The conversion of a point cloud to a DEM is necessary to ready the data for differencing operations. The high density of MBES data relative to the recommended cell resolution, reduce the importance of which interpolation technique is used. However regardless of the interpolation technique, uncertainty is always introduced when moving from a point representation to a gridded data format. This section details the implications of moving from point to a gridded format.
Concepts
Data produced from MBES generally have high sampling densities in the depths observed in rivers (< 100 feet) and relatively high quality, a reported accuracy in the magnitude of inches (Dix et al 2012; Hazel et al 2010; Ernsten et al 2006). Also, unlike in TLS studies (e.g. Leary et al. 2013), MBES data in most rivers generally don't suffer from vegetatoin obscuring the bed or ground returns. Studies have shown that there is little difference observed between interpolation techniques when sampling density is high (Chaplot, Darboux et al. 2006; Heritage, Milan et al. 2009). However certain land morphology, specifically the presence of high surface roughness and large relief, has the potential to affect the accuracy of interpolation techniques (Heritage, Milan et al. 2009).
Rock Shadows
Large boulders combined with the swath style data collection of MBES present a particular challenge for interpolation techniques. The swath data collection style does not accurately report the elevation of the backside of the boulder, creating a shadow zone where no depth measurement is reported on the side of the boulder further from the MBES. This shadow zone will increase in size with increasing depths, boulder size, and beam angles.
Figure 1 - Rock Shadow
Example of the potential for a shadow zone where no data is collected due to the obstruction of a large boulder and the swath style collection of MBES.
To explore the difference between interpolation techniques a simple analytical experiment was performed to compare and contrast the different techniques: inverse distance weighting (IDW), multiquadratic radial basis function (MRBF), regularized spline with tension (RST), ordinary kriging (OK) and universal kriging (UK). Due to the large size of the study site a subset of data was taken from the Wild Sheep Reach. The point cloud was divided in half with one half being used as the training set to interpolate a surface from while the other half, the test set, was used to compare the interpolated values. The difference between the interpolated values at the test set locations is a measure of interpolation error.
To assess precision root mean square error (RMSE) and mean error (ME) were calculated for each interpolation method in addition to these metrics max, min and percentage of uncertainty larger than two standard deviations of the mean uncertainty were compared . The results of this analysis are presented in Table 1.
Table 1 - Results - Interpolation Methods Comparison
Comparison of the results of interpolation study for inverse distance weighting (IDW), multiquadratic radial basis function (MRBF), ordinary kriging (OK), regularized spline with tension (RST), and universal kriging (UK).
Interpolation & High Topographic Complexity
Figure 2 - Problematic Landforms for Interpolation Techniques
The location of the points greater than the mean and two standard deviations of interpolation error were analyzed and subsequently used to identify landforms causing the clusters of high interpolation error.
The interpolation comparison experiments revealed that across all interpolation techniques about 5% of all errors are greater than 2 standard deviations from the mean (row 5, Table 1). Areas with clusters of high interpolation errors as designated from the above exercise were examined in more detail to reveal the landforms creating these errors. These areas tended to contain landforms displaying abrupt change in elevation; either a rock outcropping, boulder, break in slope, shelf or shear wall. Examples of these features in relation to elevation, slope and surface roughness are examined in Figure 2, along with the profile and histogram of elevation values of the landforms.
Due to the high point density of MBES all interpolation techniques performed very well. The high point density led to virtually the same errors even in areas of extreme surface roughness. The choice of interpolation technique is more of how many inputs the user is comfortable having control over. The similarities in 'quality' across interpolation techniques suggests any of these interpolation techniques would suffice. TINs were not tested in the experiment because they are exact interpolators and preserve the values at sampled points. 'Interpolation Error' only is introduced when TINs are converted from Rasters to DEM (via a nearest neighbor or linear interpolation scheme typically). Thus, TINs are most effective at preserving the values at raw points, but rasterization introduces interpolation error that is primarily a function of cell size.
For these reason converting the original point clouds to a TIN and then converting the TIN into a DEM is the recommended method. Note that for exceptionally dense point-clouds, or point clouds over very long (> 5 km) reaches it may be desireable to decimate the original point cloud first.
Uncertainty Due to Interpolation
Errors due to interpolation are an unavoidable relic that occur because of the need to convert data to raster format in order to perform raster-based analyses (e.g. GCD). It is important to recognize and quantify interpolation error, particularly large interpolation error. A tool for quantifying this error is provided in the MBES Toolkit: Create Interpolation Error Surface.
Resources
- Chaplot, V., F. Darboux, et al. (2006). "Accuracy of interpolation techniques for derivation of digital elevation models in relation to landform types and data density." Geomorphology 77: 126-141.
- Dix, M., Abd-Elrahman, A., Dewitt, B. & Nash, L. (2012). "Accuracy of terrestrial LIDAR and multibeam sonar systems mounted on a survey vessel". Journal of Surveying Engineering 138, 203-213.
- Ernstsen, V.B., Noormets, R., Hebbeln, D., Bartholoma, A. & Flemming, B.W. (2006). "Precision of high-resolution multibeam echo sounding coupled with high-accuracy positioning in shallow water coastal environment . Geo-Marine Letters 26, 3, 141-149.
- Hazel, J. E., P. E. Grams, et al. (2010). Sandbar Response in Marble and Grand Canyons, Arizona, Following the 2008 High Flow Experiment on the Colorado River.
- Heritage, G. L. and D. J. Milan (2009). "Terrestrial Laser Scanning of grain roughness in a gravel-bed river." Geomorphology 113: 4-11.
- Heritage, G. L., D. J. Milan, et al. (2009). "Influence of survey strategy and interpolation model on DEM quality." Geomorphology 112: 334-344.
- Leary RJ, Hensleigh JW, Wheaton JM , and DeMeurichy KD. 2012. Recommended Geomorphic Change Detection Procedures for Repeat TLS Surveys from Hells Canyon, Idaho. Ecogeomorphology and Topographic Analysis Lab, Utah State University, Prepared for Idaho Power Company, Logan, Utah, 144 pp.
Relevant GCD Online Help or Tutorials for this Topic
Slides and/or Handouts
- Lecture Slides - Basic Concepts of TINs
GIS References on Spatial Estimation & Interpolation
