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This study aimed to accurately estimate daily wheat evapotranspiration using two remote sensing algorithms, Surface Energy Balance System (SEBS) and Surface Energy Balance Algorithm for Land (SEBAL), in central Khuzestan province during 2019–2020. The results of two algorithms were compared with lysimeter (as a direct method), FAO-Penman–Monteith (FAO-PM), two temperature-based methods (Hargreaves-Samani and Blaney-Criddle), two radiation-based methods (Priest- ley–Taylor and Doorenbos–Pruitt), and two mass transfer-based methods (Mahringer and World Meteorology Organization) (as indirect methods). Coefficient of Determination (R ), Root-Mean-Square Error (RMSE), Percentage of Bias (PBIAS), Mean Bias Error, Mean Absolute Percentage Error, and Nash–Sutcliffe indicators used for comparing the results. Accord- ing to the results, both SEBAL and SEBS algorithms showed the highest compatibility with lysimeter data (R = 0.92 and 0.96, RMSE = 2.15 and 1.53 mm/day, respectively). Comparing both algorithms with the FAO-PM method, resulted in RMSE and R of 2.42 mm/day and 0.87 for SEBS and 3.14 mm/day and 0.79 for SEBAL. The Hargreaves-Samani method 2 2 (R = 0.72, RMSE = 16.4 mm/day) and (R = 0.8, RMSE = 10.4 mm/day) among temperature-based methods, Doorenbos– 2 2 Pruitt (R = 0.71, RMSE = 3.33 mm/day) and (R = 0.79, RMSE = 2.63 mm/day) among radiation-based methods, and the 2 2 Mahringer method (R = 0.6, RMSE = 6.8 mm/day mm/day) and (R = 0.68, RMSE = 5.51 mm/day) among mass transfer- based methods yielded better estimations than SEBAL and SEBS algorithms, respectively. Owing to the high accuracy of SEBAL and SEBS algorithms, in estimating the amount of evapotranspiration in the study area and close to the actual values in the field, using energy balance algorithms is recommended in Khuzestan province. Keywords Evapotranspiration · Lysimeter · FAO-Penman–Monteith · Remote sensing Introduction of great importance in water use planning and optimization (Asadi et al. 2022). It is also necessary for irrigation and Crop evapotranspiration (ET) plays a key role in determin- water resources management, increasing yield, and better ing crop water requirements and ultimately correctly design- crop management (Shamloo et al. 2021). ET is correctly ing irrigation systems (Djaman et al. 2015). ET is a major estimated using different methods, the accuracy of which component of water balance, and its accurate estimation is depends on the climatic conditions of the study areas (Racz et al. 2013). The actual ET can be measured directly using the water balance method, which is often a costly and com- * Amir Soltani Mohammadi plicated technique, but it is considered an effective tool for A.soltani@scu.ac.ir the validation and calibration of ET estimation models. Elahe Zoratipour Although indirect methods, such as mathematical models elahezoratipour@gmail.com for ET estimation, can be employed easily, they are used Amin Zoratipour when measurement methods are difficult (Obada et al. 2017). Zoratipour@asnrukh.ac.ir Based on the literature, conventional ET estimation methods Faculty of Water and Environmental Engineering, Shahid are classified into three main groups, namely temperature- Chamran University of Ahvaz, Ahvaz, Iran based, radiation-based, and mass transfer-based methods Department of Nature Engineering, Agricultural Sciences (Xu and Singh. 2002). In the FAO-Penman–Monteith (FAO- and Natural Resources University of Khuzestan, Mollasani, PM) method, the weather parameters are considered related Iran Vol.:(0123456789) 1 3 137 Page 2 of 15 Applied Water Science (2023) 13:137 to these three categories (Obada et al. 2017). Climatic data the SEBAL model in the India. The results demonstrated are limited in most areas, and it is not the ability to use the that the SEBAL-based ET conformed with lysimeter method FAO-PM method; thus, other methods are recommended with R value of 0.91 (Rawat et al. 2017). Wang et al. in for ET calculation (Djaman et al. 2015). Remote sensing the Heihe River Basin, Northwestern China, estimated daily makes it possible to obtain the amount of daily ET in differ - ET using the SEBS algorithm, and assessed its performance ent areas, with wide scales at the least possible time and with with Eddy Covariance and Priestley-Taylor methods. The high economic benefit (Saboori et al. 2021). results revealed that the SEBS model has a relatively accu- Most RS-based Surface Energy Balance algorithms have rate performance, particularly for vegetated areas (Wang been developed for crop ET determination in specific condi - et al. 2017). Elnmer et al. studied daily ET of crops, using tions in terms of land use and crop management, consider- the SEBAL algorithm compared to the FAO-PM method, in ing the accordance of empirical functions and parameters the Nile Delta, resulting in an RMSE of 0.46 mm (Elnmer with these algorithms (Wolff et al. 2022). They are easily et al. 2019). Ghaderi et al. estimated wheat ET, using the used in accurate agricultural management systems for better SEBAL algorithm and Landsat 8 satellite images in Ilam decision-making and higher yields (Shamloo et al. 2021). province. Compared to the FAO-PM method, the SEBAL To determine actual crop ET, many temperature-based, algorithm demonstrated adequate precision for ET estima- radiation-based, and mass transfer-based empirical meth- tion. They obtained the Root-Mean-Square Error (RMSE), ods were compared with FAO-PM and lysimeter methods Mean Absolute Percentage Error (MAPE), Mean Bias Error in different climatic and spatial conditions. This indicates (MBE), and Coefficient of Determination (R ) at 0.46, 2.9%, the importance of crop ET estimation, including cereals, to 0.22 mm/day, and 0.97, respectively (Ghaderi et al. 2020). determine crop water requirements and the optimal use of Tan et al. estimated ET based on the SEBAL algorithm by water resources. In this context, Djaman et al. assessed 16 using RS and Landsat 8 images upstream of the Heihe River ET methods under coastal conditions in the Senegal River Basin in China. The algorithm performance was evaluated Delta, and the results indicated the good performance of the using four empirical methods Irmak, Turc, FAO-PM and Mahringer and Terabert methods (Djaman et al. 2015). Lang Jensen-Haise. The results indicated that the SEBAL algo- et al. compared eight ET estimation methods with the FAO- rithm could present accurate ET estimations in the studied PM method in southwest China. The results revealed that the area (Tan et al. 2021). Khand et al. assessed wheat ET mod- performance of these methods was dependent on the regional eling based on SEBAL, METRIC, and SEBS algorithms and climate type in each area. However, the best performance obtained a smaller RMSE (0.14 mm/day) for the METRIC was reported for Makkink and Hargreaves-Samani methods model than those of SEBAL and SEBS algorithms (Khand from radiation and temperature-based methods, respectively et al. 2021). Shamloo et al. evaluated the SEBS algorithm (Lang et al. 2017). Zoratipour et al. studied the spatial and to estimate maize ET and crop coefficient using Landsat 8 temporal evaluation of different methods for the prediction images in the Adana Mediterranean Area, Turkey. Accord- of ET in Khuzestan province. According to the results, the ing to the results, the SEBAL estimated ET values mostly best ET estimations in this province were recorded for the corresponded to the FAO-PM method with R = 0.91 and Hargreaves-Samani among the temperature-based method, RMSE = 1.14 mm/day. It was also highly correlated with Doorenbos–Pruitt among the radiation-based method, and Turc, Hargreaves, and Makkink methods (Shamloo et al. Mahringer and the World Meteorological Organization 2021). Asadi et al. compared actual wheat crop ET based on (WMO) among the mass transfer-based methods (Zoratipour SEBAL algorithm using 12 Landsat 7 and Landsat 8 images et al. 2019). Empirical methods have limitations due to the during the crop development period in the Parsabad Moghan need for measuring all effective parameters at more time Plain, Northwestern Iran. The results demonstrated that the and higher cost for the necessary equipment preparation SEBAL algorithm (RSME = 0.633 mm/day and R = 0.93) and agricultural operations; also it is not easy to measure had the minimum error rate and maximum similarity com- soil water balance data at depths. Given the limitations of pared to lysimeter data (Asadi and Valizadeh Kamran. various empirical methods, the possibility of errors in field 2022). Yang et al. investigated actual ET in different land measurements, and their non-allocation to large extents, the uses based on the SEBAL algorithm and landsat 8 images in results can be feasibly extended with a combination of land Ecotone, Northwestern China. The SEBAL algorithm had an and RS data as a Surface Energy Balance model. Accord- appropriate estimation (RMSE = 0.9 mm/day and R = 0.81), ingly, Lian et al. estimated wheat ET in the Heihe River which was suitable for research on water resources, but it basin based on Landsat8 satellite imagery and Mapping ET overestimated ET (Yang et al. 2022). In another study, Wei at High Resolution with Internalized Calibration (METRIC) et al. evaluated daily ET estimation of rice fields, using the algorithm, which was reported to be able to present accurate SEBAL algorithm in a subtropical region in Southern China. estimations in various heterogeneous land uses (Lian and The results showed a high precision of the SEBAL algo- Huang 2015). Rawat et al. determined wheat crop ET using rithm, on a daily scale, with R , NSE, and RMSE values 1 3 Applied Water Science (2023) 13:137 Page 3 of 15 137 of 0.85, 0.81, and 0.84 mm/day, which confirmed SEBAL Comparing the SEBS and SEBAL-estimated ET with FAO-PM, Hargreaves-Samani, Blaney-Criddle, Dooren- application to logically allocate water resources in subtropi- cal regions (Wei et al. 2022). Tariqul Islam et al. determined bos–Pruitt, Priestley-Taylor, Mahringer, and WMO empirical methods. actual wheat evapotranspiration by the lysimeter method and SEBAL algorithm using Landsat 8 and Sentinel 2 satellite images. The results concluded the ET of wheat estimated by SEBAL had maximum similarity compared to lysimeter Materials and methods data. Also the average seasonal wheat ET was calculated to be 253 mm (Tariqul Islam et al. 2023). Liu et al. used the Study area SEBS algorithm and Landsat 8 satellite images to estimate regional evapotranspiration in Beijing. The results showed Khuzestan province is located at 47° 41′ to 50° 39′ E from the prime meridian and 29° 58′ to 33° 4′ N from the equa- that ET decreased with increasing land surface tempera- ture (LST) and daily evapotranspiration ranged from 3.47 tor in the southwest of Iran, with an area of about 64,057 km . The province shares borders with the Persian Gulf and to 5.47 mm (Liu et al. 2023). Khoshnood et al. evaluated SEBS algorithm to investigate the rate of evapotranspiration Iraq in the south and west, respectively. In this study, daily weather data (2019–2020) were collected for the Shahid change in different land cover use classes in the entire Urmia lake basin from 2016 to 2020. They stated that there is a high Modarres Basin in Ahvaz (Khuzestan province). The study area and the specifications of the studied station are repre- correlation between the results of the SEBS algorithm and the values measured (Khoshnood et al. 2023). sented in Fig. 1 and Table 1, respectively. The soil physico- chemical and irrigation water properties are also listed in ET evaluation in every region and choosing the best methods tailored to each weather type contribute to the opti- Tables 2 and 3, respectively. mal use of water resources. With extensive crop cultivation, Khuzestan province is the central hub of agriculture, cereal Data calculation production, and ultimately, its distributor to other provincial regions and Iran. The accurate ET estimation using RS can In this research, weather data were obtained from the Emam Khomeini agro industry Synoptic Station to implement the result in irrigation management, wheat water requirement supply, and optimal water use in a short temporal interval SEBS and SEBAL algorithms and evaluate the obtained results in comparison with other methods. Minimum and with a minimum economic cost. The climate of Khuzestan province is dry and hyperarid with annual evapotranspiration maximum air temperatures (°C), dew point temperature (°C), average relative humidity (%), maximum and mini- above 3000 mm and annual rainfall of 200 mm. Also, wheat is one of the most important strategic and widely consumed mum relative humidity (%), wind speed at the height of 2 m (m/s), number and maximum hours of sunshine, precipita- products (with extensive crop cultivation about 700–800 thousand hectares) in Iran, especially in Khuzestan prov- tion, and air pressure (Pa) were the data used in this study. These data were prepared from the mentioned synoptic sta- ince. Therefore, the evaluation of wheat evapotranspiration is necessary based on remote sensing algorithms and com- tion in Khuzestan province according to satellite passing days. The results of SEBS and SEBAL algorithms were parison with actual and empirical methods. Also, the evalu- ated results of the present algorithms in different researches compared by lysimeter and conventional empirical methods for ET estimation, including two temperature-based, two are not the same and in many studies, the SEBAL algorithm has better results among the energy balance algorithms and radiation-based, two mass transfer-based, and FAO-PM methods. Due to little incomplete (missing) data, they were in a number of others, the SEBS algorithm. In addition, in this research, remote sensing algorithms are investigated in estimated using appropriate renewal techniques (regression relative to the situation of each adjacent stations) and were comparison with various empirical methods categorized in the form of temperature, radiation, and mass transfer meth- controlled qualitatively before use. The ET obtained from SEBS and SEBAL algorithms were compared with all the ods. Thus, it is essential to estimate the wheat crop ET based on SEBS and SEBAL algorithms compared to actual and mentioned methods using statistical indices to introduce the best method. To this aim, six Landsat 8 OLI satellite images empirical methods. Also, this topic has not been evaluated on the wheat crop in the study region, sofar. Therefore, this (2019–2020) obtained from the US Geological Survey were used during the wheat growth period. It was attempted to work intends to: select images with good cloudless weather conditions to • provide ET comparisons. The accurate dates of the images Estimating the wheat crop ET using SEBS and SEBAL algorithms. used in this study are presented in Table 4. • To estimate actual ET, cloudless Landsat 8 satel- Comparing the ET estimated using SEBS and SEBAL algorithms with the lysimeter method. lite images were used during the wheat growth period 1 3 137 Page 4 of 15 Applied Water Science (2023) 13:137 Fig. 1 The location of the study area in Khuzestan province of Iran Table 1 Specifications of the study area located in Khuzestan province Station Longitude Latitude Elevation(mm) Average annual precipitation Dumarten coefficient Period (mm) Shahid Modarres Basin of 31° 20ʹ 48° 40ʹ 22.5 246.9 5.6 2019–2020 Ahvaz Table 2 Soil physical and chemical properties Table 3 Chemical properties of 7.7 pH irrigation water Chemical properties Physical properties 4.8 EC (ds/m) 2.07 TDS (mg/l) 7.6 pH 1.65 Bulk density (g/cm ) 0.43 SAR 4.8 (dS/m)Salinity 16 Clay(%) 22 Ca (meq/l) 0.4 Organic matter(%) 24 Silt(%) 28 Mg (meq/l) 60 Sand(%) 2.15 Na (meq/l) Sandy loam Soil texture 1 3 Applied Water Science (2023) 13:137 Page 5 of 15 137 Table 4 Meteorological Date Tmax(°C) Tmin(°C) RH(%) U (m/s) Hours of P(kpa) statistics and the accurate dates sunshine(hr) of the images landsat 8 2019/11/27 17.1 11.4 80 5 0.0 100.9 2019/12/29 21.8 9.0 69 2 8.1 101.6 2020/01/30 22.2 7.4 68 2 8.4 101.7 2020/03/01 21.8 10.1 56 4 9.8 101.5 2020/04/03 29.9 17.6 37 4 11.1 101.1 2020/05/21 33.0 18.8 44 3 7.7 100.7 Table 5 Landsat 8 satellite Date Satellite Spatial and temporal resolution Percentage of Pass Row characteristics cloud cover 2019–11-27 Landsat8(OLI/TIRS) 30 m, 16 day 2.03 165 38 2019–12-29 2.16 2020–01-30 5.96 2020–03-01 13.32 2020–04-03 1.22 2020–05-21 0.22 (November. 27 to May. 5 from 2019 to 2020). Since there In the following, the relationships required are introduced are numerous errors in Landsat 8 images, the errors were for the calculation of the five factors mentioned above. eliminated by using two types of atmospheric and radio- metric correction. The characteristics of the used images Soil heat flux (SHF) are shown in Table 5. Directly, it is not possible to measure soil heat flux (SHF) Surface Energy Balance Algorithm for Land (SEBAL) using RS, but associations between the value and such factors as NDVI, surface temperature, and albedo have been The SEBAL algorithm provides a total balance of surface reported in many investigations. In the present investigation, radiation and energy together with sensible heat flow and SHF was estimated with empirical Eq. (3) developed by Bas- aerodynamic roughness, and ET is calculated as a compo- tiaanssen 2000, nent of energy per pixel. As mentioned, SEBAL includes an algorithm that solves complete energy balance (Eq. 1). s = 0.0038α+ 0.0074α2)(1 − 0.98NDVI4) (3) R ∝ ET = R −G−H (1) The Normalized Difference Vegetation Index (NDVI) is where λET is the latent heat flux ( W / m ), R is the net showed rate of vegetation coverage and its condition. This radiations, G is the soil heat flux (W / m ), and H is the sen- index estimates the earth's surface reflectance, leaf area sible heat flux (W / m ) (Bastiaanssen and Ali 2002). index, area under cultivation, and plant biomass growth intensity (Bastianssen and Chandrapala 2003). The NDVI Net solar radiation (Rn) index is calculated by Eq. (4), NIR − R The Rn in each pixel was calculated using Eq. (2), where α NDVI = (4) NIR + R is the surface albedo (dimensionless), RS↓ is the incoming short wavelength radiation flux, RL↓ is incoming wavelength where NIR and R are, respectively, reflectances in radiation flux, RL↑ is the outgoing long wavelength radia- the near- and the red infrared bands. This index ranges tion flux, and εo is the surface emissivity (a dimensionless between − 1 and + 1. Densely vegetated lands have positive quantity). values of 0.3 to 0.8, whereas negative values belong to snow- Rn = 1 − RS ↓ + RL ↓ − RL ↑ − 1 − 0 RL ↓ covered regions. ( ) ( ) (2) 1 3 137 Page 6 of 15 Applied Water Science (2023) 13:137 boundary layer (PBL), atmospheric boundary layer (ABL), Sensible heat flux and atmospheric surface layer (ASL) are differentiated in this algorithm. ABL refers to the part of the atmosphere The sensible heat flux of air value is obtained from wind speed and the earth surface temperature using a unique inter- directly affected by the earth's surface reactions and forces at a timescale below one hour. ASL represents the 10% lower nal calibration consisting of the die ff rence between the earth surface temperature and the adjacent air temperature (dT). ABL in which tensions and turbulent fluxes change less than 10%. In the ASL layer, the simulation relationships for the The formula developed by Bastiaanssen 2000 is calculated through Eq. (5), average wind speed profile (u) are written as Eq. 7. z − d z − d z × C × dT u air p ∗ 0 0 om u = ln −Ψ +Ψ ( ) H = (7) (5) m m k z L L om ah In these equations, u and u represent wind speed and where ρ is air density (kg/m ), C indicates specific heat air p friction velocity (m/s), respectively, k is the von Karman of the air (J/kg/K), dT represents temperature difference T constant equal to 0.4, z indicates the reference height (m), and T (K) between two heights Z and Z , and r is aerody- 2 1 2 ah −1 d is the zero displacement height (m), z denotes rough- namic resistance to heat transport( sm ). 0 om ness height for momentum (m), Ψ is the stability correc- tion factor for atmospheric heat transfer, and L indicates the Surface Energy Balance System (SEBS) Monin–Obukhov length (m) (Su and Jacobs 2001). To avoid the repeated introduction of more details on The Surface Energy Balance System (SEBS) was proposed the applied equations, readers are referred to articles Bas- by Su and Jacobs 2001, to estimate heat flow fluxes and tiaanssen 2000; Bastiaanssen and Ali 2002 (for the SEBAL evaporative fractions. Similar to the SEBAL algorithm, the algorithm) and article Su and Jacobs 2001, (for the SEBS SEBS algorithm is based on the energy balance equation algorithm). (Eq. 1). Among the components of the energy balance equa- tion, the calculation method for net solar radiation (R ) in SEBAL is identical to that of SEBS. To avoid repetition, lysimeter the equations mentioned above are not presented in this sec- tion. Here, the equations are present for calculating two other Cylindrical lysimeters (with 0.5 m diameter and 1.2 m height) were established to directly measure ET and crop components of the energy balance equation in the SEBS algorithm. coefficients. After grass and wheat crop ET (ET ) measure- ments, crop coefficients (K ) were obtained at each growth Soil heat flux (SHF) stage using Eq. (8), ET Soil heat flux (SHF) in the SEBS algorithm is determined K = (8) ET from Eq. (6), where ET and ET represent the evapotranspiration of the c 0 G = R Γ + 1 − f Γ −Γ (6) 0 n c c s c crop and reference crop (mm/day), respectively, and K is the crop coefficient (dimensionless). where Γ is the ratio of SHF to net radiation (R ) for dense c n vegetation, which is considered equal to 0.05. Γ is the ratio of SHF to R for bare soil, which is taken equal to 0.315, and Empirical methods of ET estimation f is the partial canopy coverage. In this research, the results of SEBS and SEBAL RS algo- rithms were evaluated using lysimeter and conventional Sensible heat flux empirical methods for ET estimation to introduce the best method using statistical indices. The empirical methods used In the SEBS algorithm, the sensible and latent heat flux are obtained from a similar theory. The definitions of planet by each group are introduced in Tables 6, 7, 8. Table 6 ET estimation methods based on temperature Dependent parameters Reference Formula Method 0.5 T, u, Tmin, Tmax, RH, n, φ Hargreaves–Samani(1985) Hargreaves–Samani ET0 = 0.408 ∗ 0.0025 ∗(T + 16.8)∗(T − T ) ∗ R a max min a T, n, RHmin, φ, u Blaney–Criddle(1950) ET0 = a + b[P(0.46 T + 8.13)] Blaney–Criddle 1 3 Applied Water Science (2023) 13:137 Page 7 of 15 137 Table 7 ET estimation Dependent parameters Reference Formula Method methods based on solar radiation α Δ RH, T, P, h, u, Rnl, Rns Priestley–Taylor(1972) Priestley–Taylor ETO = (R − G) λ Δ+γ RH, U, T, P, h, u, T , T , n, φ Doorenbos–Pruitt(1977) Doorenbos–Pruitt ET0 = a( R )+ b min max Δ+γ Table 8 ET estimation Method Formula Reference Dependent parameters methods based on mass transfer Mahringer Mahringer(1970) T, Tmin, Tmax, RH, u ET0 = 0.15072 3.6u(e − e ) s a World meteorology ET0 = (0.1298 + 0.0934u) World meteorology T, Tmin, Tmax, RH, u organization (WMO) (e − e ) organization(1966) s a In Tables 6, 7, and 8, ET is reference crop evapotran- In this equation, U and U are, respectively, wind 0 2m Z spiration (mm/day),T ,T ,T , and T are average, maxi- speeds at height of 2 and Z m, and Z is the height measured a max min d mum, minimum, and dew point temperature, respectively at which wind speed. (˚C),R , extraterrestrial solar radiation (MJ/m /day), a and b, Since this study used data from weather stations, where empirical coefficients were presented by Doorenbos–Pruitt wind speed is measured at 10 m height, the wind speed was (1977), P, coeci ffi ent related to the length of the day, u, wind converted to a 2 m height using Eq. (10). speed at the height of 2 m (m/s), n, actual sunshine duration (hr), φ, latitude (rad).RH , average relative humidity (%),R , Statistical indicators solar radiation (MJ/m /day), h, elevation of sea level (m), K andα , empirical coefficients, Rn, is net solar radiation (MJ/ To validate the results, the ET values estimated by SEBAL m /day), e ande , maximum and minimum saturation and SEBS algorithms were compared with lysimeter, FAO- Smax Smin vapor pressure, respectively (kPa), ∆ represents the slope of PM, and empirical methods through conventional statistical the vapor pressure curve (kPa/˚C),λ , latent heat of vapori- indicators. In this investigation, the best method for the study zation (MJ/kg), P, vapor pressure (kPa), Rnl and Rns, net area was determined using R , RMSE (mm/day), PBIAS (Lang solar radiation with long and short wavelength, respectively et al. 2017), MBE, MAPE, and NS statistical indices (Ghaderi (MJ/m /day), e , ande , saturated and actual vapor pressure, et al. 2020). x a respectively (kPa). [ (P − P)(O − O)] i i 2 i=1 R = � � � � (11) 2 2 ∑ ∑ n n P − P O − O i i FAO‑Penman–Monteith (FAO‑PM) method i=1 i=1 0.408Δ R − G + × u (e − e ) � n 2 x a T+273 (9) 2 ET = 0 (P −O ) i i Δ+ (1 + 0.34u ) i=1 (12) RMSE = In this method, ∆ represents the slope of the vapor pres- sure curve (kPa/˚C), R is net solar radiation (MJ/m ∕day ), n, O − P i i i=1 G is soil heat flux (MJ/m /day), γ, psychometric constants PBIA = ∑ × 100 (13) (kPa/˚C), T, average air temperature (˚C), u average wind i i=1 2, speed at a height of 2 m (m/s), e , saturated vapor pressure (kPa), e , actual vapor pressure (kPa), ex – ea water vapor n a , 1 MBE = O − P (14) i i pressure deficiency(kPa). i=1 If wind speed is measured at an height other than 2 m, it should be converted to speed at a 2 m height for use in the n O − P 1 i i MAPE = [ ]× 100 (15) FAO-PM formula, the general equation of which is shown i=1 N O in the following: 0.2 U = U (10) 2m Z 1 3 137 Page 8 of 15 Applied Water Science (2023) 13:137 Table 9 Wheat crop coefficients in different stages of growth Also, the ET value of 203 mm was obtained for rainfed wheat for 155 days from November to April, in Khuzestan Date Growth period K Growth stage province (Porgholam Amiji et al., 2019). This difference (days) can be attributed to cultivation conditions and time. 2019/11/27 32 0.82 Initial 2019/12/29 42 1.35 Development 2020/01/30 42 1.20 Development Calculation of wheat evapotranspiration using 2020/03/01 42 1.06 Development satellite image SV 2020/04/03 48 1.03 Mid 2020/05/21 22 0.58 End To better illustrate different ET values during the growth period, the maximum and minimum values of wheat ET values are presented in Table 10. Accordingly, the mini- Table 10 Specifications of the limit values ETc from satellite images mum wheat ET values based on SEBAL and SEBS algo- rithms (0.28 and 0.93 mm/day) were recorded on Decem- Date Min Max ber 29 and November 27, respectively. Moreover, the SEBAL SEBS SEBAL SEBS maximum wheat ET values based on SEBAL and SEBS algorithms (5 and 7.95 mm/day, respectively) occurred on 2019–11-27 1.22 0.93 3.52 4.55 April 03, 2020. 2019–12-29 0.28 1.10 2.83 3.95 Figures 2 and 3 depict the spatiotemporal changes of daily 2020–01-30 0.76 1.00 2.24 4.51 ET values in the whole study area for SEBAL and SEBS 2020–03-01 0.96 1.40 4.62 5.80 algorithms, respectively. As shown in the figures, the ET 2020–04-03 1.25 1.08 5.00 7.95 dispersion obtained from SEBAL images is slightly more 2020–05-21 1.29 1.00 3.72 3.74 from SEBS images. Reasons of this observation may be a high estimation of the net radiation flux, which is confirmed by Wang et al. 2017 and Khand et al. 2021. ⎡ ⎤ � � O − P ⎢ ⎥ i i i=1 NS = 1 − (16) ⎢ ⎥ � � 2 Comparison of evapotranspiration estimated ⎢ ⎥ O − O i=1 ⎣ ⎦ with lysimeter method P and O are the values predicted with each RS algorithm i i Tables 11 and 12 compare the ET values estimated by and those obtained from comparative methods, respectively, P SEBAL and SEBS algorithms with those of the lysimeter and O are the mean values predicted with each RS algorithm method. According to Table 11, the maximum ET val- and those obtained from comparative methods, respectively, ues estimated by SEBAL and SEBS algorithms (16.67 and n represents the total data. and 14.21 mm/day, respectively), similar to the lysimeter (11.50 mm/day), were recorded on 2020/05/21. The mini- mum ET values estimated by these two algorithms (1.29 and 1.22 mm/day, respectively), similar to the lysimeter Results and discussion (1.70 mm/day), were documented on 2019/12/29. Figure 4 displays the dispersion of ET values estimated Crop coefficient by SEBAL and SEBS algorithms compared to the lysimeter method. As indicated by the assessments, SEBAL and SEBS The wheat crop coefficient was calculated at each cul- algorithms correspond to the actual lysimeter method, and tivation stage by considering reference crop ET as ET the results of energy balance algorithms can be generalized and wheat crop ET of lysimeter data (ET ). According to to the lysimeter method. These findings agree with those Table 9, the highest crop coefficient (kc) belongs to the reported by Rawat et al. 2017, Asadi and Valizadeh Kamran. development stage on 29/12/2019 (42 days after cultiva- 2022, Tariqul Islam et al. 2023, Liu et al. 2023, and Khosh- tion), and the lowest level (0.58) was recorded for the nood et al. 2023. final wheat growth period on 21/05/2020 (22 days after Table 12 compares R and RMSE values obtained for cultivation). The total actual ET was measured 460.1 mm SEBAL (0.92 and 2.15 mm/day) and SEBS (0.96 and during wheat cultivation for 144 days. The maximum and 1.53 mm/day) algorithms with the lysimeter method. Thus, minimum water requirements were reported to be 231.23 the estimated and observed ET values are close to each and 19.47 mm/day during plant growth, respectively, in other on the mentioned days. Hence, SEBS and SEBAL the Einkhosh Plain of Ilam in Iran (Ghaderi et al. 2020). algorithms are relatively good alternatives to the lysimeter 1 3 Applied Water Science (2023) 13:137 Page 9 of 15 137 Fig. 2 The process of spatial and temporal changes of actual wheat ET using the SEBAL algorithm Fig. 3 The process of spatial and temporal changes of actual wheat ET using the SEBS algorithm 1 3 137 Page 10 of 15 Applied Water Science (2023) 13:137 Table 11 Estimated actual ET values and lysimeter (mm/day) Comparison of evapotranspiration estimated and empirical methods Date SEBAL SEBS Lysimeter 2019–11-27 2.27 2.33 2.07 According to Table 13, the maximum ET values estimated 2019–12-29 1.22 1.29 1.70 from SEBS and SEBAL algorithms (16.67 and 14.21 mm/ 2020–01-30 3.03 3.86 3.50 day, respectively) and empirical methods (except for the 2020–03-01 2.09 4.02 3.40 2020–04-03 4.08 5.73 6.21 Blaney-Criddle method) were recorded on 2020/05/21. 2020–05-21 14.21 16.67 11.50 The minimum ET values estimated from SEBS and SEBAL algorithms (1.67 and 1.22 mm/day, respectively) were similar to FAO-PM (1.80 mm/day) on 2019/12/29. method and can be considered a valuable criterion com- Figures 5 and 6 illustrate the dispersion of ET values pared to other empirical methods. Compared SEBAL estimated by SEBAL and SEBS algorithms compared to (MBE = 0.25,MAPE = 25% and NS = 0.88) and SEBS empirical methods. According to the evaluations, SEBAL (MBE = − 0.92,MAPE = 20% and NS = 0.82), the lysimeter and SEBS algorithms (R = 0.79 and 0.87, respectively) method showed good compatibility with the data of these showed high compatibility with the FAO-PM method. two algorithms. Among temperature-based methods, the Har - greaves–Samani method showed good accuracy com- 2 2 pared to SEBAL (R = 0.72) and SEBS (R = 0.80) data. Table 12 Comparison of estimated and lysimeter ET values using statistical indicators Statistical indicators Method SEBAL SEBS 2 2 R RMSE BIAS% MBE MAPE% NS R RMSE BIAS% MBE MAPE% NS Lysimeter 0.92 2.15 5.25 0.25 25 0.88 0.96 1.53 4.40 -0.92 20 0.82 Fig. 4 Scatter plot of ET y = 1.2731x -1.5407 y = 1.4973x -1.4339 estimated with SEBAL and R² = 0.962 R² = 0.9265 SEBS algorithms and lysimeter 15.00 15.00 method 10.00 10.00 5.00 5.00 0.00 0.00 0.00 5.00 10.0015.00 0.00 5.00 10.0015.00 Lysimeter Lysimeter Table 13 Estimated and empirical values of actual ET (mm/day) Date SEBAL SEBS FAO-PM Blaney— Hargreaves- Priestley Taylor Doorenbos WMO Mahringer Criddle Samani and Pruitt 2019–11-27 2.27 2.33 1.95 2.12 1.45 1.14 1.31 0.36 0.39 2019–12-29 1.22 1.29 1.80 2.98 2.25 1.34 2.19 0.46 0.59 2020–01-30 3.03 3.86 2.65 3.85 2.54 1.39 2.55 0.52 0.67 2020–03-01 2.09 4.02 4.20 4.28 3.55 2.90 4.16 0.69 0.79 2020–04-03 4.08 5.73 6.15 7.65 5.32 4.46 6.45 1.11 1.26 2020–05-21 14.21 16.67 9.08 6.35 7.03 4.93 8.75 1.17 1.42 1 3 SEBS SEBAL Applied Water Science (2023) 13:137 Page 11 of 15 137 Fig. 5 Scatter plot of actual ET estimated with SEBAL algorithm and empirical methods Also, in the temperature-based group, a weak estimation energy, leading to many errors. Therefore, better results was observed for the Blaney-Criddle method relative to were obtained with the Mahringer method among mass SEBAL and SEBS algorithms (R = 0.31 and 0.39, respec- transfer-based methods. According to the results, SEBAL tively). The reasons may include limited parameters in and SEBS algorithms mainly were compatible with the this method and its unsuitability according to the climate actual lysimeter method (R = 0.92 and 0.96, respectively). of the study area. Among radiation-based methods, the The high accuracy of these two algorithms in ET estima- Doorenbos–Pruitt method showed good outcomes with tion suggests their copious applicability for studying large 2 2 SEBAL (R = 0.71) and SEBS (R = 0.79) data. Thus, the extents. Doorenbos–Pruitt method performs better in arid climates Table 14 compares the estimated data obtained from among radiation-based methods and can be used for ET SEBAL and SEBS with ET data measured by the FAO-PM estimation in arid and semiarid areas. Additionally, the reference, Hargreaves-Samani, Blaney-Criddle, Priestley- Doorenbos–Pruitt method needs more input parameters Taylor, Doorenbos–Pruitt, Mahringer, and WMO methods. than the other methods, which can account for its improved According to Table 14, the RMSE values for the FAO-PM efficiency compared to SEBS and SEBAL. In the mass method were obtained at 2.42 and 3.14 mm/day for SEBS transfer-based group, both Mahringer and WMO meth- and SEBAL algorithms, respectively. The scatter plots ods presented less effective estimations versus SEBAL (Figs. 5 and 6) represent less dispersion and more correla- 2 2 (R = 0.60 and 0.68, respectively) and SEBS (R = 0.55 tion of SEBS than SEBAL compared to the other methods. and 0.64, respectively). This might be due to the unsuit- The scatter plots show higher R and lower RMSE values ability of related parameters in mass transfer-based meth- for SEBS (with a slight difference) than SEBAL, with more ods with energy balance algorithms in the study area. It acceptable accuracy closer to actual values. The PBIAS is noteworthy that a limitation of SEBAL and SEBS algo- index also reveals underestimations for both SEBAL and rithms is that the presence of some empirical relationships SEBS, with a more significant underestimation for SEBAL. during ET estimation may result in errors. These models This result can be attributed to the high estimation of the net also require a bright cloudless sky because even a thin radiation flux parameter, the main factor among the fluxes cloud layer can reduce the estimated heat radiation and in the energy balance equation, which has caused a more 1 3 137 Page 12 of 15 Applied Water Science (2023) 13:137 Fig. 6 Scatter plot of actual ET estimated with SEBS algorithm and empirical methods Table 14 Comparison of estimated and empirical methods actual ET values using statistical indicators SEBAL SEBS 2 2 Statistical indicators R RMSE BIAS% MBE MAPE% NS R RMSE BIAS% MBE MAPE% NS Methods (FAO-PM) 0.79 3.14 9.00 -1.17 33 0.70 0.87 2.42 7.47 -1.34 31 0.62 Hargreaves-Samani 0.72 16.4 16.77 1.79 48 0.52 0.80 10.4 18.50 -1.96 52 0.38 Blaney—Criddle 0.31 4.34 17.63 1.26 52 0.3 0.39 3.71 4.47 -1.11 43 0.28 Priestley Taylor 0.55 7.62 37.80 -2.25 75 0.23 0.64 3.89 29.20 -2.96 65 0.16 Doorenbos and Pruitt 0.71 3.33 21.36 -1.79 47 0.65 0.79 2.63 12.68 -1.43 46 0.58 Mahringer 0.60 6.80 35.36 − 3.63 70 -0.55 0.68 5.51 32.36 − 4.70 55 -0.76 WMO 0.55 6.93 32.53 − 3.76 80 − 0.62 0.64 5.64 29.35 − 4.80 63 − 0.83 significant underestimation of SEBAL than SEBS. It is note- in comparison with direct and indirect methods, which can worthy that the heat flux is low in farmlands or lands with be attributed to a low SHF in the SEBAL model. Compared intensive and semi-intensive vegetation. The soil heat flux SEBAL (MBE = − 1.17,MAPE = 33%, and NS = 0.70) and is also low in densely vegetated lands. This is because the SEBS (MBE = − 0.92,MAPE = 20%, and NS = 0.62) with soil under vegetation is not exposed to radiation energy in empirical methods, the FAO-PM method showed the most dense vegetation, and the flux reaches a medium value with compatibility with the data of these two algorithms among decreasing vegetation intensity. SHFs decline during the the other empirical methods. Based on the comparison of growing season because of plant growth and increasing crop all tested methods with SEBAL (Table 15), the first, sec- coverage. The heat flux will be high in barren and arid zones. ond, and third ranks belong to FAO-PM, Doorenbos–Pruitt, Thus, the SEBAL algorithm shows some underestimation and Hargreaves-Samani methods, respectively, followed by 1 3 Applied Water Science (2023) 13:137 Page 13 of 15 137 Table 15 Ranking the results of Statistical indicators Methods comparison empirical methods with the SEBAL algorithm SEBAL R RMSE BIAS% MBE MAPE% NS Ave Rank (FAO-PM) 1 1 1 1 1 1 1.0 1 Hargreaves-Samani 2 7 2 3 3 3 3.3 3 Blaney—Criddle 6 3 3 2 4 4 3.6 4 Priestley Taylor 5 6 7 4 5 5 5.3 6 Doorenbos and Pruitt 3 2 4 3 2 2 2.6 2 Mahringer 4 4 6 5 6 6 5.1 5 WMO 5 5 5 6 7 7 5.8 7 Table 16 Ranking the results of Statistical indicators Methods comparison empirical methods with the SEBS algorithm SEBS R RMSE BIAS% MBE MAPE% NS Ave Rank (FAO-PM) 1 1 2 2 1 1 1.3 1 Hargreaves-Samani 2 7 4 4 4 3 4 4 Blaney—Criddle 6 3 1 1 2 4 2.8 3 Priestley Taylor 5 4 5 5 7 5 5.1 5 Doorenbos and Pruitt 3 2 3 3 3 2 2.6 2 Mahringer 4 5 7 6 5 6 5.5 6 WMO 5 6 6 7 6 7 6.1 7 Blaney-Criddle, Mahringer, Priestley-Taylor, and WMO 2017, Khand et al. 2021, Yang et al. 2022, Wei et al. 2022, empirical methods in order. Moreover, the comparison of all Liu et al. 2023, and Khoshnood et al. 2023) suggest the abil- tested empirical methods with SEBS in Table 16 indicates ity of energy balance algorithms, in particular SEBS, in crop that FAO-PM, Doorenbos–Pruitt, and Blaney-Criddle are in actual ET estimation. Among temperature-based methods, the first, second, and third ranks, respectively, followed by the Hargreaves-Samani showed better performance, which Hargreaves-Samani, Priestley-Taylor, Mahringer, and WMO agrees with Lang et al. 2017, and Zoratipour et al. 2019. empirical methods in order. Tables 15 and 16 show the sat- Among radiation-based methods, the Doorenbos–Pruitt per- isfactory results of the ET values estimated from SEBS formed better than the Priestley-Taylor, which is similar to and SEBAL compared to the FAO-PM empirical method. its good performance in ET estimation reported by Wang Since FAO-PM has been introduced as one of the most reli- et al. 2017, Zoratipour et al. 2019, and Shamloo et al. 2021. able reference methods in ET calculations, validation with Among mass transfer-based methods, the Mahringer method this method is also important and helpful when direct land presented a better estimation, as reported by Djaman et al. measurement data (lysimeter) are not available. During the 2015 and Zoratipour et al. 2019. wheat growth, the highest ET values with SEBS (16.67 mm/ day) and SEBAL (14.21 mm/day) correspond to the maxi- mum values with lysimeter (11.50 mm/day) and FAO-PM Conclusion (9.08 mm/day) at the final growth phase on 2020/05/21 (Tables 11 and 13). These tables also indicate that the In this research, wheat daily ET values were estimated accu- minimum wheat ET values with SEBS (1.29 mm/day) and rately using SEBAL and SEBS algorithms as well as Landsat SEBAL (1.22 mm/day) at the development phase match with 8 satellite images at six satellite passing dates from 2019 to the least values with lysimeter (1.70 mm/day) and FAO-PM 2020, and their results were compared with the lysimeter (1.80 mm/day) on 2020/05/21. The results demonstrate the method. The results demonstrated that the ETc estimated acceptable performance of energy balance algorithms in ETc with SEBS and SEBAL (R = 0.96 and 0.92, RMSE = 1.53 estimation. The SEBS shows higher precision than SEBAL and 2.42 mm/day, respectively) corresponded well to actual in ET estimation compared to the data of the lysimeter and lysimeter data and can be compared with empirical meth- FAO-PM, which yielded better results than the other empiri- ods. Therefore, SEBS and SEBAL results were compared cal methods. Previous studies (Wang etal. 2017, Rawat et al. with FAO-PM, Hargreaves-Samani, and Blaney-Criddle 1 3 137 Page 14 of 15 Applied Water Science (2023) 13:137 Asadi M, Valizadeh Kamran K (2022) Comparison of SEBAL, MET- temperature-based methods, Priestley-Taylor and Dooren- RIC, and ALARM algorithms for estimating actual evapotran- bos–Pruitt radiation-based methods, and Mahringer and spiration of wheat crop. Theor Appl Climatol. https:// doi. org/ 10. WMO mass transfer-based methods, using statistical indices. 1007/ s00704- 022- 04026-3 Based on the findings, FAO-PM showed good compatibility Bastiaanssen WG (2000) SEBAL-based sensible and latent heat fluxes in the irrigated Gediz Basin. Turkey J Hydrol 229(1–2):87–100. with SEBS and SEBAL (R = 0.87 and 0.79, RMSE = 2.42 https:// doi. org/ 10. 1016/ S0022- 1694(99) 00202-4 and 3.14 mm/day, respectively) among the mentioned Bastiaanssen WGM, Ali S (2002) A new crop yield forecasting model empirical methods. Altogether, the ET values obtained from based on satellite measurements applied across the Indus Basin, SEBAL, SEBS, and the lysimeter method (26.9, 33.9, and Pakistan. Agr Ecosyst Environ 94:321–343. https:// doi. org/ 10. 1016/ S0167- 8809(02) 00034-8 28.38 mm/day, respectively) were not highly different. In Bastianssen WGM, Chandrapala L (2003) Water balance variability addition, the ET value estimated from SEBS is about 12% across Sri lanka for assessing agricultural and environmental higher than that obtained from SEBAL. Thus, SEBS with water use. Agr Water Manag 58(2):171–291. https:// doi. org/ 10. more outstanding scores (R = 0.96 and RMSE = 1.53 mm/ 1016/ S0378- 3774(02) 00128-2 Blaney HF, Criddle WD (1950) Determining water requirements in day) presented better results than SEBAL. Compared to the irrigated areas from climatological and irrigation data. Soil con- lysimeter method, SEBS and SEBAL algorithms are appro- servation service technical paper 96; Soil conservation service. priate alternatives for use in the study area owing to their US Department of Agriculture, Washington high compatibility in the absence of adequate data and no Djaman KB, Alde AB, Sow A, Muller B, Irmak S, Ndiaye MK, Man- neh B, Moukoumbi YD, Futakuchi K, Saito K (2015) Evaluation use of direct methods. of sixteen reference evapotranspiration methods under Sahelian conditions in the Senegal river valley. J Hydrol Reg Stud 78:139– Acknowledgements This paper is derived from a research project with 159. https:// doi. org/ 10. 1016/j. ejrh. 2015. 02. 002 the number 1349, for which the authors are grateful to the Research Doorenbos J, Pruitt WO (1977) Crop water requirements. FAO Irriga- Council of Shahid Chamran University of Ahvaz for financial support tion and Drainage. Paper no. 24 (rev.). FAO, Rome. (GN: SCU.WI1400.273). Elnmer A, Khadr M, Kana S, Tawfik A (2019) Mapping daily and seasonally evapotranspiration using remote sensing techniques Data availability The datasets generated and/or analyzed during the over the Nile delta. Agr Water Manag 213:682–692. https://doi. current study are available upon request by contact with the corre- org/ 10. 1016/j. agwat. 2018. 11. 009 sponding author. Ghaderi A, Dasineh M, Shokri M, Abraham J (2020) Estimation of actual evapotranspiration using the remote sensing method Declarations and SEBAL algorithm: a case study in Ein Khosh Plain Iran. Hydrology 7(36):1–14. h t t p s :/ / d o i . o r g / 1 0 . 3 3 9 0/ h y dr o l o g y7 Conflict of interest The authors declare that they have no known com- peting financial interests or personal relationships that could have ap- Hargreaves GL, Samani ZA (1985) Reference crop evapotranspiration peared to influence the work reported in this paper. from temperature. Appl Eng Agric 1(2):96–99. https:// doi. org/ 10. 13031/ 2013. 26773 Ethical approval This manuscript does not involve ethical approval. Khand K, Bhattarai N, Taghvaeian S, Wagle P, Gowda PH, Alderman PD (2021) Modeling evapotranspiration of winter wheat using Consent to publish All authors have read and agreed to the published contextual and pixel-based surface energy balance models. Trans version of the manuscript. ASABE 64(2):507–519 Khoshnood S, Lotfata A, Mombeni M, Daneshi A, Verrelst J, Ghorbani Open Access This article is licensed under a Creative Commons Attri- K (2023) A spatial and temporal correlation between remotely bution 4.0 International License, which permits use, sharing, adapta- sensing evapotranspiration with land use and land cover. Water tion, distribution and reproduction in any medium or format, as long 15(1068):1–20. https:// doi. org/ 10. 3390/ w1506 1068 as you give appropriate credit to the original author(s) and the source, Lang D, Zheng J, Shi J, Liao F, Ma X, Wang W, Chen X, Zhang M provide a link to the Creative Commons licence, and indicate if changes (2017) A comparative study of potential evapotranspiration esti- were made. The images or other third party material in this article are mation by eight methods with FAO Penman-Monteith method in included in the article's Creative Commons licence, unless indicated South Western China. Water J 74:1–18. https:// doi. org/ 10. 3390/ otherwise in a credit line to the material. 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Applied Water Science – Springer Journals
Published: Jun 1, 2023
Keywords: Evapotranspiration; Lysimeter; FAO-Penman–Monteith; Remote sensing
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