Uncertainty Analysis


To separate real geomorphic change from spurious changes it is necessary to account for uncertainties in the surveyed points that are ultimately passed onto the DEM surface. This section covers the concepts of MBES survey uncertainty and how these can be accounted for by creating slope and surface roughness rasters. 

ET-AL Recommendation to IPC

This section details a concise summary of some of the most relevant uncertainty analyses and experiments undertaken in Hensleigh (2013). The analyses summarized here form the basis for the subsequent GCD and MBES data preparation recommendations throughout the rest of the website.


Uncertainty & Topographic Complexity - Theory

The amount of surface roughness has a direct influence on the ability of the MBES to collect the minimum depth in the beam footprint region (Hare et al 1995; de Jong et al 2002). Figure 1 depicts this phenomenon in the across-track dimension. The depth measurement returned to the MBES is the shortest path, the point z1 from both examples in Figure 1. The potential uncertainty in the final derived surfaces will increase with increasing surface roughness and increasing beam footprint.

The slope of a surface influences the MBES ability to accurately collect depth measurements (de Jong et al 2002; International Hydrographic Bureau 2005). This is a function of the beam footprint and slope of the surface. This phenomenon is shown in Figure 1. Similar to uncertainty due to surface roughness, surface uncertainty in the final derived surfaces due to slope will increase with an increasing beam footprint.

Figure 1 - Beam footprint and Topographic Complexities

Depiction of how surface roughness and slope contribute to uncertainty in depth measurements. Surveying in the presence of slope is on the left and in the presence of surface roughness is on the right.

Survey overlap from separate SONAR passes during the same survey creates situations where soundings have struck the exact same spot. Sites where this occurs create the opportunity to compare the elevation measurements between the points to get an estimation of the vertical accuracy of measurements. To acquire this information an algorithm was designed to cycle through the original point clouds and extract only the points that have multiple measurements. Points were considered to be matching only if they had the exact same x and y coordinates as measured by the IPC MBES survey equipment, which returns coordinates to hundredths of a foot. 

Uncertainty & Topographic Complexity - Statistical Analysis 

To gain a greater understanding of how surface roughness and slope explicitly influence MBES measurement uncertainty slope and surface roughness values were extracted from rasters where two measurements were observed. These values were used to create scatter plots of measurement uncertainty explained by surface roughness and slope and are presented in Figure 2 below.

Figure 2 - Influence of Topographic Complexities on Measurement Uncertainty

Measurement uncertainty versus surface roughness and slope. Both parameters have a statistically significant effect on measurement uncertainty.

To further quantify the effect of surface roughness and slope on measurement uncertainty, surface roughness and slope were classified into 3 groups of low, medium and high values derived from the boxplot of each parameter, a non-parametric metric of distribution. To do this the boxplot was used to divide the data at understandable breaks that can be applied to other data sets and potentially other data types. The low class was designated as values less than or equal to the median, medium was greater than the median but less than or equal to the upper whisker of the boxplot, and high was classified as greater than the upper whisker of the boxplot. An ANOVA analysis assuming unequal variances was run on these groupings to determine if there was a difference in effect on the variance and mean of the measurement uncertainty values between groups. This analysis reveals there is a statistically significant difference in the mean and variance in the measurement uncertainty values based on slope and surface roughness groups. The statistical significance and graphical representation of this analysis is presented in Figure 3.

Figure 3 - Influence of Topographic Complexities on Uncertainty by Groups

Measurement error by grouping of low, medium and high of both slope and surface roughness. ANOVA of surface roughness groups resulted in a F-stat of 1009 on 789 degrees of freedoma while the same analysis of the slope groups resulted in a F-stat of 435 on 930 degrees of freedom.


Developing Proxy for Surface Roughness

The locally detrended standard deviation of a surface is a metric of surface roughness (Heritage and Milan 2009Rychkov, Brasington et al. 2012).  Locally detrending a surface before taking the standard deviation ensures that only local variations in height are being modeled. On a cell by cell basis this operation is computationally expensive and is not a standard tool in popular GIS. Work done by Rychkov et al led to the creation of a software package called Topographic Point Cloud Analysis Toolkit, or ToPCAT, that efficiently applies a thinning algorithm on a cell by cell basis.  Point cloud thinning or binning is common practice when using MBES and TLS data to reduce the computation times and memory requirements of their large point clouds (Kearns and Breman 2010). Point thinning is the process of setting a defined grid size and using the point values that are contained within those grids to calculate a representative value for each grid cell. PcTools uses the point values contained within the defined grid size to calculate the minimum, maximum, mean, detrended mean, range, standard deviation, detrended standard deviation, skew, detrended skew, kurtosis, detrended kurtosis, and point density. A minimum number of points is necessary, generally 4, to calculate the detrended standard deviation; the necessity to have more than one point within the cell resolution of analysis is in support of many of the concepts presented in Determining Cell Resolution.  Having these statistics in a regularly spaced grid is invaluable for developing a detrended standard deviation raster to represent surface roughness.
The video below is a tutorial of how to use ToPCAT in combination with ArcGIS to make a surface roughness raster:

Developing Slope Raster

The calculation of slope is a straight forward process in popular GIS software. The slope is calculated for each cell using a moving window. The slope value for each cell is calculated when it is the center of the moving window. This measurement gives an estimate of slope. Slope should be calculated in degrees as opposed to percent rise.




Relevant Literature

  • Hare , R. Godin, A. & Mayer, L.(1995) "Accuracy estimation of Canadian swath (multibeam) and sweep (multi- transducer) sounding systems". University of New Brunswick, Ocean Mapping Group. October 1995.
  • International Hydrographic Bureau.(2005). "Manual on Hydrography: Publication M-13". 1st Edition May 2005. 
  • de Jong, C.D., Lachapelle, G., Skone, S. & Elema, I.A.(2002). "Hydrography: Navtech Part #1150". DUP Blue Print, Delf University Press. 1st Edition, 2002.