Mathematical modelling of evapotranspiration by using remote sensing and data mining


 Precise evaluation of evapotranspiration in an extended area is crucial for water requirement. By using remote sensing evapotranspiration algorithms, many climatological variables are needed. In case of using climatological variable measurements, many climatic stations must be established in that specific area. By using data mining method integrated with remote sensing, evapotranspiration can be calculated with high accuracy. A physical-based SEBAL evapotranspiration algorithm was modeled by GIS model builder for ET calculations. Albedo, emissivity, and Normalized Difference Water Index (NDWI) were considered as M5 decision tree model inputs. Evapotranspiration was evaluated for 3 April 2020 to 17 September 2020 and the equations were extracted in the M5 decision tree model and these equations were modeled in GIS by using python scripts for 3 April 2020 to 17 September 2020. The results make clear that the mathematical decision tree model can estimate the evapotranspiration gained by physical-based SEBAL algorithm in high accurately.


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Irrigation scheduling of crops can be done by using meteorological data for evapotranspiration  Penman-Monteith, Blaney-Criddle, etc. Ground observations represent the results for one 3 specific point in which high accuracy is needed to generalize them for extended region Hence 48 evaporation is different from station to station. By using remote sensing technologies, one can 49 reach acceptable and high accuracy for a specific extended region. By using satellite images as a 50 remote sensing technic, ground observations transformed to soft data. Among different methods 51 of data mining, the M5 decision tree was used to estimate the evapotranspiration in an extended 52 area (Gibert et al., 2018). 53 This research is intended to establish an applicable different linear relation by using the M5 54 decision tree between independent remote sensing parameters (albedo, emissivity, and 55 Normalized difference water index) with the dependent parameter (evapotranspiration) by using 56 data mining which is the most important innovation of this research.

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Landsat8 satellite images and SEBAL algorithm were used for evapotranspiration estimation.  Landsat 8 OLI satellite images were the main data for remote sensing processes 88 (http://glovis.usgs.gov). Thermal bands have lower resolution compared to other optic bands. As 89 for Landsat8, band10 image represents a thermal band that provides less spatial resolution 90 (100m) but Thermal bands are critical for evapotranspiration estimation and Landsat8 has the 91 most appropriate thermal band for agricultural evapotranspiration estimation in a great variety The SEBAL algorithm was used to calculate the evapotranspiration (ET) of Sugarcane for the 106 Amir-Kabir agro-industry plantation. SEBAL algorithm uses thermal and multispectral digital 107 images of Landsat or other sensors to estimate the evapotranspiration (Bastiaanssen et al., 1998).

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The ET calculation process is obtained by the amount of energy remained from the classical 109 equation of energy balance presented in equation (1): Where λET is the latent heat flux in the atmospheric boundary layer (W/m 2 ), Rn is the net 112 radiation (W/m 2 ), H is the sensible heat flux (W/m 2 ) and G is the soil heat flux (W/m 2 ) (   Where εv is the vegetation canopy emissivity and εs is the bare soil emissivity; in this paper εv = 213 0.986 and εs = 0.973. the effect of the geometrical distribution of the natural surfaces is measured 214 as dε in Eq.6 . Pυ is the vegetation proportion obtained according to (Carlson and Ripley, 1997) 215 as Eq. (7): The minimum value of the NDVI for bare soil over the study region is presented as NDVIS and  The M5 decision tree model takes Albedo, emissivity, and a vegetation index as input and after 232 the data mining process on these data, linear equations will be extracted. By inserting linear 233 equations, the evapotranspiration map was obtained as an output with higher spatial resolution.   In this study albedo is one of model input parameters which was calculated for each image in 284 the study period. In the first growth stage of sugarcane, vegetative cover is very low and the 285 plant is not developed and canopy cover did not reach to its highest development. Figure 4 286 shows the albedo images as input parameters of the decision tree for the study duration. In 287 satellite images canopy cover area is much lower than soil area at the first growth stage    The emissivity of the surface of a material refers to the effectiveness of the surface in emitting 304 energy as thermal radiation (electromagnetic radiation with wavelength depending on the 305 temperature). Emissivity is mathematically defined as the ratio of the thermal radiation from the 306 surface to the radiation from an ideal black surface at the same temperature; the value varies 307 from 0 to 1. For C/SiC, the emissivity at 1600°C is ∼0.7, which is high (Alfano et al., 2009).   In the end of sugarcane growth stage, the temperature increases which also makes the emissivity 320 to increase. Figure 5 makes clear that emissivity has suitable spatial variability which can make 321 the evaluation of evapotranspiration by using M5 decision tree with acceptable accuracy.    The emissivity variable was considered as the diffused light has less importance in the decision 377 tree divisions which by considering the geographical location of the study area it shows that most 378 of the received light was absorbed than diffused.   Figure 8 shows the results of the comparison between the SEBAL algorithm and M5 decision 401 tree for this two month study duration. Table 1 shows statistical coefficients for 3 April 2020 to 402 17 September 2020. According to figure 8 and table 1 by comparing the obtained results for 403 these two months, it could be possible to calculate evapotranspiration with fewer input.

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Mathematical models can be used instead of physically-based models with acceptable accuracy.    This study discovered that by using less input parameters and selecting the right parameters,

6.Acknowledgments 498
We are grateful to the Research Council of Shahid Chamran University of Ahvaz for financial support 499 (GN:SCU.WI98.281). 500

Ethical Approval 501
Not applicable 502

Consent to participate 503
Consent was obtained from all individual participants included in the study. 504

Consent to publish 505
The participant has consented to the submission of the case report to the journal. 506

Author contribution 507
All authors contributed to the study conception and design. Material preparation, data collection and  Funding 512 This study was funded by "Shahid Chamran University of Ahvaz". 513

Competing Interests 514
The authors declare that there are no competing interests. 515

Availability of data and materials 516
Data will be made available on request.