Chapter 3 : Reservoir models - KU Leuven

3.2.4 Runoff models
After the calibration of the routing through the sewer system against a verified detailed
hydrodynamic model, the runoff model can be calibrated separately. As the
variability of the rainfall and consequently of the water input into the sewer system is
high, the calibration of the runoff model must be carried out using a wide range of
measurements. The calibration must be performed in such a way that the input volumes
are similar in the model and in the measurements. Most often it is not possible to also
obtain similar instantaneous discharges in model and measurements, because of the
high uncertainty on the parameters. There are significant uncertainties on the rainfall
measurements, on the runoff coefficients, on the losses and on the contributing area.
If the cumulative input is corresponding well in the model and measurements, the errors
on the instantaneous discharges are only of second order importance. An example of
the calibration of a runoff model is given in paragraph 6.5.
A wide range of runoff models can be used. From the modelling point of view the most
extreme runoff models are on the one hand a fixed runoff coefficient and on the other
hand a fixed depression storage (i.e. the storage in depressions on the surface).
Using a fixed runoff coefficient leads to rainfall losses which are a fixed percentage
of the rainfall input. This is a model with a linear behaviour, because the output is
linearly varying with the input. The losses are independent of the antecedent rainfall.
Using a fixed depression storage on the other hand, leads to a non-linear relationship
between in- and outflow. If the depression storage is empty, it will be filled during
the first part of the storm and the shape of the inlet hydrograph might be changed.
If the depression storage is already filled by antecedent rainfall, it will have no
influence on the storm. For this kind of model the antecedent rainfall and the intrinsic
variability of the rainfall are very important.
For continuous simulations the runoff models should not be event based, even if they
are calibrated using single measured events. For that reason a depression storage model
cannot simply be used to subtract the first volume of a storm as is often proposed in
event based models [Van den Herik & Van Luytelaar, 1990; WS, 1996], because of the
subjective definition of a ‘storm’. The depression storage must be written as a function
of instantaneous parameters. This can for instance be performed using a simple
reservoir model for which the outflow is linearly varying with the inflow and with the
depression storage (figure 3.22). The depression storage S is thus limited to S max . If
this relationship is incorporated in the continuity equation and this differential equation
is solved, an exponential filling of the depression storage is obtained :
S
⎡ Vin
= S − ⎛ ⎞ ⎤
max ⎢1 exp⎜−
⎟ ⎥
(3.2)
⎣⎢
⎝ Smax
⎠ ⎦⎥
In equation (3.2), V in is the cumulative inflow into the reservoir.
Chapter 3 : Reservoir models 3.21