# Retrieving the Diurnal FPAR of a Maize Canopy from the Jointing Stage to the Tasseling Stage with Vegetation Indices under Different Water Stresses and Light Conditions

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## Abstract

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^{2}) of the FPAR-VIs models generated for the sunny nondrought data, the cloudy nondrought data, and all of the nondrought data were 0.895, 0.88, and 0.828, respectively. The VIs—including normalized difference vegetation index (NDVI), green NDVI (GNDVI), red-edge simple ratio (SR

_{705}), modified simple ratio 2 (mSR2), red-edge normalized difference vegetation index (NDVI

_{705}), and enhanced vegetation index (EVI)—that were related to the canopy structure had higher estimation accuracies (R

^{2}> 0.8) than the other VIs that were related to the soil adjustment, chlorophyll, and physiology. The estimation accuracies of the GNDVI and some red-edge VIs (including NDVI

_{705}, SR

_{705}, and mSR2) were higher than the estimation accuracy of the NDVI. (2) Under drought stress, the FPAR decreased significantly because of leaf wilting and the effective leaf area index decrease around noon. When we included drought data in the model, accuracies were reduced dramatically and the R

^{2}value of the best model was only 0.59. When we built the regression models based only on drought data, the EVI, which can weaken the influence of soil, had the best estimate accuracy (R

^{2}= 0.68).

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Experimental Scheme

#### 2.2. Canopy Hyperspectral Reflectance Data

#### 2.3. Canopy FPAR

#### 2.4. Soil Moisture

#### 2.5. Effective Leaf Area Index

_{b}is the beam fraction (i.e., the ratio of the direct sunlight radiation to the total incoming radiation from all ambient sources). The beam fraction was automatically calculated with the instrument based on the latitude and the local time. K is the canopy extinction coefficient which was calculated with an assumption of a spherical leaf angle distribution and χ (leaf angle distribution parameter) was set to the default value of 1. A is a coefficient describing the canopy absorptivity and it is empirically related to the leaf’s absorptivity parameter. In this study, we adopted the default value (0.9) for the leaf absorptivity parameter.

#### 2.6. Hyperspectral VIs

#### 2.7. Data Fitting

^{2}) and the root mean squared error (RMSE) for the estimation of in situ–measured FPAR. The RMSE was calculated using Equation (4):

_{m}and y

_{p}represent the measured values and the predicted values, respectively; and the N term represents the number of samples.

## 3. Results

#### 3.1. Soil Moisture and Effective LAI during Canopy Development

#### 3.2. FPAR and NDVI under Different Conditions

#### 3.3. Retrieving the FPAR with VIs under Different Conditions

#### 3.3.1. Effect of Light Conditions on the Model Determination

_{705}, and EVI, were optimal indices for estimating the diurnal FPAR under nondrought conditions. The R

^{2}of the models built by these six VIs was greater than 0.8, whether using sunny- or cloudy-day data (Table 4). Changes in light conditions did not significantly influence the determination of these six FPAR-VI models under nondrought conditions.

_{705}, which is also related to chlorophyll, was better than that of the MCARI whether under sunny nondrought or cloudy nondrought conditions. The precision of the models built with the MSAVI, OSAVI, RDVI, RDVI

_{705}, and PRI was not ideal.

#### 3.3.2. Effect of a Drought on Model Accuracy

^{2}value was only 0.590. The fitting effects of all FPAR-VIs models were significantly improved after removing the data from drought days. The R

^{2}values of the six FPAR-VIs models, which were mentioned earlier, were all above 0.75. In addition, the models built by the other VIs had poor fitting effects.

^{2}value of only 0.685. The fitting effect of the PRI that had a poor performance under nondrought conditions significantly improved under drought conditions.

#### 3.3.3. Comparison of the Prediction Results of the Different Models

## 4. Discussions

_{705}) that were related to the canopy structure, and this accuracy was higher than that of the other VIs that were related to soil adjustment, chlorophyll, and physiology (Table 4 and Table 5). Because the effective LAI was large in the study period, the soil background was not a main factor affecting the canopy diurnal FPAR. The models built using VIs (MSAVI, OSAVI) that were related to soil adjustment did not have a good fitting effect. In addition, the pigment content and physiological state of the vegetation did not changed much within one day in nondrought condition. Thus, the models built by VIs (i.e., TCARI

_{705}, MCARI, and PRI) that were related to chlorophyll and physiology also did not have a good fitting effect.

## 5. Conclusions

- The influence of the illumination change on the effect of the FPAR-VIs models was not significant. The maximum coefficients of determination (R
^{2}) of the FPAR-VIs models generated by the sunny nondrought data, the cloudy nondrought data, and all of the nondrought data were 0.895, 0.88, and 0.828, respectively. The VIs (including NDVI, GNDVI, SR_{705}, mSR2, NDVI_{705}, and EVI) that were related to the canopy structure had a higher estimation accuracy (R^{2}> 0.8) than the other VIs that were related to the soil adjustment, chlorophyll, and physiology. The estimation accuracies of the GNDVI and some red-edge VIs (including NDVI_{705}, SR_{705}, and mSR2) were higher than those of the NDVI. - Drought greatly reduced the accuracy of the FPAR-VI models. When we compared the quadratic VI-FPAR models under drought and normal conditions in the maize canopy, the maximum R
^{2}value for the quadratic FPAR-VI models built using all of the data (including the drought data) was only 0.590. The maximum R^{2}value was 0.828 for the quadratic VI-FPAR models after eliminating the drought data. When we built the regression models based on only the drought data, the EVI had a better performance in estimating the diurnal canopy FPAR than the other VIs that were related to the canopy structure. - The quadratic models for the VIs were suitable for the prediction of the FPAR under nondrought conditions. No quadratic models of VIs could predict the characteristics of a sudden sharp decrease in the FPAR at noon under drought stress. Further research is required to develop a power model (e.g., a higher-order polynomial model) between the FPAR and the VIs to predict the diurnal dynamics of the FPAR under drought stress.

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Monteith, J.L.; Moss, C.J. Climate and the Efficiency of Crop Production in Britain. Philos. Trans. R. Soc. Lond.
**1977**, 281, 277–294. [Google Scholar] [CrossRef] - Rahman, M.M.; Stanley, J.N.; Lamb, D.W.; Trotter, M.G. Methodology for measuring fAPAR in crops using a combination of active optical and linear irradiance sensors: A case study in Triticale (X Triticosecale Wittmack). Precis. Agric.
**2014**. [Google Scholar] [CrossRef] - Hanan, N.P.; Burba, G.; Verma, S.B.; Berry, J.A.; Suyker, A.; Walter-Shwa, E.A. Inversion of net ecosystem CO2 flux measurements for estimation of canopy PAR absorption. Glob. Chang. Biol.
**2002**, 8, 563–574. [Google Scholar] [CrossRef] - Gallo, K.P.; Daughtry, C.S.T. Techniques for measuring intercepted and absorbed photosynthetically active radiation in corn canopies. Agron. J.
**1986**, 78, 752–756. [Google Scholar] [CrossRef] - Shabanov, N.V.; Wang, Y.; Buermann, W.; Dong, J.; Hoffman, S.; Smith, G.R.; Tian, Y.; Knyazikhin, Y.; Myneni, R.B. Effect of foliage spatial heterogeneity in the MODIS LAI and FPAR algorithm over broadleaf forests. Remote Sens. Environ.
**2003**, 85, 410–423. [Google Scholar] [CrossRef] [Green Version] - Gobron, N.; Pinty, B.; Taberner, M.; Melin, F.; Widlowski, J.-L.; Verstraete, M.M. Monitoring FAPAR over land surfaces with remote sensing data. In Remote Sensing for Agriculture, Ecosystems, and Hydrology V, Proceedings of the Remote Sensing, Barcelona, Spain, 8–12 September 2003; SPIE: Bellingham, WA, USA, 2003; Volume 5232, pp. 237–244. [Google Scholar]
- Bacour, C.; Baret, F.; Béal, D.; Weiss, M.; Pavageau, K. Neural network estimation of LAI, fAPAR, fCover and LAI × Cab, from top of canopy MERIS reflectance data: Principles and validation. Remote Sens. Environ.
**2006**, 105, 313–325. [Google Scholar] [CrossRef] - Baret, F.; Hagolle, O.; Geiger, B.; Bicheron, P.; Miras, B.; Huc, M.; Berthelot, B.; Niño, F.; Weiss, M.; Samain, O.; et al. LAI, fAPAR and fCover CYCLOPES global products derived from VEGETATION: Part 1: Principles of the algorithm. Remote Sens. Environ.
**2007**, 110, 275–286. [Google Scholar] [CrossRef] [Green Version] - Dong, T.; Meng, J.; Wu, B. Overview on Methods of Deriving Fraction of Absorbed Photosynthetically Active Radiation (FPAR) Using Remote Sensing. Acta Ecol. Sin.
**2012**, 32, 7190–7201. [Google Scholar] [CrossRef] - Gitelson, A.A.; Peng, Y.; Huemmrich, K.F. Relationship between Fraction of Radiation Absorbed by Photosynthesizing Maize and Soybean Canopies and NDVI from Remotely Sensed Data Taken at Close Range and from MODIS 250m Resolution Data. Remote Sens. Environ.
**2014**, 147, 108–120. [Google Scholar] [CrossRef] - Huemmrich, K.F.; Goward, S.N. Vegetation Canopy PAR Absorptance and NDVI: An Assessment for Ten Tree Species with the SAIL Model. Remote Sens. Environ.
**1997**, 61, 254–269. [Google Scholar] [CrossRef] - Pinty, B.; Lavergne, T.; Widlowski, J.L.; Gobron, N.; Verstraete, M.M. On the Need to Observe Vegetation Canopies in the Near-Infrared to Estimate Visible Light Absorption. Remote Sens. Environ.
**2009**, 113, 10–23. [Google Scholar] [CrossRef] - Tan, C.; Samanta, A.; Jin, X.; Tong, L.; Ma, C.; Guo, W.; Knyazikhin, Y.; Myneni, R.B. Using Hyperspectral Vegetation Indices to Estimate the Fraction of Photosynthetically Active Radiation Absorbed by Corn Canopies. Int. J. Remote Sens.
**2013**, 34, 8789–8802. [Google Scholar] [CrossRef] - Goward, S.N.; Huemmrich, K.F. Vegetation Canopy PAR Absorptance and the Normalized Difference Vegetation Index: An Assessment Using the SAIL Model. Remote Sens. Environ.
**1992**, 39, 119–140. [Google Scholar] [CrossRef] - Ridao, E.; Conde, J.R.; Mínguez, M.I. Estimating fAPAR from Nine Vegetation Indices for Irrigated and Nonirrigated Faba Bean and Semileafless Pea Canopies. Remote Sens. Environ.
**1998**, 66, 87–100. [Google Scholar] [CrossRef] - Epiphanio, J.C.N.; Huete, A.R. Dependence of NDVI and SAVI on Sun/Sensor Geometry and Its Effect on fAPAR Relationships in Alfalfa. Remote Sens. Environ.
**1995**, 51, 351–360. [Google Scholar] [CrossRef] - Roujean, J.-L.; Breon, F.-M. Estimating PAR Absorbed by Vegetation from Bidirectional Reflectance Measurements. Remote Sens. Environ.
**1995**, 51, 375–384. [Google Scholar] [CrossRef] - Goel, N.S.; Qin, W. Influences of Canopy Architecture on Relationships between Various Vegetation Indices and LAI and FPAR: A Computer Simulation. Remote Sens. Rev.
**1994**, 10, 309–347. [Google Scholar] [CrossRef] - Viña, A.; Gitelson, A.A. New developments in the remote estimation of the fraction of absorbed photosynthetically active radiation in crops. Geophys. Res. Lett.
**2005**, 32. [Google Scholar] [CrossRef] [Green Version] - Gitelson, A.A.; Kaufman, Y.J.; Merzlyak, M.N. Use of a Green Channel in Remote Sensing of Global Vegetation from EOS-MODIS. Remote Sens. Environ.
**1996**, 58, 289–298. [Google Scholar] [CrossRef] - Daughtry, C.S.T.; Walthall, C.L.; Kim, M.S.; de Colstoun, E.B.; McMurtrey, J.E., III. Estimating corn leaf chlorophyll concentration from leaf and canopy reflectance. Remote Sens. Environ.
**2000**, 74, 229–239. [Google Scholar] [CrossRef] - Chen, X.; Meng, J.; Wu, B.; Zhu, J.; Du, X.; Zhang, F.; Niu, L. Monitoring Corn FPAR Based on HJ-1 CCD. Trans. Chin. Soc. Agric. Eng.
**2010**, 26, 241–245. [Google Scholar] - Cao, R.; Shen, M.; Chen, J.; Tang, Y. A Simple Method to Simulate Diurnal Courses of PAR Absorbed by Grassy Canopy. Ecol. Indic.
**2014**, 46, 129–137. [Google Scholar] [CrossRef] - Xu, S.; Liu, Z.; Zhao, L.; Zhao, H.; Ren, S. Diurnal Response of Sun-Induced Fluorescence and PRI to Water Stress in Maize Using a Near-Surface Remote Sensing Platform. Remote Sens.
**2018**, 10, 1510. [Google Scholar] [CrossRef] - Zhou, X.; Liu, Z.; Xu, S.; Zhang, W.; Wu, J. An Automated Comparative Observation System for Sun-Induced Chlorophyll Fluorescence of Vegetation Canopies. Sensors
**2016**, 16, 775. [Google Scholar] [CrossRef] [PubMed] - Qu, Y.; Han, W.; Fu, L.; Li, C.; Song, J.; Zhou, H.; Bo, Y.; Wang, J. LAINet—A Wireless Sensor Network for Coniferous Forest Leaf Area Index Measurement: Design, Algorithm and Validation. Comput. Electron. Agric.
**2014**, 108, 200–208. [Google Scholar] [CrossRef] - Black, C.A. Methods of Soil Analysis: Part I Physical and Mineralogical Properties; American Society of Agronomy: Madison, WI, USA, 1965. [Google Scholar]
- Zhao, T.H.; Shen, X.Y.; Yang, D.G.; Ma, X.F. Effects on Chlorophyll Content and Photosynthetic Rate of Maize Leaves under Water Stress and Rewatering. Rain Fed Crops
**2003**, 23, 33–35. [Google Scholar] - Garrigues, S.; Shabanov, N.V.; Swanson, K.; Morisette, J.T.; Baret, F.; Myneni, R.B. Intercomparison and sensitivity analysis of Leaf Area Index retrievals from LAI-2000, AccuPAR; digital hemispherical photography over croplands. Agric. For. Meteorol.
**2008**, 148, 1193–1209. [Google Scholar] [CrossRef] - Norman, J.M.; Jarvis, P.G. Erratum: Photosynthesis in Sitka spruce (Picea sitchensis (Bong.) Carr.). V. Radiation penetration theory and a test case. J. Appl. Ecol.
**1975**, 12, 792–804. [Google Scholar] [CrossRef] - Dong, T.; Meng, J.; Shang, J.; Liu, J.; Wu, B. Evaluation of Chlorophyll-Related Vegetation Indices Using Simulated Sentinel-2 Data for Estimation of Crop Fraction of Absorbed Photosynthetically Active Radiation. IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens.
**2015**, 8, 4049–4059. [Google Scholar] [CrossRef] - Jin, X.L.; Li, S.K.; Wang, K.R.; Xiao, C.H.; Wang, F.-Y.; Chen, B.; Chen, J.L.; Lu, Y.L.; Diao, W.Y. Estimating Cotton FPAR Based on the Different Vegetation Indexes. Cotton Sci.
**2011**, 23, 447–453. [Google Scholar] - Yang, F.; Zhu, Y.; Zhang, J.; Yao, Z. Estimating Fraction of Photosynthetically Active Radiation of Corn with Vegetation Indices and Neural Network from Hyperspectral Data. Chin. Geogr. Sci.
**2012**, 22, 63–74. [Google Scholar] [CrossRef] - Liu, H.Q.; Huete, A. A feedback based modification of the NDVI to minimize canopy background and atmospheric noise. IEEE Trans. Geosci. Remote Sens.
**1995**, 33, 457–465. [Google Scholar] - Luo, S. Correlation Analysis on Drought Resistance and Identification Indexes of Maize. Agric. Res. Arid. Areas
**1990**, 3, 72–78. [Google Scholar] - Gu, L.; Baldocchi, D.; Verma, S.B.; Black, T.A.; Vesala, T.; Falge, E.M.; Dowty, P.R. Advantages of diffuse radiation for terrestrial ecosystem productivity. J. Geophys. Res. Atmos.
**2002**, 107, ACL 2-1–ACL 2-23. [Google Scholar] [CrossRef] - Roderick, M.L.; Farquhar, G.D.; Berry, S.L.; Noble, I.R. On the Direct Effect of Clouds and Atmospheric Particles on the Productivity and Structure of Vegetation. Oecologia
**2001**, 129, 21–30. [Google Scholar] [CrossRef] [PubMed] - Wu, C.; Zheng, N.; Quan, T.; Wenjiang, H. Estimating chlorophyll content from hyperspectral vegetation indices: Modeling and validation. Agric. For. Meteorol.
**2008**, 148, 1230–1241. [Google Scholar] [CrossRef] - Haboudane, D.; Tremblay, N.; Miller, J.R.; Vigneault, P. Remote Estimation of Crop Chlorophyll Content Using Spectral Indices Derived from Hyperspectral Data. IEEE Trans. Geosci. Remote Sens.
**2008**, 46, 423–437. [Google Scholar] [CrossRef]

**Figure 2.**Diurnal FPAR, NDVI, and PAR during (

**a**) a cloudy day without drought stress, (

**b**) a sunny day with drought stress, and (

**c**) a sunny day without drought stress.

**Figure 3.**Measured FPAR and predicted FPAR of four models for (

**a**) a cloudy nondrought day, (

**b**) a sunny drought day, and (

**c**) a sunny nondrought day.

Name | Index | Formulation |
---|---|---|

Re-normalized difference vegetation index | RDVI | (R_{800} − R_{670})/($\sqrt{{\mathrm{R}}_{800}+{\mathrm{R}}_{670}}$) |

Enhanced vegetation index | EVI | 2.5 × (R_{800} − R_{690})/(R_{800} + 6.0 × R_{690} − 7.5 × R_{490}) |

Green normalized difference vegetation index | GNDVI | (R_{800} − R_{550})/(R_{800} + R_{550}) |

Modified soil-adjusted vegetation index | MSAVI | (2 × R_{800} + 1 − $\sqrt{{(2\times {\mathrm{R}}_{800}+1)}^{2}-8\times \left({\mathrm{R}}_{800}-{\mathrm{R}}_{670}\right)}$)/2 |

Normalized difference vegetation index | NDVI | (R_{800} − R_{670})/(R_{800} + R_{670}) |

Red-edge simple ratio | SR_{705} | R_{750}/R_{705} |

Modified simple ratio 2 | mSR2 | (R_{750}/R_{705} − 1)/($\sqrt{{\mathrm{R}}_{750}/{\mathrm{R}}_{705}+1}$) |

Red-edge normalized difference vegetation index | NDVI_{705} | (R_{750} − R_{705})/(R_{750} + R_{705}) |

Optimal soil-adjusted vegetation index | OSAVI | (1 + 0.16) × (R_{800} − R_{670})/(R_{800} + R_{670} + 0.16) |

Red-edge re-normalized difference vegetation index | RDVI_{705} | (R_{800} − R_{705})/($\sqrt{{\mathrm{R}}_{800}+{\mathrm{R}}_{705}}$) |

Red-edge transformed chlorophyll absorption in reflectance index | TCARI_{705} | 3 × [(R_{750} − R_{705}) − 0.2 × (R_{750} − R_{550}) × (R_{750}/R_{705})] |

Modified chlorophyll absorption in reflectance index | MCARI | ((R_{700} − R_{670}) − 0.2 × (R_{700} − R_{550})) × (R_{700}/R_{670}) |

Photochemical reflectance index | PRI | (R_{531} − R_{570})/(R_{531} + R_{570}) |

**Table 2.**Weight moisture capacity (WMC) and relative moisture content (RMC) at different depths (Irrigation was carried out on the nights of 14 July and 30 July).

Depth (cm) | 16 July | 30 July | 1 August | |||
---|---|---|---|---|---|---|

WMC | RMC | WMC | RMC | WMC | RMC | |

0~5 | 14.3 | 58.23% | 3.0 | 36.92% | 14.4 | 56.83% |

5~10 | 13.7 | 6.2 | 14.1 | |||

10~20 | 12.7 | 8.9 | 14.6 | |||

20~30 | 10.2 | 9.1 | 8.3 | |||

30~40 | 15.3 | 14.7 | 13.1 | |||

40~50 | 16.7 | 16.5 | 15.4 | |||

50~60 | 17.3 | 69.34% | 17.0 | 69.02% | 14.4 | 62.63% |

60~70 | 15.9 | 16.1 | 13.8 | |||

70~80 | 15.1 | 15.0 | 13.5 | |||

80~90 | 14.2 | 13.8 | 13.9 | |||

90~100 | 15.2 | 15.6 | 14.3 |

Date | Effective LAI | Weather | Date | Effective LAI | Weather |
---|---|---|---|---|---|

18 July 2017 | 2.65 | Sunny | 29 July 2017 | 2.08 | Sunny |

19 July 2017 | 2.4 | Sunny | 30 July 2017 | 2.12 | Sunny |

20 July 2017 | 2.21 | Cloudy | 31 July 2017 | 2.56 | Sunny |

27 July 2017 | 2.46 | Cloudy | 1 August 2017 | 3.31 | Sunny |

28 July 2017 | 2.28 | Cloudy | 3 August, 2017 | 2.99 | Sunny |

**Table 4.**Regression equations between the FPAR (y) and VIs (x) on sunny days and cloudy days without drought stress.

Cloudy Nondrought Days | Sunny Nondrought Days | ||||||
---|---|---|---|---|---|---|---|

VIs | Formula | R^{2} | RMSE | VIs | Formula | R^{2} | RMSE |

GNDVI | y = 35.3025x^{2} − 54.0546x + 21.4547 | 0.880 | 0.014 | mSR2 | y = −0.0506x^{2} + 0.5376x − 0.0347 | 0.895 | 0.015 |

SR_{705} | y = 0.0227x^{2} − 0.2325x + 1.3599 | 0.873 | 0.014 | SR_{705} | y = −0.0073x^{2} + 0.1723x + 0.0288 | 0.895 | 0.014 |

mSR2 | y = 0.4326x^{2} − 1.4608x + 1.9994 | 0.872 | 0.014 | GNDVI | y = −6.435x^{2} + 12.8143x − 5.301 | 0.889 | 0.015 |

NDVI_{705} | y = 16.9178x^{2} − 22.9836x + 8.5701 | 0.867 | 0.014 | NDVI | y = 23.2133X^{2} − 39.6909x + 17.6786 | 0.889 | 0.015 |

NDVI | y = 24.69x^{2} + −43.4435x + 19.8771 | 0.844 | 0.016 | NDVI_{705} | y = 6.0087x^{2} − 6.5581x + 2.4183 | 0.888 | 0.015 |

EVI | y = 2.4251x^{2} − 9.9697x + 11.0135 | 0.833 | 0.016 | EVI | y = 2.2449x^{2} − 8.8946x + 9.5286 | 0.857 | 0.017 |

TCARI_{705} | y = 0.0033x^{2} − 0.0244x + 0.8056 | 0.799 | 0.018 | TCARI_{705} | y = −0.0022x^{2} + 0.0618x + 0.4854 | 0.626 | 0.028 |

MSAVI | y = 6.5224x^{2} − 10.4731x + 4.9721 | 0.789 | 0.018 | MSAVI | y = 2.0351x^{2} − 2.4975x + 1.4337 | 0.611 | 0.028 |

OSAVI | y = 9.2741x^{2} − 14.9208x + 6.7686 | 0.771 | 0.019 | OSAVI | y = −1.8846x^{2} + 4.5102x − 1.6842 | 0.568 | 0.030 |

RDVI_{705} | y = 3.7319x^{2} − 4.1813x + 1.9315 | 0.765 | 0.019 | RDVI_{705} | y = −2.6621x^{2} + 4.2621x − 0.8434 | 0.473 | 0.033 |

PRI | y = 51.7959x^{2} + 1.2097x + 0.775 | 0.756 | 0.020 | RDVI | y = −3.3692x^{2} + 5.7419x − 1.6118 | 0.384 | 0.036 |

RDVI | y = 3.0198x^{2} − 3.9242x + 2.0366 | 0.713 | 0.021 | PRI | y = −40.9556x^{2} + 3.5204x + 0.7674 | 0.363 | 0.036 |

MCARI | y = 1.11x^{2} + 1.7204x + 0.6741 | 0.595 | 0.025 | MCARI | y = −73.7611x^{2} + 13.8129x + 0.1759 | 0.360 | 0.036 |

**Table 5.**Regression equations between the FPAR (y) and VIs (x) for three different kinds of conditions.

18 July to 3 August (All Days) | 18 July to 3 August (Nondrought Days) | 18 July to 3 August (Drought Days) | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|

VIs | Formula | R^{2} | RMSE | VIs | Formula | R^{2} | RMSE | VIs | Formula | R^{2} | RMSE |

GNDVI | y = 4.9269x^{2} − 6.1141x + 2.5617 | 0.590 | 0.036 | GNDVI | y = 10.201x^{2} − 13.8935x + 5.4054 | 0.828 | 0.018 | EVI | y = −0.3955x^{2} + 1.833x − 1.2591 | 0.685 | 0.044 |

SR_{705} | y = 0.0034x^{2} + 0.0038x + 0.658 | 0.549 | 0.038 | NDVI_{705} | y = 7.51x^{2} − 9.189x + 3.5267 | 0.813 | 0.018 | NDVI | y = −7.5738x^{2} + 14.2627x − 5.8525 | 0.654 | 0.046 |

mSR2 | y = 0.073x^{2} − 0.0915x + 0.7175 | 0.547 | 0.038 | NDVI | y = 24.4468x^{2} − 42.6451x + 19.3503 | 0.811 | 0.019 | GNDVI | y = −12.0055x^{2} + 19.859x − 7.3489 | 0.653 | 0.046 |

NDVI_{705} | y = 2.7775x^{2} − 2.8914x + 1.4561 | 0.536 | 0.039 | mSR2 | y = 0.0852x^{2} − 0.0673x + 0.6179 | 0.807 | 0.019 | NDVI_{705} | y = −4.2147x^{2} + 6.4723x − 1.6216 | 0.645 | 0.046 |

EVI | y = 0.281x^{2} − 0.8641x + 1.3689 | 0.500 | 0.040 | SR_{705} | y = 0.0011x^{2} + 0.0483x + 0.4642 | 0.805 | 0.019 | mSR2 | y = −0.1857x^{2} + 0.8028x − 0.0022 | 0.621 | 0.048 |

NDVI | y = 3.8763x^{2} − 5.7719x + 2.8513 | 0.495 | 0.040 | EVI | y = 2.6888x^{2} − 11.011x + 12.0306 | 0.790 | 0.019 | SR_{705} | y = −0.0129x^{2} + 0.1845x + 0.2076 | 0.602 | 0.049 |

TCARI_{705} | y = 0.0006x^{2} + 0.0124x + 0.7002 | 0.427 | 0.043 | TCARI_{705} | y = 0.0007x^{2} + 0.0159x + 0.6604 | 0.662 | 0.025 | PRI | y = −34.9698x^{2} + 0.8984x + 0.8607 | 0.580 | 0.050 |

MSAVI | y = 1.7611x^{2} − 2.3618x + 1.5346 | 0.398 | 0.044 | MSAVI | y = 5.0591x^{2} − 7.8632x + 3.8112 | 0.658 | 0.025 | OSAVI | y = −5.0779x^{2} + 8.9373x − 3.0722 | 0.522 | 0.054 |

OSAVI | y = 2.0062x^{2} − 2.6163x + 1.5778 | 0.395 | 0.044 | OSAVI | y = 5.6676x^{2} − 8.6318x + 4.0299 | 0.624 | 0.026 | TCARI_{705} | y = −0.0037x^{2} + 0.0641x + 0.595 | 0.481 | 0.057 |

RDVI_{705} | y = 0.8962x^{2} − 0.5841x + 0.8075 | 0.378 | 0.045 | RDVI_{705} | y = 0.6643x^{2} − 0.1069x + 0.586 | 0.581 | 0.028 | MSAVI | y = −1.785x^{2} + 3.2967x − 0.663 | 0.461 | 0.057 |

RDVI | y = 0.8471x^{2} − 0.7532x + 0.8937 | 0.325 | 0.047 | PRI | y = 42.5846x^{2} + 1.5045x + 0.7736 | 0.506 | 0.030 | RDVI_{705} | y = −2.8878x^{2} + 4.0519x − 0.5601 | 0.459 | 0.058 |

PRI | y = 6.8559x^{2} + 1.5202x + 0.7968 | 0.322 | 0.047 | RDVI | y = 0.6001x^{2} − 0.2575x + 0.6511 | 0.500 | 0.030 | RDVI | y = −2.5379x^{2} + 4.0916x − 0.7887 | 0.410 | 0.060 |

MCARI | y = 5.9394x^{2} + 0.6518x + 0.7253 | 0.216 | 0.050 | MCARI | y = 4.0202x^{2} + 1.1067x + 0.693 | 0.375 | 0.034 | MCARI | y = −26.3964x^{2} + 5.7026x + 0.5679 | 0.242 | 0.068 |

All-GNDVI | ND-GNDVI | D-EVI | CND-GNDVI | |
---|---|---|---|---|

20 July | 0.033 | 0.020 | 0.085 | 0.017 |

30 July | 0.063 | 0.075 | 0.049 | 0.134 |

31 July | 0.031 | 0.034 | 0.034 | 0.044 |

© 2018 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 (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Zhao, L.; Liu, Z.; Xu, S.; He, X.; Ni, Z.; Zhao, H.; Ren, S.
Retrieving the Diurnal FPAR of a Maize Canopy from the Jointing Stage to the Tasseling Stage with Vegetation Indices under Different Water Stresses and Light Conditions. *Sensors* **2018**, *18*, 3965.
https://doi.org/10.3390/s18113965

**AMA Style**

Zhao L, Liu Z, Xu S, He X, Ni Z, Zhao H, Ren S.
Retrieving the Diurnal FPAR of a Maize Canopy from the Jointing Stage to the Tasseling Stage with Vegetation Indices under Different Water Stresses and Light Conditions. *Sensors*. 2018; 18(11):3965.
https://doi.org/10.3390/s18113965

**Chicago/Turabian Style**

Zhao, Liang, Zhigang Liu, Shan Xu, Xue He, Zhuoya Ni, Huarong Zhao, and Sanxue Ren.
2018. "Retrieving the Diurnal FPAR of a Maize Canopy from the Jointing Stage to the Tasseling Stage with Vegetation Indices under Different Water Stresses and Light Conditions" *Sensors* 18, no. 11: 3965.
https://doi.org/10.3390/s18113965