1. Creation of Bathymetric Surfaces Using High-Density Point Surveys
Mark Schmelter
CEE 6440
GIS in Water Resource Engineering
Fall 2007

2. Relevance to W.R. Engineering
New methods of data collection and analysis are constantly evolving
e.g., multi-dimensional hydraulic models
e.g., LiDAR, SoNAR
Hydraulics = f(bathymetry, planform)
Habitat models rely upon hydraulics
Geomorphic models rely upon hydraulics
Etc.

3. Objectives Evaluate: Differences between interpolation methods
Differences between interpolated surfaces resulting from differing point densities

4. Data and their Origins
Point data file from Trinity River Restoration Project (TRRP)
Collected using Airborne LiDAR Bathymetry (ALB) technology
Helicopter-mounted green and infra-red LiDAR
Horizontal precision = 2.5m
Vertical precision = 0.25m
Rated to water depth of 50m in ‘good’ conditions
Trinity data collected in December 2003 (6m max depth)

6. Inverse Distance Weighted Ordinary Kriging
"Everything is related to everything else, but near things are more related than distant things" (Tobler 1970)
Inverse Distance Weighted
Fast, very simple algorithm, easy paramaterization
Ordinary Kriging
Not fast, complicated parameterization
Robust statistical method
Local Polynomial Interpolation
Fast, easy parameterization (idiot-proof?)
Complicated; fits polynomial eqns to data
Tobler, W. R. (1970). "A computer model simulation of urban growth in the Detroit region." Economic Geography, 46(2),

7. Full dataset
10% of full dataset
100%
85%
70%
55%
40%
25%
10%

8. Reminder of objectives 1 & 2
See how surfaces vary between methods
See how surfaces vary with changing point densities
Subset, %
IDW OK
LPI
100% ?
85%
70%
55%
40%
25%
10%

9. Metrics RMSE Mean residuals Time to compute Cross-validation:
Remove one point from the data, interpolate, then compare the interpolated value at the removed location to the removed value
Red: Mean residual = ; RMSE = 8.094
Black: Mean residual = ; RMSE =

10. RMSE
Mean Residual
Time to compute

11. In the end…
12:12 versus 0:46
Unless you need to have a standard deviation surface (e.g., to create a confidence interval on your surface), just use IDW or LPI
If you want to have a confidence interval on your surface, you must use kriging

12. Questions? Kriged map of 55% subset
Standard deviation map of 55% subset