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create IUH (Instant Unit Hydrograph)

Source: R/RcppExports.R
confluenIUH.Rd

The process confluenIUH return a series of portions, that means how many flux water will in those moment into the river. The sum of this series will always in 1.

So we can give the function:

\[u = f_{confluenIUH}(t_r, ...)\]

where

  • \(u\) is series of portions

  • \(t_r\) is confluen_responseTime_TS

Usage

confluenIUH_GR4J1(confluen_responseTime_TS)

confluenIUH_GR4J2(confluen_responseTime_TS)

confluenIUH_Kelly(confluen_responseTime_TS, param_confluen_kel_k)

confluenIUH_Nash(confluen_responseTime_TS, param_confluen_nas_n)

confluenIUH_Clark(confluen_responseTime_TS)

Arguments

confluen_responseTime_TS

(TS) response or concentration time in every routeline

param_confluen_kel_k

<1, 4> parameter forconfluenIUH_Kelly()

param_confluen_nas_n

<1, 8> parameter forconfluenIUH_Nash()

Value

IUH (list of num vector)

_GR4J1 (Perrin et al. 2003) :

\[u(i) = S(i) - S(i-1)\] \[S(i) = \left( \frac{i}{t_r} \right)^{2.5}, \quad 0 \leq i \leq t_r\] where

  • \(u\) is IUH series

  • \(i\) is index

_GR4J2 (Perrin et al. 2003) :

\[u(i) = S(i) - S(i-1)\] \[S(i) = 0.5\left( \frac{i}{t_r} \right)^{2.5}, \quad 0 \leq i \leq t_r\] \[S(i) = 1 - 0.5\left(2 - \frac{i}{t_r} \right)^{2.5}, \quad t_r < i < 2t_r\] \[S(i) = 0, \quad i = 2t_r\] where

  • \(u\) is IUH series

  • \(i\) is index

_Kelly (O Kelly 1955) :

\[u(i) = \frac{4}{t_r^2} \left( i + k \left( e^{-i/k} \right) \right), \quad i \leq t_r / 2 \] \[u(i) = - \frac{4}{t_r^2}(i - k - t_r) + \frac{4ke^{-i/k}}{t_r^2} (1 - 2 e^{t_r/(2k)}), \quad t_r / 2 < i \leq t_r \] \[u(i) = \frac{4ke^{-i/k}}{t_r^2} (1 - 2 e^{t_r/(2k)} + e^{t_r/k}), \quad i > t_r \] where

  • \(k\) is param_confluen_kel_k

_Nash (Nash 1957) :

\[u(i) = \frac{1}{t_r\Gamma(n)} \left(\frac{4}{t_r^2}\right)^{n -1}e^{-i/t_r}\] where

  • \(n\) is param_confluen_nas_n

_Clark (Clark 1945) :

\[u(i) = \frac{1}{t_r} e^{-i/t_r} \] where

  • \(t_r\) is confluen_responseTime_TS

References

Clark CO (1945). “Storage and the Unit Hydrograph.” Transactions of the American Society of Civil Engineers, 110(1), 1419--1446. doi: 10.1061/TACEAT.0005800 .

Nash JE (1957). “The Form of the Instantaneous Unit Hydrograph.” In Comptes Rendus et Rapports Assemblee Generale de Toronto, volume III, 114--121.

O Kelly JJ (1955). “The Employment of Unit Hydrographs to Determine the Flows of Irish Arterial Drainage Channels.” Proceedings of the Institution of Civil Engineers, 4(4), 365--412. doi: 10.1680/ipeds.1955.11869 .

Perrin C, Michel C, Andr攼㸹assian V (2003). “Improvement of a Parsimonious Model for Streamflow Simulation.” Journal of Hydrology, 279(1-4), 275--289. ISSN 00221694, doi: 10.1016/S0022-1694(03)00225-7 .