A hydrograph is a graph of the flow in a stream over a period of time. Below is a picture of a hydrograph, with stream flow (discharge) in cubic feet per second on the y-axis and time in months on the x-axis. Peaks in the hydrograph are usually a result of precipitation events, while troughs represent drier times.
To read a hydrograph, pick an approximate date and trace a vertical line up to where it intersects the graph. Reading horizontally to the left, you can determine the discharge of the stream for that date.
To say that a hydrograph is flashy means that the graph depicts sharp vertical jumps and equally steep vertical declines. What this means for the actual stream represented by the graph is that a flashy stream is one that exhibits significantly increased flows immediately following the onset of a precipitation event and a rapid return to pre-rain conditions shortly after the end of the precipitation. That is to say, water that precipitates within a flashy stream's watershed will make its way quickly from the land into the stream and be flushed through the system rapidly. On the other hand, in watersheds supplying a stream that is not flashy, the transport of water will be slowed through absorption into and seepage through soils, containment on the surface in lakes, and retention in the soil as moisture.
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