# Spectrum Index for Estimating Ground Water Content Using Hyperspectral Information

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

_{2}emissions [7,8]. In South Korea, development and research on smart roads are being actively conducted, which mainly requires automation equipment, datafication of information, and accurate quality control in a wide area [9,10].

^{2}value of calculated water content and measured water content. The most suitable spectrum index model still has a disadvantage: the target site does not reflect the low water content of agricultural land (measured water content of 10–30%).

## 2. Methodology for Estimating Ground Water Content in Road Construction Site

_{i}refers to reflectance at a wavelength of i-nm, and i ranges from 400 nm to 1000 nm. Reflectance (R) is the ratio of the reflected energy to the total energy incident on the body, and it is expressed as a percentage. R is expressed through a complex process of reflection, absorption, and transmission of energy; it varies with wavelength and enables features to be identified on the body or surface to be measured [31].

_{i}in the function may represent one, two, or more points. Corresponding combinations and analyses are described in a later section.

## 3. Laboratory Tests for Obtaining Hyperspectral Information

#### 3.1. System for Obtaining Hyperspectral Information

#### 3.2. Laboratory Test of Soil Sample

#### 3.2.1. Sieve Test

_{10}was not measured at 20% and 30% of fine contents, but the pass rate for fine contents did not exceed 50%; D

_{10}increased as it acted as a denominator in the coefficient of uniformity and the coefficient of curvature. Therefore, all samples used as a result of classification according to [39] could be classified as Poor Sand with uneven particle sizes.

#### 3.2.2. Standard Compaction Test

#### 3.2.3. Composition of Specimens

^{3}, and the maximum weight of soil that the experimental can could contain was 914 g (standard sand), 870 g (standard sand + fine content 10%), 790 g (standard sand + fine content 20%), and 742 g (standard sand + fine content 30%), according to the maximum dry unit weights presented in Figure 5.

#### 3.3. Hyperspectral Information of Soil Sample

## 4. Estimation of the Spectrum Index for Water Content Prediction

#### 4.1. Variability Analysis of Hyperspectral Information

#### 4.1.1. Effects of Fine Contents

#### 4.1.2. Effects of Water Contents

#### 4.2. Spectrum Index Reflected by Selected Wavelength and Reflection

_{720}. The variability analysis showed that COV exhibited a similar trend in the wavelength band of 600–880 nm. Therefore, all reflectance in the wavelength band of 600–880 nm are considered, and the spectrum index is expressed as an integral. In this paper, the integral is expressed as I

_{600–820}(integral from 600 nm to 820 nm of wavelength), and it refers to the area between the wavelength–reflectance curve and the x-axis (range of 600–820 nm).

#### 4.3. Equation for Predicting Water Content Using Spectrum Index

_{720}and I

_{600–880}were plotted on the x-axis against water content on the y-axis. The total number of data was 64. Figure 13 shows that the water content gradually decreased as the spectrum index increased, but the relationship was nonlinear. Therefore, it is necessary to derive a non-linear equation for the relationship.

^{2}values. After fitting, R

^{2}was low for I

_{600–880}(using the integral area) compared with that of R

_{720}(calculated as a single point). Therefore, it was appropriate to select R

_{720}as a spectrum index; an exponential fitting model with a high correlation coefficient was selected as the equation for water content prediction.

#### 4.4. Comparison of the Literature with Proposed Spectrum Index Method

^{2}prediction equations investigated by Ge et al. [30] are presented in Table 3. Because the existing equations target only the spectrum index, a separate fitting should be performed for the water content prediction equation. According to [30], a linear fitting was performed. Therefore, to obtain the equation for predicting water content, the spectral information from this study was substituted into the spectrum index, and the equations were obtained individually through linear fitting.

^{2}value was distributed from 0.002 to 0.122, indicating an extremely low correlation. Therefore, when the spectral information obtained in this study was substituted into the existing spectrum index, a considerable error was obtained, demonstrating that the water content prediction equation using the proposed R

_{720}is appropriate.

## 5. Conclusions

- In this study, sophisticated specimens were created by adding fine contents to standard sand, and hyperspectral information was obtained according to water content through precise laboratory tests. For hyperspectral information, a spectrum index was selected through various correlation analyses, and an equation to convert the spectrum index to water content was proposed.
- The suitable wavelength for calculating the spectrum index was 600–880 nm, as determined through variability analysis based on the water content and fine contents. The variability analysis results showed that no difference existed in the results of the equation for water content prediction even when a single wavelength within the range was selected. When the integral value of reflectance was used at 600–880 nm, R
^{2}was rather low. This phenomenon was the result of the overlapping variability of wavelength and reflectance. Even when the R^{2}of the corresponding index was measured, it was not appropriate as it increased the time for calculating the spectrum index. - The available equation for the prediction of the groundwater content is when the reflectance at a wavelength of 720 nm is applied to the exponential model. As a result of the linear regression analysis according to the measured and predicted water content, R
^{2}was measured to be the highest, which means that it is most suitable for representing the water content in the ground. In terms of spectral range, 720 nm is deep red light. - The correlation (R
^{2}: 0.009–0.122) when the existing spectrum index for water content prediction was substituted into the hyperspectral information obtained in this study was measured to be very low. Even when the existing equation was substituted into the hyperspectral information obtained by Ge et al. [26], the R^{2}ranged from 0.052 to 0.398, indicating that the reliability of the existing formula was low. Therefore, the R^{2}(0.7067) of our proposed equation for water content prediction according to R_{720}was large and reliable. This is because the existing method calculated the water content in a linear line through a simple linear regression analysis of the spectrum index. - The disadvantage of this study is that the proposed equation was derived without going through an actual field test. Thus, in the field, errors may occur depending on actual variables, such as weather, temperature, humidity, and the skill level of the drone operator. Therefore, it is necessary to test the accuracy and reliability of the equation derived from this study in the field, and the equation must be modified through additional data acquisition.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Basu, D.; Misra, A.; Puppala, A.J. Sustainability and geotechnical engineering: Perspectives and review. Can. Geotech. J.
**2015**, 52, 96–113. [Google Scholar] [CrossRef] - Brown, R.L. Building a Sustainable Society; W.W. Norton: New York, NY, USA, 1981. [Google Scholar]
- Brundtland, G.H. Our Common Future: Report of the World Commission on Environment and Development; Oxford University Press: Oxford, UK, 1987. [Google Scholar]
- Socolow, R.; Andrews, C.; Berkhout, F.; Thomas, V. Industrial Ecology and Global Change; Cambridge University Press: Cambridge, UK, 1997; pp. 23–41. [Google Scholar]
- Kibert, C.J. Sustainable Construction; John Wiley and Sons Inc.: Hoboken, NJ, USA, 2008. [Google Scholar]
- Corriere, F.; Rizzo, A. Sustainability in road design: A methodological proposal for the drafting of guideline. Procedia-Soc. Behav. Sci.
**2012**, 53, 39–48. [Google Scholar] [CrossRef] [Green Version] - Muench, S.T.; Anderson, J.; Bevan, T. Greenroads: A Sustainability Rating System for Roadways. Int. J. Pavement Res. Technol.
**2010**, 3, 270–279. [Google Scholar] - Muench, S.T.; Anderson, J.L.; Hatfield, J.P.; Koester, J.R.; Söderlund, M.; Weiland, C. Greenroads Manual v1. 5; University of Washington: Washington, DC, USA, 2011. [Google Scholar]
- Jeon, D.H.; Cho, J.Y.; Jhun, J.P.; Ahn, J.H.; Jeong, S.; Jeong, S.Y.; Kumar, A.; Ryu, C.H.; Hwang, W.; Park, H.; et al. A lever-type piezoelectric energy harvester with deformation-guiding mechanism for electric vehicle charging station on smart road. Energy
**2021**, 218, 119540. [Google Scholar] [CrossRef] - Kim, T.W.; Ryu, I.; Lee, H.; Jang, J.A. Dynamic Spatial Area Design for Transportation Management at Smart Road Lighting Platform System in Korea. In Proceedings of the 2021 International Conference on Information and Communication Technology Convergence (ICTC), Jeju, Korea, 20–22 October 2021. [Google Scholar]
- Ma, Y.; Luan, Y.C.; Zhang, W.G.; Zhang, Y.Q. Numerical simulation of intelligent compaction for subgrade construction. J. Cent. South Univ.
**2020**, 27, 2173–2184. [Google Scholar] [CrossRef] - Ahmed, H.A. Electrical Resistivity Method for Water Content Characterization of Unsaturated Clay Soil. Doctoral Theses, Durham University, Durham, UK, 2014. [Google Scholar]
- Roodposhti, H.R.; Hafizi, M.K.; Kermani, M.R.S.; Nik, M.R.G. Electrical resistivity method for water content and compaction evaluation, a laboratory test on construction material. J. Appl. Geophys.
**2019**, 168, 49–58. [Google Scholar] [CrossRef] - Abdullah, N.H.H.; Kuan, N.W.; Ibrahim, A.; Ismail, B.N.; Majid, M.R.A.; Ramli, R.; Mansor, N.S. Determination of soil water content using time domain reflectometer (TDR) for clayey soil. In Proceedings of the AIP Conference Proceedings, Maharashtra, India, 5–6 July 2018. [Google Scholar]
- Wen, M.M.; Liu, G.; Horton, R.; Noborio, K. An in situ probe-spacing-correction thermo-TDR sensor to measure soil water content accurately. Eur. J. Soil Sci.
**2018**, 69, 1030–1034. [Google Scholar] [CrossRef] [Green Version] - Peng, W.; Lu, Y.; Xie, X.; Ren, T.; Horton, R. An improved thermo-TDR technique for monitoring soil thermal properties, water content, bulk density, and porosity. Vadose Zone J.
**2019**, 18, 1–9. [Google Scholar] [CrossRef] [Green Version] - Ercoli, M.; Di Matteo, L.; Pauselli, C.; Mancinelli, P.; Frapiccini, S.; Talegalli, L.; Cannata, A. Integrated GPR and laboratory water content measures of sandy soils: From laboratory to field scale. Constr. Build. Mater.
**2018**, 159, 734–744. [Google Scholar] [CrossRef] - Klotzsche, A.; Jonard, F.; Looms, M.C.; van der Kruk, J.; Huisman, J.A. Measuring soil water content with ground penetrating radar: A decade of progress. Vadose Zone J.
**2018**, 17, 1–9. [Google Scholar] [CrossRef] [Green Version] - Zhou, L.; Yu, D.; Wang, Z.; Wang, X. Soil water content estimation using high-frequency ground penetrating radar. Water
**2019**, 11, 1036. [Google Scholar] [CrossRef] - Eismann, M.T.; Stocker, A.D.; Nasrabadi, N.M. Automated hyperspectral cueing for civilian search and rescue. Proc. IEEE
**2009**, 97, 1031–1055. [Google Scholar] [CrossRef] - Van Der Meer, F.D. Imaging Spectrometry-Basic Principles and Prospective Applications; Kluwer Academic Publishers: Dordrecht, The Netherlands, 2003. [Google Scholar]
- Bassani, C.; Cavalli, R.M.; Cavalcante, F.; Cuomo, V.; Palombo, A.; Pascucci, S.; Pignatti, S. Deterioration status of asbestos-cement roofing sheets assessed by analyzing hyperspectral data. Remote Sens. Environ.
**2007**, 109, 361–378. [Google Scholar] [CrossRef] - Smith, M.L.; Ollinger, S.V.; Martin, M.E.; Aber, J.D.; Hallett, R.A.; Goodale, C.L. Direct estimation of aboveground forest productivity through hyperspectral remote sensing of canopy nitrogen. Ecol. Appl.
**2002**, 12, 1286–1302. [Google Scholar] [CrossRef] - Kokaly, R.F.; Asner, G.P.; Ollinger, S.V.; Martin, M.E.; Wessman, C.A. Characterizing canopy biochemistry from imaging spectroscopy and its application to ecosystem studies. Remote Sens. Environ.
**2009**, 113, S78–S91. [Google Scholar] [CrossRef] - Zhang, F.; Zhou, G.S. Research progress on monitoring vegetation water content by using hyperspectral remote sensing. Chin. J. Plant Ecol.
**2018**, 42, 517. [Google Scholar] - Zhang, F.; Zhou, G. Estimation of vegetation water content using hyperspectral vegetation indices: A comparison of crop water indicators in response to water stress treatments for summer maize. BMC Ecol.
**2019**, 19, 1–12. [Google Scholar] [CrossRef] [Green Version] - Kovar, M.; Brestic, M.; Sytar, O.; Barek, V.; Hauptvogel, P.; Zivcak, M. Evaluation of hyperspectral reflectance parameters to assess the leaf water content in soybean. Water
**2019**, 11, 443. [Google Scholar] [CrossRef] [Green Version] - Prošek, J.; Gdulová, K.; Barták, V.; Vojar, J.; Solský, M.; Rocchini, D.; Moudrý, V. Integration of hyperspectral and LiDAR data for mapping small water bodies. Int. J. Appl. Earth Obs. Geoinf.
**2020**, 92, 102181. [Google Scholar] [CrossRef] - Guo, Y.; Bi, Q.; Li, Y.; Du, C.; Huang, J.; Chen, W.; Shi, L.; Ji, G. Sparse Representing Denoising of Hyperspectral Data for Water Color Remote Sensing. Appl. Sci.
**2022**, 12, 7501. [Google Scholar] [CrossRef] - Ge, X.; Wang, J.; Ding, J.; Cao, X.; Zhang, Z.; Liu, J.; Li, X. Combining UAV-based hyperspectral imagery and machine learning algorithms for soil moisture content monitoring. PeerJ
**2019**, 6926, 1–27. [Google Scholar] [CrossRef] [PubMed] - Jain, S.K.; Singh, V.P. Water Resources Systems Planning and Management; Elsevier: Amsterdam, The Netherland, 2003. [Google Scholar]
- Lu, G.; Fei, B. Medical hyperspectral imaging: A review. J. Biomed. Opt.
**2014**, 19, 010901. [Google Scholar] [CrossRef] [PubMed] - Angel, Y.; Turner, D.; Parkes, S.; Malbeteau, Y.; Lucieer, A.; McCabe, M.F. Automated georectification and mosaicking of UAV-based hyperspectral imagery from push-broom sensors. Remote Sens.
**2020**, 12, 34. [Google Scholar] [CrossRef] [Green Version] - Jurado, J.M.; Pádua, L.; Hruška, J.; Feito, F.R.; Sousa, J.J. An Efficient Method for Generating UAV-Based Hyperspectral Mosaics Using Push-Broom Sensors. IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens.
**2021**, 14, 6515–6531. [Google Scholar] - Yi, L.; Chen, J.M.; Zhang, G.; Xu, X.; Ming, X.; Guo, W. Seamless Mosaicking of UAV-Based Push-Broom Hyperspectral Images for Environment Monitoring. Remote Sens.
**2021**, 13, 4720. [Google Scholar] [CrossRef] - Ortega, S.; Guerra, R.; Diaz, M.; Fabelo, H.; López, S.; Callico, G.M.; Sarmiento, R. Hyperspectral push-broom microscope development and characterization. IEEE Access
**2019**, 7, 122473–122491. [Google Scholar] [CrossRef] - ISO 679; Cement-Test Methods-Determination of Strength. International Organization for Standardization: Geneva, Switzerland, 2009.
- ASTM D422; Standard Test Method for Particle-Size Analysis of Soils. American Society for Testing of Materials: West Conshohocken, PA, USA, 2016.
- ASTM D2487; Standard Practice for Classification of Soils for Engineering Purposes (Unified Soil Classification System). American Society for Testing of Materials: West Conshohocken, PA, USA, 2017.
- ASTM D698; Standard Test Methods for Laboratory Compaction Characteristics of Soil Using Standard Effort (12,400 ft-lbf/ft3 (600 kN-m/m
^{3})). American Society for Testing of Materials: West Conshohocken, PA, USA, 2017. - Liang, L.; Di, L.; Zhang, L.; Deng, M.; Qin, Z.; Zhao, S.; Lin, H. Estimation of crop LAI using hyperspectral vegetation indices and a hybrid inversion method. Remote Sens. Environ.
**2015**, 165, 123–134. [Google Scholar] [CrossRef] - Haboudane, D.; Miller, J.R.; Pattey, E.; Zarco-Tejada, P.J.; Strachan, I.B. Hyperspectral vegetation indices and novel algorithms for predicting green LAI of crop canopies: Modeling and validation in the context of precision agriculture. Remote Sens. Environ.
**2004**, 90, 337–352. [Google Scholar] [CrossRef] - Sims, D.A.; Gamon, J.A. Relationships between leaf pigment content and spectral reflectance across a wide range of species, leaf structures and developmental stages. Remote Sens. Environ.
**2002**, 81, 337–354. [Google Scholar] [CrossRef] - Broge, N.H.; Leblanc, E. Comparing prediction power and stability of broadband and hyperspectral vegetation indices for estimation of green leaf area index and canopy chlorophyll density. Remote Sens. Environ.
**2001**, 76, 156–172. [Google Scholar] [CrossRef] - Yao, X.; Wang, N.; Liu, Y.; Cheng, T.; Tian, Y.; Chen, Q.; Zhu, Y. Estimation of wheat LAI at middle to high levels using unmanned aerial vehicle narrowband multispectral imagery. Remote Sens.
**2017**, 9, 1304. [Google Scholar] [CrossRef] [Green Version] - Vogelmann, J.E.; Rock, B.N.; Moss, D.M. Red edge spectral measurements from sugar maple leaves. Int. J. Remote Sens.
**1993**, 14, 1563–1575. [Google Scholar] [CrossRef]

**Figure 6.**Composition of specimens: (

**a**) Mixing of a soil sample with standard sand and water; (

**b**) Compaction of the specimen in a circular petri; (

**c**) Specimens of soil samples with fine and water contents.

**Figure 7.**Relationship between wavelength and reflectance at fine contents of (

**a**) 0%, (

**b**) 10%, (

**c**) 20%, and (

**d**) 30%.

**Figure 10.**Analysis of using COV to select an appropriate wavelength for minimizing fine content effect.

**Figure 11.**Analysis of COV for selecting appropriate wavelength for maximizing water content effect.

**Figure 14.**Comparison of predicted and measured water contents by (

**a**) R

_{720}, (

**b**) mNDVI705, (

**c**) NDVI, (

**d**) NDCI, (

**e**) NDVI705, (

**f**) RVI, (

**g**) NDRE, (

**h**) GNDVI, (

**i**) OSAVI, (

**j**) VOG1, (

**k**) VOG2, and (

**l**) VOG3.

Fine Content in Standard Sand (%) | D_{10} ^{1}(mm) | D_{30} ^{2}(mm) | D_{60} ^{3}(mm) | Coefficient of Uniformity, C _{u} ^{4} | Coefficient of Curvature, C _{c} ^{5} | Percentage Passing No. 200 Sieve (%) | Soil Classification |
---|---|---|---|---|---|---|---|

0 | 0.274 | 0.363 | 0.530 | 1.934 | 0.907 | 0.06 | SP |

10 | 0.150 | 0.329 | 0.505 | 3.367 | 1.429 | 9.15 | SP |

20 | - | 0.300 | 0.482 | - | - | 16.72 | SP |

30 | - | 0.272 | 0.461 | - | - | 23.13 | SP |

^{1}D

_{10}: Particle diameter in percent finer of the soil corresponding to 10%;

^{2}D

_{30}: Particle diameter in percent finer of the soil corresponding to 30%;

^{3}D

_{60}: Particle diameter in percent finer of the soil corresponding to 60%;

^{4}C

_{u}: Coefficient of uniformity that calculated by C

_{u}= D

_{60}/D

_{10};

^{5}C

_{c}: Coefficient of curvature that calculated by D

_{30}

^{2}/(D

_{10}D

_{60}).

Index | Fitting Model | Equation | R^{2} |
---|---|---|---|

R_{720} | Linear | $w=-0.379{\mathrm{R}}_{720}+21.021$ | 0.636 |

Polynomial | $w=-8.38\times {10}^{-6}{{\mathrm{R}}_{720}}^{4}+0.0012{{\mathrm{R}}_{720}}^{3}-0.0462{{\mathrm{R}}_{720}}^{2}\phantom{\rule{0ex}{0ex}}-0.2631{\mathrm{R}}_{720}122\left(0\text{}\mathrm{index}+33.7973\right)$ | 0.687 | |

Logarithm | $w=25.767-7.004\mathrm{ln}\left({\mathrm{R}}_{720}-19.738\right)$ | 0.695 | |

Exponential | $w=-1.172+79.648\mathrm{exp}\left(-0.0666{\mathrm{R}}_{720}\right)$ | 0.697 | |

I_{600–880} | Linear | $w=-0.00883{\mathrm{I}}_{600\u2013880}+14.658$ | 0.579 |

Polynomial | $w=-5.37\times {10}^{-12}{{\mathrm{I}}_{600\u2013880}}^{4}+2.159\times {10}^{-8}{{\mathrm{I}}_{600\u2013880}}^{3}$ $-7.782\times {10}^{-5}{{\mathrm{I}}_{600\u2013880}}^{2}+0.0479{\mathrm{I}}_{600\u2013880}122(0\text{}\mathrm{index}+10.0868)$ | 0.637 | |

Logarithm | $w=48.239-6.432\mathrm{ln}\left({\mathrm{I}}_{600\u2013880}-144.708\right)$ | 0.643 | |

Exponential | $w=-0.2228+25.032\mathrm{exp}\left(-0.00167{\mathrm{I}}_{600\u2013880}\right)$ | 0.645 |

Spectrum Index | Equation for Water Content Prediction | Ref. | |
---|---|---|---|

Sort | Equation | ||

mNDVI705 | (R_{750} − R_{705})/(R_{740} + R_{705} + 2R_{445}) | $w=-105.01\mathrm{mNDVI}705+13.40$ | [41] |

NDVI | (R_{800} − R_{680})/(R_{800} + R_{680}) | $w=161.11\mathrm{NDVI}-20.57$ | [42] |

NDCI | (R_{762} − R_{527})/(R_{762} + R_{527}) | $w=8.04\mathrm{NDCI}+1.44$ | [41] |

NDVI705 | (R_{750} − R_{705})/(R_{750} + R_{705}) | $w=-120.54\mathrm{NDV}705\mathrm{I}+14.53$ | [43] |

RVI | R_{800}/R_{680} | $\mathsf{\omega}=55.28\mathrm{RVI}-71.13$ | [43] |

NDRE | (R_{750} − R_{705})/(R_{750} + R_{705}) | $w=-120.54\mathrm{NDRE}+14.53$ | [44] |

GNDVI | (R_{750} − R_{550})/(R_{750} + R_{550}) | $w=3.79\mathrm{GNDVI}+5.10$ | [45] |

OSAVI | [(1 + 0.16) (R_{800} − R_{670})]/(R_{800} + R_{670} + 0.16) | $w=115.04\mathrm{OSAVI}-19.52$ | [42] |

VOG1 | R_{740}/R_{720} | $w=-114.33\mathrm{VOG}1+127.58$ | [46] |

VOG2 | (R_{734} − R_{747})/(R_{715} − R_{726}) | $w=2.71\mathrm{VOG}2+5.66$ | [46] |

VOG3 | (R_{734} − R_{747})/(R_{715} + R_{720}) | $w=577.11\mathrm{VOG}3+14.58$ | [46] |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Lee, K.; Kim, K.S.; Park, J.; Hong, G.
Spectrum Index for Estimating Ground Water Content Using Hyperspectral Information. *Sustainability* **2022**, *14*, 14318.
https://doi.org/10.3390/su142114318

**AMA Style**

Lee K, Kim KS, Park J, Hong G.
Spectrum Index for Estimating Ground Water Content Using Hyperspectral Information. *Sustainability*. 2022; 14(21):14318.
https://doi.org/10.3390/su142114318

**Chicago/Turabian Style**

Lee, Kicheol, Ki Sung Kim, Jeongjun Park, and Gigwon Hong.
2022. "Spectrum Index for Estimating Ground Water Content Using Hyperspectral Information" *Sustainability* 14, no. 21: 14318.
https://doi.org/10.3390/su142114318