# An Improved Exponential Model Considering a Spectrally Effective Moisture Threshold for Proximal Hyperspectral Reflectance Simulation and Soil Salinity Estimation

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

^{2}being generally larger than 0.9 and RMSE being less than 0.1. More importantly, MT-SSREM performed substantially better than SSREM for SSC estimation; in the statistical performance of the former case, R

^{2}was in range of 0.60~0.66, RMSE was in range of 0.29~0.33 dS m

^{−1}; in the latter case, R

^{2}was in range of 0.10~0.16, RMSE was in the range of 0.26~0.29 dS m

^{−1}. MT-SSREM proposed in this study thus provides a new direction for estimating hyperspectral reflectance and SSC under various soil moisture conditions at wavelengths from 400 to 1000 nm. It also provides an approach for SSC and SMC mapping in salinization regions by incorporating remote sensing data, such as GF-5.

## 1. Introduction

_{0}), needs further verification [52]; (5) The sensitive wavelengths of SMC and SSC could be identical. In this case, how to distinguish between the spectral signals of SMC and SSC needs to be further explored.

## 2. Methodology

#### 2.1. Experimental Site Description

#### 2.2. Data Collection

^{+}), sodium (Na

^{+}), calcium (Ca

^{2+}) and magnesium (Mg

^{2+}), using an inductive coupling plasma emission spectrometer (ICP-OES).

#### 2.3. Hyperspectral Reflectance Data Preprocessing

#### 2.4. Theoretical Approach

#### 2.4.1. Description of SSREM

_{0}(i) is the reflectance for wavelength i which is not affected by moisture and salt; SMC is soil mass moisture content, g g

^{−1}; SSC is soil EC, dS m

^{−1}; a(i) and b(i) are the changing rates of soil spectral reflectance corresponding to band i caused by soil moisture and salt, respectively.

_{1}and SMC

_{2}, and the EC are SSC

_{1}and SSC

_{2}, respectively, the corresponding spectral reflectance R

_{1}and R

_{2}(corresponding to values measured from the first part of the soil samples) are as follows:

_{3}, R

_{4}) (corresponding to values measured from the second part of the soil samples) are described as,

_{0}(i).

#### 2.4.2. Establishment of MT-SSREM

_{min}and SMC

_{max}), ${x}_{0}$ is the extremum point, g g

^{−1}.

#### 2.5. Research Framework

#### 2.6. Model Calibration and Validation

^{2}), root mean square error (RMSE) and SD were used to quantify the prediction accuracy of the models

## 3. Results

#### 3.1. SMC, SSC and Major Cation Concentrations

^{−1}, with SDs of 0.048 and 0.052 g g

^{−1}, respectively. Furthermore, the SSC of the calibration dataset and validation dataset range from 0.10 to 2.84 and 0.095 to 3.29 dS m

^{−1}, respectively. We also tested concentration and correlation among four cations in the samples. The experimental field was irrigated by brackish water, which was prepared by mixing local deep groundwater with NaCl. As a result, the soil samples were rich in NaCl and KCl. The concentrations of the four cations follow the order of Na

^{+}, K

^{+}, Ca

^{2+}, and Mg

^{2+}. The four cations showed significant correlations, especially for Ca

^{2+}and Mg

^{2+}, with the correlation coefficient above 0.80.

#### 3.2. Soil Hyperspectral Reflectance at Different SSC Levels

#### 3.3. Soil Hyperspectral Reflectance at Different SMC Levels

^{−1}, reflectance in visible bands is generally negatively correlated with SMC, and the reflectance in NIR bands decreases at first and then increases with the increase of SMC, with the turning point at 0.15 g g

^{−1}for 750 nm (Figure 6a). For the soil samples with an EC of 0.5 dS m

^{−1}, the reflectance decreases at first and then increases with an increase of SMC, with a turning point at 0.089 g g

^{−1}for 400~532 nm and 0.12 g g

^{−1}for 533~1000 nm, shown in Figure 6b. With respect to EC of 1.6 dS m

^{−1}, the spectral reflectance decreases first and then increases for 400~500 nm, with a turning point at 0.14 g g

^{−1}for 500 nm, while the spectral reflectance decreases with an increase of SMC for 500~1000 nm.

#### 3.4. Suitable Bands for Estimating SSC

#### 3.5. Determination of MT Based on the Relationship between Reflectance and SMC

^{2}values of quadratic and cubic functions are higher than those of linear and exponential equations. Besides, because the linear and exponential functions are monotonic functions, they are unable to depict the impact of MT on spectral reflectance. Therefore, quadratic and cubic functions are more suitable to be used. The R

^{2}values of these two functions are similar for the spectral range of 600 to 1000 nm, while R

^{2}by quadratic functions are higher than cubic functions for 400~600 nm. Therefore, we used quadratic functions to quantify the relationship between spectral reflectance and SMC. With an example of wavelength at 400 and 650 nm, as in Figure 8b, the spectral reflectance quadratically correlated with SMC and the SMCs of minimum reflectance in the curve at 400 nm and 600 nm are 0.12 and 0.15 g g

^{−1}, respectively.

^{−1}at 660 nm and the minimum 0.12 g g

^{−1}at 475 nm. The shape of R

^{2}(Figure 8a) and MT (Figure 8b) curves are similar and the R

^{2}and MT values peak in the range of 600~715 nm.

#### 3.6. Evaluation of Model Performance

#### 3.6.1. Model Parameters

_{0}of the models (SSREM and MT-SSREM) were obtained based on average reflectance for wet (i.e., $\overline{{R}_{1}}$, $\overline{{\mathrm{SMC}}_{1}}$, $\overline{{\mathrm{SSC}}_{1}}$, $\overline{{R}_{2}}$, $\overline{{\mathrm{SMC}}_{2}}$ and $\overline{{\mathrm{SSC}}_{2}}$ as shown in Figure 3) and air-dried (i.e.,$\overline{{R}_{3}}$,$\overline{{\mathrm{SSC}}_{1}}$, $\overline{{R}_{4}}$ and $\overline{{\mathrm{SSC}}_{2}}$) soils, and the results are shown in Figure 9. The value of parameter a varies in the range of −5.27 to 8.07. It increases with the wavelength following a logarithmic function, with a negative value for the wavelength smaller than 534 nm and a positive value for the wavelength larger than 534 nm (Figure 9a). Parameter b varies in the range of −0.068 to 0.25, which first increases and then decreases with wavelength. It is negative when the wavelength is in the range of 400~421 nm, and positive for wavelengths greater than 421 nm. SMC exerts greater influence on spectral reflectance than SSC because the absolute value of parameter a was larger than that of parameter b at the same wavelength. Using a similar method, the parameter R

_{0}was determined for each band in the range of 400~1000 nm (Figure 9b). The R

_{0}values show an increasing trend in the whole wavelength, and the maximum spectral reflectance is 0.58 at 1000 nm.

#### 3.6.2. Results of the SSREM

^{2}and RMSE values are in the range of 0~0.98 and 0.014~0.23, respectively. Validation R

^{2}and RMSE values are in the range of 0~0.98 and 0.018 to 0.22, respectively.

^{−1}. Figure 10e,g,h shows that the spectral reflectance is overestimated in the visible bands and underestimated in the NIR bands by SSREM when the SMC value is greater than the maximum of MT(i) (i = [400, 1000]), i.e., 0.15 g g

^{−1}. At the same time, the shape of the simulated spectral curves differs from that of the measured spectral curves. When the SMC value is greater than the MT value, the error between the simulated and measured reflectance values is small for some bands, but the correlation is poor (Figure 10d,f). When the SMC value is less than the minimum of MT(i) (0.12 g g

^{−1}), the shapes of the simulated spectral curves of SSREM are similar to the measured spectral curves (Figure 10c), indicating SSREM has a good simulation accuracy.

#### 3.6.3. Results of the MT-SSREM

^{2}and RMSE values ranging from 0.53 to 0.98 and 0.014 to 0.16, respectively, and validation R

^{2}and RMSE values ranging from 0.75 to 0.98 and 0.016 to 0.17, respectively).

#### 3.6.4. SSC Estimation

^{2}values of 0.66 and corresponding RMSEs of 0.33 dS m

^{−1}for the three bands. The SSC estimation models for 672 nm to 685 nm and 938 nm also performed well, with R

^{2}in the range of 0.60 to 0.63 and RMSE in the range of 0.29 to 0.31 dS m

^{−1}. However, wavelengths at 939 nm and 961 nm could not be used to estimate SSC. It is caused by the absorption properties at 939 nm and 961 nm, which led to their poor performance for the SSC estimation, i.e., they are within the specific absorption wavelengths of the water. For SSREM, the estimation model based on the simulated bands could not estimate the SSC. The R

^{2}values were no more than 0.16 and the RMSEs were in the range of 0.17~0.29 dS m

^{−1}. In particular, when SSC < 1 dS m

^{−1}, the SSC estimation model performed poorly as shown in Figure 12.

## 4. Discussion

#### 4.1. The MT-SSREM Parameters

_{0}. The MT parameter can be difficult to determine, given its dependence on many potential factors. Soil particle-size distribution, salt concentration, salt composition and wavelength are considered the main factors that significantly affect MT [13,21,23,25]. In this study, spectral reflectance data were fitted with the SMC data of the soils by quadratic functions. The resulted MTs are in the range of 0.12~0.15 g g

^{−1}for the whole spectrum (400~1000 nm). This result is different from some previous studies. Liu et al. [24] reported that MTs for 1000 nm band, under different levels of soil organic matter contents in black soil, were in the range of 0.28~0.54 g g

^{−1}, with higher values corresponding to lower organic matter contents. Some studies simply assumed MT was equal to field moisture capacity [23,25]. Soil type (the soil sand content in this study was greater than that in previous studies [24]), soil color (e.g., the soil color was yellow in this study and black in previous study) and SMC (SMCs in this study were lower than SMCs in previous study [25,45]) might cause the difference in the estimated MT values between this study and previous studies. We determined MT following a consistent procedure (quadratic function) and contributed a new way for quantifying the effects of SMC on saline soil spectral reflectance.

_{0}, Wang et al. [15] and Yang and Yu [31] found that parameter b increased with wavelength. It was negative for the range of 350~600 nm and positive for the range of 600~1000 nm. The spectral pattern of parameter b of this study is similar, but approaches zero at the wavelength of 421 nm, which might be caused by the difference in salt composition between this study and previous ones. Furthermore, we assumed SMC equals zero for air-dried soil samples, which might slightly affect the values of the parameters.

_{0}, a and b, were obtained based on the average reflectance for wet and dry soils in this study. Yang and Yu [31] and Zhang et al. [51] fitted these parameters using the least-squares method. Somers et al. [61] modelled parameter a by establishing a function of parameter a and specific surface area (SSA). In addition, the absolute value of parameter a was larger than that of parameter b (as shown in Figure 9a), which showed that SMC had greater influence on soil spectral reflectance than SSC, sometimes the spectral signal of SMC even covered up the spectral signal of SSC. Previous results also confirmed that the influence of moisture on soil spectrum was commonly greater than other factors [17,26]. SMC affects the reflectance signal in the field and affects the accuracy of SSC estimation based on reflectance, especially in arid lands. Therefore, it is vital to establish a model that can eliminate the noise of SMC on SSC estimation for potential in situ field applications.

#### 4.2. Features of Suitable Bands for Estimating SSC

#### 4.3. MT-SSREM Model Performance

^{2}and a mean decrease of 0.012 in RMSE. In addition, MT-SSREM appears to be more robust than SSREM for various SMC and SSC conditions, with MT-SSREM having a much smaller variation of R

^{2}and RMSE (SD = 0.035 and 0.035) than SSREM (SD = 0.24 and 0.037). Meanwhile, the R

^{2}values of MT-SSREM simulations are above 0.75, accounting for 100% (in the 183 saline soil samples of the validation dataset), and RMSE values are below 0.1, accounting for 80.33% soil samples.

#### 4.4. Application and Limitations of MT-SSREM

_{0}and MT) to facilitate the application. Furthermore, future work is required to incorporate MT-SSREM and remote sensing data like GF-5, which is significant for the SSC mapping.

## 5. Conclusions

- (1)
- The relationship of spectral reflectance and SMC can be fitted with a quadratic function, and the MT value of each waveband can be determined at the minimum point of the corresponding quadratic function.
- (2)
- SSREM is not suitable for simulating the spectral reflectance of saline soil with high SMC. An improved model, MT-SSREM has been proposed to incorporate the MT effect on saline soil spectral reflectance modelling.
- (3)
- MT-SSREM performed better than SSREM for hyperspectral reflectance simulation and SSC estimation in various SMC and SSC conditions.
- (4)
- SMC has greater influence on soil spectral reflectance than SSC, which make it difficult to eliminate SMC noise when estimating SSC from spectral reflectance. It is suggested to use spectral reflectance of 628~640 and 728~735 nm bands for estimating SMC, and that of 658~660, 671~685 and 938 nm for estimating SSC.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

- Butcher, K.; Wick, A.F.; DeSutter, T.; Chatterjee, A.; Harmon, J. Soil Salinity: A Threat to Global Food Security. Agron. J.
**2016**, 108, 2189–2200. [Google Scholar] [CrossRef] - Heung, B.; Ho, H.C.; Zhang, J.; Knudby, A.; Bulmer, C.E.; Schmidt, M.G. An overview and comparison of machine-learning techniques for classification purposes in digital soil mapping. Geoderma
**2016**, 265, 62–77. [Google Scholar] [CrossRef] - Singh, A. Soil salinization and waterlogging: A threat to environment and agricultural sustainability. Ecol. Indic.
**2015**, 57, 128–130. [Google Scholar] [CrossRef] - Mitran, T.; Ravisankar, T.; Fyzee, M.; Suresh, J.R.; Sujatha, G.; Sreenivas, K. Retrieval of soil physicochemical properties towards assessing salt-affected soils using Hyperspectral Data. Geocarto Int.
**2015**, 30, 701–721. [Google Scholar] [CrossRef] - Zhang, X.; Huang, B. Prediction of soil salinity with soil-reflected spectra: A comparison of two regression methods. Sci. Rep.
**2019**, 9, 5067. [Google Scholar] [CrossRef] [Green Version] - Wang, Z.; Zhang, X.; Zhang, F.; Chan, N.W.; Kung, H.-T.; Liu, S.; Deng, L. Estimation of soil salt content using machine learning techniques based on remote-sensing fractional derivatives, a case study in the Ebinur Lake Wetland National Nature Reserve, Northwest China. Ecol. Indic.
**2020**, 119, 106869. [Google Scholar] [CrossRef] - Wang, J.; Li, X. Comparison on quantitative inversion of characteristic ions in salinized soils with hyperspectral based on support vector regression and partial least squares regression. Eur. J. Remote Sens.
**2020**, 53, 340–348. [Google Scholar] [CrossRef] - Chang, C.-W.; Laird, D.A.; Hurburgh, C.R. influence of soil moisture on near-infrared reflectance spectroscopic measurement of soil properties. Soil Sci.
**2005**, 170, 244–255. [Google Scholar] [CrossRef] [Green Version] - Ben-Dor, E.; Patkin, K.; Banin, A.; Karnieli, A. Mapping of several soil properties using DAIS-7915 hyperspectral scanner data—A case study over clayey soils in Israel. Int. J. Remote Sens.
**2002**, 23, 1043–1062. [Google Scholar] [CrossRef] - Ganjegunte, G.K.; Sheng, Z.; Clark, J.A. soil salinity and sodicity appraisal by electromagnetic induction in soils irrigated to grow cotton. Land Degrad. Dev.
**2012**, 25, 228–235. [Google Scholar] [CrossRef] - Pessoa, L.G.M.; Dos Santos Freire, M.B.G.; Wilcox, B.P.; Green, C.H.M.; De Araújo, R.J.T.; De Araújo Filho, J.C. Spectral reflectance characteristics of soils in northeastern Brazil as influenced by salinity levels. Environ. Monit. Assess.
**2016**, 188, 616. [Google Scholar] [CrossRef] [PubMed] - Musick, H.B.; Pelletier, R.E. Response to soil moisture of spectral indexes derived from bidirectional reflectance in thematic mapper wavebands. Remote Sens. Environ.
**1988**, 25, 167–184. [Google Scholar] [CrossRef] - Liu, W.D.; Baret, F.; Gu, X.F.; Tong, Q.; Zheng, L.F.; Zhang, B. Relating soil surface moisture to reflectance. Remote Sens Environ.
**2002**, 81, 238–246. [Google Scholar] - Metternicht, G.I.; Zinck, J.A. Remote sensing of soil salinity: Potentials and constraints. Remote Sens. Environ.
**2003**, 85, 1–20. [Google Scholar] [CrossRef] - Wang, Q.; Li, P.; Chen, X. Modeling salinity effects on soil reflectance under various moisture conditions and its inverse application: A laboratory experiment. Geoderma
**2012**, 170, 103–111. [Google Scholar] [CrossRef] - Bartholomeus, H.; Schaepman, M.; Kooistra, L.; Stevens, A.; Hoogmoed, W.; Spaargaren, O. Spectral reflectance based indices for soil organic carbon quantification. Geoderma
**2008**, 145, 28–36. [Google Scholar] [CrossRef] - Wang, Y.P.; Lee, C.K.; Dai, Y.H.; Shen, Y. Effect of wetting on the determination of soil organic matter content using visible and near-infrared spectrometer. Geoderma
**2020**, 376, 114528. [Google Scholar] [CrossRef] - Haubrock, S.-N.; Chabrillat, S.; Lemmnitz, C.; Kaufmann, H. Surface soil moisture quantification models from reflectance data under field conditions. Int. J. Remote Sens.
**2008**, 29, 3–29. [Google Scholar] [CrossRef] - Lesaignoux, A.; Fabre, S.; Briottet, X. Influence of soil moisture content on spectral reflectance of bare soils in the 0.4–14 μm domain. Int. J. Remote Sens.
**2012**, 34, 2268–2285. [Google Scholar] [CrossRef] - Baumgardner, M.F.; Silva, L.F.; Biehl, L.L.; Stoner, E.R. Reflectance Properties of Soils. Adv. Agron.
**1986**, 38, 1–44. [Google Scholar] [CrossRef] - Lobell, D.B.; Asner, G.P. Moisture effects on soil reflectance. Soil Sci. Soc. Am. J.
**2002**, 66, 722–727. [Google Scholar] [CrossRef] - Anderson, K.; Croft, H. Remote sensing of soil surface properties. Prog. Phys. Geogr. Earth Environ.
**2009**, 33, 457–473. [Google Scholar] [CrossRef] - Bablet, A.; Vu, P.; Jacquemoud, S.; Viallefont-Robinet, F.; Fabre, S.; Briottet, X.; Sadeghi, M.; Whiting, M.; Baret, F.; Tian, J. MARMIT: A multilayer radiative transfer model of soil reflectance to estimate surface soil moisture content in the solar domain (400–2500 nm). Remote Sens. Environ.
**2018**, 217, 1–17. [Google Scholar] [CrossRef] [Green Version] - Liu, H.-J.; Zhang, Y.-Z.; Zhang, X.-L.; Zhang, B.; Song, K.-S.; Wang, Z.-M.; Tang, N. Quantitative Analysis of Moisture Effect on Black Soil Reflectance. Pedosphere
**2009**, 19, 532–540. [Google Scholar] [CrossRef] - Wang, X.; Dou, X.; Zhang, X.; Liu, H.; Li, H.; Meng, X. Development of soil spectral allocation models considering the effect of soil moisture. Soil Tillage Res.
**2019**, 195, 104374. [Google Scholar] [CrossRef] - Muller, E.; Décamps, H. Modeling soil moisture–reflectance. Remote Sens Environ.
**2001**, 76, 173–180. [Google Scholar] [CrossRef] [Green Version] - Hapke, B. Bidirectional Reflectance Spectroscopy: 5. The Coherent Backscatter Opposition Effect and Anisotropic Scattering. Icarus
**2002**, 157, 523–534. [Google Scholar] [CrossRef] [Green Version] - Zhang, Y.; Tan, K.; Wang, X.; Chen, Y. Retrieval of Soil Moisture Content Based on a Modified Hapke Photometric Model: A Novel Method Applied to Laboratory Hyperspectral and Sentinel-2 MSI Data. Remote Sens.
**2020**, 12, 2239. [Google Scholar] [CrossRef] - Yuan, J.; Wang, X.; Yan, C.-X.; Wang, S.-R.; Ju, X.-P.; Li, Y. Soil Moisture Retrieval Model for Remote Sensing Using Reflected Hyperspectral Information. Remote Sens.
**2019**, 11, 366. [Google Scholar] [CrossRef] [Green Version] - Vargas, W.E.; Niklasson, G. Applicability conditions of the Kubelka–Munk theory. Appl. Opt.
**1997**, 36, 5580–5586. [Google Scholar] [CrossRef] - Yang, X.; Yu, Y. Estimating Soil Salinity Under Various Moisture Conditions: An Experimental Study. IEEE Trans. Geosci. Remote Sens.
**2017**, 55, 2525–2533. [Google Scholar] [CrossRef] - Bannari, A.; Musa, N.H.M.; Abuelgasim, A.; El-Battay, A. Sentinel-MSI and Landsat-OLI Data Quality Characterization for High Temporal Frequency Monitoring of Soil Salinity Dynamic in an Arid Landscape. IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens.
**2020**, 13, 2434–2450. [Google Scholar] [CrossRef] - Wang, J.; Peng, J.; Li, H.; Yin, C.; Liu, W.; Wang, T.; Zhang, H. Soil Salinity Mapping Using Machine Learning Algorithms with the Sentinel-2 MSI in Arid Areas, China. Remote Sens.
**2021**, 13, 305. [Google Scholar] [CrossRef] - Rao, B.R.M.; Sharma, R.C.; Sankar, T.R.; Das, S.; Dwivedi, R.S.; Thammappa, S.S.; Venkataratnam, L. Spectral behavior of salt-affected soils. Int. J. Remote Sens.
**1995**, 16, 2125–2136. [Google Scholar] [CrossRef] - Mirzaei, S.; Boloorani, A.D.; Bahrami, H.A.; Alavipanah, S.K.; Mousivand, A.; Mouazen, A.M. Minimising the effect of moisture on soil property prediction accuracy using external parameter orthogonalization. Soil Tillage Res.
**2021**, 215, 105225. [Google Scholar] [CrossRef] - Xu, C.; Zeng, W.; Huang, J.; Wu, J.; Van Leeuwen, W.J. Prediction of Soil Moisture Content and Soil Salt Concentration from Hyperspectral Laboratory and Field Data. Remote Sens.
**2016**, 8, 42. [Google Scholar] [CrossRef] [Green Version] - Mashimbye, Z.; Cho, M.; Nell, J.; DE Clercq, W.; VAN Niekerk, A.; Turner, D. Model-Based Integrated Methods for Quantitative Estimation of Soil Salinity from Hyperspectral Remote Sensing Data: A Case Study of Selected South African Soils. Pedosphere
**2012**, 22, 640–649. [Google Scholar] [CrossRef] - Jiang, H.; Rusuli, Y.; Amuti, T.; He, Q. Quantitative assessment of soil salinity using multi-source remote sensing data based on the support vector machine and artificial neural network. Int. J. Remote Sens.
**2018**, 40, 284–306. [Google Scholar] [CrossRef] - Hu, J.; Peng, J.; Zhou, Y.; Xu, D.; Zhao, R.; Jiang, Q.; Fu, T.; Wang, F.; Shi, Z. Quantitative Estimation of Soil Salinity Using UAV-Borne Hyperspectral and Satellite Multispectral Images. Remote Sens.
**2019**, 11, 736. [Google Scholar] [CrossRef] [Green Version] - Roberts, J.; Cozzolino, D. Wet or dry? The effect of sample characteristics on the determination of soil properties by near infrared spectroscopy. TrAC Trends Anal. Chem.
**2016**, 83, 25–30. [Google Scholar] [CrossRef] - Farifteh, J.; Van der Meer, F.; Atzberger, C.; Carranza, E. Quantitative analysis of salt-affected soil reflectance spectra: A comparison of two adaptive methods (PLSR and ANN). Remote Sens. Environ.
**2007**, 110, 59–78. [Google Scholar] [CrossRef] - Moreira, L.C.J.; Teixeira, A.D.S.; Galvao, L. Laboratory Salinization of Brazilian Alluvial Soils and the Spectral Effects of Gypsum. Remote Sens.
**2014**, 6, 2647–2663. [Google Scholar] [CrossRef] [Green Version] - Xia, K.; Xia, S.; Shen, Q.; Yang, B.; Song, Q.; Xu, Y.; Zhang, S.; Zhou, X.; Zhou, Y. Moisture spectral characteristics and hyperspectral inversion of fly ash-filled reconstructed soil. Spectrochim. Acta Part A Mol. Biomol. Spectrosc.
**2021**, 253, 119590. [Google Scholar] [CrossRef] [PubMed] - Minasny, B.; McBratney, A.B.; Bellon-Maurel, V.; Roger, J.-M.; Gobrecht, A.; Ferrand, L.; Joalland, S. Removing the effect of soil moisture from NIR diffuse reflectance spectra for the prediction of soil organic carbon. Geoderma
**2011**, 167-168, 118–124. [Google Scholar] [CrossRef] [Green Version] - Liu, Y.; Deng, C.; Lu, Y.; Shen, Q.; Zhao, H.; Tao, Y.; Pan, X. Evaluating the characteristics of soil vis-NIR spectra after the removal of moisture effect using external parameter orthogonalization. Geoderma
**2020**, 376, 114568. [Google Scholar] [CrossRef] - Nawar, S.; Munnaf, M.A.; Mouazen, A.M. Machine Learning Based On-Line Prediction of Soil Organic Carbon after Removal of Soil Moisture Effect. Remote Sens.
**2020**, 12, 1308. [Google Scholar] [CrossRef] [Green Version] - Tan, Y.; Jiang, Q.; Yu, L.; Liu, H.; Zhang, B. Reducing the Moisture Effect and Improving the Prediction of Soil Organic Matter With VIS-NIR Spectroscopy in Black Soil Area. IEEE Access
**2021**, 9, 5895–5905. [Google Scholar] [CrossRef] - Ogen, Y.; Faigenbaum-Golovin, S.; Granot, A.; Shkolnisky, Y.; Goldshleger, N.; Ben-Dor, E. Removing Moisture Effect on Soil Reflectance Properties: A Case Study of Clay Content Prediction. Pedosphere
**2019**, 29, 421–431. [Google Scholar] [CrossRef] - Philips-Invernizzi, B.; Dupont, D.; Caze, C. Bibliographical review for reflectance of diffusing media. Opt. Eng.
**2001**, 40, 1082–1092. [Google Scholar] [CrossRef] - Farifteh, J. Interference of salt and moisture on soil reflectance spectra. Int. J. Remote Sens.
**2011**, 32, 8711–8724. [Google Scholar] [CrossRef] - Zhang, Z.T.; Du, R.Q.; Yang, S.; Yang, N.; Wei, G.F.; Yao, Z.H.; Qiu, Y.L. Effects of water-salt interaction on soil spectral characteristics in Hetao Irrigation Areas of Inner Mongolia, China. Trans. CSAE
**2020**, 36, 153–164. [Google Scholar] - Du, R.Q.; Chen, J.Y.; Zhang, Z.T.; Chen, Y.W.; He, Y.J.; Yin, H.Y. Simultaneous estimation of surface soil moisture and salinity during irrigation with the moisture-salinity-dependent spectral response model. Agric. Water Manag.
**2022**, 265, 107538. [Google Scholar] [CrossRef] - Qin, S.; Li, S.; Kang, S.; Du, T.; Tong, L.; Ding, R.; Wang, Y.; Guo, H. Transpiration of female and male parents of seed maize in northwest China. Agric. Water Manag.
**2018**, 213, 397–409. [Google Scholar] [CrossRef] - Zhao, Y.; Mao, X.; Shukla, M.K. A modified SWAP model for soil water and heat dynamics and seed–maize growth under film mulching. Agric. For. Meteorol.
**2020**, 292-293, 108127. [Google Scholar] [CrossRef] - Guo, H.; Li, S.; Wong, F.-L.; Qin, S.; Wang, Y.; Yang, D.; Lam, H.-M. Drivers of carbon flux in drip irrigation maize fields in northwest China. Carbon Balance Manag.
**2021**, 16, 12. [Google Scholar] [CrossRef] [PubMed] - Wang, Y.L.; Mao, X.M.; Chen, S.; Bo, L.Y. Experiments and simulation of soil moisture, temperature and salinity dynamics and oil sunflower growth in saline border irrigated farmland. Trans. CSAE
**2021**, 37, 76–86. [Google Scholar] - Lao, C.; Chen, J.; Zhang, Z.; Chen, Y.; Ma, Y.; Chen, H.; Gu, X.; Ning, J.; Jin, J.; Li, X. Predicting the contents of soil salt and major water-soluble ions with fractional-order derivative spectral indices and variable selection. Comput. Electron. Agric.
**2021**, 182, 106031. [Google Scholar] [CrossRef] - Wang, S.; Chen, Y.; Wang, M.; Zhao, Y.; Li, J. SPA-Based Methods for the Quantitative Estimation of the Soil Salt Content in Saline-Alkali Land from Field Spectroscopy Data: A Case Study from the Yellow River Irrigation Regions. Remote Sens.
**2019**, 11, 967. [Google Scholar] [CrossRef] [Green Version] - Chen, S.; Hu, T.; Luo, L.; He, Q.; Zhang, S.; Li, M.; Cui, X.; Li, H. Rapid estimation of leaf nitrogen content in apple-trees based on canopy hyperspectral reflectance using multivariate methods. Infrared Phys. Technol.
**2020**, 111, 103542. [Google Scholar] [CrossRef] - Whiting, M.L.; Li, L.; Ustin, S. Predicting water content using Gaussian model on soil spectra. Remote Sens. Environ.
**2004**, 89, 535–552. [Google Scholar] [CrossRef] - Somers, B.; Gysels, V.; Verstraeten, W.W.; Delalieux, S.; Coppin, P. Modelling moisture-induced soil reflectance changes in cultivated sandy soils: A case study in citrus orchards. Eur. J. Soil Sci.
**2010**, 61, 1091–1105. [Google Scholar] [CrossRef] - Zhang, T.T.; Zeng, S.-L.; Gao, Y.; Ouyang, Z.-T.; Li, B.; Fang, C.-M.; Zhao, B. Using hyperspectral vegetation indices as a proxy to monitor soil salinity. Ecol. Indic.
**2011**, 11, 1552–1562. [Google Scholar] [CrossRef] - Chen, H.; Zhao, G.; Sun, L.; Wang, R.; Liu, Y. Prediction of Soil Salinity Using Near-Infrared Reflectance Spectroscopy with Nonnegative Matrix Factorization. Appl. Spectrosc.
**2016**, 70, 1589–1597. [Google Scholar] [CrossRef] - Song, K.; Li, L.; Li, S.; Tedesco, L.; Hall, B.; Li, Z. Hyperspectral retrieval of phycocyanin in potable water sources using genetic algorithm–partial least squares (GA–PLS) modeling. Int. J. Appl. Earth Obs. Geoinf.
**2012**, 18, 368–385. [Google Scholar] [CrossRef] - Jin, J.; Wang, Q. Selection of Informative Spectral Bands for PLS Models to Estimate Foliar Chlorophyll Content Using Hyperspectral Reflectance. IEEE Trans. Geosci. Remote Sens.
**2018**, 57, 3064–3072. [Google Scholar] [CrossRef] - Chen, X.; Dong, Z.; Liu, J.; Wang, H.; Zhang, Y.; Chen, T.; Du, Y.; Shao, L.; Xie, J. Hyperspectral characteristics and quantitative analysis of leaf chlorophyll by reflectance spectroscopy based on a genetic algorithm in combination with partial least squares regression. Spectrochim. Acta Part A Mol. Biomol. Spectrosc.
**2020**, 243, 118786. [Google Scholar] [CrossRef] - Huang, S.; Zhang, H.; Pizurica, A. Subspace Clustering for Hyperspectral Images via Dictionary Learning With Adaptive Regularization. IEEE Trans. Geosci. Remote Sens.
**2021**, 60, 1–17. [Google Scholar] [CrossRef] - Lloyd, S.P. Least squares quantization in PCM. IEEE Trans. Inf. Theory
**1982**, 28, 129–137. [Google Scholar] [CrossRef] [Green Version] - Duan, L.; Xu, L.; Guo, F.; Lee, J.; Yan, B. A Local-Density Based Spatial Clustering Algorithm with Noise. Inf. Syst.
**2007**, 32, 978–986. [Google Scholar] [CrossRef]

**Figure 2.**Study framework. Note: RSR is raw reflectance spectra reflectance; SSREM is the soil spectral reflectance exponential model; MT is the moisture threshold; MT-SSREM is the modified model based on SSREM considering MT; FD is the first derivative of RSR; SD is the second derivative of RSR; MSC is the multiplicative scatter correction of RSR; SNV is the standard normal variate transform of RSR.

**Figure 4.**The distribution and correlation between each pair of four cation concentrations (g kg

^{−1}) in soil samples. Note: ** marks a significant correlation at a level of p < 0.01.

**Figure 5.**The relationship between SSC and spectral reflectance: (

**a**) variation of spectral reflectance of soil with SSC with SMC 0.11 g g

^{−1}; (

**b**) correlation analysis of SSC with reflectance and log(reflectance), respectively.

**Figure 6.**Variation of spectral reflectance of soils with SMC under three SSC conditions: (

**a**) SSC 0.15 dS m

^{−1}, (

**b**) SSC 0.50 dS m

^{−1}and (

**c**) SSC 1.6 dS m

^{−1}.

**Figure 7.**The correlation coefficients of five kinds of spectral data with SMC (

**a**–

**e**) and SSC (

**f**–

**j**) under different preprocessing methods. (

**a**,

**f**) raw spectral reflectance; (

**b**,

**g**) first derivative; (

**c**,

**h**) second derivative; (

**d**,

**i**) multiplicative scatter correction; (

**e**,

**j**) standard normal transformation.

**Figure 8.**Relationship between SMC and spectral reflectance: (

**a**) fitting R

^{2}of spectral reflectance and SMC by different functions; (

**b**) spectral reflectance variation with SMC at the wavelength 400 and 650 nm; (

**c**) MT value of each band.

**Figure 9.**Calibration results of parameters a, b and R

_{0}in the soil spectral reflectance exponential model: (

**a**) parameters a and b; (

**b**) R

_{0}.

**Figure 10.**Comparison of simulated reflectance based on SSREM with measured reflectance: (

**a**) simulation accuracy of calibration dataset; (

**b**) simulation accuracy of validation dataset; (

**c**–

**e**) measurement and simulation of wet-soil reflectance from calibration dataset and (

**f**–

**h**) from validation dataset.

**Figure 11.**Comparison of simulated reflectance based on MT-SSREM with measured reflectance: (

**a**) simulation accuracy of calibration dataset; (

**b**) simulation accuracy of validation dataset; (

**c**–

**e**) measurement and simulation of wet-soil reflectance from calibration dataset and (

**f**–

**h**) from validation dataset.

**Figure 12.**Performance of suggested bands to estimate SSC based on MT-SSREM and SSREM. (

**a**–

**t**) 658~660, 672~685, 938, 939 and 961 nm.

Properties | Mean | Standard Deviation (SD) | |
---|---|---|---|

Soil particle-size distribution (%) | Sand (2~0.05 mm) | 4.91 | 0.054 |

Silt (0.05~0.002 mm) | 36.54 | 0.13 | |

Clay (<0.002 mm) | 58.55 | 4.57 |

Calibration Dataset | Validation Dataset | ||
---|---|---|---|

n | 276 | 183 | |

SMC (g g^{−1}) | Max | 0.27 | 0.29 |

Min | 0.050 | 0.070 | |

Average | 0.10 | 0.12 | |

SD | 0.048 | 0.052 | |

SSC (dS m^{−1}) | Max | 2.84 | 3.29 |

Min | 0.10 | 0.095 | |

Average | 0.41 | 0.42 | |

SD | 0.43 | 0.50 |

R^{2} | Range | Mean | SD | Proportion (%) | ||
---|---|---|---|---|---|---|

≤0.53 | 0.53 < R^{2} < 0.75 | ≥0.75 | ||||

SSREM-cal | 0~0.98 | 0.75 | 0.28 | 18.48 | 11.59 | 69.93 |

SSREM-val | 0~0.98 | 0.77 | 0.24 | 14.21 | 14.75 | 71.04 |

MT-SSREM-cal | 0.53~0.98 | 0.92 | 0.062 | 0 | 2.17 | 97.83 |

MT-SSREM-val | 0.75~0.98 | 0.94 | 0.035 | 0 | 0 | 100 |

RMSE | Range | Mean | SD | Proportion (%) | ||

≤0.05 | 0.05 < RMSE < 0.1 | ≥0.1 | ||||

SSREM-cal | 0.014~0.23 | 0.081 | 0.039 | 26.09 | 46.01 | 27.90 |

SSREM-val | 0.018~0.22 | 0.079 | 0.037 | 25.68 | 47.54 | 26.78 |

MT-SSREM-cal | 0.014~0.16 | 0.069 | 0.034 | 36.96 | 43.84 | 19.20 |

MT-SSREM-val | 0.016~0.17 | 0.068 | 0.035 | 37.71 | 42.62 | 19.67 |

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**

Huang, X.; Bai, T.; Guan, H.; Wei, X.; Wang, Y.; Mao, X.
An Improved Exponential Model Considering a Spectrally Effective Moisture Threshold for Proximal Hyperspectral Reflectance Simulation and Soil Salinity Estimation. *Remote Sens.* **2022**, *14*, 6396.
https://doi.org/10.3390/rs14246396

**AMA Style**

Huang X, Bai T, Guan H, Wei X, Wang Y, Mao X.
An Improved Exponential Model Considering a Spectrally Effective Moisture Threshold for Proximal Hyperspectral Reflectance Simulation and Soil Salinity Estimation. *Remote Sensing*. 2022; 14(24):6396.
https://doi.org/10.3390/rs14246396

**Chicago/Turabian Style**

Huang, Xi, Tiecheng Bai, Huade Guan, Xiayong Wei, Yali Wang, and Xiaomin Mao.
2022. "An Improved Exponential Model Considering a Spectrally Effective Moisture Threshold for Proximal Hyperspectral Reflectance Simulation and Soil Salinity Estimation" *Remote Sensing* 14, no. 24: 6396.
https://doi.org/10.3390/rs14246396