## 4 Discussion
It was shown that the magnitude of the largest negative height error was associated with the proportion of inventory plots with LiDAR density between 0-4 points/m\({}^{2}\) per county. In other words, counties with higher LiDAR density were less prone to severe height underestimation. It should be noted that the values of the y axis in Figure 18 are minimum values of height measurement error. The CHM of Southeastern Indiana counties should be carefully used when measuring canopy height since it can underestimate actual height value (Figures 12, 17 and 18). Height accuracy can particularly decrease on areas without a LiDAR return (initialized with zero in our case) or areas with lower point density. One can create a CHM with a larger pixel size by assigning maximum canopy height in each pixel area, or one can interpolate nearby valid canopy height can reduce the error. The accuracy of plot-wise canopy height can be minimally affected unless the highest tree is located near a plot boundary or a pixel boundary. Tree height was heavily overestimated up to approximately 20 m when inventory height was under 12 m (Figure 13). The overestimation could have occurred when the geolocation of the plot center was not accurate or when large trees with 12.7 cm or less in diameter were not included in measurement due to the CFI protocol. The main challenge in comparing the tree height using the CFI and CHM data was the positional error of GPS coordinates in plot center measurement (Figures 2, 16 and A1). The ninetieth percentile of positioning error of common handheld GPS devices was previously reported as 13.1 m in high forest [34]. The GPS error under a tree canopy increases due to unfavorable satellite constellation geometry, atmospheric interference, multi-path effect, and lower signal-to-noise ratio [35; 36]. Since the positioning error can far exceed the inventory plot radius (7.3 m), it is possible that there is minor or no overlap between an actual and a nominal plot area in extreme cases. Inventory plots with positional difference within 0.1 m were selectively used to mitigate co-registration issue between geospatial data (LiDAR) and plot center location. A more rigorous accuracy assessment would have been possible if accurate GPS remeasurements  
Figure 18: The largest negative height measurement error with respect to the proportion of inventory plots in counties with low LiDAR point density (0–4 points/m\({}^{2}\)). Data include Indiana counties where 3D Elevation Program (3 DEP) LiDAR data was collected in 2018. Counties having 20 or less inventory plots were excluded to highlight a statistical trend. Southeast Indiana counties with a large negative error (Figure 17a) were labeled. on plot centers were available across the state. However, the criteria used to select the inventory plots could still result in a biased set of evaluation points because the accuracy issues with GPS measurement were not completely eradicated. The positional uncertainty issue can be potentially alleviated if the plot centers are measured using a high-precision GPS device with real-time kinematic (RTK), post-processed kinematic (PPK) positioning, networked transport of RTCM via internet protocol (NTRIP) correction, or by other precision surveying techniques. If the issue with positional accuracy is resolved, diverse studies regarding the relationships between forest inventory attributes and remote sensing data can be conducted. We conducted accuracy assessment based on point density (points/m\({}^{2}\)). However, it is more desirable to use pulse density since it is less affected by characteristics of targets and more dependent on sensor configuration. Pulse density of multiple return LiDAR data can be computed by counting the number of the first returns in unit area. The characteristics of LiDAR and foliage density could adversely affect the accuracy of tree height measurement. A tree with a low foliage density can cause LiDAR pulse to travel a longer distance before being reflected at a thick branch or trunk.