NASA Jet Propulsion Laboratory California Institute of Technology
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.
[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 - 14:30] Fenty, I. ECCO Products and Tools. The Estimating the Circulation and Climate of the Ocean (ECCO) consortium endeavors to produce the best possible estimates of ocean circulation and its role in climate.
View the zoom presentation.
[21-May-2019 - 09:00] Campin, J-M. Ocean Modeling, Part I. Ocean Model equations; discretised equations, mainly focused on MITgcm formulation; and some modeling recipes (stability, accuracy, conservation).
[21-May-2019 - 10:45] Fukumori, I. State Estimation Part 2: Methods of State Estimation. Methods of state estimation: Kalman filter, Rauch-Tung-Striebel smoother, and Adjoint method.
[21-May-2019 - 13:30] McPhaden, M. Understanding and Predicting El Niño and the Southern Oscillation. Topics: ENSO and climate impacts; observing ENSO; 2015-16 El Niño: description, dynamics, predictability and prediction; ENSO in a changing climate.
View the zoom presentation.
[23-May-2019 - 14:30] Fukumori, I. Other Uses of the Adjoint. Methods of state estimation: Kalman filter, Rauch-Tung-Striebel smoother, and Adjoint method.
[25-May-2019 - 11:00] Ponte, R.M. Satellite Observations. Outline: Some of the satellite data sets in use by ECCO; issues related to satellite data use as constraints in the state estimates (e.g., defining errors, choosing
products); other data sets for possible future use; and some upcoming satellite systems (GRACE Follow-On, SWOT).
View the movie that accompanies the video presentation.
[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 - 14:30] Fenty, I., NASA Advancing Collaborative Connections for Earth System Science (ACCESS): Data Access and the ECCO Ocean and Ice State Estimate. The ECCO global ocean state estimation system is the premier tool for synthesizing NASA's diverse Earth system observations into a complete physically-consistent description of Earth's time-evolving full-depth ocean and sea ice system.
[28-May-2019 - 09:15] Molod, A., Introduction to Coupled Atmosphere/ocean Modeling and Data Assimilation [for NWP, Subseasonal to Seasonal Prediction, Reanalysis]
[30-May-2019 - 09:30] Menemenlis, D., Ocean Biogeochemistry with ECCO and Darwin. Ocean Biogeochemistry with ECCO and Darwin by Dimitris Menemenlis begins in the video at 00:30:37.
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).
Software
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 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 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.