[EmilyA1997 (OP)]

Can anyone help me find the percent rate of annual erosion of the Grand Canyon? [?]

[DoctorBeaver]

Percentage of what? The Colorado river cuts the canyon deeper, while other factors (wind, rain, etc) erode the canyon walls. How can you put a percentage on the amount eroded? Do you class all of the uplands as part of the canyon? And how deep into the river bed rocks would you want to include?

What I can tell you, though, is that approximately half a million tons of sediment is removed from the canyon every day. That may sound a lot, but when you consider the size of the Grand Canyon (250 miles long, up to 20 miles wide, and a mile deep) and the billions upon billions of tons of rock there must be, it's not really that much.

[EmilyA1997 (OP)]

[O8)] [O8)] [O8)] [O8)] [O8)] [O8)] [O8)] [O8)] [O8)] [O8)] [O8)]
How do you think I am supposed to know?
I am only 10 years old???!!!!!!!!!!

[DoctorBeaver]

Emily, I apologise. I didn't realise you were just a sprog  []

Personally, I don't think you can calculate a percentage for it. As I said, you have to know what it is a percentage of before you can put a figure to it. I suppose you could calculate the total surface area of the canyon (sides & bottom) and then re-do the calculation a year later and see what the increase is.

However, it would be horrendously difficult to calculate the surface area in the same way that it is almost impossible to measure the length of a coastline. Where do you draw the line? Do you include the surface of this rock? Of that rock? Of that clump of mud sticking out of the canyon wall? In fact, with a canyon wall, it would be even more difficult due to all the lumps and dips you would find. You would have to measure top to bottom every couple of inches along the wall, making sure your measuring instrument went right into any dips in the wall.

Has a teacher set this question for you? If so, I would ask them what exactly it is that they want the percentage of.

We do have a geologist here who, hopefully, will read this thread & reply.

[JimBob]

It has all happened within the past 5 million years. It would take calculus and a lot of variables such as degree of consolidation of the rocks, amount of water flowing at any one time (greater during glacial periods) and about 247 other variables. SO - it is too tough for me to answer. And I are a geologer.

You are forgiven Doctor, but still a water ...

 

[DoctorBeaver]

You are forgiven Doctor, but still a water ...

Now, where's that big rock?  [!]

[DoctorBeaver]

Jim - Your method would give the present daily erosion as a percentage of the total erosion over the past 5 million years. That's something I hadn't considered and makes it even more essential to know exactly what it is a percentage of that Emily needs to find out.

Thinking about it, your method is actually easier. Once you establish the type(s) of rock involved you can calculate the total weight of eroded rock since it began (length x avg depth x avg width x avg weight of rocks) and then work out what 500,000 tons is as a percentage of that.

I know the length is 250 miles and the average height is about 5000', but I'm not sure of the average width.

However, that would give a misleading figure as 500,000 would decrease as a percentage of the total erosion. On day 1, 500,000 would be 100% of the total; after 4 days it would be 25% etc (although I doubt the figure was as high as 500,00 in the early days of erosion)

[JimBob]

Just a few of the variables to consider:

The steepness of the gradient of the river
The rate of uplift of the Colorado Plateau over time and how it varied - pulsations
The amount of sediment load - besides the water itself, the mechanical action of the
    sand and larger stuff in the river bed does more cutting than the water.
The height of sea level and how it varied
How much chemical erosion of the limestones and limestone cement of the sands
The toughness of the rock - granite is harder than sandstone
The rainfall variation within the entire drainage basin - a huge area
Glaciation and other climate variables

These are just what I could think of in 2 minutes - there are more, such as dams formed by igneous rocks and the effect of erosion when they finally break up - it is greater than at a "normal" river flow.

The easiest thing to do is to try to figure the volume of rock removed. Then divide that by 5 million years to get an average percentage rate of erosion.

Look on the web for the average depth of the canyon, the average width, assume that it is a "V" shape, and then get - in linear miles (including the twists and turns) the length and figure volume of the canyon. The divide that number by 5 million. you will get X cubic miles per year. That is a decent first approximation.

[DoctorBeaver]

A 10-year-old is expected to do this? Oo-wee!  []

[JimBob]

Just the last paragraph. Or a kindly beaver who builds dams would know just by instinct alone how much water the Grand Canyon would hold if that beaver were the real thing. Hum, makes one wonder.

[DoctorBeaver]

Not a problem - 2,770miles³ of water. 1yard³ of water weighs 1,685 Imperial pounds. So, the total weight of water would be 25,445,891,891,200,000lbs or 11,359,773,165,714.3 Imperial tons.

[JimBob]

so - the amount of earth removed would be be of an approximate density of 2.65 (that of quartz) - the density of quartz. It therefore follows that the weight of material removed is 2240 pounds X 11,359,773,165,714.3 X 2.65 = 67,431,613,511,680,084.8 pounds of sediment. The AVERAGE erosion rate over 5,000,000 years would be 13,486,322,702.336 pounds of sediment per year.

[DoctorBeaver]

So, the current daily percentage of erosion (as a percentage of the total erosion over the past 5,000,000 years would be approximately ((100/500,000)*(13,486,322,702.336/5,000,000/365)) = 0.0015%

QED!  []

Just as a point of interest, why did you choose quartz?

[JimBob]

Quartz is the most common rock on earth. Sandstones and carbonates are usually slightly lower in density and metamorphic and igneous rocks are slightly more dense - USUALLY.

[DoctorBeaver]

OK. So it's a good rock to use as an average.

[JimBob]

Oui.

[DoctorBeaver]

I bet Emily doesn't even return to see the fruits of our labours  []

[JimBob]

But then when we get old, our attention span attenuates to that of a 10 year old, as well. SO - who are we to gripe?

[DoctorBeaver]

But then when we get old, our attention span attenuates to that of a 10 year old, as well. SO - who are we to gripe?

Sorry? What were we talking about?

[JimBob]

I can't remember.