en:hydro:nash
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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: | 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: | ||
- | $$h(t) = (t/ | + | $$h(t) = (t/ |
+ | |||
+ | 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. | ||
+ | |||
+ | <code R |Nash.R> | ||
+ | |||
+ | n <- 3 | ||
+ | k <- 0.2 | ||
+ | ks <- 0.1 | ||
+ | kl <- 0.3 | ||
+ | x <- seq(0.1, | ||
+ | y <- 1/ | ||
+ | plot(x, | ||
+ | abline( h = seq( 5, 25, 5 ),lty = 2,col = colors()[440]) | ||
+ | abline( v = seq( 1, 4, 1 ),lty = 2,col = colors()[440]) | ||
+ | curve(1/ | ||
+ | curve(1/(k *gamma(n))*(x/ | ||
+ | curve(1/ | ||
+ | </ | ||
+ | |||
+ | <code py |Nash.py> | ||
+ | from pylab import * | ||
+ | from scipy import * | ||
+ | from math import * | ||
+ | from numpy import * | ||
+ | |||
+ | N = 5 | ||
+ | k = 0.5 | ||
+ | t = arange(0.0, 100, 1) | ||
+ | |||
+ | def Nash(t, | ||
+ | h = (t/ | ||
+ | return h | ||
+ | |||
+ | plot(t, Nash(t, | ||
+ | xtext = xlabel(' | ||
+ | ytext = ylabel(' | ||
+ | setp(xtext, size=' | ||
+ | setp(ytext, size=' | ||
+ | show() | ||
+ | </ | ||
+ | |||
+ | Model in R: [[https:// | ||
- | 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. | ||
/usr/www/users/uhydro/doku/data/attic/en/hydro/nash.1481653543.txt.gz · Zuletzt geändert: 2024/04/10 10:15 (Externe Bearbeitung)