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:

$Q$ : flow rate $[m^3 s^{-1}]$

$K_s$ : Strickler $[m^{1/3} s^{-1}]$

$Z_v$ : downstream height $[m]$

$Z_m$ : upstream height $[m]$

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

The model depends on four parameters:

the height of the dyke: $H_d = 3$ $[m]$ ,

the altitude of the river banks: $Z_b = 55.5$ $[m]$ ,

the river length: $L = 5000$ $[m]$ ,

the river width: $B = 300$ $[m]$ .

The altitude of the dyke is:

$Z_d = Z_b + H_d$

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

$\alpha = \frac{Z_m - Z_v}{L},$

if $Z_m \geq Z_v$ .

The water depth is:

$H = \left(\frac{Q}{K_s B \sqrt{\alpha}}\right)^{0.6},$

for any $K_s, Q>0$ .

The flood altitude is:

$Z_c = H + Z_v.$

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:

$S = Z_c - Z_d$

is greater than zero.

The following figure presents the model with more details.

flooding section details — Flooding section detail¶

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

$S = \left(\frac{Q}{300 Ks \sqrt{(Zm-Zv)/5000}}\right)^{3/5} +Zv-58.5.$

We assume that the four inputs have the following distributions:

$Q$ ~ Gumbel(mode=1013, scale=558), $Q$ > 0

$K_s$ ~ Normal(mu=30.0, sigma=7.5), $K_s$ > 0

$Z_v$ ~ Uniform(a=49, b=51)

$Z_m$ ~ Uniform(a=54, b=56)

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

We want to estimate the flood probability:

$P_f = P(S>0).$

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

Load the use case¶

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()

API documentation¶

See FloodModel.

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An Open source initiative for the Treatment of Uncertainties, Risks'N Statistics

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A flood model¶

Introduction¶

References¶

Load the use case¶

API documentation¶

Examples based on this use case¶