Articles | Volume 13, issue 12
https://doi.org/10.5194/gmd-13-5935-2020
© Author(s) 2020. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/gmd-13-5935-2020
© Author(s) 2020. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Development and technical paper
| 
01 Dec 2020
Development and technical paper |
| 01 Dec 2020
| 01 Dec 2020
Numerical integrators for Lagrangian oceanography
SINTEF Ocean, Trondheim, Norway
Department of Physics, Norwegian University of Science and Technology, Trondheim, Norway
Rodrigo Duran
National Energy Technology Laboratory, Albany, OR 97321, USA
Theiss Research, San Diego, CA 92037, USA
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EGUsphere, https://doi.org/10.5194/egusphere-2025-2109, https://doi.org/10.5194/egusphere-2025-2109, 2025
This preprint is open for discussion and under review for Geoscientific Model Development (GMD).
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A common task in applied oceanography is to calculate the trajectories of floating objects in the ocean. We propose an alteration to some common numerical methods to improve their performance in such computations, and compare results with and without this alteration. This will help researchers to ensure they obtain a higher accuracy in their results without compromising on computer resources.
Tor Nordam, Ruben Kristiansen, Raymond Nepstad, Erik van Sebille, and Andy M. Booth
Geosci. Model Dev., 16, 5339–5363, https://doi.org/10.5194/gmd-16-5339-2023, https://doi.org/10.5194/gmd-16-5339-2023, 2023
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We describe and compare two common methods, Eulerian and Lagrangian models, used to simulate the vertical transport of material in the ocean. They both solve the same transport problems but use different approaches for representing the underlying equations on the computer. The main focus of our study is on the numerical accuracy of the two approaches. Our results should be useful for other researchers creating or using these types of transport models.
Johannes Röhrs, Knut-Frode Dagestad, Helene Asbjørnsen, Tor Nordam, Jørgen Skancke, Cathleen E. Jones, and Camilla Brekke
Ocean Sci., 14, 1581–1601, https://doi.org/10.5194/os-14-1581-2018, https://doi.org/10.5194/os-14-1581-2018, 2018
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Simulations of hypothetical oil spills are presented to investigate how the vertical mixing of oil affects transport towards various directions. It is shown that the horizontal transport of oil greatly varies for different oil types and weather conditions. These differences are a consequence of the entrainment of oil from the surface into the ocean. While oil spills often get entrained into the water by waves, we show that submerged oil typically resurfaces after a few hours or days.
Jenny Margareta Mørk, Tor Nordam, and Siren Rühs
EGUsphere, https://doi.org/10.5194/egusphere-2025-2109, https://doi.org/10.5194/egusphere-2025-2109, 2025
This preprint is open for discussion and under review for Geoscientific Model Development (GMD).
Short summary
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A common task in applied oceanography is to calculate the trajectories of floating objects in the ocean. We propose an alteration to some common numerical methods to improve their performance in such computations, and compare results with and without this alteration. This will help researchers to ensure they obtain a higher accuracy in their results without compromising on computer resources.
Luca Kunz, Alexa Griesel, Carsten Eden, Rodrigo Duran, and Bruno Sainte-Rose
Ocean Sci., 20, 1611–1630, https://doi.org/10.5194/os-20-1611-2024, https://doi.org/10.5194/os-20-1611-2024, 2024
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Transient Attracting Profiles (TRAPs) indicate the most attracting regions of the flow and have the potential to facilitate offshore cleanups in the Great Pacific Garbage Patch. We study the characteristics of TRAPs and the prospects for predicting debris transport from a mesoscale-permitting dataset. Our findings show the relevance of TRAP lifetime estimations to an operational application, and our TRAP tracking algorithm may even benefit other challenges that are related to search at sea.
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Geosci. Model Dev., 16, 5339–5363, https://doi.org/10.5194/gmd-16-5339-2023, https://doi.org/10.5194/gmd-16-5339-2023, 2023
Short summary
Short summary
We describe and compare two common methods, Eulerian and Lagrangian models, used to simulate the vertical transport of material in the ocean. They both solve the same transport problems but use different approaches for representing the underlying equations on the computer. The main focus of our study is on the numerical accuracy of the two approaches. Our results should be useful for other researchers creating or using these types of transport models.
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Ocean Sci., 14, 1581–1601, https://doi.org/10.5194/os-14-1581-2018, https://doi.org/10.5194/os-14-1581-2018, 2018
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Simulations of hypothetical oil spills are presented to investigate how the vertical mixing of oil affects transport towards various directions. It is shown that the horizontal transport of oil greatly varies for different oil types and weather conditions. These differences are a consequence of the entrainment of oil from the surface into the ocean. While oil spills often get entrained into the water by waves, we show that submerged oil typically resurfaces after a few hours or days.
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We developed a modelling system of the northwest Atlantic Ocean that simulates the currents, temperature, salinity, and parts of the biochemical cycle of the ocean, as well as sea ice. The system combines advanced, open-source models and can be used to study, for example, the ocean capture of atmospheric carbon dioxide, which is a key process in the global climate. The system produces realistic results, and we use it to investigate the roles of tides and sea ice in the northwest Atlantic Ocean.
Eui-Jong Kang, Byung-Ju Sohn, Sang-Woo Kim, Wonho Kim, Young-Cheol Kwon, Seung-Bum Kim, Hyoung-Wook Chun, and Chao Liu
Geosci. Model Dev., 17, 8553–8568, https://doi.org/10.5194/gmd-17-8553-2024, https://doi.org/10.5194/gmd-17-8553-2024, 2024
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Qin Zhou, Chen Zhao, Rupert Gladstone, Tore Hattermann, David Gwyther, and Benjamin Galton-Fenzi
Geosci. Model Dev., 17, 8243–8265, https://doi.org/10.5194/gmd-17-8243-2024, https://doi.org/10.5194/gmd-17-8243-2024, 2024
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We introduce an accelerated forcing approach to address timescale discrepancies between the ice sheets and ocean components in coupled modelling by reducing the ocean simulation duration. The approach is evaluated using idealized coupled models, and its limitations in real-world applications are discussed. Our results suggest it can be a valuable tool for process-oriented coupled ice sheet–ocean modelling and downscaling climate simulations with such models.
Jan D. Zika and Taimoor Sohail
Geosci. Model Dev., 17, 8049–8068, https://doi.org/10.5194/gmd-17-8049-2024, https://doi.org/10.5194/gmd-17-8049-2024, 2024
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We describe a method to relate fluxes of heat and freshwater at the sea surface to the resulting distribution of seawater among categories such as warm and salty or cold and salty. The method exploits the laws that govern how heat and salt change when water mixes. The method will allow the climate community to improve estimates of how much heat the ocean is absorbing and how rainfall and evaporation are changing across the globe.
Xinxin Wang, Jiuke Wang, Wenfang Lu, Changming Dong, Hao Qin, and Haoyu Jiang
Geosci. Model Dev. Discuss., https://doi.org/10.5194/gmd-2024-181, https://doi.org/10.5194/gmd-2024-181, 2024
Revised manuscript accepted for GMD
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Large-scale wave modeling is essential for science and society, typically relying on resource-intensive numerical methods to simulate wave dynamics. In this study, we introduce a rolling AI-based method for modeling global significant wave height. Our model achieves accuracy comparable to traditional numerical methods while significantly improving speed, making it operable on standard laptops. This work demonstrates AI's potential to enhance the accuracy and efficiency of global wave modeling.
Gloria Pietropolli, Luca Manzoni, and Gianpiero Cossarini
Geosci. Model Dev., 17, 7347–7364, https://doi.org/10.5194/gmd-17-7347-2024, https://doi.org/10.5194/gmd-17-7347-2024, 2024
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Monitoring the ocean is essential for studying marine life and human impact. Our new software, PPCon, uses ocean data to predict key factors like nitrate and chlorophyll levels, which are hard to measure directly. By leveraging machine learning, PPCon offers more accurate and efficient predictions.
Rafael Santana, Richard Gorman, Emily Lane, Stuart Moore, Cyprien Bosserelle, Glen Reeve, and Christo Rautenbach
Geosci. Model Dev. Discuss., https://doi.org/10.5194/gmd-2024-110, https://doi.org/10.5194/gmd-2024-110, 2024
Revised manuscript accepted for GMD
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This research explores improving wave forecasts in New Zealand, particularly at Banks Peninsula and Baring Head. We used detailed models, finding that forecasts at Baring Head improved significantly due to its strong tidal currents, but changes at Banks Peninsula were minimal. The study demonstrates that local conditions greatly influence the effectiveness of wave prediction models, highlighting the need for tailored approaches in coastal forecasting to enhance accuracy in the predictions.
Renbo Pang, Fujiang Yu, Yuanyong Gao, Ye Yuan, Liang Yuan, and Zhiyi Gao
EGUsphere, https://doi.org/10.5194/egusphere-2024-2515, https://doi.org/10.5194/egusphere-2024-2515, 2024
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The application of the distributed graph communication topology in earth models has been rarely studied. We tested and compared this topology with the traditional point-to-point communication method using a global wave model. We found that this topology is more efficient. Additionally, using this topology can greatly improve the performance of the wave model and could help improve the performance of other earth models.
Jan De Rydt, Nicolas C. Jourdain, Yoshihiro Nakayama, Mathias van Caspel, Ralph Timmermann, Pierre Mathiot, Xylar S. Asay-Davis, Hélène Seroussi, Pierre Dutrieux, Ben Galton-Fenzi, David Holland, and Ronja Reese
Geosci. Model Dev., 17, 7105–7139, https://doi.org/10.5194/gmd-17-7105-2024, https://doi.org/10.5194/gmd-17-7105-2024, 2024
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Global climate models do not reliably simulate sea-level change due to ice-sheet–ocean interactions. We propose a community modelling effort to conduct a series of well-defined experiments to compare models with observations and study how models respond to a range of perturbations in climate and ice-sheet geometry. The second Marine Ice Sheet–Ocean Model Intercomparison Project will continue to lay the groundwork for including ice-sheet–ocean interactions in global-scale IPCC-class models.
Qian Wang, Yang Zhang, Fei Chai, Y. Joseph Zhang, and Lorenzo Zampieri
Geosci. Model Dev., 17, 7067–7081, https://doi.org/10.5194/gmd-17-7067-2024, https://doi.org/10.5194/gmd-17-7067-2024, 2024
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We coupled an unstructured hydro-model with an advanced column sea ice model to meet the growing demand for increased resolution and complexity in unstructured sea ice models. Additionally, we present a novel tracer transport scheme for the sea ice coupled model and demonstrate that this scheme fulfills the requirements for conservation, accuracy, efficiency, and monotonicity in an idealized test. Our new coupled model also has good performance in realistic tests.
Adrien Garinet, Marine Herrmann, Patrick Marsaleix, and Juliette Pénicaud
Geosci. Model Dev., 17, 6967–6986, https://doi.org/10.5194/gmd-17-6967-2024, https://doi.org/10.5194/gmd-17-6967-2024, 2024
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Mixing is a crucial aspect of the ocean, but its accurate representation in computer simulations is made challenging by errors that result in unwanted mixing, compromising simulation realism. Here we illustrate the spurious effect that tides can have on simulations of south-east Asia. Although they play an important role in determining the state of the ocean, they can increase numerical errors and make simulation outputs less realistic. We also provide insights into how to reduce these errors.
Mohamed Ayache, Jean-Claude Dutay, Anne Mouchet, Kazuyo Tachikawa, Camille Risi, and Gilles Ramstein
Geosci. Model Dev., 17, 6627–6655, https://doi.org/10.5194/gmd-17-6627-2024, https://doi.org/10.5194/gmd-17-6627-2024, 2024
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Water isotopes (δ18O, δD) are one of the most widely used proxies in ocean climate research. Previous studies using water isotope observations and modelling have highlighted the importance of understanding spatial and temporal isotopic variability for a quantitative interpretation of these tracers. Here we present the first results of a high-resolution regional dynamical model (at 1/12° horizontal resolution) developed for the Mediterranean Sea, one of the hotspots of ongoing climate change.
Cara Nissen, Nicole S. Lovenduski, Mathew Maltrud, Alison R. Gray, Yohei Takano, Kristen Falcinelli, Jade Sauvé, and Katherine Smith
Geosci. Model Dev., 17, 6415–6435, https://doi.org/10.5194/gmd-17-6415-2024, https://doi.org/10.5194/gmd-17-6415-2024, 2024
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Autonomous profiling floats have provided unprecedented observational coverage of the global ocean, but uncertainties remain about whether their sampling frequency and density capture the true spatiotemporal variability of physical, biogeochemical, and biological properties. Here, we present the novel synthetic biogeochemical float capabilities of the Energy Exascale Earth System Model version 2 and demonstrate their utility as a test bed to address these uncertainties.
Iria Sala and Bingzhang Chen
Geosci. Model Dev. Discuss., https://doi.org/10.5194/gmd-2024-130, https://doi.org/10.5194/gmd-2024-130, 2024
Revised manuscript accepted for GMD
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Phytoplankton, tiny photosynthetic organisms, produce nearly half of Earth's oxygen. To analyze their physiology, diversity, and evolution in the ocean, we developed a model that treats phytoplankton as individual particles. Moreover, our model considers phytoplankton size, temperature, and light traits, and allows for mutations in phytoplankton cells. Thus, our model provides a valuable tool for advancing the study of phytoplankton physiology, diversity, and evolution.
Ye Yuan, Fujiang Yu, Zhi Chen, Xueding Li, Fang Hou, Yuanyong Gao, Zhiyi Gao, and Renbo Pang
Geosci. Model Dev., 17, 6123–6136, https://doi.org/10.5194/gmd-17-6123-2024, https://doi.org/10.5194/gmd-17-6123-2024, 2024
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Accurate and timely forecasting of ocean waves is of great importance to the safety of marine transportation and offshore engineering. In this study, GPU-accelerated computing is introduced in WAve Modeling Cycle 6 (WAM6). With this effort, global high-resolution wave simulations can now run on GPUs up to tens of times faster than the currently available models can on a CPU node with results that are just as accurate.
Krysten Rutherford, Laura Bianucci, and William Floyd
Geosci. Model Dev., 17, 6083–6104, https://doi.org/10.5194/gmd-17-6083-2024, https://doi.org/10.5194/gmd-17-6083-2024, 2024
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Nearshore ocean models often lack complete information about freshwater fluxes due to numerous ungauged rivers and streams. We tested a simple rain-based hydrological model as inputs into an ocean model of Quatsino Sound, Canada, with the aim of improving the representation of the land–ocean connection in the nearshore model. Through multiple tests, we found that the performance of the ocean model improved when providing 60 % or more of the freshwater inputs from the simple runoff model.
Neill Mackay, Taimoor Sohail, Jan David Zika, Richard G. Williams, Oliver Andrews, and Andrew James Watson
Geosci. Model Dev., 17, 5987–6005, https://doi.org/10.5194/gmd-17-5987-2024, https://doi.org/10.5194/gmd-17-5987-2024, 2024
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The ocean absorbs carbon dioxide from the atmosphere, mitigating climate change, but estimates of the uptake do not always agree. There is a need to reconcile these differing estimates and to improve our understanding of ocean carbon uptake. We present a new method for estimating ocean carbon uptake and test it with model data. The method effectively diagnoses the ocean carbon uptake from limited data and therefore shows promise for reconciling different observational estimates.
Lucille Barré, Frédéric Diaz, Thibaut Wagener, Camille Mazoyer, Christophe Yohia, and Christel Pinazo
Geosci. Model Dev., 17, 5851–5882, https://doi.org/10.5194/gmd-17-5851-2024, https://doi.org/10.5194/gmd-17-5851-2024, 2024
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The carbonate system is typically studied using measurements, but modeling can contribute valuable insights. Using a biogeochemical model, we propose a new representation of total alkalinity, dissolved inorganic carbon, pCO2, and pH in a highly dynamic Mediterranean coastal area, the Bay of Marseille, a useful addition to measurements. Through a detailed analysis of pCO2 and air–sea CO2 fluxes, we show that variations are strongly impacted by the hydrodynamic processes that affect the bay.
Xuanxuan Gao, Shuiqing Li, Dongxue Mo, Yahao Liu, and Po Hu
Geosci. Model Dev., 17, 5497–5509, https://doi.org/10.5194/gmd-17-5497-2024, https://doi.org/10.5194/gmd-17-5497-2024, 2024
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Storm surges generate coastal inundation and expose populations and properties to danger. We developed a novel storm surge inundation model for efficient prediction. Estimates compare well with in situ measurements and results from a numerical model. The new model is a significant improvement on existing numerical models, with much higher computational efficiency and stability, which allows timely disaster prevention and mitigation.
Vincenzo de Toma, Daniele Ciani, Yassmin Hesham Essa, Chunxue Yang, Vincenzo Artale, Andrea Pisano, Davide Cavaliere, Rosalia Santoleri, and Andrea Storto
Geosci. Model Dev., 17, 5145–5165, https://doi.org/10.5194/gmd-17-5145-2024, https://doi.org/10.5194/gmd-17-5145-2024, 2024
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This study explores methods to reconstruct diurnal variations in skin sea surface temperature in a model of the Mediterranean Sea. Our new approach, considering chlorophyll concentration, enhances spatial and temporal variations in the warm layer. Comparative analysis shows context-dependent improvements. The proposed "chlorophyll-interactive" method brings the surface net total heat flux closer to zero annually, despite a net heat loss from the ocean to the atmosphere.
Peter Mlakar, Antonio Ricchi, Sandro Carniel, Davide Bonaldo, and Matjaž Ličer
Geosci. Model Dev., 17, 4705–4725, https://doi.org/10.5194/gmd-17-4705-2024, https://doi.org/10.5194/gmd-17-4705-2024, 2024
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We propose a new point-prediction model, the DEep Learning WAVe Emulating model (DELWAVE), which successfully emulates the Simulating WAves Nearshore model (SWAN) over synoptic to climate timescales. Compared to control climatology over all wind directions, the mismatch between DELWAVE and SWAN is generally small compared to the difference between scenario and control conditions, suggesting that the noise introduced by surrogate modelling is substantially weaker than the climate change signal.
Susanna Winkelbauer, Michael Mayer, and Leopold Haimberger
Geosci. Model Dev., 17, 4603–4620, https://doi.org/10.5194/gmd-17-4603-2024, https://doi.org/10.5194/gmd-17-4603-2024, 2024
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Oceanic transports shape the global climate, but the evaluation and validation of this key quantity based on reanalysis and model data are complicated by the distortion of the used modelling grids and the large number of different grid types. We present two new methods that allow the calculation of oceanic fluxes of volume, heat, salinity, and ice through almost arbitrary sections for various models and reanalyses that are independent of the used modelling grids.
Xiaoyu Fan, Baylor Fox-Kemper, Nobuhiro Suzuki, Qing Li, Patrick Marchesiello, Peter P. Sullivan, and Paul S. Hall
Geosci. Model Dev., 17, 4095–4113, https://doi.org/10.5194/gmd-17-4095-2024, https://doi.org/10.5194/gmd-17-4095-2024, 2024
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Simulations of the oceanic turbulent boundary layer using the nonhydrostatic CROCO ROMS and NCAR-LES models are compared. CROCO and the NCAR-LES are accurate in a similar manner, but CROCO’s additional features (e.g., nesting and realism) and its compressible turbulence formulation carry additional costs.
Jilian Xiong and Parker MacCready
Geosci. Model Dev., 17, 3341–3356, https://doi.org/10.5194/gmd-17-3341-2024, https://doi.org/10.5194/gmd-17-3341-2024, 2024
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The new offline particle tracking package, Tracker v1.1, is introduced to the Regional Ocean Modeling System, featuring an efficient nearest-neighbor algorithm to enhance particle-tracking speed. Its performance was evaluated against four other tracking packages and passive dye. Despite unique features, all packages yield comparable results. Running multiple packages within the same circulation model allows comparison of their performance and ease of use.
Sylvain Cailleau, Laurent Bessières, Léonel Chiendje, Flavie Dubost, Guillaume Reffray, Jean-Michel Lellouche, Simon van Gennip, Charly Régnier, Marie Drevillon, Marc Tressol, Matthieu Clavier, Julien Temple-Boyer, and Léo Berline
Geosci. Model Dev., 17, 3157–3173, https://doi.org/10.5194/gmd-17-3157-2024, https://doi.org/10.5194/gmd-17-3157-2024, 2024
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In order to improve Sargassum drift forecasting in the Caribbean area, drift models can be forced by higher-resolution ocean currents. To this goal a 3 km resolution regional ocean model has been developed. Its assessment is presented with a particular focus on the reproduction of fine structures representing key features of the Caribbean region dynamics and Sargassum transport. The simulated propagation of a North Brazil Current eddy and its dissipation was found to be quite realistic.
Gaetano Porcile, Anne-Claire Bennis, Martial Boutet, Sophie Le Bot, Franck Dumas, and Swen Jullien
Geosci. Model Dev., 17, 2829–2853, https://doi.org/10.5194/gmd-17-2829-2024, https://doi.org/10.5194/gmd-17-2829-2024, 2024
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Here a new method of modelling the interaction between ocean currents and waves is presented. We developed an advanced coupling of two models, one for ocean currents and one for waves. In previous couplings, some wave-related calculations were based on simplified assumptions. Our method uses more complex calculations to better represent wave–current interactions. We tested it in a macro-tidal coastal area and found that it significantly improves the model accuracy, especially during storms.
Colette Gabrielle Kerry, Moninya Roughan, Shane Keating, David Gwyther, Gary Brassington, Adil Siripatana, and Joao Marcos A. C. Souza
Geosci. Model Dev., 17, 2359–2386, https://doi.org/10.5194/gmd-17-2359-2024, https://doi.org/10.5194/gmd-17-2359-2024, 2024
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Ocean forecasting relies on the combination of numerical models and ocean observations through data assimilation (DA). Here we assess the performance of two DA systems in a dynamic western boundary current, the East Australian Current, across a common modelling and observational framework. We show that the more advanced, time-dependent method outperforms the time-independent method for forecast horizons of 5 d. This advocates the use of advanced methods for highly variable oceanic regions.
Ivan Hernandez, Leidy M. Castro-Rosero, Manuel Espino, and Jose M. Alsina Torrent
Geosci. Model Dev., 17, 2221–2245, https://doi.org/10.5194/gmd-17-2221-2024, https://doi.org/10.5194/gmd-17-2221-2024, 2024
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The LOCATE numerical model was developed to conduct Lagrangian simulations of the transport and dispersion of marine debris at coastal scales. High-resolution hydrodynamic data and a beaching module that used particle distance to the shore for land–water boundary detection were used on a realistic debris discharge scenario comparing hydrodynamic data at various resolutions. Coastal processes and complex geometric structures were resolved when using nested grids and distance-to-shore beaching.
Ngoc B. Trinh, Marine Herrmann, Caroline Ulses, Patrick Marsaleix, Thomas Duhaut, Thai To Duy, Claude Estournel, and R. Kipp Shearman
Geosci. Model Dev., 17, 1831–1867, https://doi.org/10.5194/gmd-17-1831-2024, https://doi.org/10.5194/gmd-17-1831-2024, 2024
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A high-resolution model was built to study the South China Sea (SCS) water, heat, and salt budgets. Model performance is demonstrated by comparison with observations and simulations. Important discards are observed if calculating offline, instead of online, lateral inflows and outflows of water, heat, and salt. The SCS mainly receives water from the Luzon Strait and releases it through the Mindoro, Taiwan, and Karimata straits. SCS surface interocean water exchanges are driven by monsoon winds.
Louis Thiry, Long Li, Guillaume Roullet, and Etienne Mémin
Geosci. Model Dev., 17, 1749–1764, https://doi.org/10.5194/gmd-17-1749-2024, https://doi.org/10.5194/gmd-17-1749-2024, 2024
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We present a new way of solving the quasi-geostrophic (QG) equations, a simple set of equations describing ocean dynamics. Our method is solely based on the numerical methods used to solve the equations and requires no parameter tuning. Moreover, it can handle non-rectangular geometries, opening the way to study QG equations on realistic domains. We release a PyTorch implementation to ease future machine-learning developments on top of the presented method.
Zheqi Shen, Yihao Chen, Xiaojing Li, and Xunshu Song
Geosci. Model Dev., 17, 1651–1665, https://doi.org/10.5194/gmd-17-1651-2024, https://doi.org/10.5194/gmd-17-1651-2024, 2024
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Parameter estimation is the process that optimizes model parameters using observations, which could reduce model errors and improve forecasting. In this study, we conducted parameter estimation experiments using the CESM and the ensemble adjustment Kalman filter. The obtained initial conditions and parameters are used to perform ensemble forecast experiments for ENSO forecasting. The results revealed that parameter estimation could reduce analysis errors and improve ENSO forecast skills.
Ali Abdolali, Saeideh Banihashemi, Jose Henrique Alves, Aron Roland, Tyler J. Hesser, Mary Anderson Bryant, and Jane McKee Smith
Geosci. Model Dev., 17, 1023–1039, https://doi.org/10.5194/gmd-17-1023-2024, https://doi.org/10.5194/gmd-17-1023-2024, 2024
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This article presents an overview of the development and implementation of Great Lake Wave Unstructured (GLWUv2.0), including the core model and workflow design and development. The validation was conducted against in situ data for the re-forecasted duration for summer and wintertime (ice season). The article describes the limitations and challenges encountered in the operational environment and the path forward for the next generation of wave forecast systems in enclosed basins like the GL.
Qiang Wang, Qi Shu, Alexandra Bozec, Eric P. Chassignet, Pier Giuseppe Fogli, Baylor Fox-Kemper, Andy McC. Hogg, Doroteaciro Iovino, Andrew E. Kiss, Nikolay Koldunov, Julien Le Sommer, Yiwen Li, Pengfei Lin, Hailong Liu, Igor Polyakov, Patrick Scholz, Dmitry Sidorenko, Shizhu Wang, and Xiaobiao Xu
Geosci. Model Dev., 17, 347–379, https://doi.org/10.5194/gmd-17-347-2024, https://doi.org/10.5194/gmd-17-347-2024, 2024
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Increasing resolution improves model skills in simulating the Arctic Ocean, but other factors such as parameterizations and numerics are at least of the same importance for obtaining reliable simulations.
Andrew C. Ross, Charles A. Stock, Alistair Adcroft, Enrique Curchitser, Robert Hallberg, Matthew J. Harrison, Katherine Hedstrom, Niki Zadeh, Michael Alexander, Wenhao Chen, Elizabeth J. Drenkard, Hubert du Pontavice, Raphael Dussin, Fabian Gomez, Jasmin G. John, Dujuan Kang, Diane Lavoie, Laure Resplandy, Alizée Roobaert, Vincent Saba, Sang-Ik Shin, Samantha Siedlecki, and James Simkins
Geosci. Model Dev., 16, 6943–6985, https://doi.org/10.5194/gmd-16-6943-2023, https://doi.org/10.5194/gmd-16-6943-2023, 2023
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We evaluate a model for northwest Atlantic Ocean dynamics and biogeochemistry that balances high resolution with computational economy by building on the new regional features in the MOM6 ocean model and COBALT biogeochemical model. We test the model's ability to simulate impactful historical variability and find that the model simulates the mean state and variability of most features well, which suggests the model can provide information to inform living-marine-resource applications.
Cited articles
Ali, S. and Shah, M.: A Lagrangian Particle Dynamics Approach for Crowd Flow Segmentation and Stability Analysis, in: 2007 IEEE Conference on Computer Vision and Pattern Recognition, Minneapolis, MN, USA, 17–22 June 2007, IEEE, 1–6, https://doi.org/10.1109/CVPR.2007.382977, 2007. a, b
Allshouse, M. R., Ivey, G. N., Lowe, R. J., Jones, N. L., Beegle-Krause, C., Xu, J., and Peacock, T.: Impact of windage on ocean surface Lagrangian coherent structures, Environ. Fluid Mech., 17, 473–483, 2017. a
Barkan, R., McWilliams, J. C., Molemaker, M. J., Choi, J., Srinivasan, K., Shchepetkin, A. F., and Bracco, A.: Submesoscale dynamics in the northern Gulf of Mexico. Part II: Temperature–salinity relations and cross-shelf transport processes, J. Phys. Oceanogr., 47, 2347–2360, 2017. a
Beron-Vera, F. J., Olascoaga, M. J., and Goni, G. J.: Oceanic mesoscale eddies as revealed by Lagrangian coherent structures, Geophys. Res. Lett., 35, L12603, https://doi.org/10.1029/2008GL033957, 2008. a
Beron-Vera, F. J., Olascoaga, M. J., Brown, M. G., Koçak, H., and Rypina, I. I.: Invariant-tori-like Lagrangian coherent structures in geophysical flows, Chaos, 20, 017514, https://doi.org/10.1063/1.3271342, 2010. a
Bogacki, P. and Shampine, L. F.: A 3(2) pair of Runge-Kutta formulas, Appl. Math. Lett., 2, 321–325, 1989. a
Breivik, Ø. and Allen, A. A.: An operational search and rescue model for the Norwegian Sea and the North Sea, J. Marine Syst., 69, 99–113, 2008. a
de Boor, C.: A practical guide to splines, Springer-Verlag, New York Berlin Heidelberg, 2001. a
De Dominicis, M., Pinardi, N., Zodiatis, G., and Lardner, R.: MEDSLIK-II, a Lagrangian marine surface oil spill model for short-term forecasting – Part 1: Theory, Geosci. Model Dev., 6, 1851–1869, https://doi.org/10.5194/gmd-6-1851-2013, 2013. a
Dieci, L. and Lopez, L.: A survey of numerical methods for IVPs of ODEs with discontinuous right-hand side, J. Comput. Appl. Math., 236, 3967–3991, https://doi.org/10.1016/j.cam.2012.02.011, 2012. a
Dormand, J. and Prince, P.: A family of embedded Runge-Kutta formulae, J. Comput. Appl. Math., 6, 19–26, 1980. a
Dormand, J. and Prince, P.: A reconsideration of some embedded Runge-Kutta formulae, J. Comput. Appl. Math., 15, 203–211, https://doi.org/10.1016/0377-0427(86)90027-0, 1986. a
Dugstad, J., Fer, I., LaCasce, J., Sanchez de La Lama, M., and Trodahl, M.: Lateral Heat Transport in the Lofoten Basin: Near-Surface Pathways and Subsurface Exchange, J. Geophys. Res.-Oceans,124, 2992–3006, https://doi.org/10.1029/2018JC014774, 2019. a
Duran, R., Beron-Vera, F. J., and Olascoaga, M. J.: Extracting quasi-steady Lagrangian transport patterns from the ocean circulation: An application to the Gulf of Mexico, Scientific Reports, 8, 5218, https://doi.org/10.1038/s41598-018-23121-y, 2018. a, b
Enright, W., Jackson, K., Nørsett, S., and Thomsen, P.: Effective solution of discontinuous IVPs using a Runge-Kutta formula pair with interpolants, Appl. Math. Comput., 27, 313–335, https://doi.org/10.1016/0096-3003(88)90030-6, 1988. a
Farazmand, M. and Haller, G.: Computing Lagrangian coherent structures from their variational theory, Chaos, 22, 013128, https://doi.org/10.1063/1.3690153, 2012. a
García-Martínez, R. and Flores-Tovar, H.: Computer modeling of oil spill trajectories with a high accuracy method, Spill Sci. Technol. B., 5, 323–330, 1999. a
Gladwell, I., Shampine, L., and Thompson, S.: Solving ODEs with MATLAB, Cambridge University Press, New York, NY, USA, 2003. a
Gräwe, U.: Implementation of high-order particle-tracking schemes in a water column model, Ocean Model., 36, 80–89, 2011. a
Griffiths, D. F. and Higham, D. J.: Numerical methods for ordinary differential equations, Springer-Verlag, London, 2010. a
Hairer, E. and Wanner, G.: Solving Ordinary Differential Equations II: Stiff and Differential-Algebraic Problems, Springer-Verlag, Berlin, Heidelberg, 1996. a
Hairer, E., Nørsett, S. P., and Wanner, G.: Solving Ordinary Differential Equations I: Nonstiff Problems, 1st edn., Springer-Verlag Berlin Heidelberg, ISBN 978-3-662-12609-7, https://doi.org/10.1007/978-3-662-12607-3, 1987. a, b, c
Hairer, E., Wanner, G., and Lubich, C.: Geometric Numerical Integration, in:
Structure-Preserving Algorithms for Ordinary Differential Equations, Springer-Verlag, Berlin, Heidelberg, https://doi.org/10.1007/3-540-30666-8, 2006. a
Isaacson, E. and Keller, H. B.: Analysis of Numerical Methods, Dover Publications, New York, USA, 1994. a
Kloeden, P. E. and Platen, E.: Numerical Solution of Stochastic Differential
Equations, Springer-Verlag, Berlin, Heidelberg, 1992. a
Kress, R.: Numerical Analysis, in: Graduate Texts in Mathematics, Springer-Verlag, New York, https://doi.org/10.1007/978-1-4612-0599-9, 1998. a
Lekien, F. and Marsden, J.: Tricubic interpolation in three dimensions, Int. J. Numer. Meth. Eng., 63, 455–471, https://doi.org/10.1002/nme.1296, 2005. a, b
Lévy, M., Resplandy, L., Klein, P., Capet, X., Iovino, D., and Éthé, C.: Grid degradation of submesoscale resolving ocean models: Benefits for offline passive tracer transport, Ocean Model., 48, 1–9, 2012. a
Maslo, A., de Souza, J. M. A. C., Andrade-Canto, F., and Outerelo, J. R.: Connectivity of deep waters in the Gulf of Mexico, J. Marine
Syst., 203, 103267, https://doi.org/10.1016/j.jmarsys.2019.103267, 2020. a
Narváez, D. A., Klinck, J. M., Powell, E. N., Hofmann, E. E., Wilkin, J., and Haidvogel, D. B.: Modeling the dispersal of eastern oyster (Crassostrea virginica) larvae in Delaware Bay, J. Mar. Res., 70, 381–409, 2012. a
Nieto, R. and Gimeno, L.: A database of optimal integration times for Lagrangian studies of atmospheric moisture sources and sinks, Scientific Data, 6, 59, https://doi.org/10.1038/s41597-019-0068-8, 2019. a
Nordam, T.: nordam/ODE-integrators-for-Lagrangian-particles 0.9, Version 0.9, Zenodo, https://doi.org/10.5281/zenodo.4041979, 2020. a, b
Nordam, T., Brønner, U., Skancke, J., Nepstad, R., Rønningen, P., and Alver, M. O.: Numerical integration and interpolation in marine pollutant transport modelling, in: Proceedings of the 40th AMOP Technical Seminar, Calgary, AB, Canada, 3–5 October 2017, Environment and Climate Change Canada, Ottawa, 586–609, https://hdl.handle.net/11250/2652834, 2017. a
North, E. W., Adams, E. E., Schlag, Z., Sherwood, C. R., He, R., Hyun, K. H., and Socolofsky, S. A.: Simulating Oil Droplet Dispersal From the Deepwater Horizon Spill With a Lagrangian Approach, in: Monitoring and Modeling the Deepwater Horizon Oil Spill: A Record Breaking Enterprise, Wiley, 195, 217–226, 2011. a
Onink, V., Wichmann, D., Delandmeter, P., and van Sebille, E.: The Role of Ekman Currents, Geostrophy, and Stokes Drift in the Accumulation of Floating Microplastic, J. Geophys. Res.-Oceans, 124, 1474–1490, https://doi.org/10.1029/2018JC014547, 2019. a
Onu, K., Huhn, F., and Haller, G.: LCS Tool: A computational platform for Lagrangian coherent structures, J. Computat. Sci., 7, 26–36, 2015. a
Peng, J. and Dabiri, J. O.: Transport of inertial particles by Lagrangian coherent structures: application to predator–prey interaction in jellyfish feeding, J. Fluid Mech., 623, 75–84, https://doi.org/10.1017/S0022112008005089, 2009. a
Povinec, P., Gera, M., Holý, K., Hirose, K., Lujaniené, G., Nakano, M., Plastino, W., Sýkora, I., Bartok, J., and Gažák, M.: Dispersion of Fukushima radionuclides in the global atmosphere and the ocean, Appl. Radiat. Isotopes, 81, 383–392, https://doi.org/10.1016/j.apradiso.2013.03.058, 2013. a
Riuttanen, L., Hulkkonen, M., Dal Maso, M., Junninen, H., and Kulmala, M.: Trajectory analysis of atmospheric transport of fine particles, SO2, NOx and O3 to the SMEAR II station in Finland in 1996–2008, Atmos. Chem. Phys., 13, 2153–2164, https://doi.org/10.5194/acp-13-2153-2013, 2013. a
Rivas, D. and Samelson, R. M.: A Numerical Modeling Study of the Upwelling Source Waters along the Oregon Coast during 2005, J. Phys. Oceanogr., 41, 88–112, https://doi.org/10.1175/2010JPO4327.1, 2011. a, b
Rye, H., Reed, M., and Ekrol, N.: The ParTrack model for calculation of the spreading and deposition of drilling mud, chemicals and drill cuttings, Environ. Modell. Softw., 13, 431–441, 1998. a
Serra, M., Sathe, P., Rypina, I., Kirincich, A., Ross, S. D., Lermusiaux, P., Allen, A., Peacock, T., and Haller, G.: Search and rescue at sea aided by hidden flow structures, Nat. Commun., 11, 2525, https://doi.org/10.1038/s41467-020-16281-x, 2020. a
Shadden, S. C. and Taylor, C. A.: Characterization of Coherent Structures in the Cardiovascular System, Ann. Biomed. Eng., 36, 1152–1162, https://doi.org/10.1007/s10439-008-9502-3, 2008. a
Shadden, S. C., Astorino, M., and Gerbeau, J.-F.: Computational analysis of an aortic valve jet with Lagrangian coherent structures, Chaos: An Interdisciplinary J. Nonlinear Sci., 20, 017512, https://doi.org/10.1063/1.3272780, 2010. a
Siegel, D., Kinlan, B., Gaylord, B., and Gaines, S.: Lagrangian descriptions of marine larval dispersion, Mar. Ecol. Prog. Ser., 260, 83–96, 2003. a
Sirois, A. and Bottenheim, J. W.: Use of backward trajectories to interpret the 5-year record of PAN and O3 ambient air concentrations at Kejimkujik National Park, Nova Scotia, J. Geophys. Res., 100, 2867–2881, https://doi.org/10.1029/94JD02951, 1995. a
Spivakovskaya, D., Heemink, A. W., and Deleersnijder, E.: Lagrangian modelling of multi-dimensional advection-diffusion with space-varying diffusivities: theory and idealized test cases, Ocean Dynam., 57, 189–203, 2007. a
van Sebille, E., Scussolini, P., Durgadoo, J. V., Peeters, F. J., Biastoch, A., Weijer, W., Turney, C., Paris, C. B., and Zahn, R.: Ocean currents generate large footprints in marine palaeoclimate proxies, Nat. Commun., 6, 6521, https://doi.org/10.1038/ncomms7521, 2015. a
van Sebille, E., Griffies, S. M., Abernathey, R., Adams, T. P., Berloff, P., Biastoch, A., Blanke, B., Chassignet, E. P., Cheng, Y., Cotter, C. J., Deleersnijder, E., Döös, K., Drake, H. F., Drijfhout, S., Gary, S. F., Heemink, A. W., Kjellsson, J., Koszalka, I. M., Lange, M., Lique, C., MacGilchrist, G. A., Marsh, R., Mayorga Adame, C. G., McAdam, R., Nencioli, F., Paris, C. B., Piggott, M. D., Polton, J. A., Rühs, S., Shah, S. H., Thomas, M. D., Wang, J., Wolfram, P. J., Zanna, L., and Zika, J. D.: Lagrangian ocean analysis: Fundamentals and practices, Ocean Model., 121, 49–75, 2018. a
Visser, A. W.: Lagrangian modelling of plankton motion: From deceptively simple random walks to Fokker-Planck and back again, J. Marine Syst., 70, 287–299, 2008. a
Williams, J.: Bspline-Fortran: Multidimensional B-Spline Interpolation of Data on a Regular Grid (Version 5.4.0), Zenodo, https://doi.org/10.5281/zenodo.1215290, 2018. a
Woods, J.: The Lagrangian Ensemble metamodel for simulating plankton ecosystems, Prog. Oceanogr., 67, 84–159, 2005. a
Yang, Y., He, G.-W., and Wang, L.-P.: Effects of subgrid-scale modeling on Lagrangian statistics in large-eddy simulation, J. Turbul., 9, 1–24, https://doi.org/10.1080/14685240801905360, 2008. a
Zelenke, B., O'Connor, C., Barker, C., Beegle-Krause, C. J., and Eclipse, L. (Eds.): General NOAA Operational Modeling Environment (GNOME) Technical Documentation, U.S. Dept. of Commerce, NOAA Technical Memorandum NOS OR&R 40, Emergency Response Division, Seattle, WA, NOAA, 105 pp., available at: https://response.restoration.noaa.gov/sites/default/files/GNOME_Tech_Doc.pdf (last access: 17 November 2020), 2012. a
Short summary
In applied oceanography, a common task is to calculate the trajectory of objects floating at the sea surface or submerged in the water. We have investigated different numerical methods for doing such calculations and discuss the benefits and challenges of some common methods. We then propose a small change to some common methods that make them more efficient for this particular application. This will allow researchers to obtain more accurate answers with fewer computer resources.
In applied oceanography, a common task is to calculate the trajectory of objects floating at the...
