Uplift Rate Calculations
Description
Spreadsheet showing the methods used to calculate average rock uplift rates and propagate the errors from the OSL data and elevation measurements.
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We calculated both an arithmetic average (A) and a weighted average for the ages of three samples (X, Y, Z) from each terrace. Because there was little difference, we used the arithmetic averages. For each OSL sample (X), there is a methodological error (x). Error propagation was used to calculate average error (a) to report with each average OSL age (A): (Equation 2) a=(1/n)*√(x^2+y^2+z^2 ) where (n) equals the number of samples. This yields (A ± a) ka. Fluvial incision rates are widely considered valid proxies for inland area rock uplift rates (Litchfield and Berryman, 2006). Average rock uplift rates can be calculated between any displaced paleosurface elevation (E) above the river channel with a known age (A) and a younger paleosurface elevation above the river channel (F) with a known age (B). The modern river channel, where (F=0) and (B=0) can also be used. The equation divides the difference in elevation by the difference in age: (Equation 3) U= ((E-F))/((A-B)) The errors associated with elevation measurements (E) and (F) are represented by (e) and (f). The errors calculated in Equation 2 from ages (A) and (B) are represented by (a) and (b). These errors were propagated as follows. Variable (D) is the distance between levels, where (D = E-F). Variable (d) is the measurement error between two levels in an average uplift rate calculation. Variable (T) is the time between the landform ages, where (T = A-B). Variable (t) is the temporal error between the error margins of each landform age. Propagation of each of these errors uses the same equation: (Equation 4) d= √(e^2+f^2 ) (Equation 5) t= √(a^2+b^2 ) After solving for the average uplift (U) in Equation 2, the uplift rate error (u) can be solved with the following equation: (Equation 6) u=(U)*√(〖(d/D)〗^2+〖(t/T)〗^2 ) This produces an average uplift rate (U) with an error (±u). The Excel spreadsheet shows the steps taken with the calculations.