Articles | Volume 7, issue 1
https://doi.org/10.5194/gmd-7-225-2014
© Author(s) 2014. This work is distributed under
the Creative Commons Attribution 3.0 License.
the Creative Commons Attribution 3.0 License.
https://doi.org/10.5194/gmd-7-225-2014
© Author(s) 2014. This work is distributed under
the Creative Commons Attribution 3.0 License.
the Creative Commons Attribution 3.0 License.
Methods for assessment of models
| 
29 Jan 2014
Methods for assessment of models |
| 29 Jan 2014
divand-1.0: n-dimensional variational data analysis for ocean observations
GHER, University of Liège, Liège, Belgium
Invited contribution by A. Barth, recipient of the EGU Arne Richter Award for Outstanding Young Scientists 2010.
J.-M. Beckers
GHER, University of Liège, Liège, Belgium
C. Troupin
IMEDEA, Esporles, Illes Balears, Spain
A. Alvera-Azcárate
GHER, University of Liège, Liège, Belgium
L. Vandenbulcke
seamod.ro/Jailoo srl, Sat Valeni, Com. Salatrucu, Jud. Arges, Romania
CIIMAR, University of Porto, Porto, Portugal
Related authors
Aida Alvera-Azcárate, Dimitry Van der Zande, Alexander Barth, Antoine Dille, Joppe Massant, and Jean-Marie Beckers
EGUsphere, https://doi.org/10.5194/egusphere-2024-1268, https://doi.org/10.5194/egusphere-2024-1268, 2024
Short summary
Short summary
This work presents an approach to increase the spatial resolution of satellite data and interpolate gaps dur to cloud cover, using a method called DINEOF (Data Interpolating Empirical Orthogonal Functions). The method is tested on turbidity and chlorophyll-a concentration data in the Belgian coastal zone and the North Sea. The results show that we are able to improve the spatial resolution of these data in order to perform analysis of spatial and temporal variability in the coastal regions.
Alexander Barth, Julien Brajard, Aida Alvera-Azcárate, Bayoumy Mohamed, Charles Troupin, and Jean-Marie Beckers
EGUsphere, https://doi.org/10.5194/egusphere-2024-1075, https://doi.org/10.5194/egusphere-2024-1075, 2024
Short summary
Short summary
Most satellite observations have gaps, for example, due to clouds. This paper presents a method to reconstruct missing data in satellite observation of the chlorophyll a concentration in the Black Sea. Rather than giving a single possible reconstructed field, the discussed method provides an ensemble of possible reconstructions using a generative neural network. The resulting ensemble is validated using techniques from numerical weather prediction and ocean modelling.
Francesca Doglioni, Robert Ricker, Benjamin Rabe, Alexander Barth, Charles Troupin, and Torsten Kanzow
Earth Syst. Sci. Data, 15, 225–263, https://doi.org/10.5194/essd-15-225-2023, https://doi.org/10.5194/essd-15-225-2023, 2023
Short summary
Short summary
This paper presents a new satellite-derived gridded dataset, including 10 years of sea surface height and geostrophic velocity at monthly resolution, over the Arctic ice-covered and ice-free regions, up to 88° N. We assess the dataset by comparison to independent satellite and mooring data. Results correlate well with independent satellite data at monthly timescales, and the geostrophic velocity fields can resolve seasonal to interannual variability of boundary currents wider than about 50 km.
Alexander Barth, Aida Alvera-Azcárate, Charles Troupin, and Jean-Marie Beckers
Geosci. Model Dev., 15, 2183–2196, https://doi.org/10.5194/gmd-15-2183-2022, https://doi.org/10.5194/gmd-15-2183-2022, 2022
Short summary
Short summary
Earth-observing satellites provide routine measurement of several ocean parameters. However, these datasets have a significant amount of missing data due to the presence of clouds or other limitations of the employed sensors. This paper describes a method to infer the value of the missing satellite data based on a convolutional autoencoder (a specific type of neural network architecture). The technique also provides a reliable error estimate of the interpolated value.
Malek Belgacem, Katrin Schroeder, Alexander Barth, Charles Troupin, Bruno Pavoni, Patrick Raimbault, Nicole Garcia, Mireno Borghini, and Jacopo Chiggiato
Earth Syst. Sci. Data, 13, 5915–5949, https://doi.org/10.5194/essd-13-5915-2021, https://doi.org/10.5194/essd-13-5915-2021, 2021
Short summary
Short summary
The Mediterranean Sea exhibits an anti-estuarine circulation, responsible for its low productivity. Understanding this peculiar character is still a challenge since there is no exact quantification of nutrient sinks and sources. Because nutrient in situ observations are generally infrequent and scattered in space and time, climatological mapping is often applied to sparse data in order to understand the biogeochemical state of the ocean. The dataset presented here partly addresses these issues.
Alexander Barth, Aida Alvera-Azcárate, Matjaz Licer, and Jean-Marie Beckers
Geosci. Model Dev., 13, 1609–1622, https://doi.org/10.5194/gmd-13-1609-2020, https://doi.org/10.5194/gmd-13-1609-2020, 2020
Short summary
Short summary
DINCAE is a method for reconstructing missing data in satellite datasets using a neural network. Satellite observations working in the optical and infrared bands are affected by clouds, which obscure part of the ocean underneath. In this paper, a neural network with the structure of a convolutional auto-encoder is developed to reconstruct the missing data based on the available cloud-free pixels in satellite images.
Luc Vandenbulcke and Alexander Barth
Ocean Sci., 15, 291–305, https://doi.org/10.5194/os-15-291-2019, https://doi.org/10.5194/os-15-291-2019, 2019
Short summary
Short summary
In operational oceanography, regional and local models use large-scale models (such as those run by CMEMS) for their initial and/or boundary conditions, but unfortunately there is no feedback that improves the large-scale models. The present study aims at replacing normal two-way nesting by a data assimilation technique. This
upscalingmethod is tried out in the north-western Mediterranean Sea using the NEMO model and shows that the basin-scale model does indeed benefit from the nested model.
J.-M. Beckers, A. Barth, I. Tomazic, and A. Alvera-Azcárate
Ocean Sci., 10, 845–862, https://doi.org/10.5194/os-10-845-2014, https://doi.org/10.5194/os-10-845-2014, 2014
J. Marmain, A. Molcard, P. Forget, A. Barth, and Y. Ourmières
Nonlin. Processes Geophys., 21, 659–675, https://doi.org/10.5194/npg-21-659-2014, https://doi.org/10.5194/npg-21-659-2014, 2014
Aida Alvera-Azcárate, Dimitry Van der Zande, Alexander Barth, Antoine Dille, Joppe Massant, and Jean-Marie Beckers
EGUsphere, https://doi.org/10.5194/egusphere-2024-1268, https://doi.org/10.5194/egusphere-2024-1268, 2024
Short summary
Short summary
This work presents an approach to increase the spatial resolution of satellite data and interpolate gaps dur to cloud cover, using a method called DINEOF (Data Interpolating Empirical Orthogonal Functions). The method is tested on turbidity and chlorophyll-a concentration data in the Belgian coastal zone and the North Sea. The results show that we are able to improve the spatial resolution of these data in order to perform analysis of spatial and temporal variability in the coastal regions.
Alexander Barth, Julien Brajard, Aida Alvera-Azcárate, Bayoumy Mohamed, Charles Troupin, and Jean-Marie Beckers
EGUsphere, https://doi.org/10.5194/egusphere-2024-1075, https://doi.org/10.5194/egusphere-2024-1075, 2024
Short summary
Short summary
Most satellite observations have gaps, for example, due to clouds. This paper presents a method to reconstruct missing data in satellite observation of the chlorophyll a concentration in the Black Sea. Rather than giving a single possible reconstructed field, the discussed method provides an ensemble of possible reconstructions using a generative neural network. The resulting ensemble is validated using techniques from numerical weather prediction and ocean modelling.
Francesca Doglioni, Robert Ricker, Benjamin Rabe, Alexander Barth, Charles Troupin, and Torsten Kanzow
Earth Syst. Sci. Data, 15, 225–263, https://doi.org/10.5194/essd-15-225-2023, https://doi.org/10.5194/essd-15-225-2023, 2023
Short summary
Short summary
This paper presents a new satellite-derived gridded dataset, including 10 years of sea surface height and geostrophic velocity at monthly resolution, over the Arctic ice-covered and ice-free regions, up to 88° N. We assess the dataset by comparison to independent satellite and mooring data. Results correlate well with independent satellite data at monthly timescales, and the geostrophic velocity fields can resolve seasonal to interannual variability of boundary currents wider than about 50 km.
Alexander Barth, Aida Alvera-Azcárate, Charles Troupin, and Jean-Marie Beckers
Geosci. Model Dev., 15, 2183–2196, https://doi.org/10.5194/gmd-15-2183-2022, https://doi.org/10.5194/gmd-15-2183-2022, 2022
Short summary
Short summary
Earth-observing satellites provide routine measurement of several ocean parameters. However, these datasets have a significant amount of missing data due to the presence of clouds or other limitations of the employed sensors. This paper describes a method to infer the value of the missing satellite data based on a convolutional autoencoder (a specific type of neural network architecture). The technique also provides a reliable error estimate of the interpolated value.
Malek Belgacem, Katrin Schroeder, Alexander Barth, Charles Troupin, Bruno Pavoni, Patrick Raimbault, Nicole Garcia, Mireno Borghini, and Jacopo Chiggiato
Earth Syst. Sci. Data, 13, 5915–5949, https://doi.org/10.5194/essd-13-5915-2021, https://doi.org/10.5194/essd-13-5915-2021, 2021
Short summary
Short summary
The Mediterranean Sea exhibits an anti-estuarine circulation, responsible for its low productivity. Understanding this peculiar character is still a challenge since there is no exact quantification of nutrient sinks and sources. Because nutrient in situ observations are generally infrequent and scattered in space and time, climatological mapping is often applied to sparse data in order to understand the biogeochemical state of the ocean. The dataset presented here partly addresses these issues.
Arthur Capet, Luc Vandenbulcke, and Marilaure Grégoire
Biogeosciences, 17, 6507–6525, https://doi.org/10.5194/bg-17-6507-2020, https://doi.org/10.5194/bg-17-6507-2020, 2020
Short summary
Short summary
The Black Sea is 2000 m deep, but, due to limited ventilation, only about the upper 100 m contains enough oxygen to support marine life such as fish. This oxygenation depth has been shown to be decreasing (1955–2019). Here, we evidence that atmospheric warming induced a clear shift in an important ventilation mechanism. We highlight the impact of this shift on oxygenation. There are important implications for marine life and carbon and nutrient cycling if this new ventilation regime persists.
Alexander Barth, Aida Alvera-Azcárate, Matjaz Licer, and Jean-Marie Beckers
Geosci. Model Dev., 13, 1609–1622, https://doi.org/10.5194/gmd-13-1609-2020, https://doi.org/10.5194/gmd-13-1609-2020, 2020
Short summary
Short summary
DINCAE is a method for reconstructing missing data in satellite datasets using a neural network. Satellite observations working in the optical and infrared bands are affected by clouds, which obscure part of the ocean underneath. In this paper, a neural network with the structure of a convolutional auto-encoder is developed to reconstruct the missing data based on the available cloud-free pixels in satellite images.
Luc Vandenbulcke and Alexander Barth
Ocean Sci., 15, 291–305, https://doi.org/10.5194/os-15-291-2019, https://doi.org/10.5194/os-15-291-2019, 2019
Short summary
Short summary
In operational oceanography, regional and local models use large-scale models (such as those run by CMEMS) for their initial and/or boundary conditions, but unfortunately there is no feedback that improves the large-scale models. The present study aims at replacing normal two-way nesting by a data assimilation technique. This
upscalingmethod is tried out in the north-western Mediterranean Sea using the NEMO model and shows that the basin-scale model does indeed benefit from the nested model.
Athanasia Iona, Athanasios Theodorou, Sarantis Sofianos, Sylvain Watelet, Charles Troupin, and Jean-Marie Beckers
Earth Syst. Sci. Data, 10, 1829–1842, https://doi.org/10.5194/essd-10-1829-2018, https://doi.org/10.5194/essd-10-1829-2018, 2018
Short summary
Short summary
The paper introduces a new product composed of a set of climatic indices from 1950 to 2015 for the Mediterranean Sea. It is produced from a high-resolution decadal climatology of temperature and salinity on a 1/8 degree regular grid based on the SeaDataNet V2 historical data collection. The climatic indices can contribute to the studies of the long-term variability of the Mediterranean Sea and the better understanding of the complex response of the region to the ongoing global climate change.
Athanasia Iona, Athanasios Theodorou, Sylvain Watelet, Charles Troupin, Jean-Marie Beckers, and Simona Simoncelli
Earth Syst. Sci. Data, 10, 1281–1300, https://doi.org/10.5194/essd-10-1281-2018, https://doi.org/10.5194/essd-10-1281-2018, 2018
Short summary
Short summary
We compute a new, high-resolution hydrographic atlas for the Mediterranean Sea using the Data-Interpolating Variational Analysis technique and the latest SeaDataNet aggregated data collection in an effort to contribute to the studies of the long-term variability of the hydrological characteristics of the Mediterranean region and its climate change.
Arthur Capet, Emil V. Stanev, Jean-Marie Beckers, James W. Murray, and Marilaure Grégoire
Biogeosciences, 13, 1287–1297, https://doi.org/10.5194/bg-13-1287-2016, https://doi.org/10.5194/bg-13-1287-2016, 2016
Short summary
Short summary
We show that the Black Sea oxygen inventory has decreased by 44 % from 1955 to 2015, while oxygen penetration depth decreased from 140 to 90 m. A transient increase of the oxygen inventory during 1985–1995 supported the perception of a stable oxic interface and of a general recovery of the Black Sea after a strong eutrophication phase (1970–1990). Instead, we show that ongoing high oxygen consumption was masked by high ventilation rates, which are now limited by atmospheric warming.
J.-M. Beckers, A. Barth, I. Tomazic, and A. Alvera-Azcárate
Ocean Sci., 10, 845–862, https://doi.org/10.5194/os-10-845-2014, https://doi.org/10.5194/os-10-845-2014, 2014
J. Marmain, A. Molcard, P. Forget, A. Barth, and Y. Ourmières
Nonlin. Processes Geophys., 21, 659–675, https://doi.org/10.5194/npg-21-659-2014, https://doi.org/10.5194/npg-21-659-2014, 2014
A. Capet, J.-M. Beckers, and M. Grégoire
Biogeosciences, 10, 3943–3962, https://doi.org/10.5194/bg-10-3943-2013, https://doi.org/10.5194/bg-10-3943-2013, 2013
Related subject area
Oceanography
An optimal transformation method for inferring ocean tracer sources and sinks
PPCon 1.0: Biogeochemical-Argo profile prediction with 1D convolutional networks
Experimental design for the Marine Ice Sheet–Ocean Model Intercomparison Project – phase 2 (MISOMIP2)
Development of a total variation diminishing (TVD) sea ice transport scheme and its application in an ocean (SCHISM v5.11) and sea ice (Icepack v1.3.4) coupled model on unstructured grids
Spurious numerical mixing under strong tidal forcing: a case study in the south-east Asian seas using the Symphonie model (v3.1.2)
Modelling the water isotope distribution in the Mediterranean Sea using a high-resolution oceanic model (NEMO-MED12-watiso v1.0): evaluation of model results against in situ observations
LIGHT-bgcArgo-1.0: using synthetic float capabilities in E3SMv2 to assess spatiotemporal variability in ocean physics and biogeochemistry
Towards a real-time modeling of global ocean waves by the fully GPU-accelerated spectral wave model WAM6-GPU v1.0
A simple approach to represent precipitation-derived freshwater fluxes into nearshore ocean models: an FVCOM4.1 case study of Quatsino Sound, British Columbia
An optimal transformation method applied to diagnose the ocean carbon budget
Implementation and assessment of a model including mixotrophs and the carbonate cycle (Eco3M_MIX-CarbOx v1.0) in a highly dynamic Mediterranean coastal environment (Bay of Marseille, France) – Part 2: Towards a better representation of total alkalinity when modeling the carbonate system and air–sea CO2 fluxes
DALROMS-NWA12 v1.0, a coupled circulation-ice-biogeochemistry modelling system for the northwest Atlantic Ocean: Development and validation
Development of a novel storm surge inundation model framework for efficient prediction
Skin sea surface temperature schemes in coupled ocean–atmosphere modelling: the impact of chlorophyll-interactive e-folding depth
DELWAVE 1.0: deep learning surrogate model of surface wave climate in the Adriatic Basin
StraitFlux – precise computations of water strait fluxes on various modeling grids
Comparison of the Coastal and Regional Ocean COmmunity model (CROCO) and NCAR-LES in non-hydrostatic simulations
Intercomparisons of Tracker v1.1 and four other ocean particle-tracking software packages in the Regional Ocean Modeling System
CAR36, a regional high-resolution ocean forecasting system for improving drift and beaching of Sargassum in the Caribbean archipelago
Implementation of additional spectral wave field exchanges in a three-dimensional wave–current coupled WAVEWATCH-III (version 6.07) and CROCO (version 1.2) configuration: assessment of their implications for macro-tidal coastal hydrodynamics
Comparison of 4-dimensional variational and ensemble optimal interpolation data assimilation systems using a Regional Ocean Modeling System (v3.4) configuration of the eddy-dominated East Australian Current system
LOCATE v1.0: numerical modelling of floating marine debris dispersion in coastal regions using Parcels v2.4.2
New insights into the South China Sea throughflow and water budget seasonal cycle: evaluation and analysis of a high-resolution configuration of the ocean model SYMPHONIE version 2.4
MQGeometry-1.0: a multi-layer quasi-geostrophic solver on non-rectangular geometries
Parameter estimation for ocean background vertical diffusivity coefficients in the Community Earth System Model (v1.2.1) and its impact on El Niño–Southern Oscillation forecasts
A revised ocean mixed layer model for better simulating the diurnal variation of ocean skin temperature
Great Lakes wave forecast system on high-resolution unstructured meshes
Impact of increased resolution on Arctic Ocean simulations in Ocean Model Intercomparison Project phase 2 (OMIP-2)
Evaluating an accelerated forcing approach for improving computational efficiency in coupled ice sheet-ocean modelling
A high-resolution physical–biogeochemical model for marine resource applications in the northwest Atlantic (MOM6-COBALT-NWA12 v1.0)
A flexible z-layers approach for the accurate representation of free surface flows in a coastal ocean model (SHYFEM v. 7_5_71)
Implementation and assessment of a model including mixotrophs and the carbonate cycle (Eco3M_MIX-CarbOx v1.0) in a highly dynamic Mediterranean coastal environment (Bay of Marseille, France) – Part 1: Evolution of ecosystem composition under limited light and nutrient conditions
Ocean wave tracing v.1: a numerical solver of the wave ray equations for ocean waves on variable currents at arbitrary depths
Design and evaluation of an efficient high-precision ocean surface wave model with a multiscale grid system (MSG_Wav1.0)
Evaluation of the CMCC global eddying ocean model for the Ocean Model Intercomparison Project (OMIP2)
Barents-2.5km v2.0: an operational data-assimilative coupled ocean and sea ice ensemble prediction model for the Barents Sea and Svalbard
Open-ocean tides simulated by ICON-O, version icon-2.6.6
Using Probability Density Functions to Evaluate Models (PDFEM, v1.0) to compare a biogeochemical model with satellite-derived chlorophyll
Data assimilation sensitivity experiments in the East Auckland Current system using 4D-Var
Using the COAsT Python package to develop a standardised validation workflow for ocean physics models
Improving Antarctic Bottom Water precursors in NEMO for climate applications
Formulation, optimization, and sensitivity of NitrOMZv1.0, a biogeochemical model of the nitrogen cycle in oceanic oxygen minimum zones
Waves in SKRIPS: WAVEWATCH III coupling implementation and a case study of Tropical Cyclone Mekunu
Adding sea ice effects to a global operational model (NEMO v3.6) for forecasting total water level: approach and impact
Enhanced ocean wave modeling by including effect of breaking under both deep- and shallow-water conditions
An internal solitary wave forecasting model in the northern South China Sea (ISWFM-NSCS)
The 3D biogeochemical marine mercury cycling model MERCY v2.0 – linking atmospheric Hg to methylmercury in fish
Global seamless tidal simulation using a 3D unstructured-grid model (SCHISM v5.10.0)
Arctic Ocean simulations in the CMIP6 Ocean Model Intercomparison Project (OMIP)
ChemicalDrift 1.0: an open-source Lagrangian chemical-fate and transport model for organic aquatic pollutants
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
Short summary
Short summary
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.
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
Short summary
Short summary
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.
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
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.
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
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.
Kyoko Ohashi, Arnaud Laurent, Christoph Renkl, Jinyu Sheng, Katja Fennel, and Eric Oliver
EGUsphere, https://doi.org/10.5194/egusphere-2024-1372, https://doi.org/10.5194/egusphere-2024-1372, 2024
Short summary
Short summary
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 oceans’ 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.
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
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.
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. Discuss., https://doi.org/10.5194/gmd-2024-23, https://doi.org/10.5194/gmd-2024-23, 2024
Revised manuscript accepted for GMD
Short summary
Short summary
The recently available ERA5 hourly ocean skin temperature (Tint) data is expected to be valuable for various science studies. However, when analyzing the hourly variations of Tint, questions arise about its reliability, the deficiency of which may be related to errors in the ocean mixed layer (OML) model. To address this, we reexamined and corrected significant errors in the OML model. Validation of the simulated SST using the revised OML model against observations demonstrated good agreement.
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
Short summary
Short summary
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
Short summary
Short summary
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.
Qin Zhou, Chen Zhao, Rupert Gladstone, Tore Hattermann, David Gwyther, and Benjamin Galton-Fenzi
Geosci. Model Dev. Discuss., https://doi.org/10.5194/gmd-2023-244, https://doi.org/10.5194/gmd-2023-244, 2024
Revised manuscript accepted for GMD
Short summary
Short summary
We have introduced an "accelerated forcing" approach to address the discrepancy in timescales between ice sheet and ocean models in coupled modelling, by reducing the ocean model simulation duration. We evaluate the approach's applicability and limitations based on idealized coupled models. Our results suggest that, when used carefully, the approach can be a useful tool in coupled ice sheet-ocean modelling, especially relevant to studies on sea level rise projections.
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
Short summary
Short summary
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.
Luca Arpaia, Christian Ferrarin, Marco Bajo, and Georg Umgiesser
Geosci. Model Dev., 16, 6899–6919, https://doi.org/10.5194/gmd-16-6899-2023, https://doi.org/10.5194/gmd-16-6899-2023, 2023
Short summary
Short summary
We propose a discrete multilayer shallow water model based on z-layers which, thanks to the insertion and removal of surface layers, can deal with an arbitrarily large tidal oscillation independently of the vertical resolution. The algorithm is based on a two-step procedure used in numerical simulations with moving boundaries (grid movement followed by a grid topology change, that is, the insertion/removal of surface layers), which avoids the appearance of very thin surface layers.
Lucille Barré, Frédéric Diaz, Thibaut Wagener, France Van Wambeke, Camille Mazoyer, Christophe Yohia, and Christel Pinazo
Geosci. Model Dev., 16, 6701–6739, https://doi.org/10.5194/gmd-16-6701-2023, https://doi.org/10.5194/gmd-16-6701-2023, 2023
Short summary
Short summary
While several studies have shown that mixotrophs play a crucial role in the carbon cycle, the impact of environmental forcings on their dynamics remains poorly investigated. Using a biogeochemical model that considers mixotrophs, we study the impact of light and nutrient concentration on the ecosystem composition in a highly dynamic Mediterranean coastal area: the Bay of Marseille. We show that mixotrophs cope better with oligotrophic conditions compared to strict auto- and heterotrophs.
Trygve Halsne, Kai Håkon Christensen, Gaute Hope, and Øyvind Breivik
Geosci. Model Dev., 16, 6515–6530, https://doi.org/10.5194/gmd-16-6515-2023, https://doi.org/10.5194/gmd-16-6515-2023, 2023
Short summary
Short summary
Surface waves that propagate in oceanic or coastal environments get influenced by their surroundings. Changes in the ambient current or the depth profile affect the wave propagation path, and the change in wave direction is called refraction. Some analytical solutions to the governing equations exist under ideal conditions, but for realistic situations, the equations must be solved numerically. Here we present such a numerical solver under an open-source license.
Jiangyu Li, Shaoqing Zhang, Qingxiang Liu, Xiaolin Yu, and Zhiwei Zhang
Geosci. Model Dev., 16, 6393–6412, https://doi.org/10.5194/gmd-16-6393-2023, https://doi.org/10.5194/gmd-16-6393-2023, 2023
Short summary
Short summary
Ocean surface waves play an important role in the air–sea interface but are rarely activated in high-resolution Earth system simulations due to their expensive computational costs. To alleviate this situation, this paper designs a new wave modeling framework with a multiscale grid system. Evaluations of a series of numerical experiments show that it has good feasibility and applicability in the WAVEWATCH III model, WW3, and can achieve the goals of efficient and high-precision wave simulation.
Doroteaciro Iovino, Pier Giuseppe Fogli, and Simona Masina
Geosci. Model Dev., 16, 6127–6159, https://doi.org/10.5194/gmd-16-6127-2023, https://doi.org/10.5194/gmd-16-6127-2023, 2023
Short summary
Short summary
This paper describes the model performance of three global ocean–sea ice configurations, from non-eddying (1°) to eddy-rich (1/16°) resolutions. Model simulations are obtained following the Ocean Model Intercomparison Project phase 2 (OMIP2) protocol. We compare key global climate variables across the three models and against observations, emphasizing the relative advantages and disadvantages of running forced ocean–sea ice models at higher resolution.
Johannes Röhrs, Yvonne Gusdal, Edel S. U. Rikardsen, Marina Durán Moro, Jostein Brændshøi, Nils Melsom Kristensen, Sindre Fritzner, Keguang Wang, Ann Kristin Sperrevik, Martina Idžanović, Thomas Lavergne, Jens Boldingh Debernard, and Kai H. Christensen
Geosci. Model Dev., 16, 5401–5426, https://doi.org/10.5194/gmd-16-5401-2023, https://doi.org/10.5194/gmd-16-5401-2023, 2023
Short summary
Short summary
A model to predict ocean currents, temperature, and sea ice is presented, covering the Barents Sea and northern Norway. To quantify forecast uncertainties, the model calculates ensemble forecasts with 24 realizations of ocean and ice conditions. Observations from satellites, buoys, and ships are ingested by the model. The model forecasts are compared with observations, and we show that the ocean model has skill in predicting sea surface temperatures.
Jin-Song von Storch, Eileen Hertwig, Veit Lüschow, Nils Brüggemann, Helmuth Haak, Peter Korn, and Vikram Singh
Geosci. Model Dev., 16, 5179–5196, https://doi.org/10.5194/gmd-16-5179-2023, https://doi.org/10.5194/gmd-16-5179-2023, 2023
Short summary
Short summary
The new ocean general circulation model ICON-O is developed for running experiments at kilometer scales and beyond. One targeted application is to simulate internal tides crucial for ocean mixing. To ensure their realism, which is difficult to assess, we evaluate the barotropic tides that generate internal tides. We show that ICON-O is able to realistically simulate the major aspects of the observed barotropic tides and discuss the aspects that impact the quality of the simulated tides.
Bror F. Jönsson, Christopher L. Follett, Jacob Bien, Stephanie Dutkiewicz, Sangwon Hyun, Gemma Kulk, Gael L. Forget, Christian Müller, Marie-Fanny Racault, Christopher N. Hill, Thomas Jackson, and Shubha Sathyendranath
Geosci. Model Dev., 16, 4639–4657, https://doi.org/10.5194/gmd-16-4639-2023, https://doi.org/10.5194/gmd-16-4639-2023, 2023
Short summary
Short summary
While biogeochemical models and satellite-derived ocean color data provide unprecedented information, it is problematic to compare them. Here, we present a new approach based on comparing probability density distributions of model and satellite properties to assess model skills. We also introduce Earth mover's distances as a novel and powerful metric to quantify the misfit between models and observations. We find that how 3D chlorophyll fields are aggregated can be a significant source of error.
Rafael Santana, Helen Macdonald, Joanne O'Callaghan, Brian Powell, Sarah Wakes, and Sutara H. Suanda
Geosci. Model Dev., 16, 3675–3698, https://doi.org/10.5194/gmd-16-3675-2023, https://doi.org/10.5194/gmd-16-3675-2023, 2023
Short summary
Short summary
We show the importance of assimilating subsurface temperature and velocity data in a model of the East Auckland Current. Assimilation of velocity increased the representation of large oceanic vortexes. Assimilation of temperature is needed to correctly simulate temperatures around 100 m depth, which is the most difficult region to simulate in ocean models. Our simulations showed improved results in comparison to the US Navy global model and highlight the importance of regional models.
David Byrne, Jeff Polton, Enda O'Dea, and Joanne Williams
Geosci. Model Dev., 16, 3749–3764, https://doi.org/10.5194/gmd-16-3749-2023, https://doi.org/10.5194/gmd-16-3749-2023, 2023
Short summary
Short summary
Validation is a crucial step during the development of models for ocean simulation. The purpose of validation is to assess how accurate a model is. It is most commonly done by comparing output from a model to actual observations. In this paper, we introduce and demonstrate usage of the COAsT Python package to standardise the validation process for physical ocean models. We also discuss our five guiding principles for standardised validation.
Katherine Hutchinson, Julie Deshayes, Christian Éthé, Clément Rousset, Casimir de Lavergne, Martin Vancoppenolle, Nicolas C. Jourdain, and Pierre Mathiot
Geosci. Model Dev., 16, 3629–3650, https://doi.org/10.5194/gmd-16-3629-2023, https://doi.org/10.5194/gmd-16-3629-2023, 2023
Short summary
Short summary
Bottom Water constitutes the lower half of the ocean’s overturning system and is primarily formed in the Weddell and Ross Sea in the Antarctic due to interactions between the atmosphere, ocean, sea ice and ice shelves. Here we use a global ocean 1° resolution model with explicit representation of the three large ice shelves important for the formation of the parent waters of Bottom Water. We find doing so reduces salt biases, improves water mass realism and gives realistic ice shelf melt rates.
Daniele Bianchi, Daniel McCoy, and Simon Yang
Geosci. Model Dev., 16, 3581–3609, https://doi.org/10.5194/gmd-16-3581-2023, https://doi.org/10.5194/gmd-16-3581-2023, 2023
Short summary
Short summary
We present NitrOMZ, a new model of the oceanic nitrogen cycle that simulates chemical transformations within oxygen minimum zones (OMZs). We describe the model formulation and its implementation in a one-dimensional representation of the water column before evaluating its ability to reproduce observations in the eastern tropical South Pacific. We conclude by describing the model sensitivity to parameter choices and environmental factors and its application to nitrogen cycling in the ocean.
Rui Sun, Alison Cobb, Ana B. Villas Bôas, Sabique Langodan, Aneesh C. Subramanian, Matthew R. Mazloff, Bruce D. Cornuelle, Arthur J. Miller, Raju Pathak, and Ibrahim Hoteit
Geosci. Model Dev., 16, 3435–3458, https://doi.org/10.5194/gmd-16-3435-2023, https://doi.org/10.5194/gmd-16-3435-2023, 2023
Short summary
Short summary
In this work, we integrated the WAVEWATCH III model into the regional coupled model SKRIPS. We then performed a case study using the newly implemented model to study Tropical Cyclone Mekunu, which occurred in the Arabian Sea. We found that the coupled model better simulates the cyclone than the uncoupled model, but the impact of waves on the cyclone is not significant. However, the waves change the sea surface temperature and mixed layer, especially in the cold waves produced due to the cyclone.
Pengcheng Wang and Natacha B. Bernier
Geosci. Model Dev., 16, 3335–3354, https://doi.org/10.5194/gmd-16-3335-2023, https://doi.org/10.5194/gmd-16-3335-2023, 2023
Short summary
Short summary
Effects of sea ice are typically neglected in operational flood forecast systems. In this work, we capture these effects via the addition of a parameterized ice–ocean stress. The parameterization takes advantage of forecast fields from an advanced ice–ocean model and features a novel, consistent representation of the tidal relative ice–ocean velocity. The new parameterization leads to improved forecasts of tides and storm surges in polar regions. Associated physical processes are discussed.
Yue Xu and Xiping Yu
Geosci. Model Dev., 16, 2811–2831, https://doi.org/10.5194/gmd-16-2811-2023, https://doi.org/10.5194/gmd-16-2811-2023, 2023
Short summary
Short summary
An accurate description of the wind energy input into ocean waves is crucial to ocean wave modeling, and a physics-based consideration of the effect of wave breaking is absolutely necessary to obtain such an accurate description, particularly under extreme conditions. This study evaluates the performance of a recently improved formula, taking into account not only the effect of breaking but also the effect of airflow separation on the leeside of steep wave crests in a reasonably consistent way.
Yankun Gong, Xueen Chen, Jiexin Xu, Jieshuo Xie, Zhiwu Chen, Yinghui He, and Shuqun Cai
Geosci. Model Dev., 16, 2851–2871, https://doi.org/10.5194/gmd-16-2851-2023, https://doi.org/10.5194/gmd-16-2851-2023, 2023
Short summary
Short summary
Internal solitary waves (ISWs) play crucial roles in mass transport and ocean mixing in the northern South China Sea. Massive numerical investigations have been conducted in this region, but there was no systematic evaluation of a three-dimensional model about precisely simulating ISWs. Here, an ISW forecasting model is employed to evaluate the roles of resolution, tidal forcing and stratification in accurately reproducing wave properties via comparison to field and remote-sensing observations.
Johannes Bieser, David J. Amptmeijer, Ute Daewel, Joachim Kuss, Anne L. Soerensen, and Corinna Schrum
Geosci. Model Dev., 16, 2649–2688, https://doi.org/10.5194/gmd-16-2649-2023, https://doi.org/10.5194/gmd-16-2649-2023, 2023
Short summary
Short summary
MERCY is a 3D model to study mercury (Hg) cycling in the ocean. Hg is a highly harmful pollutant regulated by the UN Minamata Convention on Mercury due to widespread human emissions. These emissions eventually reach the oceans, where Hg transforms into the even more toxic and bioaccumulative pollutant methylmercury. MERCY predicts the fate of Hg in the ocean and its buildup in the food chain. It is the first model to consider Hg accumulation in fish, a major source of Hg exposure for humans.
Y. Joseph Zhang, Tomas Fernandez-Montblanc, William Pringle, Hao-Cheng Yu, Linlin Cui, and Saeed Moghimi
Geosci. Model Dev., 16, 2565–2581, https://doi.org/10.5194/gmd-16-2565-2023, https://doi.org/10.5194/gmd-16-2565-2023, 2023
Short summary
Short summary
Simulating global ocean from deep basins to coastal areas is a daunting task but is important for disaster mitigation efforts. We present a new 3D global ocean model on flexible mesh to study both tidal and nontidal processes and total water prediction. We demonstrate the potential for
seamlesssimulation, on a single mesh, from the global ocean to a few estuaries along the US West Coast. The model can serve as the backbone of a global tide surge and compound flooding forecasting framework.
Qi Shu, Qiang Wang, Chuncheng Guo, Zhenya Song, Shizhu Wang, Yan He, and Fangli Qiao
Geosci. Model Dev., 16, 2539–2563, https://doi.org/10.5194/gmd-16-2539-2023, https://doi.org/10.5194/gmd-16-2539-2023, 2023
Short summary
Short summary
Ocean models are often used for scientific studies on the Arctic Ocean. Here the Arctic Ocean simulations by state-of-the-art global ocean–sea-ice models participating in the Ocean Model Intercomparison Project (OMIP) were evaluated. The simulations on Arctic Ocean hydrography, freshwater content, stratification, sea surface height, and gateway transports were assessed and the common biases were detected. The simulations forced by different atmospheric forcing were also evaluated.
Manuel Aghito, Loris Calgaro, Knut-Frode Dagestad, Christian Ferrarin, Antonio Marcomini, Øyvind Breivik, and Lars Robert Hole
Geosci. Model Dev., 16, 2477–2494, https://doi.org/10.5194/gmd-16-2477-2023, https://doi.org/10.5194/gmd-16-2477-2023, 2023
Short summary
Short summary
The newly developed ChemicalDrift model can simulate the transport and fate of chemicals in the ocean and in coastal regions. The model combines ocean physics, including transport due to currents, turbulence due to surface winds and the sinking of particles to the sea floor, with ocean chemistry, such as the partitioning, the degradation and the evaporation of chemicals. The model will be utilized for risk assessment of ocean and sea-floor contamination from pollutants emitted from shipping.
Cited articles
Arfken, G.: Mathematical Methods for Physicists, Academic Press, Orlando, FL, 3rd Edn., 795 pp., 1985.
Bannister, R. N.: A review of forecast error covariance statistics in atmospheric variational data assimilation. II: Modelling the forecast error covariance statistics, Q. J. R. Meteorol. Soc., 134, 1971–1996, https://doi.org/10.1002/qj.340, 2008.
Barth, A., Alvera-Azcárate, A., Troupin, C., Ouberdous, M., and Beckers, J.-M.: A web interface for griding arbitrarily distributed in situ data based on Data-Interpolating Variational Analysis (DIVA), Adv. Geosci., 28, 29–37, https://doi.org/10.5194/adgeo-28-29-2010, 2010.
Beckers, J.-M., Barth, A., and Alvera-Azcárate, A.: DINEOF reconstruction of clouded images including error maps – application to the Sea-Surface Temperature around Corsican Island, Ocean Sci., 2, 183–199, https://doi.org/10.5194/os-2-183-2006, 2006.
Bennett, A. F., Chua, B. S., and Leslie, L. M.: Generalized inversion of a global numerical weather prediction model, Meteor. Atmos. Phys., 60, 165–178, 1996.
Bennett, A. F., Chua, B., and Leslie, L.: Generalized inversion of a global numerical weather prediction model, II: Analysis and implementation, Meteor. Atmos. Phys., 62, 129–140, https://doi.org/10.1007/BF01029698, 1997.
Benzi, M.: Preconditioning Techniques for Large Linear Systems: A Survey, J. Comput. Phys., 182, 418–477, https://doi.org/10.1006/jcph.2002.7176, 2002.
Brankart, J.-M. and Brasseur, P.: The general circulation in the Mediterranean Sea: a climatological approach., J. Marine Sys., 18, 41–70, https://doi.org/10.1016/S0924-7963(98)00005-0, 1998.
Brankart, J.-M. and Brasseur, P.: Optimal analysis of in situ data in the Western Mediterranean using statistics and cross-validation., J. Atmos.\ Ocean. Tech., 13, 477–491, https://doi.org/10.1175/1520-0426(1996)013<0477:OAOISD>2.0.CO;2, 1996.
Brasseur, P.: Reconstitution de champs d'observations o\-cé\-a\-no\-gra\-phi\-ques par le Modèle Variationnel Inverse: Méthodologie et Applications., Ph.D. thesis, Université de Liège, Collection des publications, Sciences appliquées, Liège, Belgium, 1994.
Brasseur, P. and Haus, J.: Application of a 3–D variational inverse model to the analysis of ecohydrodynamic data in the Northern Bering and Southern Chuckchi Seas., J. Marine Sys., 1, 383–401, https://doi.org/10.1016/0924-7963(91)90006-G, 1991.
Brasseur, P., Beckers, J.-M., Brankart, J.-M., and Schoenauen, R.: Seasonal Temperature and Salinity Fields in the Mediterranean Sea: Climatological Analyses of an Historical Data Set., Deep-Sea Res., 43, 159–192, https://doi.org/10.1016/0967-0637(96)00012-X, 1996.
Bretherton, F. P., Davis, R. E., and Fandry, C. B.: A technique for objective analysis and design of oceanographic experiment applied to MODE-73., Deep-Sea Res., 23, 559–582, https://doi.org/10.1016/0011-7471(76)90001-2, 1976.
Buongiorno Nardelli, B.: A novel approach for the high-resolution interpolation of in situ sea surface salinity, J. Atmos. Ocean. Tech., 29, 867–879, https://doi.org/10.1175/JTECH-D-11-00099.1, 2012.
Buongiorno Nardelli, B., Colella, S., Santoleri, R., Guarracino, M., and Kholod, A.: A re-analysis of Black Sea surface temperature, J. Marine Sys., 79, 50–64, https://doi.org/10.1016/j.jmarsys.2009.07.001, 2010.
Carrier, M. J. and Ngodock, H.: Background-error correlation model based on the implicit solution of a diffusion equation, Ocean Modell., 35, 45 – 53, https://doi.org/10.1016/j.ocemod.2010.06.003, 2010.
Carton, J. and Hackert, E.: Data assimilation applied to the temperature and circulation in the tropical Atlantic, 1983-84, J. Phys. Oceanogr., 20, 1150–1165, https://doi.org/10.1175/1520-0485(1990)020<1150:DAATTT>2.0.CO;2, 1990.
Chaves, J. C., Nehrbass, J., Guilfoos, B., Gardiner, J., Ahalt, S., Krishnamurthy, A., Unpingco, J., Chalker, A., Warnock, A., and Samsi, S.: Octave and Python: High-level scripting languages productivity and performance evaluation, in: HPCMP Users Group Conference, 2006, 429–434, IEEE, 2006.
Chen, Y., Davis, T. A., Hager, W. W., and Rajamanickam, S.: Algorithm 887: CHOLMOD, Supernodal Sparse Cholesky Factorization and Update/Downdate, ACM Trans. Math. Soft., 35, 22:1–22:14, https://doi.org/10.1145/1391989.1391995, 2008.
Chua, B. S. and Bennett, A. F.: An inverse ocean modeling system, Ocean Modell., 3, 137–165, https://doi.org/10.1016/S1463-5003(01)00006-3, 2001.
Cohn, S. E., da Silva, A., Guo, J., Sienkiewicz, M., and Lamich, D.: Assessing the effects of data selection with the DAO Physical-space Statistical Analysis System, Mon. Weather Rev., 126, 2913–2926, 1998.
Courtier, P.: Dual formulation of four-dimensional variational assimilation, Q. J. R. Meteorol. Soc., 123, 2449–2461, https://doi.org/10.1002/qj.49712354414, 1997.
Courtier, P., Thépaut, J.-N., and Hollingsworth, A.: A strategy for operational implementation of 4D-Var, using an incremental approach, Q. J.\ R. Meteorol. Soc., 120, 1367–1387, https://doi.org/10.1002/qj.49712051912, 1994.
Courtier, P., Andersson, E., Heckley, W., Pailleux, J., Vasiljevic, D., Hamrud, M., Hollingsworth, A., Rabier, F., and Fisher, M.: The ECMWF implementation of three-dimensional variational assimilation (3D-Var). I: Formulation, Q. J. R. Meteorol. Soc., 124, 1783–1808, https://doi.org/10.1002/qj.49712455002, 1998.
Cullen, M. J. P.: Four-dimensional variational data assimilation: A new formulation of the background-error covariance matrix based on a potential-vorticity representation, Q. J. R. Meteorol. Soc., 129, 2777–2796, https://doi.org/10.1256/qj.02.10, 2003.
Daley, R.: Atmospheric Data Analysis, Cambridge University Press, New York, 457 pp., 1991.
Davis, T. A. and Hager, W. W.: Dynamic supernodes in sparse Cholesky update/downdate and triangular solves, ACM Trans. Math. Soft., 35, 27:1–27:23, https://doi.org/10.1145/1462173.1462176, 2009.
Dee, D. P. and da Silva, A. M.: The Choice of Variable for Atmospheric Moisture Analysis, Mon. Weather Rev., 131, 155–171, https://doi.org/10.1175/1520-0493(2003)131<0155:TCOVFA>2.0.CO;2, 2003.
Derber, J. and Rosati, A.: A global oceanic data assimilation system, J. Phys. Oceanogr., 19, 1333–1347, https://doi.org/10.1175/1520-0485(1989)019<1333:AGODAS>2.0.CO;2, 1989.
Dhatt, G. and Touzot, G.: Une présentation de la méthode des éléments finis., in: Collection Université de Compiègne, Paris, S. A. Maloine, editor, 1984.
Dobricic, S. and Pinardi, N.: An oceanographic three-dimensional variational data assimilation scheme, Ocean Modell., 22, 89–105, https://doi.org/10.1016/j.ocemod.2008.01.004, 2008.
Evensen, G.: Data assimilation: the Ensemble Kalman Filter, Springer, 279 pp., 2007.
Gandin, L. S.: Objective analysis of meteorological fields, Israel Program for Scientific Translation, Jerusalem, 242 pp., 1965.
Gaspari, G. and Cohn, S. E.: Construction of correlation functions in two and three dimensions, Q. J. R. Meteorol. Soc., 125, 723–757, https://doi.org/10.1002/qj.49712555417, 1999.
Gauthier, P., Charette, C., Fillion, L., Koclas, P., and Laroche, S.: Implementation of a 3d variational data assimilation system at the Canadian Meteorological Centre, Part I: The global analysis, Atmos.-Ocean, 37, 103–156, https://doi.org/10.1080/07055900.1999.9649623, 1999.
Gneiting, T.: Correlation functions for atmospheric data analysis, Q. J.\ R.\ Meteorol. Soc., 125, 2449–2464, https://doi.org/10.1002/qj.49712555906, 1999.
Golub, G. H. and Van Loan, C. F.: Matrix Computations, Johns Hopkins University Press, Baltimore, 3rd Edn., 1996.
Guinehut, S., Larnicol, G., and Traon, P. L.: Design of an array of profiling floats in the North Atlantic from model simulations, J. Marine Sys., 35, 1–9, https://doi.org/10.1016/S0924-7963(02)00042-8, 2002.
Guttorp, P. and Gneiting, T.: Studies in the history of probability and statistics XLIX On the Matérn correlation family, Biometrika, 93, 989–995, https://doi.org/10.1093/biomet/93.4.989, 2006.
Haben, S. A., Lawless, A. S., and Nichols, N. K.: Conditioning of incremental variational data assimilation, with application to the Met Office system, Tellus A, 63, 782–792, https://doi.org/10.1111/j.1600-0870.2011.00527.x, 2011.
Hayden, C. M., R. J. P.: Recursive Filter Objective Analysis of Meteorological Fields: Applications to NESDIS Operational Processing, J. Appl. Meteor., 34, 3–15, https://doi.org/10.1175/1520-0450-34.1.3, 1995.
Høyer, J. L. and She, J.: Optimal interpolation of sea surface temperature for the North Sea and Baltic Sea, J. Marine Sys., 65, 176–189, https://doi.org/10.1016/j.jmarsys.2005.03.008, 2007.
Jones, M. T. and Plassmann, P. E.: An improved incomplete Cholesky factorization, ACM Trans. Math. Softw., 21, 5–17, https://doi.org/10.1145/200979.200981, 1995.
Kaplan, A., Kushnir, Y., Cane, M., and Blumenthal, M.: Reduced Space Optimal Analysis for Historical Datasets: 136 Years of Atlantic Sea Surface Temperatures, J. Geophys. Res., 102, 27835–27860, https://doi.org/10.1029/97JC01734, 1997.
Legler, D. M. and Navon, I. M.: VARIATM-A FORTRAN program for objective analysis of pseudostress wind fields using large-scale conjugate-gradient minimization, Comput. Geosci., 17, 1–21, https://doi.org/10.1016/0098-3004(91)90077-Q, 1991.
Leros, A., Andreatos, A., and Zagorianos, A.: Matlab-Octave science and engineering benchmarking and comparison, in: Proceedings of the 14th WSEAS international conference on Computers: part of the 14th WSEAS CSCC multiconference, 746–754, 2010.
Lorenc, A. C.: Iterative analysis using covariance functions and filters, Q.\ J. R. Meteorol. Soc., 118, 569–591, https://doi.org/10.1002/qj.49711850509, 1992.
Lorenc, A. C.: Development of an operational variational assimilation scheme, J. Meteor. Soc. Japan, 75, 339–346, 1997.
Lorenc, A. C., Ballard, S. P., Bell, R. S., Ingleby, N. B., Andrews, P. L. F., Barker, D. M., Bray, J. R., Clayton, A. M., Dalby, T., Li, D., Payne, T. J., and Saunders, F. W.: The Met Office global 3-dimensional variational data assimilation scheme, Q. J. R. Meteorol. Soc., 126, 2991–3012, https://doi.org/10.1002/qj.49712657002, 2000.
Lorenzo, E. D., Moore, A. M., Arango, H. G., Cornuelle, B. D., Miller, A. J., Powell, B., Chua, B. S., and Bennett, A. F.: Weak and strong constraint data assimilation in the inverse Regional Ocean Modeling System (ROMS): Development and application for a baroclinic coastal upwelling system, Ocean Modell., 16, 160–187, https://doi.org/10.1016/j.ocemod.2006.08.002, 2007.
Martin, M. J., Hines, A., and Bell, M. J.: Data assimilation in the FOAM operational short-range ocean forecasting system: a description of the scheme and its impact, Q. J. R. Meteorol. Soc., 133, 981–995, https://doi.org/10.1002/qj.74, 2007.
Matérn, B.: Spatial Variation, Springer-Verlag, Berlin, 2nd Edn., 1986.
Mathiot, P., Goosse, H., Fichefet, T., Barnier, B., and Gallée, H.: Modelling the seasonal variability of the Antarctic Slope Current, Ocean Sci., 7, 455–470, https://doi.org/10.5194/os-7-455-2011, 2011.
McIntosh, P. C.: Oceanographic data interpolation: Objective analysis and splines, J. Geophys. Res., 95, 13529–13541, https://doi.org/10.1029/JC095iC08p13529, 1990.
Mirouze, I. and Weaver, A. T.: Representation of correlation functions in variational assimilation using an implicit diffusion operator, Q. J. R.\ Meteorol. Soc., 136, 1421–1443, https://doi.org/10.1002/qj.643, 2010.
Moore, A. M., Arango, H. G., Broquet, G., Edwards, C., Veneziani, M., Powell, B., Foley, D., Doyle, J. D., Costa, D., and Robinson, P.: The Regional Ocean Modeling System (ROMS) 4-dimensional variational data assimilation systems: Part II – Performance and application to the California Current System, Prog. Oceanog., 91, 50–73, https://doi.org/10.1016/j.pocean.2011.05.003, 2011a.
Moore, A. M., Arango, H. G., Broquet, G., Powell, B. S., Weaver, A. T., and Zavala-Garay, J.: The Regional Ocean Modeling System (ROMS) 4-dimensional variational data assimilation systems: Part I – System overview and formulation, Prog. Oceanog., 91, 34–49, https://doi.org/10.1016/j.pocean.2011.05.004, 2011b.
Muccino, J. C., Luo, H., Arango, H. G., Haidvogel, D., Levin, J. C., Bennett, A. F., Chua, B. S., Egbert, G. D., Cornuelle, B. D., Miller, A. J., Lorenzo, E. D., Moore, A. M., and Zaron, E. D.: The Inverse Ocean Modeling System. Part II: Applications, J. Atmos. Ocean. Tech., 25, 1623–1637, https://doi.org/10.1175/2008JTECHO522.1, 2008.
Nelder, J. A. and Mead, R.: A simplex method for function minimization, Comput. J., 7, 308–313, https://doi.org/10.1093/comjnl/7.4.308, 1965.
Nerger, L., Janjić, T., Schröter, J., and Hiller, W.: A regulated localization scheme for ensemble-based Kalman filters, Q. J. R. Meteorol.\ Soc., 138, 802–812, https://doi.org/10.1002/qj.945, 2012.
Purser, R., Wu, W.-S., Parish, D., and Roberts, N.: Numerical aspects of the application of recursive filters to variational statistical analysis. Part II: spatially inhomogeneous and anisotropic covariances, Mon. Weather Rev., 131, 1524–1535, https://doi.org/10.1175//2543.1, 2003a.
Purser, R. J., Wu, W.-S., Parrish, D. F., and Roberts, N. M.: Numerical Aspects of the Application of Recursive Filters to Variational Statistical Analysis. Part I: Spatially Homogeneous and Isotropic Gaussian Covariances, Mon. Weather Rev., 131, 1524–1535, https://doi.org/10.1175//1520-0493(2003)131<1524:NAOTAO>2.0.CO;2, 2003b.
Rabier, F. and Courtier, P.: Four-dimensional assimilation in the presence of baroclinic instability, Q. J. R. Meteorol. Soc., 118, 649–672, https://doi.org/10.1002/qj.49711850604, 1992.
Rabier, F., Jarvinen, H., Klinker, E., Mahfouf, J.-F., and Simmons, A.: The ECMWF operational implementation of four-dimensional variational assimilation. I: Experimental results with simplified physics, Q. J. R.\ Meteorol. Soc., 126, 1143–1170, https://doi.org/10.1002/qj.49712656415, 2000.
Rayner, N. A., Parker, D. E., Horton, E. B., Folland, C. K., Alexander, L. V., Rowell, D. P., Kent, E. C., and Kaplan, A.: Global analyses of sea surface temperature, sea ice, and night marine air temperature since the late nineteenth century, J. Geophys. Res., 108, 4407, https://doi.org/10.1029/2002JD002670, 2003.
Roberts-Jones, J., Fiedler, E. K., and Martin, M. J.: Daily, Global, High-Resolution SST and Sea Ice Reanalysis for 1985–2007 Using the OSTIA System, J. Climate, 25, 6215–6232, https://doi.org/10.1175/JCLI-D-11-00648.1, 2012.
Robinson, A. R.: Physical processes, field estimation and an approach to interdisciplinary ocean modeling, Earth-Sci. Rev., 40, 3–54, https://doi.org/10.1016/0012-8252(95)00030-5, 1996.
Troupin, C., Machin, F., Ouberdous, M., Sirjacobs, D., Barth, A., and Beckers, J.-M.: High-resolution Climatology of the North-East Atlantic using Data-Interpolating Variational Analysis (\textsfDiva), J. Geophys. Res., 115, C08005, https://doi.org/10.1029/2009JC005512, 2010.
Troupin, C., Barth, A., Sirjacobs, D., Ouberdous, M., Brankart, J.-M., Brasseur, P., Rixen, M., Alvera-Azcárate, A., Belounis, M., Capet, A., Lenartz, F., Toussaint, M.-E., and Beckers, J.-M.: Generation of analysis and consistent error fields using the Data Interpolating Variational Analysis (DIVA), Ocean Modell., 52–53, 90–101, https://doi.org/10.1016/j.ocemod.2012.05.002, 2012.
Štajner, I., Riish\ojgaard, L. P., and Rood, R. B.: The GEOS ozone data assimilation system: Specification of error statistics, Q. J. R.\ Meteorol. Soc., 127, 1069–1094, https://doi.org/10.1002/qj.49712757320, 2001.
Wahba, G.: Spline models for observational data, vol. 59 of CBM-NSF Regional Conference Series in Applied Mathematics\/, SIAM J. Appl. Math., Philadelphia, PA, 169 pp., 1990.
Wahba, G. and Wendelberger, J.: Some new mathematical methods for variational objective analysis using splines and cross validation., Mon. Weather Rev., 108, 1122–1143, https://doi.org/10.1175/1520-0493(1980)108<1122:SNMMFV>2.0.CO;2, 1980.
Weaver, A. T. and Courtier, P.: Correlation modelling on the sphere using a generalized diffusion equation, Q. J. R. Meteorol. Soc., 127, 1815–1842, https://doi.org/10.1002/qj.49712757518, 2001.
Weaver, A. T. and Mirouze, I.: On the diffusion equation and its application to isotropic and anisotropic correlation modelling in variational assimilation, Q. J. R. Meteorol. Soc., 139, 242–260, https://doi.org/10.1002/qj.1955, 2013.
Weaver, A. T., Vialard, J., and Anderson, D. L. T.: Three- and Four-Dimensional Variational Assimilation with a General Circulation Model of the Tropical Pacific Ocean. Part I: Formulation, Internal Diagnostics, and Consistency Checks, Mon. Weather Rev., 131, 1360–1378, https://doi.org/10.1175/1520-0493(2003)131<1360:TAFVAW>2.0.CO;2, 2003.
Yaremchuk, M. and Sentchev, A.: Mapping radar-derived sea surface currents with a variational method, Cont. Shelf Res., 29, 1711–1722, https://doi.org/10.1016/j.csr.2009.05.016, c09009, 2009.
Yari, S., Kovačević, V., Cardin, V., Gačić, M., and Bryden, H. L.: Direct estimate of water, heat, and salt transport through the Strait of Otranto, J. Geophys. Res., 117, C09009 https://doi.org/10.1029/2012JC007936, 2012.
Zaron, E. D., Chavanne, C., Egbert, G. D., and Flament, P.: Baroclinic tidal generation in the Kauai Channel inferred from high-frequency radio Doppler current meters, Dyn. Atmos. Oceans, 48, 93–120, https://doi.org/10.1016/j.dynatmoce.2009.03.002, 2009.
