Exercises: 1. Evapotranspiration rate is an imporant ecological and climatological variable. It describes how fast water is being evaporated from Earth’s surface and transpired by vegetation. Thus it describes the rate at which moisture is supplied to the atmosphere from the land. The evapotranspiration rate (or ET for short) usually cannot be estimated directly, and instead is calculated from the difference between the rates of rainfall (or P for short) and runoff (or R for short). (Note: the expression below assumes that recharge and discharge to groundwater are in balance, so that there are no changes in storage.) ET = P – R At the Birkenes watershed in southern Norway, 16 years of monitoring data indicate that annual rainfall is 1483±265 mm/yr (mean±standard deviation) and annual runoff is 1170±306 mm/yr (mean±standard deviation) (a)  If this was all you knew (i.e., if you knew nothing about whether the rainfall and runoff were correlated positively or negatively, and so assumed they were uncorrelated), what would you estimate to be the mean and the standard deviation of annual ET at this site? (b)  Contrary to your assumption in (a), rainfall and runoff are highly correlated here (see graph below). In fact, the correlation, r, between rainfall and runoff is 0.9772. Knowing this, what would you now estimate to be the mean and standard deviation of annual ET at this site?

Exercises:

1. Evapotranspiration rate is an imporant ecological and climatological variable. It describes how fast water is being evaporated from Earth’s surface and transpired by vegetation. Thus it describes the rate at which moisture is supplied to the atmosphere from the land. The evapotranspiration rate (or ET for short) usually cannot be estimated directly, and instead is calculated from the difference between the rates of rainfall (or P for short) and runoff (or R for short). (Note: the expression below assumes that recharge and discharge to groundwater are in balance, so that there are no changes in storage.)

ET = P – R

At the Birkenes watershed in southern Norway, 16 years of monitoring data indicate that annual rainfall is 1483±265 mm/yr (mean±standard deviation) and annual runoff is 1170±306 mm/yr (mean±standard deviation)

(a)  If this was all you knew (i.e., if you knew nothing about whether the rainfall and runoff were correlated positively or negatively, and so assumed they were uncorrelated), what would you estimate to be the mean and the standard deviation of annual ET at this site?

(b)  Contrary to your assumption in (a), rainfall and runoff are highly correlated here (see graph below). In fact, the correlation, r, between rainfall and runoff is 0.9772. Knowing this, what would you now estimate to be the mean and standard deviation of annual ET at this site?