Desbordes Model

This is one of a number of runoff models that can used when running a simulation. It is the standard runoff model used in France. You select which runoff model to be used on the Runoff Surface Grid Window of the Subcatchments Grid.

Basic function

To calculate the flow generated by the runoff during a rainfall event, at the different inlets to the drainage system network.

Runoff model's function in the hydrology model

To calculate the storm water discharges into the drainage system from rainfall hyetograph data and catchment data. The software uses these discharges as inflow data for the hydraulic calculations.

Runoff computation is in parallel with the washoff computation at each timestep. The runoff module provides data to the washoff module.

Application

The software calculates runoff for each subcatchment at each time step.

Technical concepts

The basic hypothesis is that of the single linear reservoir. The software assumes that the flow at the catchment outlet is proportional to the volume of storm water present on that catchment.

Note: The term catchment here means the ground surface and the non-explicitly modelled network that contributes storm water to that point of the urban drainage system.

The basic equation is:

S(t) = K Q(t) (1) where: S(t) - Volume of storm-water stored on the catchment (m3) at a point in time. Q(t) - Discharge at the catchment outlet (m3/s) at a point in time. K - Linear reservoir coefficient (s). The software calculates this from the catchment and the rainfall data.

To take into account the effects of depression storage and other initial losses, the first millimetre(s) of rainfall may not contribute to the runoff. The software models depression storage in the same way as for the other runoff models.

Note: This runoff module is event based, and is not designed to be used for continuous simulation. However, you can link a set of sub-events together in the rainfall data. In this case, each sub-event will have its own K value.

Initialising parameters for the Desbordes runoff module

The process for initialising the parameters for the Desbordes runoff calculations is as follows:

1. Determine the total effective rainfall:

   Hpe = (Hper - Hrn) / 1000 (2) where: Hpe - total accumulated effective rainfall (m) Hper - total rainfall (cumulated) (mm) calculated from the rainfall event. Hrn - the initial losses (mm). The software determines this from the depression storage and antecedent rainfall.

2. Determine the calibrated coefficient:

   Kdesb = 50 (3)

   This value was determined from calibrated data.

3. Determine the linear reservoir coefficient:

   (4) where: Ar - subcatchment area (ha) Pnt - subcatchment slope (%) C - proportion of subcatchment area that is impermeable (between 0 and 1) T3 - duration of the rainfall subevent (s) L - subcatchment length (m)

4. Calculate the initial discharge coefficient:

   (5) where: Q0 - initial discharge (m3/s). Q0 is zero unless starting from a saved hydrology state file. q(0) - initial discharge per unit of active surface (m/s).

Calculating runoff using the Desbordes runoff module

The process for calculating runoff using the Desbordes model is as follows.

For each timestep:

1. Runoff discharge per active surface unit:

   (6) where: dt - run timestep(s) q(t) - discharge per unit of active surface (m/s) K - linear reservoir coefficient (s) i - effective rainfall intensity (m/s)

2. Runoff discharge:

   Q (t+dt) = C . Ar . q(t+dt) . 1000 (7) where: Q - total discharge (m3/s) C - proportion impermeable catchment area (0...1) Ar - catchment area (ha)