The evolution of a non-autonomous chaotic system under non-periodic forcing: a climate change example

Complex Earth System Models are widely utilised to make conditional statements about the future climate under some assumptions about changes in future atmospheric greenhouse gas concentrations; these statements are often referred to as climate projections. The models themselves are high-dimensional nonlinear systems and it is common to discuss their behaviour in terms of attractors and low-dimensional nonlinear systems such as the canonical Lorenz `63 system. In a non-autonomous situation, for instance due to anthropogenic climate change, the relevant object is sometimes considered to be the pullback or snapshot attractor. The pullback attractor, however, is a collection of {\em all} plausible states of the system at a given time and therefore does not take into consideration our knowledge of the current state of the Earth System when making climate projections, and are therefore not very informative regarding annual to multi-decadal climate projections. In this article, we approach the problem of measuring and interpreting the mid-term climate of a model by using a low-dimensional, climate-like, nonlinear system with three timescales of variability, and non-periodic forcing. We introduce the concept of an {\em evolution set} which is dependent on the starting state of the system, and explore its links to different types of initial condition uncertainty and the rate of external forcing. We define the {\em convergence time} as the time that it takes for the distribution of one of the dependent variables to lose memory of its initial conditions. We suspect a connection between convergence times and the classical concept of mixing times but the precise nature of this connection needs to be explored. These results have implications for the design of influential climate and Earth System Model ensembles, and raise a number of issues of mathematical interest.Comment: The model output data used in this study is freely available on Zenodo: https://doi.org/10.5281/zenodo.836802

Seasonality in Carbon Flux Attenuation Explains Spatial Variability in Transfer Efficiency

AbstractEach year, the biological carbon pump (BCP) transports large quantities of carbon from the ocean surface to the interior. The efficiency of this transfer varies geographically, and is a key determinant of the atmosphere‐ocean carbon dioxide balance. Traditionally, the attention has been focused on explaining perceived geographical variations in this transfer efficiency (TE) in an attempt to understand it, an approach that has led to conflicting results. Here we combine observations and modeling to show that the spatial variability in TE can instead be explained by the seasonal variability in carbon flux attenuation. We also show that seasonality can explain the contrast between known global estimates of TE, due to differences in the date and duration of sampling. Our results suggest caution in the mechanistic interpretation of annual‐mean patterns in TE and demonstrates that seasonally and spatially resolved data sets and models might be required to generate accurate evaluations of the BCP.</jats:p

The biological carbon pump in CMIP6 models: 21st century trends and uncertainties

The biological carbon pump (BCP) stores ∼1,700 Pg C from the atmosphere in the ocean interior, but the magnitude and direction of future changes in carbon sequestration by the BCP are uncertain. We quantify global trends in export production, sinking organic carbon fluxes, and sequestered carbon in the latest Coupled Model Intercomparison Project Phase 6 (CMIP6) future projections, finding a consistent 19 to 48 Pg C increase in carbon sequestration over the 21st century for the SSP3-7.0 scenario, equivalent to 5 to 17% of the total increase of carbon in the ocean by 2100. This is in contrast to a global decrease in export production of –0.15 to –1.44 Pg C y–1. However, there is significant uncertainty in the modeled future fluxes of organic carbon to the deep ocean associated with a range of different processes resolved across models. We demonstrate that organic carbon fluxes at 1,000 m are a good predictor of long-term carbon sequestration and suggest this is an important metric of the BCP that should be prioritized in future model studies

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Neste trabalho, discutimos o problema de interação hidrodinâmica entre corpos rígidos, com foco no caso em que o escoamento é potencial e bidimensional. Apresentamos, de maneira suficientemente auto-contida, um 'cálculo' que permite obter em condições gerais o potencial de velocidade devido por um escoamento em torno de um número qualquer, porém finito, de corpos rígidos de geometria arbitrária. Como aplicação, fazemos um completo estudo quantitativo da interação hidrodinâmica entre dois cilindros estacionários e sujeitos a incidência de um escoamento uniforme.not availabl

Model output used in the manuscript "The evolution of a non-autonomous chaotic system under non-periodic forcing: a climate change example"

This *.rar file contains the model output from ensemble simulations for the Lorenz 84-Stommel 61 model (Van Veen et al, 2001; Daron and Stainforth, 2013). To run these simulations, we used the E-forth ensemble generator (de Melo Viríssimo and Stainforth, in preparation), which is a MATLAB toolboox that allows for large ensembles of low-dimensional dynamical systems to be run and studied in a systematic way (de Melo Viríssimo and Stainforth, 2023). These model outputs are presented and discussed in the Preprint "The evolution of a non-autonomouys chaotic system under non-periodic forcing: a climate change example". The manuscript describes the experiments performed, the parameter values used and the modifications done to the original L84-S61 model. For this matter, we also refer you to Daron and Stainforth (2013). All files uploaded were generated from simulations run by the authors. For specific information about each file uploaded, please refer to the README file. If you have any questions, please feel free to contact me. References: Van Veen et al. (2003): https://doi.org/10.1034/j.1600-0870.2001.00241.x Daron and Stainforth (2013): https://dx.doi.org/10.1088/1748-9326/8/3/034021 de Melo Viríssimo and Stainforth (2023): https://doi.org/10.5194/egusphere-egu23-14755 de Melo Viríssimo and Stainforth (2023): in preparatio

Model output used in the manuscript "The evolution of a non-autonomous chaotic system under non-periodic forcing: a climate change example"

This *.rar file contains the model output from ensemble simulations for the Lorenz 84-Stommel 61 model (Van Veen et al, 2001; Daron and Stainforth, 2013). To run these simulations, we used the E-forth ensemble generator (de Melo Viríssimo and Stainforth, in preparation), which is a MATLAB toolboox that allows for large ensembles of low-dimensional dynamical systems to be run and studied in a systematic way (de Melo Viríssimo and Stainforth, 2023). These model outputs are presented and discussed in the Preprint "The evolution of a non-autonomouys chaotic system under non-periodic forcing: a climate change example". The manuscript describes the experiments performed, the parameter values used and the modifications done to the original L84-S61 model. For this matter, we also refer you to Daron and Stainforth (2013). All files uploaded were generated from simulations run by the authors. For specific information about each file uploaded, please refer to the README file. If you have any questions, please feel free to contact me. References: Van Veen et al. (2003): https://doi.org/10.1034/j.1600-0870.2001.00241.x Daron and Stainforth (2013): https://dx.doi.org/10.1088/1748-9326/8/3/034021 de Melo Viríssimo and Stainforth (2023): https://doi.org/10.5194/egusphere-egu23-14755 de Melo Viríssimo and Stainforth (2023): in preparation Note: This version (v1.1) is the same version as v1.0 but with the correct README file.Version (v1.1) is the same version as v1.0 but with the correct README file

Model output used in the manuscript "Seasonal variability in particle flux attenuation in the global ocean generates spatial variability in annual transfer efficiency"

This *.rar file contains the model output from seasonal variability experiments using the NPZD-DOP GEOMAR biogeochemical model (Kriest et al., 2010) coupled with the MITgcm 2.8deg ocean circulation via the transport matrix method (Khatiwala et al., 2005; Khatiwala, 2007, 2018). These model outputs are presented and discussed in the Preprint "Seasonal variability in particle flux attenuation in the global ocean generates spatial variability in annual transfer efficiency". The manuscript describes the experiments performed, the parameter values used and the modifications done to the original model. For this matter, we also refer you to de Melo Viríssimo et al. (2022). All files uploaded were generated from simulations run by the authors, except: the grid file, the salinity field, and the temperature field, which came with the model; and the density fields, who were computed from the MITgcm 2.8deg transport matrix by Rafaelle Bernadello, using a TEOS-10 matlab routine (http://www.teos-10.org/). For specific information about each file uploaded, please refer to the README file. If you have any questions, please feel free to contact me. References: Kriest et al. (2010): https://doi.org/10.1016/j.pocean.2010.05.002 Khatiwala et al. (2005): https://doi.org/10.1016/j.ocemod.2004.04.002 Khatiwala (2007): https://doi.org/10.1029/2007GB002923 Khatiwala (2018): https://doi.org/10.5281/zenodo.1246300 de Melo Viríssimo et al. (2022): https://doi.org/10.1029/2021GB00710