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Stochastic Modeling

Attendance of both Parts is strongly recommended, but not mandatory.

PART 1 - Stochastic Dynamical Modeling

Lecturer: Prof. Henk Dijkstra (DICAM/Utrecht)

Timetable: 30 January - 10 February 2023

The lectures will be taken every 2 days from January 30 to February 10, 2023 in room 1L from 9:30 to 12:30, as follows: 

Week 1:

30/1,  (2h): Stochastic Processes

          (1h): Exercises (analytical + Python)

1/2,   (2h): Stochastic Differential Equations (SDE)

         (1h): Exercises (analytical + Python)

3/2,   (2h): Numerical Simulation of SDEs

         (1h): Exercises (Python)

Week 2:

6/2,  (2h): Case Study 1: Lake mixed-layer variability

        (1h): Exercises (analytical + Python)

8/2,  (2h): Case Study 2: River Discharge + Salt Intrusion in Estuaries

        (1h): Exercises (analytical + Python)

10/2, (3h): Exam (written + python exercise) 

Programme:

For many problems in the environmental sciences, deterministic dynamical models have their limitations as possibly relevant processes/scales  are  not resolved (or not considered).  Often  these unresolved processes/scales can be considered to have stochastic properties. Taking these into  account leads to stochastic dynamical  models from which the statistics of the resolved scales can be determined quite efficiently. In this course, an elementary introduction to stochastic dynamical modeling is provided  with its application to environmental sciences problems. Focus will be on examples and both analytic calculations and numerical (python) computations.

Duration: 18 hours (2 credits)

Registration: in order to register for the course please send an email to dicamphd [at] unitn.it

PART 2 - Geostatistics and random field models

Lecturers: Prof. Alberto Bellin (DICAM), dr. Diego Avesani (DICAM)

Timetable: from 13 to 17 February 2023 (room 1L from 13 to 15 February and 17 February, 2023; room T4 on February 16, 2023), detailed timetable in the attachment.

Programme (more details in the attachment):

The term geostatistics encapsulates a broad family of tools for spatializing and modeling a large class of data. Geostatistics as discipline started in the sixties in the mining industry to provide an answer to the need to estimate the size of ore deposits from scarce and uncertain data. Today a suite of geostatistical methodologies are available for the spatial analysis of environmental data. Important fields of applications are hydrology, meteorology, health exposure analysis, ecology and regional planning. The course offers a suite of geostatistical techniques for the spatialization of data and the construction of risk maps to be used in spatial analysis, spatial pattern recognition and risk analysis. The course provides also theoretical and practical skills to make better use of secondary information and to quantify uncertainty associated to spatial analysis. The study of uncertainty propagation through the use of stochastic modeling closes the course and will provide the skill needed to a complete spatial analysis.
The course is intended mainly for PhD) students and professionals interested in performing spatial analysis.

Duration: 24 hours (3 credits)

Registration: in order to register for the course please send an email to dicamphd [at] unitn.it

application/pdfGeostatistics_course(PDF | 103 KB)
application/pdfTimetable_Geostatistics and random field models(PDF | 24 KB)