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Leaf Area Index (LAI) is an important input variable for forest ecosystem modeling as it is a factor in predicting productivity and biomass, two key aspects of forest health. Current ^{−2}) and high spatial resolution WorldView-2 data (2 m). Multiple Linear Regression (MLR) models were generated using these variables. Results from these analyses demonstrate: (i) moderate explanatory power (^{2} = 0.53) for LiDAR height and density metrics that have proven to be related to canopy structure; (ii) no relationship when using SVIs; and (iii) no significant improvement of LiDAR models when combining them with SVI variables. The results suggest that LiDAR models in boreal forest environments provide satisfactory estimations of LAI, even with narrow ranges of LAI for model calibration. Models derived from low point density LiDAR in a mixedwood boreal environment seem to offer a reliable method of estimating LAI at high spatial resolution for decision makers in the forestry community. This method can be easily incorporated into simultaneous modeling efforts for forest inventory variables using LiDAR.

The Boreal Forest of Canada covers over 300 million hectares, stretching more than 1,000 km from the Atlantic to Pacific coasts [

In order to monitor vegetation health and sustainability at strategic (

When focusing on the need to monitor forest health for commercial or conservation applications, we are interested in assessing and monitoring primary productivity or biomass over large areas. Leaf Area Index (LAI), a key input to productivity models, can be estimated using a variety of remote sensing techniques (e.g., [

LAI has been used in many studies to derive, or correlate to, primary productivity or biomass (e.g., [

LiDAR LAI models have the potential to provide fast, repeat assessments of a forest, returning variables that can provide accurate estimations of biomass and productivity. Studies have been carried out around the world that assess LAI using LiDAR (e.g., [

The other aspect of this research,

It is hypothesized that there will be a statistically significant relationship between

The field campaign to collect

The majority of the tree species in the Hearst Forest are coniferous, with black spruce (

The plots selected for this project were extracted from a pre-existing pool of 446 plots. These plots were established in 2010 in support of two integrated LiDAR projects,

LiDAR data were acquired by North West Geomatics Ltd. during the period of 4 July to 4 September 2007 during leaf-on conditions. LiDAR data were collected using an Optech ALS50 sensor mounted in a Cessna 310 aircraft. These data were discrete pulse, with up to four returns measured. The properties of the LiDAR acquisition are summarized in ^{−2} across the Hearst Forest. Filtered and classified data were provided by North West Geomatics Ltd to partners at the Ontario Ministry of Natural Resources, who then generated the full suite of LiDAR predictor variables, including height and density metrics (

One hundred km^{2} tiles of WorldView-2 data were acquired on 26 June, 2011 between 13:02 and 13:03 local time (

WorldView-2 images were delivered in five segments spanning the three areas of interest. Image calibration was first done to convert relative radiance to absolute radiance, then conversion of the raw. TIFF image file to .BIL (binary interleaved by line) to prepare the image for atmospheric correction. Atmospheric correction was performed using the FLAASH module in ENVI

At each plot, DHPs were taken in order to estimate LAI using methods described in the DHP/TRACwin software manual [

The images were taken with a Nikon© D700 (Tokyo, Japan) and Fisheye-Nikkor© 8 mm f/2.8 lens (Tokyo, Japan) (

Images were taken with the focal point at standardized breast height (

Using a combination of

_{e}). To derive LAI, data were exported from

After all images were processed, the mean of each set of nine individual LAI values for each plot was calculated to provide an estimate of plot LAI. Any plots with a mixed species composition where the minority species had greater than 20 percent coverage by basal area of trees ≥ 10 cm DBH were linearly weighted. That is to say, a plot with 85% black spruce and 15% jack pine would be treated entirely as black spruce. This methodology was consistent with LAI processing work conducted by Karin van Ewijk [

There is a temporal gap between LiDAR collection (2007) and DHP/WorldView-2 collection (2011), but it has been shown that annual variability in maximum LAI is relatively stable [

Multiple Linear Regression (MLR) was the statistical method used for modeling LAI using the LiDAR variables. A preliminary goodness-of-fit test of LAI normality resulted in identifying a normal distribution, though with distinct outliers. An assessment of outliers determined that they corresponded to plots that included balsam fir, a species whose ^{2}, to avoid multicollinearity due to the high similarity between some variables. Most notably, the percentile (^{2}) the more straightforward (

From the much smaller subset of variables, several automated techniques were used to further investigate the relationships for modeling. Forward and backward stepwise selection of variables was run using the minimum Akaike Information Criterion (AIC) as the criteria for termination. Also, an automated decision tree approach provided insight into some of the variables with the most explanatory power. Variable reduction was completed beforehand even though automated stepwise methods in ^{2} was offset by an overabundance of predictor variables and a minimized AIC [

Descriptive statistics for the final set of plots can be seen in

The statistics presented in

While the statistics below demonstrate that there are only small statistical variations in LAI between sampling designs, ^{2} = 0.84) at the single DHP level, albeit with a moderate spread and general overestimation at higher LAI values. The variability around the 1:1 line results from the lack of any averaging, and the overestimation is likely because of the nature of the original plot selection. A small number of plots represent smaller forest stands close to the size of the DHP grid. These few small stands were originally visited to ensure adequate species representation in the initial studies undertaken in Hearst. This size discrepancy means that the central photograph was usually placed in the densest, central part of the stand. Examining some WorldView-2 scenes in both the multispectral and panchromatic confirms that several of the overestimated plots indeed fall in these smaller pockets. When using five DHPs within the plot a near-perfect correlation (R^{2} = 0.98) to the full nine photograph sample is observed, with minor variability around the 1:1 line and only slight overestimation at higher LAI values. From this figure it could be argued that future research in this area could be completed using a five photograph cross pattern with almost no loss of accuracy.

From the 53 original LiDAR predictor variables, variable selection was performed using scatterplot matrices and correlation analysis. Some of the most simple exclusions were variables from different sets that had similar calculations (e.g., median and P50, standard and absolute deviation). As median and P50 are actually the same value, it was simple to remove P50 from the potential list. Other variables like the Shannon Weaver Index (H) and the VCI were so closely related that it was easy to eliminate the more complex variable, H. The most difficult variables to exclude were height and density metrics, as they provided a large amount of information, but were also severely inter-correlated. Percentile variables correlated strongly with their adjacent variables (^{2}’s of 0.80 to 0.98, and adjacent density variables were even more inter-correlated, ranging from R^{2}’s of 0.89 to 0.97. Based on inter-correlations and correlations to LAI itself, 22 predictor variables were selected for model development (

Using automated decision tree and forward and backward, step-wise, automated variable selection methods within the model generation framework of JMP

Using manual entry and expert knowledge, in conjunction with monitoring the sum of squares and F-ratios, these remaining key variables were passed together in various combinations. This analysis generated the final model from the randomly selected calibration dataset of 150 plots (

This model has an adjusted R^{2} of 0.53 and RMSE of 0.57 (RMSE% = 24.7). All parameters are statistically significant at the <0.0001 level, with the exception of VCI at a slightly higher value (

Using the remaining 75 plots as validation, the model was run with the same predictor variables. This dataset results in an adjusted R^{2} of 0.58 (^{2} corresponds well to the explanatory power of both the calibration model (R^{2} = 0.53). A matched pairs test of the predicted and _{0} = the data sets means are statistically different)

Using the atmospherically corrected WorldView-2 data, an NDVI surface with 2 m spatial resolution was created and mean values were extracted for each plot. These NDVI values were compared to plot LAI values in an attempt to determine whether there was a relationship between NDVI and LAI for the Hearst Forest using these high resolution data (^{2} = 0.01) that the expected relationship between NDVI, as derived from WorldView-2 data, and LAI was not present.

While optical instruments alone proved insufficient to model LAI, further testing was done to investigate whether WorldView-2 data could improve the LiDAR model. MLR models may be able to extract information from a combination of predictor variables that may not have been apparent in a simple regression model [^{2} of 0.52 and RMSE of 0.52 (RMSE% = 22.2); coefficients can be seen in

Although it uses a different, reduced data set, it is apparent that the addition of the new NDVI variable does not improve the predictive ability of the existing LiDAR model. In fact, the NDVI predictor coefficient has a statistically non-significant p-value of 0.64.

The second model used the forward stepwise technique with the NDVI predictor variable pre-inserted into the selection. An additional four variables were automatically added to generate a comparable model to ^{2} of this model is 0.55 with an RMSE of 0.50 (RMSE% = 21.6).

Unlike the previous models, only three variables are statistically significant in this model, with NDVI and VCI having statistically non-significant

The inclusion of the four final variables presented above suggests some interesting aspects about the model and LiDAR prediction of LAI in general. The COVAR exhibited a strong, negative correlation to LAI (R^{2} = 0.42),

Other predictor variables did not exhibit strong correlations to LAI. However, the nature of MLR is that the combination and interplay of trends between predictor variables can often generate more explanatory power than an individual variable.

DA (

Crown closure (≥6 m; cc6) was the predictor variable most unlike the others as it was not a measure of statistical spread or the direct complexity of the canopy. Crown closure at each height was calculated as a proportion of the number of 2 m sub-pixels within the 20 m pixel that matched the height criteria to the total number of pixels (

The lack of height (P‘XX’) and density (D‘X’) metrics captured in the model was noteworthy as these tend to be predominant in modeling many other forest inventory variables (e.g., biomass, height, density) (e.g., [^{2}’s (e.g., 0.40–0.45). The lower accuracy may be an acceptable trade-off for users hoping to generate more basic, easily interpretable models, where simplicity could outweigh a small level of error. Overall, this portion of the study provides interesting insight into the relationships between these height and density metrics and variables more related to overall canopy characteristics and crown closure. LAI seems to be more reliably estimated with the latter.

Using the regression model created with the calibration dataset to estimate values of LAI for the validation dataset resulted in the trend of predicted

Existing work using LiDAR data alone to estimate LAI tends to show marginally better results than what was demonstrated here, but for different forest environments. A temperate coniferous forest study by Jensen ^{2} of 0.65 for their true LAI model and a slightly higher value (R^{2} = 0.68) when examining LAI values without clumping index processing. Their final model also used four predictors:

Another coniferous study in the eastern United States showed even better results [^{−2}) for intensively managed loblolly pine (^{2} ranged from 0.61 with two predictors to 0.82 with six predictors. The comparable, four variable model to our study obtained an adjusted R^{2} of 0.78 and used very different predictors,

The results of this portion of the study were not entirely unexpected. A previous study by [^{2}’s of 0.50 and 0.42 for their two campaigns. LAI values ranged from 0.92 to 4.17.

A Landsat-5 scene, acquired 14 August, 2008, was obtained for the same region as the WorldView-2 coverage and an NDVI surface was generated. The positive relationship between the two NDVI datasets was R^{2} = 0.61. A matched-pairs test of the WorldView-2 and Landsat values shows no statistical difference, with a null hypothesis-refuting p-value of 0.37. This relationship shows that the WorldView-2 NDVI values are comparable to the Landsat NDVI values.

It was originally surmised that the poor correlation was primarily due to a combination of the high spatial resolution of the sensor and the low spatial density of individual trees in the Hearst Forest (

The most reasonable explanation for the poor performance of optical data in estimating LAI is due to the open canopies and the introduction of alternate understory spectra into the NDVI calculations. One of the failings of the DHP product was that it only provided an estimate of LAI from the focal point of the lens upwards,

Deriving a statistical relationship was also difficult, given the narrow range of the NDVI and LAI values being compared. NDVI values ranged from 0.47 to 0.77 (range of 0.30) and LAI from 0.57 to 4.20 (range of 3.63). This range affected the ability of regression models to accurately depict trends in these data. Previously discussed successful models (e.g., [

It would seem that the addition of other LiDAR variables in conjunction with NDVI does not improve the models sufficiently to warrant further testing. This result was not unexpected considering the extremely poor correlation of NDVI values to LAI. While the model in ^{2} of 0.75 to 0.79 [

The results discussed here present a strong case for LiDAR modeling of LAI as opposed to more traditional optical approaches, particularly for the boreal mixedwood forests of central Ontario. Given the open canopies typical of the Hearst Forest, high resolution optical data tend to integrate surface spectra from all components of the plot (

This study was undertaken to examine several potential methods to remotely estimate Leaf Area Index (LAI) in a boreal mixedwood forest of northern Ontario. This research is unique in examining LAI in this particular setting in Ontario, using low density Light Detection and Ranging (LiDAR). Accurate and precise models of LAI allow for the monitoring of a wide array of LAI-dependant variables, e.g., biomass, productivity, general forest health. The ecological and commercial benefits to provincial and federal government agencies, as well as commercial forest managers, are far reaching. These benefits include more accurate predictions of harvest yields, better timing of forest management practices, periodic monitoring of invasive species progression, tracking carbon sequestration by vegetation, and more. The general result from this study shows that LiDAR data provide adequate LAI estimations to predict the variable over large spatial extents at moderate resolution. The final model included DA, COVAR, VCI and crown closure (≥6 m). The variables selected tended to be representative of whole canopy distribution, rather than individual statistical metrics (e.g., percentiles). The overall model produced an adjusted R^{2} of 0.53 with a 24.7% RMSE (validation dataset R^{2} = 0.58, RMSE% = 25.1). The validation dataset produced statistically consistent results.

There was no relationship observed when comparing Normalized Difference Vegetation Index (NDVI) derived from WorldView-2 data and LAI derived from digital hemispherical photographs (DHPs). Averaging at the plot level inherently smoothed some of the variability expected from the higher resolution WorldView-2 data. Testing concluded that this lack of relationship was not erroneous,

The combined model utilizing LiDAR and optical data also proved unsuccessful. Neither the original LiDAR model with NDVI inserted nor a new model built around NDVI improved the explanatory power of the original LiDAR-only model. This lack of success demonstrated that there were no within-data trends that could be exploited by the multiple linear regression (MLR) framework.

It was determined that there were no statistical differences in

In order to obtain a better understanding of patterns within the data it may be beneficial to reduce the full dataset down into smaller subsets,

Since NDVI derived from WorldView-2 data provided little insight into LAI, it may be suitable to investigate spectral vegetation indices (SVIs) that incorporate a soil or understory vegetation baseline coefficient derived from spectral endmembers. To test other SVIs that incorporate spectral unmixing to distinguish canopy from understory reflectance, would require spectral measurements from beneath the canopy [

Support for this project was provided by a GEOIDE Network Centre of Excellence (NCE) grant. Thanks also to Hearst Management Forest Inc. for providing the LiDAR data. Thanks to Murray Woods and Dave Nesbitt of the Ontario Ministry of Natural Resources-Southern Science and Information Section for LiDAR data processing. The authors would also like to thank Fraser McLeod for his assistance in the field. Treitz also acknowledges research support from the Natural Sciences and Engineering Research Council of Canada.

The authors declare no conflict of interest.

^{2}in best subset regression

LiDAR predictor variable descriptions.

LG%Hwd | Percent Hardwood by Basal Area for trees ≥ 10 cm |

LG%Con | Percent Conifer by Basal Area for trees ≥ 10 cm |

Sm%Hwd | Percent Hardwood by Basal Area for trees < 10 cm |

Sm%Con | Percent Conifer by Basal Area for trees < 10 cm |

MEAN | Mean height (m) |

STD_DEV | Standard Deviation |

ABS_DEV | Absolute Standard Deviation |

SKEW | Skewness |

KURTOSIS | Kurtosis |

MIN | Minimum height (m) |

P10 | First Decile (10th Percentile) LiDAR Height (m) |

P20 | Second Decile (20th Percentile) LiDAR Height (m) |

... | ... |

P90 | Ninth Decile (90th Percentile) LiDAR Height (m) |

MAX | Maximum height (m) |

D1 | Cumulative percentage of the number of returns found in Bin 1 of 10 |

D2 | Cumulative percentage of the number of returns found in Bin 2 of 10 |

... | ... |

D9 | Cumulative percentage of the number of returns found in Bin 9 of 10 |

DA | First returns/All Returns |

DB | First and only return/All Returns |

DV | First Vegetation Returns/All Returns |

MEDIAN | Median Height (m) |

VDR | Vertical Distribution Ratio = VDR=[Max − Median]/Max |

COVAR | Coefficient of variation (STD/Mean) |

CanCOVAR | Coefficient of variation (STD/Mean) of first returns only |

H | Shannon-Weaver Index |

VCI | Vertical Complexity Index |

FIRST | Number of First Returns |

ALLRETURNS | Number of all Returns |

FIRSTVEG | Number of First Vegetation Returns only |

ALLGROUND | Number of Ground Returns |

cc0 | Crown closure > 0 m |

cc2 | Crown closure ≥ 2 m |

cc4 | Crown closure ≥ 4 m |

… | … |

cc28 | Crown closure ≥ 28 m |

Map depicting Hearst, Ontario and surrounding cities.

Plot distribution in the Hearst Forest.

WorldView-2 satellite image coverage in the Hearst Forest.

Digital hemispherical photographs (DHP) sampling design.

Setup of camera and lens system in a plot.

DHP image example (Jack Pine LAI = 1.5).

Logarithm of digital number histogram used for thresholding and initial threshold placement (relative y-axis scaling of image digital numbers).

DHP thresholding example (1:1 resolution image (

Frequency Histogram of LAI values from 225 final model plots.

Comparison of plot LAI between the nine sample DHP average (x-axis); the five sample DHP cross pattern average (y-axis) and the single sample DHP estimate (y-axis).

WorldView-2 Normalized Difference Vegetation Index (NDVI)

Comparison of LAI and (

Predicted

Light Detection and Ranging (LiDAR) acquisition properties [

Pulse Rate | 119 KHz |

Scan Rate | 32 Hz |

Field of View | 30 Degrees |

Flying Height | 2,400 m |

Line Spacing | 1,000 m |

Overlap | 20% |

Point Density | 0.81 m^{−2} |

Vertical Accuracy | <30 cm |

Horizontal Accuracy |

Species TRACWin ratios.

Black Spruce | 1.35 | 0.14 |

Tamarack | 1.35 | 0.14 |

White Spruce | 1.35 | 0.14 |

Balsam Fir | 1.77 | 0.08 |

Jack Pine | 1.30 | 0.03–0.34 |

White Birch | 0.21 | |

Trembling Aspen | 0.21 | |

Baslam Poplar | 0.21 |

Leaf Area Index (LAI) statistics for final plots.

Mean | 2.26 |

Standard Deviation | 0.83 |

Range | 4.64 |

Minimum | 0.37 |

Maximum | 5.01 |

| |

Total Count (n) | 225 |

Descriptive statistics of three trials using different combinations of DHPs to estimate LAI.

Mean | 2.26 | 2.26 | 2.26 |

Standard Deviation | 0.83 | 0.86 | 0.97 |

Range | 4.64 | 4.68 | 6.00 |

Minimum | 0.37 | 0.32 | 0.12 |

Maximum | 5.01 | 5.00 | 6.12 |

Intra-plot Standard Deviation | 0.38 | 0.36 | -- |

Final suite of LiDAR predictor variables.

ABS_DEV | Absolute Standard Deviation |

KURTOSIS | Kurtosis |

P10 | First Decile LiDAR Height (m) |

P40 | Fourth Decile LiDAR Height (m) |

P60 | Sixth Decile LiDAR Height (m) |

MAX | Maximum height (m) |

D1 | Cumulative percentage of the number of returns found in Bin 1 of 10 |

D5 | Cumulative percentage of the number of returns found in Bin 5 of 10 |

D9 | Cumulative percentage of the number of returns found in Bin 9 of 10 |

DA | First returns/All Returns |

DV | First Vegetation Returns/All Returns |

MEDIAN | Median Height (m) |

VDR | Vertical Distribution Ratio = VDR = [Max−Median]/Max |

COVAR | Coefficient of variation (STD/Mean) |

CanCOVAR | Coefficient of variation (STD/Mean) of first returns only |

VCI | Vertical Complexity Index |

FIRSTVEG | Number of First Vegetation Returns only |

ALLGROUND | Number of Ground Returns |

cc2 | Crown closure ≥ 2 m |

cc6 | Crown closure ≥ 6 m |

cc12 | Crown closure ≥ 12 m |

cc20 | Crown closure ≥ 20 m |