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Parameter Sensitivity in Hydrologic Modeling - page 42 / 163

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W = dw

= k W 2 1 2

+ d m k d θ

Equation 3.2

Since the planimeter begins and ends in the same position, the net change in the angle dθ is zero. The net change in the scale reading is due only to the change in the scale reading. Integration of dm over the entire circuit is M, the final reading in the scale as also shown in Equation 3.3.

dθ = 0

d m k W = W = kM

Equation 3.3

In Figure 3.5, Kunkle (2001) shows how the final area is determined. When the arm is sliding backwards, the area covered is subtracted from the total area. The result is only the area crossed by the tracing arm, k.

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