# 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.

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.

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: We can load this classical model from the use cases module as follows :

>>> from openturns.usecases import flood_model as flood_model
>>> # Load the use case flood model
>>> fm = flood_model.FloodModel()


## Examples based on this use case¶    