If a unit hydrograph shows how a river responds to one inch of rain, how would you use it to find the river's response to three inches of rain?

A unit hydrograph is a graph that shows how a river's discharge, or flow rate, changes over time in response to one unit of effective rainfall falling uniformly over a specific drainage basin for a specified duration. The term "effective rainfall" refers to the portion of total precipitation that actually contributes to surface runoff, after accounting for losses such as infiltration into the ground, interception by vegetation, and evaporation. The output of the unit hydrograph is a hydrograph, which is a plot of discharge versus time.

To find the river's response to three inches of rain, assuming these three inches represent three inches of *effective rainfallof the same duration and spatial distribution as the unit hydrograph's rainfall, you would use the principle of linearity, also known as the principle of superposition and proportionality. This fundamental assumption of unit hydrograph theory states that if an input to a hydrologic system is scaled by a factor, the output is scaled by the same factor.

Therefore, to determine the river's response to three inches of effective rainfall, you would multiply every ordinate (the discharge value at a specific time interval) of the given unit hydrograph by three. For example, if the unit hydrograph shows a discharge of 10 cubic feet per second (cfs) at hour 4, then for three inches of effective rainfall, the discharge at hour 4 would be 30 cfs. You would perform this multiplication for every single ordinate point across the entire duration of the unit hydrograph. The resulting set of multiplied ordinates, when plotted against the same time axis as the unit hydrograph, will form the new hydrograph representing the river's response to three inches of effective rainfall. This process directly scales the flow rates proportionally to the increased effective rainfall input.