# Estimation of Actual Evapotranspiration Using the Remote Sensing Method and SEBAL Algorithm: A Case Study in Ein Khosh Plain, Iran

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Area

#### 2.2. Satellite Images

#### 2.3. Calculation of Solar Radiation and ET

_{n}), soil heat (G), latent heat (λET) fluxes, and sensible heat (H) in units of W/m

^{2}. The latent heat flux (λET) represents the rate of heat loss from the surface due to ET, which was calculated for each pixel according to Equation (1):

_{n}) is the difference between the incoming and outgoing radiative fluxes and was calculated as shown in Equation (2).

_{0}is the surface emissivity. These radiant fluxes were calculated as shown in Equations (3)–(5):

_{sc}is the solar constant (1367 W/m

^{2}), cosθ is the cosine of the solar incidence angle, r is the Earth–Sun distance, and τ

_{sw}is the atmospheric transmissivity. Values for ${R}_{s\downarrow}$ can range from 200 to 1000 W·m

^{−2}, depending on the time and location of the image and on local weather conditions. The symbol σ is the Stefan–Boltzmann constant (5.67 × 10

^{−8}W·m

^{−2}·K

^{−4}), T

_{s}is the surface temperature (K), ε

_{a}is the atmospheric emissivity, and T

_{a}is the atmospheric temperature (K). The following empirical equation for ε

_{a}was applied using data from alfalfa fields in Idaho [18]:

_{sw}is the atmospheric transmissivity calculated assuming clear sky and relatively dry conditions. It was calculated using the elevation-based relationship of Allen et al. [19]. The soil heating (G) is the rate of heat storage in the soil and vegetation due to conduction. The ratio of G/R

_{n}was computed using the following empirical equation [20]:

_{s}is the surface temperature (°C), α is the surface albedo, and NDVI is the normalized difference in vegetation indices between −1 and +1. Values between 0 and ~0.2 correspond to bare soil or very sparse vegetation, and NDVI > 0.2 for vegetated regions. If the NDVI value is less than zero, the surface is assumed to be water and G/R

_{n}= 0.5. For areas where T

_{s}< 4 °C and α > 0.45, it is assumed to be snow-covered and G/R

_{n}= 0.5 (Allen et al. [21]). NDVI was calculated from Equation (8):

^{3}), C

_{p}is the specific heat of the air at a constant pressure (1004 J·kg

^{−1}·K

^{−1}), T

_{s}is the surface temperature (K), T

_{r}is the air temperature at a reference level (K), and r

_{a}is the aerodynamic resistance to heat transport (s/m) (Allen et al. [19]). The term r

_{a}was computed using Equation (10):

_{H}is the convective heat transfer coefficient and V is the wind speed at the reference level (Tasumi et al. [23]). The term ET

_{inst}(instantaneous value of ET) (J/kg) is the ratio of λET to λ (the latent heat of vaporization) (J/kg) (Equation (11)):

_{a}is the atmospheric temperature (K). The ET

_{24}(actual daily ET estimation) (mm/day) is more applicable than ET

_{inst}. SEBAL calculates ET

_{24}assuming that the ET

_{r}F is a 24-hour average (fixed over 24 h), according to

_{r −24}is the 24-h ET

_{r}for the day on which the image was captured; it is calculated as the sum of the hourly ET

_{r}values for that day (Allen et al. [19]). A reference value of ET (ET

_{0}) could be obtained by using the FAO-Penman–Monteith method (Equation (14)):

^{3}), C

_{P}is the specific heat of the air (kJ/g°C), e

_{a}–e

_{d}represents the water vapor pressure deficiency (kPa), and the terms r

_{c}and r

_{a}are the (bulk) surface and aerodynamic resistances (s/m) and γ psychometric constants (0.665 $\times $ 10

^{−3}Pa) (Allen et al. [24]). The actual annual ET (Equation (16)) was calculated using daily ET data (Equation (15)) as follows:

_{ai}is the actual ET obtained from the images on the same day of the image being taken (ith day of the year) (mm), ET

_{oi}is the reference ET from the FAO-Penman–Monteith equation (also for the ith day of the year) (mm), ET

_{oj}, is the ET related to the number of days in the period of image i that varies from the kth to the lth day of the year, and j represents the number of days. The last term, ET

_{annual}, is the actual annual ET obtained from the sum of the ET

_{period}i (mm).

^{2}) were used to evaluate the model. These metrics were calculated as follows:

_{i}represents the observed values of the FAO-Penman–Monteith equation as the standard model; P

_{i}represents the estimated values from the SEBAL algorithm; and $\overline{{O}_{i}}$ and $\overline{{P}_{i}}$ are the mean values from the FAO Penman–Monteith model and SEBAL, respectively.

## 3. Results and Discussions

#### 3.1. The Net Radiation (R_{n}), Soil Heat (G), and Sensible Heat (H) Fluxes

_{n}), soil heat (G), and sensible heat (H) fluxes for the Ein Khosh Plain. According to the map and the R

_{n}values, the maximum radiation occurs in areas of vegetation growth and minimum values occur in areas without vegetation. Additionally, it was observed that the values of G in vegetated areas were in the range of 0.05 to 0.15, which is the rate of conduction heat transfer within the soil. The sensible heat results are also plotted in Figure 3.

#### 3.2. Evaluation of SEBAL’s Performance in Actual ET Validation Estimation

_{n}, G, and H, it was possible to determine the daily ET rates and the results could be compared with calculations using the FAO-Penman–Monteith equation as the reference method. The nearest station with daily and hourly data is located at 32° 15′ north and 48° 24′ east. Using 3-h station data, the daily ET was calculated and the water requirements were obtained during the growth period. The ET rates obtained from the FAO-Penman–Monteith and SEBAL methods are presented in Table 3. Furthermore, Figure 4 shows a comparison of the actual ET values calculated by SEBAL with the FAO-Penman–Monteith model values.

#### 3.3. Estimation of the Water Requirement for the Ein Khosh Plain

^{2}. Taking into account the area of the Ein Khosh Plain and the cultivated land, the cultivation density is 17.21%. The normalized difference vegetation index (NDVI) was calculated according to Equation (7) and is shown in Figure 8.

#### 3.4. Water Required for Irrigation of Ein Khosh Plain in Each Period

## 4. Conclusions

_{n}), soil heat (G), and sensible heat (H) fluxes and NDVI were plotted and analyzed. The evaluation of SEBAL with the FAO-Penman–Monteith method as a reference showed that the values of RMSE, MAPE, and MBE were 0.466, 2.9%, and 0.222 mm/day, respectively, with a correlation coefficient of 0.97. It was proven that SEBAL has a sufficient accuracy for estimating the actual ET. The results of the SEBAL algorithm are as follows:

- The rainfall rate in the Ein Khosh Plain, except for the last month of cultivation with very low rainfall, meets water-use requirements, except for late May and early June. Despite the lower ET rate for wheat in the last month, there is a need for irrigation during this month;
- An evaluation of irrigation requirements using monthly rainfall data showed that the Ein Khosh Plain in March (the rainfall corresponds to the ET rate for wheat corps), which displays the maximum ET, has no deficiency of rainfall. Some parts of the plain in several months, such as April and May, expect a rainfall value of up to 50 and 70 mm, respectively;
- While the total area of the plain is equal to 363.11 km
^{2}, only 17.21% of the region is cultivated. Given that the average ET rate is 121 mm in the agricultural lands, a maximum of 20 mm of irrigation is required; - During the wheat plant growth periods, the highest amount of water required was found in the fourth period (March 16 to April 13), with a value of 231.23 mm/hr, and the lowest was found in the third period (February 16 to March 15), with a value of 19.47 mm/hr, for agricultural land use.

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 2.**Principal components of the Surface Energy Balance Algorithm for Land (SEBAL) model [17].

**Figure 4.**Comparison of the actual ET values calculated using SEBAL with the FAO-Penman–Monteith method.

**Table 1.**Landsat 8 satellite characteristics [16].

Landsat 8 Operational Land Imager (OLI) and Thermal Infrared Sensor (TIRS) | Bands | Wavelength (µm) | Spatial Resolution (m) |

Band 1 – Coastal aerosol | 0.43 – 0.45 | 30 | |

Band 2 - Blue | 0.45 – 0.51 | 30 | |

Band 3 - Green | 0.53 – 0.59 | 30 | |

Band 4 - Red | 0.64 – 0.67 | 30 | |

Band 5 – Near Infrared (NIR) | 0.85 – 0.88 | 30 | |

Band 6 –SWIR 1 | 1.57 – 1.65 | 30 | |

Band 7 – SWIR 2 | 2.11 – 2.29 | 30 | |

Band 8 - Panchromatic | 0.50 – 0.68 | 15 | |

Band 9 - Cirrus | 1.36 – 1.38 | 30 | |

Band 10 - Thermal Infrared (TIRS) 1 | 10.60 – 11.19 | 100 | |

Band 11 – Thermal Infrared (TIRS) 2 | 11.50 – 12.51 | 100 |

Satellite | Date of Pictures (AD) |
---|---|

Landsat 8 | 11-12-2014 |

Landsat 8 | 10-1-2015 |

Landsat 8 | 29-2-2015 |

Landsat 8 | 27-3-2015 |

Landsat 8 | 20-4-2015 |

Landsat 8 | 17-5-2015 |

Landsat 8 | 04-6-2015 |

Date of Pictures (AD) | FAO-Penman-Monteith | SEBAL |
---|---|---|

ET_{0} (mm/day) | ET_{0} (mm/day) | |

11-12-2014 | 3.87 | 3.51 |

10-01-2015 | 4.21 | 4.53 |

29-02-2015 | 4.89 | 5.01 |

27-03-2015 | 5.73 | 5.16 |

20-04-2015 | 8.22 | 8.44 |

17-05-2015 | 9.54 | 8.98 |

04-06-2015 | 9.51 | 8.74 |

Plain | Uses | Area (km^{2}) | Average Actual Annual ET |
---|---|---|---|

Ein Khosh | Rangeland and wasteland | 239.99 | 75 |

Cultivated | 62.89 | 121 | |

Not cultivated | 60.23 | 113 |

Image Date | Study Period | Uses | Area (hr) | Amount of Water Required (mm/hr) |
---|---|---|---|---|

11-12-2014 | 1st—18 November to 25 December | agricultural lands | 6318.5 | 127.11 |

10-01-2015 | 2nd—26 December to 15 February | agricultural lands | 6318.5 | 177.62 |

29-02-2015 | 3rd—16 February to 15 March | agricultural lands | 6318.5 | 19.47 |

27-03-2015 | 4th—16 March to 13 April | agricultural lands | 6318.5 | 231.23 |

20-04-2015 | 5th—14 April to 9 May | agricultural lands | 6318.5 | 227.22 |

17-05-2015 | 6th—10–25 May | agricultural lands | 6318.5 | 143.57 |

04-06-2015 | 7th—26 May to 10 June | agricultural lands | 6318.5 | 24.53 |

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**MDPI and ACS Style**

Ghaderi, A.; Dasineh, M.; Shokri, M.; Abraham, J. Estimation of Actual Evapotranspiration Using the Remote Sensing Method and SEBAL Algorithm: A Case Study in Ein Khosh Plain, Iran. *Hydrology* **2020**, *7*, 36.
https://doi.org/10.3390/hydrology7020036

**AMA Style**

Ghaderi A, Dasineh M, Shokri M, Abraham J. Estimation of Actual Evapotranspiration Using the Remote Sensing Method and SEBAL Algorithm: A Case Study in Ein Khosh Plain, Iran. *Hydrology*. 2020; 7(2):36.
https://doi.org/10.3390/hydrology7020036

**Chicago/Turabian Style**

Ghaderi, Amir, Mehdi Dasineh, Maryam Shokri, and John Abraham. 2020. "Estimation of Actual Evapotranspiration Using the Remote Sensing Method and SEBAL Algorithm: A Case Study in Ein Khosh Plain, Iran" *Hydrology* 7, no. 2: 36.
https://doi.org/10.3390/hydrology7020036