en:hydro:nash
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Nash-Cascade
The Nash cascade is a sequence of $N$ linear stores in series, each having a residence time of $K$ time units. The resulting mathematical form of the Nash-cascade is:
$$h(t) = (t/K)^{N-1}*exp\left(\frac{-t/K}{K*\Gamma(N)}\right)$$
where $h(t)$ is the unit hydrograph in terms of a unit discharge and $\Gamma$ is the gamma function $\gamma(N)=(N-1)!$ for integer values $N$. $N$ can also have rational values.
- |Nash.py
from pylab import * from scipy import * from math import * from numpy import * N = 3 k = 0.5 t = arange(0.0, 60, 1) def Nash(t,N,k): h = (t/k)**(N-1)*exp((-t/k)/(k*gamma(N))) return h plot(t, Nash(t,N,k)) xtext = xlabel('time') ytext = ylabel('response') setp(xtext, size='medium', name='courier', weight='bold', color='g') setp(ytext, size='medium', name='helvetica', weight='light', color='b') show()
/usr/www/users/uhydro/doku/data/attic/en/hydro/nash.1496899980.txt.gz · Zuletzt geändert: 2024/04/10 10:15 (Externe Bearbeitung)