Which equations does the IDF Curve Tool fit?
In short: The IDF Curve Tool fits two closed-form models: a Sherman equation separately for every selected return period and one Koutsoyiannis equation across the complete set of selected durations and return periods.
Sherman equation
For a selected return period T, the Sherman form is i(t; T) = a / (t + b)n. The coefficients a, b, and n are fitted independently for each return-period curve. This provides a compact duration-intensity equation for every chosen T.
Koutsoyiannis equation
The global form is i(t, T) = a · Tm / (t + b)n. One set of a, m, b, and n coefficients describes the IDF surface across all selected return periods.
Fit output and interpretation
The dialog reports R2 and RMSE for both forms and can export the coefficients to CSV. Duration t is expressed in hours, return period T in years, and intensity i in the input-data units. These metrics show how closely an equation reproduces the fitted IDF curves; they do not measure whether the underlying rainfall distribution predicts future extremes correctly.
See the equation derivation and software workflow.