Modelling for Sustainable Development: Inundation Risk Management and Decision Making in Water Sector

Actually, for all the world, at different levels and scales (international, national, regional, local, zone) there is an urgent request suggested by scientific experts, environmentalists, academicians, decision makers, policy makers, economists, sociologists consisting to propose models and tools based on mathematical formulations using new technology in the purpose to study the physics phenomenon behind floods in order to give solutions minimising their effects and to make the right decision concerning the water sector (resources, adduction network and distribution network) for all human usages: domestic, services, agricultural, industrial.


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from experimental study done at laboratory level to estimate the effect of streaming through planes liable to flooding will be mentioned. A first application of a model established using the geographic information system to analyse the water sector for all usages to a region in the North-east of Tunisia (Siliana) would be detailed.

Calculus for floods monitoring and their risk management
Monitoring floods and managing their risks necessitate first methods and tools to foresee the instant of averse happening, their intensities and the geographical positions of their descents (Martin 2010,Nor Azliza 2006, Plate 2002. Which means to formulate the transport phenomenon at the atmosphere level. Second we have to follow the streaming on the ground by detecting their geographical directions, estimating the debit of the flows and quantifying their energies. Which signify to calculate the water height, water velocity in all directions and the pressure exerted by the streams. We can then make maps for vulnerable zones the most menaced by inundation and classify the other by priority linked to a degree of averse danger (Martin 2010, Li B et al 2006, Evan et al 2006. Also, on the ground we can evaluate the resistance level against streaming for human infrastructure either in urban or rural regions, for soils and for vegetation canopies. Which make us capable to propose the adequate technical solutions for protecting human properties, to envisage the ideal places for implanting new projects (buildings, infrastructures, agriculture fields…) and finally to reserve the suitable budget for planes liable to flooding (United States Department of Agriculture. Natural Resources Conservation Service (USDANRCS) 2010, 2011, Nor Azliza 2006).

Formulating atmospheric water circulation to localise the precipitation
In plus of the water evaporated from soils, lakes, oceans, the amount of water transpired by plant canopies constitutes a mass of humid air that will absorbs and emits energy, losses or gains material, moves up, and participates with the action of earth rotation (coriolis force) and atmospheric vapour pressure difference in the formation of wind, cloud displacement and giving out precipitation. The mass of air has tendency to displace vertically from position of high pressure to another characterised by a weak pressure value. The effect of earth rotation will generate the displacement of that mass in different directions. The direction of motion of the air mass represents the wind direction and the speed of its displacement is exactly the wind velocity (Sellami 2011). Localising the geographic position of averse and pelting rains and determining their intensities consist in fact to map the atmospheric water pressure and to estimate the wind velocity for all directions. The most used equations formulating the problem suggested above are the atmospheric primitive equations. They are well used in meteorology and oceanography for numerical models of time forecasting and when simulating the future behaviour of the atmosphere (Edward 2010, Firth Robert 2006, Beniston 1998, Pielke Roger A 1984. A general analytical solution of the primitive equations that consider the latitude and the altitude and formulating wind velocities in all directions and the potential pressure is (Sellami 2011, Edwards 2010, Comolet R. 1963 (2) f : Coriolis parameter proportional to the earth rotation P: Water vapour pressure at a designed point in the atmosphere x, y: Coordinate of a point in atmosphere V : Velocity vector ρ : Volumic mass The vertical direction is not considered because in the hypothesis adopted we have neglected the vertical variation on behalf of the horizontal ones.
So we can say that estimating the wind speed in all positions of the atmosphere, monitoring its variation over time permit to localise the zone of low pressure, indicator of minimum local pressure and precipitation, the zone of high pressure, indicator of maximum local pressure, fine weather and absence of precipitation.

Formulating the streaming after precipitation
In the case of inundation, the flowing of the free water on the planes liable to flooding, either for urban or rural zones, obeys the fact that the scales for the vertical variation of motion are neglected in front of those horizontals and that the representation of all phenomenon by surface coordinates (not on the space) is well sufficient. With those considerations, the Navier Stockes equations (combination between the equation of mass conservation, equation of energy conservation and equations of motion conservation) are transformed to the Saint Venant equations also said « shallow water equations » which are the most used for modelling the fluvial flowing (Pascal 2009, Lorenzo et al. 2008, Aldrighetti 2007, Berreksi et al 2006, Li B et al 2006. Hostache 2006, Ranjit and Steven 1995, Comolet R. 1963. They are represented by the following system: The friction slopes can be expressed as follow (Pascal 2009, Berreksi et al 2006: n: Maning Coefficient B: Width of the streaming water layer x: Coordinate x representing the direction of the water flow The Width of the streaming water layer is expressed by: B(x) : Width of the streaming water layer at the longitudinal coordinate x from a zero point b 1 : Width at the upstream F 1 : Incident Froude Number The resolution of those equations either numerically or analytically permits to determine the streaming water height and the streaming water speed at every point on the plane liable to inundation by considering the ground topography (Syme 2008, Smith et al. 2006, Huthoff and Augustijn 2006. Then we can calculate the energy accompanying the flow for every position by (Moghadam 2010, Davide et al. 2009, Lorenzo et al. 2008, Yen Ben Chie 2002, Arcement and Schneider 1981 Zhang et al 2005). We will in the following paragraphs formulate the resistance of obstacles to water flowing in order to test if they can dissipate the flow power and after to foresee the risk of damage.

Formulating the resistance of obstacle to water streaming
In the case of inundation, the flow of water streaming through plains either in rural or urban zones will suffer resistance from all existing obstacles on its scheme. Those obstacles can be plant canopies (grass, single separated trees, agriculture fields, forests, wetlands) or buildings, houses, and infrastructures (hydraulic constructers, barrages, bridges, roads…) (Bewsher Consulting 2009, Lorenzo et al. 2008, Syme 2008. Modelling the force of resistance of every obstacle to the effect of water streaming after averse permits to evaluate the risk of damage in every region or zone, to diagnose the resistance situation of all installed projects, to propose technical solutions ameliorating the toughness for the different components of new projects (emplacement, specie of vegetation for agriculture projects, material of construction and architecture for infrastructure, buildings and houses) so we minimise the risk of losses after floods, to size up tools and techniques absorbing the power of water flow and protecting human properties (USDANRCS 2011, Roca and Davison 2010, Bewsher Consulting 2009, Hilary and James 2007, Moghadam 2007, Nor Azliza 2006, Zhang et al 2005, Plate 2002, Martin 2001. To do so we will try in this part to give a general formulation of obstacle resistance.

Resistance Force of vegetation to water streams
Modelling for hydrological or agriculture studies, at regional scale or at vegetation field scale, necessitates to express the phenomenon of water flowing and streaming by considering the effects of roughness, shear, friction and drag for both soil type and vegetation specie (Sadeghi et al 2010, Mauro 2009, Baptist et al 2007, Austin 2007, Huthoff and Augustijn 2006, Arcement and Schneider 1981. Those effects intervene, generally, in the www.intechopen.com Sustainable Development -Education, Business and Management -Architecture and Building Construction -Agriculture and Food Security 86 expression of the bulk energy losses coefficients and every kind of vegetation canopy could be considered as a type of superficial roughness. Depending on its height, density, flexibility, distribution and species, it can significantly decrease the capacity of river or waterway, extending flow resistance; alter backwater profiles and exchange sediment transport and deposition. (Roca and Davison 2010, Yen Chang Chen et al 2009, Yen Ben Chie 2002. To investigate the resistance effect of vegetation we must differentiate between the flexible vegetation like grass plants and less flexible vegetation (bushes, trees), and we have to consider the cases when the plants are partially or totally submerged (Mauro 2009, Moghadam 2007, Maarten et al 2005, Yen 2002, Juha 2004). We will try in the following reasoning to give a general formulation for the problem.
In order to propose an expression for the drag force taking in account the physical effect of vegetation, we apply force balance between gravitational force, drag force and friction force for a uniform flow in the direction of vegetation.
The drag force for submerged vegetation can be expressed by (Mauro N. 2009, Fredrik et al 2007, Juha 2004, Ranjit and Steven 1995, Arcement and Schneider 1981 The mean velocity of water flow through submergent vegetation is:  For the urban zone, where the obstacles resisting to flow are not flexible, the water flowing between houses and buildings, through roads and fences suffered a lost of load as results of the roughness effect exerted by every obstacle (Syme 2008). This roughness effect is generally expressed by a friction coefficient depending on the size of the obstacle (height, width, length, weight…) and the area it occupies (Peng andAthol 2004, Martin 2001). The physics signification of the friction coefficient is that it translates the roughness degree and the resistance power to water flow of obstacles and their retardance effects , Hilary and James 2007, Yu D. and Lane 2006. To make empirical formulas for the friction factor based on global experimental studies that could be extrapolated at large scale for flood management, many researchers, on behalf of a dimensional analysis, suggested that the friction factor could be formulated as function of the following parameters (  Flooding in urban areas presents a range of challenges to the modellers due to the complexity of the flow patterns and paths that occur (Syme 2008, Smith et al. 2006). In fact the major problems signalled are how to give a drag coefficient or friction factor the most appropriate to every kind of building, house, fence... ? How considering the storage effect?, how to represent the blockage of interior and exterior walls?, if to model the buildings as porous?. The additional complexity that occurs due to fence collapses, debris blockages, and the displacement of cars and other obstructions how to calculate their effects? Actually, the global tendency of many researchers is to determine the drag coefficient by kind of obstacle from experimental data at laboratory level and to extrapolate the results for real cases (Sadeghi et al 2010, Mauro 2009, Nian-Sheng. 2008, Fredirik et al 2007, Ranjit and Steven 1995, Julien 2002, Kidson et al. 2002, Martin 2001, Guellouz and Tavoularis 2000, Julien and Wargadalam 1995. It is the objective of the following paragraph.

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Experimental study at laboratory level
We will erect in this part the first results from an experimental protocol we have realised at laboratory level to determine the effect of obstacles on water flowing through an open canal. The system is composed from a storage tank linked to a pump, which aspires and delivers water to a second tank occupied with a filter installed at the upstream of the canal. On the exhaust pipe of the pump there is a control weir permitting to fix the discharge debit. The driven water crosses the canal, reaches the down river, and falls in the storage tank to be forced again toward the up river. Between the down stream and the storage tank we have installed a water balance to measure the repressed debit. The study consists to measure, every 0.5 m inside the canal, the water height and the water speed for different obstacle positioning scenarios 's and many discharge debits. The scenarios are when the canal is without obstacles (S 0 ), canal with one rectangular obstacle placed one meter from the upstream (S 1 ), canal with two rectangular obstacles the second is at four meters from the upstream (S 2 ) and canal with three obstacles the third has a convex form and is placed at the middle of the rectangular ones which means at 2.5 m from the upstream (S 3 ). The extrapolation of the results to real scale can be easily done when considering the size of the obstacle, the geometry of its form and the values of the debit which are analogous to the streaming flow for the floods (Sadeghi et al 2010, Moghadam et al. 2010, Pascal 2009, Limantara 2009, Yen Chang Chen et al 2009, Davide et al. 2009, Lorenzo et al. 2008, Chao and Peifang 2007, Berreksi et al 2006, Peng and Athol 2004, Kidson et al. 2002, Guellouz and Tavoularis 2000. The results from measurement of the water height for the four scenarios and for one discharge debit (Q 1 = 6.9767 10 -3 m 3 /s) are presented in the following figure. We note clearly that the water height decreases from the upstream to the downstream of the canal for all the scenarios. We notice also that between the upstream of the canal tell the position 4 m inside, the height of water is the most important for the scenario three obstacles, followed by the scenario tow obstacles, one obstacle and finally canal without obstacles. Which revolt the effect of obstacle number on the flowing. At the down stream we remark that water height for the four scenarios are very closes to each other and that the height is the most important for the scenarios canal without obstacle and canal with one obstacle. Compared to results from other experimental studies, our work is promising (Pascal 2009, Berreksi et al 2006. The importance of this experimental study is that the correspondent results could be used to validate an eventual resolution of the shallow water equations either analytically or numerically and also to determine the drag coefficients associated to each obstacles which can be extrapolated for real cases (Andrew et al 2006). It's the purpose of a future work in preparation.

Calculus for the decision making in the water sector
Knowing the fact that floods on urban or rural zones affect directly the water circuit by two contradictories phenomenon. The first is the risk to damage the hydraulic infrastructures, forages, pumping stations, pipes, adduction/distribution networks… (USDANRCS 2010(USDANRCS , 2011. The second is that the surplus water that accompanied inundation can enhance our water resources for the surface ones or the groundwater. So proposing model for completely managing the inundation risk must necessarily be done by revolting the necessaries equations formulating the water circuit monitoring (Martin 2010, Yangwen et al 2007, Chao and Peifang 2007, Evan et al 2006, Li B et al 2006. As consequence, we will put in at this part, the different steps to follow, the mathematical equations/models and the necessary materials that can be used to control, to monitor and to evaluate, by geographical position, the actual and future situation of water circuit: water availability at the resources level, the state of the adduction/distribution networks, the consumer requirements (agricultural sector, industrial sector, service sector). So we can after evaluate if the existing resources and water networks could satisfy all consumers categories and for what time, to propose solutions of rehabilitation, to install new schemes of water networks for the consumers not yet connected or for those whose the existing network could not assume their water need in the future

Calculus for water resources
Generally there are two classes of resources: the surface resources and the ground water resources. The amount of water available is generally linked to climatic conditions: precipitation, temperature, and evaporation. The prediction of resources efficiencies can be done easily for any region by applying this reasoning: After limiting the different surface lakes, all waterways, the different water sheets (water table and deep water sheet) in every region, we consider every one of them as a closed system for which we apply the balance equation. This later is presented as the equilibrium between the inflow, out flow, income and lost of water for every system defined. It can be written in global form as follow (Mauro 2009, Sellami 2008, Yangwen et al 2007, Chao and Peifang 2007: www.intechopen.com Sustainable Development -Education, Business and Management -Architecture and Building Construction -Agriculture and Food Security 92 V w : variation of water volume in the defined system V i,w : initial water volume in the defined system P: precipitation Q l,in : the lateral inflow for the defined system from all the directions Q e : water lost by evaporation from the defined system Q l,out : the lateral outflow for the defined system from all the directions So then we can formulate the fictive water debit at a determined time for the defined system by: Q f : fictitious water flux V w : variation of water volume in the defined system for the desired period t: variation of time in the defined system for the desired period The determination of every term in the balance equation depends on the climatic conditions, soil structure, soil occupation and the geologic characteristics in the region studied. We can measure them directly by using the necessary apparatus and methods (piezometric and geological mapping, hydrological measurements, meteorological measurements).
If we consider the system occupied by water as a reservoir, its volume is calculated by the following relationship (Yangwen et al 2007): V r : Total volume of the reservoir A occ : Area or extent occupied by the water H tot : Total height of the reservoir (distance between the bottom and the top for the considered system) The volume of water continued in the reservoir is defined by: V w : Water volume in the reservoir H w : Water height inside the reservoir (distance between the bottom and the surface of water sheet) For the surface resource, they are formed from the hydrographical networks (rivers), natural lakes, barrages lakes', and natural water sources. Their localisations are possible by establishing numerical maps and land numerical models using land altimetry measures, thematic maps and aerial photos (satellite and planes). We must limit the fluvial network (length and capacity of the primary line water, secondary line water, tertiary line water…) and we have to determine the capacities of the existing lakes (geographical localisation, extent and water height). L river : Length of the river V river : Water volume of a river The debit through a river can be expressed as follow (Comolet 1963): S m : Wet surface of the river R H : Hydraulic radius of the river i: Slope of the river C: Friction coefficient For the ground water and table water resources, they are considered, generally, as nonrenewable resources. They don't depend largely on climatic parameters but they are sustained our days to an overexploitation. Determining the amount of water that exists, for how time it can assume our needs and the possibility of their artificial recharges are questions that we can model (Younes et al 2010;Mauro N. 2009). So we must make a geological sweeping, a piezometric scanning and mapping and we have to make many types of forage for testing and controlling the existing sheets and to discover if possible the new ones. Then by using thematic maps and models for underground hydraulic we can elaborate equations for water sheet folding, expanse, height and volume. By utilising the statistical studies, land use plan, agricultural maps, economic plans, directing plans for development by region we can propose mathematically relationships for the evolution of water consumption by sector and by region. We can then determine the life duration of the ground water and the amount of water to add when thinking to their recharge. The most used equations formulating the debit of their exploitation are (Comolet 1963): For the Q v : Pumped debit www.intechopen.com Sustainable Development -Education, Business and Management -Architecture and Building Construction -Agriculture and Food Security 94 h 1 : Piezometric height at the position of action radius (R) h 2 : Water height in the pumping well r 0 : Radius of the pumping well k: Hydraulic conductivity R: Action radius of the pumping well h 0 : Distance between the two substratums

Calculus for the adduction/distribution water networks
The adduction/distribution networks are defined as the course that the water flow follows from the source to the consumer. Our days, in rural or urban zones, to assume the water needed at time and to avoid its loss in route there is tendency to conduct the water by special canalisations (pipes, conduits), hydraulic accessories and apparatus (pump, tanks, treatment stations, floodgates, bends, diaphragm...). The differentiation between adduction and distribution is arbitrary. It depends on the sector to supply with water and is only to facilitate the conception of the network when making hydraulic studies. Generally, the adduction part is that from the sources to the tank or to the series of tanks for water storage and treatment. The distribution is that from the tanks to the consumer: fields and plants for agricultural sector, houses for potable sector (service sector) and factories for the industrial sector. Calculating a water network signifies determining the length of pipes, their diameters, nature or material of fabrication, number of conduits sections', types and number of hydraulic accessories, their capacities (surface, volume, power, energy…) and finally the cost. There are many mathematical relationships, formulas and models that are used to make the hydraulic calculus. They are based on the energy balance between the initial points of the network (resource) to the end point of the network (entrance to the consumer property). This energetic balance is formulated by the theorem of Bernoulli expressed as follow: H initial is the energy at the initial point of network H final is the energy at the final point of the network J initial-final is the total lost of energy between the initial point and the final point of the network Generally, between the initial and final points of a water line, and because of topographical problems, we have to consider many particular points where there is change of slope, change of direction and/or obstacles. They are called knots. The distance between two successive particular points (knots) defines the length of a pipe section. If we note A and B the two successive knots, we can, by applying the Bernoulli theorem to the pipe section AB, write (Sellami and Trabelsi 2009, Sellami2008, Comolet 1963: The total lost of energy J A-B , is defined as the sum of the singular energy lost (J A and J B ) and the linear energy lost between A and B (j A-B ).
For every hydraulic accessory in the network corresponds a particular singular energy lost (floodgates, bends, diaphragm, change of section…). We give the general formula: While for the linear energy lost there are many empirical formulas. They express generally the linear energy lost by the water inside the pipes as function of the diameter, the water flow, the conduit roughness and the nature of fabrication material. We can give here as example the following (Sellami and Trabelsi 2009, Ennabli 2001, Punmia and Ashok, 1998 Where Q is the debit (m 3 /s), j is the linear lost of energy (m/m), D is the pipe diameters (m), V water velocity (m/s), λ coefficient for energy lost So we have to know the altitude of the particular points (from topographical measurements and level curves maps) and the pressure needed to assume the distribution of water to all the consumers which must be superior to the highest manometeric level at the streamside. By applying the Bernoulli theorem for every pipe section we can deduce all the needed parameters for the hydraulic network conception. I must signal here that there are many models and soft wares that can be used and that they are established from the precedent reasoning and formulas (Sellami & Trabelsi 2009, Sellami 2008).

Calculus for the consumer level
In the conception of a hydraulic network, we must begin by defining the consumers. This means calculating the amount of water they need and the minimum pressure permitting to lead water to the consumer at the highest manometeric level now and in the future.
As said above, there are three categories of consumers depending on their activities: agricultural activities, industrial activities and services activities.

For the agricultural activities
The amount of water to lead is that needed by the plants in the field and by field in the region for all vegetal speculations that exist. There are many models permitting to estimate the water needed by plants as function of the physiological characteristics of every specie (leaf area index, sap flow, stomata resistance…), soils types (texture, structure, permeability, porosity…), climatic parameters (solar radiation, temperature, precipitation, evaporation, transpiration, heat…) and the economical and demographic evolution by region. Their use is possible and it depends on the precision asked. We present here a simple and general formula permitting to calculate the amount of water needed by plants in the field (Sellami 2011, Sellami 2008, Sellami and Sifaoui 2008, Battaglia and Sands 1997, Tournebize and Sinoquet, 1995: Q : amount of water needed K c : cultural coefficient that depends on the types of plants and soils ETP: potential evapotranspiration we have to utilize the agricultural maps, land-use plan, the data basis for vegetations characteristics, the gene banks, climatic data basis, models for plants transpiration, biosphere models, circulation and climatic models. (Ciret andHenderson-Sellers, 1997b, Sellers et al 1986).

For the industrial activities
The amount of water needed depends on the type of product and the different process used inside the industry. So we must do multi audit studies to evaluate the real need by process for every product. A general formulation of the water needed by type of industry can be formulated as follow (Sellami 2011): ,, For a zone where there is many industry the total water needed by a defined unity can be expressed globally by: The defined unity can be a linear meter unity from the occupied surface, m² unity from the occupied area, m 3 unity from the occupied volume, unity of mass (kg), number of product….
We can give here some examples of water needed by sort of industry: for the textile industry (cotton tissue) we need 4500 l/kg (the defined unity is a kg of product), for dairy industry we need 10 l/l milk (the defined unity is a litre of product), for the paper industry we need 222 -330 m 3 /t, for the sugar industry we need 1929 m3 /t (the defined unity is a tonne of product), For bovine, mutton and goat meat we need 13 500 m3/t, for poultry meat we need 4100 m3/t, for eggs we need 2700 m3/t, for olive oil industry we need 11350 m3/t, for soybean oil industry we need 5405 m3/t, for sunflower seed oil we need we need 7550 m3/t, for palm oil we need 5500 m3/t, dates industry we need 1660 m3/t, Apples 387m3/t, Bananas 499m3/t oranges and citrus we need 378 m3/t, onions we need 168 m3/t, tomatoes 130 m3/t, coffee 5790 m3/t, for the cotton 496 m3/t (Chapagain et al 2006, Zimmer andRenault 2000).
For the future, the water needed is evaluated as function of the orientation of the durable development axis by region, census studies, economic plan, the technology evolution and the market demand. We can intervene here to advice about what industry to install in what region after studying the water circuits (Sellami 20111, Sellami and Trabelsi 2009).

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For the service activities
The amount of water needed here is that to consume as potable water. It depends on the number of residents by region, their requirement in comfort, their evolution in the future. We have to use the census studies and the statistical models to evaluate the change in the future. They are generally based on the following equations (Sellami et Trabelsi 2009, Sellami 2008, Baroudi et al 2006, Ennabli 2001: For the demographic evolution we have: P y = P y0 (1 + τ) y -y 0 (52) P y : is the population number for the year (y) P y0 : is the population number for the reference year (y 0 ) τ: is the population evolution rate For the consumption evolution we have: C y = C y-1 (1 + ) n (53) C y : is the water consumption for the year (y) C y-1 : is the water consumption for the year (y-1) n: number of years for which we estimate the consumption : consumption evolution rate

Representation of data on numerical support
We will identify here the data processing support to use in order to make the link between data bases, maps, models and equations established and to show the results in maps, graphics, tables formats and files. So we can evaluate the actual situation, take decision and intervene at moment. Also, we can foresee the future state for the resources, networks and consumers, propose the adequate scenarios for management, rehabilitation and development. After propounding the necessaries equations, mathematical models, software and maps to use, we can organize the data we dispose in the form of a data conceptual model, data logical model data physical model and land numerical model. The GIS tools' to utilize are (Sellami and Trabelsi 2009): -The equations presented above for the direct calculation for the two parts -Epanet 2.0 for hydraulic calculus and pressure verification -ENVI 4.2: The environment for visualizing image to elaborate the land numerical model -ArcView GIS 3.2 to digitalize the information layers from maps, to organise the data tables and to make the link with mathematical models and software of calculus -Power AMC Designor 6.0 for data arrangement -Hydrogen as interface of link with hydraulic calculus -3D Analyst and Spatial Analyst for spatial and 3 D analysis and representation Depending on the quantity of items and data basis we dispose (input), the thematic maps/plans to realise (output) are those representing the different information layers needed in decision making (proposing a solution scenario). We list here the following: geologic maps, hydrographic network maps (primer, secondary, tertiary rivers), topographic maps for the land numerical model, soil type maps, land use maps, lakes and The same reasoning and the same tools were used for the region of SILIANA as we will present later.

Results from partially validation of the modelling approach
A first application of the model has been done to the region of SILIANA in the West-North of Tunisia (Sellami and Trabelsi 2009). At the beginning we have identified, limited and evaluated the water resources available (surfaces resources, ground water resources, artificial resources…). After, by using the necessaries equations, we have diagnosed the different adduction/distribution networks that exist and calculated their hydraulic parameters: the lengths of pipes, diameters, pressures and debit at different positions, types and capacities of hydraulic accessories, risk of conduits corrosions and filling, risks of pipe damage and water leak. Experimental verification of calculus has been done by measurement of pressure and water flow at different positions (GPS, pressure captors, debit captors). Finally we have distinguished all types of water consumers in the region, calculated their water needs and determined those connected to the water network and those who are not yet connected.
By using the GIS tools and the brut data we dispose, we have established the multi-layers information map'. It is presented in figure 3. It comports the following items: Topographic layer (level curves), hydrographic networks layer (first, secondary and tertiary river lines), geologic layer, forages for ground water resources layer, adduction network layer, hydraulic accessories layers.
After using the necessary calculus and the existing databases we have numerated the actual water distribution network. We have deduced the next results: -Geographical situation: The zone studied is referenced by these coordinates: Longitude 2° 27' 33"; Latitude: 71° 18' 16", Altitude: 400 and 460 m NGT -Water resources: Because the flow in the rivers networks is irregular, the region is supplied by water only from ground water sheet via 4 forages. Here with their characteristics (  After modelling the water network functioning situation for the year 2007, we have remarked that there is five pressure levels in the network: less than 20 m, between 20 and 40 m, between 40 and 50 and more than 60m (Sellami and Trabelsi 2009). But for the majority of knots, the pressure is between 20 and 40 m which is a threshold fixed by the Tunisian National Society of Water Distribution for each subscriber. The singular knots for which we have recorded feeble pressures are between 10 and 20 m and those for which we have registered high pressures are not too distant from 50 m and for both the problem is due to the subscriber altitude. So there is no real problems of pressure for the year 2007. Figure 4 shows the calculated prevention of the pressure and the energy lost for the year 2030 in the adduction and distribution networks.
We notice a high pressures (much more than 50 m) and an important lost of energy (more than 3 m/km) in the pipes of the high zone. We can suggest here many scenarios of rehabilitation. After hydraulic modelling, we have proposed to replace many conduits sections by others with a diameter varying between 400 and 500 mm. The new pressure and energy lost repartitions for the year 2030 appears in figure 5.
For all the pipes, we notice a net amelioration for the pressure (between 20 and 50 m) and for the energy lost (between 1 and 2 m/km). The same reasoning and simulation could be effectuated for different paces of time (daily, monthly, yearly…) in order to take the appropriate decision at time.

Conclusion
The modelling approach presented here is constituted from two complementary parts. In the first we have revolted the necessary equations to use when to evaluate the inundations effects and to manage their risks. In this sense and as beginning, we have disengaged the formulations to foresee the timing of precipitation descent, to position the averse starting and to estimate their intensities so we can localise the plains liable to floods and map the most vulnerable zones. After we can avert the decision makers about for what region we must be prepared first and which budget we can reserve and advice them where to install our new projects. To characterise the streaming after precipitation we must be able to detect the directions of flows, their speeds and the water depth in all position of plains by considering the topography and the sorts of obstacles either in rural or urban zones. To reach that purpose we have developed a system of linear equations which can be easily resolved either analytically or numerically and permitting the estimation of those parameters. The resistance of obstacles (vegetation canopies, agriculture fields, buildings and houses, hydraulic infrastructures, water resources, forages, water adduction/distribution networks, roads/ bridges networks…) to water flow must be estimated in order to evaluate the risk of their damage as function of averse intensity for many scenarios, to size means and tools absorbing the power of water flow or deviating the water speed, to invent the adequate material of construction and to architect the efficient positioning of our projects inside villages or towns in the objective to protect human properties. To do so we have aroused the appropriate reasoning and detailed the useful formulas calculating the drag coefficients and friction factors by kind of obstacle for divers cases (totally submerged, partially submerges, flexible, solid) in either rural or urban zone.
The complete modelling of the inundation risk management can not be done successfully without responding to the question how to manage the water circuit. Because the floods have tow antagonistic effects on that circuit: on one hand they can damage the water networks (forages, pumps, treatment stations, pipes system, hydraulic accessories…), on the other hand the surplus water flowing over plains can be exploited to enhance the water resources either the surface water resources or the ground water resources. In this meaning we have evolved a basic methodology with the necessary formulas and tools permitting to test, evaluate and monitor both the actual and future situations of the water resources, the adduction/distribution network pipes and the consumers water need. It provides an interface to connect mathematical models and software to thematic maps and data basis in the hope to be capable to take momentarily the appropriate decision about the adequate solution and scenario for management, rehabilitation, renewal and projection A first application of this model has been done for the water circuit of SILIANA region in the West-North of Tunisia. After exploiting the disposed data basis and thematic maps and by applying the mathematical models established, we have diagnosed the actual water circuit till the year 2007, we have estimated the yearly evolution of water volume for both resources and consumers and we have calculated the pressure repartition in all the knots of the adduction/distribution network until the year 2030. We have realised that the resources could not satisfy the consumers after 2030 and that we will have pressures insufficiencies in many zones of the network. We have proposed a scenario of rehabilitation, we have calculated the new hydraulic parameters of the network propounded and we have prescribed the correspondent map. We notice a net amelioration.
Finally we allow our self to say that the out puts of this approach could be easily analysed, interpreted and brought up to date and the making decision process could be ran for a moment. But a work for ameliorating this approach is needed particularly by using new and more precise models for estimating the water needed and its evolution for the agricultural, industrial and services sectors