Schwarz Waveform Relaxation for a Single Column Climate Model with Activated Sea Ice Component
(2025) In Master's Theses in Mathematical Sciences NUMM03 20242Mathematics (Faculty of Engineering)
Mathematical Statistics
Mathematics (Faculty of Sciences)
Centre for Mathematical Sciences
- Abstract
- Sea ice is strongly impacted by global warming, and its decline further alters the global climate. Climate models are important tools for examining those future sea ice changes and the interaction of sea ice with other Earth system components such as the atmosphere and the ocean. Typically, these components are simulated with separate codes. The interaction between these components is typically modeled through interface conditions that include surface data from the respective other component. However, the exchanged data lags behind the model state for which the interface conditions are computed, consequently introducing a so-called coupling error. This thesis examines this coupling error in an environment with sea ice, by running the... (More)
- Sea ice is strongly impacted by global warming, and its decline further alters the global climate. Climate models are important tools for examining those future sea ice changes and the interaction of sea ice with other Earth system components such as the atmosphere and the ocean. Typically, these components are simulated with separate codes. The interaction between these components is typically modeled through interface conditions that include surface data from the respective other component. However, the exchanged data lags behind the model state for which the interface conditions are computed, consequently introducing a so-called coupling error. This thesis examines this coupling error in an environment with sea ice, by running the coupled EC-Earth atmosphere-ocean single-column model at locations with varying initial sea ice thickness and concentration. In particular, interface conditions in the presence of sea ice are specified, and the processes and influence of the sea ice model SI³ are examined in detail. Simulations are performed using the Schwarz waveform relaxation (SWR) coupling scheme for handling the data exchange. The SWR scheme is an iterative algorithm that resynchronizes the interface conditions and the model state. If the SWR scheme is terminated, a more accurate solution of the model is found which can be compared with the results obtained with the standard coupling schemes to estimate the so-called coupling error. However, our simulations did not terminate at locations with ice cover larger than 0.005%. We investigate this behavior and show that the coupling variables (e.g. sea ice surface temperature, shortwave radiation, or snow thickness) oscillate between SWR iterations. We observe that the sea ice surface temperature varies in a range of more than 1°C for some locations, which could initiate sea ice growth or melt in climate simulations. (Less)
- Popular Abstract
- Sea ice, frozen seawater that covers the oceans in the Arctic and Antarctic, is an important component of the Earth's system. Its bright surface reflects sunlight which has a cooling effect on the climate. However, during the last decades, the sea ice cover has decreased significantly, and consequently, more sunlight is absorbed due to the darker surface of the ocean, which in turn can accelerate global warming.
To understand the influence of sea ice on the Earth system, researchers use, among others, climate models: computer tools based on mathematical equations that describe the Earth system. In climate models, the components of the Earth system, such as the ocean, the atmosphere, and the sea ice, are typically described through... (More) - Sea ice, frozen seawater that covers the oceans in the Arctic and Antarctic, is an important component of the Earth's system. Its bright surface reflects sunlight which has a cooling effect on the climate. However, during the last decades, the sea ice cover has decreased significantly, and consequently, more sunlight is absorbed due to the darker surface of the ocean, which in turn can accelerate global warming.
To understand the influence of sea ice on the Earth system, researchers use, among others, climate models: computer tools based on mathematical equations that describe the Earth system. In climate models, the components of the Earth system, such as the ocean, the atmosphere, and the sea ice, are typically described through separate programs, which exchange information such as surface temperatures and the amount of incoming sunlight. However, in contrast to the real world, where interactions are happening all the time, these systems interact only at specific times, leading to errors.
One error is due to the exchanged data being outdated, as the data characterizes the state of the components at a time before the data is transferred, but it is applied in calculations afterward. Luckily, three exists an algorithm that can eliminate this error by ensuring that the transferred data is up to date. However, the algorithm is not applicable for long-term climate simulations since it takes a lot of computation time. Today, climate models can already take several months to run. Instead, researchers use the algorithm in short simulations and compare its more accurate solutions with the results of the standard (more inaccurate) algorithms typically used in climate models. From this comparison, the error caused by the outdated data is estimated.
In colder regions, sea ice is an additional component that influences the already complex interaction between the atmosphere and the ocean, making the interaction processes even more prone to errors than without sea ice. In this thesis, we show that the occurrence of sea ice indeed significantly influences the described error. This is realized by conducting smaller scale climate model simulations with the more accurate algorithm at locations where the ocean is covered with sea ice. (Less)
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/student-papers/record/9183501
- author
- Rockstroh, Anna LU
- supervisor
- organization
- course
- NUMM03 20242
- year
- 2025
- type
- H2 - Master's Degree (Two Years)
- subject
- keywords
- Schwarz waveform relaxation, climate modeling, coupling scheme, sea ice, single column climate model
- publication/series
- Master's Theses in Mathematical Sciences
- report number
- LUNFNA-3044-2025
- ISSN
- 1404-6342
- other publication id
- 2025:E6
- language
- English
- id
- 9183501
- date added to LUP
- 2025-02-11 14:16:13
- date last changed
- 2025-02-11 14:16:13
@misc{9183501,
abstract = {{Sea ice is strongly impacted by global warming, and its decline further alters the global climate. Climate models are important tools for examining those future sea ice changes and the interaction of sea ice with other Earth system components such as the atmosphere and the ocean. Typically, these components are simulated with separate codes. The interaction between these components is typically modeled through interface conditions that include surface data from the respective other component. However, the exchanged data lags behind the model state for which the interface conditions are computed, consequently introducing a so-called coupling error. This thesis examines this coupling error in an environment with sea ice, by running the coupled EC-Earth atmosphere-ocean single-column model at locations with varying initial sea ice thickness and concentration. In particular, interface conditions in the presence of sea ice are specified, and the processes and influence of the sea ice model SI³ are examined in detail. Simulations are performed using the Schwarz waveform relaxation (SWR) coupling scheme for handling the data exchange. The SWR scheme is an iterative algorithm that resynchronizes the interface conditions and the model state. If the SWR scheme is terminated, a more accurate solution of the model is found which can be compared with the results obtained with the standard coupling schemes to estimate the so-called coupling error. However, our simulations did not terminate at locations with ice cover larger than 0.005%. We investigate this behavior and show that the coupling variables (e.g. sea ice surface temperature, shortwave radiation, or snow thickness) oscillate between SWR iterations. We observe that the sea ice surface temperature varies in a range of more than 1°C for some locations, which could initiate sea ice growth or melt in climate simulations.}},
author = {{Rockstroh, Anna}},
issn = {{1404-6342}},
language = {{eng}},
note = {{Student Paper}},
series = {{Master's Theses in Mathematical Sciences}},
title = {{Schwarz Waveform Relaxation for a Single Column Climate Model with Activated Sea Ice Component}},
year = {{2025}},
}