Study of determining geomorphologic unit hydrograph by means of probability density functions of path length and slop

The instantaneous unit hydrograph (IUH) was interpreted as the probability density function (PDF) of water drop travel time in the basin by Rodriguez-Iturbe et al and Gupat et al.As the water drop travel time in the basin equals to proportionality of the water drop path length to its velocity,a new method for determining IUH is suggested by means of the PDFs of path length and velocity of water drop based on law of the probability theory.The PDF of the water drop path length can be viewed as the width function,and the PDF of water drop velocity is transformed by the PDF of slop.Otherwise,the analytical equation of slop PDF is derived by the principle of maximization information entropy.Technical support of the new method is of the digital elevation model.The example watershed given in this paper is located at Hubei province,China,and the simulation accuracy is satisfactory.