# Assessment of Close-Range Remote Sensing Methods for DTM Estimation in a Lowland Deciduous Forest
## 2 Materials and Methods
### Methods  
Point clouds obtained using various close-range remote sensing methods were further processed to generate the regular 2D grid DTM. A morphological filtering algorithm and linear interpolation were used to produce the DTM, as presented in [PERSON] et al. 2015 [PERSON] et al. (2015). The lowest three-dimensional (3D) points in the regular grid were chosen as ground seed points. The seed points were grouped based on the connectivity of neighboring points. The largest group was classified as ground, and the ground was expanded based on the maximal expected slope and occlusion gap in the area. The DTM was generated based on classified ground points and linear interpolation. The same parameters were set for all datasets, i.e., the slope was gentle and maximal gap was set to 2 m. No manual editing was conducted on the point cloud, classification results or DTM. On average, 28.6%, 36.2%, 3.4% and 47.9% of the points were classified as a ground for TLS, PLS\({}_{\text{hh}}\), ULS and UAV\({}_{\text{image}}\) data, respectively. A DTM grid at a resolution of 0.3 m was created from all datasets. The DTMs estimated using different close-range remote sensing data sources were compared to checkpoints to evaluate the capacity of each system to produce high accuracy DTMs. Total station measurements are generally understood as the best ones available for DTM evaluation [10]. In total, 167 measurements were available within a 20 m distance from the plot center; there were 23, 27, 28, 27, 29 and 33 checkpoints at 6 plots, respectively. Data normality and outliers were inspected, and accuracy measures for both normal and robust assessments were given, according to [PERSON] and [PERSON] [29]. The outliers were filtered out using three times the RMSE value, i.e., if the absolute value of discrepancy was greater than three times the RMSE, the measurement was removed from the dataset. Although non-robust statistics are frequently used to evaluate DTM [1, 30], previous studies [26, 29] have indicated that ALS and DAP errors rarely follow a normal distribution and can contain outliers; hence, the normality of the data was examined. Both graphical and numerical assessment were applied to test the data normality. For graphical assessment, Q-Q plots [19] (Appendix A, Figure A1), discrepancy histograms and theoretical normal distribution (Appendix A, Figure A2) were applied. Numerical data normality testing was based on the Shapiro-Wilk test \(p\) value. All tests indicated that neither dataset was normally distributed (\(p<0.05\)) (Appendix A, Table A1). The non-robust and robust statistics were both calculated for the sake of comparison with other studies. The non-robust statistics were RMSE (Equation (1)), mean error (ME) (Equation (2)) and standard deviation (Equation (3)) as follows:  
\[\text{RMSE}=\sqrt{\frac{1}{n}\sum_{i=1}^{n}\Delta h_{i}^{2}} \tag{1}\]  
\[\text{ME}=\frac{1}{n}\sum_{i=1}^{n}\Delta h_{i} \tag{2}\]  
\[\text{SD}=\sqrt{\frac{1}{(n-1)}\sum_{i=1}^{n}\left(\Delta h_{i}-\Delta\overline {h}\right)^{2}} \tag{3}\]  
where \(\Delta h_{i}\) is a discrepancy between the reference and estimated height, \(i\) is the checkpoint index, \(n\) is the total number of checkpoints and \(\Delta\overline{h}\) is an average discrepancy. Robust statistics were median (Equation (4)), normalized median absolute deviation (NMAD) (Equation (5)), 68.3% quantile (Equation (6)) and 95% quantile (Equation (7)) as follows:  
\[\text{Median}=Q_{\Delta h}(0.5) \tag{4}\]  
\[\text{NMAD}=1.4826\cdot\text{median}(|\Delta h_{i}-m_{\Delta h}|) \tag{5}\]  
\[68.3\%\text{ quantile}=Q_{|\Delta h|}(0.683) \tag{6}\]  
\[95\%\text{ quantile}=Q_{|\Delta h|}(0.95) \tag{7}\]  
where \(Q\) denotes quantile and m denotes median. The PLS\({}_{\text{hh}}\) and TLS dataset results were analyzed to assess a relationship between achieved accuracy and the distance to the ground. The accuracy of the LiDAR devices depends on the distance to the object, and the object (reflecting properties, shape etc.) that laser beam reflects from.