{

U.S. Department of the Interior U.S. Geological Survey Frank Velasquez / Kristina Yamamoto

GIS in the Rockies 24 September 2015

Point Spacing and Pixel Size

Agenda

Objective Literature Alpha Table Concept of Operations Study Areas Point Clouds Process Flow RMSE Results Charts Discussions

Objective

• Attempt to fill in the literature surrounding the optimal point space (DEMpost space)

• For a given nominal point space (nps) distance (or point density) of a lidar point cloud, what is the optimal grid resolution without overly interpolating pixels or losing data quality

• i.e. What is the scalar to apply to nps to achieve optimal DEMpost spacing • α = nps ÷ DEMpost

• Empirical research problem • Experimental design is complete • Execution of the designed tests are (mostly) complete • Analysis of results is ongoing

Literature

• Rees and Arnold (2007) created a 2m raster grid from a 0.8 m nps

• Hopkinson et al. (2009) had varying nps between 1 and 4m and created two DEMs; one at 5m and one at 25m

• Perroy et al. (2010) created a raster grid at resolution equal to the nps • Gonzalez et al. (2010) suggest creating a grid of 2m or 5m from a 1m nominal point spacing

• Jones et al. (2010) used a 2m resolution grid from a 1.6m nps • Dong et al. (2010) suggested a raster resolution of one-third to one-fifth the nps; i.e. of 3 to 5m, raster resolution would be 1m

• Long et al. (2011) contradicts (or inverted) this suggesting that for spacing you would construct a 3m resolution grid.

• Keith Clarke (UCSB) suggested a DEMpost of 2 times the min, max, mean, or median of the nearest neighbor interpoint spacing

Alpha Table Technique No.

Name Formula NPS Alpha DEM Post

(cell size m2)

1 Nyquist-Shannon * p ≤ (h-bar [sub ij]/2)

2 Finn et al. (2012) 1.4 .90 1.6

3a Clarke min * DEM Post = 2 x spacing min

3b Clarke max * DEM Post = 2 x spacing max

3c Clarke mean * DEM Post = 2 x spacing mean

3d Clarke median * DEM Post = 2 x spacing median

4 Rees and Arnold (2007) 0.8 .40 2.0

5a Hopkinson et al. (2009) 1.0 .20 5.0

5b Hopkinson et al. (2009) 4.0 .16 25.0

5c Hopkinson et al (2009) 4.0 .80 5.0

6 Perroy et al. (2010) 1.5 1.0 1.5

7a Gonzalez et al. (2010) 1.0 .50 2.0

7b Gonzalez et al (2010) Same as 5a 1.0 .20 5.0

8 Jones et al (2010) Same as 5c 1.6 .80 2.0

9a Dong et al. (2010) 3.0 3.0 1.0

9b Dong et al (2010) 5.0 5.0 1.0

10 Long et al. (2011) 1.0 .33 3.0

11 Heideman 2.0 .67 3.0

* Postgres/PostGIS algorithm developed by Mike Gleason of NREL to calculate nearest neighbor All other alphas were derived from the literature (α = nps ÷ DEMpost)

Concept of Operations Raw point

cloud Filter ground

points

Reclassify ~5% of points for

control group

Generate DEM

Ground points

Generate shapefile of

control points

Shapefile DEM

Compare DEM to shapefile, calculate Δz

Reclassified point cloud

Output csv & generate

charts

Great Smoky Mtn. Study Area

Grand Canyon Study Area

Great Smoky Mtn. Point Clouds

All Points Ground Points Control Points 5,614,743 879,891 46,210 (5.25%)

Grand Canyon Point Clouds

All Points Ground Points Control Points 37,975,517 12,003,692 558,699 (4.65%)

Process Flow • LP360 to filter ground points from raw point cloud (Kim Mantey) • lasthin to filter/reclassify ~5% control points • ArcMap to create las dataset, calculate point statistics, verify reclassified point % • las2shp to generate shapefile of control points • Global Mapper to generate GeoTIFF DEM at various grid resolutions • ArcMap to verify DEM grid size • Global Mapper to compare DEM pixel z values to control group z values

Select all points in shapefile Rename “elevation” attribute to “point elevation” Add coordinates attributes to control points Apply elevation attributes from terrain layer (DEM) to control points Verify points now have two elevation attributes Calculate elevation delta

Create a new attribute (“elevation delta”) Subtract “elevation” from “point elevation” Generate statistics report (included slope attributes for possible future analysis)

Calculate RMSE and generate charts

Great Smoky Mtn. Technique No. Name Alpha DEM Post (Cell size m2) Columns and Rows RMSE

1 Nyquist-Shannon * .599 1.15 1305 x1305 0.35286

2 Finn et al. .90 .7667 1957 x 1957 0.19809

3a Clarke min * 3.383 .2039 7356 x 7356 0.17018

3b Clarke max * .077 8.9833 167 x 167 1.08971

3c Clarke mean * .288 2.3964 626 x 626 0.53171

3d Clarke median * .285 2.4252 619 x 619 0.54222

4 Rees and Arnold .40 1.725 870 x 870 0.47653

5a Hopkinson et al. .20 3.45 435 x 435 0.80557

5b Hopkinson et al. .16 4.3125 348 x 348 1.06316

5c Hopkinson et al. .80 .8625 1740 x 1740 0.18409

6 Perroy et al. 1.0 .69 2174 x 2174 0.18965

7a Gonzalez et al. .50 1.38 1087 x 1087 0.35112

9a Dong et al. 3.0 .23 6523 x 6523 0.17358

9b Dong et al. 5.0 .1380 10872 x 10872 0.17227

10 Long et al. .33 2.0909 718 x 718 0.59202

11 Heideman .67 1.0299 1457 x 1457 0.34911

Yamamoto .069 10.0 150 x 150 1.10687

1 meter cell .69 1.0 1500 x 1500 0.33047

• NPS .69 • Gonzalez 7b alpha same as Hopkinson 5a • Jones 8 alpha same as Hopkinson 5c

* Gleason algorithm nearest neighbor results: Min: 0.1019 m Mean: 1.1982 m Max: 4.4916 m Median: 1.2126 m

Grand Canyon Technique No. Name Alpha DEM Post (Cell size m2) Columns and Rows RMSE

2 Finn et al. .90 .3522 4259 x 4259 0.0890

4 Rees and Arnold .40 .7925 1893 x 1893 0.6000

5a Hopkinson .20 1.59 943 x 943 0.9363

5b Hopkinson .16 1.9813 757 x 757 0.9603

5c Hopkinson .80 .3963 3785 x 3785 0.4815

6 Perroy et al. 1.0 .317 4688 x 4688 0.3395

7a Gonzalez et al. .50 .63 2381 x 2381 0.4714

9a Dong et al. 3.0 .11 13638 x 13638 0.3430

9b Dong et al. 5.0 0.0634 23662 x 23662 0.3456

10 Long et al. .33 .9606 1562 x 1562 0.6401

11 Heideman .67 .4731 3171 x 3171 0.4699

Yamamoto .069 10.0 150 x 150 1.5501

1 meter cell .69 1.0 1500 x 1500 0.6350

• NPS .317 (Reported point density 9.97m2) • Nyquist-Shannon and Clarke inter-point spacing data unavailable at this time • Gonzalez 7b alpha same as Hopkinson 5a • Jones 8 alpha same as Hopkinson 5c

Great Smoky Mtn. Alpha / RMSE

y = 0.2766x-0.531 R² = 0.8711

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

0.00 1.00 2.00 3.00 4.00 5.00

RM

SE

Alpha

Great Smoky Mtn. DEM Post / RMSE

y = 0.3369x0.5311 R² = 0.8711

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 10.00

RM

SE

DEM Post

Grand Canyon Alpha / RMSE

y = 0.3886x-0.38 R² = 0.5059

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

1.60

0.00 1.00 2.00 3.00 4.00 5.00

RM

SE

Alpha

Grand Canyon DEM Post / RMSE

y = 0.6015x0.3803 R² = 0.5059

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

1.60

0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 10.00

RM

SE

DEM Post

{

U.S. Department of the Interior U.S. Geological Survey Frank Velasquez / Kristina Yamamoto

GIS in the Rockies 24 September 2015

Point Spacing and Pixel Size

Discussions