A field study in the Oregon Coast Range estimated that 175 m

A field study in the Oregon Coast Range estimated that 175 metric tons (t) was eroded from a .40 mi^2 catchment over a 6 year period. The soil had an average bulk density of 1500 kg/m^3. Express this erosion rate as a \'ground surface lowering rate\', in centimeters per million years.

Solution

We know that 1 mile = 1.609344 km so that 0.40 miles² = 0.4*0.4 = 0.16 square miles = 0.16( 1.609344)² sq. km = 0.414398097 sq km = 0.41 sq. km (on rounding off to 2 decimal places).

Now, the average bulk soil density is 1500kg/meter³. This means that the average weight of soil of 1 meter thickness in 1 square meter area, is 1500 kg. Then, the average weight of soil of 1 meter thickness in 0.41 sq. km area = 0.41*1500*1000*1000 kg = 615000000 kg = 615000 metric tons ( as 1 km = 1000 meters and 1 metric ton = 1000 kg).

We know that 175 metric tons of soil was eroded from a 0.41 sq. km area in 6 years. The thickness of soil erosion = 175/615000 meter in 6 years which is equivalent to (175/615000)( 1/6)(1000000) = 47.425 meters = 4742.5 cm per million years.