ET0 Methods Research Articles

Establishment of a Reference Evapotranspiration Forecasting Model Based on Machine Learning

Water scarcity is a global problem. Deficit irrigation (DI) reduces evapotranspiration, improving water efficiency in agriculture. Reference evapotranspiration (ET0) is an important factor in determining DI. ET0 forecasting predicts field water consumption and enables proactive irrigation decisions, offering guidance for water resource management. However, implementation of ET0 forecasting faces challenges due to complex calculations and extensive meteorological data requirements. This project aims to develop a machine learning system for ET0 forecasting. The project involves studying ET0 methods and identifying required meteorological parameters. Historical meteorological data and weather forecasts were obtained from meteorological websites and analyzed for accuracy after preprocessing. A machine learning-based model was created to forecast reference crop evapotranspiration. The model’s input parameters were selected through path analysis before it was optimized using Bayesian optimization to reduce overfitting and improve accuracy. Three forecasting models were developed: one based on historical meteorological data, one based on weather forecasts, and one that corrects the weather forecasts. All three models achieved good accuracy, with root mean square errors ranging from 0.52 to 0.81 mm/day. Among them, the model based on weather forecast had the highest accuracy; the RMSE six days before the forecast period was between 0.52 and 0.75 mm/day, and the RMSE on the seventh day of the forecast period was 1.12 mm/day. In summary, this project has established a mathematical model of ET0 prediction based on machine learning, which can achieve more accurate predictions for within a few days.

Optimal Selection of Empirical Reference Evapotranspiration Method in 36 Different Agricultural Zones of China

The Food and Agriculture Organization has proposed the current version of the Penman–Monteith method (FAO56-PM) as the standard for calculating reference evapotranspiration (ET0); however, high meteorological data requirements limit its application in many areas. There is thus an urgent need to identify the best alternative empirical method to accurately calculate ET0 in regions that lack sufficient meteorological data. In this study, three temperature-based methods and five radiation-based methods were evaluated using ET0 values generated using the FAO56-PM method in 36 agricultural zones in China based on meteorological data from 823 stations, measured between 2011 and 2020. The results showed that the optimal temperature-based method and radiation-based method differed for different agricultural zones, and no one temperature method or radiation method could be suitable for all agricultural zones. The eight empirical methods were regionally calibrated to improve the ET0 calculation accuracy in the different zones. The relationship between the optimal methods and climatic conditions showed that the most reliable empirical method could be selected according to the local annual mean temperature and aridity index. The results provide useful guidance for the selection of reliable empirical ET0 methods in agricultural zones outside China.

Characterization of climatic parameters in the perspective of irrigated agriculture in Uttar Kannada district of Karnataka, India

A rainfall and potential evapotranspiration characteristics together determine the agro-meteorological regime of a region and influences decision concerning the magnitudes and timing of irrigation application. In the present study, historical rainfall and climate data pertaining to the study area, Uttar Kannada district, Karnataka, was analyzed with a view to characterizing irrigation water requirements. In addition to rainfall input, an important aspect of the water balance model is the crop evapotranspiration (ETcrop), which is the main factor in determining the irrigation schedule. ETcrop could be estimated by reference evapotranspiration (ET0) and crop coefficient. Atmospheric demand for water is represented by ‘potential evapotranspiration’ (PET) and calculated from climatic variables which is crucial for irrigation planning. It has been reported that the Penman-Monteith method gives more consistently correct ET0 estimates to other ET0 methods. While recognizing the importance of both rainfall and PET, an effective measure is known as the ‘Moisture Availability Index’ (MAI), which is computed as the ratio of 75% dependable rainfall and potential evapotranspiration. An MAI value of 1.00 indicates that dependable precipitation is equal to potential evapotranspiration. An MAI value of 0.33 or less for one month during the crop growing season is considered to be a signal of water deficit resulting reduction in crop yield. The findings of this study on MAI are used to decide the selection of the sowing period of crops so as to avoid water stress during the critical harvesting period.

Evaluation of reference evapotranspiration methods and sensitivity analysis of climatic parameters for sub-humid sub-tropical locations in western Himalayas (India)

ABSTRACT The estimation of crop evapotranspiration (ETc) uses reference evapotranspiration (ET0) as a key variable. Physically based FAO-56 Penman–Monteith method provides accurate ET0 estimates; however, various methods are still used in different climatic regions worldwide, either due to simplicity of the methods or due to insufficiency of data required for Penman–Monteith method. The present study is conducted at sub-humid sub-tropical locations of western Himalayan agro-climate in the Indian state of Himachal Pradesh. Performance of 12 ET0 methods, representing combination type, pan evaporation, radiation and temperature based, is compared with Penman–Monteith method. Different ET0 methods are ranked on the basis of quantitative comparison performed on mean daily ET0 obtained for a period of 6 years. The temperature-based methods performed better than radiation and pan evaporation-based methods. Linear regression equations are developed between Penman–Monteith ET0 (dependent variable) and ET0 estimates from alternate method (independent variable). Relative significance of meteorological factors essential for accurate ET0 estimation in the climate considered is investigated using sensitivity analysis. Solar radiation is identified as the most sensitive parameter for ET0 estimation in the climate of the study area, followed by maximum temperature and relative humidity.

Evaluation of impacts of future climate change and water use scenarios on regional hydrology

Abstract. General circulation models (GCMs) have been widely used to simulate current and future climate at the global scale. However, the development of frameworks to apply GCMs to assess potential climate change impacts on regional hydrologic systems, ability to meet future water demand, and compliance with water resource regulations is more recent. In this study eight GCMs were bias-corrected and downscaled using the bias correction and stochastic analog (BCSA) downscaling method and then used, together with three ET0 methods and eight different water use scenarios, to drive an integrated hydrologic model previously developed for the Tampa Bay region in western central Florida. Variance-based sensitivity analysis showed that changes in projected streamflow were very sensitive to GCM selection, but relatively insensitive to ET0 method or water use scenario. Changes in projections of groundwater level were sensitive to both GCM and water use scenario, but relatively insensitive to ET0 method. Five of eight GCMs projected a decrease in streamflow and groundwater availability in the future regardless of water use scenario or ET method. For the business as usual water use scenario all eight GCMs indicated that, even with active water conservation programs, increases in public water demand projected for 2045 could not be met from ground and surface water supplies while achieving current groundwater level and surface water flow regulations. With adoption of 40 % wastewater reuse for public supply and active conservation four of the eight GCMs indicate that 2045 public water demand could be met while achieving current environmental regulations; however, drier climates would require a switch from groundwater to surface water use. These results indicate a high probability of a reduction in future freshwater supply in the Tampa Bay region if environmental regulations intended to protect current aquatic ecosystems do not adapt to the changing climate. Broad interpretation of the results of this study may be limited by the fact that all future water use scenarios assumed that increases in water demand would be the result of intensification of water use on existing agricultural, industrial, and urban lands. Future work should evaluate the impacts of a range of potential land use change scenarios, with associated water use change projections, over a larger number of GCMs.

Validation and calibration of various reference evapotranspiration alternative methods under the climate conditions of Bosnia and Herzegovina

In Bosnia and Herzegovina (BiH), the number of weather stations (WS) that are monitoring all climatic parameters required for FAO-56 Penman-Monteith (FAO-PM) equation is limited. In fact, it is of great need and importance to achieve the possibility of calculating reference evapotranspiration (ET0) for every WS in BiH (around 150), regardless of the number of climate parameters which they collect. Solving this problem is possible by using alternative equations that require less climatological data for reliable estimation of daily and monthly ET0. The main objective of this study was to validate and determine, compared to the FAO-PM method, a suitable and reliable alternative ET0 equations that are requiring less input data and have a simple calculation procedure, with a special focus on Thornthwaite and Turc as methods previously often used in BiH. To fulfill this objective, 12 alternative ET0 calculation methods and 21 locally adjusted versions of same equations were validated against FAO-PM ET0 method. Daily climatic data, recorded at sixteen WS, including mean maximum and minimum air temperature (°C), precipitation (mm), minimum and maximum relative humidity (%), wind speed (ms−1) and sunshine hours (h) for the period 1961–2015 (55 years) were collected and averaged over each month. Several types of statistical indicators: the determination coefficient (R2), mean bias error (MBE), the variance of the distribution of differences (sd2), the root mean square difference (RMSD) and the mean absolute error (MAE) were used to assess alternative ET0 equation performance. The results, confirmed by various statistical indicators, shows that the most suitable and reliable alternative equation for monthly ET0 calculation in BiH is the locally adjusted Trajkovic method. Adjusted Hargreaves-Samani method was the second best performing method. The two most frequently used ET0 calculation methods in BiH until now, Thornthwaite and Turc, were ranked low.

Calibration of Hargreaves model for reference evapotranspiration estimation in Sichuan basin of southwest China

Accurate estimation of reference evapotranspiration is vital to hydrological and ecological processes. The FAO-56 Penman–Monteith (PM) model has the higher accuracy for ET0 estimation, but it requires many meteorological inputs that are not commonly available. Therefore an ideal method is needed requiring as minimal as possible input data variables without affecting the accuracy of estimation. The temperature-based models are especially interesting due to its input data, air temperature, can be monitored easily and is one of the commonly available climatic inputs. Among the temperature-based models, the Hargreaves (HG) model requiring maximum and minimum air temperature as the inputs is considered as one of the simplest and accurate ET0 methods, but this method needed a local calibration. The present study calibrated the HG model using Bayesian theory at 19 meteorological stations in Sichuan basin of southwest China. Meteorological data during 1961–1990 were used for the calibration and data during 1991–2014 were used for the validation. The results confirmed that the locally calibrated HG model (with average RRMSE, MAE and NS of 0.284, 0.433mm/d and 0.783) performed better than the original HG model (with average RRMSE, MAE and NS of 0.567, 0.959mm/d and 0.134). Both of the calibrated and original HG models overestimated ET0 at daily, monthly and annual timescale, but the calibrated HG model provided closer average values with PM ET0, which could confirm the good performances of the calibrated HG model. Therefore, the calibrated HG model could be highly recommended for estimating ET0 when only temperature data are available.

Predicting the reference evapotranspiration based on tensor decomposition

Most of the available models for reference evapotranspiration (ET0) estimation are based upon only an empirical equation for ET0. Thus, one of the main issues in ET0 estimation is the appropriate integration of time information and different empirical ET0 equations to determine ET0 and boost the precision. The FAO-56 Penman–Monteith, adjusted Hargreaves, Blaney–Criddle, Priestley–Taylor, and Jensen–Haise equations were utilized in this study for estimating ET0 for two stations of Belgrade and Nis in Serbia using collected data for the period of 1980 to 2010. Three-order tensor is used to capture three-way correlations among months, years, and ET0 information. Afterward, the latent correlations among ET0 parameters were found by the multiway analysis to enhance the quality of the prediction. The suggested method is valuable as it takes into account simultaneous relations between elements, boosts the prediction precision, and determines latent associations. Models are compared with respect to coefficient of determination (R 2), mean absolute error (MAE), and root-mean-square error (RMSE). The proposed tensor approach has a R 2 value of greater than 0.9 for all selected ET0 methods at both selected stations, which is acceptable for the ET0 prediction. RMSE is ranged between 0.247 and 0.485 mm day−1 at Nis station and between 0.277 and 0.451 mm day−1 at Belgrade station, while MAE is between 0.140 and 0.337 mm day−1 at Nis and between 0.208 and 0.360 mm day−1 at Belgrade station. The best performances are achieved by Priestley–Taylor model at Nis station (R 2 = 0.985, MAE = 0.140 mm day−1, RMSE = 0.247 mm day−1) and FAO-56 Penman–Monteith model at Belgrade station (MAE = 0.208 mm day−1, RMSE = 0.277 mm day−1, R 2 = 0.975).

Sensitivity of future continental United States water deficit projections to general circulation models, the evapotranspiration estimation method, and the greenhouse gas emission scenario

Abstract. Projecting water deficit under various possible future climate scenarios depends on the choice of general circulation model (GCM), reference evapotranspiration (ET0) estimation method, and Representative Concentration Pathway (RCP) trajectory. The relative contribution of each of these factors must be evaluated in order to choose an appropriate ensemble of future scenarios for water resources planning. In this study variance-based global sensitivity analysis and Monte Carlo filtering were used to evaluate the relative sensitivity of projected changes in precipitation (P), ET0, and water deficit (defined here as P–ET0) to choice of GCM, ET0 estimation method, and RCP trajectory over the continental United States (US) for two distinct future periods: 2030–2060 (future period 1) and 2070–2100 (future period 2). A total of 9 GCMs, 10 ET0 methods, and 3 RCP trajectories were used to quantify the range of future projections and estimate the relative sensitivity of future projections to each of these factors. In general, for all regions of the continental US, changes in future precipitation are most sensitive to the choice of GCM, while changes in future ET0 are most sensitive to the choice of ET0 estimation method. For changes in future water deficit, the choice of GCM is the most influential factor in the cool season (December–March), and the choice of ET0 estimation method is most important in the warm season (May–October) for all regions except the Southeast US, where GCMs and ET0 have approximately equal influence throughout most of the year. Although the choice of RCP trajectory is generally less important than the choice of GCM or ET0 method, the impact of RCP trajectory increases in future period 2 over future period 1 for all factors. Monte Carlo filtering results indicate that particular GCMs and ET0 methods drive the projection of wetter or drier future conditions much more than RCP trajectory; however, the set of GCMs and ET0 methods that produce wetter or drier projections varies substantially by region. Results of this study indicate that, in addition to using an ensemble of GCMs and several RCP trajectories, a range of regionally relevant ET0 estimation methods should be used to develop a robust range of future conditions for water resources planning under climate change.

Uncertainty in future irrigation water demand and risk of crop failure for maize in Europe

While crop models are widely used to assess the change in crop productivity with climate change, their skill in assessing irrigation water demand or the risk of crop failure in large area impact assessments is relatively unknown. The objective of this study is to investigate which aspects of modeling crop water use (reference crop evapotranspiration (ET0), soil water extraction, soil evaporation, soil water balance and root growth) contributes most to the variability in estimates of maize crop water use and the risk of crop failure, and demonstrate the resulting uncertainty in a climate change impact study for Europe. The SIMPLACE crop modeling framework was used to couple the LINTUL5 crop model in factorial combinations of 2–3 different approaches for simulating the 5 aspects of crop water use, resulting in 51 modeling approaches. Using experiments in France and New Zeland, analysis of total sensitivity revealed that ET0 explained the most variability in both irrigated maize water use and rainfed grain yield levels, with soil evaporation also imporatant in the French experiment. In the European impact study, net irrigation requirement differed by 36% between the Penman and Hargreaves ET0 methods in the baseline period. Average EU grain yields were similar between models, but differences approached 1–2 tonnes in parts of France and Southern Europe. EU wide esimates of crop failure in the historical period ranged between 5.4 years for Priestley–Taylor to every 7.9 years for the Penman ET0 methods. While the uncertainty in absolute values between models was significant, estimates of relative changes were similar between models, confirming the utility of crop models in assessing climate change impacts. If ET0 estimates in crop models can be improved, through the use of appropriate methods, uncertainty in irrigation water demand as well as in yield estimates under drought can be reduced.

Reference evapotranspiration variability and trends in Spain, 1961–2011

In this study we analyzed the spatial distribution, temporal variability and trends in reference evapotranspiration (ET0) in Spain from 1961 to 2011. Twelve methods were analyzed to quantify ET0 from quality controlled and homogeneous series of various meteorological variables measured at 46 meteorological stations. Some of the models used are temperature based (e.g., Thornthwaite, Hargreaves, Linacre), whereas others are more complex and require more meteorological variables for calculation (e.g., Priestley–Taylor, Papadakis, FAO–Blaney–Criddle). The Penman–Monteith equation was used as a reference to quantify ET0, and for comparison among the other methods applied in the study. No major differences in the spatial distribution of the average ET0 were evident among the various methods. At annual and seasonal scales some of the ET0 methods requiring only temperature data for calculation provided better results than more complex methods requiring more variables. Among them the Hargreaves (HG) equation provided the best results, at both the annual and seasonal scales. The analysis of the temporal variability and trends in the magnitude of ET0 indicated that all methods show a marked increase in ET0 at the seasonal and annual time scales. Nevertheless, results obtained suggested substantial uncertainties among the methods assessed to determine ET0 changes, due to differences in temporal variability of the resulting time series, but mainly for the differences in the magnitude of change of ET0 and its spatial distribution. This suggests that ET0 trends obtained by means of methods that only require temperature data for ET0 calculations should be evaluated carefully under the current global warming scenario.

Simulating the yields of bioenergy and food crops with the crop modeling software BioSTAR: the carbon-based growth engine and the BioSTAR ET0 method

With a growing production and use of agricultural substrates in biogas facilities, the competition between food and energy production, environmental issues, and sustainability goals has seen an increase in the last decade and poses a challenge to policy makers. Statistical yield data has a low spatial resolution and only covers standard crops and makes no statement in regard to yields under climate change. To support policy makers and regional planners in an improved allocation of agricultural land use, a new crop model (BioSTAR) has been developed. Simulations with weather and yield data from 7 years and four regions in Lower Saxony have rendered overall good modeling results with prediction errors (RMSE and percentage) ranging from 1.6 t and 9.8% for winter wheat to 2.1 t and 11.9% for maize. The model-generated ET0 and ETa values (mean of four locations) are lower than ET0/ETa values calculated with the Penman-Monteith method but appear more realistic when compared to field trial data from northern and eastern Germany. The model has proven to be a functioning tool for modeling site-specific biomass potentials at the farm level, and because of its Access® database interface, the model can also be used for calculating biomass yields of larger areas, like administration districts or states. Out of the seven crops modeled in this study, only limited yield and test site data was available for winter barley, winter rye, sorghum, and sunflower. For further improvement of model performance and model calibration, more trial data and data testing are required for these crops.

四种参考作物蒸散量综合法在我国农业主产区的适用性

参考作物蒸散量(ET0)的准确估算是作物需水量计算的关键。目前的许多ET0方法在为需水量估算带来便利的同时，也造成选择上的困惑。本文利用我国农业主产区六个站点的数据，以FAO 56 Penman- Monteith (PM)为标准，评价了国内外常用的四种综合法的适用性。结果表明，1963 Penman、FAO- ppp-17及1996 Kimberly penman都高估PM，在六站点平均高估0.28 mmd−1、0.52 mmd−1和0.14 mmd−1，相当于16.0%、25.2%和2.4%；而FAO 24 penman低估PM，六站点平均−0.17 mmd−1，相当于−5.3%。总体上，四种综合法与PM间的日值差异显著。依据RMSE(均方根误差)的吻合程度排序为：FAO 24 > 1963 Penman > 1996 Kimberly penman > FAO-ppp-17，但南、北方站点有差异：北方站点1963 Penman与PM最吻合，南方站点FAO 24与PM最吻合。此外，1963 Penman的普适性最好，FAO- ppp-17最差，故应用前对其评价更重要。四种综合法在北方站点表现较差，在南方站点较好，其中在沙坪坝适用性最好，在哈尔滨最差，表明Penman法及其衍生的多种综合法在湿润气候下适用性更好。逐月日ET0比较显示，绝对差值在夏季月份较大、冬季月份较小，但相对差值则是夏季月份较小、冬季月份较大。影响四种综合法与PM差异的关键因子为总辐射、净辐射和相对湿度。 Accurate estimation of reference crop evapotranscpiration (ET0) is critical for computation of crop water requirement. The currently numerous ET0 methods, which bring convenience for computing water requirement, cause confusion in method choice. Using data from six sites in main agricultural areas in China and with FAO 56 Penman-Monteith (PM) as reference, four commonly used combination methods were assessed. Results showed that the 1963 Penman, FAO-ppp-17 and 1996 Kimberly Penman overestimated the PM by 0.28, 0.52 and 0.14 mmd−1 (averaged over six sites), respectively, corresponding to 16.0%, 25.2% and 2.4%. In contrast, the FAO 24 underestimated the PM by 0.17 mmd−1 or −5.3%. Overall, daily ET0 of the four methods differed significantly from that of the PM, and their performance based on RMSE showed the order: FAO 24 > Pen63 > Kpen > FAO-ppp-17, which varied among southern and northern sites: the 1963 Penman was the best at northern sites and the FAO 24 was the best at southern sites. In addition, validity of the 1963 Penman was the best, and that of the FAO-ppp-17 was the poorest, implying the importance to evaluate the latter before use. As a whole, the four methods performed poorer at the northern sites than that at the southern ones, and they gave best performance at Shapingba and poorest at Haerbin, meaning that the Penman and its derivative versions are more applicable in humid climates. Daily comparison at each month indicated that mean bias error (MBE) was larger at summer months and smaller at winter months, but it was opposite for relative error (RMBE). Total solar radiation, net radiation and humidity are the most important factors influencing performance of the four methods.

Performance Evaluation of Reference Evapotranspiration Equations across a Range of Indian Climates

Reference crop evapotranspiration ( ET0 ) is a key variable in procedures established for estimation of evapotranspiration rates of agricultural crops. In recent years, there is growing evidence to show that the more physically based FAO-56 Penman–Monteith (PM) combination method yields consistently more accurate ET0 estimates across a wide range of climates and is being proposed as the sole method for ET0 computations. However, other methods continue to remain popular among Indian practitioners either because of traditional usage or because of their simpler input data requirements. In this study, we evaluated the performances of several ET0 methods in the major climate regimes of India with a view to quantify differences in ET0 estimates as influenced by climatic conditions and also to identify methods that yield results closest to the FAO-56 PM method. Performances of seven ET0 methods, representing temperature-based, radiation-based, pan evaporation-based, and combination-type equations, were compared ...

Solar and Net Radiation-Based Equations to Estimate Reference Evapotranspiration in Humid Climates

Two equations for estimating grass reference evapotranspiration (ET0) were derived using the Food and Agriculture Organization Penman–Monteith (FAO56-PM) method as an index. The first equation, solar radiation (Rs) based, estimates ET0 from incoming Rs and maximum and minimum air temperature, and the second equation, net radiation (Rn) based, uses Rn and maximum and minimum air temperature. The equations were derived using 15 years (1980–1994) of daily ET0 values estimated from the FAO56-PM method using the measured and carefully screened weather data from near Gainesville, Florida. The performance of the derived equations was evaluated for 6 validation years (1995–2000), including dry and wet years, for the same site and for other humid locations in the Southeast United States. Comparisons of the performance of the derived equations with the other commonly used methods indicated that they estimate ET0 as good or better than those other ET0 methods. The Rs- and Rn-based equations resulted in the lowest 6 year average standard error of estimate (SEE) of daily ET0 (0.44 and 0.41 mm day−1, respectively). Both equations performed quite well for estimating peak month ET0 and had the lowest 6 year average daily SEE for the peak month ET0 (0.24 mm day−1 for both equations). Estimates for annual total ET0 were very close to those obtained from the FAO56-PM method. The 6 year average ratio of ET0 method to ET0 FAO56-PM were 1.05 and 1.03 for the Rs- and Rn-based equations, respectively. The derived equations were further evaluated in other humid locations in the Southeast United States, including two locations in coastal regions in Florida, one location in Georgia, and another location in Alabama. The comparisons showed that both equations are likely to provide good estimates of ET0 in humid locations of the Southeast United States. When the required input variables are considered, the Priestley–Taylor (PT) method was the closest method to the second derived equation (Rn based). Therefore, it was necessary to evaluate how the PT method would perform compared to the Rn-based equation relative to the FAO56-PM method after it is calibrated locally. Although the performance of the PT method improved slightly after the calibration, its performances for estimating daily and peak month ET0 remained poorer than the Rn-based equation in all cases. Considering the limitations associated with the availability and reliability of the climatological data, especially in developing countries, the derived equations presented in this study are suggested as practical methods for estimating ET0 if the standard FAO56-PM equation cannot be used because of the above-mentioned limitations. These equations are recommended over the other commonly used simplified temperature and radiation-based methods evaluated in this study for humid climates in the Southeast United States.