## SIO 221B: Analysis of Physical Oceanographic Data

- I.
- Principles of ocean instruments (2)
- A.
- How are sea water properties, velocity, air-sea fluxes, and surface waves measured?
- 1.
- How do instruments work?
- 2.
- How are observations made?
- 3.
- What does data look like?
- B.
- Some simple observational problems
- 1.
- Drake Passage transport
- 2.
- Observing the Ekman spiral
- II.
- Randomness and statistics (6)
- A.
- The origin of ``randomness'' in dynamical systems.
- 1.
- The concepts of dynamical degrees of freedom and unpredictability based on a simple chaos model.
- 2.
- Relevance to scale ranges in the ocean/atmosphere system.
- B.
- Basic probability.
- 1.
- Probability density functions (PDFs) and joint probability density functions.
- 2.
- Averages and moments.
- 3.
- Averages from PDFs.
- 4.
- Scatter plots, covariance and correlation.
- 5.
- Conditional probability and the approach to determinism.
- 6.
- Correlation of independent events.
- 7.
- PDFs of functions.
- C.
- Discrete random walks.
- 1.
- Central limit theorem.
- 2.
- Serially correlated discrete random walks.
- 3.
- Continuous random walks (Taylor diffusion).
- 4.
- The diffusion equation from random walk and central limit theorem.
- III.
- Decomposition of signals (1)
- A.
- The philosophy of signal vs. noise decompositions.
- 1.
- The algebraic problem: Inverse theory.
- 2.
- The statistical problem: Statistical Estimation.
- B.
- Some examples.
- 1.
- Function fitting.
- 2.
- Fourier analysis of time series.
- IV.
- Inverse problems (9)
- A.
- Examples of oceanographic inverse problems.
- 1.
- Beta spiral.
- 2.
- Control volumes.
- B.
- Least-squares problems.
- 1.
- ``Over-'' and ``under-'' determined problems.
- 2.
- Constraints.
- 3.
- Simultaneous minimization of misfit to data and solution size.
- C.
- A practical review of linear algebra.
- D.
- Singular value decomposition.
- 1.
- Relationship to the simultaneous minimization problem.
- E.
- Resolution and error as measures of goodness.
- V.
- Applying probability concepts to data (3)
- A.
- Construction ``ensembles'' for statistical treatment of observations.
- 1.
- What stationarity really means.
- 2.
- Ergodicity.
- B.
- Sampling errors of mean and variance.
- 1.
- convergence.
- 2.
- Bias, mean-square error and probable error of sample estimates.
- 3.
- Estimating variance: an introduction to statistical ``beauty'' principles.
- 4.
- Effect of serial correlation on sampling errors.
- VI.
- Statistical estimation (6)
- A.
- Regression models.
- 1.
- Joint-normal distributions.
- 2.
- Statistical forecasting.
- 3.
- Improving persistence forecasts.
- B.
- Objective mapping as multivariate regression.
- 1.
- Unbiased estimates and the mean.
- 2.
- Mixing observations of different types.
- 3.
- Imposing constraints.
- 4.
- Model testing from mapped fields vs. statistical tests.
- VII.
- Efficiency of representations (3)
- A.
- Principal axes.
- B.
- Review of Fourier spectra.
- C.
- Empirical Orthogonal Functions (EOFs).
- 1.
- Relation of EOFs to Fourier analysis.