Based on the following record of weekly low flows in a river, determine the MA7CD10 drough...

Based on the following record of weekly low flows in a river, determine the MA7CD10 drought flow. Use the probability graph of Figure; multiply vertical axis values by 10.

FIGURE

Logarithmic probability paper is used to estimate the MA7CD10 drought flow in a stream or river. (See Example)

Example

Given the following record of streamflow data, estimate the MA7CD10 for the stream:

Solution

First, rearrange the flow data in decreasing order of magnitude and assign a rank or m value to each flow, beginning with 1 and increasing by 1 sequentially. The probability of observing an equal or higher flow in any given year is estimated by dividing the rank m by the number of years of record plus 1(n + 1); in this example, n = 5. In formula form, the probability P = m/(n + 1). We have

Hydrologic data are often plotted on a special type of graph paper called logarithmic probability paper. The points usually plot as a straight line or close to it. The low flows and their corresponding probabilities in this problem are plotted in Figure. A straight line of best fit has been drawn through the plotted points and extended, or extrapolated, to the 90 percent probability value. This identifies a flow rate on the vertical axis of the graph that would be exceeded nine times out of ten in any given subsequent year. Conversely, the probability of observing a lower flow (a more severe drought) is 10 percent. This flow, therefore, represents the MA7CD10 flow. As seen in Figure, the MA7CD10 flow for this stream (based on the very limited 5 years of record) is estimated at 2.4 m3/s.