Reservoir lifetime. You are asked to estimate the useful lifetime of the reservo

Question

Reservoir lifetime. You are asked to estimate the useful lifetime of the reservoir created by the Three Rivers Gorge dam on the Yangtze River in China. By using your knowledge of the topography being dammed, and the height of the dam to be constructed, you calculate that the initial volume of the reservoir when filled with water is 39.3 km3. Using 10Be in river sediments, you determine that the mean erosion rate of the landscape delivering sediment to the reservoir is 2.5x10-4 m/yr. The catchment area is 106 km2. Let us say that we will define the “useful lifetime” of the reservoir to be the time it takes to fill half of the volume of the reservoir with sediment. What is this lifetime, in years?

Explanation / Answer

Given,

the initial volume of the reservoir= 39.3km3

the catchment area of the reservoir= 106km2

mean rate of erosion= 2.5*10-4 m/yr

=2.5*10-7 km/yr

therefore the volume of sediment delivered per year= mean rate of erosion * catchment area of the reservoir

=2.5*10-7 * 106 km3/yr

=2.65 * 10-5 km3/yr

If the useful lifetime of the reservoir is defined as the time the reservoir takes to fill half of the volume of the reservoir with sediment then,

half of the reservoir volume =39.3 km3 * 1/2

=19.65km3

Therefore at the given rate of sediment supply the reservoir's lifetime= half of the reservoir volume/ volume of sediment delivered per year

=19.65km3/(2.65*10-5 km3/yr)

=741509.4 years

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