Given a set of sanitation technologies it finds all compatible systems assesses the appropriateness of a technology for the given case context assesses the overall appropriateness of the generated sanitation systems for the given context calculates the mass flows for each system for total phosphor, total nitrogen, totalsolids, and water optionally with uncertainly quantification selects a meaningful subset of suitable systems for the given context for further evaluation github.
Andreas Scheidegger Tel. Scientific website of the SPUX project Documentation Source code respository You are welcome to browse through the results gallery of the models already coupled to spux.
Calibration of individual based models IBMs , successful in modeling complex ecological dynamical systems, is often performed only ad-hoc. Bayesian inference can be used for both parameter estimation and uncertainty quantification, but its successful application to realistic scenarios has been hindered by the complex stochastic nature of IBMs.
Computationally expensive techniques such as Particle Filter PF provide marginal likelihood estimates, where multiple model simulations particles are required to get a sample from the state distribution conditional on the observed data.
Particle ensembles are re-sampled at each data observation time, requiring particle destruction and replication, which lead to an increase in algorithmic complexity. Adaptive load re-balancing techniques are used to mitigate computational work imbalances introduced by re-sampling. Framework performance is investigated and significant speed-ups are observed for a simple predator-prey IBM model.
See DOI. See Institutional Repository. Marco Bacci Tel. AQUASIM Computer Program for the Identification and Simulation of Aquatic Systems Short Program Description In order to support environmental scientists in finding an «adequate» model of the system they are investigating, a computer program is necessary, which allows its users to perform simulations using different models, to assess the identifiability and to estimate the values of model parameters using measured data , and to estimate prediction uncertainty.
References Please cite the use of the program by referring to one of the following publications. Survey of program features Reichert, P. The following zip file contains the executables for the three program versions and the required initialization file: aquasim. Tabellarische Ausgabe der Resultate.
Resultataustausch via Exportdateien. The expression for the density may not depend on time. Note that the values entered for the surface detachment coecient only has an eect if the radio button individual rate of the option Surf.
Similarly the expressions entered for volume attachment and detachment coecients are only used if the radio button with free particles is selected for the option Pore Volume of the dialog box shown in Fig. Otherwise the values entered here are ignored. It contains a list box with the names of all dened dissolved variables.
Note Figure 3. Good behaviour of the numerical algorithmsis usually achieved if the absolute accuracy and the product of the relative accuracy times a typical value of the variable both are 4 to 6 orders of magnitude smaller than typical values of the variable. Identier for zones within compartments returns a value of 0 in the bulk volume zone, a value of 1 in the biolm matrix, and a value of 2 in the biolm pore volume.
Volumetric fraction of water. Depth coordinate in the biolm zero at the substratumbiolm interface. Volume of mixed water zone outside of the biolm. Thickness of the biolm. Advective velocity of biolm solid matrix. Velocity of the interface between biolm and bulk uid. Detachment velocity of particles from the biolm surface. Attachment velocity of particles onto the biolm surface.
For the case of the advective-diusive reactor compartment, 3 types of components of a conservation law must be distinguished. The one-dimensional density of water volume in the compartment volume per unit length is given by the cross-sectional area, A, of the compartment. Their onedimensional densities are given as the product of the cross-sectional area, rA, and the laterally averaged concentration, Ci. The value of the variable A must be specied as a function of the distance along the compartment, x.
Its current value is then generally accessible by the program variable Cross Sectional Area. The variables Ci are represented by dynamic volume state variables, and the variables Si are represented by dynamic surface state variables. For equilibrium state variables algebraic equations specied as equilibrium processes are solved everywhere along the compartment.
The one-dimensional uxes of the quantities with one-dimensional densities as described by equation 3. In many cases, this longitudinal inow is zero and the only inow is that at the compartment inlet. This inow is specied as a boundary condition below 3. The second component describes the eect of transformation processes in the compartment and the eect of lateral inows or outows Clat;i is the concentration in the lateral inow q. The last component describes the eect of transformation processes on settled of sorbed substances or of growing organisms.
Application of the general law for dierential conservation laws 3. Positive values of q inow increase the downstream discharge, negative values outow decrease the downstream discharge. Note that settling or sorption must also be formulated as a transformation process transforming dissolved species, Ci , to settled or sorbed species, Si.
In order to make the solution to the above system of dierential equations unique, one boundary condition for the ordinary dierential equation 3. The ordinary dierential equation 3. According to equation 3. The boundary conditions for equation 3. The second of these boundary conditions 3.
Index' can be used to specify a nonnegative inter number as a compartment index. The values of variables are resolved continuously with the space coordinate x between these two locations. Note that when the advective-diusive reactor compartment is used to model a porous medium, A is given as the product of the porosity and the total cross-sectional area. It is not allowed to use a time dependence or a dependence on state variables for the speciction of the cross-sectional area.
This coecient can be made dependent on time, discharge or cross-sectional area by using the program variables Time, Discharge or Cross-Sectional Area. The number of grid points is used to specify by how many discrete points the continuous x-axis is approximated. If the number of grid points is set to ngp, the compartment is resolved longitudinally into 2 boundary points and ngp , 2 grid points located in the middle of ngp , 2 cells of equal thickness.
This action 3. If an active variable is selected while activating another variable, the new active variable is inserted in the list of active variables immediately before the selected variable, otherwise it is appended to the end of the list of active variables. Each line of the list box contains the name of a variable, followed by the zone of the compartment for which the initial condition is specied in brackets and by the algebraic expression specifying the initial value.
If an initial condition is selected while adding a new initial condition, the new initial condition is inserted in the list immediately before the selected initial condition, otherwise it is appended to the end of the list of initial conditions. Initial conditions for any type of variables can be specied, but only initial conditions for state variables are used by the program.
A user can change a state variable to a variable of another type without the requirement ot editing the lists of initial conditions of the compartments. Initial conditions of an advective-diusive reactor compartment may not depend on state variables and they can only depend on the program variables Calculation Number, Time and Space Coordinate X.
In this dialog box the user can select which type of input to edit. There exist two dierent types of inputs to an advective-diusive reactor compartment.
In the following paragraphs, the dialog boxes used to dene each of these input types are described. For each variable only one unique inlet loading can be specied. If a loading is selected while adding a new loading, the new loading is inserted in the list immediately before the selected loading, otherwise it is appended to the end of the list of the loadings.
Note that this input loading represents a mass per unit of time. An inlet loading to an advective-diusive reactor compartment may depend on the program variables Discharge and on dynamic volume state variables.
These variables return the discharge and the concentrations of dynamic volume state variables resulting from all advective links connected to the inlet 66 CHAPTER 3. The reason for allowing to dene loadings for variables of other types is to facilitate the users switching between models with dierent state variables. A user can change a state variable to a variable of another type without the requirement ot editing the lists of loadings of the compartments.
A positive value of q represents a ow into the compartment, a negative value represents an outow. According to the equations 3. For each variable only one unique lateral inow concentration can be specied. If an inow concentration is selected while adding a new inow concentration, the new inow concentration is inserted in the list immediately before the selected inow concentration, otherwise it is appended to the end of the list of inow concentrations.
This gives the user the possibility to inuence the order of the 3. A lateral inow concentration of an advective-diusive reactor compartment may depend on the program variables Discharge and on state variables. These variables return the discharge and the current values of state variables in the compartment as a function of the location x. Inow concentrations for any type of variables can be specied, but only inow concentrations for dynamic volume state variables are used by the program.
The reason for allowing to dene inow concentrations for variables of other types is to facilitate the users switching between models with dierent state variables.
A user can change a state variable to a variable of another type without the requirement of editing the lists of lateral inow concentrations of the compartments. Space coordinate along the compartment. Area of water body perpendicular to the ow direction.
Within the soil column, fast sorption processes can be used to describe equilibrium sorption and slower sorption processes to model the eects of sorption kinetics.
The use of any linear or nonlinear sorption isotherm is possible. The soil column compartment has a variable number of zones. Variables present in more than one zone are distinguished by the index mob for the mobile zone and imjk for the mixed zone k of the immobile region j. In order to formulate the equations for the saturated soil column, 5 types of components of a conservation law must be distinguished.
The one-dimensional density of water volume in the mobile zone of the column volume in the mobile zone per unit length of the column is given by the product of the cross-sectional area, A, and the porosity of the mobile zone, mob of the column.
Their one-dimensional densities are given as the product of the cross-sectional area, A, the porosity of the mobile zone, mob , and the laterally averaged concentration in the mobile zone, Cmob;i.
Their one-dimensional densities are given as the product of the cross-sectional area, A, the porosity of the zone, imjk , and the laterally averaged concentration, Cimjk ;i. The two last components of equation 3. Its value is then accessible by the program variable Cross Sectional Area. The variables Cmob;i and Cimjk ;i are represented by dynamic volume state variables, and the variables Smob;i and Simjk ;i are represented by dynamic surface state variables. For equilibrium state variables, algebraic equations, specied as equilibrium processes, are solved in all zones everywhere along the column.
The one-dimensional uxes of the substances with one-dimensional densities as described by equation 3. There are no uxes in the direction along the column within the immobile zones and sorbed substances are not transported at all. The lateral diusive exchange processes of dissolved substances between the mobile zone and the immobile regions and within the immobile regions are described as source terms in the next paragraph.
The second component describes the eect on the mobile zone concentrations of the exchange between the mobile zone and the rst mixed zones im11 to imnr ;1 of the nr immobile regions that are adjacent to the mobile zone, the eect of transformation processes in the mobile zone and the eect of lateral inows or outows Clat;i is the concentration in the lateral inow q.
The third component describes the eect of the exchange with neighbouring zones of the nz;j serially connected mixed zones of the immobile region j.
The rst row of this component describes the exchange of the rst mixed zone with the mobile zone and the second mixed zone, the second row the exchange of an intermediate mixed zone with the neighbouring mixed zones, and the last row the exchange of the last mixed zone with the second to last mixed zone of the immobile region j. All exchange processes are assumed to be proportional to the dierence between the concentration in one of the adjacent zones and a concentration multiplied with a conversion factor, fex;imjk ;i , in the other zone.
The consideration of a conversion factor makes the description of systems with dierent solvents possible. If all zones are lled with the same solvent, all conversion factors are unity.
The substance-specic exchange coecent is qex;imjk ;i represents the volume exchange rate per unit length of the soil column for the substance described by the concentration Ci. Note that sorption must also be formulated as a transformation process transforming the dissolved species, Ci , to the sorbed species, Si. If the concentrations are expressed as mass per unit of total column volume, C in zone zo must be converted to zoC multiplication of C with the porosity of the zone , and S must be converted to Ssolid 1 , multiplication with the density of the solid phase and with the volume fraction of the solid phase.
Considering these conversion factors, sorption can be described by a dynamic sorption process with a process rate of ki Seq;i Ci , Si 3. In these equations solid is the density of the solid material in the soil column, Seq;i Ci is the equilibrium isotherm and the process describes relaxation of the actually sorbed concentration to the equilibrium concentration with a rate constant ki.
If ki is set to a suciently large value, this model is a good approximation to equilibrium sorption. The ordinary dierential equations 3. The boundary condition for equation 3. Variables and process rates can be made dependent on the zone by using the program variable Zone Index, which takes the value 0 in the mobile zone and a user-dened positive integer value in each of the immobile zones.
Similarly to the cross-sectional area, A, mob can be a function of the space coordinate x and it is not allowed to use a time dependence in this variable. This editing of immobile regions is described later in this subsection.
If the number of grid points is set to ngp, the column is resolved longitudinally into 2 boundary points and ngp , 2 grid points located in the middle of ngp , 2 cells of equal thickness. The reason for allowing other types of variables in the list of active state 3.
This dialog box shows a list of all initial conditions already Figure 3. This gives the user the possibility to inuence the order of 3. Initial conditions of a saturated soil column compartment may not depend on state variables and they can only depend on the program variables Calculation Number, Time and Space Coordinate X.
There Figure 3. If a loading is selected while adding a new loading, the new loading is inserted in the list immediately before the selected loading, otherwise it is appended to the end of the list of input loadings. This gives the user the possibility to inuence the order of the input loadings the order is irrelevant for the program, but it may be convenient for the user to have a certain order. Note that this loading represents mass per unit of time.
An inlet loading of a saturated soil column compartment may depend on the program variables Discharge and on dynamic volume state variables. These variables return the discharge and the concentrations of dynamic volume state variables resulting from all advective links connected to the inlet 80 CHAPTER 3.
Input loadings for any type of variables can be specied, but only input loadings for dynamic volume state variables are used by the program. A positive value of q represents a ow into the column, a negative value represents an outow. This gives the user the possibility to inuence the 3. A lateral inow concentration of a saturated soil column compartment may depend on the program variables Discharge and on state variables.
Several immobile regions, each of which with an arbitrary number of serially connected mixed zones can be dened. Each immobile region needs a unique name as an identier. The list box of the dialog box shown in Fig. At least one mixed zone is required in order to specify a valid immobile region.
If a mixed zone is selected while adding a new zone, the new zone is inserted in the list immediately before the selected zone, otherwise it is appended to the end of the list of mixed zones.
This gives the user the possibility to inuence the order of the mixed zones. The Fig. This value can be accessed with the aid of the program variable Zone Index to make variables or process rates dependent on the zone in the mobile zone, the program variable Zone Index returns zero. Note that the sum of the volume fraction of the mobile zone and all volume fractions of the immobile zones must be smaller than unity. The conversion factor can be used to describe transitions between dierent solvents in the pores.
If all pores are lled with the same solvent, the conversion factors are unity. If an exchange coecient is selected while adding a new exchange coecient, the new exchange coecient is inserted in the list immediately before the selected exchange coecient, otherwise it is appended to the 3. This gives the user the possibility to inuence the order of the exchange coecients the order is irrelevant for the program, but it may be convenient for the user to have a certain order.
The Figure 3. In this dialog box the elds Figure 3. Exchange coecients for any type of variables can be specied, but only exchange coecients for dynamic volume state variables are used by the program. Identier for compartments value set in the dialog box shown in Figs.
Identier for zones within compartments returns a value of 0 in the mobile zone and a value set in the dialog box shown in Fig. Volumetric fraction of water returns the value of the porosity. In the presence of signicant hydraulic structures or tributaries, several river sections can be linked advectively to model the river reach of interest.
The description of the river section is one-dimensional. This means that all variables are averaged over the river cross section and the depth of the sediment is not resolved. Such a description is in many cases adequate when the main interest is to model transformation processes over relatively long distances, but it makes the application of the river section compartment to local mixing phenomena impossible.
The two most important approximations to these so-called St. The equations for river hydraulics are coupled with advection-diusion equations to describe transport of substances dissolved or suspended in the water.
An empirical, substanceindependent diusion coecient is used to describe the longitudinal mixing eect due to dispersion. For the case of a river section compartment, 3 types of components of a conservation law must be distinguished. The one-dimensional density of water volume in the river volume per unit length is given by the wetted cross-sectional area, A, of the water body. The value of the variable A must be specied as a function of the distance along the river, x, and of the elevation of the water level, z0.
Calculation of river hydraulics requires the formulation of the cross-sectionally averaged friction force as an empirical function of averaged ow properties. Usually, instead of the friction force, the non-dimensional friction slope, Sf , the ratio of the friction force to the gravity force of the water body, is parameterized empirically as a function of wetted cross-sectional area, wetted perimeter and discharge.
The discharge Q, for the kinematic or the diusive approximation to the St. The applicability of the kinematic approximation given by the equation 3. This approximation assumes the driving gravity force to be equilibrated by the friction force everywhere along the river. In addition to the gravity and the friction forces, the diusive approximation given by the equation 3.
In contrast to the kinematic approach, the diusive approximation allows to describe backwater eects of weirs or other hydraulic controls and it can be applied if the river bed is not monotonically decreasing. This variable can be used to describe the integral eect of small tributaries or the eect of groundwater in- or exltration. Larger tributaries must be modelled as upstream input boundary conditions to a new river section compartment.
The last component describes the eect of transformation processes on settled or sorbed substances or on growing organisms. A negative spatial gradient of the discharge causes an increase in the wetted cross-sectional area because more water ows into a river segment from upstream then leaves it downstream.
Obviously, a positive lateral inow also increases the wetted cross-sectional area. Note that the equation 3. Note that settling or sorption must also be formulated as a transformation process from the dissolved or suspended species, Ci , to the sorbed or settled species, Si. In order to make the solution to the above system of dierential equations unique, one or two boundary conditions are necessary for equation 3.
The rst boundary condition for the equation 3. In the case of the diusive approximation according to equation 3. Venant equations. This water level is also approached in the diusive case with a prismatic river bed at distances far away from hydraulic controls. This boundary condition can be used if the calculation ends within a uniform reach where the water level is not inuenced by hydraulic structures. The critical depth is a boundary condition reasonable at drops. Acceleration' is used to specify the value of the gravitational acceleration, g, in the units as used by the user of the program.
The gravitational acceleration is required in order to calculate the critical water level 3. Slope' is used to specify an empirical formula for the nondimensional friction slope. As a next option in the dialog box shown in Fig. An estimation of the dispersion coecient can be calculated as follows Fischer et al.
The next option of the dialog box shown in Fig. Venant equations according to equation 3. In the case of the diusive approximation, an end water level must be specied as a downstream boundary condition. If the number of grid points is set to ngp, the river section is resolved longitudinally into 2 boundary points and ngp , 2 grid points located in the middle of ngp , 2 cells of equal thickness. Each line of the list box contains the name of a variable, followed by the zone of the compartment for which the initial condition is specied in brackets and by the 3.
Initial conditions for any type of variables can be specied, but only initial conditions for state variables and for the program variable Discharge are used by the program. An initial condition for this program variable is required. A user can change a state variable to a variable of another type without the requirement ot editing the lists of initial conditions of the 94 CHAPTER 3.
Initial conditions of a river section compartment may not depend on state variables and they can only depend on the program variables Calculation Number, Time and Space Coordinate X. There exist two dierent Figure 3. For each variable only one unique upstream input loading can be specied. If a loading is selected while adding a new loading, 3. An upstream loading to a river section compartment may depend on the program variables Discharge and on dynamic volume state variables.
These variables return the discharge and the current values of dynamic volume state variables resulting from all advective links connected to the upstream end of the river section. A user can change a state variable to a variable of another type without the requirement ot editing the lists of input loadings of the compartments. This gives the user the possibility to inuence the order of the inow concentrations the order is irrelevant for the program, but it may be convenient for the user to have a certain order.
A lateral inow concentration of a river section compartment may depend on the program variables Discharge and on state variables. Good behaviour at the numerical algorithms is usually achieved if the absolute accuracy and the product of the relative accuracy times a typical value of the variable both are 4 to 6 oders of magnitude smaller than typical values of the variable.
Elevation of water level above an absolute reference level. Length of the interface between water and the river bed perpendicular to the ow velocity. Length of the interface between water and the atmosphere perpendicular to the ow velocity. Nondimensional friction force: Friction force divided by gravity force.
A one-dimensional description is used that averages all variables over horizontal cross sections. This limits the applicability of this compartment to situations in which the dimensions of the lake, the stratication and the time scales of the investigated processes make a horizontally averaged description reasonable.
The current version of the lake compartment has no connections to advective or diusive links, so that it can only be used to describe a single lake with given inputs and processes. The user can specify the coecient of vertical turbulent diusion as a given function of time and space, but it is also possible to use a parameterization depending on the stability of the water column and on turbulent kinetic energy and dissipation. In this subsection, the full set of equations is described. However, in order to make the use of simpler models easier and faster, the sediment submodel and the turbulence submodel can be inactivated independently of each other.
Several zones are distinguished in the lake compartment: one zone for the water column and one zone for each sediment layer. Variables present in all zones are distinguished by the index L for the lake water column and the index Sj for the sediment layer j. The vertical dimension of the lake is resolved by the space coordinate z.
In the following, the lake equations are formulated with the z -axis pointing upwards, however, the program runs with both denitions of the direction of the z -axis. In order to formulate the lake equations, 8 types of components of a conservation law must be distinguished. The array of one-dimensional densities of these types of components 3. The one-dimensional density of water volume volume per unit of depth is given by the cross-sectional area, A, of the lake.
This component is used in mixing models to calculate the production of turbulent kinetic energy by shear forces of wind induced water ow. The one-dimensional density of horizontal water discharge is given as the product of the cross-sectional area, A, and the horizontally averaged horizontal ow velocity, U.
The one-dimensional density of turbulent kinetic energy is given as the product of the cross-sectional area of the lake, A, the density of water, , and the turbulent kinetic energy, k turbulent kinetic energy per unit mass of water. The fourth component of equation 3. This quantity together with k can be used to estimate the coecient of turbulent diusion, Kz , of substances dissolved or suspended in the water column see below.
The fth and the sixth components of equation 3. AQUASIM Computer Program for the Identification and Simulation of Aquatic Systems Short Program Description In order to support environmental scientists in finding an «adequate» model of the system they are investigating, a computer program is necessary, which allows its users to perform simulations using different models, to assess the identifiability and to estimate the values of model parameters using measured data , and to estimate prediction uncertainty.
References Please cite the use of the program by referring to one of the following publications. Survey of program features Reichert, P. The following zip file contains the executables for the three program versions and the required initialization file: aquasim. Peter Reichert Group leader "Systems analysis and water management" Tel. SIMBOX Computer program for the simulation of material-, substance-, energy- and monetary flows in anthropogenic systems The evaluation, modelling, controlling and assessment of substance flows is crucial for environmental management.
Data checking : using a table or graphically Definition of the model equations: Built in standard models or user defined Model equations for stationary as well as dynamic systems using an interface. SIMBOX Calculation module: SIMBOX offers many calculation modules for different purposes: Standard module including the calculation of transfer coefficients from mass flows, the determination of missing flows, the total amount of substance flows etc, all quantities with the corresponding uncertainty.
Least square fit: best estimates for a given set of flow data. Simulations: Solving the model equations including uncertainty, sensitivity analysis and parameter variation respectively. Visualisation of substance flows and their uncertainties. Tables and list of results. Data files to export results to other programs. Graphical representation of key quantities and key functions. Time series analysis , qualitative measures SIMBOX has been further developed since and used by many companies, institutes and universities.
Ruth Scheidegger Tel. Thus, the IRRM is developed as a 1-dimensional model which simulates the expected river morphology reach specific means e. Assessing the decline of brown trout Salmo trutta in Swiss rivers using a Bayesian probability network.
Ecological Modelling , —, Yoshimura, C. Concepts of decision support for river rehabilitation. Ecological Economics 62, , Publications Abbaspour et al. Dimensioning of aerated submerged fixed bed biofilm reactors based on a mathematical biofilm model applied to petrochemical wastewater - the link between theory and practice. The description of a biofilm mathematical model application for dimensioning an aerated fixed bed biofilm reactor ASFBBR for petrochemical wastewater polishing is presented.
A simple … Expand. View 2 excerpts, cites methods. Computer Science, Chemistry. Concepts underlying a computer program for the identification and simulation of aquatic systems. View 2 excerpts, references background. To pose mathematically tractable boundary conditions for finite porous media it is necessary to regard the representative elementary volume REV as infinitesimal.
In so doing, continuity of … Expand. View 1 excerpt, references background. View 2 excerpts, references methods. On the physical meaning of the dispersion equation and its solutions for different initial and boundary conditions.
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