A note on my previous post that included an elevation profile from Google Earth: I wrote, "This is probably the most accurate and detailed profile yet." It's certainly detailed, but I realize that it includes some artifacts. For example, notice the steep, narrow dips at around 0.22 km and 1.48 km. These are places where a creek or drainage ditch passes under the street. The street includes a bridge or other built-up structure so it remains level. But Google Earth determines elevations by mathematically fitting the general shape of the earth's surface, ignoring built-up structures like bridges. So it displays a profile as if runners ran right into the creek or ditch!
These artifacts may impact some of the statistics displayed with Google's profile, such as Elevation Gain/Loss and Max Slopes.
The elevations in MapMyRun are ultimately derived from the same Google database, but they aren't as fine-grained, so aren't as sensitive to these artifacts. My preferred method for deriving the steepness integral is still to display the profile in MapMyRun (Full Screen view). Hover over the plot and copy all the data points. Then enter in a spreadsheet to compute the steepness integral.
As an interesting observation: While Google Earth seems to totally ignore the built-up structures that maintain levelness of streets and roads, I think the contour lines on old-fashioned topo maps may have done a better job of accounting for such features.
The fact that Google Earth's elevations don't include bridges may also be an issue in deriving elevation profiles for courses with significant portions on bridges, such as the New York Marathon, which crosses the Verrazano Bridge at its start.