powuh {hydromad} | R Documentation |

A power-law form of unit hydrograph (transfer function).

powuh.sim(U, delay = 0, a, b = 1, c = 1, init = 0, uhsteps = 100, na.action = na.pass, epsilon = hydromad.getOption("sim.epsilon"))

`U` |
input time series. |

`delay` |
lag (dead time) between input and response, in time steps. |

`a` |
the time for flow to drop by half after a peak, if |

`b` |
persistence of the flow response; defines the recession curve tail. |

`c` |
curvature at half-peak point. |

`init` |
initial flow value(s) used in convolution filter. |

`uhsteps` |
number of time steps to use in approximating the unit hydrograph convolution filter. |

`na.action` |
function to remove missing values,
e.g. |

`epsilon` |
values smaller than this will be set to zero. |

The power law form of the unit hydrograph is:

*H = 1 / (1 + (t/a)^{b/c}) ^ c*

where H is the fraction of peak flow, t is the time since peak, and a, b and c are parameters.

From Croke (2006):

Parameter a is the value of t (time since peak) at which the ordinate
of the asymptote *(t/a)^(-b)* has a value of 1, b determines the
persistence of the flow response and c defines the shape of the response
curve near its peak. The c parameter appears twice in order to reduce
interaction between the b and c parameters (in this form, the c
parameter only influences the curvature near t = a, and doesn't
influence the asymptote, which is determined solely by the b
parameter). The time for H to decrease to 0.5 is *a(2^(1/c) -
1)^(c/b)*. While this is a three parameter model, for *t >> a* only
the b parameter is significant. Since the value of the a parameter is
typically significantly less than one (see Table 1) the recession curve
can be written as

*H = (t_r / t)^b*

where *t_r* is some reference time (*t_r >> a*) at which the
hydrograph profile has been normalized. Thus the remaining two
parameters (a and c) only influence the response curve near the event
peak, and [the equation above] can be taken as a single parameter
recession model.

the model output as a `ts`

object,
with the same dimensions and time window as the input `U`

.

Felix Andrews felix@nfrac.org

Croke, B.F.W. (2006). A technique for deriving an average event unit
hydrograph from streamflow-only data for ephemeral quick-flow-dominant
catchments. *Advances in Water Resources* 29, pp. 493–502.

U <- ts(c(1, rep(0, 99))) xyplot(cbind("a = 5" = powuh.sim(U, a = 5), "& b = 2" = powuh.sim(U, a = 5, b = 2), "& c = 2" = powuh.sim(U, a = 5, c = 2)), superpose = TRUE)

[Package *hydromad* version 0.9-18 Index]