Fitting Equations to Families of Dimensionless Cumulative Hyetographs

MANY times equations for families of curves are needed in engineering practice. The equation for each curve in the family may need to be constrained, depending on the particular problem. Linear programming (LP) provides an attractive alternative to least squares fitting because the curve being fitted can be constrained. The simultaneous fitting of a family of curves using LP is illustrated by fitting equations to families of design storms known as Huff curves. Tenth degree polynomials are fitted to 12 9-curve families. The results showed that the LP method generally works well, but that it is possible that constraints may not be satisfied in intervals between data points used in the formulation of the problem, and that numerical problems may result if a high degree polynomial is used. The effects of these numerical problems are dependent on the particular data set being used, but the errors in the design-storm illustration were not important for the flood-estimation objective for which they were developed. The use of LP to fit constrained equations to data in general has wide applicability in engineering.