ECCO Summer School

Global Ocean State & Parameter Estimation:
From Methods to Applications in Oceanographic Research
Friday Harbor Laboratories
College of the Environment, University of Washington
May 19-31, 2019

Ocean state estimation requires expertise in diverse subjects including estimation theory, numerical modeling, and observational oceanography. The individual subject matters are often treated separately, leading to misunderstandings about model-data synthesis. Students at the ECCO Summer School examined these subjects in a coherent manner in order to gain a working understanding of ocean state estimation and its use in ocean research.

The summer school introduced the tools and mathematics of ocean state and parameter estimation and their application to ocean science through a mix of foundational lectures, hands-on tutorials, and projects. In so doing, the school aimed to help nurture the next generation of oceanographers and climate scientists in the subject matter so that they may utilize the ECCO products and underlying modeling/estimation tools most effectively to further advance the state-of-the-art in ocean state estimation and ocean science.

Summer School Topics

  • Data assimilation (global & regional)
  • State & parameter estimation
  • Learning from observations and models
  • Adjoint method
  • Kalman filtering and related smoothing
  • Sensitivity analysis
  • Algorithmic differentiation
  • Ocean modeling
  • Ocean dynamics and variability
  • The ocean's role in climate
  • Global ocean observing system (satellite and in-situ observations)
  • Physics of sea level
  • Ocean mixing
  • Sea ice dynamics
  • Ice sheet-ocean interactions
  • Ice shelf dynamics
  • Ocean tides
  • Cyberinfrastructure & data analytics
  • Diversity and inclusion in oceanography

The principles of numerical modeling were described using the MITgcm as an example. Advanced modeling algorithms and concepts, especially those employed in the ECCO Central Estimate, were treated including mixing schemes, coordinate systems, and boundary conditions. Practical issues were discussed, such as the basics of model parallelization and the nature of model errors. Different observing systems were described, focusing on their complementary nature and impact on state estimation. Sources of data error were examined and issues of data reduction were discussed. A range of analysis tools developed within the ECCO consortium were introduced through tutorials and projects.

Presentations: Week 1

  • [20-May-2019 - 09:00] Introduction »
  • [20-May-2019 - 09:30] Fukumori, I. State Estimation Part 1: Basic Machinery. State estimation (data assimilation) is a means to analyze observations using models, equivalent to fitting a curve through data. Topics: The mathematical problem (inverse problem); Linear inverse methods; Singular value decomposition (SVD); Rank deficiency; Gauss-Markov theorem; Minimum variance estimate; Least-squares. View the zoom presentation.  »
  • [20-May-2019 - 11:00] Cronin, M. Observations I: Overview - The Global Ocean Observing System.  »
  • [20-May-2019 - 13:30] Thompson, L. Heat Content, Heat Fluxes, and Feedback  »

Presentations: Week 2

  • [27-May-2019 - 08:30] Students, Week 2 Introduction and Recap (Day 6) »
  • [27-May-2019 - 09:15] Losch, M., Introduction to Sea Ice Modelling  »
  • [27-May-2019 - 11:00] Schanze, J.J., Salinity and the Global Ocean Water Cycle. Overview: The Global Ocean Freshwater Cycle; Links to Salinity; Changes in the Water Cycle and Salinity; E-P-R, Recycling, and Implied Exports through E:P Ratios; NASA Field Campaigns: Satellites and In Situ Measurements; and Conclusions  »
  • [27-May-2019 - 13:30] Hill, C., Review of Ocean Ecosystem Modeling and ECCO »

Observed and estimated heat content changes. Credit: Piecuch, C.G. (Tracer Budgets in ECCO - Part I: Overview and Some Applications).

Credit: Jackson, R. (Ocean-glacier Interactions in Greenland).


A python package designed specifically for reading, manipulating, and plotting ECCO output which lives on the unique lat-lon-cap (LLC) grid. Along with basic examples, the documentation includes an extensive tutorial on basic python routines and descriptions of the underlying data structures which is particularly suitable for MATLAB users.
Python package designed specifically for reading MITgcm model output in mds format into xarray data structures.
Python package which enables low level manipulation such as interpolation and finite differencing on general circulation output through generic grid operations. See this documentation and the ECCOv4-py documentation for MITgcm specific examples.
A python package which defines a flexible data structure for multi-dimensional fields, which is particularly useful in the geosciences.
A MATLAB/Octave package for analyzing fields gridded on any of the grid types familiar to the MITgcm. It was originally designed for analyzing ECCO output and has since remained as the standard analysis tool.
A MATLAB/Octave package for analyzing, manipulating, and formatting heterogeneous in-situ oceanographic measurement data. It was designed particularly for the ECCO state estimate.

The global telecommunication system. Credit: Cronin, M. (Observations 1: Overview - The Global Ocean Observing System).
Friday Harbor
Friday Harbor Laboratories on San Juan Island, Washington.