapotranspiration equations for semiarid conditions

The methodology proposed by the Food and Agriculture Organization (FAO) (Doorenbos, J., Pruitt, W.O., 1977. Crop water requirements. FAO irrigation and drainage. Paper No. 24. FAO, Rome) and updated by Allen et al. (Allen, R.G., Pereira, L.S., Raes, D., Smith, M., 1998. Crop evapotranspiration. Guidelines for computing crop water requirements. FAO irrigation and drainage. Paper No. 56. FAO, Rome) for calculating crop water requirements is the most extended and accepted method worldwide. This method requires the prior calculation of reference evapotranspiration (ET_o). This study evaluates the FAO-56 and American Society of Civil Engineers (ASCE) Penman–Monteith (PM) equations for estimation of hourly ET_o under the semiarid conditions of the province of Albacete (Spain). The FAO-56 and ASCE equations (hourly time step) were compared against measured lysimeter ET_o values at Albacete for 13 days during the period of April–October 2002 and 16 days during April–October 2003. The average of estimated FAO-56 Penman–Monteith ET_o values was equal to the average of measured values. However, the average of estimated ASCE Penman–Monteith values was 4% higher than the average of measured lysimeter ET_o values. This method overestimated measured lysimeter ET_o values by 0.45 mm h⁻¹.Simple linear regression and error analysis statistics suggest that agreement between both estimation methods and the lysimeter was quite good for the province of Albacete.In this paper, the FAO-56 Penman–Monteith equation for calculating hourly ET_o values was more accurate than the ASCE Penman–Monteith method under semiarid weather conditions in Albacete.     

An evaluation of the net radiation sub-model in the ASCE standardized reference evapotranspiration equation: Implications for evapotranspiration prediction

Net radiation (R_n) is a key component of the surface energy balance, but it is expensive and difficult to measure accurately. For these reasons, R_n is often predicted in evapotranspiration (ET) calculations with a model requiring measurements of incoming shortwave radiation, air temperature, and vapor pressure. We compared R_n predictions from the R_n sub-model used in the American Society of Civil Engineers (ASCE) standardized reference ET equation to mean R_n measurements from five 4-component reference net radiometers. The radiometers were part of a recent comparison study of multiple net radiometer models conducted over irrigated and clipped turfgrass in northern Utah (Blonquist et al., 2009). In the R_n model, net shortwave radiation is determined by direct measurement of solar radiation and an assumed value of albedo for the surface (0.23 for fully vegetated surfaces), and net longwave radiation is calculated with a Brunt (1932, 1952) approach for predicting net surface emissivity, calculated from near surface vapor pressure. Additionally, the ratio of measured incoming shortwave radiation to predicted clear-sky shortwave radiation is used as a surrogate variable for cloud cover in the net longwave radiation calculation. Relative to the reference R_n measurements (average of five 4-component net radiometers), modeled R_n was high during the day by an average of 8.6% and high in magnitude (more negative) at night by an average of 13.4% over hourly time intervals. Daily total R_n calculated by summing the hourly model predictions was always higher than the reference measurements, by an average of 8.1%, whereas daily total R_n calculated from the model over daily time intervals was closer to the reference measurements, 2% high on average. The model R_n error during the day was partly caused by the assumption in the model that surface albedo is a constant value of 0.23. Measurements showed albedo ranged from approximately 0.21 at solar noon to 0.30 near the beginning and end of the day, with a mean value of 0.23. However, most of the model R_n error was due to the prediction of net longwave radiation, where the empirical equation in the model typically yielded values that were too low in magnitude (less negative), by approximately 20% on average, but the error was dependent on time of day. The R_n error at night was largely caused by the inability to measure the surrogate for cloud cover at night, which relies on measurement of solar radiation from a previous time period of sufficient solar zenith angle. All five of the net radiometer models tested in the comparison study matched the mean of the reference net radiometers better than the ASCE model. When modeled hourly R_n was used to calculate ET over hourly time intervals, or when hourly ET values were summed to yield daily ET, ET was typically high, by 6% on average, relative to ET calculated from measured reference R_n. When modeled R_n was calculated over daily time intervals and used to calculate ET over daily time intervals, ET was more accurate, 1% high on average, relative to ET calculated over daily time intervals from measured reference R_n. While new models for R_n are being developed, the sub-model in the ASCE standardized reference ET equation has been in use for the past two decades in thousands of ET stations. As newer models are developed we hope to use this data set to evaluate them.     

基于ELM的西北旱区参考作物蒸散量预报模型

为实现气象资料缺失情况下ET₀的精确预报,选取中国西北旱区4个代表性站点的气象资料,建立15种基于极限学习机(ELM)的ET₀预报模型,并通过与其他ET₀计算模型对比和可移植性分析探究ELM在西北旱区的适用性.结果表明:基于温度和风速的ELM₇预报精度较高(整体评价指标GPI排名第4);基于温度和辐射的ELM₅预报精度(GPI排名第6)明显高于Iramk模型和Jensen-Haise模型;仅基于温度的ELM₉预报精度(GPI排名第8)高于Hargreaves-Samani模型.通过模型可移植性分析发现,ELM₇在西北旱区内各训练站点和预测站点组合下预报精度良好.因此,可将ELM₅(输入温度和辐射)、ELM₇(输入温度和风速)和ELM₉(输入温度)作为西北旱区较少气象参数输入情况下精确预报ET₀的推荐模型.     

Water requirements of olive orchards: I simulation of daily evapotranspiration for scenario analysis

Water requirements of olive orchards are difficult to calculate, since they are influenced by heterogeneous factors such as age, planting density and irrigation systems. Here we propose a model of olive water requirements, capable of separately calculating transpiration (E _p), intercepted rainfall evaporation (E _pd) and soil evaporation (E _s) from the wet and dry fraction of the soil surface under localized irrigation. The model accounts for the effects of canopy dimension on E _p and of the wetted soil surface fraction on E _s. The model was tested against actual measurements of olive evapotranspiration (ET) obtained by the eddy covariance technique in a developing olive orchard during 3 years. The predicted ET and crop coefficients showed good agreement with the measured data. The model was then used to simulate the average water requirements of two mature orchards using 20-year meteorological datasets of Cordoba (Spain) and Fresno (CA, USA). Average annual ET of a 300 trees ha⁻¹ orchard at Cordoba was 1,025 mm, while the same orchard at Fresno had an average ET of 927 mm. Transpiration losses were 602 mm at Cordoba and 612 mm at Fresno. Evaporation from the soil can have a large effect on olive ET; thus, olive crop coefficients (K _c) are very sensitive to the rainfall regime.     

基于公共天气预报的广东青年运河灌区参考作物腾发量预报方法比较

为提出高精度适合广东青年运河灌区参考作物腾发量(ET₀)预报方法,制定精准的灌溉预报,降低农业用水量,本研究以灌区内的湛江站为研究对象,收集了该站点2003-01-01-2017-05-31逐日气象观测数据和2016-01-01-2017-05-31日的预见期为7 d的逐日公共天气预报数据,采用FAO-56 Penman-Monteith计算值作为基准,比较Hargreaves-Samani(HS)法、简化Penman-Monteith(PT)、逐日均值修正法的预报效果.结果表明:以上3种方法1~7 d预见期平均绝对误差平均值分别为0.908 3,0.903 1,0.947 9 mm/d,平均绝对误差分别为1.099 1,1.099 9,1.192 4 mm/d,相关系数分别为0.649 5,0.649 8,0.615 9,PT法的平均绝对误差以及相关系数均最好.就每个预见期而言,1~5 d预见期的最优预报方法均为PT法,6~7 d为HS法.因此,建议采用PT法进行青年运河灌区的ET₀预报.     

参考作物蒸发蒸腾量计算方法在海河流域的适用性

参考作物蒸发蒸腾量（ET0）的计算公式很多,各公式所需参数各异,为寻找一种所需资料少而又精度较高的替代方法,选用1998年FAO-56分册推荐的Penman－Monteith（PM）、Hargreaves、Irmark-Allen等6种方法分别计算海河流域10个典型气象站30 a的参考作物蒸发蒸腾量,并以PM公式为标准,对其他方法进行评价。结果表明,10个站点中除了五台山地区,Hargreaves与FAO-24 Radiation 这2种方法更接近于PM方法的计算结果,其误差较小,在海河流域缺少辐射和风速