The leaf area index (LAI) is a crucial structural parameter of forest canopies. Light Detection and Ranging (LiDAR) provides an alternative to passive optical sensors in the estimation of LAI from remotely sensed data. However, LiDAR-based LAI estimation typically relies on empirical models, and such methods can only be applied when the field-based LAI data are available. Compared with an empirical model, a physically-based model—e.g., the Beer–Lambert law based light extinction model—is more attractive due to its independent dataset with training. However, two challenges are encountered when applying the physically-based model to estimate LAI from discrete LiDAR data: i.e., deriving the gap fraction and the extinction coefficient from the LiDAR data. We solved the first problem by integrating LiDAR and hyperspectral data to transfer the LiDAR penetration ratio to the forest gap fraction. For the second problem, the extinction coefficient was estimated from tiled (1 km × 1 km) LiDAR data by nonlinearly optimizing the cost function of the angular LiDAR gap fraction and simulated gap fraction from the Beer–Lambert law model. A validation against LAI-2000 measurements showed that the estimates were significantly correlated to the reference LAI with an R2 of 0.66, a root mean square error (RMSE) of 0.60 and a relative RMSE of 0.15. We conclude that forest LAI can be directly estimated by the nonlinear optimization method utilizing the Beer–Lambert model and a spectrally corrected LiDAR penetration ratio. The significance of the proposed method is that it can produce reliable remotely sensed forest LAI from discrete LiDAR and spectral data when field-measured LAI are unavailable.


  • The vegetation leaf area index (LAI), defined as one half of the total leaf area per unit ground surface area [1], is one of the important variables related to many ecological applications [2]

  • These indicate that, for naturally growing trees, there is a predominant leaf angle distribution, and this feature results in a more concentrated distribution of extinction coefficient due to the nonlinear relationship between the mean tilt angle and leaf angle distribution. This finding is demonstrated by the decreasing coefficient of variation (CV) of the LAI, mean tilt angle and extinction coefficient from 0.27 to 0.18 and 0.16

  • Our research is one of the few attempts to derive LAI using discrete Light Detection and Ranging (LiDAR) data based on a physically-based model rather than empirical methods

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The vegetation leaf area index (LAI), defined as one half of the total leaf area per unit ground surface area [1], is one of the important variables related to many ecological applications [2]. Remote sensing technology offers a cost-effective method for surveying LAI in a large coverage area of land. Passive remote sensing data from sensors such as MODIS are routinely used to estimate vegetation LAI for large areas [3]. The most commonly used method to estimate LAI from LiDAR data is based on fitting empirical models linking field-measured LAI to LiDAR-derived metrics. These metrics include cover fractions [5,6], height [7] or height percentiles [8], and varied penetration metrics [9,10]. In the above empirical methods, the field-measured LAI data are required as training data, and such data sets are not always available


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