The forecast of raw the is the modeling of the quantities of precipitations, solids or liquids, received in a catchment area and from their effect on the flow in the rivers. The national weather services roll of the models of numerical Prévision of time to estimate the quantity of Pluie or Neige which will fall but often, in fact local territorial collectivities use note the received quantities, the flow of the rivers and roll the programmes of modeling of the risings to envisage the overflow and to limit the damage of Inondation to the residents. These systems are often used to control the rain systems of sewer S, the level of the Barrage S and the diversion canals of the risings.

Data

Strong accumulations of rain or snow are the cause of the floods. A strong rain causes a volume of water suddenly slackened in a catchment area. On another side, the snow accumulated during the cold season will melt in spring and will increase the flow of the rivers. According to the quantity of snow and the speed of the warming, the Ruissellement created will be more or less important. A system of sensors must thus be established in the area concerned to note the quantities of precipitations (Pluviomètre and nevemeter), the Température and the Vent in order to be able to calculate liquid volume moving towards the river and to be able to estimate the potential of flood.

Moreover, to anticipate the level of water, it is necessary to know the quantities which will be added during the next days. Indeed, water which falls into a catchment area takes a certain time to run out, according to the type of ground and the slope. During this period, the quantities which will be added will affect the streaming. The forecast of time make it possible to add this variable. The intensity of precipitations is measured throughout an event and one draws a hyétogramme from it: the representation, in the form of a Histogram, intensity of the rain according to time. It represents the derivative in a given point, compared to time, of the curve of cumulated precipitations.

Mathematical model

By knowing the rainfall records, the configuration of the ground and his holding capacity, one can mathematically calculate the flow of the collecting rivers. the equations that one car are complex and requires very a data-processing great power for their resolution. The flow will be calculated in selected points of the river. Hyétogramme, which represents the intensity of the input in time (mm/h), one will obtain a Hydrogramme, which represents the flow of the river in time (m3/s). To transform the data pluviomeric into flow, it is necessary to know:

The development of these mathematical models is prone to the precise knowledge of the characteristics of the ground and contains approximations since the exact knowledge of these last always prone to the resolution and the Paramétrisation of the data. Moreover, the measurement of the received quantities of the system of measurement which in general is very dispersed. The data of accumulations can be improved by systems of teledetection as the weather Radar in as much as its calibration is well made.

River division

It is essential to cut out the river in homogeneous sections, because a river is irregular, before evaluating its characteristics. One will generally place the measuring instruments at the ends of each section to evaluate flow entering and outgoing. A model comprises a variable number of points according to the rivers, drawn from these measurements. The intersection of two affluents of a river is a place generally favourable with the placement of a point because the nature of the river generally changes there, in particular its width and its flow.

Parameters

Parameters of the catchment area

The catchment area is the zone on which any water drop which falls joined the point from alarm, and enters thus counts some in the calculation of the flow in this point.

Physical parameters

The physical parameters are measurable starting from cartographic data or of measurements of ground.

The catchment area is the zone on which any water drop which falls joined the point from alarm, and enters thus counts some in the calculation of the flow in this point. It is thus necessary to precisely know its surface to know which is the quantity of water drained at the time of a rainy event.

Its limits generally correspond to the watershed which takes shape around the river. It is in this case called topographic basin. However, when there exist layers of permeable rocks under ground, the topographic boundary line of two different basins always does not correspond to the effective dividing line of subterranean water.

Surface area catchment and of the under-basins slopes: To calculate the surface of the catchment area, there exist several methods.

A method consists in delimiting with the pencil the area catchment on a chart IGN to the 1/25000, thanks to the level lines which appear all there the 10m of altitude. One traces then squares largest possible, of known surface, inside the limits of the catchment area. One continues by decreasing the size of the squares until covering the entirety of the catchment area. One thus adds surfaces with the squares to know that of the catchment area. One can operate in the same way to trace under basin slopes. The objective is to delimit the space into which a water drop can fall a drop to join the point downstream of each section of river delimited. a section, and to return thus counts some in the calculation of the flow at the point.

Conceptual parameters

the model consists of two tanks whose size represents the capacity of the area catchment to store water. This storage intervenes between the moment or the drop of rain touches the ground and the moment or it reaches the river. The principle of operation of this parameter is simple: more the tank is full, it arrives quickly at saturation and thus more water joined the river quickly.

• the first tank is called " tank sol". It corresponds to the depressions which form the ground.

• the second tank is called " tank gravitaire". It corresponds to the storage capacity of the basement after infiltration.

Each tank represents a parameter of the model. Their value expresses their size. It varies from 20 to 200 (without unit).

Parameters of the river

physical parameters

They are the physical characteristics of the river necessary to the modeling of the Crue. It are given for each homogeneous section already definite:

• the length. It is the length of the river on which it is permanent.
• average Slope of each section of the river.

Altitude of each point.

• roughness to be estimated is that of the bed of the river. More the bottom and the banks of the rivers are rough, more water is slowed down and spends time to move, and more this coefficient is low. It is generally included/understood in a fork going from 10 to 30. Roughness intervenes in the calculation of the propagation of the flow in the river.

Section by section homogeneous of river we estimated the roughness of the banks according to grid of assistance to their estimate

One considers initially S wet surface, i.e. the surface occupied by water on a transverse section, and P the wet perimeter.

One a:

$Q\; =\; V\; \backslash \; times\; S$ with

• Q flow in m/s
• V mean velocity of water
• S wet surface.

The speed V or U of displacement of water is calculated thanks to the formula of Chezy:

$U=\; C\; \backslash \; times\; \backslash \; sqrt\; \{Rh\; \backslash \; times\; I\}$ With:

• U: rate of travel of water

• C: the coefficient of Chézy depend on the type of surface
• I: Slope of the river in m/m
• Rh: the hydraulic ray, i.e. the quotient of S by P defines below.

Roughness intervenes then in the calculation of the coefficient of Chézy C, thanks to the law of Manning-Strickler:

$C=K\; \backslash times\; Rh^\{1/6\}$

Where K Strickler coefficient (or N coefficient of Manning with n=1/K).

The chock of the model

After having returned in the model the data necessary to its operation, the results are still far away from reality. It is thus necessary to carry out its adjustment. For that one uses measured data of rain as well as the heights of water observed in the river at the time of this rainy episode. These data thus will be used as references. The parameters of the model will be fixed so that with the use of these data of rains, the model gives the heights of water observed like results. The chock aims thus to bring closer the hydrogramme modelled hydrogramme observed.

In practice, once the parameters of the model informed, the chock consists in estimating by successive test the initial values of filling of the two tanks as well as possible to reproduce the rising observed. Concretely if the rain observed intervenes following a first rain, the tanks are partially or entirely full what will generate a streaming then a more important discharge of river.

Estimate of the flood at the point of alarm

The point of alarm corresponds to the point of the river or one wishes to know and envisage the flood so as to inform as soon as possible the population. The overflow of the river is noted for a certain height of water in the river. The developed model calculates starting from the data of rains the flow generated in the river in this point. This flow must then be converted into height of water. The form and the cut of the section of the river in this point make it possible to establish a relation between the heights of water and the flows. Thus to height of alarm (height for which the flood occurs), thus corresponds a flow of alarm.

Alarm

Scenarios can be set up according to the level of water (information, evacuation, mobilization of the emergency services, etc)

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