Sensitivity for Correlated Input Variables and Propagated Errors in Evapotranspiration Estimates From a Humid Region

A sensitivity and uncertainty analysis of the Penman‐Brutsaert evapotranspiration (ET) model was conducted using meteorological data collected from the humid South Florida region. Since net radiation and relative humidity were found to be correlated (ρ = −0.74) in this region, a method was developed to analyze the sensitivity with the correlation effect of these two independent variables. After conducting sensitivity analyses with and without the correlation effect, the results were evaluated using conditional probability density functions. Both theoretical and computed results show that the conditional probability with the correlation effect increases in proportion to the increasing absolute correlation coefficient of two independent variables. This finding suggests that the sensitivity analysis with the correlation effect represents more adequately a given set of meteorological data in South Florida than that without the correlation effect. After defining the random errors of the independent variables based on multiple measurements, the ET model error as well as the propagated error caused by erroneous independent variables are presented.