Hargreaves Samani Research Articles

Evaluation of artificial intelligence models for daily prediction of reference evapotranspiration using temperature, rainfall and relative humidity in a warm sub-humid environment

Accurate estimation of reference evapotranspiration is essential for agricultural management and water resources engineering applications. In the present study, the ability and precision of three artificial intelligence (AI) models (i.e., Support Vector Machines (SVMs), Adaptive Neuro-Fuzzy Inference System (ANFIS) and Categorical Boosting (CatBoost)) were assessed for estimating daily reference evapotranspiration (ET0) using limited weather data from five locations in a warm sub-humid climate in Mexico. The Penman–Monteith FAO-56 equation was used as a reference target for ET0 values. Three different input combinations were investigated, namely: temperature-based (minimum and maximum air temperature), rainfall-based (minimum air temperature, maximum air temperature and rainfall), and relative humidity-based (minimum air temperature, maximum air temperature and relative humidity). Extraterrestrial radiation values were used in all combinations. The temperature-based AI models were compared with the conventional Hargreaves–Samani (HS) model commonly used to estimate ET0 when only temperature records are available. The goodness of fit for all models was assessed in terms of the coefficient of determination (R2), Nash–Sutcliffe model efficiency coefficient (NSE), root mean square error (RMSE) and mean absolute error (MAE). The results showed that among the AI models evaluated, the SVM models outperformed ANFIS and CatBoost for modeling ET0. Further, the influence of relative humidity and rainfall on the performance of the models was investigated. The analysis indicated that relative humidity significantly improved the accuracy of the models. Finally, the results showed a better response of the temperature-based AI models over the HS method. AI models can be an adequate alternative to conventional models for ET0 modeling.

Evaluating the Influence of Deficit Irrigation on Fruit Yield and Quality Indices of Tomatoes Grown in Sandy Loam and Silty Loam Soils

The most important biotic stress factor impacting tomato crop biophysical, biochemical, physiological, and morphological features is water stress. A pot experiment was undertaken in a greenhouse to study the drought responsiveness of tomato (Solanum lycopersicum) yield and quality indices in sandy loam and silty loam soils. For both sandy loam and silty loam soils, the water supply levels were 70–100% FC, 60–70% FC, 50–60% FC, and 40–50% FC of ETo (crop evapotranspiration) from the vegetative stage to the fruit ripening stage, calculated using the Hargreaves–Samani (HS) model compared to the time-domain reflectometer (TDR) values calibrated using volumetric water content (VWC). The experiment was conducted as a 2 × 4 factorial experiment, arranged in a completely randomized block design, with four treatments replicated four times. In this study, we examined how sandy loam and silty loam soils at different % FC affect the total marketable yield and quality components of tomatoes, concentrating on total soluble solids (Brix), fruit firmness, dry fruit mass, pH, titratable acid (TA), ascorbic acid (Vit. C), and carotenoid composition. Lycopene and β-Carotene were estimated using the UV spectroscopy method, with absorption spectra bands centered at 451 nm, 472 nm, 485 nm, and 502 nm. The results revealed that even though there were some limitations, TDR-based soil moisture content values had a strong positive correlation with HS-based evapotranspiration, with R2 = 0.8, indicating an improvement whereby TDR can solely be used to estimate soil water content. Tomato plants subjected to 40–50% FC (ETo) water stress in both sandy loam and silty loam soils recorded the highest total soluble solids, titratable acidity, ascorbic acid content, and β-carotene content at an absorption peak of 482 nm, and lycopene content at an absorption peak of 472 nm, with lower fruit firmness, fruit juice content, and fruit juice pH, and a reduced marketable yield. Similarly, tomato plants subjected to 60–70% FC throughout the growing season achieved good fruit firmness, percent juice content, total soluble solids, titratable acidity, ascorbic acid content, and chlorophyll content (SPAD), with minimum fruit juice pH and high marketable yield in both soil textural types. It is concluded that subjecting tomato plants to 60–70% FC (ETo) has a constructive impact on the marketable yield quality indices of tomatoes.

Solar Fertigation: A Sustainable and Smart IoT-Based Irrigation and Fertilization System for Efficient Water and Nutrient Management

The agricultural sector is one of the major users of water resources. Water is an important asset that needs to be preserved using the latest available technologies. Modern technologies and digital tools can transform the agricultural domain from being manual and static to intelligent and dynamic leading to higher production with lesser human supervision. This study describe the agronomic models that should be integrated with the intelligent system which schedule the irrigation and fertilization according to the plant needs, and monitors and maintains the desired soil moisture content via automatic watering. Solar fertigation is a fertigation support system based on photovoltaic solar power energy and an IoT system for precision irrigation purposes. The system monitors the temperature, radiation, humidity, soil moisture, and other physical parameters. An agronomic DSS platform based on the integration of soil, weather, and plant data and sensors was described. Furthermore, a three-year study on seven ETo models, such as three temperature-, three radiation-, and a combination-based models were tested to evaluate the sustainable ETo estimation and irrigation scheduling in a Mediterranean environment. Results showed that solar fertigation and Hargreaves–Samani (H-S) equation represented a nearby correlation to the standard FAO P–M and does offer a small increase in accuracy of ETo estimates. Furthermore, the hybrid agronomic DSS is suitable for smart fertigation scheduling.

Estimation of evapotranspiration from measured meteorological parameters

Five empirical equations, namely, FAO-56 Penman–Monteith, Hargreaves–Samani, Makkink, Turc, and Priestley–Taylor are utilized in the estimation of evapotranspiration for the month of May in 2018 for Trombay site in Maharashtra. Evapotranspiration from a given surface is a function of incoming solar radiation, net radiation, ground heat flux, air temperature, relative humidity, and wind speed. Daily average measurements of these parameters are utilized in the empirical equations for the estimation of evapotranspiration. These estimated values are compared with the measured data from pan evaporimeter installed at Trombay. The measured data from the pan evaporimeter are corrected using the pan coefficient Kp which in turn is also estimated using empirical equations. The average value of the pan coefficient Kp is 0.8 for the site. The average measured value of evapotranspiration is 4.7 mm/d for May 2018, whereas the values estimated using the five empirical equations range from 3.3 mm/d to 12.7 mm/d. Among the five equations, the Turc equation was found to be in the best agreement with the measured values of evapotranspiration. Such studies are useful in the estimation of groundwater recharge, latent heat flux, and agriculture meteorology.

Environmental Assessment of Future Potential Evaporation for Al-Najaf Governorate, Iraq through Evaluating Various Estimation Methods Using Statistical Downscaling Model

The hydrological cycle in nature is affected by climate changes, which are reflected in the water resources on the Earth (surface and underground) as evapotranspiration, thereby causing water scarcity. Increasing global temperature rates have exacerbated evaporation rates (PET). To estimate PET, scientists invented many mathematical equations, the most prominent of which is the Penman-Monteith equation. Most of the innovative methods require the provision of many parameters to be implemented; therefore, feasibly worthless for application in data mingy regions. The performance of the four PET estimation methods has been investigated depending either on temperature or radiation observed at Al-Najaf Governorate, Iraq. The accuracy and efficiency of each method have been evaluated with the outputs of the reference Penman-Monteith method. Through assessment, Hargreaves Samani temperature-based method reveals high acceptability of the estimated PET than the Jensen-Haise method and the other radiation-based methods (Penman and Makkink). The Statistical Downscaling Model/Tool (SDSM version 5.2) is applied to predict temperature values for the years 2050 and 2100. Estimated PET using Hargreaves Samani formula for 2050 and 2100 shows that Al-Najaf Governorate will encounter severe water scarcity due to the expected future increase in evaporation rates. Overall, regions classified as dry with high temperatures are compatible with methods of estimating PET values that depend on temperatures more than those that depend on radiation.

Reference evapotranspiration estimation using long short‐term memory network and wavelet‐coupled long short‐term memory network

AbstractEvapotranspiration (ET) is a vital component of the hydrological cycle, and accurate estimation of reference evapotranspiration (ET0) is of great importance in agriculture water resources planning and management. In this study, long short‐term memory network (LSTM), artificial neural network (ANN), extreme learning machine (ELM), and their wavelet‐coupled models were used for daily ET0 estimation. For comparison purposes, this study also investigated the ET0 estimation capability of three typical empirical models, that is, the Hargreaves–Samani (HS) equation, Penman (PM) equation, and Priestley–Taylor (PT) equation. Daily meteorological data were obtained from two weather stations, Beijing and Baoding, located in the northern part of the North China Plain. Results demonstrated that single machine learning (ML) models, for example, ANN, ELM, LSTM, are steadier and generally have better overall performance than wavelet‐coupled ML models. Besides, the LSTM model performed best among the single ML models and was far superior to the HS, PM, and PT models. The LSTM model helped the root mean square error (RMSE) and mean absolute error (MAE) of the ANN and ELM models decrease by 5%–69% and 8%–72%, respectively. Moreover, the LSTM model helped the RMSE and MAE of the empirical models decrease by 6%–83% and 5%–84%, respectively.

Spatial statistics techniques for SPEI and NDVI drought indices: a case study of Khuzestan Province.

Drought is a major water resources management issue in Iran. Khuzestan Province is in a drought state due to water shortage. Therefore, identifying areas at high risk of drought and when drought occurs is essential for drought management. For this purpose, this study used precipitation and temperature data of 12 selected stations and MODIS sensor images from the United States Geological Survey database in 2000–2017. The Standardized Precipitation Evapotranspiration Index (SPEI) and the Standardized Normalized Difference Vegetation Index (NDVI) were calculated using the Hargreaves–Samani method and ENVI software. Moreover, different spatial statistics techniques were used in the ArcGIS environment to analyze the results. Also, time series diagrams were drawn, and the trend was evaluated using the Mann–Kendall test. Finally, the distribution of NDVI values was investigated using EasyFit software, and the amount of drought damage was determined using NDVI. The investigation of the cluster maps of the Anselin Local Moran’s Index along with hot and cold spots formed for both SPEI and NDVI showed that drought severity was higher at the southern stations than at the semi-northern and northwestern ones in the province. Moreover, the survey results using the EasyFit software showed that the southern stations, including the Ahvaz, Mahshahr, and Omidiyeh-Aghajari stations, were more at risk of drought than the other stations due to the drought threshold. Furthermore, the total damage caused by drought for the Ahvaz and Abadan stations showed a damage rate of 50%.

Modification of Hargreaves–Samani Model for Estimation of Reference Evapotranspiration in Semi-Arid Region of Punjab, India

Modification of Hargreaves–Samani Model for Estimation of Reference Evapotranspiration in Semi-Arid Region of Punjab, India

Spatio-temporal calibration of Hargreaves\u2013Samani model in the Northern Region of Nigeria

One of the significant components of the hydrological cycle is evapotranspiration. Monthly meteorological parameters of 35 years from 19 meteorological stations across the Northern Region of Nigeria (NRN) were obtained and utilized for the calibration of Hargreaves–Samani (HS) model by comparing between potential evapotranspiration (ETo) values estimated from the original HS and the Penman–Monteith (FAO-56 PM) models. The calibrated HS equation was assessed using trend patterns and some statistical indices. The average value of root mean square error (RMSE) and the mean absolute error (MAE) decreased by 37.1 and 40%, respectively, after the calibration of the model. Also, the correlation coefficients (R) of stations that had values > 0.8 increased from 6 to 11 and the minimum R value increased by 12% above that of the original HS equation. The trend and spatial map of the statistical tests conducted also indicate better performance in most climatic regions after calibration. The precision of the HS equation improved significantly after calibration for semi-arid, humid, and sub-humid regions. However, few stations in the semi-arid, humid, and sub-humid regions did not show drastic improvement due to the peculiarity of the location and high variations in the wind speed and relative humidity parameters.

Development of Boosted Machine Learning Models for Estimating Daily Reference Evapotranspiration and Comparison with Empirical Approaches

Proper irrigation scheduling and agricultural water management require a precise estimation of crop water requirement. In practice, reference evapotranspiration (ETo) is firstly estimated, and used further to calculate the evapotranspiration of each crop. In this study, two new coupled models were developed for estimating daily ETo. Two optimization algorithms, the shuffled frog-leaping algorithm (SFLA) and invasive weed optimization (IWO), were coupled on an adaptive neuro-fuzzy inference system (ANFIS) to develop and implement the two novel hybrid models (ANFIS-SFLA and ANFIS-IWO). Additionally, four empirical models with varying complexities, including Hargreaves–Samani, Romanenko, Priestley–Taylor, and Valiantzas, were used and compared with the developed hybrid models. The performance of all investigated models was evaluated using the ETo estimates with the FAO-56 recommended method as a benchmark, as well as multiple statistical indicators including root-mean-square error (RMSE), relative RMSE (RRMSE), mean absolute error (MAE), coefficient of determination (R2), and Nash–Sutcliffe efficiency (NSE). All models were tested in Tabriz and Shiraz, Iran as the two studied sites. Evaluation results showed that the developed coupled models yielded better results than the classic ANFIS, with the ANFIS-SFLA outperforming the ANFIS-IWO. Among empirical models, generally the Valiantzas model in its original and calibrated versions presented the best performance. In terms of model complexity (the number of predictors), the model performance was obviously enhanced by an increasing number of predictors. The most accurate estimates of the daily ETo for the study sites were achieved via the hybrid ANFIS-SFLA models using full predictors, with RMSE within 0.15 mm day−1, RRMSE within 4%, MAE within 0.11 mm day−1, and both a high R2 and NSE of 0.99 in the test phase at the two studied sites.

Evapotranspiration in the Brazilian municipalities surrounding the Itaipu Binacional reservoir: characterization process and estimation methods

Seeking to contribute with the management of water resources in the Itaipu Binacional reservoir region, this research aimed to characterize the dynamics of evapotranspiration and evaluate the performance of different mathematical methods, which determine reference evapotranspiration (ETo) from air temperature values. Fifteen municipalities were analyzed. After obtaining the data series, ETo was estimated using six methods: Camargo (C), Hargreaves-Samani (HG-S), Jensen-Haise (JH), Penman-Monteith with missing data (PMm), Thornthwaite-Camargo (TW-C) and Penman-Monteith (PM) – the latter was the reference method. The performance of the methods was analyzed by several statistical indexes. Daily ETo values ranged from 2 to 10 mm d-1, with an annual mean of 5.78 mm d-1. We also observed that it is determined predominantly by radioactive parameters, which annually represent 76% of the evapotranspiration process, while aerodynamic parameters represent 24%. Among the ETo estimation methods, HG-S and PMm were the most suitable for estimating.

Comparison of Three Daily Rainfall-Runoff Hydrological Models Using Four Evapotranspiration Models in Four Small Forested Watersheds with Different Land Cover in South-Central Chile

We used the lumped rainfall–runoff hydrologic models Génie Rural à 4, 5, 6 paramètres Journalier (GR4J, GR5J and GR6J) to evaluate the most robust model for simulating discharge on four forested small catchments (<40 ha) in south-central Chile. Different evapotranspiration methods were evaluated: Oudin, Hargreaves–Samani and Priestley–Taylor. Oudin’s model allows the achievement of the highest efficiencies in the flow simulation. The more sensitive parameters for each model were identified through a Generalized Probability Uncertainty Estimation (GLUE) model. Our results demonstrate that the three hydrological models were capable of efficiently simulating flow in the four study catchments. However, the GR6J model obtained the most satisfactory results in terms of simulated to measured streamflow closeness. In general, the three models tended to underestimate peak flow, as well as underestimate and overestimate flow events in most of the in situ observations, according to the probability of non-exceedance. We also evaluated the models’ performance in a simulation of summer discharge due to the importance of downstream water supply in the months of greatest scarcity. Again, we found that GR6J obtained the most efficient simulations.

A Simple Application for Computing Reference Evapotranspiration with Various Levels of Data Availability—ETo Tool

Reference evapotranspiration (ETo) estimations may be used to improve the efficiency of irrigated agriculture. However, its computation can be complex and could require numerous weather data that are not always available for many locations. Different methods are available to estimate ETo when limited data are available, and the assessment of the most accurate one can be difficult and time consuming. There are some standalone softwares available for computing ETo but none of them allow for the comparison of different methods for the same or different datasets simultaneously. This paper aims to present an application for estimating ETo using several methods that require different levels of data availability, namely FAO-56 Penman–Monteith (PM), the Original and the three modified Hargreaves–Samani (HS and MHS1, MHS2 and MHS3), Trajkovic (TR) and the single temperature procedure (MaxTET). Also, it facilitates the comparison of the accuracy estimation of two selected methods. From an example case, for where the application was used to compute ETo for three different locations, results show that the application can easily and successfully estimate ETo using the proposed methods, allowing for statistical comparison of those estimations. HS proves to be the most accurate method for the studied locations; however, the accuracy of all methods tends to be lower for costal locations than for more continental sites. With this application, users can select the best ETo estimation methods for a specific location and use it for irrigation purposes.

Estimation of Daily Reference Evapotranspiration from NASA POWER Reanalysis Products in a Hot Summer Mediterranean Climate

This study aims at assessing the accuracy of estimating daily reference evapotranspiration (ETo) computed with NASA POWER reanalysis products. Daily ETo estimated from local observations of weather variables in 14 weather stations distributed across Alentejo Region, Southern Portugal were compared with ETo derived from NASA POWER weather data, using raw and bias-corrected datasets. Three different methods were used to compute ETo: (a) FAO Penman-Monteith (PM); (b) Hargreaves-Samani (HS); and (c) MaxTET. Results show that, when using raw NASA POWER datasets, a good accuracy between the observed ETo and reanalysis ETo was observed in most locations (R2 > 0.70). PM shows a tendency to over-estimating ETo with an RMSE as high as 1.41 mm d−1, while using a temperature-based ET estimation method, an RMSE lower than 0.92 mm d−1 is obtained. If a local bias correction is adopted, the temperature-based methods show a small over or underestimation of ETo (–0.40 mm d−1 ≤ MBE < 0.40 mm d−1). As for PM, ETo is still underestimated for 13 locations (MBE < 0 mm d−1) but with an RMSE never higher than 0.77 mm d−1. When NASA POWER raw data is used to estimate ETo, HS_Rs proved the most accurate method, providing the lowest RMSE for half the locations. However, if a data regional bias correction is used, PM leads to the most accurate ETo estimation for half the locations; also, when a local bias correction is performed, PM proved the be the most accurate ETo estimation method for most locations. Nonetheless, MaxTET proved to be an accurate method; its simplicity may prove to be successful not only when only maximum temperature data is available but also due to the low data required for ETo estimation.

The Seasonal Water Balance of Western-Juniper-Dominated and Big-Sagebrush-Dominated Watersheds

The combined impacts of woody plant encroachment and climate variability have the potential to alter the water balance in many sagebrush steppe ecosystems in the Western USA, leading to reduced water availability in these already water-scarce regions. This study compared the water-balance characteristics of two adjacent semiarid watersheds in central Oregon, USA: one dominated by big sagebrush and one dominated by western juniper. Precipitation, springflow, streamflow, shallow groundwater levels, and soil moisture were measured. The potential evapotranspiration was calculated using the Hargreaves–Samani method. Potential evapotranspiration and a water-balance approach were used to calculate seasonal actual evapotranspiration. The shallow aquifer recharge was calculated using the Water-Table-Fluctuation-Method. Evapotranspiration, followed by deep percolation, accounted for the largest portion (83% to 86% of annual precipitation) of water output for both watersheds. Springflow and streamflow rates were generally greater at the sagebrush-dominated watershed. Snow-dominated years showed greater amounts of groundwater recharge and deep percolation than years where a larger portion of precipitation fell as rain, even when total annual precipitation amounts were similar. This study’s results highlight the role of vegetation dynamics, such as juniper encroachment, and seasonal precipitation characteristics, on water availability in semiarid rangeland ecosystems.

Natural Groundwater Recharge Response to Climate Variability and Land Cover Change Perturbations in Basins with Contrasting Climate and Geology in Tanzania

The response of aquifers with contrasting climate and geology to climate and land cover change perturbations through natural groundwater recharge remains inadequately understood. In Tanzania and elsewhere in the world, studies have been conducted to assess the impact of climate change and variability, and land use/cover changes on stream flow using different models, but similar studies on groundwater dynamics are inadequate. This study, therefore, examined the influence of land use/cover and climate dynamics on natural groundwater recharge in basins with contrasting climate and geology in Tanzania, applying the modified soil moisture balance method, coupled with the curve number (CN). The method hinges on the balance between the incoming water from precipitation and the outflow of water by evapotranspiration. The different parameters in the soil moisture balance method were computed using the Thornthwaite Water Balance software. The potential evapotranspiration (PET) was calculated using the daily maximum and minimum temperatures, utilizing two-temperature-based PET methods, Penman–Monteith (PM) and Hargreaves–Samani (HS). The rainfall data were obtained from the gauging stations under the Tanzania Meteorological Agency and some additional data were acquired from climate observatories management by water basins. The results show that there has been a quasi-stable CN in the Singida semi-arid, fractured crystalline basement aquifer (74.2 in 1997, 73.64 in 2005, and 73.87 in 2018). In the Kimbiji, humid, Neogene sedimentary aquifer, the CN has been steadily increasing (66.69 in 1997, 69.08 in 2008, and 71.42 in 2016), indicating the rapid land cover changes in the Kimbiji aquifer as compared to the Singida aquifer. For the Kimbiji humid aquifer, the PET calculated using the Penman–Monteith (PM) method for the 1996/1997, 2007/2008, and 2015/2016 hydrological years were 1156.5, 1079.5, and 1143.9 mm/year, respectively, while for the Hargreaves–Samani (HS) method, the PET was found to be 1046.1, 1138.3, and 1204.4 mm/year for the 1996/1997, 2007/2008, and 2015/2016 hydrological years, respectively. For the Singida semi-arid aquifer, the PM PET method resulted in 2083.3, 2053.6, and 1875.4 mm/year for the 1996/1997, 2004/2005, and 2017/2018 hydrological years, respectively. The HS method produced relatively lower PET values for the semi-arid area (1839.4, 1814.7, and 1710.2 mm/year) for the 1996/1997, 2004/2005, and 2017/2018 hydrological years, respectively. It was equally revealed that the recharge and aridity indices correspond with the PET calculated using two temperature-dependent methods. The decline of certain land covers (forests) and increase in others (built-up areas) have contributed to the increase in surface runoff in each study area, possibly resulting in the decreasing trend of groundwater recharge. An overestimation of the PET using the HS method in the Kimbiji humid aquifer was observed, which was relatively smaller than the overestimation of the PET using the PM method in the Singida semi-arid aquifer. Despite the difference in climate and geology, the response of the two aquifers to rainfall is similar. The combined influence of climate and land cover changes on natural groundwater recharge was observed to be prominent in the Kimbiji aquifer, while only climate variability appreciably influences natural groundwater recharge in the Singida semi-arid aquifer. El Nino and the Southern Oscillation as part of the climate variability phenomenon dwarfed the time lags between rainfall and recharge in the two basins, regardless of their difference in climate and geology.

Calculation of Potential Evapotranspiration and Calibration of the Hargreaves Equation Using Geostatistical Methods over the Last 10 Years in Central Italy

Potential evapotranspiration (ET0) is an indicator of great interest for water budget analysis and the agricultural sector. Therefore, the purpose of this study was to make the calculation reliable even if only the temperature data were present. In this research, the ET0 was initially calculated for a limited number of weather stations (12) using the Penman–Monteith method. In some cases, the simplified Penman–Monteith formula was adopted, while in others, as in the case of mountain weather stations, the complete formula was employed to consider the differences in vegetation, deduced from satellite surveys. Subsequently, the ET0 was calculated with the Hargreaves–Samani (HS) formula, calibrating the Hargreaves coefficient, through the spatialization of ET0, by the geostatistical method. The results showed a high reliability of the HS method in comparison with simplified PM (PM) method, and complete Penman–Monteith (cPM) method, with a minimum calibration of the empirical Hargreaves coefficient. In particular, a very good correlation between the results obtained in the mountain environment with the uncalibrated HS method and the cPM method was also observed in this area, while PM showed discordant and much higher results than ET0 compared with the other methods. It follows that this procedure allowed a more accurate estimate of potential evapotranspiration with a view to territory management, both in terms of water resources and the irrigation needs of the vegetation.

Performance of potential evapotranspiration models in Peninsular Malaysia

Abstract Potential evapotranspiration (PET) is an important parameter for the operation of irrigation projects and water resources management. The globally recognized PET estimation model, the FAO-56 Penman–Monteith (FAO-56 PM) model, had been criticized for its requirement of many detailed meteorological variables, but nevertheless has been accepted as the baseline model in many worldwide studies. The performances of different PET models can be found to be excellent for a specific location but may not be representative in other regions. The aim of this study is to select the most suitable PET model to estimate PET in Malaysia. Three radiation-based models and four temperature-based models were compared with the FAO-56 PM model at seven selected meteorological stations in Peninsular Malaysia. The mean bias error, relative error (Re) and normalized root-mean-square error (NRMSE) and coefficient of determination (R2) were used to evaluate the performances of the PET models. The Re values of Turc models were below 0.2 at all stations, while Priestly–Taylor, Thornthwaite, Thornthwaite-corrected and Blaney–Criddle models were above 0.2. The Makkink and Hargreaves–Samani models were below 0.2 at most of the stations. Thus, the Turc model was recommended as the best model to estimate PET in Peninsular Malaysia.

A note on some uncertainties associated with Thornthwaite's aridity index introduced by using different potential evapotranspiration methods

Potential evapotranspiration (PET) is a key parameter for climate classification and aridity assessment. The widely used UNEP (1992) classification system is based on the estimation of the aridity index AI, which requires annual average values of precipitation P and PET. For the calculation of PET the Thornthwaite's (1948) formula is, in principle, suggested. Recent studies use more advanced and accurate methods for PET estimation but apply to AI the same thresholds proposed by UNEP for aridity classification. This work deals with the uncertainties introduced by the use of different PET methods in the estimation of the aridity index AI. Specifically, the Hargreaves-Samani (HS) method and four of its modifications, three modifications of Thornthwaite's formula and the equation of Hamon, are evaluated against the widely used Thornthwaite's original method, by assessing their impact on the AI. Climatic data as monthly average values of at least 30 years of measurements from 122 stations in the Greek peninsula are used. Results show that AI is highly affected by the PET method adopted, resulting thus to changes in climatic classification of a region. Further, results imply the need for an adjustment of the threshold values that determine aridity classes according to the method each time adopted. Therefore, new threshold values for the aridity classes are developed and presented in this work. The proposed threshold values cover a range of sites that belong to semi-arid SA, sub-humid SH and humid H aridity classes of the Greek peninsula.

Assessing of evapotranspiration models using limited climatic data in Southeast Anatolian Project Region of Turkey.

Evapotranspiration carries vital importance in areas with arid and semi-arid climate properties for many issues, including the planning of irrigation water as a scarce resource, the establishment of irrigation programs and conducting project design for drainage. The empirical equations used for determining plant water consumption are classified subject to the diversity of the utilized data. The Penman–Monteith method used frequently in many parts of the world as a standard method needs more climate data. Models that yield results that are similar to those of the standard method with less climate parameters are preferred due to their ease of use and wide impact. Temperature, relative humidity and radiation data for the years 2008–2017 were utilized to analyze the usability of the Hargreaves–Samani and Turc-1961 equations with regard to the estimation of reference evapotranspiration in four provinces located in Southeastern Anatolia Region. Results obtained via models were compared in pairs by way of the standard method in order to define the performance of the models. While the best performances were obtained from the comparison with the standard method and Hargreaves–Samani value pair, the comparison of the standard model with Turc displayed the lowest performance. Based on the study data, ETo-Turc values were higher in the provinces analyzed, thus displaying a lower performance. While maximum long term annual monthly average ETo-HS value was identified as 7.6 mm at Diyarbakır in July, whereas the lowest value was determined at Kilis with 5.8 mm; the highest and lowest ETo-Turc values were obtained in the same month at Diyarbakır and Kilis with 13.3 and 10.3 mm respectively. It was calculated based on the long term average annual total ETo values that while highest ETo-HS was calculated at Diyarbakır with 1,500 mm, whereas the lowest value was calculated at Batman with 1,183 mm. The highest value for ETo-Turc was obtained at Diyarbakır with 2,365 mm while Mardin had the lowest ETo value with 1,920 mm. Accordingly, based on the ETo values calculated at both cities studies based on both models, Diyarbakır had the highest values, whereas Kilis had the lowest ETo values. According to the standard method known as PM, lowest daily ETo values were calculated in all provinces, which displayed the highest performance among the models. As a result of this study, it is possible to use the Hargreaves-Samani model instead of the standard model in the absence of reliable climatic data.