THE DRAINAGE DENSITY ENVELOPE.

Abstract

A conceptual model for the development of a drainage net by headward erosion is developed and described mathematically. The theoretical maximum stream length for any size basin is shown by plotting total stream length (sum L) versus the square root of basin area (square root of A). An envelope line is fit for maximum skewness, giving the 'drainage density envelope': sum L = square root of A tan gamma - N sub 1 Xc, where tan gamma is the slope of the line, N sub 1 is the number of first order streams, and Xc is the critical distance. The influence of basin order, soil type, and climate on the envelope parameters is investigated theoretically and from preliminary map and field data. Secondly, growth model is proposed for the headward extension of a stream as a function of time: Tc = 1/KWb ln Xc/L sub b where Tc is the time required to extend to the 'belt of no erosion', L sub b and W sub b are the length and width of the rectangular basin and K is a constant depending on the erodibility of the soil. The equation gave correct relative ages of drainage patterns on different age drift sheets in Iowa. (Author)

Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1967
Accession Number
AD0645838

Entities

People

  • R. A. Lohnes
  • R. L. Handy

Organizations

  • Iowa State University

Tags

DTIC Thesaurus Topics

  • Equations
  • Mathematics
  • Numbers
  • Plotting
  • Skewness
  • Square Roots

Readers

  • Coastal and Marine Engineering/Sediment Transport/Hydraulic Engineering
  • Mathematics or Statistics
  • Statistical inference.