# A flood model¶

## Introduction¶

The following figure presents a dyke protecting industrial facilities. When the river level exceeds the dyke height, flooding occurs. The model is based on a crude simplification of the 1D hydrodynamical equations of Saint-Venant under the assumptions of uniform and constant flow rate and large rectangular sections.

Flooding section

Four independent random variables are considered:

• : flow rate

• : Strickler

• : downstream height

• : upstream height

When the Strickler coefficient increases, the riverbed generates less friction.

The model depends on four parameters:

• the height of the dyke: ,

• the altitude of the river banks: ,

• the river length: ,

• the river width: .

The altitude of the dyke is:

The slope of the river is assumed to be close to zero, which implies:

if .

The water depth is:

for any .

The flood altitude is:

The altitude of the surface of the water is greater than the altitude of the top of the dyke (i.e. there is a flood) if:

is greater than zero.

The following figure presents the model with more details.

Flooding section detail

If we substitute the parameters into the equation, we get:

We assume that the four inputs have the following distributions:

• ~ Gumbel(mode=1013, scale=558), > 0

• ~ Normal(mu=30.0, sigma=7.5), > 0

• ~ Uniform(a=49, b=51)

• ~ Uniform(a=54, b=56)

Moreover, we assume that the input random variables are independent.

We want to estimate the flood probability:

## References¶

• Iooss B, Lemaître P (2015) A review on global sensitivity analysis methods. In: Meloni C., Dellino G. (eds) Uncertainty management in Simulation-Optimization of Complex Systems: Algorithmsand Applications, Springer

• Baudin M., Dutfoy A., Iooss B., Popelin AL. (2015) OpenTURNS: An Industrial Software for Uncertainty Quantification in Simulation. In: Ghanem R., Higdon D., Owhadi H. (eds) Handbook of Uncertainty Quantification. Springer

>>> from openturns.usecases import flood_model as flood_model