How to Determine a Downstream Hydrograph From an Upstream Hydrograph

Hydrographs are mathematical descriptions of flood stage -- how the flooding looks at a particular time and place. If you know the hydrograph at an upstream location, you can predict the hydrograph at a downstream location. Hydrographs are based on the water flowing into a location, the water flowing out of a region and the water stored in a region. To accurately predict flooding for a particular river system you must also have a set of constants that describe the river. These constants can be found by observing previous flooding.

Instructions

- 1
  Start with the general flood-routing equation. This equation relates the inflow at a location measured at two different times (I1 and I2), the outflow at these times (O1 and O2), the change in storage (S1 and S2), and the difference between the two times (delta-T). The equation is: one-half (I1 + I2) - one-half (O1 + O2) = (S2 -- S1) / delta-T.
- 2
  Use a little algebraic manipulation and change of parameters to get: S = XKI^m/d + (1 – X) KO^m/d. X, K, m and d are stage-discharge, stage-storage and channel parameters. This form of the general flood-routing equation is the jumping-off point for all flood stage prediction equations.
- 3
  Employ the "convex method” to get the most popular flood-routing equation. This method uses X = 0 and m/d = 1 to get S = KO. Substituting this in the general flood-routing equation, we get O2 = I1 (delta-T/K) + O1 (1 – delta-T/K), which is usually written O2 = CI2 + (1 - C) O1, where C is a known constant for the specific river system. You can use this last equation to predict how much water will be at a certain location at a given time.

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