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The Earth’s surface roughness constitutes an important parameter in terrain analysis for studying different environmental and engineering problems. Authors gave different definitions and measures for the earth’s surface roughness that usually depend on exploitation of digital elevation data for its reliable determination. This research aimed at exploring the different approaches for defining and extraction of the Earth’s surface roughness from Airborne LiDAR Measurements. It also aimed at evaluating the effects of the window size of the standard deviation filter on the created roughness maps in downtown landscapes using three known approaches namely; standard deviation filtering of the Digital Elevation Model (DEM), standard deviation filtering of the slope gradient model and standard deviation filtering of the profile curvature model. In this context, different roughness maps have been created from Airborne LiDAR measurements of the City of Toronto, Canada using the three filtering approaches with varying window sizes. Visual analysis has shown color tones of small roughness values with smooth textures dominate the roughness maps from small window sizes of the standard deviation filter, however, increasing the window sizes has produced wider variations of the color tones and rougher texture roughness maps. The standard deviations and ranges of the roughness maps from LiDAR DEM have increased due to increasing the filter window size while the skewness and kurtosis have decreased due to increasing the window size, indicating that the roughness maps from larger window sizes are statistically more symmetrical and more consistent. Thus, kurtosis has decreased by 53% and 82% due to increasing the window size to 7 × 7 and 15 × 15 respectively. The standard deviations of the roughness maps from the slope gradient model have increased due to increasing the window size till 15 × 15 while they have decreased with more increases. However, skewness has decreased due to increasing the window size till 15 × 15 and the kurtosis has decreased with higher rate till window size of 11 × 11. In the roughness maps from the profile curvature model, the ranges and skewness have decreased by 93.6% and 82.6% respectively due to increasing the window size to 15 × 15 while, kurtosis has decreased by 58.6%, 76.3% and 93.76% due to increases in the filter window size to 5 × 5, 7 × 7 and 15 × 15 respectively.

The Earth’s surface roughness is an important parameter for terrain analysis as it reflects numerous geophysical parameters such as landform characteristics in addition to playing an important role in analyzing different natural phenomena [

Grohmann et al. 2011 & 2009 [

Big advances in computing technology and increasing of storage capacity motivated digital elevation models to be widely used in different applications supported by the availability of high-resolution digital elevation data at horizontal and vertical domains that allows accurate calculations of the parameters extracted from a DEM [

Digital elevation data derived from new technologies employing active remote sensing methods such as airborne laser scanning and radar ranging are becoming more widespread where past research need to be re-evaluated in the near future to accommodate such new elevation data products and its applications in extraction of different surface parameters such as surface roughness [

1) It is much easier to separate tall objects from roads with the use of LiDAR.

2) Surface roughness can be easily obtained from LiDAR data.

3) Airborne LiDAR data from narrow scanning angle and active sensing technology suffers less occlusions and smaller shadows allowing features such as roads to be more complete compared to that from the imageries.

4) The intensity of the reflectance of LiDAR measurements can provide useful means for road extraction since road surfaces should have similar reflectance.

5) Rivers are easy to be detected from LiDAR measurements since water steams absorb laser light to be represented as no-data.

Fan and Atkinson 2018 [

This research aimed at exploring the different approaches for defining and extraction of the Earth’s surface roughness from digital elevation data in general. However, great emphasis has been given to extraction and analysis of surface roughness maps from Airborne LiDAR Measurements in urban landscapes characterized by intensive varieties of different geometry, size, shape and elevation features expected to provide great roughness to resist water movements during flooding. This is added to the wide involvements of the Earth’s surface roughness in many other applications. The study also, aimed at evaluating the effects of the size of the user defined window of the standard deviation filtering process on the created roughness maps from airborne LiDAR data in urban downtown landscape using three known approaches for defining and measuring the surface roughness namely; the standard deviation of the surface elevations, the standard deviation of the surface slope gradients and the standard deviation of the surface profile curvatures.

A sample of LiDAR data of the ISPRS WG III/4 Test Project on Urban Classification and 3D Building Reconstruction has been provided by ISPRS WG III/4. The Optech airborne laser-scanner ALTM-ORION M captured the airborne laser scanning data for a limited area at the city center of the City of Toronto in Canada [^{2}. The data is formatted in ASPRS (American Society of Photogrammetry and Remote Sensing)’s LAS 1.3 format [^{2} of approximate dimensions of about 508 meters in swath width by about 1412 meters as the swath length. The sample data consists of 2747785 LiDAR data measurements giving LiDAR point cloud density of 3.83074 points per one meter squared (pts/m^{2}). This means that one LiDAR measurement has been recorded for every 0.261045 squared meters in average. The statistical analysis of the data set showed a minimum elevation of −9.69 meters and a maximum elevation of 165.02 meters giving a range of elevations of 174.71 meters as shown by the legend in

A digital elevation model has been created from the Toronto_Strip_03.las LiDAR data file using SAGA 6.4 open source GIS software where the Inverse Distance Weighting (IDW) interpolation technique with the power of four and grid resolution of half a meter have been used. In addition, a slope gradient model and a profile curvature model have been extracted from the generated DEM of the downtown of the City of Toronto in Canada. Also, each of the generated DEM, slope gradient model and the profile curvature model have been subject to standard deviation filtering of varied window sizes for the production of different surface roughness maps from some of the selected popular surface roughness measures. In this study, standard deviation filters of windows of sizes of 3 × 3, 5 × 5, 7 × 7, 9 × 9, 11 × 11, 15 × 15, 21 × 21, 25 × 25, 31 × 31, 35 × 35 and 41 × 41 have been used under the surfer 15 commercial software package. The generated surface roughness maps extracted from the standard deviation filtering of elevations, the standard deviation filtering of slope gradient and the standard deviation filtering of profile curvature at varying filter window sizes have been subjected to visual and statistical analysis for the purpose of studying of the effects of the standard deviation filter window size on the extracted roughness maps from Airborne LiDAR measurements in downtown urban landscape.

Figures 2-9 depict surface roughness maps created as a result of standard deviation filtering of Airborne LiDAR DEM using filters of varied window sizes of 3 × 3, 5 × 5, 7 × 7, 11 × 11, 15 × 5, 21 × 21, 31 × 31 and 41 × 41 respectively. In

Stdev. filter size | DEM stdev. filter 3 × 3 | DEM stdev. filter 7 × 7 | DEM stdev. filter 11 × 11 | DEM stdev. filter 15 × 15 | DEM stdev. filter 21 × 21 | DEM stdev. filter 25 × 25 | DEM stdev. filter 31 × 31 | DEM stdev filter 35 × 35 | DEM stdev. filter 41 × 41 |
---|---|---|---|---|---|---|---|---|---|

Statist. quantity | |||||||||

Min. (m) | 0 | 0 | 0 | 0 | 0 | 0.00065 | 0.000651 | 0.00973 | 0.01150 |

Max. (m) | 117.120 | 127.107 | 129.277 | 129.759 | 130.123 | 130.548 | 131.060 | 130.910 | 130.036 |

Mean (m) | 0.901 | 2.125 | 3.304 | 4.448 | 6.092 | 7.146 | 8.663 | 9.624 | 10.981 |

Median (m) | 0.160 | 0.496 | 0.9581 | 1.517 | 2.474 | 3.216 | 4.399 | 5.188 | 6.317 |

RMS(m) | 2.693 | 5.454 | 7.589 | 9.388 | 11.685 | 13.031 | 14.849 | 15.951 | 17.468 |

Stdev. (m) | 2.539 | 5.023 | 6.832 | 8.267 | 9.9716 | 10.896 | 12.060 | 12.721 | 13.586 |

Range (m) | 117.12 | 127.11 | 129.277 | 129.759 | 130.123 | 130.547 | 131.059 | 130.900 | 130.024 |

Skewness (m) | 8.822 | 6.6597 | 5.5461 | 4.8534 | 4.206 | 3.906 | 3.567 | 3.390 | 3.172 |

Kurtosis | 141.498 | 75.771 | 52.152 | 39.905 | 30.130 | 26.160 | 22.054 | 20.0759 | 17.805 |

Sum (m) | 2,420,492 | 5,710,244 | 8,879,719 | 11,953,851 | 16,372,277 | 19,205,322 | 23,281,319 | 25,866,209 | 29,512,019 |

In this study surface roughness maps have been created from standard deviation filtering of a slope gradient model extracted from airborne LiDAR measurements where varying sizes of the standard deviation filter widow as 3 × 3, 5 × 5, 7 × 7, 9 × 9, 11 × 11, 15 × 5, 21 × 21, 25 × 25, 31 × 31, 35 × 35 and 41 × 41 have been used. Figures 12-19 represent eight of the created surface roughness maps with the use of the standard deviation filtering of varying window sizes of 3 × 3, 5 × 5, 7 × 7, 11 × 11, 15 × 5, 21 × 21, 31 × 31 and 41 × 41 respectively. In

The statistical analysis results of the roughness maps created from standard deviation filtering of the slope gradient model extracted from LiDAR measurements with varying window sizes are shown in

Stdev. filter size | Slope stdev filter 3 × 3 | Slope stdev filter 5 × 5 | Slope stdev filter 9 × 9 | Slope stdev filter 15 × 15 | Slope stdev filter 21 × 21 | Slope stdev filter 25 × 25 | Slope stdev filter 31 × 31 | Slope stdev filter 35 × 35 | Slope stdev filter 41 × 41 |
---|---|---|---|---|---|---|---|---|---|

Statist. quantity | |||||||||

Min. (deg.) | 0 | 0 | 0 | 0 | 0 | 0.114319 | 0.11432 | 0.11432 | 0.34275 |

Max (deg.). | 44.478 | 44.464 | 43.846 | 43.468 | 43.307 | 43.177 | 42.856 | 42.616 | 42.286 |

Mean (deg.) | 6.450 | 9.666 | 14.125 | 18.3424 | 20.987 | 22.255 | 23.666 | 24.363 | 25.154 |

Median (deg.) | 4.935 | 8.759 | 14.103 | 18.680 | 21.809 | 23.246 | 24.741 | 25.399 | 26.102 |

RMS. (deg.) | 8.937 | 12.437 | 16.84 | 20.532 | 22.694 | 23.699 | 24.809 | 25.360 | 25.990 |

Stdev. (deg.) | 6.186 | 7.826 | 9.169 | 9.226 | 8.634 | 8.146 | 7.445 | 7.0419 | 6.542 |

Range (deg.) | 44.478 | 44.464 | 43.846 | 43.468 | 43.307 | 43.062 | 42.742 | 42.502 | 41.943 |

Skewness (deg.) | 1.340 | 0.765 | 0.280 | −0.115 | −0.334 | −0.431 | −0.549 | −0.614 | −0.683 |

Kurtosis (deg.) | 5.509 | 3.292 | 2.371 | 2.279 | 2.481 | 2.662 | 2.958 | 3.138 | 3.348 |

Sum (deg.) | 17,335,550 | 25,977,889 | 37,960,617 | 49,296,268 | 56,403,673 | 59,811,826 | 63,602,679 | 65,477,095 | 67,601,670 |

Figures 22-29 represent the surface roughness maps created as results of standard deviation filtering of the profile curvature model extracted from Airborne LiDAR measurements using filter of varied window sizes as 3 × 3, 5 × 5, 7 × 7, 11 × 11, 15 × 15, 21 × 21, 31 × 31 and 41 × 41 respectively. In

The statistical analysis results of the roughness maps created from standard deviation filtering of the profile curvature model extracted from LiDAR measurements with the use of varying filter window sizes are shown in

Three measures of the Earth’s surface roughness have been tested for creation and analysis of surface roughness maps from airborne LiDAR measurements. A group of surface roughness maps have been created from standard deviation filtering of LiDAR DEM with varying filter window sizes. Also, another group of surface roughness maps have been obtained from standard deviation filtering of LiDAR slope gradient model with varying filter window sizes. Additionally, a

Stdev. filter size | Profile curvat. filter 3 × 3 | Profile curvat. filter 5 × 5 | Profile curvat. filter 7 × 7 | Profile curvat. filter 9 × 9 | Profile curvat. filter 11 × 11 | Profile curvat. filter 15 × 15 | Profile curvat. filter 25 × 25 | Profile curvat. filter 35 × 35 | Profile curvat. filter 41 × 41 |
---|---|---|---|---|---|---|---|---|---|

Statist. quantity | |||||||||

Min. (m^{−1}) | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0.0031 | 0 |

Max. (m^{−1}) | 61.434 | 36.631 | 26.120 | 20.137 | 16.467 | 12.010 | 7.324 | 5.322 | 8.623 |

Mean(m^{−1}) | 0.266 | 0.333 | 0.374 | 0.402 | 0.423 | 0.452 | 0.493 | 0.516 | 0.515 |

Median (m^{−1}) | 0.146 | 0.229 | 0.285 | 0.320 | 0.341 | 0.367 | 0.399 | 0.415 | 0.420 |

RMS.(m^{−1}) | 0.573 | 0.606 | 0.617 | 0.623 | 0.627 | 0.630 | 0.634 | 0.636 | 0.632 |

Stdev. (m^{−1}) | 0.508 | 0.506 | 0.491 | 0.476 | 0.462 | 0.439 | 0.399 | 0.372 | 0.365 |

Range (m^{−1}) | 61.434 | 36.631 | 26.120 | 20.137 | 16.470 | 12.010 | 7.324 | 5.319 | 8.623 |

Skewness (m^{−1}) | 18.424 | 12.569 | 10.040 | 8.608 | 7.663 | 6.457 | 4.984 | 4.248 | 3.934 |

Kurtosis (m^{−1}) | 938.40 | 405.66 | 244.52 | 171.44 | 130.38 | 86.86 | 46.666 | 32.234 | 29.100 |

Sum (m^{−1}) | 713,782 | 894,517 | 1,004,256 | 1,080,285 | 1,136,434 | 1,214,443 | 1,324,695 | 1,386,030 | 1,549,376 |

third group of surface roughness maps have been generated from standard deviation filtering of LiDAR profile curvature model with varying filter window sizes. The three measures have been examined against the window size of the standard deviation filter in downtown urban landscape characterized by high intensity of varied geometry, sizes, shapes, heights, and types of features.

Visual analysis of the surface roughness maps from standard deviation filtering of LiDAR DEM has shown dark blue color tones dominate the roughness map from window size of 3 × 3 referring to small roughness values. Small changes have occurred on the roughness maps from window size of 5 × 5 where brighter color tone roughness map has been obtained but high degree of feature smoothing is still there. However, more increases in the window sizes of the standard deviation filters has given more structured roughness maps of rougher textures. The roughness map created with the use of window sizes of 31 × 31 and 41 × 41 have been the most structured roughness maps with relatively wide variation of the color tones within the maps and rough texture. Statistical analysis of the roughness maps generated from standard deviation filtering of LiDAR DEM has indicated that the standard deviation, mean, median and root mean square of the surface roughness maps have increased with increasing the window size of the standard deviation filter while the skewness has decreased with increasing the window size of standard deviation filter indicating that larger window sizes have produced statistically more symmetrically surface roughness maps. Additionally, the ranges of the surface roughness have increased by about 71.6% with changing the window size from 3 × 3 to 5 × 5, however it decreases with window sizes greater than 31 × 31. Moreover, the kurtosis has decreased sharply with increasing the window size till 15 × 15 while the rate of decreasing has become milder with more increases. That is kurtosis has decreased by about 53% and 82% due to increasing the window size to 7 × 7 and 15 × 15 respectively.

The surface roughness maps from standard deviation filtering of LiDAR slope gradient model have showed differences compared to their corresponding from filtering of LiDAR DEM where brighter blue color tones dominate the roughness map from window size of 3 × 3 referring to roughness values at the middle of the legend. The main streets have been represented in low roughness values of dark blue color tones as expected while the blocks of buildings have given roughness of bright blue color tones producing rough texture map. Similar to the roughness maps from LiDAR DEM, with increasing the window sizes of the standard deviation filters more structured roughness maps have been obtained with increases in the brighter blue tones and rougher textures. The roughness maps from window sizes of 31 × 31 and 41 × 41 have showed wide changes in the color tones producing rough texture roughness maps. Again, the statistical analysis of the LiDAR slope gradient roughness maps has indicated that the mean, median and root mean square of the roughness maps have increased due to increasing the size of the standard deviation filter with higher rates till 15 × 15 while the ranges of the roughness maps have decreased gradually with the increases in the window size. Also, the standard deviation of the roughness map has increased due to increasing the window size till 15 × 15 but more increases in the window size have given decreases in the standard deviation of the roughness map. Moreover, the skewness has decreased due to increasing the window size till 15 × 15 while it has increased with more increases indicating that the roughness maps from window size of 15 × 15 is the most symmetrical one. Furthermore, the kurtosis has decreased with relatively high rate due to increasing the filter window size till 11 × 11 where milder rates of decreases have occurred with larger window sizes indicating that the roughness map from window size of 11 × 11 is the most consistent.

Visual analysis of the standard deviation filtering of profile curvature model has indicated that dark blue color tones of small roughness values dominate the roughness maps from window sizes of 3 × 3 and 5 × 5 with the edges of the building cannot be easily distinguishable. With increasing the filter window sizes to 15 × 15 and 21 × 21 brighter but burred roughness maps have been obtained. However, in the roughness maps from window sizes of 31 × 31 and 41 × 41 much brighter color tones dominate the roughness maps but much blurred maps with hardly distinguishable features. The statistical analysis results of the roughness maps from standard deviation filtering of the profile curvature model have not been much different from those discussed earlier. The mean, median and root mean square of the roughness maps have increased with high rates due to increasing the filter window sizes till 15 × 15 where the rate of increase become smaller with larger sizes however, the standard deviation of the roughness map has decreased gradually due to increasing the filter window size. On the other hand, the ranges and skewness of the roughness maps have decreased with high rates due to increases in the filter window sizes till 15 × 15 while the rate of decreases become smaller with bigger window sizes. In this context, the ranges and skewness have decreased by about 93.6% and 82.6% respectively of the total decrease due to increasing the filter window size to 15 × 15. Also, the kurtosis has decreased with high rates due to increasing the filter window size where decreases in kurtosis of 58.6%, 76.3% and 93.76% have occurred due to increases in the window sizes to 5 × 5, 7 × 7 and 15 × 15 respectively.

The Earth’s surface roughness constitutes an important parameter in terrain analysis for studying different environmental and engineering problems. Authors gave different definitions and measures for the earth’s surface roughness that usually depend on exploitation of digital elevation data for its reliable determination. This research aimed at exploring the different approaches for defining and extraction of the Earth’s surface roughness from Airborne LiDAR Measurements. It also aimed at evaluating the effects of the window size of the standard deviation filter on the created roughness maps in downtown landscapes using three different measures for surface roughness namely; standard deviation filtering of the DEM, standard deviation filtering of the slope gradient model and standard deviation filtering of the profile curvature model. A complete tile of Airborne LiDAR measurement for the downtown of the City of Toronto, Canada has been exploited in creation of three groups of surface roughness maps with the use of the above mentioned three measures at varying window sizes of the standard deviation filter. The created surface roughness maps have been analyzed visually and statistically against the window size of the standard deviation filter in downtown urban landscape characterized by high intensity of varied sizes, shapes, heights, and types of features. Visual analysis has shown dark blue color tones of small roughness values dominate the roughness map from standard deviation filtering of LiDAR DEM with window size of 3 × 3, however, with increasing the filter window size, brighter blue color tones of higher roughness values and thicker edges of the buildings with more structured roughness maps have been obtained. However, bright blue color tones dominate the surface roughness map from standard deviation filtering of LiDAR slope gradient model using 3 × 3 window size while the main streets have been represented in dark blue color tones. Also, increasing the window size of the filter has given structured roughness maps of higher roughness values and wider changes in the color tones starting from dark blue to bright blue to yellow to orange color tones and finally to red color tones of high roughness values producing rough texture roughness maps. In the case of the roughness maps from standard deviation filtering of LiDAR profile curvature model, dark blue color tones have dominated the roughness maps from window sizes of 3 × 3 and 5 × 5 indicating that small window sizes produce small roughness values with edges of buildings not being easily distinguishable. However, with increasing the window sizes, brighter but blurred roughness maps have been obtained with wide areas of different color patches giving rough texture maps.

Statistical analysis has provided more understanding of the outcomes from the visual analysis where in the roughness maps from LiDAR DEM, the standard deviation, mean, median, root mean square and range have increased with increasing the filter window size where the ranges have increased by 71.6% due to increasing the window size from 3 × 3 to 5 × 5. On the other hand, the skewness and kurtosis have decreased with increasing the window size of the filter indicating that roughness maps from larger window sizes are statistically more symmetrical and more consistent since kurtosis has decreased by about 53% and 82% due to increasing the window size to 7 × 7 and 15 × 15 respectively. Close results have been obtained from the analysis of the roughness maps created from slope gradient model where, the mean, median and root mean square of the roughness maps have increased with high rates due to increasing the filter window size till 15 × 15 while the range has decreased gradually with increasing the window size. Additionally, the standard deviation of the roughness map has increased with increasing the window size till 15 × 15 while it has decreased with more increases. However, the skewness analysis has shown that window size of 15 × 15 has given the most symmetrical roughness map while the kurtosis analysis has shown that window size of 11 × 11 has given the most consistent one. Moreover, the statistical analysis of the roughness maps from profile curvature model has indicated that the mean, median and root mean square of the roughness maps have increased due to increasing the window size with high rate till 15 × 15 where the rate of increase become smaller with larger window sizes. However, the standard deviation, range, skewness and kurtosis of the roughness map have decreased due to increasing the window size of the filter where the range and skewness have decreased by 93.6% and 82.6% respectively due to increasing the window sizes to 15 × 15 while kurtosis has decreased by 58.6%, 76.3% and 93.76% due to window size increases to 5 × 5, 7 × 7 and 15 × 15 respectively. Exploitation of the roughness maps from the different approaches in real applications such as hydrodynamic modelling and flood studies could determine the efficiency of the different surface roughness measures in creation of reliable surface roughness maps in different landscapes.

The author would like to acknowledge the provision of the Downtown Toronto data set by Optech Inc., First Base Solutions Inc., GeoICT Lab at York University, and ISPRS WG III/4.

The author declares no conflicts of interest regarding the publication of this paper.

Asal, F.F.F. (2019) Creation and Analysis of Earth’s Surface Roughness Maps from Airborne LiDAR Measurements in Downtown Urban Landscape. Journal of Geographic Information System, 11, 212-238. https://doi.org/10.4236/jgis.2019.112015