Relict shoreline features at Cockburn Island, Ontario

Abstract

Cockburn Island, Ontario (45°55′ N, 83°20′ W), holds at least six sets of elevated lake bluffs, scarps and bar deposits that mark distinctive water planes above the Nipissing Great Lakes water plane (∼198 m). These relict shoreline features occur at elevations that correspond closely with the elevations of others at nearby St. Joseph Island and in eastern upper Michigan. Together, the elevations and relative locations of steep relict bluffs suggest a proto-Cockburn Island once interrupted the surface of proglacial Lake Algonquin. The islet appears to have emerged and grown through a period of uplift and a sequence of lowering water levels. The highest relict shoreline (280.2 m) is correlated with the Main phase of Lake Algonquin. Lower shorelines at Cockburn Island cannot be correlated consistently, so additional work is required.

Appendix

Data processing methods

Locations referenced to the NAD83 were projected onto the Universal Transverse Mercator (UTM) 17 North grid. UTM coordinate values were offset by an affine transformation to situate a false origin (0,0) at 318,600 m E, 5,087,600 m N, which is roughly the geometric center of McCaigs Hill, and converted to kilometer units of measure. Elevations are reported as orthometric heights (H) and were calculated as:

$$ \hbox{H}=h-\hbox{N} $$

(1)

where h is the average of sampled heights above the WGS84 ellipsoid as obtained from GPS leveling; and N is the geoidal undulation obtained from the GEOID03 model. Users of GEOID03 in nearby Michigan are able to convert between NAD83 and NAVD88 to within 2.7 cm (Roman et al. 2004: 11, Table 1).

Analysis of GPS observations

First-order trend surface models provide useful estimates of water plane elevations and tilt over small areas:

$${\varvec{\hat{\beta }}}=({X}^T{X})^{-1}{X}^T{y} $$

(2)

where y is a vector of orthometric heights measured at sampled sites; X is a vector of coordinate pairs at sampled locations; and ${\varvec{\hat{\beta}}}$ is a vector of intercept (b ₀) and slope parameters (b ₁, b ₂) to be estimated when a trend model is fitted to each subset of data. Because a false origin was situated at the geometric center of McCaigs Hill, each intercept term (b ₀) can be interpreted as the average water plane elevation at the proto-island. The set of slope coefficients (b ₁ and b ₂) can be interpreted as estimates of tilt (m/km) with respect to the UTM 17 N grid axes. As mentioned above, however, estimates of tilt are not reported because slope values calculated over such small areas may not be significant.