Chapter 20, Problem 25P

In water-resources engineering, the sizing of reservoirs depends on accurate estimates of water flow in the river that is being impounded. For some rivers, long-term historical records of such flow data are difficult to obtain. In contrast, meteorological data on precipitation is often available for many years past. Therefore, it is often useful to determine a relationship between flow and precipitation. This relationship can then be used to estimate flows for years when only precipitation measurements were made. The following data are available for a river that is to be dammed:

Precipitation, cm	88.9	108.5	104.1	139.7	127	94	116.8	99.1
Flow, $m^{\text{3}}\text{/s}$	14.6	16.7	15.3	23.2	19.5	16.1	18.1	16.6

(a) Plot these data.

(b) Fit a straight line to these data with linear regression. Superimpose this line on your plot.

(c) Use the best-fit line to predict the annual water flow if the precipitation is 120 cm.

(d) If the drainage area is 1100 km², estimate what fraction of the precipitation is lost via processes such as evaporation, deep groundwater infiltration, and consumptive use.