# Simulation of Evapotranspiration at a 3-Minute Time Interval Based on Remote Sensing Data and SEBAL Model

^{1}

^{2}

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## Abstract

**:**

## Featured Application

**Our research not only provides a method for estimating evapotranspiration, but also provides the possibility for additional remote sensing models to appear on a “minute” or even “second” time scale.**

## Abstract

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Materials

#### 2.1.1. Remote Sensing Data

#### 2.1.2. Meteorological and Flux Data

#### 2.1.3. Location and Study Area

#### 2.2. Methods

#### 2.2.1. SEBAL Model

#### 2.2.2. Calculation of NDVI

^{2}·ster·μm)

^{−1}, θ

_{s}is the solar zenith angle in degrees, and d is the earth-sun distance in astronomical units. ${L}_{\mathsf{\lambda}\text{}}$is the at-satellite spectral radiance in W·(m

^{2}·ster·μm)

^{−1}. θ

_{s}can be obtained from the head file. The ESUN value for each GF-4 band has not been published yet, but can be calculated using the spectral response function of the solar spectrum curve and the sensor, as shown in Equation (3) [37].

_{1}and λ

_{2}denote the upper and the lower integration limit of wavelength of band range; E(λ) denotes the solar spectrum radiation of the remote sensor out of the atmosphere at band λ, where different solar spectrum curves have different E(λ) values. Current studies show that the World Radiation Center (WRC) solar spectrum curve is the most favorable for the calculation of the ESUN using this sensor at a medium resolution in China [38]. According to the WRC solar spectrum curve, the E(λ) value could be in the range of λ

_{1}and λ

_{2}; and S(λ) denotes the spectral response function of the remote sensor at band λ. The ESUN values for all GF-4 bands calculated using Equation (3) are shown in Table 3.

#### 2.2.3. Calculation of Land Surface Temperature

_{B,set}denotes the LST at sunset; T

_{B,max}denotes the daily maximum LST; W

_{2}= π/(DL − 2p) denotes the angular frequency of the sinusoid in the second stage; DL denotes the daytime length; p = TIME

_{x}− NOON, TIME

_{x}denotes the time when the maximum LST appears, TIME

_{x}can be attained from meteorological stations, NOON denotes the time when the largest solar altitude appears, which is usually selected as 12.0; and φ

_{2}= π/2 − W

_{2}× TIME

_{x}denotes the phase angle.

_{B,max}, T

_{B,min}, and T

_{B,set}, and then calculated the LST at GF-4 imaging time using Equations (5) and (6).

#### 2.2.4. Calculation of Daytime Air Temperature

_{a}denotes daytime air temperature, and T

_{min}and T

_{max}denote daily minimum and daily maximum air temperature. In Equation (11), S(t) is a function of time (t) with data range of 0–1, represented as:

_{min}denotes the lowest air temperature at present day in Equation (11); when air temperature decreases, T

_{min}denotes the lowest air temperature on the next day.

#### 2.2.5. Calculation of Wind Speed

_{1}) in the morning, at which point the wind speed gradually increases to the maximum value until a time (t

_{2}) in the afternoon, then gradually decreases to the minimum value until a time (t

_{3}) at night. The t

_{1}, t

_{2}, and t

_{3}vary with location: in the study area, t

_{1}= 1.0, t

_{2}= 14.0, and t

_{3}= 0.0, and the variation of wind speed with time is expressed by the following equation [42]:

_{a}denotes wind speed at any time (m/s), W

_{max}and W

_{min}denote daily maximum and daily minimum wind speed (m/s), respectively, t

_{a}denotes any time, tw

_{1}= t

_{1}, tw

_{2}= 2(t

_{2}− t

_{3}), SF

_{1}= 4(t

_{2}− t

_{1}), and SF

_{2}= 4(t

_{3}− t

_{2}).

_{w}denotes daily air movement distance (km/d), which can be calculated from the daily average wind speed (m/s) available from meteorological stations and the length of a day (24 h × 3600 s/h).

#### 2.2.6. Verification and Evaluation of Simulation Results

_{8}) using ET of MODIS at 11:35 (MT

_{0}). Then ET at 13:50 (${\mathrm{T}}_{5}^{\prime}$) of GF-4 and 13:45 (${\mathrm{MT}}_{1}^{\prime}$) of MODIS were cross-verified. Finally, we used the field measured ET data to verify them from the Flux sites in South Korea, which was close to the imaging time of remote sensing images. Since the measuring time interval at KoFlux sites was 30 min, we chose the measured ET at 11:30 and 14:00 to verify the simulated ET at 11:22 (${\mathrm{T}}_{4}^{\prime}$) and 13:58 (${\mathrm{T}}_{7}^{\prime}$) of GF-4 respectively. Then, the field measure ET at 12:00 (${\mathrm{MT}}_{0}^{\prime}$) was used to verify the simulated ET of MODIS at 12:10 (${\mathrm{MT}}_{0}^{\prime}$).

_{i}is the measured value, Y

_{i}′ is the simulated value obtained from the model, and n is the number of sample points [43,44]. The smaller the values of RMSE and MRE, the higher the simulation accuracy of the model [43,44].

## 3. Results

_{8}) of GF-4 and ET at 11:35 (MT

_{0}) of MODIS in CB, CF and CG regions, respectively.

_{1}–T

_{15}in areas CB, CG and CF, ${\mathrm{T}}_{1}^{\prime}-{\mathrm{T}}_{7}^{\prime}$in areas KB, KE and KD, the minimum, maximum, and average values, and the standard error of ET at above time was calculated by ArcMAP 10.3 for all pixels, as shown in Figure 7 and Figure 8.

_{1}–T

_{15}does not. The minimum ET does not vary in study area at time T

_{1}–T

_{15}, and the pixel with ET = 0 always exists. As shown in Figure 7 and Figure 8, the maximum value trend in all areas is the same as that of the average values, while the fluctuation in trend of the maximum and minimum value in all areas is different. This is mainly due to the difference among soil types and meteorological conditions in the six areas, causing the impacts on ET to vary [3,45]. This validates that due to the different of surface types and meteorological conditions, even two MODIS remote sensing images show daily variation in remote sensing pixel ETs. This daily variation does not follow the constant linear rule, meaning that extrapolating instantaneous ET at the imaging time to a hourly or daily time scale will cause relatively large errors [46,47]. Although GF-4 has no thermal infrared band and the LST at imaging time could not be obtained, its temporal resolution is relatively high and the land surface ET at a three-minute time interval can be attained by using all available meteorological and MODIS data. By using this method, the error associated with extrapolating instantaneous ET from one remote sensing image could be avoided and the real spatial diversity of ET at various imaging time could be obtained.

## 4. Discussion

## 5. Conclusions

## 6. Perspectives

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 5.**Cross-validation of simulated ET of GF-4 and MODIS; (

**a**) ET at 11:35 of MODIS and 11:36 of GF-4 in areas CB,CG and CF; (

**b**)ET at 13:45 of MODIS and 13:50 of GF-4 in areas KB,KE and KD).

**Figure 6.**Comparison of simulated and measured ET at KoFlux Sites. (Black squares are ET values simulated by GF4, while black triangles are ET values simulated by MODIS).

**Figure 7.**ET of GF-4 at time T

_{1}–T

_{15}in areas CB, CG, and CF (the minimum value, the maximum value, the average value, and the standard error).

Band | Spectral Range (μm) | Spatial Resolution (m) | |
---|---|---|---|

Visible and near infrared (VNIR) | 1 | 0.45~0.90 (pan) | 50 |

2 | 0.45~0.52 (blue) | ||

3 | 0.52~0.60 (green) | ||

4 | 0.63~0.69 (red) | ||

5 | 0.76~0.90 (near-infrared) | ||

Medium-wave infrared (MWIR) | 6 | 3.5~4.1 | 400 |

Region | CB,CG,CF | KB,KE,KD |
---|---|---|

Imaging date of MODIS and GF-4 | 2 December 2016 | 29 April 2017 |

Imaging time of MODIS(Local solar time) | 11:35 (MT_{0})13:10 (MT _{1}) | 12:10 (${\mathrm{MT}}_{0}^{\prime}$) 13:45 (${\mathrm{MT}}_{1}^{\prime}$) |

Imaging time of GF-4(Local solar time) | 11:14 (T_{1})/11:17 (T_{2})/11:20 (T_{3})/11:23 (T _{4})/11:26 (T_{5})/11:29 (T_{6})/11:32 (T _{7})/11:36 (T_{8})/11:39 (T_{9})/11:42 (T _{10})/11:45 (T_{11})/11:48 (T_{12})/11:51 (T _{13})/11:54 (T_{14})/11:57 (T_{15}) | 11:14 (${\mathrm{T}}_{1}^{\prime}$)/11:16 (${\mathrm{T}}_{2}^{\prime}$)/11:19 (${\mathrm{T}}_{3}^{\prime}$) /11:22 (${\mathrm{T}}_{4}^{\prime}$)/13:50 (${\mathrm{T}}_{5}^{\prime}$)/13:55 (${\mathrm{T}}_{6}^{\prime}$) /13:58 (${\mathrm{T}}_{7}^{\prime}$) |

^{1}Although the temporal resolution of GF-4 is 20 s, these data are only provided to specific institutions. The GF-4 data for the 3-min time interval used in this paper is open to all researchers, but the number of images and imaging time in each region will not be the same. Therefore, the number of GF-4 images in Table 2 is different between China and South Korea.

Bands | B1 | B2 | B3 | B4 | B5 |
---|---|---|---|---|---|

ESUNW·(m ^{2}·ster·μm)^{−1} | 1609.81 | 1634.44 | 1839.33 | 1578.12 | 1104.77 |

Status | Gain Values (A) | ||||
---|---|---|---|---|---|

B_{1} | B_{2} | B_{3} | B_{4} | B_{5} | |

2-6-4-6-6 | 0.5215 | 0.9400 | 0.9885 | 0.7847 | 0.5641 |

4-16-12-16-16 | 0.3100 | 0.3484 | 0.3484 | 0.3095 | 0.2257 |

6-20-16-20-20 | 0.1681 | 0.3263 | 0.2472 | 0.2806 | 0.1997 |

6-40-30-40-40 | 0.1681 | 0.1252 | 0.1226 | 0.1102 | 0.0796 |

6-30-20-30-30 | 0.1235 | 0.1784 | 0.1878 | 0.1515 | 0.1080 |

Region | Data of Verification | MRE (%) | RMSE (mm/min) |
---|---|---|---|

KE | KoFlux data | 16.95 | 0.00072 |

CB, CG and CF | MODIS | 48.64 | 0.00451 |

KB, KE and KD | MODIS | 48.33 | 0.00655 |

Region | Data of Verification | MRE (%) | RMSE (mm/min) |
---|---|---|---|

CB, CG and CF | Landsat 8 | 79.21 | 0.00462 |

KB, KE and KD | Landsat8 | 190.36 | 0.00383 |

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**MDPI and ACS Style**

Li, G.; Armstrong, A.; Chang, X.
Simulation of Evapotranspiration at a 3-Minute Time Interval Based on Remote Sensing Data and SEBAL Model. *Appl. Sci.* **2020**, *10*, 4919.
https://doi.org/10.3390/app10144919

**AMA Style**

Li G, Armstrong A, Chang X.
Simulation of Evapotranspiration at a 3-Minute Time Interval Based on Remote Sensing Data and SEBAL Model. *Applied Sciences*. 2020; 10(14):4919.
https://doi.org/10.3390/app10144919

**Chicago/Turabian Style**

Li, Guoqing, Alona Armstrong, and Xueli Chang.
2020. "Simulation of Evapotranspiration at a 3-Minute Time Interval Based on Remote Sensing Data and SEBAL Model" *Applied Sciences* 10, no. 14: 4919.
https://doi.org/10.3390/app10144919