Using common and consistent vocabulary is vital for working in teams. This section exemplifies a glossary with technical terms recurring in this eBook.


Advection is the motion of particles along with the bulk flow. The properties (e.g., heat) of an advected particle or substance are conserved. Mathematically, advection of incompressible fluids (e.g., water) is described by the Continuity equation [KC08].

French: Advection
German: Advektion


An anabranched river (section) is characterized by one or more side channels diverting from the main river stem. Anabranching (or also anastomosing) channels occur primarily in alluvial channel beds where more sediment is available than the water runoff can transport (transport capacity-limited rivers). Thus, an anabranching river has high sediment loads and channel avulsion is likely to occur during floods [HN07, NK96, RPLV17]. This eBook shows an example for an anabranching river section in the morphdynamic modeling tutorial in Fig. 148.

French: Anabranche
German: Flussarm

Anastomosing rivers

See Anabranch.


The American Standard Code for Information Interchange (ASCII) is an encoding standard for text on computers. The development of ASCII goes back to telegraphy and was first published in 1961 for the Latin alphabet. It was later extended by other alphabets and special characters [Mac80]. ASCII code represents characters in the form of numbers. For instance, the ASCII code 77 represents uppercase A. In Python applications, ASCII code numbers can be useful to iterate through the alphabet (e.g., alphabetic column names), where chr(ASCII) returns a letter. For example, in Python print(chr(78)) returns uppercase B.


Bedload (also referred to as bed load) \(Q_b\) (or \(q_b\) for unit bedload) in kg\(\cdot\)s\(^{-1}\) (or kg\(\cdot\)s\(^{-1}\cdot\)m\(^{-1}\)) is a special type of Sediment transport describing the displacement of coarse particles by rolling, sliding, and/or jumping on the riverbed. In river hydraulics, the so-called Dimensionless bed shear stress or also referred to as Shields parameter [Shi36] is often used as the threshold value for the mobilization of sediment from the riverbed. The dimensionless expression of bedload transport is [Ein50]:

\[ \Phi_b = \frac{q_b}{\rho_{w} \sqrt{(s - 1) g D^{3}_{pq}}} \approx \frac{Q_b}{0.5\cdot(b + B)\rho_{w} \sqrt{(s - 1) g D^{3}_{pq}}} \]

where \(\rho_{w}\) is the density of water; \(s\) is the ratio of sediment grain and water density (typically 2.68) [Sch17]; \(g\) is gravitational acceleration; \(D_{pq}\) is the grain diameter of which \(pq \%\) of the mixture are finer; and \(b\) and \(B\) are the channel bottom and surface width, respectively (or cell width/height in a 2d numerical model).

Read more about the calculation of bedload in this eBook in the Python exercises or the Telemac2d-Gaia tutorial. In numerical models, bedload transport is often computed using the Exner equation.

In addition, the term traveling bedload refers to a transport mode that is similar to wash load, but without suspended load [Pit16, YWZ+09].

French: Charriage
German: Geschiebtransport


The Boussinesq approximation of the Continuity equation assumes that density variations can be neglected except for the gravity term (i.e., in the vertical momentum equations). In addition, the Boussinesq approximation assumes that a fluid is incompressible and that wave motion is inviscid [SV60].


In the field of hydrodynamics, the abbreviation CFL commonly refers to the Courant-Friedrichs-Lewy condition, which represents a convergence criterion for the numerical solution to the Navier-Stokes partial differential equations. The CFL applies to explicit time integration schemes that may become unstable for large time steps as a function of the size of mesh cells. Today, most numerical software uses an internal value for the CFL to adaptively calculate the maximum time step that is required for the stability of explicit solvers. In 2d modelling, the CFL condition is defined as \(c_{cfl}={u_x \cdot \Delta t}/\Delta x + {u_y \cdot \Delta t}/\Delta y\), where \(\Delta t\) is the time step, \(\Delta x\) and \(\Delta y\) are grid cell sizes in \(x\) and \(y\) directions of the coordinate reference system, and \(u_x\) and \(u_y\) are the flow velocities in the \(x\) and \(y\) directions. An explicit solver is assumed to be stable when \(c_{cfl} \leq c_{cfl, crit}\), where the critical value \(c_{cfl, crit}\) for the CFL condition must be smaller than 1.0. To this end, numerical modelling software, such as BASEMENT, uses a default value of \(c_{cfl, crit} = 0.9\).

French: Nombre de Courant
German: CFL-Zahl

Continuity equation

The differential form of the continuity equation is \(\frac{\partial \psi}{\partial t}+\mathbf{u} \cdot \nabla \psi = 0\) where \(\psi\) is a constant of the particle/substance in consideration and \(\mathbf{u}\) is the fluid velocity vector. The \(\nabla\) operator is literally a vector of partial differential operators \(\frac{\partial}{\partial x_i}\) where \(x_i\) refers to the dimensions of the flow field. In the case of steady flow (no variability in time) the advection equation becomes \(\mathbf{u} \cdot \nabla \psi = 0\) [KC08].

The mass continuity equation of an incompressible fluid, such as water, considers the constant \(\Psi\) as a mass and has the form \(\nabla \cdot \mathbf{u} = 0\) or \(\frac{\partial u_i}{\partial x_i} = 0\) [KC08].

French: Équation de continuité
German: Kontinuitätsgleichung


Convection encompasses Advection and Diffusion [KC08]. Thus, convection is fluid motion because of bulk transport (water flowing in a river with reference to Advection) and dispersion of a fluid component from high-density to low-density regions (Diffusion) in the flow field (e.g., an ink drop dispersing in a river).

French: Convection
German: Konvektion


A Coordinate Reference System (CRS), also referred to as Spatial Reference System (SRS), is an orientation unit system to geographically locate objects in a map. The CRS involves an origin (\(x\)=0.0 and \(y\)=0.0) and a projection. Objects of one map can be put into another map through the transformation of their CRS with respect to the coordinates and the projection. Read more about CRS in the section on Projections and Coordinate Systems.

French: Système de coordonnées
German: Koordinatenreferenzsystem / Koordinatenbezugsystem (KBS)


The Comma-Separated Values (CSV) file format describes the structure of a text file storing simply structured data. The file name extension is *.csv, which may also contain Tab-Separated Values (TSV). The separator (i.e., comma, semicolon, or tab) sign delimits (or separates) colon values in one line of a *.csv file. Spreadsheet software, such as Libre Office Calc, enables to import and process *.csv files for cell-formula based data analyses.


A Digital Elevation Model (DEM) represents the bare Earth’s topographic surface excluding objects such as buildings or trees. In contrast, a Digital Surface Model (DSM) includes objects such as trees or buildings. In addition, a Digital Terrain Model (DTM) represents similar data to a DEM and both DEM and DTM can be used synonymously in many regions of the world. However, in the United States, a DTM refers to a Vector (regularly spaced points) dataset while a DEM is a Gridded Cell (Raster) Data dataset. The translation into other languages does not go along with the same definition of a DEM, DSM, and DTM, and the following translations refer to the English definitions rather than the same (translated) words.

French for DSM: Modèle numérique d’élévation (MNE)
German for DSM: Digitales Höhenmodell (DHM)

French for DEM: Modèle numérique de terrain (MNT)
German for DEM: Digitales Oberflächenmodell (DOM)

French for DTM: Modèle numérique d’élévation (MNE)
German for DTM: Digitales Geländemodell (DGM)

Ultimately, there are many options for correct DEM-terminology depending on the region where you are. Now, what is the correct term in which language? There is no universal answer to this question and a good choice is to be patient with the communication partner.


Diffusion is the result of random motion of particles, driven by differences in concentration (e.g., dissipation of highly concentrated particles towards regions of low concentration). Mathematically, diffusion is described by \(\frac{\partial \psi}{\partial t} = \nabla \cdot (D \nabla \psi)\) where \(\psi\) is a constant of the particle/substance in consideration; \(D\) is a diffusion coefficient (or diffusivity) in m\(^2\)/s, which is a proportionality constant between molecular flux and the gradient of a substance (or species). The \(\nabla\) (nabla) operator is a vector of partial differentials \(\frac{\partial}{\partial x_i}\) where \(x_i\) refers to the dimensions of the flow field [KC08].

French: Diffusion
German: Diffusion

Dimensionless bed shear stress

The dimensionless bed shear stress \(\tau_x\) (in the literature often called \(\theta\)) is derived from the shear forces that act on the riverbed as a result of flowing water. \(\tau_x\) is a key parameter in the calculation of Bedload transport where many semi-empiric equations assume that a sediment grain is mobile when a particle size-related, critical value of the dimensionless bed shear stress is exceeded. This critical value of dimensionless bed shear stress is also referred to as Shields parameter. To this end, \(\tau_x\) is calculated based on hydraulic characteristics and the characteristic grain size \(D_{pq}\) [Kra32, VK30]:

\[ \tau_{x} = \frac{R_h~\cdot~S_e}{\left(s-1\right)~\cdot~D_{pq}} \]

where \(R_h\) is the hydraulic radius (cf. calculation in the 1d hydraulic Python exercise); \(S_{e}\) is energy slope; and \(s\) is the ratio of sediment grain and water density (typically 2.68) [Sch17]. \(R_h\) may be substituted by water depth in wide rivers with monotonous cross-sectional shape and for (grid) cells of a 2d numerical model.

French: Cisaillement adimensionel
German: Dimensionslose Schubspannung

Echo sounder

An echo sounder emits an acoustic signal under water, which is reflected by the objects of the underwater landscape. Echo sounding is an active Sonar technique and enables the creation of an underwater DEM, which is also referred to as bathymetry. To perform echo sounding a probe must be installed on a boat that requires a minimum navigable water depth. In addition, the use of the echo sounder (probe) itself also requires a minimum water depth to operate with little noise inference. Therefore, by experience, a minimum water depth of 1-2 m is necessary to survey the bathymetry of a river by echo sounding.

French: Échosondeur / Sondeur acoustique
German: Echolot

Exner equation

The Exner [Exn25] equation yields sediment mass conservation in a hydro-morphodynamic model (see also the TELEMAC-Gaia tutorial) and expresses that the time-dependent Topographic change rate \(\frac{\partial \eta}{\partial t}\) equals the unit sediment (Bedload) fluxes \(q_b\) over the boundaries [BRP03, Hir71]:

\[ \frac{\partial \eta}{\partial t} = -\frac{1}{\epsilon}\frac{\partial q_b}{\partial x} \]

where \(\epsilon\) is the porosity of the active transport (riverbed) layer, and \(\eta\) is the thickness of the active (riverbed) transport layer.

French: Équation de Exner
German: Exner-Gleichung (?)

Froude number

The Froude number \(Fr\) is the ratio between inertia and gravity forces and it is a key number of wave propagation. Thus, \(Fr\) states whether information can be transmitted in upstream direction or not [Cho59, Hag10, HS09]:

\[\begin{split} Fr^2 = \frac{Q^2}{A^3 g} \frac{\partial A}{\partial h}\begin{cases} < 1 \rightarrow \mbox{ subcritical flow (upstream and downstream wave propagation)} \\ = 1 \rightarrow \mbox{critical flow (standing waves in upstream direction)} \\ > 1 \rightarrow \mbox{ supercritical flow (downstream wave propagation only)} \end{cases} \end{split}\]

The transition from supercritical flow to subcritical flow is called hydraulic jump. For a rectangular cross section \(A\), the Froude number becomes:

\[ Fr = \frac{u}{\sqrt{g \cdot h}} \]

The Froude number is also the basis for scaling many sediment transport phenomena in open channel flow [Yal71, Yal77].

French: Nombre de Froude
German: Froude-Zahl


The Georeferenced Tag Image File Format (GeoTIFF) links geographic positions to Gridded Cell (Raster) Data images. A GeoTIFF involves multiple files containing the tagged image itself (*.tif file), a world file (*.tfw file) containing information about the geographic reference and projection system, and potentially an *.ovr file that links the GeoTIFF with other resource data. Read more at the Open Geospatial Consortium’s standard for GeoTIFF.


The Hierarchical Data Format (HDF) provides the *.h5 (HDF4) and *.h5 (HDF5) file formats that store large datasets in an organized manner. HDF is often used with high-performance computing (HPC) applications, such as numerical models, to store large amounts of data output. This eBook impinges on HDF datasets in the BASEMENT tutorial where xdmf files represent the model output, and in the TELEMAC tutorials. In particular, TELEMAC builds on mesh and boundary files of the EnSim Core that is described in the user manual of the pre- and post-processing software Blue KenueTM (the newest Blue Kenue installer contains an updated version of the user manual). Understanding the HDF format significantly facilitates troubleshooting structural errors of computational meshes for numerical models.

Krylov space

Krylov (sub) spaces are used in numerical approximation schemes for finding solutions to sparse (many zero entries), high-dimensional linear systems [BH74]. To this end, Krylov (sub) space methods use Gaussian elimination (e.g., LU decomposition) to speed up calculations [Gut07].

French: Sous-espaces de Krylov / Méthode de la puissance itérée
German: Krylowraum


The International Association for Hydro-Environment Engineering and Research (IAHR) is an independent non-profit organization that unites professionals in the field of water resources. The IAHR has multiple branches and publishes several journals in collaboration with external publishing companies. Read more about the IAHR at


Light Detection and Ranging (LiDAR or lidar) uses laser pulses to measure earth surface properties such as canopy or terrain elevation. The laser pulses are sent from a remote sensing platform (fix station or airborne) to surfaces, which reflect the pulses with different speed (time-of-flight informs about terrain elevation) and energy pattern (leaves behave differently than rock). In its raw form, lidar data is a point cloud with various, geo-referenced information about the reflected signal. Lidar point clouds for end users are typically stored in las format or compressed laz format. las-formatted data are much faster to process, but also much larger than laz-formatted data. For this reason, lidar data are preferably transferred in laz format, while the las format is preferably used for processing lidar data.

LU decomposition

A lower-upper (LU) decomposition applies to the solution of linear systems (matrices) by re-organizing a matrix of equations into an upper and a lower triangular matrix. Thus, LU decomposition is a form of Gaussian elimination, which is typically applied in numerical analysis (e.g., Telemac2d) or machine learning.

French: Décomposition LU
German: LR Zerlegung (Gaußsches Eliminationsverfahren)


In computing, MPI stands for Message Passing Interface, which is a portable message passing standard. MPI is implemented in many open-source C, C++, and Fortran applications to enable parallel computing.

Navier-Stokes equations

The general form of the Navier-Stokes equations describes the motion of a Newtonian fluid and expresses the conservation of mass and momentum [Bat00]. The Navier-Stokes equations is a special type of Continuity equation that is derived from Cauchy’s equation (conservation of momentum). The equation simplifies with the assumption of incompressible fluids and reduces to the Euler equation when viscous effects are negligible, which is generally the case in far distance from the boundaries [KC08]. A theoretical, exact solution of the Navier-Stokes equations would yield a perfect description of many natural processes. However, the underlying system equations involves more unknown parameters than equations. For this reason, rigorous simplifications (e.g., the Shallow water equations) and numerical approximations with considerably larger computational effort than for an analytical solution are necessary for the solution of the Navier-Stokes equations. Simplification hypotheses are, for example, a hydrostatic pressure distribution (leading to the shallow water equations) or the assumption that a fluid is incompressible.

French: Équations de Navier-Stokes
German: Navier-Stokes-Gleichungen

Operating System

An Operating System (OS) manages the hardware of a computer, software (resources), and services for any program you want to install.

French: Système d’exploitation
German: Betriebssystem

Plane bed

A plane bed refers to a type of riverbed that is characterized by irregular bedforms with distant, varying confinement, often in transition between transport capacity-limited and sediment supply-limited river sections [Sch17].

planebed plane bed river stream example geomorphology

Fig. 151 Example of a plane bed river section at the Drance (VS, Switzerland). Picture: Sebastian Schwindt (2016).

Rating curve

See Stage-discharge relation.

Reynolds number

The Reynolds number \(Re\) relates viscous forces to inertia and is a key parameter for flow turbulence [Cho59]:

\[\begin{split} Re = \frac{u h}{\nu} \begin{cases} < 800 \rightarrow \mbox{ laminar flow} \\ \geq 800 \mbox{ and } \leq 2000 \rightarrow \mbox{ transitional flow} \\ > 10000 \rightarrow \mbox{ turbulent flow} \end{cases} \end{split}\]

Where \(\nu\) denotes the kinematic viscosity (10\(^{-6}\) m\(^{2}\) s\(^{-1}\) for water at 20\(^{\circ}\)C). In gravel-cobble bed rivers, inertia forces are typically dominant compared with viscous forces; therefore \(Re\) is generally larger than 2000 and the flow is turbulent [Cho59, Woh00].

French: Nombre de Reynolds
German: Reynolds-Zahl

Rich Text Format

The proprietary Rich Text Format (RTF) wraps raw text in functional blocks that enable graphically flavored Word-like processors to identify document properties such as font size and type. Common RTFs are, for instance, docx or odf and enable exchanging text files between different Word-like processors on different operating systems.

Saint-Venant equations

Cf. Shallow water equations.

Sediment transport

Fluvial sediment transport encompasses two modes of particle displacement: (1) suspended load and (2) bedload (see figure below). Finer particles with a weight that can be carried by the fluid (water) are transported as Suspended load. Coarser particles rolling, sliding, and jumping on the channel bed are transported as Bedload. There is third type of transport, the so-called wash load, which is finer than the coarse bed load, but too heavy (large) to be transported in suspension [Ein50]. The units for sediment transport are for an integral flow cross-section kg\(^3\cdot\)s\(^{-1}\) or per unit width kg\(^3\cdot\)s\(^{-1}\)m\(^{-1}\).

French: Transport solide
German: Sedimenttransport

Sediment yield

The sediment yield is the amount of sediment eroded per unit area (tons\(\cdot\)km\(^{-2}\cdot\)year\(^{-1}\)) of a watershed [GHW06].

French: Apport solide
German: Feststoffeintrag

Shallow water equations

In shallow (i.e., small water depths) and wide waters (many rivers), the assumption of hydrostatic pressure distribution can be made to simplify the Navier-Stokes equations. The corresponding simplified form of the Navier-Stokes equations is referred to as the shallow water equations. The shallow water equations imply that vertical flow velocity is negligible compared to horizontal (and longitudinal) flow velocity. This assumption is valid in many river systems, but there are several cases for which the shallow water equations are not suited [KC08].

For instance, the depth-averaged shallow water equations are not suited for any pressurized flows (e.g., at weirs or in pipes). This eBook recommends to use the shallow water equations only when the water depth is smaller than a 1/20 times the characteristic wavelength (e.g., flood waves or in tsunami/oceanic models) and when the water depth is smaller than 1/10 of the wetted channel width. The application of the shallow water equations is featured in this eBook with the tutorials on 2d numerical modeling (i.e., in the BASEMENT and Telemac2d chapters).

French: Équations (de Barré) de Saint-Venant
German: Flachwassergleichungen / Saint-Venant-Gleichungen

Shields parameter

The Shields [Shi36] parameter \(\tau_{x,cr}\) (in the literature also often named \(\theta_{cr}\)) is a dimensionless value of critical bed shear stress for sediment mobility. For this reason, the Shields parameter is also often referred to as dimensionless critical bed shear stress. Flow conditions and grain sizes with a Dimensionless bed shear stress \(\tau_x\) smaller than the Shields parameter curve are considered immobile. Vice versa, flow conditions and grains associated with a Dimensionless bed shear stress larger than the Shields parameter are considered mobile. In fully turbulent flow, the Shields parameter can be taken as a constant value of approximately 0.047\(\pm\)0.15 [Kra32, SJ83, VK30]. To evaluate if a grain is in motion, its Dimensionless bed shear stress value is plotted against its dimensionless diameter \(D_x\) in the so-called Shields diagram (also referred to as the Hunter-Rouse [Rou65] diagram). \(D_x\) is calculated for any grain with a diameter \(D_{pq}\) (in m) as [Ein50]:

\[ D_x = \left[\frac{(s-1)\cdot g}{\nu^2}\right]^{1/3}\cdot D_{pq} \]

where \(s\) is the ratio of sediment grain and water density (typically 2.68); \(g\) is gravitational acceleration; and \(\nu\) is the kinematic viscosity of water (\(\approx\)10\(^{-6}\)m\(^{2}\) s\(^{-1}\)) [Sch17]. Read the definition of Dimensionless bed shear stress for the calculation of \(\tau_{x}\). Figure 152 shows the Shields diagram where the Shields curve is plotted based on descriptions in Guo [Guo02].

Shields diagram guo hunter critical bed shear stress

Fig. 152 The Shields parameter \(\tau_{x,cr}\) (critical dimensionless bed shear stress) for grain mobility as a function of the dimensionless particle diameter \(D_x\), according to Guo [Guo02] (image source: Schwindt [Sch17]).

Beyond grain size and local hydrodynamics, \(\tau_{x,cr}\) is also a function of global channel roughness and slope, relative submergence and bedload transport intensity [Fer12, Gre08, LDV08, RFP+08, Wil93].

Suspended load

Suspended load is a special type of Sediment transport describing the displacement of fine particles with the bulk flow.

French: Transport en suspension
German: Schwebstofftransport

SMS 2dm

SMS (Surface-water Modeling System) is a proprietary software suite from Aquaveo for surface water modeling. 2dm file format is natively produced with SMS and represents a computational grid with x, y, and z coordinates of nodes along with node ids. The developer’s wiki provides a comprehensive description of the file format.


Sound navigation and ranging (Sonar) is a technique for locating objects in space and underwater by emitting sound pulses. An active Sonar system, such as radio detecting and ranging (radar), emits and receives sound signals to map objects underwater (time-of-flight measurement). Passive Sonar detects signals emitted by an object itself (e.g., vibrations from fish motion or Whale chant), but cannot accurately map underwater objects.


See CRS.

Stage-discharge relation

A stage-discharge relation (also referred to as rating curve) plots discharge (in m\(^3\)/s or CFS) as a function of water surface elevation function (in m above sea level or ft) at a specific river cross-section. Most stream gauging stations have a regularly calibrated stage-discharge relation that is often maintained by a state authority. This is why, it is mostly state authorities that provide stage-discharge functions for their gauging stations online, such as the state of Bavaria at the Mühldorf am Inn gauge.

French: Courbe d’étalonnage / Courbe hauteur-débit / Courbe de tarage
German: Wasserstands-Abfluss Beziehung, bzw. Abflusskurve / Abflussschlüsselkurve


The Standard Tessellation Language (STL) file format is native to a three-dimensional (3d) printing CAD software type called stereolithography. An STL file describes 3d structures in the form of unstructured triangulated surfaces with arbitrary units.


The term Thalweg stems from old German spelling for valley (today: Tal) and should be more correctly referred to as Talweg. The literal translation of Talweg is valley path and originally refers to a line that longitudinally connects the lowest points of valley cross-section profiles. Geomorphologists sometimes use slightly different definitions of Talweg. International law is more explicit, referring to the Thalweg as the primary navigable channel at boarders between two countries.

French: talweg / thalweg
German: Talweg

Topographic change

Topographic change is the increase or decrease in elevation of the Earth’s surface as a function of time. Conceptually, tracking topographic changes could consist of a simple comparison (i.e., subtraction) of elevation changes at two different moments. However, topographic change detection is not quite that simple, since every measurement technique has spatial inaccuracies with regards to the exact location and elevation of recorded points. For this reason, methods have been developed that, based on a level of detection (LoD), generate topographic change maps conveying and accounting for spatial uncertainty. Depending on the method, either strict global LoD raster [PW17] or less strict pixel-based LoD values [WBDS10] are used to remove uncertainty from topographic change maps. Topographic change maps also enable the visualization of soil loss (i.e., erosion), which is a growing challenge for agriculture and beyond. To this end, the USGS developed a publicly available website that is dedicated to topographic change (visit

French: Changement du terrain (non-technique)
German: Topografischer Wandel (kein technischer Begriff)


The eXtensible Data Model and Format (XDMF) library provides standard routines for exchanging (scientific) datasets that result from high performance computing (HPC) tasks. XDMF files redundantly store light and heavy data in XML and HDF5 format and Python interfaces exist for both formats. Thus, XDMF or XMF files are often linked to a *.h4 or *.h5 (HDF) file that contains heavy simulation datasets.