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
