# Hydraulic Calculation

For the assessment of floods in rivers and channels, a hydrodynamic-numerical model (hn-model) is most of the times required. A "hydrodynamic" model is in fact able to consider the relevant forces like gravity, frictional resistance and inertia, which are responsible for the flow processes. The solution of the complex mathematical equations, describing the flow process of surface water, is usually possible only through a "numerical" discretization of the continuum (space and time). Ein- und Ausgangsdaten von HN-Modellen

The movement of flood waters through the landscape can be approximated using many different methods. Depending on the objectives and dimensional resolution of the required modelling outcomes - especially the water level and flow velocity - the basic equations can be simplified in various ways, without significantly limiting their validity. This leads to models with different advantages and disadvantages:

• 3-dimensional models: 3D-hn-models find their use in small-scale calculation fields, as for flow around structures or at intake structures of hydroelectric power stations, where the mapping of possible vortices and the knowledge of all three velocity components is important. The enormous demand for computing capacity is the main limiting factor. For the flow calculation, the full Navier-Stokes equations in x-, y- and z-direction are used. Widespread 3D hn-models are i.a. Flow 3D, MIKE 3D, ANSYS CFX, FLUENT and Delft 3D.
• 2-dimensional models: For 2D-hn-models the information in one direction (usually the vertical) is removed. The on flow depth averaged equations (the so-called "shallow water equations") allow accurate detection of flow characteristics (flow velocity v, water level W, shear stress τ, ...). For rivers with flood plains and formation of velocity gradients perpendicular to the flow direction the 2D-hn-models are a good compromise between creating effort and accurate mapping of the flow processes. These models are commonly used successfully for the calculation of flood waves. The field of application ranges from the investigation of a local object protection up to calculating of flood areas of several square kilometers. The software most commonly used are: MIKE 21, Hydro_AS-2D, SOBEK, FloodArea and Flow 2D.
• 1-dimensional models: The solution of 1D-hn-models is usually faster in computation compared to the 2D and 3D models. For 1D models the distribution of the flow parameters (W, v, ...) perpendicular to flow direction is averaged to the "Saint-Venant equations". The parameters are thus only calculated in the main flow direction. It is possible to divide the calculation for main bed and flood plains / riparian zones (waterbodies with structured sections). The typical application is the determination of the water surface curve in rivers with mainly uniform cross-sections. The investigated flow paths can range from a few hundred meters to several hundred kilometers. There are a wide variety of 1D hn models, including: HEC-RAS, Jabron, WSPWIN, MIKE 11 and FLUSS. Flooding area made of intersection of 1D-hn-model HEC-RAS with the DEM

More and more hybrid models are used, where 1D river sections are coupled with 2D regions, resulting in a flood assessment within the desired detail level and distribution.

The choice of a suitable model is also determined by; the area size (limited section of the river, the total catchment area) and by the availability of data (Digital Elevation Model DEM, terrestrial surveying).

A clear advantage of a 2D-hn-model is that for each element or cell, in which the region is divided, the velocity vector can be output. The 1D model distinguishes between velocity in the river and on the foreland. The direction of flow is not calculated but is specified within the geometry.

## Stationary and transient models

Although all natural processes are time-dependent (transient), a flood wave may be simulated with sufficient accuracy by a sequence of time-independent (stationary) states.

Thus, in regard to the time dependency (e.g. the discharge Q from the time t), a distinction is made between:

• Stationary models, which describe a state where the time changes are negligible [Q = const]
• quasi-stationary models that simulate the changes over time as a sequence of stationary states [Q = Q (t1), Q (t2) ... Q (tn)] and
• transient models, which preserve the time-dependence of the processes [Q = Q (t)].

Only transient models can take into account the inherent flattening process a flood wave (retention), as well as the impact of retention areas. Although the wave attenuation can be taken into account in the quasi-stationary models by an upstream hydrological model, only the unsteady models grant a proper volume balance (compliance of the continuity condition). However, stationary models don´t have exact volumes.

The transient approach for the calculation of flood is always preferable if the inflows are available or estimated as hydrographs Q = Q (t).

It should take into account that the amount of computation increases disproportionately with the dimensionality of the transient processes and the extension of the model.

## Model creation

To construct a hn-model for simulating a flood, several basic data items are required:

• Discharge from the headwaters, inflow from the sewer system as well as side flows: as hydrograph Q (t) for a transient calculation or as constant values for the quasi-stationary as well as stationary approach (upper or internal boundary condition).
• Velocity distribution at the inflow boundary for 2D and 3D models.
• Water level (1D) or water level distribution (2D and 3D) or runoff-water level-relationship (calibration curve) at the outlet from the model (lower boundary condition).
• Topography of the river bed and the flood plains as a Digital Elevation Model (DEM) or terrestrial surveying, LiDAR or LaserScan data.
• Matching friction coefficients for the different texture of sole, embankments, structures, vegetation and flood plains. For this a water body-inspection is essential by competent professionals.
• Initial conditions: In addition, the initial value of the relevant parameters (water level and velocity vector) throughout the model area is pretending for the non-stationary models.

In both 1D and 2D-hn-models the existing transverse structures (bridges, culverts, weirs, sills, ...) and other structures which are used to control runoff (side weirs, control elements and for 1D also polders) must be entered manually. Flooding as a result of HQ100 at the Wierau (2D-hn-model FloodArea)

## Calibration and Validation

Despite their conceptual legality flow equations also contain empirical approaches (frictional losses, vegetation effect, turbulence models, ...). For hn-models, the roughness is the parameter afflicted with the greatest uncertainties. Therefore each model necessarily requires a calibration. The empirical parameters are varied in an iterative process until the calculated results (mostly the water level) have a sufficiently good match with the directly measured respectively indirectly derived values. After a flood the line of the debris deposition at the highest water level is usually clearly visible. Often the wetness on facades or a certain abrasion on bridge piers is visible for a long time. For historical events flood marks may be present. Level data can of course be used during calibration, if available.

With calibration, the model is adjusted on an event that the results correspond to the observation. Checking if the selected parameter set retains its validity for other events is called validation. It verifies the model performance, which means the transferability of the model to other events as the one used during the calibration (e.g. flood with different return period). If necessary, different sets of parameters have to be chosen.

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 Flood Hydraulic Calculation 