Development of environmental data analysis and model building skills using common mathematical and statistical tools. Matlab is the preferred development platform.
Marsili-Libelli S. (2016) Environmental Systems Analysis with Matlab. CRC Press, ISBN 9781498706353
Learning Objectives
Acquire the main numerical techniques for the analysis of environmental data and for environmental model building
Prerequisites
Basic knowledge of calculus, linear algebra, statistics.
Teaching Methods
Room lectures using proprietary slides and Matlab scripts.
Further information
The course material is uploaded in a DropBox folder shared with the students attending the course.
Type of Assessment
The final exam consists of an interview on the course subjects. This can be integrated on a voluntary basis by a project on a topic chosen by the student.
Course program
Time-series analysis in time and frequency: frequency analysis by Fast Fourier Transform, de-trending, outlier detection, smoothing and denoising by either splines or wavelets. Time-series synthesis for model input.
Wavelet analysis: The need to reconcile time and frequency analyses. The concept of local representation in scale and frequency. Continuous-time wavelet transform, the course of dimensionality. Dyadic wavelet decomposition: decomposing for smoothing and de-noising. Hard or soft thresholding. Applications to environmental data: circadian dissolved oxygen variations in open waters.
Fuzzy logic: Fuzzy representation of everyday concepts, fuzzification, fuzzy inference, defuzzification. The Mamdani and the Sugeno inferential schemes. Fuzzy modelling of dynamic systems, empirical versus neuro-fuzzy approaches. The ANFIS environment. Fuzzy clustering for environmental data analysis: introduction of the Euclidean metrics (Fuzzy C- means) and variable metrics methods (Gustafson-Kessel e Fuzzy Maximum Likelihood Estimation). Application to the detection of malfunctions in an anaerobic digester. Possibilistic clustering: application to the algal blooms in the Adriatic sea.
General rules for environmental model building. Distinction between theory-driven (first principles) and data-driven models. Data requirements. Example of fitting a numerical model in the wider DPSIR scheme (European Water Directive 60/2000). Survey of several simple environmental models to be used for parameter calibration.
Parameter calibration: sensitivity analysis (static and dynamic). Gradient-free optimization methods: optimal flexible polyhedron search. Model validation: parametric and non-parametric tests. Confidence regions of estimated parameters. Application in microbial kinetics and river quality models.