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Weak Constraint 4D-Var Data Assimilation in ROMS using a Saddle-Point Algorithm: Application to the California Current Circulation

Citation: Moore, A., Arango, H., Wilkin, J. and Edwards, C.A., (2023), Weak Constraint 4D-Var Data Assimilation in ROMS using a Saddle- Point Algorithm: Application to the California Current Circulation. Ocean Modelling, p.102262,

The saddle-point formulation of weak constraint 4-dimensional variational (4D-Var) data assimilation has been developed for the Regional Ocean Modeling System (ROMS), and is applied here to the California Current System (CCS). Unlike the conventional primal and dual forcing formulation of weak constraint 4D-Var, the saddle-point formulation can be efficiently parallelized in time, leading to a substantial decrease in wall-clock run time. The performance of the ROMS saddle-point 4D-Var algorithm is assessed here and compared to that of the dual forcing formulation which is the current standard in ROMS. While the rate of convergence of the saddle-point formulation is slower than the dual forcing formulation, the increase in computational speed due to time-parallelization can more than compensate for the additional inner-loop iterations required by the saddle-point algorithm in the CCS configuration considered here. Further gains in performance can be achieved by running the 4D-Var inner-loop iterations at reduced resolution and/or reduced arithmetic precision. The results presented here indicate that in high performance computing environments with large numbers of available compute cores, the saddle-point formulation of 4D-Var could significantly reduce the run-time compared to the dual forcing formulation for large data assimilation problems.

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The NOAA Ocean Acidification Program (OAP) works to prepare society to adapt to the consequences of ocean acidification and conserve marine ecosystems as acidification occurs. Learn more about the human connections and adaptation strategies from these efforts.

Adaptation approaches fostered by the OAP include:


Using models and research to understand the sensitivity of organisms and ecosystems to ocean acidification to make predictions about the future, allowing communities and industries to prepare


Using these models and predictions as tools to facilitate management strategies that will protect marine resources and communities from future changes


Developing innovative tools to help monitor ocean acidification and mitigate changing ocean chemistry locally


On the Road

Drive fuel-efficient vehicles or choose public transportation. Choose your bike or walk! Don't sit idle for more than 30 seconds. Keep your tires properly inflated.

With your Food Choices

Eat local- this helps cut down on production and transport! Reduce your meat and dairy. Compost to avoid food waste ending up in the landfill

With your Food Choices

Make energy-efficient choices for your appliances and lighting. Heat and cool efficiently! Change your air filters and program your thermostat, seal and insulate your home, and support clean energy sources

By Reducing Coastal Acidification

Reduce your use of fertilizers, Improve sewage treatment and run off, and Protect and restore coastal habitats

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You've taken the first step to learn more about ocean acidification - why not spread this knowledge to your community?

Every community has their unique culture, economy and ecology and what’s at stake from ocean acidification may be different depending on where you live.  As a community member, you can take a larger role in educating the public about ocean acidification. Creating awareness is the first step to taking action.  As communities gain traction, neighboring regions that share marine resources can build larger coalitions to address ocean acidification.  Here are some ideas to get started:

  1. Work with informal educators, such as aquarium outreach programs and local non-profits, to teach the public about ocean acidification. Visit our Education & Outreach page to find the newest tools!
  2. Participate in habitat restoration efforts to restore habitats that help mitigate the effects of coastal acidification
  3. Facilitate conversations with local businesses that might be affected by ocean acidification, building a plan for the future.
  4. Partner with local community efforts to mitigate the driver behind ocean acidification  – excess CO2 – such as community supported agriculture, bike & car shares and other public transportation options.
  5. Contact your regional Coastal Acidification Network (CAN) to learn how OA is affecting your region and more ideas about how you can get involved in your community
       More for Taking Community Action