# Estimation of Forest LAI Using Discrete Airborne LiDAR: A Review

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

^{2}/m

^{2}), and its concept has progressed through a long process of definition and clarification [4,5,6,7]. In quantitative remote sensing, the most popular and widely accepted definition of LAI refers to half of the total leaf area per unit ground area [6].

## 2. An Overview of the DALS System

## 3. LAI Retrieval Methods Using DALS PCD

#### 3.1. Physical Method

#### 3.1.1. Estimating LPIs from DALS PCD

- For PNB LPIs, the $LP{I}_{SR}$, derived from the single return, typically underestimates GF due to the lack of sensitivity of a single echo to the small gap within the crown [41,47,55,56], resulting in 20–30% overestimation of LAI [51]. Conversely, $LP{I}_{SR\_LR}$, which is calculated by single and last return, typically overestimates GF, thus underestimates LAI [33,55]. Weighted LPIs (e.g., $LP{I}_{SCI}$, $LP{I}_{MCI}$) are typically plagued with the suitability of the weights for different return types [20,57]. Voxel-based LPIs, however, may be biased due to a wrong cell size selected subjectively [23,36,58].
- For IB LPIs, the reflectance of background and vegetation is an important factor that affects the energy from either the background or vegetation [40,59]. Therefore, it is necessary to calibrate IB LPIs for better performance [41,47,60] by introducing the backscattering coefficient of background and vegetation, or at least their ratio ($\mu $).

#### 3.1.2. Estimating G from DALS PCD

^{2}) [23]. Ma et al. also applied the method to DALS PCD to obtain the leaf orientation distribution of the inclinational and azimuthal angles simultaneously [71]. The “occlusion effect,” i.e., the upper canopy element, blocks some of the LiDAR pulses completely (Figure 1) and prevents it from sampling behind upper elements [41,76], but would less limit the application of this method because measuring some samples is enough to represent the LAD of the whole canopy [14]. While the pulse footprint size (>10 cm) and the footprint space interval (>20 cm) [46] of the DALS system is generally larger than the leaf characteristic size, a study has proved that the canopy extinction coefficient (i.e., $\frac{G\left(\theta ,\alpha \right)}{cos\left(\theta \right)}$ in Equation (1)) extracted from DALS PCD can also effectively characterize the canopy in some specific view zenith angles [71].

#### 3.2. Empirical Regression Based on Proxy Variables

## 4. The Validation of DALS PCD-Based LAI

## 5. Challenges of Estimation of Forest LAI Based on DALS PCD

#### 5.1. Model Scalability

#### 5.2. Calibration of LPIs with a Target Spectral Property

^{2}in a linear regression between retrieval LAI and ground-based measured LAI [41]; and (3) calculating μ using return intensities [42,62,94]. The first two methods require additional ground-based measurements in addition to LiDAR data and thus require more effort to collect auxiliary data, i.e., spectral or LAI data, that are consistent with the LiDAR data in both time and space. If no field spectral data are available, field spectral data collected in the historical database can be used as a reference [61,95]. However, the term “ground” in LiDAR data does not mean “soil” because the classifying threshold of LiDAR to differentiate vegetation and ground is a standardized height [94], which indicates that all points below the given threshold are classified as a ground [96]. This discrepancy partly explains the relatively low correlation of the LiDAR intensity with the field-measured spectrum [97]. It indicates that there is significant uncertainty in using the μ calculated from the field spectral or hyperspectral data for the LPIs correction directly. The third method using returns’ intensity from vegetation and ground to calibrate LPIs, cannot accurately separate spectrally independent quantities from return intensities [98,99]. One reason for these difficulties is that the LiDAR manufacturers do not release all LiDAR system parameters, e.g., the intensity quantification algorithm, to end-users due to confidential considerations [21,100]. The missing DALS system parameters limit the radiation correction of point cloud intensity [1,54,101,102], indicating that the methods extracting μ directly from the intensity of returns must be validated.

#### 5.3. Correcting Impact from the Clumping Effect and Woody Material

#### 5.4. Saturation Effect

## 6. Conclusions and Future Direction

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Riaño, D.; Valladares, F.; Condés, S.; Chuvieco, E. Estimation of leaf area index and covered ground from airborne laser scanner (Lidar) in two contrasting forests. Agric. For. Meteorol.
**2004**, 124, 269–275. [Google Scholar] [CrossRef] - Fang, H.L.; Baret, F.; Plummer, S.; Schaepman-Strub, G. An Overview of Global Leaf Area Index (LAI): Methods, Products, Validation, and Applications. Rev. Geophys.
**2019**, 57, 739–799. [Google Scholar] [CrossRef] - GCOS. Systematic Observation Requirements for Satellite-Based Products for Climate Supplemental Details to the Satellite-Based Component of the Implementation Plan for the Global Observing System for Climate in Support of the UNFCCC-2011 Update; Word Meteorological Organization: Geneva, Switzerland, 2011; Available online: https://library.wmo.int/doc_num.php?explnum_id=3710 (accessed on 4 January 2021).
- Watson, D.J. Comparative Physiological Studies on the Growth of Field Crops: I. Variation in Net Assimilation Rate and Leaf Area between Species and Varieties, and within and between Years. Ann. Bot.
**1947**, 11, 41–76. [Google Scholar] [CrossRef] - Ross, J. The Radiation Regime and Architecture of Plant Stands; W. Junk.: The Hague, The Netherlands, 1981; ISBN 9061936071. [Google Scholar]
- Black, T.A.; Chen, J.M.; Lee, X.H.; Sagar, R.M. Characteristics of shortwave and longwave irradiances under a Douglas-fir forest stand. Can. J. For. Res.
**1991**, 21, 1020–1028. [Google Scholar] [CrossRef] - Chen, J.M.; Black, T.A. Defining leaf area index for non-flat leaves. Plant Cell Env.
**1992**, 15, 421–429. [Google Scholar] [CrossRef] - Chen, J.M.; Rich, P.M.; Gower, S.T.; Norman, J.M.; Plummer, S. Leaf area index of boreal forests: Theory, techniques, and measurements. J. Geophys. Res.
**1997**, 102, 29429–29443. [Google Scholar] [CrossRef] - Wilson, J.W. Inclined point quadrats. N. Phytol.
**1960**, 59, 1–7. [Google Scholar] [CrossRef] - Levy, E.B.; Madden, E.A. The point method of pasture analysis. N. Z. J. Agric.
**1933**, 46, 267–279. [Google Scholar] - Caldwell, M.M.; Harris, G.W.; Dzurec, R.S. A fiber optic point quadrat system for improved accuracy in vegetation sampling. Oecologia
**1983**, 59, 417–418. [Google Scholar] [CrossRef] - Lang, A.R.G.; Xiang, Y.Q.; Norman, J.M. Crop structure and the penetration of direct sunlight. Agric. For. Meteorol.
**1985**, 35, 83–101. [Google Scholar] [CrossRef] - Anderssen, R.; Jackett, D.; Jupp, D.; Norman, J. Interpretation of and simple formulas for some key linear functionals of the foliage angle distribution. Agric. For. Meteorol.
**1985**, 36, 165–188. [Google Scholar] [CrossRef] - Yan, G.J.; Hu, R.H.; Luo, J.H.; Weiss, M.; Jiang, H.L.; Mu, X.H.; Xie, D.H.; Zhang, W.M. Review of indirect optical measurements of leaf area index: Recent advances, challenges, and perspectives. Agric. For. Meteorol.
**2019**, 265, 390–411. [Google Scholar] [CrossRef] - Yu, L.; Shang, J.; Cheng, Z.; Gao, Z.; Wang, Z.; Tian, L.; Wang, D.; Che, T.; Jin, R.; Liu, J.; et al. Assessment of Cornfield LAI Retrieved from Multi-Source Satellite Data Using Continuous Field LAI Measurements Based on a Wireless Sensor Network. Remote Sens.
**2020**, 12, 3304. [Google Scholar] [CrossRef] - White, M.A.; Asner, G.P.; Nemani, R.R.; Privette, J.L.; Running, S.W. Measuring Fractional Cover and Leaf Area Index in Arid Ecosystems. Remote Sens. Environ.
**2000**, 74, 45–57. [Google Scholar] [CrossRef] - Knyazikhin, Y.; Glassy, J.; Privette, J.; Tian, Y.; Lotsch, A.; Zhang, Y.; Wang, Y.; Morisette, J.; Votava, P.; Myneni, R.; et al. MODIS Leaf Area Index (LAI) and Fraction of Photosynthetically Active Radiation Absorbed by Vegetation (FPAR) Product (MOD15) Algorithm Theoretical Basis Document. Available online: http://modis.gsfc.nasa.gov/data/atbd/atbd_mod15.pdf (accessed on 10 April 2021).
- Deng, F.; Chen, J.M.; Plummer, S.; Chen, M.Z.; Pisek, J. Algorithm for global leaf area index retrieval using satellite imagery. IEEE Trans. Geosci. Remote Sens.
**2006**, 44, 2219–2229. [Google Scholar] [CrossRef] [Green Version] - 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. Remote Sens. Environ.
**2007**, 110, 275–286. [Google Scholar] [CrossRef] [Green Version] - Solberg, S.; Brunner, A.; Hanssen, K.H.; Lange, H.; Næsset, E.; Rautiainen, M.; Stenberg, P. Mapping LAI in a Norway spruce forest using airborne lase r scanning. Remote Sens. Environ.
**2009**, 113, 2317–2327. [Google Scholar] [CrossRef] - Sumnall, M.; Peduzzi, A.; Fox, T.R.; Wynne, R.H.; Thomas, V.A.; Cook, B. Assessing the transferability of statistical predictive models for leaf area index between two airborne discrete return LiDAR sensor designs within multiple intensely managed Loblolly pine forest locations in the south-eastern USA. Remote Sens. Environ.
**2016**, 176, 308–319. [Google Scholar] [CrossRef] [Green Version] - Zhao, J.; Li, J.; Liu, Q.H. Review of forest vertical structure parameter inversion based on remote sensing technology. J. Remote Sens.
**2013**, 17, 697–716. [Google Scholar] [CrossRef] - Zheng, G.; Ma, L.X.; Eitel, J.U.H.; He, W.; Magney, T.S.; Moskal, L.M.; Li, M. Retrieving Directional Gap Fraction, Extinction Coefficient, and Effective Leaf Area Index by Incorporating Scan Angle Information From Discrete Aerial Lidar Data. IEEE Trans. Geosci. Remote Sens.
**2017**, 55, 577–590. [Google Scholar] [CrossRef] - Qu, Y.H.; Shaker, A.; Silva, C.; Klauberg, C.; Pinagé, E. Remote Sensing of Leaf Area Index from LiDAR Height Percentile Metrics and Comparison with MODIS Product in a Selectively Logged Tropical Forest Area in Eastern Amazonia. Remote Sens.
**2018**, 10, 970. [Google Scholar] [CrossRef] [Green Version] - Qu, Y.H.; Shaker, A.; Korhonen, L.; Silva, C.A.; Jia, K.; Tian, L.; Song, J.L. Direct Estimation of Forest Leaf Area Index based on Spectrally Corrected Airborne LiDAR Pulse Penetration Ratio. Remote Sens.
**2020**, 12, 217. [Google Scholar] [CrossRef] [Green Version] - Wulder, M.A.; White, J.C.; Nelson, R.F.; Næsset, E.; Ørka, H.O.; Coops, N.C.; Hilker, T.; Bater, C.W.; Gobakken, T. Lidar sampling for large-area forest characterization: A review. Remote Sens. Environ.
**2012**, 121, 196–209. [Google Scholar] [CrossRef] [Green Version] - Cui, Y.K.; Zhao, K.G.; Fan, W.J.; Xu, X.R. Retrieving crop fractional cover and LAI based on airborne Lidar data. J. Remote Sens.
**2011**, 15, 1276–1288. [Google Scholar] [CrossRef] - Ma, H.; Song, J.L.; Wang, J.D. Forest Canopy LAI and Vertical FAVD Profile Inversion from Airborne Full-Waveform LiDAR Data Based on a Radiative Transfer Model. Remote Sens.
**2015**, 7, 1897. [Google Scholar] [CrossRef] [Green Version] - Liu, Y.; Liu, R.G.; Chen, J.M.; Cheng, X.; Zheng, G. Current Status and Perspectives of Leaf Area Index Retrieval from Optical Remote Sensing Data. J. Geo-Inf. Sci.
**2013**, 15, 734–744. [Google Scholar] [CrossRef] - Wang, Y.S.; Weinacker, H.; Koch, B. A Lidar Point Cloud Based Procedure for Vertical Canopy Structure Analysis and 3D Single Tree Modelling in Forest. Sens. (Basel)
**2008**, 8, 3938–3951. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Jensen, J.L.; Humes, K.S.; Hudak, A.T.; Vierling, L.A.; Delmelle, E. Evaluation of the MODIS LAI product using independent lidar-derived LAI: A case study in mixed conifer forest. Remote Sens. Environ.
**2011**, 115, 3625–3639. [Google Scholar] [CrossRef] [Green Version] - Hu, R.H.; Yan, G.J.; Nerry, F.; Liu, Y.S.; Jiang, Y.M.; Wang, S.R.; Chen, Y.M.; Mu, X.H.; Zhang, W.M.; Xie, D.H. Using Airborne Laser Scanner and Path Length Distribution Model to Quantify Clumping Effect and Estimate Leaf Area Index. IEEE Trans. Geosci. Remote Sens.
**2018**, 56, 3196–3209. [Google Scholar] [CrossRef] - Zhao, K.G.; Popescu, S. Lidar-based mapping of leaf area index and its use for validating GLOBCARBON satellite LAI product in a temperate forest of the southern USA. Remote Sens. Environ.
**2009**, 113, 1628–1645. [Google Scholar] [CrossRef] - Chasmer, L.; Hopkinson, C.; Smith, B.; Treitz, P. Examining the Influence of Changing Laser Pulse Repetition Frequencies on Conifer Forest Canopy Returns. Photogramm. Eng. Remote Sens.
**2006**, 72, 1359–1367. [Google Scholar] [CrossRef] [Green Version] - Yang, X.B.; Wang, C.; Pan, F.F.; Nie, S.; Xi, X.H.; Luo, S.Z. Retrieving leaf area index in discontinuous forest using ICESat/GLAS full-waveform data based on gap fraction model. ISPRS J. Photogramm. Remote Sens.
**2019**, 148, 54–62. [Google Scholar] [CrossRef] - Wang, Y.; Fang, H.L. Estimation of LAI with the LiDAR Technology: A Review. Remote Sens.
**2020**, 12, 3457. [Google Scholar] [CrossRef] - Disney, M.I.; Kalogirou, V.; Lewis, P.; Prieto-Blanco, A.; Hancock, S.; Pfeifer, M. Simulating the impact of discrete-return lidar system and survey characteristics over young conifer and broadleaf forests. Remote Sens. Environ.
**2010**, 114, 1546–1560. [Google Scholar] [CrossRef] - Li, Z.Y.; Liu, Q.W.; Pang, Y. Review on forest parameters inversion using LiDAR. J. Remote Sens. (China)
**2016**, 20, 1138–1150. [Google Scholar] [CrossRef] - Pearse, G.D.; Morgenroth, J.; Watt, M.S.; Dash, J.P. Optimising prediction of forest leaf area index from discrete airborne lidar. Remote Sens. Environ.
**2017**, 200, 220–239. [Google Scholar] [CrossRef] - Solberg, S.; Næsset, E.; Hanssen, K.H.; Christiansen, E. Mapping defoliation during a severe insect attack on Scots pine using airborne laser scanning. Remote Sens. Environ.
**2006**, 102, 364–376. [Google Scholar] [CrossRef] - Solberg, S. Mapping gap fraction, LAI and defoliation using various ALS penetration variables. Int. J. Remote Sens.
**2010**, 31, 1227–1244. [Google Scholar] [CrossRef] - Armston, J.; Disney, M.; Lewis, P.; Scarth, P.; Phinn, S.; Lucas, R.; Bunting, P.; Goodwin, N. Direct retrieval of canopy gap probability using airborne waveform lidar. Remote Sens. Environ.
**2013**, 134, 24–38. [Google Scholar] [CrossRef] - Chasmer, L.; Hopkinson, C.; Treitz, P. Investigating laser pulse penetration through a conifer canopy by integrating airborne and terrestrial lidar. Can. J. Remote Sens.
**2006**, 32, 116–125. [Google Scholar] [CrossRef] [Green Version] - Su, W.; Zhan, J.G.; Zhang, M.Z.; Wu, D.Y.; Zhang, R. Estimation Method of Crop Leaf Area Index Based on Airborne LiDAR Data. Trans. Chin. Soc. Agric. Mach.
**2016**, 47, 272–277. [Google Scholar] [CrossRef] - Woodgate, W.; Jones, S.D.; Suarez, L.; Hill, M.J.; Armston, J.D.; Wilkes, P.; Soto-Berelov, M.; Haywood, A.; Mellor, A. Understanding the variability in ground-based methods for retrieving canopy openness, gap fraction, and leaf area index in diverse forest systems. Agric. For. Meteorol.
**2015**, 205, 83–95. [Google Scholar] [CrossRef] - Beland, M.; Parker, G.; Sparrow, B.; Harding, D.; Chasmer, L.; Phinn, S.; Antonarakis, A.; Strahler, A. On promoting the use of lidar systems in forest ecosystem research. For. Ecol. Manag.
**2019**, 450, 117484–117493. [Google Scholar] [CrossRef] - Morsdorf, F.; Kötz, B.; Meier, E.; Itten, K.I.; Allgöwer, B. Estimation of LAI and fractional cover from small footprint airborne laser scanning data based on gap fraction. Remote Sens. Environ.
**2006**, 104, 50–61. [Google Scholar] [CrossRef] - ASPRS. LASer (LAS) File Format Exchange Activities. Available online: https://www.asprs.org/wp-content/uploads/2010/12/asprs_las_format_v12.pdf (accessed on 8 April 2021).
- Monsi, M.; Saeki, T. On the Factor Light in Plant Communities and its Importance for Matter Production. Ann. Bot.
**2004**, 95, 549–567. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Nilson, T. Inversion of gap frequency data in forest stands. Agric. For. Meteorol.
**1999**, 98–99, 437–448. [Google Scholar] [CrossRef] - Solberg, S. Comparing discrete echoes counts and intensity sums from ALS for estimating forest LAI and gap fraction. In Proceedings of the 8th International Conference on LiDAR Application in Forest Assessment and Inventory, Edinburgh, UK, 17–19 September 2008. [Google Scholar]
- Hopkinson, C.; Chasmer, L.E. Modelling canopy gap fraction from lidar intensity. In Proceedings of the ISPRS Workshop on Laser Scanning 2007 and SilviLaser 2007, Espoo, Finland, 12–14 September 2007; ISPRS: Espoo, Finland, 2007; pp. 190–194. [Google Scholar]
- Yin, T.G.; Qi, J.B.; Cook, B.D.; Morton, D.C.; Wei, S.S.; Gastellu-Etchegorry, J.-P. Modeling Small-Footprint Airborne Lidar-Derived Estimates of Gap Probability and Leaf Area Index. Remote Sens.
**2020**, 12, 4. [Google Scholar] [CrossRef] [Green Version] - Boyd, D.; Hill, R. Validation of airborne LIDAR intensity values from a forested landscape using HYMAP data: Preliminary analysis. In Proceedings of the ISPRS Workshop on Laser Scanning 2007 and SilviLaser 2007, Espoo, Finland, 12–14 September 2007; ISPRS: Espoo, Finland, 2007. [Google Scholar]
- Lovell, J.L.; Jupp, D.L.; Culvenor, D.S.; Coops, N.C. Using airborne and ground-based ranging lidar to measure canopy structure in Australian forests. Can. J. Remote Sens.
**2003**, 29, 607–622. [Google Scholar] [CrossRef] - Alonzo, M.; Bookhagen, B.; McFadden, J.P.; Sun, A.; Roberts, D.A. Mapping urban forest leaf area index with airborne lidar using penetration metrics and allometry. Remote Sens. Environ.
**2015**, 162, 141–153. [Google Scholar] [CrossRef] - Korhonen, L.; Korpela, I.; Heiskanen, J.; Maltamo, M. Airborne discrete-return LIDAR data in the estimation of vertical canopy cover, angular canopy closure and leaf area index. Remote Sens. Environ.
**2011**, 115, 1065–1080. [Google Scholar] [CrossRef] - Zheng, G.; Moskal, L.M. Computational-Geometry-Based Retrieval of Effective Leaf Area Index Using Terrestrial Laser Scanning. IEEE Trans. Geosci. Remote Sens.
**2012**, 50, 3958–3969. [Google Scholar] [CrossRef] - Ni-Meister, W.; Jupp, D.; Dubayah, R. Modeling lidar waveforms in heterogeneous and discrete canopies. IEEE Trans. Geosci. Remote Sens.
**2001**, 39, 1943–1958. [Google Scholar] [CrossRef] [Green Version] - Luo, S.Z.; Chen, J.M.; Wang, C.; Gonsamo, A.; Xi, X.H.; Lin, Y.; Qian, M.J.; Peng, D.L.; Nie, S.; Qin, H.M. Comparative Performances of Airborne LiDAR Height and Intensity Data for Leaf Area Index Estimation. IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens.
**2018**, 11, 300–310. [Google Scholar] [CrossRef] - Tang, H.; Dubayah, R.; Swatantran, A.; Hofton, M.; Sheldon, S.; Clark, D.B.; Blair, B. Retrieval of vertical LAI profiles over tropical rain forests using waveform lidar at La Selva, Costa Rica. Remote Sens. Environ.
**2012**, 124, 242–250. [Google Scholar] [CrossRef] - Tian, L.; Qu, Y.H.; Korhonen, L.; Korpela, I.; Heiskanen, J. Estimation of forest leaf area index based on spectrally corrected airborne LiDAR pulse penetration index by intensity of point cloud. J. Remote Sens. (China)
**2020**, 24, 1450–1463. [Google Scholar] [CrossRef] - Lemeur, R. A method for simulating the direct solar radiation regime in sunflower, jerusalem artichoke, corn and soybean canopies using actual stand structure data. Agric. Meteorol.
**1973**, 12, 229–247. [Google Scholar] [CrossRef] - Campbell, G.S. Extinction coefficients for radiation in plant canopies calculated using an ellipsoidal inclination angle distribution. Agric. For. Meteorol.
**1986**, 36, 317–321. [Google Scholar] [CrossRef] - Chen, S.G.; Shao, B.Y.; Impens, I.; Ceulemans, R. Effects of plant canopy structure on light interception and photosynthesis. J. Quant. Spectrosc. Radiat. Transf.
**1994**, 52, 115–123. [Google Scholar] [CrossRef] - Yan, G.J.; Hu, R.H.; Luo, J.H.; Mu, X.H.; Xie, D.H.; Zhang, W.M. Review of indirect methods for leaf area index measurement. J. Remote Sens.
**2016**, 20, 958–978. [Google Scholar] [CrossRef] - Lang, A.R.G. Leaf-Area and Average Leaf Angle From Transmission of Direct Sunlight. Aust. J. Bot.
**1986**, 34, 349–355. [Google Scholar] [CrossRef] - Mu, X.H.; Hu, R.H.; Zeng, Y.L.; McVicar, T.R.; Ren, H.Z.; Song, W.J.; Wang, Y.Y.; Casa, R.; Qi, J.B.; Xie, D.H.; et al. Estimating structural parameters of agricultural crops from ground-based multi-angular digital images with a fractional model of sun and shade components. Agric. For. Meteorol.
**2017**, 246, 162–177. [Google Scholar] [CrossRef] - Sun, G.Q.; Ranson, K.J. Modeling lidar returns from forest canopies. IEEE Trans. Geosci. Remote Sens.
**2000**, 38, 2617–2626. [Google Scholar] [CrossRef] - Goel, N.S.; Strebel, D.E. Simple Beta Distribution Representation of Leaf Orientation in Vegetation Canopies 1. Agron.J.
**1984**, 76, 800–802. [Google Scholar] [CrossRef] - Ma, L.X.; Zheng, G.; Eitel, J.U.; Magney, T.S.; Moskal, L.M. Retrieving forest canopy extinction coefficient from terrestrial and airborne lidar. Agric. For. Meteorol.
**2017**, 236, 1–21. [Google Scholar] [CrossRef] - Wilson, J.W. Estimation of foliage denseness and foliage angle by inclined point quadrats. Aust. J. Bot.
**1963**, 11, 95–105. [Google Scholar] [CrossRef] - Miller, J.B. A formula for average foliage density. Aust. J. Bot.
**1967**, 15, 141–144. [Google Scholar] [CrossRef] - Itakura, K.; Hosoi, F. Estimation of Leaf Inclination Angle in Three-Dimensional Plant Images Obtained from Lidar. Remote Sens.
**2019**, 11, 344. [Google Scholar] [CrossRef] [Green Version] - Zheng, G.; Moskal, L.M. Leaf Orientation Retrieval From Terrestrial Laser Scanning (TLS) Data. IEEE Trans. Geosci. Remote Sens.
**2012**, 50, 3970–3979. [Google Scholar] [CrossRef] - Grau, E.; Durrieu, S.; Fournier, R.; Gastellu-Etchegorry, J.-P.; Yin, T. Estimation of 3D vegetation density with Terrestrial Laser Scanning data using voxels. A sensitivity analysis of influencing parameters. Remote Sens. Environ.
**2017**, 191, 373–388. [Google Scholar] [CrossRef] - Richardson, J.J.; Moskal, L.M.; Kim, S.H. Modeling approaches to estimate effective leaf area index from aerial discrete-return LIDAR. Agric. For. Meteorol.
**2009**, 149, 1152–1160. [Google Scholar] [CrossRef] - Lin, Y.; West, G. Retrieval of effective leaf area index (LAIe) and leaf area density (LAD) profile at individual tree level using high density multi-return airborne LiDAR. Int. J. Appl. Earth Obs. Geoinf.
**2016**, 50, 150–158. [Google Scholar] [CrossRef] - Weiss, M.; Baret, F.; Smith, G.J.; Jonckheere, I.; Coppin, P. Review of methods for in situ leaf area index (LAI) determination. Agric. For. Meteorol.
**2004**, 121, 37–53. [Google Scholar] [CrossRef] - Zhu, X.; Liu, J.; Skidmore, A.K.; Premier, J.; Heurich, M. A voxel matching method for effective leaf area index estimation in temperate deciduous forests from leaf-on and leaf-off airborne LiDAR data. Remote Sens. Environ.
**2020**, 240, 111696–111710. [Google Scholar] [CrossRef] - Peduzzi, A.; Wynne, R.H.; Fox, T.R.; Nelson, R.F.; Thomas, V.A. Estimating leaf area index in intensively managed pine plantations using airborne laser scanner data. For. Ecol. Manag.
**2012**, 270, 54–65. [Google Scholar] [CrossRef] [Green Version] - Chen, J.M.; Cihlar, J. Plant canopy gap-size analysis theory for improving optical measurements of leaf-area index. Appl. Opt.
**1995**, 34, 6211–6222. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Roberts, S.D.; Dean, T.J.; Evans, D.L.; McCombs, J.W.; Harrington, R.L.; Glass, P.A. Estimating individual tree leaf area in loblolly pine plantations using LiDAR-derived measurements of height and crown dimensions. For. Ecol. Manag.
**2005**, 213, 54–70. [Google Scholar] [CrossRef] - Farid, A.; Goodrich, D.C.; Bryant, R.; Sorooshian, S. Using airborne lidar to predict Leaf Area Index in cottonwood trees and refine riparian water-use estimates. J. Arid Environ.
**2008**, 72, 1–15. [Google Scholar] [CrossRef] [Green Version] - Pope, G.; Treitz, P. Leaf Area Index (LAI) Estimation in Boreal Mixedwood Forest of Ontario, Canada Using Light Detection and Ranging (LiDAR) and WorldView-2 Imagery. Remote Sens.
**2013**, 5, 5040–5063. [Google Scholar] [CrossRef] [Green Version] - Jensen, J.; Humes, K.; Vierling, L.; Hudak, A. Discrete return lidar-based prediction of leaf area index in two conifer forests. Remote Sens. Environ.
**2008**, 112, 3947–3957. [Google Scholar] [CrossRef] [Green Version] - Roberts, O.; Bunting, P.; Hardy, A.; McInerney, D. Sensitivity Analysis of the DART Model for Forest Mensuration with Airborne Laser Scanning. Remote Sens.
**2020**, 12, 247. [Google Scholar] [CrossRef] [Green Version] - North, P.R.J.; Rosette, J.A.B.; Suárez, J.C.; Los, S.O. A Monte Carlo radiative transfer model of satellite waveform LiDAR. Int. J. Remote Sens.
**2010**, 31, 1343–1358. [Google Scholar] [CrossRef] - Gastellu-Etchegorry, J.-P.; Yin, T.G.; Lauret, N.; Cajgfinger, T.; Gregoire, T.; Grau, E.; Feret, J.-B.; Lopes, M.; Guilleux, J.; Dedieu, G.; et al. Discrete Anisotropic Radiative Transfer (DART 5) for Modeling Airborne and Satellite Spectroradiometer and LIDAR Acquisitions of Natural and Urban Landscapes. Remote Sens.
**2015**, 7, 1667–1701. [Google Scholar] [CrossRef] [Green Version] - Wagner, W.; Ullrich, A.; Ducic, V.; Melzer, T.; Studnicka, N. Gaussian decomposition and calibration of a novel small-footprint full-waveform digitising airborne laser scanner. ISPRS J. Photogramm. Remote Sens.
**2006**, 60, 100–112. [Google Scholar] [CrossRef] - Liu, J.; Skidmore, A.K.; Jones, S.; Wang, T.; Heurich, M.; Zhu, X.; Shi, Y.F. Large off-nadir scan angle of airborne LiDAR can severely affect the estimates of forest structure metrics. ISPRS J. Photogramm. Remote Sens.
**2018**, 136, 13–25. [Google Scholar] [CrossRef] - Luo, S.Z.; Chen, J.M.; Wang, C.; Xi, X.H.; Zeng, H.C.; Peng, D.L.; Li, D. Effects of LiDAR point density, sampling size and height threshold on estimation accuracy of crop biophysical parameters. Opt. Express
**2016**, 24, 11578–11593. [Google Scholar] [CrossRef] - Qin, H.M.; Wang, C.; Xi, X.H.; Tian, J.L.; Zhou, G.Q. Simulating the Effects of the Airborne Lidar Scanning Angle, Flying Altitude, and Pulse Density for Forest Foliage Profile Retrieval. Appl. Sci.
**2017**, 7, 712. [Google Scholar] [CrossRef] [Green Version] - Xing, Y.Q.; Da, H.; You, H.T.; Tian, X.; Jiao, Y.T.; Xie, J.; Yao, S.T. Estimation of birch forest LAI based on single laser penetration index of airborne LiDAR data. Chin. J. Appl. Ecol.
**2016**, 27, 3469–3478. [Google Scholar] [CrossRef] - Lefsky, M.A.; Cohen, W.B.; Acker, S.A.; Parker, G.G.; Spies, T.A.; Harding, D. Lidar Remote Sensing of the Canopy Structure and Biophysical Properties of Douglas-Fir Western Hemlock Forests. Remote Sens. Environ.
**1999**, 70, 339–361. [Google Scholar] [CrossRef] - You, H.T.; Wang, T.J.; Skidmore, A.; Xing, Y.Q. Quantifying the Effects of Normalisation of Airborne LiDAR Intensity on Coniferous Forest Leaf Area Index Estimations. Remote Sens.
**2017**, 9, 163. [Google Scholar] [CrossRef] [Green Version] - Qin, Y.C.; Yao, W.; Vu, T.T.; Li, S.H.; Niu, Z.; Ban, Y.F. Characterizing Radiometric Attributes of Point Cloud Using a Normalized Reflective Factor Derived From Small Footprint LiDAR Waveform. IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens.
**2015**, 8, 740–749. [Google Scholar] [CrossRef] - Korpela, I.; Hovi, A.; Morsdorf, F. Understory trees in airborne LiDAR data—Selective mapping due to transmission losses and echo-triggering mechanisms. Remote Sens. Environ.
**2012**, 119, 92–104. [Google Scholar] [CrossRef] - Höfle, B.; Pfeifer, N. Correction of laser scanning intensity data: Data and model-driven approaches. ISPRS J. Photogramm. Remote Sens.
**2007**, 62, 415–433. [Google Scholar] [CrossRef] - Lim, K.; Treitz, P.; Baldwin, K.; Morrison, I.; Green, J. Lidar remote sensing of biophysical properties of tolerant northern hardwood forests. Can. J. Remote Sens.
**2003**, 29, 658–678. [Google Scholar] [CrossRef] - Korpela, I.; Hovi, A.; Korhonen, L. Backscattering of individual LiDAR pulses from forest canopies explained by photogrammetrically derived vegetation structure. ISPRS J. Photogramm. Remote Sens.
**2013**, 83, 81–93. [Google Scholar] [CrossRef] - Kashani, A.G.; Olsen, M.J.; Parrish, C.E.; Wilson, N. A Review of LIDAR Radiometric Processing: From Ad Hoc Intensity Correction to Rigorous Radiometric Calibration. Sens. Basel
**2015**, 15, 28099–28128. [Google Scholar] [CrossRef] [Green Version] - Chen, J.M.; Black, T.A. Foliage area and architecture of plant canopies from sunfleck size distributions. Agric. For. Meteorol.
**1992**, 60, 249–266. [Google Scholar] [CrossRef] - Hu, R.H.; Yan, G.J. Indirect Measurement of Forest LAI to Deal with the Underestimation Problem Based on Beer-Lambert Law. Geo-Inf. Sci.
**2012**, 14, 366–375. [Google Scholar] [CrossRef] - Chen, J.M.; Cihlar, J. Quantifying the effect of canopy architecture on optical measurements of leaf area index using two gap size analysis methods. IEEE Trans. Geosci. Remote Sens.
**1995**, 33, 777–787. [Google Scholar] [CrossRef] - Bréda, N.J.J. Ground-based measurements of leaf area index: A review of methods, instruments and current controversies. J. Exp. Bot.
**2003**, 54, 2403–2417. [Google Scholar] [CrossRef] - Lang, A.R.G. Estimation of leaf area index from transmission of direct sunlight in discontinuous canopies. Agric. For. Meteorol.
**1986**, 37, 229–243. [Google Scholar] [CrossRef] - Leblanc, S.G. Correction to the plant canopy gap-size analysis theory used by the Tracing Radiation and Architecture of Canopies instrument. Appl. Opt.
**2002**, 41, 7667–7670. [Google Scholar] [CrossRef] [PubMed] - Hu, R.H.; Yan, G.J.; Mu, X.H.; Luo, J.H. Indirect measurement of leaf area index on the basis of path length distribution. Remote Sens. Environ.
**2014**, 155, 239–247. [Google Scholar] [CrossRef] - García, M.; Gajardo, J.; Riaño, D.; Zhao, K.; Martín, P.; Ustin, S. Canopy clumping appraisal using terrestrial and airborne laser scanning. Remote Sens. Environ.
**2015**, 161, 78–88. [Google Scholar] [CrossRef] - Hu, R.H.; Bournez, E.; Cheng, S.Y.; Jiang, H.L.; Nerry, F.; Landes, T.; Saudreau, M.; Kastendeuch, P.; Najjar, G.; Colin, J.; et al. Estimating the leaf area of an individual tree in urban areas using terrestrial laser scanner and path length distribution model. ISPRS J. Photogramm. Remote Sens.
**2018**, 144, 357–368. [Google Scholar] [CrossRef] [Green Version] - Morisita, M. I
_{σ}-Index, a measure of dispersion of individuals. Res. Popul. Ecol.**1962**, 4, 1–7. [Google Scholar] [CrossRef] - Pielou, E.C. Runs of One Species with Respect to Another in Transects through Plant Populations. Biometrics
**1962**, 18, 579–595. [Google Scholar] [CrossRef] - Korpela, I. Mapping of understory lichens with airborne discrete-return LiDAR data. Remote Sens. Environ.
**2008**, 112, 3891–3897. [Google Scholar] [CrossRef] - Brandtberg, T. Classifying individual tree species under leaf-off and leaf-on conditions using airborne lidar. ISPRS J. Photogramm. Remote Sens.
**2007**, 61, 325–340. [Google Scholar] [CrossRef] - Irish, J.L.; Lillycrop, W. Scanning laser mapping of the coastal zone: The SHOALS system. ISPRS J. Photogramm. Remote Sens.
**1999**, 54, 123–129. [Google Scholar] [CrossRef] - Krzysztof, B. Multispectral airborne laser scanning-a new trend in the development of LiDAR technology. Arch. Fotogram. Kartogr. I Teledetekcji
**2015**, 27, 25–44. [Google Scholar] [CrossRef] - Hopkinson, C.; Chasmer, L.; Gynan, C.; Mahoney, C.; Sitar, M. Multisensor and Multispectral LiDAR Characterization and Classification of a Forest Environment. Can. J. Remote Sens.
**2016**, 42, 501–520. [Google Scholar] [CrossRef] - Hopkinson, C.; Lovell, J.; Chasmer, L.; Jupp, D.; Kljun, N.; van Gorsel, E. Integrating terrestrial and airborne lidar to calibrate a 3D canopy model of effective leaf area index. Remote Sens. Environ.
**2013**, 136, 301–314. [Google Scholar] [CrossRef] - Heinzel, J.; Huber, M. Detecting Tree Stems from Volumetric TLS Data in Forest Environments with Rich Understory. Remote Sens.
**2017**, 9, 9. [Google Scholar] [CrossRef] [Green Version] - Xia, S.B.; Wang, C.; Pan, F.F.; Xi, X.H.; Zeng, H.C.; He, L. Detecting Stems in Dense and Homogeneous Forest Using Single-Scan TLS. Forests
**2015**, 6, 3923–3945. [Google Scholar] [CrossRef] [Green Version] - Luo, S.Z.; Wang, C.; Pan, F.F.; Xi, X.H.; Li, G.C.; Nie, S.; Xia, S.B. Estimation of wetland vegetation height and leaf area index using airborne laser scanning data. Ecol. Indic.
**2015**, 48, 550–559. [Google Scholar] [CrossRef] - Tesfamichael, S.G.; van Aardt, J.; Roberts, W.; Ahmed, F. Retrieval of narrow-range LAI of at multiple lidar point densities: Application on Eucalyptus grandis plantation. Int. J. Appl. Earth Obs. Geoinf.
**2018**, 70, 93–104. [Google Scholar] [CrossRef] - Moeser, D.; Roubinek, J.; Schleppi, P.; Morsdorf, F.; Jonas, T. Canopy closure, LAI and radiation transfer from airborne LiDAR synthetic images. Agric. For. Meteorol.
**2014**, 197, 158–168. [Google Scholar] [CrossRef] - Heiskanen, J.; Korhonen, L.; Hietanen, J.; Pellikka, P.K. Use of airborne lidar for estimating canopy gap fraction and leaf area index of tropical montane forests. Int. J. Remote Sens.
**2015**, 36, 2569–2583. [Google Scholar] [CrossRef] - Jia, J.Q.; Liu, W.Q.; Meng, Q.Y.; Sun, Y.X.; Sun, Z.H. Estimation of maize leaf area index based on GF-1 WFV image and machine learning random algorithm. J. Image Graph.
**2018**, 23, 719–729. [Google Scholar] [CrossRef] - Li, X.L.; Dong, Y.Y.; Zhu, Y.N.; Huang, W.J. Leaf area index estimation with EnMAP hyperspectral data based on deep neural network. J. Infrared Millim. Waves
**2020**, 39, 111–118. [Google Scholar] [CrossRef] - Xiao, Z.Q.; Liang, S.L.; Wang, J.D.; Chen, P.; Yin, X.J.; Zhang, L.Q.; Song, J.L. Use of General Regression Neural Networks for Generating the GLASS Leaf Area Index Product From Time-Series MODIS Surface Reflectance. IEEE Trans. Geosci. Remote Sens.
**2014**, 52, 209–223. [Google Scholar] [CrossRef] - Chen, Z.L.; Jia, K.; Xiao, C.C.; Wei, D.D.; Zhao, X.; Lan, J.H.; Wei, X.Q.; Yao, Y.J.; Wang, B.; Sun, Y.; et al. Leaf Area Index Estimation Algorithm for GF-5 Hyperspectral Data Based on Different Feature Selection and Machine Learning Methods. Remote Sens.
**2020**, 12, 2110. [Google Scholar] [CrossRef] - Zhao, K.G.; Popescu, S.; Meng, X.L.; Pang, Y.; Agca, M. Characterizing forest canopy structure with lidar composite metrics and machine learning. Remote Sens. Environ.
**2011**, 115, 1978–1996. [Google Scholar] [CrossRef]

**Figure 3.**Effect of μ on LPIs. Each circle marks the position of the largest difference between LPIs and $LP{I}_{adj.}$ under different μ values. The size of the circle represents the absolute difference between LPIs and $LP{I}_{adj.}$.

Classification | NRs | RN | Example in Figure 1 |
---|---|---|---|

Single Return (SR) | =1 | =1 | # 1A, # 2A |

First Return (FR) | >1 | =1 | # 3A |

Intermediate Return (IR) | >2 | <NRs & >1 | # 3B |

Last Return (LR) | >1 | =NRs | # 3C |

LPIs Form | Reference | LPIs Form | Reference |
---|---|---|---|

${\mathrm{LPI}}_{\mathrm{SR}}=\frac{{\mathrm{SR}}_{\mathrm{g}}}{\mathrm{SR}+\mathrm{FR}}$ | [40] | ${\mathrm{LPI}}_{\mathrm{SR}\_\mathrm{LR}}=\frac{{\mathrm{SR}}_{\mathrm{g}}+{\mathrm{LR}}_{\mathrm{g}}}{\mathrm{SR}+\mathrm{LR}}$ | [51] |

${\mathrm{LPI}}_{\mathrm{A}.\mathrm{C}.}=\frac{{{\displaystyle \sum}}^{}\left(\frac{1}{cos\left(\mathsf{\theta}\right)}\right)}{\mathrm{SR}+\mathrm{FR}+\mathrm{LR}+\mathrm{IR}}$ | [33] | ${\mathrm{LPI}}_{\mathrm{MCI}}=1-\frac{{{\displaystyle \sum}}^{}\left(\frac{1}{{\mathrm{NS}}_{\mathrm{v}}}\right)}{\mathrm{SR}+\mathrm{LR}}$ | [42] |

${\mathrm{LPI}}_{\mathrm{SCI}}=\frac{{\mathrm{SR}}_{\mathrm{g}}+0.5\left({\mathrm{LR}}_{\mathrm{g}}+{\mathrm{FR}}_{\mathrm{g}}\right)}{\mathrm{SR}+0.5\left(\mathrm{FR}+\mathrm{LR}\right)}$ | [20] | ${\mathrm{ILPI}}_{\mathrm{beer}}=\frac{\frac{{{\displaystyle \sum}}^{}{\mathrm{I}}_{{\mathrm{SR}}_{\mathrm{g}}}}{{\mathrm{I}}_{\mathrm{total}}}+\sqrt{\frac{{{\displaystyle \sum}}^{}{\mathrm{I}}_{{\mathrm{LR}}_{\mathrm{g}}}}{{\mathrm{I}}_{\mathrm{total}}}}}{\frac{{{\displaystyle \sum}}^{}{\mathrm{I}}_{\mathrm{FR}}+{{\displaystyle \sum}}^{}{\mathrm{I}}_{\mathrm{SR}}}{{\mathrm{I}}_{\mathrm{total}}}+\sqrt{\frac{{{\displaystyle \sum}}^{}{\mathrm{I}}_{\mathrm{IR}}+{{\displaystyle \sum}}^{}{\mathrm{I}}_{\mathrm{LR}}}{{\mathrm{I}}_{\mathrm{total}}}}}$ | [52] |

^{1}$N{S}_{v}$ is the number of returns of pulse in where a ground return was recorded. ${I}_{*}$ refers to the intensity of certain types of returns (e.g., ${I}_{S{R}_{g}}$ is the intensity of single ground return) and ${I}_{total}$ is the total intensity of ground and vegetation returns. The other variables are the same as those defined in Table 1 and Section 2.

Type of Proxies | Proxies |
---|---|

Height-related metrics | Max height [83], mean height [84], median height [85], percentiles of height [24], base height, kurtosis of height, thickness of crown [33], height variance [86], standard deviation and coefficient of variation of height [60], interquartile distance [80], etc. |

LPIs | cf. Table 2 |

Canopy cover-related metrics | Canopy cover index [77,86], crown surface area [55], crown diameter [83], density of returns from canopy [81], canopy closure at different height [85], etc. |

Others | Canopy volume [77], number of lidar pulses per return class, and the proportion of 1st, 2nd, 3rd, and 4th returns [81], etc. |

Dominate Species | LiDAR Metrics | Type of Model | Saturate at | $\mathbf{Point}\mathbf{Density}\left(\mathit{p}\mathit{t}\mathit{s}\mathit{\xb7}{\mathit{m}}^{-2}\right)$ | $\mathbf{Plot}\mathbf{Size}{}^{1}\left(\mathit{m}\right)$ | References |
---|---|---|---|---|---|---|

Picea excelsa Lam. | Gap fraction | Physical | 4 | 35.68 | $50\times 50$ | [124] |

Pseudotsuga menziesii, Tsuga heterophylla, etc. | Mean height, canopy volume, canopy cover | Empirical | ~4.5 | - | $30\times 30$ | Figure 4a–c in [77] |

Lecythis idatimon Aubl., Pouteria gongrijpii Eyma, etc. | Height percentiles, canopy cover | Empirical | ~7.5 | 4 | $50\times 50$ | Figure 11 in [24] |

Pinus taeda | IB LPIs | Physical | 4 | ~10 | $-$ | [21] |

Pinus radiata D. Don | Height related, gap fraction-like, and some complex metrics | Empirical | 5 | 11.5 | $\mathrm{Mean}\left(\mathrm{h}\right)$ | [39] |

Pinus taeda L. | Height, LPIs, and Intensity related metric | Empirical | ~4.6 | >20 | $15\times 30$ | Figure 5 in [81] |

Populus spp., Salix spp., Sabina przewalskii kom., etc. | Height metrics | Empirical | ~4 | 5.49 | $30$ | Figure 4 in [60] |

Intensity-based metrics | ~3.8 | |||||

Combination model | ~4.5 | |||||

Eucalyptus grandis, Pinus | Point density related metric | Empirical | ~1.4 | 8 | $15$ | Figures 4a and 7a in [123] |

Eucalyptus saligna, Pinus spp., Cupressus lusita-nica, etc. | PNB and IB LPIs, canopy cover | Physical | ~4 | ~8.6 | $17.84$ | Figure 2 in [125] |

Pinus banksiana Lamb., Picea glauca Moench Voss, etc. | Height, cover related metric | Empirical | ~3.5 | 0.81 | $11.3$ | Figure 13 in [85] |

^{1}A single value refers to the radius of a circular field plot, the double values represent the side length of the rectangle plot, and $h$ is the height of trees within a field plot.

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

© 2021 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**

Tian, L.; Qu, Y.; Qi, J.
Estimation of Forest LAI Using Discrete Airborne LiDAR: A Review. *Remote Sens.* **2021**, *13*, 2408.
https://doi.org/10.3390/rs13122408

**AMA Style**

Tian L, Qu Y, Qi J.
Estimation of Forest LAI Using Discrete Airborne LiDAR: A Review. *Remote Sensing*. 2021; 13(12):2408.
https://doi.org/10.3390/rs13122408

**Chicago/Turabian Style**

Tian, Luo, Yonghua Qu, and Jianbo Qi.
2021. "Estimation of Forest LAI Using Discrete Airborne LiDAR: A Review" *Remote Sensing* 13, no. 12: 2408.
https://doi.org/10.3390/rs13122408