Do Polynomials Adequately Describe the Hypsometry of Monadnock Phase Watersheds?


  • Paper No. JAWRA-12-0158-N of the Journal of the American Water Resources Association (JAWRA).
  • Discussions are open until six months from print publication.


Hypsometry has been shown to be a useful tool in geomorphic analysis of watersheds with the use of third-degree polynomial equations to express the hypsometric curve. Despite its usefulness with watersheds in the equilibrium stage, the third-degree polynomial has been found to be inadequate to describe the hypsometry of Monadnock phase watersheds. Three other equations — a modified third-degree polynomial with a rational term, a sigmoidal model, and a double exponential — were used to determine hypsometric attributes of 32 Monadnock phase watersheds and compared to the third-degree polynomial form. The three other equations were found to be better fits for Monadnock phase watersheds than the third-degree polynomial equation, regardless of which ratio — area or elevation — was plotted as the independent variable. Due to the occasional failure of each functional form to give logical values for hypsometric attributes, the importance of using more than one form equation is discussed. After determining the best-fit equation for each watershed, the usefulness of hypsometric attributes is discussed in relation to erosion processes within Monadnock phase watersheds.