How long would it take for all the land in the World to be eroded by 1 m given the following:
Rivers presently carry about 10^10 m^3 of soil and rock to the sea each year throughout the world. Roughly how long will it take at that rate for the continents to shrink by an average of 1 meter in elevation if all other processes (such as continental uplift) are ignored? You may use the fact that the total area of the continents is about 1.48×10^14 m^2 and that their mean elevation is about 840 meters. Assume also that the total area of the continents remains constant.
The total area of continents is 1.48×10^14 m^2. Rivers carry 10^10 m^3 of soil and rock to sea throughout the world. The volume of 1 m of soil on all the continents is equal to 1.48×10^14 m^3.
If this is eroded at the rate of 10^10 m^3 per year, the number of years in which the height of continents reduces by 1 m is `(1.48×10^14)/(10^10)` = 14800 years.
At the present rate of erosion the height of the continents would decrease by 1 m in 14800 years.
The mean elevation = 840m
Shrinkage required = 1m
Total area of the continents = 1.48*10^14 m2
Volume to be reduced = 1*1.48*10^14 = 1.48*10^14 m3
Average rate of soil move in to sea per year = 10^10 m3/year
Time required to shrink the continents = (1.48*10^14)/(10^10)
= 1.48*10^4 = 14,800 years
It will take approximately 14,800 years for river to shrink the continents in elevation by 1m