After successful completion of the course, students are able to understand, assess and apply simulation methods in water resource systems. The course consists of the following units:
1. Introduction and general approach: What is a model, typical problems, time scales, deterministic and stochastic models, lumped and distributed models, level of abstraction microscale and macroscale models, model complexity, reductionism and holism, typical approach in a modelling study: Modelling, verification of code, calibration, validation of the model
2. Stochastic models (1) basics: random numbers, frequency, probability, sample and population, distribution functions, parameter estimation, random number generators, realisations
3. Stochastic models (2) time series models: continuous-discrete processes: autocorrelation, autoregressive models, Markov process, parameter estimation
4. Deterministic models (1) dynamic models: Causal loop diagrams, 7 steps to building dynamic models, coupled linear models, predator-prey model, applications in water resource systems.
5. Deterministic models (2) basic equations: balance equations: mass, energy, momentum; control volume, control interval, Newton's law; transport equations; Fick, Fourier, Newton; material laws: Hook, decay, runoff, chemical reactions
6. Deterministic models (3) differential equations: first order ordinary differential equations (example: concentration in a lake, ..), initial and boundary conditions; Diffusion equation (example: groundwater flow, ..), initial and boundary conditions; convection-diffusion equation (example: transport of solutes), initial and boundary conditions
7. Deterministic models (4) solving differential equations: analytical-direct, method of characteristics, explicit differences method, stability and accuracy; implicit differences method; finite elements
8. Combined stochastic-deterministic models: Monte Carlo simulations of the first kind, second kind; combined first and second kind; example: reliability of water resource systems; example: advective transport of solutes
9. Model calibration and parameter identifiability; model calibration, updating, parameter from external information; parameter estimation, objective function, optimisation methods, dimensionality and non-linearity; methods: gradient method, simulated annealing
10. Model uncertainty and model validation: data, model, and parameter errors; methods for estimating uncertainty: plausibility tests, error calculus, Gaussian error propagation, Monte Carlo simulations of the second kind, sensitivity analyses, scenarios, split sample testing, cross validation
222.580 Modelling and Simulation Methods in Water Resource Systems
2024W, VU, 3.0h, 4.0EC
Lecturers: Günter Blöschl, Peter Valent
Mon 7 Oct. 2024, 10:00 - 13:00 SR222 AD03-1 (G. Blöschl)
Tue 8 Oct. 2024, 13:00 - 15:00 SR222 AD03-1 (G. Blöschl)
Mon 14 Oct. 2024, 10:00 - 13:00 SR222 AD03-1 (G. Blöschl)
Tue 15 Oct. 2024, 13:00 - 15:00 SR222 AD03-1 (P. Valent)
Wed 16 Oct. 2024, 15:00 - 18:00 SR222 AA02-1 (P. Valent)
Mon 21 Oct. 2024, 10:00 - 13:00 SR222 AD03-1 (P. Valent)
Tue 22 Oct. 2024, 13:00 - 15:00 SR222 AD03-1 (P. Valent)
Wed 23 Oct. 2024, 15:00 - 18:00 SR222 AA02-1 (P. Valent)
Mon 2 Dec. 2024, 10:00 - 13:00 SR222 AD03-1: Examination
Mon 9 Dec. 2024, 10:00 - 13:00 SR222 AD03-1: Examination
The course consists of
- Lectures (according to lecture programme)
- Homework project: Students develop a simulation model for a water resource system, either a stochastic model or a deterministic dynamic model (for deterministic dynamic models also see course 105.730 VU Modellierung dynamischer Umweltsysteme)
E.g.
Stochastic: Design of an irrigation reservoir
Deterministic: Daisy world or snow ball world
Examination: Oral
Homework project is presented during the oral examination (explain R code, present and interpret results)
222.580 Modelling and Simulation Methods in Water Resource Systems
2024W, VU, 3.0h, 4.0EC
1. Introduction and general approach: What is a model, typical problems, time scales, deterministic and stochastic models, lumped and distributed models, level of abstraction microscale and macroscale models, model complexity, reductionism and holism, typical approach in a modelling study: Modelling, verification of code, calibration, validation of the model
2. Stochastic models (1) basics: random numbers, frequency, probability, sample and population, distribution functions, parameter estimation, random number generators, realisations
3. Stochastic models (2) time series models: continuous-discrete processes: autocorrelation, autoregressive models, Markov process, parameter estimation
4. Deterministic models (1) dynamic models: Causal loop diagrams, 7 steps to building dynamic models, coupled linear models, predator-prey model, applications in water resource systems.
5. Deterministic models (2) basic equations: balance equations: mass, energy, momentum; control volume, control interval, Newton's law; transport equations; Fick, Fourier, Newton; material laws: Hook, decay, runoff, chemical reactions
6. Deterministic models (3) differential equations: first order ordinary differential equations (example: concentration in a lake, ..), initial and boundary conditions; Diffusion equation (example: groundwater flow, ..), initial and boundary conditions; convection-diffusion equation (example: transport of solutes), initial and boundary conditions
7. Deterministic models (4) solving differential equations: analytical-direct, method of characteristics, explicit differences method, stability and accuracy; implicit differences method; finite elements
8. Combined stochastic-deterministic models: Monte Carlo simulations of the first kind, second kind; combined first and second kind; example: reliability of water resource systems; example: advective transport of solutes
9. Model calibration and parameter identifiability; model calibration, updating, parameter from external information; parameter estimation, objective function, optimisation methods, dimensionality and non-linearity; methods: gradient method, simulated annealing
10. Model uncertainty and model validation: data, model, and parameter errors; methods for estimating uncertainty: plausibility tests, error calculus, Gaussian error propagation, Monte Carlo simulations of the second kind, sensitivity analyses, scenarios, split sample testing, cross validation