# Inferring Grassland Drought Stress with Unsupervised Learning from Airborne Hyperspectral VNIR Imagery

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## Abstract

**:**

_{512}) demonstrates the value of combining imaging spectrometry and unsupervised learning for the monitoring of vegetation stress. It also shows the potential of archetypical reflectance spectra to be used for the remote estimation of photosynthetic efficiency. More conclusive results could be achieved by using vegetation measurements instead of proxy variables for evaluation. It must also be investigated how the method can be generalised across ecosystems.

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Site and Drought Status

#### 2.2. Airborne Data

#### 2.3. Geophysical Data

^{232}Th were measured using a portable gamma ray spectrometer from GF instruments. All of the sensors were attached to sledges and pulled over the research site with GPS positioning to measure apparent electrical conductivity (ECa) and nuclide concentrations [55].

#### 2.4. Unsupervised Classification with Simplex Volume Maximisation

**W**. When compared to solving the quadratic optimisation problem as proposed by Cutler and Breiman [60] in their work on Archetypal Analysis, this approximation is computationally more efficient, and it minimizes the residual of

**H**while preserving convexity: For ${h}_{i}={h}_{1},\dots ,{h}_{k},\phantom{\rule{0.277778em}{0ex}}{h}_{ij}\ge 0$ and ${\sum}_{i}{h}_{ij}=1$. The number of archetypes should be low enough to enable generalisation, but also high enough to cover a range of different extreme reflectance signatures. In this study, the number of archetypes was set to 30. To develop a qualitative classification of grassland stress levels from the latent components, the reflectance signatures in

**W**were classified into three categories. Some archetypes resembled the spectra of healthy plants, others showed signs of stress, and a third group comprised spectra of non-vegetated pixels (background). The classification of archetypes was based on the results of field and lab experiments [63,64,65,66,67,68], visual assessment of archetype maps, and expert knowledge.

**H**provide a measure of similarity between any input pixel and the archetypical reflectance spectra in

**W**[26]. Therefore, all of the data points in

**X**can be viewed as draws from a specific Dirichlet distribution. This distribution is often used for proportional data and it has the advantage of imposing the convexity constraint on the coefficients in

**H**[61]. The Dirichlet has one parameter $\alpha $, which is a k-dimensional vector and it can be estimated with a maximum-likelihood approach as described by Minka [69]. The Dirichlet has a useful aggregation property that allows to merge parts of the sample space. For example, if one tosses a six-sided dice, then the probability of all rollable numbers can be described by $Dir({\alpha}_{1},\dots ,{\alpha}_{6})$. Now, if the goal is to obtain the probability of rolling odd and even numbers, the aggregated (two-event) sample space still follows a Dirichlet distribution with aggregated parameter $Dir({\alpha}_{1}+{\alpha}_{3}+{\alpha}_{5},{\alpha}_{2}+{\alpha}_{4}+{\alpha}_{6})$ [70]. In the same manner, archetypes were lumped together according to their category, “healthy”, “stressed”, or “background”. This allowed creating maps of drought stress by summarizing coefficient values of healthy, stressed, and background archetypes, which are abbreviated as $\zeta ,\nu $ and $\xi $ below. Each resulting aggregated archetype is still beta-distributed. Factorisation was performed with the pymf module (v0.3) [71].

#### 2.5. Evaluation with Spectral Indices and Geophysical Measurements

_{REopt}and Car

_{REopt}are used as proxies for vegetation chlorophyll (C

_{ab}) and carotenoid content (C

_{xc}). The indices were developed by Féret et al. [24] using statistical models and model inversion on a large number of experimental and synthetic datasets in order to integrate variability between species. The red edge normalised difference vegetation index (RENDVI) was used to include an established chlorophyll-related vegetation index. The index is applicable for a broad range of species and it does not saturate for high-chlorophyll cases like dense canopies [73].

_{xc}/C

_{ab}ratio [77,78,79] and is, therefore, correlated with seasonal variations in net CO

_{2}uptake [80]. Plant stress results in an increase of the C

_{xc}/C

_{ab}ratio and a decrease of photosynthetic LUE, which makes PRI well-suited for water stress detection. When compared to the original formulation, the PRI

_{512}developed by Hernández-Clemente et al. [75] is less sensitive to structural effects. We assume the former index to have very similar proxy capabilities because the PRI

_{512}has the same diagnostic band as the PRI.

_{ab}concentrations, and it has performed well when applied to grasslands for LAI estimation [83]. The improved modified soil-adjusted vegetation index (MSAVI2) [84] was included in the analysis to account for potential soil effects. It has been applied for LAI estimation and drought detection on different grassland sites [85,86]. Because MSAVI2 is a broadband index, it was calculated from the hyperspectral data based on Sentinel-2 band specifications.

**Table 3.**List of vegetation indices used for evaluation of the SiVM-based stress level estimates ($\rho $ denotes reflectance at a specific wavelength or wavelength range).

Index Name | Abbr. | Equation | Ref. |
---|---|---|---|

Opt. chlorophyll red edge index | Chl_{RE opt} | $({{\rho}_{680-730}}^{-1}-{{\rho}_{780-800}}^{-1})\times {\rho}_{755-780}$ | [24] |

Opt. carotenoid red edge index | Car_{RE opt} | $({{\rho}_{510-530}}^{-1}-{{\rho}_{680-730}}^{-1})\times {\rho}_{760-780}$ | [24] |

Red edge normalised difference vegetation index | RENDVI | $({\rho}_{750}-{\rho}_{705})/({\rho}_{750}+{\rho}_{705})$ | [73] |

Photochemical reflectance index 512 | PRI_{512} | $({\rho}_{531}-{\rho}_{512})/({\rho}_{531}+{\rho}_{512})$ | [75] |

Carter index 2 | CTR2 | ${\rho}_{695}/{\rho}_{760}$ | [81] |

Modified chlorophyll absorption ratio index 2 | MCARI2 | $\frac{1.5[2.5({\rho}_{800}-{\rho}_{670})-1.3({\rho}_{800}-{\rho}_{550})]}{\sqrt{{(2{\rho}_{800}+1)}^{2}-(6{\rho}_{800}-5\sqrt{{\rho}_{670}})-0.5}}$ | [82] |

Modified soil-adjusted vegetation index 2 | MSAVI2 | $\frac{(2{\rho}_{NIR}^{}+1-\sqrt{{(2{\rho}_{NIR}^{}+1)}^{2}-8({\rho}_{NIR}^{}-{\rho}_{RED}^{})})}{2}$ | [84] |

Water band index | WBI | ${\rho}_{900}/{\rho}_{970}$ | [87] |

First derivative @ 950.6 nm | - | ${f}^{\prime}\left({\rho}_{950.6}\right)$ | [90] |

#### 2.6. Statistical Inference

**X**and variance inflation factors (VIF) were used as criteria to determine collinearity among predictor variables. The objective of the statistical inference was to determine those variables (and, hence, plant traits) that most strongly influence the stress signal of the DE-GsB grassland site.

**X**is fitted to the gradient vector per weak learner [103]. In each boosting iteration, the model is updated with the best-performing weak learner, which leads to a strictly additive structure [99]. For boosted beta regression, a weak learner will typically be a method, like univariate linear regression, penalised regression splines, or ridge regression. Because all of the distribution parameters are estimated, the algorithm constructs a distinct additive predictor for each distribution parameter by component-wise updates of separate prediction functions per iteration. Optimizing beta regression with gamboostLSS can be written as

## 3. Results

#### 3.1. Drought Status

#### 3.2. Archetypes and Stress Maps

#### 3.3. Correlation Analysis

_{ab}content and plant vitality is positively correlated with $\zeta $. Likewise, the two optimised pigment indices Chl

_{REopt}and Car

_{REopt}point to higher pigment concentrations in less stressed vegetation, with Car

_{REopt}exhibiting the strongest correlation of all evaluation variables ($r=0.89,p0.001$). Of the two vegetation indices that are related to structural traits, the MCARI2 exhibited slightly higher correlation values than the MSAVI2. The results indicate a larger photosynthetically active leaf area in vegetation with higher $\zeta $ values, as expected. The RWC-related spectral indices WBI and ${f}^{\prime}\left({\rho}_{950.6}\right)$ lead to very similar results and suggest a good level of agreement between the latent variable-based stress index and plant water content.

#### 3.4. Boosted Beta Regression

_{512}, which had a VIF of 6.8 (see Table 4). While Car

_{REopt}had a VIF of 19, all other vegetation index VIF values were in the range of 73–216, which indicates severe multicollinearity. The rest of the predictor variables exhibited substantially lower VIF values.

_{REopt}is the most important predictor with the highest $\mu $ coefficient value in all models. Thus, increased C

_{xc}is associated with an increased probability of observing a healthy pixel. The same applies to higher PRI

_{512}values in FM $\mu $. This dependency is much weaker in the subset models M18 $\mu $ and M19 $\mu $. Increased WBI values are associated with less vegetation stress in all models, with weaker relationships in the subset models. WBI and ${f}^{\prime}\left({\rho}_{950.6}\right)$ had been almost perfectly collinear ($r=-0.98$) in the correlation analysis, so that the effect of the derivative reflectance did not contribute to FM $\mu $. The situation is less clear in the subset models where both of the predictors that are related to relative water content contribute to the regression, although ${f}^{\prime}\left({\rho}_{950.6}\right)$ has relatively small coefficient values. In contrast to the results of the correlation analysis, the coefficients for Chl

_{REopt}and MSAVI2 are negative in M18 $\mu $ and M19 $\mu $. e.g., MSAVI2 is related to green LAI, but a correspondence of lower LAI and healthier vegetation is implausible. The inclusion of collinear variables induces instability in the model and it can result in erratic coefficient estimation. We assume this to be the case for Chl

_{REopt}and MSAVI2, as both are highly correlated with Car

_{REopt}. In the subset models, MSAVI2 shows small, negative coefficient values, while the picture is not clear for Chl

_{REopt}. In conclusion, the strongest predictors in the full model are linked to carotenoids (Car

_{REopt}, PRI

_{512}), LAI (MSAVI2), and water content (WBI). The subset $\mu $ models contain three main predictors: Car

_{REopt}, Chl

_{REopt}, and WBI. The difference is especially large for the PRI

_{512}which is only relevant in the FM $\mu $. Coefficients for M19 $\mu $ are generally smaller, probably due to the prevalence of stressed vegetation and, hence, the smaller range of stress values in the 2019 dataset.

_{REopt}is the most relevant predictor in two out of three $\varphi $ models. $\varphi $ is a precision parameter and, therefore, vegetation with higher Car

_{REopt}values is associated with a larger variance of y. In contrast to the $\mu $ models, CTR2 was an important predictor in every $\varphi $ model. Likewise, the DEM and geophysical variables have small, mostly negative coefficients in the precision models, with the EM38 measurements being the most relevant. However, in this study, focus was on the location parameter $\mu $.

## 4. Discussion

#### 4.1. Archetype Classification

#### 4.2. Importance of Variables

_{REopt}(proxy for C

_{xc}), PRI

_{512}(proxy for C

_{xc}/C

_{ab}ratio and LUE) and WBI (proxy for RWC). For assessing the severity of vegetation stress, pigment-related indices Chl

_{REopt}, Car

_{REopt}, and PRI

_{512}are important. Carotenoids serve multiple purposes in plant physiology, playing an important role in capturing light energy as well as dissipating excess energy [114]. Because they protect the plants’ photosystems from damage, e.g., counteracting different forms of reactive oxygen species, increases in C

_{xc}are usually observed under severe stress conditions [115]. Therefore, we expected an increase in Car

_{REopt}(and hence C

_{xc}) in stressed vegetation, but the lower Car

_{REopt}values in the 2019 dataset imply only moderate stress conditions. However, one would expect C

_{ab}to decrease faster than total C

_{xc}[73,116] under stress conditions. Such an increase in the C

_{xc}/C

_{ab}ratio would manifest in a tendency towards lower PRI values [78]. In fact, the strong positive correlation of $\zeta $ and PRI

_{512}suggests an increase in the C

_{xc}/C

_{ab}ratio following the drought period.

_{REopt}and Car

_{REopt}(see Figure 6). We assume a close correlation of C

_{ab}and C

_{xc}as long as plants are not severely stressed [122], even though Car

_{REopt}is the vegetation index that shows the closest agreement with $\zeta $ values. PRI

_{512}is the predictor variable with the smallest VIF value in multicollinearity testing and it is an important variable in the full $\mu $ model. However, it was quite irrelevant in the subset models. This demonstrates that the PRI

_{512}tracked “long-term” stress responses of the grassland site, but it is less related to the within-image stress gradient. We reason that the PRI

_{512}contributed most unique information to the estimation procedure. The importance of this spectral trait constitutes a possible link between the latent variable model and photosynthesis.

#### 4.3. Potential of SiVM for Vegetation Monitoring

_{REopt}and PRI

_{512}, additional campaigns to collect imagery of severely stressed grassland would be required to confirm the results. This illustrates a restriction of SiVM-based stress detection that does not result in a standardised, quantitative measurement of stress, but generates a qualitative classification of stress levels occuring in the input datasets. Hyperspectral reference datasets of extreme environmental conditions can be included in an analysis to address this issue.

## 5. Conclusions

_{REopt}had the highest correlation with computed vegetation stress levels ($r=0.89$, $p<0.001$). This proxy for carotenoid content indicates higher carotenoid levels in healthier vegetation. In contrast to our expectations, Car

_{REopt}values in the 2019 dataset decreased, which suggested a C

_{xc}reduction. This shows that neither prolonged water stress during 2018 nor the re-emering drought in spring 2019 had a lasting or severe impact on vegetation health at DE-GsB. Immediately after an intensive heat and drought event, like the summer 2018 drought, increased C

_{xc}values would most likely have been observable. However, a validation with direct vegetation measurements would have generated more reliable results.

_{512}, the second carotenoid-related index, is closely related to the unsupervised stress classification in the interannual full model and it shows comparably low multicollinearity with other evaluation variables. Likewise, covariation between PRI and carbon uptake of plants has been found in a number of studies [74,80,134]. These results suggest that a relationship between the SiVM-based stress classification and photosynthetic efficiency exists. Thus, the methodology could possibly be used for the estimation of carbon fluxes based on hyperspectral data. Further research on the issue would require local hyperspectral data of high temporal resolution in combination with eddy covariance measurements to enable the calibration of remotely sensed flux estimates [25]. Local scale optical sensors are less dependent on favorable atmospheric conditions than satellites and enable continuous measurements. If carbon flux estimation with SiVM proves to be practical at the local scale, transfer to satellite scale could be considered for large-scale productivity monitoring.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

C_{ab} | Chlorophyll content |

C_{xc} | Carotenoid content |

Car_{RE opt} | Optimised carotenoid red edge index |

Chl_{RE opt} | Optimised chlorophyll red edge index |

CRS | Coordinate reference system |

CTR2 | Carter index 2 |

DE-GsB | TERENO/ICOS site “Am Grossen Bruch” |

DEM | Digital elevation model |

DESIS | DLR Earth Sensing Imaging System Spectrometers |

ECa | Apparent electrical conductivity |

EMI | Electromagnetic induction |

EnMAP | Environmental Mapping and Analysis Program |

FM | Full model |

GAM | Generalised additive model |

GAMLSS | Generalised additive models for location, scale and shape |

GR | Gamma ray |

ICOS | Integrated Carbon Observation System Research Infrastructure |

LAI | Leaf area index |

LUE | Light use efficiency |

MCARI2 | Modified chlorophyll absorption ratio index 2 |

MSAVI2 | Modified soil-adjusted vegetation index 2 |

NDVI | Normalised difference vegetation index |

NIR | Near-infrared |

PRI | Photochemical reflectance index |

PRISMA | PRecursore IperSpettrale della Missione Applicativa |

RENDVI | Red edge normalised difference vegetation index |

RWC | Relative water content |

SiVM | Simplex volume maximisation |

SPEI | Standardised precipitation-evapotranspiration index |

SWC | Soil water content |

SWIR | Short-wavelength infrared |

TDR | Time-domain reflectometer |

TERENO | TERrestrial ENvironmental Observatories |

TIR | Thermal infrared |

UAV | Unmanned aerial vehicle |

VIF | Variance inflation factor |

VNIR | Visible and near-infrared |

WBI | Water band index |

## References

- Field, C.B.; Barros, V.; Stocker, T.F.; Qin, D.; Dokken, D.J.; Ebi, K.L.; Mastrandrea, M.D.; Mach, K.J.; Plattner, G.K.; Allen, S.K.; et al. Managing the Risks of Extreme Events and Disasters to Advance Climate Change Adaptation; A Special Report of Working Groups I and II of the Intergovernmental Panel on Climate Change; Cambridge University Press: Cambridge, UK, 2012. [Google Scholar]
- Spinoni, J.; Vogt, J.V.; Naumann, G.; Barbosa, P.; Dosio, A. Will Drought Events Become More Frequent and Severe in Europe? Int. J. Climatol.
**2018**, 38, 1718–1736. [Google Scholar] [CrossRef][Green Version] - Herring, S.C.; Christidis, N.; Hoell, A.; Hoerling, M.P.; Stott, P.A. Explaining Extreme Events of 2018 from a Climate Perspective. Bull. Am. Meteorol. Soc.
**2020**, 101, S1–S140. [Google Scholar] [CrossRef][Green Version] - Ionita, M.; Tallaksen, L.; Kingston, D.; Stagge, J.; Laaha, G.; Van Lanen, H.; Scholz, P.; Chelcea, S.; Haslinger, K. The European 2015 Drought from a Climatological Perspective. Hydrol. Earth Syst. Sci.
**2017**, 21, 1397–1419. [Google Scholar] [CrossRef][Green Version] - Hari, V.; Rakovec, O.; Markonis, Y.; Hanel, M.; Kumar, R. Increased Future Occurrences of the Exceptional 2018–2019 Central European Drought under Global Warming. Sci. Rep.
**2020**, 10, 1–10. [Google Scholar] [CrossRef] - Zscheischler, J.; Mahecha, M.D.; Von Buttlar, J.; Harmeling, S.; Jung, M.; Rammig, A.; Randerson, J.T.; Schölkopf, B.; Seneviratne, S.I.; Tomelleri, E. A Few Extreme Events Dominate Global Interannual Variability in Gross Primary Production. Environ. Res. Lett.
**2014**, 9, 035001. [Google Scholar] [CrossRef][Green Version] - Lowe, A.; Harrison, N.; French, A.P. Hyperspectral Image Analysis Techniques for the Detection and Classification of the Early Onset of Plant Disease and Stress. Plant Methods
**2017**, 13, 80. [Google Scholar] [CrossRef] - Guimarães, N.; Pádua, L.; Marques, P.; Silva, N.; Peres, E.; Sousa, J.J. Forestry Remote Sensing from Unmanned Aerial Vehicles: A Review Focusing on the Data, Processing and Potentialities. Remote Sens.
**2020**, 12, 1046. [Google Scholar] [CrossRef][Green Version] - Feld, C.K.; Sousa, J.P.; Da Silva, P.M.; Dawson, T.P. Indicators for Biodiversity and Ecosystem Services: Towards an Improved Framework for Ecosystems Assessment. Biodivers. Conserv.
**2010**, 19, 2895–2919. [Google Scholar] [CrossRef] - Lausch, A.; Bastian, O.; Klotz, S.; Leitão, P.J.; Jung, A.; Rocchini, D.; Schaepman, M.E.; Skidmore, A.K.; Tischendorf, L.; Knapp, S. Understanding and Assessing Vegetation Health by in Situ Species and Remote-Sensing Approaches. Methods Ecol. Evol.
**2018**, 9, 1799–1809. [Google Scholar] [CrossRef] - Schrodt, F.; Bailey, J.J.; Kissling, W.D.; Rijsdijk, K.F.; Seijmonsbergen, A.C.; van Ree, D.; Hjort, J.; Lawley, R.S.; Williams, C.N.; Anderson, M.G.; et al. Opinion: To Advance Sustainable Stewardship, We Must Document Not Only Biodiversity but Geodiversity. Proc. Natl. Acad. Sci. USA
**2019**, 116, 16155–16158. [Google Scholar] [CrossRef] [PubMed][Green Version] - Zhu, Z.; Wulder, M.A.; Roy, D.P.; Woodcock, C.E.; Hansen, M.C.; Radeloff, V.C.; Healey, S.P.; Schaaf, C.; Hostert, P.; Strobl, P.; et al. Benefits of the Free and Open Landsat Data Policy. Remote Sens. Environ.
**2019**, 224, 382–385. [Google Scholar] [CrossRef] - Vereecken, H.; Weihermüller, L.; Jonard, F.; Montzka, C. Characterization of Crop Canopies and Water Stress Related Phenomena Using Microwave Remote Sensing Methods: A Review. Vadose Zone J.
**2012**, 11, vzj2011.0138ra. [Google Scholar] [CrossRef] - Asner, G.P.; Brodrick, P.G.; Anderson, C.B.; Vaughn, N.; Knapp, D.E.; Martin, R.E. Progressive Forest Canopy Water Loss during the 2012–2015 California Drought. Proc. Natl. Acad. Sci. USA
**2016**, 113, E249–E255. [Google Scholar] [CrossRef][Green Version] - Chen, J.M.; Liu, J.; Leblanc, S.G.; Lacaze, R.; Roujean, J.L. Multi-Angular Optical Remote Sensing for Assessing Vegetation Structure and Carbon Absorption. Remote Sens. Environ.
**2003**, 84, 516–525. [Google Scholar] [CrossRef] - Vilfan, N.; Van der Tol, C.; Muller, O.; Rascher, U.; Verhoef, W. Fluspect-B: A Model for Leaf Fluorescence, Reflectance and Transmittance Spectra. Remote Sens. Environ.
**2016**, 186, 596–615. [Google Scholar] [CrossRef] - Schimel, D.; Pavlick, R.; Fisher, J.B.; Asner, G.P.; Saatchi, S.; Townsend, P.; Miller, C.; Frankenberg, C.; Hibbard, K.; Cox, P. Observing Terrestrial Ecosystems and the Carbon Cycle from Space. Glob. Chang. Biol.
**2015**, 21, 1762–1776. [Google Scholar] [CrossRef] - Martin, R.E.; Chadwick, K.D.; Brodrick, P.G.; Carranza-Jimenez, L.; Vaughn, N.R.; Asner, G.P. An Approach for Foliar Trait Retrieval from Airborne Imaging Spectroscopy of Tropical Forests. Remote Sens.
**2018**, 10, 199. [Google Scholar] [CrossRef] - Zhu, X.; Cai, F.; Tian, J.; Williams, T.K.A. Spatiotemporal Fusion of Multisource Remote Sensing Data: Literature Survey, Taxonomy, Principles, Applications, and Future Directions. Remote Sens.
**2018**, 10, 527. [Google Scholar] [CrossRef][Green Version] - Govender, M.; Govender, P.J.; Weiersbye, I.M.; Witkowski, E.T.F.; Ahmed, F. Review of Commonly Used Remote Sensing and Ground-Based Technologies to Measure Plant Water Stress. Water SA
**2009**, 35, 741–752. [Google Scholar] [CrossRef][Green Version] - Barton, C. Advances in Remote Sensing of Plant Stress. Plant Soil
**2012**, 354, 41–44. [Google Scholar] [CrossRef] - Hernández-Clemente, R.; Hornero, A.; Mottus, M.; Penuelas, J.; González-Dugo, V.; Jiménez, J.C.; Suárez, L.; Alonso, L.; Zarco-Tejada, P.J. Early Diagnosis of Vegetation Health from High-Resolution Hyperspectral and Thermal Imagery: Lessons Learned from Empirical Relationships and Radiative Transfer Modelling. Curr. For. Rep.
**2019**, 5, 169–183. [Google Scholar] [CrossRef][Green Version] - Jones, H.G.; Vaughan, R.A. Remote Sensing of Vegetation: Principles, Techniques, and Applications; Oxford University Press: New York, NY, USA, 2010. [Google Scholar]
- Féret, J.B.; François, C.; Gitelson, A.; Asner, G.P.; Barry, K.M.; Panigada, C.; Richardson, A.D.; Jacquemoud, S. Optimizing Spectral Indices and Chemometric Analysis of Leaf Chemical Properties Using Radiative Transfer Modeling. Remote Sens. Environ.
**2011**, 115, 2742–2750. [Google Scholar] [CrossRef][Green Version] - Garbulsky, M.F.; Peñuelas, J.; Gamon, J.; Inoue, Y.; Filella, I. The Photochemical Reflectance Index (PRI) and the Remote Sensing of Leaf, Canopy and Ecosystem Radiation Use Efficiencies: A Review and Meta-Analysis. Remote Sens. Environ.
**2011**, 115, 281–297. [Google Scholar] [CrossRef] - Römer, C.; Wahabzada, M.; Ballvora, A.; Pinto, F.; Rossini, M.; Panigada, C.; Behmann, J.; Léon, J.; Thurau, C.; Bauckhage, C.; et al. Early Drought Stress Detection in Cereals: Simplex Volume Maximisation for Hyperspectral Image Analysis. Funct. Plant Biol.
**2012**, 39, 878–890. [Google Scholar] [CrossRef] [PubMed] - Peerbhay, K.Y.; Mutanga, O.; Ismail, R. Random Forests Unsupervised Classification: The Detection and Mapping ofSolanum mauritianumInfestations in Plantation Forestry Using Hyperspectral Data. IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens.
**2015**, 8, 3107–3122. [Google Scholar] [CrossRef] - Behmann, J.; Steinrücken, J.; Plümer, L. Detection of Early Plant Stress Responses in Hyperspectral Images. ISPRS J. Photogramm. Remote Sens.
**2014**, 93, 98–111. [Google Scholar] [CrossRef] - Ceamanos, X.; Valero, S. Processing Hyperspectral Images. In Optical Remote Sensing of Land Surface, 1st ed.; Elsevier: Amsterdam, The Netherlands, 2016; pp. 163–200. [Google Scholar]
- Lee, D.D.; Seung, H.S. Learning the Parts of Objects by Non-Negative Matrix Factorization. Nature
**1999**, 401, 788–791. [Google Scholar] [CrossRef] - Pauca, V.P.; Shahnaz, F.; Berry, M.W.; Plemmons, R.J. Text Mining Using Non-Negative Matrix Factorizations. In Proceedings of the 2004 SIAM International Conference on Data Mining, Lake Buena Vista, FL, USA, 22–24 April 2004; pp. 452–456. [Google Scholar] [CrossRef]
- Li, Y.; Ngom, A. The Non-Negative Matrix Factorization Toolbox for Biological Data Mining. Source Code Biol. Med.
**2013**, 8, 10. [Google Scholar] [CrossRef] [PubMed][Green Version] - Lee, J.H.; Hashimoto, R.; Wible, C.G.; Yoo, S.S. Investigation of Spectrally Coherent Resting-State Networks Using Non-Negative Matrix Factorization for Functional MRI Data. Int. J. Imaging Syst. Technol.
**2011**, 21, 211–222. [Google Scholar] [CrossRef] - Ball, N.M.; Brunner, R.J. Data Mining and Machine Learning in Astronomy. Int. J. Mod. Phys. D
**2010**, 19, 1049–1106. [Google Scholar] [CrossRef][Green Version] - Jia, S.; Qian, Y. Constrained Nonnegative Matrix Factorization for Hyperspectral Unmixing. IEEE Trans. Geosci. Remote Sens.
**2008**, 47, 161–173. [Google Scholar] [CrossRef] - Gillis, N.; Plemmons, R.J. Dimensionality Reduction, Classification, and Spectral Mixture Analysis Using Non-Negative Underapproximation. Opt. Eng.
**2011**, 50, 027001. [Google Scholar] [CrossRef][Green Version] - Karoui, M.S.; Deville, Y.; Hosseini, S.; Ouamri, A.; Ducrot, D. Contribution of Non-Negative Matrix Factorization to the Classification of Remote Sensing Images. In Proceedings of the Image and Signal Processing for Remote Sensing XIV. International Society for Optics and Photonics, Cardiff, Wales, UK, 15–18 September 2008; Volume 7109, p. 71090X. [Google Scholar] [CrossRef]
- Huang, B.; Song, H.; Cui, H.; Peng, J.; Xu, Z. Spatial and Spectral Image Fusion Using Sparse Matrix Factorization. IEEE Trans. Geosci. Remote Sens.
**2013**, 52, 1693–1704. [Google Scholar] [CrossRef] - Danaher, S.; O’mongain, E. Singular Value Decomposition in Multispectral Radiometry. Int. J. Remote Sens.
**1992**, 13, 1771–1777. [Google Scholar] [CrossRef] - Thurau, C.; Kersting, K.; Bauckhage, C. Yes We Can: Simplex Volume Maximization for Descriptive Web-Scale Matrix Factorization. In Proceedings of the 19th ACM International Conference on Information and Knowledge Management, CIKM’10, Toronto, ON, Canada, 25–29 October 2010; Association for Computing Machinery: New York, NY, USA, 2010; pp. 1785–1788. [Google Scholar] [CrossRef]
- Vicente-Serrano, S.M.; Beguería, S.; López-Moreno, J.I. A Multiscalar Drought Index Sensitive to Global Warming: The Standardized Precipitation Evapotranspiration Index. J. Clim.
**2010**, 23, 1696–1718. [Google Scholar] [CrossRef][Green Version] - Wollschläger, U.; Attinger, S.; Borchardt, D.; Brauns, M.; Cuntz, M.; Dietrich, P.; Fleckenstein, J.H.; Friese, K.; Friesen, J.; Harpke, A. The Bode Hydrological Observatory: A Platform for Integrated, Interdisciplinary Hydro-Ecological Research within the TERENO Harz/Central German Lowland Observatory. Environ. Earth Sci.
**2017**, 76, 29. [Google Scholar] [CrossRef] - Zacharias, S.; Bogena, H.; Samaniego, L.; Mauder, M.; Fuß, R.; Pütz, T.; Frenzel, M.; Schwank, M.; Baessler, C.; Butterbach-Bahl, K.; et al. A Network of Terrestrial Environmental Observatories in Germany. Vadose Zone J.
**2011**, 10, 955–973. [Google Scholar] [CrossRef][Green Version] - Rebmann, C.; Aubinet, M.; Schmid, H.; Arriga, N.; Aurela, M.; Burba, G.; Clement, R.; De Ligne, A.; Fratini, G.; Gielen, B. ICOS Eddy Covariance Flux-Station Site Setup: A Review. Int. Agrophys.
**2018**, 32, 471–494. [Google Scholar] [CrossRef] - Bernhofer, C.; Goldberg, V.; Franke, J.; Surke, M.; Adam, J. Regionale Klimadiagnose für Sachsen-Anhalt, Abschlussbericht zum Forschungsvorhaben des Landesamtes für Umweltschutz Sachsen-Anhalt; Berichte des Landesamtes für Umweltschutz Sachsen-Anhalt; Technische Universität Dresden: Dresden, Germany, 2008; Volume 5. [Google Scholar]
- Beguería, S.; Vicente-Serrano, S.M.; Reig, F.; Latorre, B. Standardized Precipitation Evapotranspiration Index (SPEI) Revisited: Parameter Fitting, Evapotranspiration Models, Tools, Datasets and Drought Monitoring. Int. J. Climatol.
**2014**, 34, 3001–3023. [Google Scholar] [CrossRef][Green Version] - Vergni, L.; Todisco, F.; Mannocchi, F. Evaluating the Uncertainty and Reliability of Standardized Indices. Hydrol. Res.
**2017**, 48, 701–713. [Google Scholar] [CrossRef] - Zink, M.; Kumar, R.; Cuntz, M.; Samaniego, L. A High-Resolution Dataset of Water Fluxes and States for Germany Accounting for Parametric Uncertainty. Hydrol. Earth Syst. Sci.
**2017**, 21, 1769–1790. [Google Scholar] [CrossRef][Green Version] - Kumar, R.; Musuuza, J.L.; Loon, A.F.V.; Teuling, A.J.; Barthel, R.; Ten Broek, J.; Mai, J.; Samaniego, L.; Attinger, S. Multiscale Evaluation of the Standardized Precipitation Index as a Groundwater Drought Indicator. Hydrol. Earth Syst. Sci.
**2016**, 20, 1117–1131. [Google Scholar] [CrossRef][Green Version] - Schläpfer, D.; Richter, R. Geo-Atmospheric Processing of Airborne Imaging Spectrometry Data. Part 1: Parametric Orthorectification. Int. J. Remote Sens.
**2002**, 23, 2609–2630. [Google Scholar] [CrossRef] - Richter, R.; Schläpfer, D. Geo-Atmospheric Processing of Airborne Imaging Spectrometry Data. Part 2: Atmospheric/Topographic Correction. Int. J. Remote Sens.
**2002**, 23, 2631–2649. [Google Scholar] [CrossRef] - DWD Climate Data Center. Historical Hourly Weather Station Measurements of Visibility in Germany; Version v002; Deutscher Wetterdienst: Offenbach, Germany, 2019. [Google Scholar]
- Cai, S.; Du, Q.; Moorhead, R.J. Hyperspectral Imagery Visualization Using Double Layers. IEEE Trans. Geosci. Remote Sens.
**2007**, 45, 3028–3036. [Google Scholar] [CrossRef] - Cook, P.G.; Hughes, M.W.; Walker, G.R.; Allison, G.B. The Calibration of Frequency-Domain Electromagnetic Induction Meters and Their Possible Use in Recharge Studies. J. Hydrol.
**1989**, 107, 251–265. [Google Scholar] [CrossRef] - Lausch, A.; Zacharias, S.; Dierke, C.; Pause, M.; Kühn, I.; Doktor, D.; Dietrich, P.; Werban, U. Analysis of Vegetation and Soil Patterns Using Hyperspectral Remote Sensing, EMI, and Gamma-Ray Measurements. Vadose Zone J.
**2013**, 12, 1–15. [Google Scholar] [CrossRef] - Brogi, C.; Huisman, J.A.; Pätzold, S.; von Hebel, C.; Weihermüller, L.; Kaufmann, M.S.; van der Kruk, J.; Vereecken, H. Large-Scale Soil Mapping Using Multi-Configuration EMI and Supervised Image Classification. Geoderma
**2019**, 335, 133–148. [Google Scholar] [CrossRef] - Martini, E.; Werban, U.; Zacharias, S.; Pohle, M.; Dietrich, P.; Wollschläger, U. Repeated Electromagnetic Induction Measurements for Mapping Soil Moisture at the Field Scale: Validation with Data from a Wireless Soil Moisture Monitoring Network. Hydrol. Earth Syst. Sci.
**2017**, 21, 495. [Google Scholar] [CrossRef][Green Version] - Müller, S.; Schüler, L.; Zech, A.; Attinger, S.; Heße, F. GeoStat-Framework/GSTools: V1.2.1. Zenodo
**2020**. [Google Scholar] [CrossRef] - Ding, C.H.; Li, T.; Jordan, M.I. Convex and Semi-Nonnegative Matrix Factorizations. IEEE Trans. Pattern Anal. Mach. Intell.
**2008**, 32, 45–55. [Google Scholar] [CrossRef] [PubMed][Green Version] - Cutler, A.; Breiman, L. Archetypal Analysis. Technometrics
**1994**, 36, 338–347. [Google Scholar] [CrossRef] - Kersting, K.; Xu, Z.; Wahabzada, M.; Bauckhage, C.; Thurau, C.; Roemer, C.; Ballvora, A.; Rascher, U.; Leon, J.; Pluemer, L. Pre-Symptomatic Prediction of Plant Drought Stress Using Dirichlet-Aggregation Regression on Hyperspectral Images. In Proceedings of the 26th AAAI Conference on Artificial Intelligence (AAAI-12), Toronto, ON, Canada, 22–26 July 2012; AAAI Press: Toronto, ON, Canada, 2012; Volume 26, pp. 302–308. [Google Scholar] [CrossRef]
- Kersting, K.; Wahabzada, M.; Römer, C.; Thurau, C.; Ballvora, A.; Rascher, U.; Léon, J.; Bauckhage, C.; Plümer, L. Simplex Distributions for Embedding Data Matrices over Time. In Proceedings of the 2012 SIAM International Conference on Data Mining, Anaheim, CA, USA, 26–28 April 2012; pp. 295–306. [Google Scholar] [CrossRef][Green Version]
- Kim, Y.; Glenn, D.M.; Park, J.; Ngugi, H.K.; Lehman, B.L. Hyperspectral Image Analysis for Plant Stress Detection. In Proceedings of the 2010 ASABE Annual International Meeting, Pittsburgh, PA, USA, 20–23 June 2010; American Society of Agricultural and Biological Engineers: Pittsburgh, PA, USA, 2010; p. 1. [Google Scholar] [CrossRef]
- El-Hendawy, S.; Al-Suhaibani, N.; Hassan, W.; Tahir, M.; Schmidhalter, U. Hyperspectral Reflectance Sensing to Assess the Growth and Photosynthetic Properties of Wheat Cultivars Exposed to Different Irrigation Rates in an Irrigated Arid Region. PLoS ONE
**2017**, 12, e0183262. [Google Scholar] [CrossRef] [PubMed] - Carter, G.A. Responses of Leaf Spectral Reflectance to Plant Stress. Am. J. Bot.
**1993**, 80, 239–243. [Google Scholar] [CrossRef] - Bayat, B.; Van der Tol, C.; Verhoef, W. Remote Sensing of Grass Response to Drought Stress Using Spectroscopic Techniques and Canopy Reflectance Model Inversion. Remote Sens.
**2016**, 8, 557. [Google Scholar] [CrossRef][Green Version] - Aldakheel, Y.Y.; Danson, F.M. Spectral Reflectance of Dehydrating Leaves: Measurements and Modelling. Int. J. Remote Sens.
**1997**, 18, 3683–3690. [Google Scholar] [CrossRef] - 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] - Minka, T. Estimating a Dirichlet Distribution; Technical Report; MIT: Cambridge, MA, USA, 2000. [Google Scholar]
- Frigyik, B.A.; Kapila, A.; Gupta, M.R. Introduction to the Dirichlet Distribution and Related Processes; Technical Report; University of Washington: Washington, DC, USA, 2010. [Google Scholar]
- Thurau, C. Python Matrix Factorization Module. 2014. Available online: https://github.com/cthurau/pymf (accessed on 11 May 2021).
- Lausch, A.; Erasmi, S.; King, D.J.; Magdon, P.; Heurich, M. Understanding Forest Health with Remote Sensing, Part I: A Review of Spectral Traits, Processes and Remote-Sensing Characteristics. Remote Sens.
**2016**, 8, 1029. [Google Scholar] [CrossRef][Green Version] - Gitelson, A.; Merzlyak, M.N. Spectral Reflectance Changes Associated with Autumn Senescence of Aesculus Hippocastanum L. and Acer Platanoides L. Leaves. Spectral Features and Relation to Chlorophyll Estimation. J. Plant Physiol.
**1994**, 143, 286–292. [Google Scholar] [CrossRef] - Gamon, J.; Serrano, L.; Surfus, J.S. The Photochemical Reflectance Index: An Optical Indicator of Photosynthetic Radiation Use Efficiency across Species, Functional Types, and Nutrient Levels. Oecologia
**1997**, 112, 492–501. [Google Scholar] [CrossRef] - Hernández-Clemente, R.; Navarro-Cerrillo, R.M.; Suárez, L.; Morales, F.; Zarco-Tejada, P.J. Assessing Structural Effects on PRI for Stress Detection in Conifer Forests. Remote Sens. Environ.
**2011**, 115, 2360–2375. [Google Scholar] [CrossRef] - Zarco-Tejada, P.J.; González-Dugo, V.; Williams, L.E.; Suárez, L.; Berni, J.A.; Goldhamer, D.; Fereres, E. A PRI-Based Water Stress Index Combining Structural and Chlorophyll Effects: Assessment Using Diurnal Narrow-Band Airborne Imagery and the CWSI Thermal Index. Remote Sens. Environ.
**2013**, 138, 38–50. [Google Scholar] [CrossRef] - Ustin, S.L.; Roberts, D.A.; Gamon, J.A.; Asner, G.P.; Green, R.O. Using Imaging Spectroscopy to Study Ecosystem Processes and Properties. BioScience
**2004**, 54, 523–534. [Google Scholar] [CrossRef] - Filella, I.; Porcar-Castell, A.; Munné-Bosch, S.; Bäck, J.; Garbulsky, M.F.; Peñuelas, J. PRI Assessment of Long-Term Changes in Carotenoids/Chlorophyll Ratio and Short-Term Changes in de-Epoxidation State of the Xanthophyll Cycle. Int. J. Remote Sens.
**2009**, 30, 4443–4455. [Google Scholar] [CrossRef] - Garrity, S.R.; Eitel, J.U.; Vierling, L.A. Disentangling the Relationships between Plant Pigments and the Photochemical Reflectance Index Reveals a New Approach for Remote Estimation of Carotenoid Content. Remote Sens. Environ.
**2011**, 115, 628–635. [Google Scholar] [CrossRef] - Stylinski, C.; Gamon, J.; Oechel, W. Seasonal Patterns of Reflectance Indices, Carotenoid Pigments and Photosynthesis of Evergreen Chaparral Species. Oecologia
**2002**, 131, 366–374. [Google Scholar] [CrossRef] - Carter, G.A. Ratios of Leaf Reflectances in Narrow Wavebands as Indicators of Plant Stress. Remote Sens.
**1994**, 15, 697–703. [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] - Li, Z.; Guo, X. A Suitable Vegetation Index for Quantifying Temporal Variation of Leaf Area Index (LAI) in Semiarid Mixed Grassland. Can. J. Remote Sens.
**2010**, 36, 709–721. [Google Scholar] [CrossRef] - Qi, J.; Chehbouni, A.; Huete, A.R.; Kerr, Y.H.; Sorooshian, S. A Modified Soil Adjusted Vegetation Index. Remote Sens. Environ.
**1994**, 48, 119–126. [Google Scholar] [CrossRef] - Liu, Z.Y.; Huang, J.F.; Wu, X.H.; Dong, Y.P. Comparison of Vegetation Indices and Red-Edge Parameters for Estimating Grassland Cover from Canopy Reflectance Data. J. Integr. Plant Biol.
**2007**, 49, 299–306. [Google Scholar] [CrossRef] - Wu, Z.; Velasco, M.; McVay, J.; Middleton, B.; Vogel, J.; Dye, D. MODIS Derived Vegetation Index for Drought Detection on the San Carlos Apache Reservation. Int. J. Adv. Remote Sens. GIS
**2016**, 5, 1524–1538. [Google Scholar] [CrossRef][Green Version] - Penuelas, J.; Filella, I.; Serrano, L.; Save, R. Cell Wall Elasticity and Water Index (R970 Nm/R900 Nm) in Wheat under Different Nitrogen Availabilities. Int. J. Remote Sens.
**1996**, 17, 373–382. [Google Scholar] [CrossRef] - Peñuelas, J.; Inoue, Y. Reflectance Indices Indicative of Changes in Water and Pigment Contents of Peanut and Wheat Leaves. Photosynthetica
**1999**, 36, 355–360. [Google Scholar] [CrossRef] - Rollin, E.M.; Milton, E.J. Processing of High Spectral Resolution Reflectance Data for the Retrieval of Canopy Water Content Information. Remote Sens. Environ.
**1998**, 65, 86–92. [Google Scholar] [CrossRef] - Clevers, J.G.; Kooistra, L.; Schaepman, M.E. Using Spectral Information from the NIR Water Absorption Features for the Retrieval of Canopy Water Content. Int. J. Appl. Earth Obs. Geoinf.
**2008**, 10, 388–397. [Google Scholar] [CrossRef] - Savitzky, A.; Golay, M.J. Smoothing and Differentiation of Data by Simplified Least Squares Procedures. Anal. Chem.
**1964**, 36, 1627–1639. [Google Scholar] [CrossRef] - R Core Team. R: A Language and Environment for Statistical Computing; R Foundation for Statistical Computing: Vienna, Austria, 2020. [Google Scholar]
- Wei, T.; Simko, V. R Package “Corrplot”: Visualization of a Correlation Matrix. 2017. Available online: https://CRAN.R-project.org/package=corrplot (accessed on 11 May 2021).
- Ferrari, S.; Cribari-Neto, F. Beta Regression for Modelling Rates and Proportions. J. Appl. Stat.
**2004**, 31, 799–815. [Google Scholar] [CrossRef] - Cribari-Neto, F.; Zeileis, A. Beta Regression in R. J. Stat. Softw.
**2010**, 34, 1–24. [Google Scholar] [CrossRef][Green Version] - Imdadullah, M.; Aslam, M.; Altaf, S. Mctest: An R Package for Detection of Collinearity among Regressors. R. J.
**2016**, 8, 495–505. [Google Scholar] [CrossRef] - Dormann, C.F.; Elith, J.; Bacher, S.; Buchmann, C.; Carl, G.; Carré, G.; Marquéz, J.R.G.; Gruber, B.; Lafourcade, B.; Leitao, P.J. Collinearity: A Review of Methods to Deal with It and a Simulation Study Evaluating Their Performance. Ecography
**2013**, 36, 27–46. [Google Scholar] [CrossRef] - Friedman, J.H. Greedy Function Approximation: A Gradient Boosting Machine. Ann. Stat.
**2001**, 29, 1189–1232. [Google Scholar] [CrossRef] - Mayr, A.; Fenske, N.; Hofner, B.; Kneib, T.; Schmid, M. Generalized Additive Models for Location, Scale and Shape for High Dimensional Data—a Flexible Approach Based on Boosting. J. R. Stat. Soc. Ser. C (Appl. Stat.)
**2012**, 61, 403–427. [Google Scholar] [CrossRef][Green Version] - Stasinopoulos, M.; Rigby, B. Generalized Additive Models for Location Scale and Shape. J. R. Stat. Soc. Ser. C (Appl. Stat.)
**2005**, 54, 507–554. [Google Scholar] [CrossRef][Green Version] - Schmid, M.; Wickler, F.; Maloney, K.O.; Mitchell, R.; Fenske, N.; Mayr, A. Boosted Beta Regression. PLoS ONE
**2013**, 8, e61623. [Google Scholar] [CrossRef][Green Version] - Hastie, T.; Tibshirani, R. Generalized Additive Models; CRC Press: Boca Raton, FL, USA, 1990. [Google Scholar]
- Bühlmann, P.; Yu, B. Boosting with the L 2 Loss: Regression and Classification. J. Am. Stat. Assoc.
**2003**, 98, 324–339. [Google Scholar] [CrossRef] - Mayr, A.; Hofner, B.; Schmid, M. The Importance of Knowing When to Stop. Methods Inf. Med.
**2012**, 51, 178–186. [Google Scholar] [CrossRef][Green Version] - Hastie, T.; Tibshirani, R.; Friedman, J. The Elements of Statistical Learning: Data Mining, Inference, and Prediction; Springer Science & Business Media: New York, NY, USA, 2009. [Google Scholar]
- Bühlmann, P.; Gertheiss, J.; Hieke, S.; Kneib, T.; Ma, S.; Schumacher, M.; Tutz, G.; Wang, C.Y.; Wang, Z.; Ziegler, A. Discussion of “the Evolution of Boosting Algorithms” and “Extending Statistical Boosting”. Methods Inf. Med.
**2014**, 53, 436–445. [Google Scholar] [CrossRef] [PubMed] - Hofner, B.; Mayr, A.; Schmid, M. gamboostLSS: An R Package for Model Building and Variable Selection in the GAMLSS Framework. arXiv
**2014**, arXiv:1407.1774. [Google Scholar] [CrossRef][Green Version] - Knipling, E.B. Physical and Physiological Basis for the Reflectance of Visible and Near-Infrared Radiation from Vegetation. Remote Sens. Environ.
**1970**, 1, 155–159. [Google Scholar] [CrossRef] - Magnusson, M.; Sigurdsson, J.; Armannsson, S.; Ulfarsson, M.; Deborah, H.; Sveinsson, J. Creating RGB Images from Hyperspectral Images Using a Color Matching Function. In Proceedings of the 2020 IEEE International Geoscience and Remote Sensing Symposium (IGARSS), Waikoloa, HI, USA, 26 September–2 October 2020; pp. 2045–2048. [Google Scholar] [CrossRef]
- Caturegli, L.; Matteoli, S.; Gaetani, M.; Grossi, N.; Magni, S.; Minelli, A.; Corsini, G.; Remorini, D.; Volterrani, M. Effects of Water Stress on Spectral Reflectance of Bermudagrass. Sci. Rep.
**2020**, 10, 15055. [Google Scholar] [CrossRef] - Asner, G.P. Biophysical and Biochemical Sources of Variability in Canopy Reflectance. Remote Sens. Environ.
**1998**, 64, 234–253. [Google Scholar] [CrossRef] - Bilotta, G.S.; Brazier, R.E.; Haygarth, P.M. The Impacts of Grazing Animals on the Quality of Soils, Vegetation, and Surface Waters in Intensively Managed Grasslands. Adv. Agron.
**2007**, 94, 237–280. [Google Scholar] [CrossRef] - Nippert, J.B.; Holdo, R.M. Challenging the Maximum Rooting Depth Paradigm in Grasslands and Savannas. Funct. Ecol.
**2015**, 29, 739–745. [Google Scholar] [CrossRef] - Hallik, L.; Kazantsev, T.; Kuusk, A.; Galmés, J.; Tomás, M.; Niinemets, Ü. Generality of Relationships between Leaf Pigment Contents and Spectral Vegetation Indices in Mallorca (Spain). Reg. Environ. Chang.
**2017**, 17, 2097–2109. [Google Scholar] [CrossRef] - Sudrajat, D.J.; Siregar, I.Z.; Khumaida, N.; Siregar, U.J.; Mansur, I. Adaptability of White Jabon (Anthocephalus Cadamba MIQ.) Seedling from 12 Populations to Drought and Waterlogging. AGRIVITA J. Agric. Sci.
**2015**, 37, 130–143. [Google Scholar] [CrossRef] - Penuelas, J.; Baret, F.; Filella, I. Semi-Empirical Indices to Assess Carotenoids/Chlorophyll a Ratio from Leaf Spectral Reflectance. Photosynthetica
**1995**, 31, 221–230. [Google Scholar] - Knapp, A.K.; Carroll, C.J.W.; Denton, E.M.; La Pierre, K.J.; Collins, S.L.; Smith, M.D. Differential Sensitivity to Regional-Scale Drought in Six Central US Grasslands. Oecologia
**2015**, 177, 949–957. [Google Scholar] [CrossRef] [PubMed][Green Version] - Chen, J.; Li, F.; Wang, R.; Fan, Y.; Raza, M.A.; Liu, Q.; Wang, Z.; Cheng, Y.; Wu, X.; Yang, F.; et al. Estimation of Nitrogen and Carbon Content from Soybean Leaf Reflectance Spectra Using Wavelet Analysis under Shade Stress. Comput. Electron. Agric.
**2019**, 156, 482–489. [Google Scholar] [CrossRef] - Wold, S.; Ruhe, A.; Wold, H.; Dunn, W. The Collinearity Problem in Linear Regression. The Partial Least Squares (PLS) Approach to Generalized Inverses. SIAM J. Sci. Stat. Comput.
**1984**, 5, 735–743. [Google Scholar] [CrossRef][Green Version] - Tomaschek, F.; Hendrix, P.; Baayen, R.H. Strategies for Addressing Collinearity in Multivariate Linguistic Data. J. Phon.
**2018**, 71, 249–267. [Google Scholar] [CrossRef] - Tuv, E. Feature Selection with Ensembles, Artificial Variables, and Redundancy Elimination. J. Mach. Learn. Res.
**2009**, 10, 1341–1366. [Google Scholar] - Gitelson, A.A.; Keydan, G.P.; Merzlyak, M.N. Three-Band Model for Noninvasive Estimation of Chlorophyll, Carotenoids, and Anthocyanin Contents in Higher Plant Leaves. Geophys. Res. Lett.
**2006**, 33. [Google Scholar] [CrossRef][Green Version] - Uarrota, V.G.; Stefen, D.L.V.; Leolato, L.S.; Gindri, D.M.; Nerling, D. Revisiting Carotenoids and Their Role in Plant Stress Responses: From Biosynthesis to Plant Signaling Mechanisms during Stress. In Antioxidants and Antioxidant Enzymes in Higher Plants; Springer: Cham, Switzerland, 2018; pp. 207–232. [Google Scholar]
- Zhang, N.; Hong, Y.; Qin, Q.; Liu, L. VSDI: A Visible and Shortwave Infrared Drought Index for Monitoring Soil and Vegetation Moisture Based on Optical Remote Sensing. Int. J. Remote Sens.
**2013**, 34, 4585–4609. [Google Scholar] [CrossRef] - Raza, S.e.A.; Smith, H.K.; Clarkson, G.J.J.; Taylor, G.; Thompson, A.J.; Clarkson, J.; Rajpoot, N.M. Automatic Detection of Regions in Spinach Canopies Responding to Soil Moisture Deficit Using Combined Visible and Thermal Imagery. PLoS ONE
**2014**, 9, e97612. [Google Scholar] [CrossRef] [PubMed][Green Version] - Lausch, A.; Borg, E.; Bumberger, J.; Dietrich, P.; Heurich, M.; Huth, A.; Jung, A.; Klenke, R.; Knapp, S.; Mollenhauer, H. Understanding Forest Health with Remote Sensing, Part III: Requirements for a Scalable Multi-Source Forest Health Monitoring Network Based on Data Science Approaches. Remote Sens.
**2018**, 10, 1120. [Google Scholar] [CrossRef][Green Version] - Jawad, H.M.; Nordin, R.; Gharghan, S.K.; Jawad, A.M.; Ismail, M. Energy-Efficient Wireless Sensor Networks for Precision Agriculture: A Review. Sensors
**2017**, 17, 1781. [Google Scholar] [CrossRef][Green Version] - Kuska, M.; Wahabzada, M.; Leucker, M.; Dehne, H.W.; Kersting, K.; Oerke, E.C.; Steiner, U.; Mahlein, A.K. Hyperspectral Phenotyping on the Microscopic Scale: Towards Automated Characterization of Plant-Pathogen Interactions. Plant Methods
**2015**, 11, 28. [Google Scholar] [CrossRef][Green Version] - Alonso, K.; Bachmann, M.; Burch, K.; Carmona, E.; Cerra, D.; De los Reyes, R.; Dietrich, D.; Heiden, U.; Hölderlin, A.; Ickes, J. Data Products, Quality and Validation of the DLR Earth Sensing Imaging Spectrometer (DESIS). Sensors
**2019**, 19, 4471. [Google Scholar] [CrossRef][Green Version] - Loizzo, R.; Guarini, R.; Longo, F.; Scopa, T.; Formaro, R.; Facchinetti, C.; Varacalli, G. PRISMA: The Italian Hyperspectral Mission. In Proceedings of the IGARSS 2018-2018 IEEE International Geoscience and Remote Sensing Symposium, Valencia, Spain, 22–27 July 2018; pp. 175–178. [Google Scholar] [CrossRef]
- Guanter, L.; Kaufmann, H.; Segl, K.; Foerster, S.; Rogass, C.; Chabrillat, S.; Kuester, T.; Hollstein, A.; Rossner, G.; Chlebek, C. The EnMAP Spaceborne Imaging Spectroscopy Mission for Earth Observation. Remote Sens.
**2015**, 7, 8830–8857. [Google Scholar] [CrossRef][Green Version] - Pugh, T.A.; Rademacher, T.; Shafer, S.L.; Steinkamp, J.; Barichivich, J.; Beckage, B.; Haverd, V.; Harper, A.; Heinke, J.; Nishina, K. Understanding the Uncertainty in Global Forest Carbon Turnover. Biogeosciences
**2020**, 17, 3961–3989. [Google Scholar] [CrossRef] - Fisher, R.; McDowell, N.; Purves, D.; Moorcroft, P.; Sitch, S.; Cox, P.; Huntingford, C.; Meir, P.; Woodward, F.I. Assessing Uncertainties in a Second-Generation Dynamic Vegetation Model Caused by Ecological Scale Limitations. New Phytol.
**2010**, 187, 666–681. [Google Scholar] [CrossRef] [PubMed][Green Version] - Peñuelas, J.; Filella, I.; Gamon, J.A. Assessment of Photosynthetic Radiation-Use Efficiency with Spectral Reflectance. New Phytol.
**1995**, 131, 291–296. [Google Scholar] [CrossRef] - Asner, G.P.; Martin, R.E. Spectranomics: Emerging Science and Conservation Opportunities at the Interface of Biodiversity and Remote Sensing. Glob. Ecol. Conserv.
**2016**, 8, 212–219. [Google Scholar] [CrossRef][Green Version]

**Figure 1.**(

**a**) Location of the research site “Am Grossen Bruch” (DE-GsB) within Germany (CRS: EPSG:3857). (

**b**) RGB representation of the 2018 hyperspectral flight strip showing the surroundings of the study area (CRS: EPSG:32632).

**Figure 3.**Time series of 91-days/3-months standardised precipitation-evapotranspiration index (SPEI) and relative soil water content (SWC) values for the research site DE-GsB. Vertical dashed lines indicate the dates of hyperspectral imaging flights.

**Figure 4.**Classified archetypical reflectance spectra from the research site “Am Grossen Bruch” (DE-GsB). (

**a**) Archetypes classified as “healthy” or “stressed”. (

**b**) All of the non-vegetation spectra were classified as “background”. The vertical blue line marks the beginning of the red edge slope at 685 nm.

**Figure 5.**Maps of the research site “Am Grossen Bruch” (DE-GsB). RGB representations were computed with the HSI2RGB python module [109]. The double layer maps show the distribution of archetype classes. Archetype coefficient values per pixel always add up to one due to the convexity constraint of simplex volume maximisation (CRS: EPSG:32632).

**Figure 6.**The correlation matrix of stress metrics $\zeta $, $\nu $ and the evaluation dataset, which includes spectral indices, geophysical measurements and a digital elevation model (DEM). All of the correlations are highly significant ($p<0.001$).

Recording Date | Ground Resolution | Field of View | Swath | Spectral Range | Spectral Resolution | Sensor | Platform |
---|---|---|---|---|---|---|---|

m | ${}^{\circ}$ | m | nm | nm | |||

7 May 2018 | 0.5 | 16 | 508 | 409–989 | 3.2 | HySpex VNIR-1800 | Cessna 207 |

23 April 2019 | 0.4 | 16 | 508 | 409–989 | 3.2 | HySpex VNIR-1800 | Cessna 207 |

**Table 2.**Overview of the variables in the evaluation dataset, which were not derived from the hyperspectral imagery.

Recording Date | Type of Measurement | Derived Variable |
---|---|---|

6 Mar. 2014 | Electromagnetic induction with EM31 | ECa (mS/m) |

6 Mar. 2014 | Electromagnetic induction with EM38 | ECa (mS/m) |

6 Mar. 2014 | Gamma-ray spectrometry | Thorium^{232} (ppm) |

6 Mar. 2014 | Gamma-ray spectrometry | Dose rate (nGy/h) |

18 Feb. 2015 | Photogrammetry | DEM (m.a.s.l.) |

**Table 4.**Variance inflation factors (VIF) from multicollinearity analysis of the evaluation variables. The estimated coefficient values from fitting the interannual full model (FM) and subset models (M18, M19) with boosted beta regression (early stopping after 300 iterations, learning rate: 0.05, coefficient values rounded to three digits).

Name | VIF | FM $\mathit{\mu}$ | M18 $\mathit{\mu}$ | M19 $\mathit{\mu}$ | FM $\mathit{\varphi}$ | M18 $\mathit{\varphi}$ | M19 $\mathit{\varphi}$ |
---|---|---|---|---|---|---|---|

Chl_{REopt} | 88.4 | −0.143 | 0.163 | −0.215 | −0.071 | 0 | −0.390 |

Car_{REopt} | 19.1 | 1.018 | 0.721 | 0.435 | −1.005 | −1.587 | 0 |

RENDVI | 214.3 | 0 | 0.052 | 0 | 0 | 0 | 0 |

PRI_{512} | 6.8 | 0.322 | 0.011 | 0.079 | 0.009 | 0.495 | 0 |

CTR2 | 139.0 | 0 | −0.031 | 0 | −0.949 | −1.065 | −0.406 |

MCARI2 | 147.4 | 0 | 0 | 0 | 0 | 0.160 | 0 |

MSAVI2 | 138.8 | −0.396 | −0.035 | −0.077 | 0.154 | 0 | 0.091 |

WBI | 73.2 | 0.265 | 0.244 | 0.143 | 0 | 0.004 | 0.179 |

${f}^{\prime}\left({\rho}_{950.6}\right)$ | 104.3 | 0 | 0.136 | −0.038 | 0 | 0 | 0 |

DEM | 5.1 | 0.004 | −0.023 | 0.010 | −0.048 | −0.160 | 0.025 |

EM31 | 2.2 | 0 | 0.042 | −0.002 | −0.063 | −0.200 | 0 |

EM38 | 5.2 | 0 | −0.032 | −0.071 | −0.251 | −0.204 | −0.149 |

GR_{DR} | 3.6 | 0 | 0.004 | 0 | 0 | 0 | 0.076 |

GR_{Th} | 3.4 | −0.009 | −0.043 | −0.014 | 0 | 0.012 | 0 |

Intercept | 0.014 | 0.206 | 0 | 2.356 | 2.566 | 1.324 |

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**MDPI and ACS Style**

Hermanns, F.; Pohl, F.; Rebmann, C.; Schulz, G.; Werban, U.; Lausch, A. Inferring Grassland Drought Stress with Unsupervised Learning from Airborne Hyperspectral VNIR Imagery. *Remote Sens.* **2021**, *13*, 1885.
https://doi.org/10.3390/rs13101885

**AMA Style**

Hermanns F, Pohl F, Rebmann C, Schulz G, Werban U, Lausch A. Inferring Grassland Drought Stress with Unsupervised Learning from Airborne Hyperspectral VNIR Imagery. *Remote Sensing*. 2021; 13(10):1885.
https://doi.org/10.3390/rs13101885

**Chicago/Turabian Style**

Hermanns, Floris, Felix Pohl, Corinna Rebmann, Gundula Schulz, Ulrike Werban, and Angela Lausch. 2021. "Inferring Grassland Drought Stress with Unsupervised Learning from Airborne Hyperspectral VNIR Imagery" *Remote Sensing* 13, no. 10: 1885.
https://doi.org/10.3390/rs13101885