E-PSCI 236: Environmental Modeling and Data Analysis
The syllabus and detailed lecture schedule are found below.
The lecture notes can be found by clicking links below. Details such as lecture dates are subject to change.
The major work in the data part of the course is captured in the final project and presentation --Click here for the Final Project Requirements.
Lecture Schedule and Summary:
Part 1a. Linear modeling of environmental systems (“box models”, Markov Chain [1])
Note: There will be a training session in the use of the R programming language on Monday, 9 Sep at 1630.
Sep 04. Introduction to EPS 236 – what we will be doing and why we will be doing it
Linear Modeling – Linear models are the common foundation for many data analysis frameworks, and for models of tracers and chemistry in the atmosphere and oceans. We therefore start EPS 236 with an exploration of the analytical properties of linear models of complex systems, starting from a "Calculus II" level and proceeding to advanced concepts in ~ 2 lectures.
Part I: time evolution operator, solutions to the general problem.
Sep 06 and Sep 11. Linear Modeling; part II Analytical properties of linear systems; Markov chain equiv. Green's functions, Mean Age and Age spectrum; time evolution operators, tangent linear approximations for non-linear dynamical systems; application to estimating global fluxes of atmospheric tracers.
Sep 13. Introduction to the 1st Class Data Project:
A 5-box model of greenhouse gases in the atmosphere (Workshop 1). Application of linear modeling methods, R coding skills development
First Class Project: Strings.of.Boxes. Representing the advection-diffusion equation as a finite volume linear system.
Part 1b. Statistical inference, regressions, curve fitting, confidence intervals —focus on concepts and advanced applications . Updated link 2019-09-25.
Sep 18. Statistical Inference – a close look at the fundamentals from the point of view of atmospheric, marine, and environmental Science
Sep 20. Linear regressions: Fitting a line (curve) to data;
Correlated parameters, degrees of freedom, overfitting.
Sep. 25. Type II regressions and Maximum Likelihood York regressions
Using locally-built YorkFit() from York.R script (click here to download). Here is the class script.
or york( ) from the R package IsoplotR -- alternate class script.
Sep. 27. Confidence intervals, t-tests, bootstrap error estimates, non-parametric assessment of data
Effron and Tibshirani Science article
Bootstrap Data Set for Download: Greenhouse gas measurements in Boston RData csv
Topics 8 and 9: Data conditioning, filtering, smoothing, interpolation, regularization
Oct. 02. Data Filtering; Classifying data smoothing methods
Loess filters (article to read)
Savitzky-Golay filtering coefficients (as a text file)
Leave-one-out Cross Validation (LOOCV) (article to read)
Oct. 04. Modeling and analyzing atmospheric time series data (Workshop 2)
WLEF N2O data: Data set ; R-code for the exercise
Packages needed: pspline, and either signal or prospectr
Oct. 09. Autoregressive data; systems with serial correlation
Oct. 11. Filtering and interpolation of data: wavelets and image processing
Oct. 16. Filtering and interpolation: Frequency domain, FFT, spectral decomposition.
The Final Class Project has been rolled out -- click here for requirements.
Oct. 18, 23. Topics 10 and 11: Wavelets (#10) and Image Processing (#11)
Data Workshop s (short): students apply the tools
- Selection and initiation of individual/group projects
Oct 25. Roll up of data analysis concepts and methods.
Oct. 25, 30. Special Lectures and Discussions
Introduction to the raster framework in R: Efficient, memory-safe computation for large data sets in geographical coordinates, including links to NetCDF and grib2 data sets, map projections, and more.
Student workshop and prospectus for the class project.
- Part 2a. Chemical transport models (Daniel Jacob)
Nov. 1. Mass continuity, transport, and chemical transformations
Nov. 6. Numerical methods for advection
Nov 8. Parameterizations of turbulent transport
Nov. 13. Lecture and Workshop: Numerical solution of chemical mechanisms (Dr. Yang Li)
- 2b. Inverse modeling (Daniel Jacob)
Nov. 15. Applications of inverse modeling to atmospheric problems, Bayes’ theorem
Nov. 20. Vector-matrix tools for inverse modeling
Analytical solution of the inverse problem
Nov. 22. Kalman filtering and 3-DVAR data assimilation
Adjoint methods and 4-DVAR data assimilation
- Reading period 3 – 8 Dec: Individuals will work with the teaching staff on their final presentations.
- Dec 9. Final Presentations
Course Summary:
Date | Details | Due |
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