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

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.

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

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)

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), 234-240.

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

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%

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 = -4.498; RMSE = 8.094 Black: Mean residual = 0.1142; RMSE = -2.817

RMSE Mean Residual Time to compute

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

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