Name

c_PROPAG — Function permitting to propagate hydrographs with simple models

Calling Sequence

[Q_DOWN,[R]] = c_PROPAG(TYPE,Param,Q_UP)

Parameters

TYPE

Type of lag and reservoir used

10: Simple Lag

11: simple lag + Linear reservoir

12: simple lag + Quadratic reservoir

20: GR4J UH

21: GR4J UH + linear reservoir

22: GR4J UH + quadratic reservoir

Param

The four parameters values

Param(1) = Lag time (expressed in number of time-steps, ex. in days for daily values).

Param(2) = Rescaling factor (dimensionless). Routing model output is multiplied by this coefficient to convert up. discharges into down. ones

Param(3) = Capacity of the routing reservoir (expressed in number of time steps for a linear reservoir or upstream discharge unit for a quadratic reservoir)

Param(4) = [ not utilised yet...]

Q_UP

Uptsream discharges (matrix [Nx1] where N is the number of time steps)

Q_DOWN

Calculated downstream discharges expressed in the upstream discharges unit (matrix [Nx1])

R

Calculated reservoir level (matrix [Nx1])

Description

  • WARNING : This function is written in C language and interfaced with SCILAB (HYDROGR.dll).

  • This propagation model associates a simple lag model (upstream hydrograph is simply temporally shifted) to a linear or quadratic reservoir. This reservoir acts like an exponentially decaying unit hydrograph. It controls flood wave attenuation.

  • To calibrate the lag-and-route model, the usual procedure is to use a "Pas à Pas" routine (cf function PasaPas).

Examples

      // Time
      t = 0:100;

      // Upstream hydrograph
      Qam=exp(-(t/10-3)^2)';
      
      // Calculated downstream hydrograph
      Qav11 =c_PROPAG(11,[20;1;1;0],Qam);
      Qav12 =c_PROPAG(12,[20;1;1;0],Qam);
      Qav21 =c_PROPAG(21,[20;1;1;0],Qam);
      Qav22 =c_PROPAG(22,[20;1;1;0],Qam);
      
      // Plot
      plot(t,Qam,'k:');xtitle('','Time','Discharge');
      plot(t,[Qav11 Qav12 Qav21 Qav22])
  

Authors

Julien Lerat

CEMAGREF Antony, HBAN Unit, julien.lerat@cemagref.fr

Bibliography

Bentura, P. L. F. and C. Michel (1997). "Flood routing in a wide channel with a quadratic lag-and-route method." Hydrological Science Journal 42: 169-189.