By the way, after I posted last night, as I was getting ready to go to sleep, I thought of a possible objection to the math I used in my previous post regarding how fast the Grand Canyon is growing. Simply put, my figures only looked at one aspect: the depth of the canyon. However, the Grand Canyon is a three dimensional object (although is it really proper to call the absense of something–rock–an object?). Anyway, that meant today I redid my figures based on these statistics. There we are told that the Grand Canyon has a volume of 4.17 trillion cubic meters, which averages out to 695,000 cubic meters of erosion per year:

4.17 trillion cubic meters = 4,170,000,000,000 cubic meters

4,170,000,000,000 cubic meters / 6,000,000 years = 695,000 cubic meters/year

This incorporates both the river’s depth and the width of the canyon as a whole averaged out over the course of the 6 million years that it is claimed the Grand Canyon took to “create.” I’ll look at this number a bit more later.

But I do have to confess that I’m not sure how they arrived at the figure of 4.17 trillion cubic meters of volume for the Grand Canyon. After all, we are told that the canyon is:

433 km long (river length)
16 km average width (with 28.81 km max width)
1.6 km average depth

Now, running those figures for volume (i.e. length x width x depth) yeilds 4,330 cubic km (using the average number for the width)–which is 4,330,000 cubic m. That’s 4.33 million, not 4.17 trillion cubic meters. Even if we use the max width, we only get 7,800 cubic km, which is 7.8 million cubic meters.

My next thought was that maybe it had something to do with the river length that they were measuring. Since rivers meander, however, it seems that using the river length would actually make the volume larger than using a straight line measurement. (To visualize this, if you have a 1 foot long/wide square, you can wrap a 3 foot long jump rope inside it easily. The area of the square is one square foot, yet the rope is three feet long. Thus, if we incorporate the river miles into the cube we’re looking at, we can actually get a vastly inflated volume. Only if the river was perfectly straight would we get the correct length for the cube we’re looking at.

In any case, I could see how simplifying this to a cube would be nowhere near accurate as a cube isn’t a canyon; however, measuring the canyon in the simpler cubic form should give results too large rather than too small, as the canyon should fit inside the cube. So, again, I’m not sure where the National Park Service got their numbers for 4.17 trillion cubic meters of volume in the Grand Canyon. In fact, if we stipulate that the length and width are correct, in order to get 4.17 trillion cubic meters of volume, the canyon would need to be:

4.17 trillion cubic meters = 4,170,000,000,000 m = 4,170,000,000 km

X km x 433 km x 28.81 km = 4,170,000,000 km^3 =
X km = (4,170,000,000 km^3)/(433 km)(28.81 km) = 334,275 km

334,275 km is about 209,000 miles. Clearly, something is weird with these figures. Unfortunately, the National Park Service does not provide enough information about their method of measurement for me to be able to do anything else with this. About the only thing I can figure is that it might have something to do with the elevation differences between the head of the canyon and the end of the canyon. Still, that would have to be pretty impressive to account for the difference between 4.17 trillion cubic meters and 7.8 million cubic meters: a difference so minute that you’re still left trying to account for 4.17 trillion cubic meters when you take rounding into consideration:

4,170,000,000,000 - 7,800,000 = 4,169,992,200,000…rounds to 4.17 trillion.