Particle-continuum multiscale modeling of sea ice floes. (English) Zbl 1542.74003
Summary: Sea ice profoundly influences the polar environment and the global climate. Traditionally, sea ice has been modeled as a continuum under Eulerian coordinates to describe its large-scale features, using, for instance, viscous-plastic rheology. Recently, Lagrangian particle models, also known as the discrete element method models, have been utilized for characterizing the motion of individual sea ice fragments (called floes) at scales of 10 km and smaller, especially in marginal ice zones. This paper develops a multiscale model that couples the particle and the continuum systems to facilitate an effective representation of the dynamical and statistical features of sea ice across different scales. The multiscale model exploits a Boltzmann-type system that links the particle movement with the continuum equations. For the small-scale dynamics, it describes the motion of each sea ice floe. Then, as the large-scale continuum component, it treats the statistical moments of mass density and linear and angular velocities. The evolution of these statistics affects the motion of individual floes, which in turn provides bulk feedback that adjusts the large-scale dynamics. Notably, the particle model characterizing the sea ice floes is localized and fully parallelized in a framework that is sometimes called superparameterization, which significantly improves computational efficiency. Numerical examples demonstrate the effective performance of the multiscale model. Additionally, the study demonstrates that the multiscale model has a linear-order approximation to the truth model.
MSC:
| 74A25 | Molecular, statistical, and kinetic theories in solid mechanics |
| 74S99 | Numerical and other methods in solid mechanics |
| 74-10 | Mathematical modeling or simulation for problems pertaining to mechanics of deformable solids |
| 86A40 | Glaciology |
| 82B21 | Continuum models (systems of particles, etc.) arising in equilibrium statistical mechanics |
Keywords:
Lagrangian particle model; discrete element method; superparametrization; multiscale Boltzmann model; small-scale dynamicsReferences:
| [1] | Alberello, A., Bennetts, L., Heil, P., Eayrs, C., Vichi, M., MacHutchon, K., Onorato, M., and Toffoli, A., Drift of pancake ice floes in the winter Antarctic marginal ice zone during polar cyclones, J. Geophys. Res. Oceans, 125 (2020), e2019JC015418. |
| [2] | Alberello, A., Bennetts, L. G., Onorato, M., Vichi, M., MacHutchon, K., Eayrs, C., Ntamba, B. N., Benetazzo, A., Bergamasco, F., Nelli, F., Pattani, R., Clarke, H., Tersigni, I., and Toffoli, A., Three-dimensional imaging of waves and floes in the marginal ice zone during a cyclone, Nat. Commun., 13 (2022), 4590. |
| [3] | Bateman, S. P., Orzech, M. D., and Calantoni, J., Simulating the mechanics of sea ice using the discrete element method, Mech. Res. Commun., 99 (2019), pp. 73-78. |
| [4] | Bennetts, L., Bitz, C., Feltham, D., Kohout, A., and Meylan, M., Marginal ice zone dynamics: Future research perspectives and pathways, Philos. Trans. Roy. Soc. A, 380 (2022), 20210267. |
| [5] | Berry, T. and Harlim, J., Variable bandwidth diffusion kernels, Appl. Comput. Harmon. Anal., 40 (2016), pp. 68-96. · Zbl 1343.94020 |
| [6] | Blockley, E., Vancoppenolle, M., Hunke, E., Bitz, C., Feltham, D., Lemieux, J.-F., Losch, M., Maisonnave, E., Notz, D., Rampal, P., Tietsche, S., Tremblay, B.Turner, A., Massonnet, F., Ólason, E., Roberts, A., Aksenov, Y., Fichefet, T., Garric, G., Iovino, D., Madec, G., Rousset, C., Salas y Melia, D., and Schroeder, D., The future of sea ice modeling: Where do we go from here?, Bull. Amer. Meteorol. Soc., 101 (2020), pp. E1304-E1311. |
| [7] | Bourke, R. H. and Garrett, R. P., Sea ice thickness distribution in the Arctic ocean, Cold Reg. Sci. Technol., 13 (1987), pp. 259-280. |
| [8] | Buluç, A., Meyerhenke, H., Safro, I., Sanders, P., and Schulz, C., Recent advances in graph partitioning, Algorithm Eng., (2016), pp. 117-158. |
| [9] | Cercignani, C., The Boltzmann equation, in The Boltzmann Equation and Its Applications, Springer-Verlag, Berlin, 1988, pp. 40-103. · Zbl 0646.76001 |
| [10] | Chen, N., Deng, Q., and Stechmann, S. N., Superfloe parameterization with physics constraints for uncertainty quantification of sea ice floes, SIAM/ASA J. Uncertain. Quantif., 10 (2022), pp. 1384-1409. · Zbl 1498.86001 |
| [11] | Chen, N., Fu, S., and Manucharyan, G., Lagrangian data assimilation and parameter estimation of an idealized sea ice discrete element model, J. Adv. Model. Earth Syst., 13 (2021), e2021MS002513. |
| [12] | Chen, N., Fu, S., and Manucharyan, G. E., An efficient and statistically accurate Lagrangian data assimilation algorithm with applications to discrete element sea ice models, J. Comput. Phys., 455 (2022), 111000. · Zbl 07518084 |
| [13] | Chen, S. and Doolen, G. D., Lattice Boltzmann method for fluid flows, Annu. Rev. Fluid Mech., 30 (1998), pp. 329-364. · Zbl 1398.76180 |
| [14] | Coon, M., Kwok, R., Levy, G., Pruis, M., Schreyer, H., and Sulsky, D., Arctic Ice Dynamics Joint Experiment (AIDJEX) assumptions revisited and found inadequate, J. Geophys. Res. Oceans, 112 (2007), doi:10.1029/2005JC003393. |
| [15] | Coon, M. D., Maykut, G. A., Pritchard, R. S., Rothrock, D. A., and Thorndike, A. S., Modeling the pack ice as an elastic-plastic material, AIDJEX Bull., (1974), 105. |
| [16] | Covington, J., Chen, N., and Wilhelmus, M. M., Bridging gaps in the climate observation network: A physics-based nonlinear dynamical interpolation of Lagrangian ice floe measurements via data-driven stochastic models, J. Adv. Model. Earth Syst., 14 (2022), e2022MS003218. |
| [17] | Cundall, P. A. and Strack, O. D., A discrete numerical model for granular assemblies, Geotechnique, 29 (1979), pp. 47-65. |
| [18] | Damsgaard, A., Adcroft, A., and Sergienko, O., Application of discrete element methods to approximate sea ice dynamics, J. Adv. Model. Earth Syst., 10 (2018), pp. 2228-2244. |
| [19] | Dansereau, V., Weiss, J., Saramito, P., and Lattes, P., A Maxwell elasto-brittle rheology for sea ice modelling, The Cryosphere, 10 (2016), pp. 1339-1359. |
| [20] | Davis, A. D. and Giannakis, D., Graph-theoretic algorithms for Kolmogorov operators: Approximating solutions and their gradients in elliptic and parabolic problems on manifolds, Calcolo, 60 (2023), pp. 1-32. · Zbl 1514.62372 |
| [21] | Davis, A. D., Giannakis, D., Stadler, G., Stechmann, S. N., and Manucharyan, G., Super-parameterized of Lagrangian sea ice dynamics using the Boltzmann equation, in AGU Fall Meeting Abstracts 2020, 2020, pp. C048-03. |
| [22] | de Masi, A., Esposito, R., and Lebowitz, J.-L., Incompressible Navier-Stokes and Euler limits of the Boltzmann equation, Comm. Pure Appl. Math., 42 (1989), pp. 1189-1214. · Zbl 0689.76024 |
| [23] | Delgado-Buscalioni, R. and Coveney, P., Continuum-particle hybrid coupling for mass, momentum, and energy transfers in unsteady fluid flow, Phys. Rev. E, 67 (2003), 046704. |
| [24] | Delle Site, L., Praprotnik, M., Bell, J. B., and Klein, R., Particle-continuum coupling and its scaling regimes: Theory and applications, Adv. Theory Simul., 3 (2020), 1900232. |
| [25] | Denton, A. A. and Timmermans, M.-L., Characterizing the sea-ice floe size distribution in the Canada Basin from high-resolution optical satellite imagery, The Cryosphere, 16 (2022), pp. 1563-1578. |
| [26] | Docquier, D., Massonnet, F., Barthélemy, A., Tandon, N. F., Lecomte, O., and Fichefet, T., Relationships between Arctic sea ice drift and strength modelled by NEMO-LIM3.6, The Cryosphere, 11 (2017), pp. 2829-2846. |
| [27] | Dolaptchiev, S. I. and Klein, R., A multiscale model for the planetary and synoptic motions in the atmosphere, J. Atmos. Sci., 70 (2013), pp. 2963-2981. |
| [28] | Dumont, D., Marginal ice zone dynamics: History, definitions and research perspectives, Philos. Trans. Roy. Soc. A, 380 (2022), 20210253. |
| [29] | Feltham, D. L., Sea ice rheology, Annu. Rev. Fluid Mech., 40 (2008), pp. 91-112. · Zbl 1136.76007 |
| [30] | Flato, G. M., Sea-ice modelling, in Mass Balance of the Cryosphere, Bamber, J. L. and Payne, A. J., eds., Cambridge University Press, Cambridge, 2004, pp. 367-392. |
| [31] | Ghaboussi, J. and Barbosa, R., Three-dimensional discrete element method for granular materials, Int. J. Numer. Anal. Methods Geomech., 14 (1990), pp. 451-472. |
| [32] | Giddy, I., Swart, S., Du Plessis, M., Thompson, A., and Nicholson, S.-A., Stirring of sea-ice meltwater enhances submesoscale fronts in the Southern Ocean, J. Geophys. Res. Oceans, 126 (2021), e2020JC016814. |
| [33] | Golden, K. M., Bennetts, L. G., Cherkaev, E., Eisenman, I., Feltham, D., Horvat, C., Hunke, E., Jones, C., Perovich, D. K., Ponte-Castañeda, P., Strong, C., Sulsky, D., and Wells, A. J., Modeling sea ice, Not. Amer. Math. Soc., 67 (2020), pp. 1535-1555, doi:10.1090/noti. · Zbl 1454.86003 |
| [34] | Golse, F., The mean-field limit for the dynamics of large particle systems, J. Équ. Dériv. Partielles, 9 (2003). · Zbl 1211.82037 |
| [35] | Golse, F., On the dynamics of large particle systems in the mean field limit, in Macroscopic and Large Scale Phenomena: Coarse Graining, Mean Field Limits and Ergodicity, Muntean, A., Rademacher, J., and Zagaris, A., eds., Springer-Verlag, Berlin, 2016, pp. 1-144. |
| [36] | Golse, F. and Saint-Raymond, L., The Navier-Stokes limit of the Boltzmann equation for bounded collision kernels, Invent. Math., 155 (2004), pp. 81-161. · Zbl 1060.76101 |
| [37] | Grabowski, W. W. and Smolarkiewicz, P. K., CRCP: A cloud resolving convection parameterization for modeling the tropical convecting atmosphere, Phys. D, 133 (1999), pp. 171-178. · Zbl 1194.86006 |
| [38] | Grooms, I. and Majda, A. J., Efficient stochastic superparameterization for geophysical turbulence, Proc. Natl. Acad. Sci. USA, 110 (2013), pp. 4464-4469. · Zbl 1292.76038 |
| [39] | Harris, S., An Introduction to the Theory of the Boltzmann Equation, Courier Corporation, North Chelmsford, MA, 2004. |
| [40] | Hendrickson, B. and Kolda, T. G., Graph partitioning models for parallel computing, Parallel Comput., 26 (2000), pp. 1519-1534. · Zbl 0948.68130 |
| [41] | Herman, A., Discrete-Element bonded-particle Sea Ice model DESIgn, version 1.3a—Model description and implementation, Geosci. Model Dev., 9 (2016), pp. 1219-1241. |
| [42] | Herman, A., Granular effects in sea ice rheology in the marginal ice zone, Philos. Trans. Roy. Soc. A, 380 (2022), 20210260. |
| [43] | Hibler, W. III, A dynamic thermodynamic sea ice model, J. Phys. Oceanogr., 9 (1979), pp. 815-846. |
| [44] | Holt, J., Hyder, P., Ashworth, M., Harle, J., Hewitt, H. T., Liu, H., New, A. L., Pickles, S., Porter, A., Popova, E., Icarus Allen, J., Siddorn, J., and Wood, R., Prospects for improving the representation of coastal and shelf seas in global ocean models, Geosci. Model Dev., 10 (2017), pp. 499-523. |
| [45] | Hopkins, M. A., A discrete element Lagrangian sea ice model, Eng. Comput., 21 (2004), pp. 409-421. · Zbl 1062.74563 |
| [46] | Hopkins, M. A., Frankenstein, S., and Thorndike, A. S., Formation of an aggregate scale in Arctic sea ice, J. Geophys. Res. Oceans, 109 (2004), doi:10.1029/2003JC001855. |
| [47] | Horvat, C. and Tziperman, E., A prognostic model of the sea-ice floe size and thickness distribution, The Cryosphere, 9 (2015), pp. 2119-2134. |
| [48] | Horvat, C. and Tziperman, E., The evolution of scaling laws in the sea ice floe size distribution, J. Geophys. Res. Oceans, 122 (2017), pp. 7630-7650. |
| [49] | Hunke, E. and Dukowicz, J., An elastic-viscous-plastic model for sea ice dynamics, J. Phys. Oceanogr., 27 (1997), pp. 1849-1867. |
| [50] | Hutter, N. and Losch, M., Feature-based comparison of sea ice deformation in lead-permitting sea ice simulations, The Cryosphere, 14 (2020), pp. 93-113. |
| [51] | Jabin, P.-E., A review of the mean field limits for Vlasov equations, Kinet. Relat. Models, 7 (2014), 661. · Zbl 1318.35129 |
| [52] | Jansson, F., van den Oord, G., Pelupessy, I., Grönqvist, J. H., Siebesma, A. P., and Crommelin, D., Regional superparameterization in a global circulation model using large eddy simulations, J. Adv. Model. Earth Syst., 11 (2019), pp. 2958-2979. |
| [53] | Kreyscher, M., Harder, M., Lemke, P., and Flato, G. M., Results of the sea ice model intercomparison project: Evaluation of sea ice rheology schemes for use in climate simulations, J. Geophys. Res. Oceans, 105 (2000), pp. 11299-11320. |
| [54] | Kwok, R. and Cunningham, G., Seasonal ice area and volume production of the Arctic ocean: November 1996 through April 1997, J. Geophys. Res. Oceans, 107 (2002), SHE-12. |
| [55] | Kwok, R., Hunke, E., Maslowski, W., Menemenlis, D., and Zhang, J., Variability of sea ice simulations assessed with RGPS kinematics, J. Geophys. Res. Oceans, 113 (2008), doi:10.1029/2008JC004783. |
| [56] | Lax, P. D., Weak solutions of nonlinear hyperbolic equations and their numerical computation, Comm. Pure Appl. Math., 7 (1954), pp. 159-193. · Zbl 0055.19404 |
| [57] | Lee, Y., Majda, A. J., and Qi, D., Stochastic superparameterization and multiscale filtering of turbulent tracers, Multiscale Model. Simul., 15 (2017), pp. 215-234. · Zbl 1361.93063 |
| [58] | Li, T., Gelb, A., and Lee, Y., Improving Numerical Accuracy for the Viscous-Plastic Formulation of Sea Ice, preprint, arXiv:2206.10061, 2022. |
| [59] | Majda, A. J. and Grooms, I., New perspectives on superparameterization for geophysical turbulence, J. Comput. Phys., 271 (2014), pp. 60-77. · Zbl 1349.86035 |
| [60] | Majda, A. J. and Stechmann, S. N., A simple dynamical model with features of convective momentum transport, J. Atmos. Sci., 66 (2009), pp. 373-392. |
| [61] | Manucharyan, G. E. and Montemuro, B. P., SubZero: A sea ice model with an explicit representation of the floe life cycle, J. Adv. Model. Earth Syst., (2022), e2022MS003247. |
| [62] | Manucharyan, G. E. and Thompson, A. F., Heavy footprints of upper-ocean eddies on weakened Arctic sea ice in marginal ice zones, Nat. Commun., 13 (2022), pp. 1-10. |
| [63] | Meylan, M. H., Horvat, C., Bitz, C. M., and Bennetts, L. G., A floe size dependent scattering model in two- and three-dimensions for wave attenuation by ice floes, Ocean Model., 161 (2021), 101779. |
| [64] | Mishra, B. and Rajamani, R. K., The discrete element method for the simulation of ball mills, Appl. Math. Model., 16 (1992), pp. 598-604. · Zbl 0768.70002 |
| [65] | Mori, M., Kosaka, Y., Watanabe, M., Nakamura, H., and Kimoto, M., A reconciled estimate of the influence of Arctic sea-ice loss on recent Eurasian cooling, Nat. Clim. Change, 9 (2019), pp. 123-129. |
| [66] | Ogawa, F., Keenlyside, N., Gao, Y., Koenigk, T., Yang, S., Suo, L., Wang, T., Gastineau, G., Nakamura, T., Cheung, H. N., Omrani, N.-E., Ukita, J., and Semenov, V., Evaluating impacts of recent Arctic sea ice loss on the northern hemisphere winter climate change, Geophys. Res. Lett., 45 (2018), pp. 3255-3263. |
| [67] | Pande, G., Numerical Methods in Rock Mechanics, John Wiley, New York, 1990. · Zbl 0725.73072 |
| [68] | Petsev, N. D., Leal, L. G., and Shell, M. S., Coupling discrete and continuum concentration particle models for multiscale and hybrid molecular-continuum simulations, J. Chem. Phys., 147 (2017), 234112. |
| [69] | Randall, D., Khairoutdinov, M., Arakawa, A., and Grabowski, W., Breaking the cloud parameterization deadlock, Bull. Amer. Meteorol. Soc., 84 (2003), pp. 1547-1564. |
| [70] | Roach, L. A., Bitz, C. M., Horvat, C., and Dean, S. M., Advances in modeling interactions between sea ice and ocean surface waves, J. Adv. Model. Earth Syst., 11 (2019), pp. 4167-4181. |
| [71] | Roach, L. A., Horvat, C., Dean, S. M., and Bitz, C. M., An emergent sea ice floe size distribution in a global coupled ocean-sea ice model, J. Geophys. Res. Oceans, 123 (2018), pp. 4322-4337. |
| [72] | Sammonds, P., Murrell, S., and Rist, M., Fracture of multiyear sea ice, J. Geophys. Res. Oceans, 103 (1998), pp. 21795-21815. |
| [73] | Shih, Y.-H., Mehlmann, C., Losch, M., and Stadler, G., Robust and efficient primal-dual Newton-Krylov solvers for viscous-plastic sea-ice models, J. Comput. Phys., 474 (2023), 111802. · Zbl 07640559 |
| [74] | Squire, V., Hosking, R. J., Kerr, A. D., and Langhorne, P., Moving Loads on Ice Plates, Vol. 45, Springer Science & Business Media, New York, 1996. |
| [75] | Squire, V. A., Marginal ice zone dynamics, Philos. Trans. Roy. Soc. A (2022), doi:10.1098/rsta.2021.0266. |
| [76] | Stechmann, S. N., Multiscale eddy simulation for moist atmospheric convection: Preliminary investigation, J. Comput. Phys., 271 (2014), pp. 99-117. · Zbl 1349.86042 |
| [77] | Stern, H. L., Schweiger, A. J., Stark, M., Zhang, J., Steele, M., Hwang, B., and Maksym, T., Seasonal evolution of the sea-ice floe size distribution in the Beaufort and Chukchi seas, Elementa Sci. Anthropocene, 6 (2018), 48. |
| [78] | Stocker, T., Climate Change 2013: The Physical Science Basis: Working Group I Contribution to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change, Cambridge University Press, Cambridge, 2014. |
| [79] | Tandon, N. F., Kushner, P. J., Docquier, D., Wettstein, J. J., and Li, C., Reassessing sea ice drift and its relationship to long-term Arctic sea ice loss in coupled climate models, J. Geophys. Res. Oceans, 123 (2018), pp. 4338-4359. |
| [80] | Toppaladoddi, S. and Wettlaufer, J. S., Theory of the sea ice thickness distribution, Phys. Rev. Lett., 115 (2015), 148501. |
| [81] | Toyota, T., Haas, C., and Tamura, T., Size distribution and shape properties of relatively small sea-ice floes in the Antarctic marginal ice zone in late winter, Deep Sea Res. II Top. Stud. Oceanogr., 58 (2011), pp. 1182-1193. |
| [82] | Tuhkuri, J. and Polojärvi, A., A review of discrete element simulation of ice-structure interaction, Philos. Trans. Roy. Soc. A, 376 (2018), 20170335. |
| [83] | Wilchinsky, A. V. and Feltham, D. L., Modelling the rheology of sea ice as a collection of diamond-shaped floes, J. Non-Newton. Fluid Mech., 138 (2006), pp. 22-32. · Zbl 1195.74112 |
| [84] | Xu, Z., Tartakovsky, A. M., and Pan, W., Discrete-element model for the interaction between ocean waves and sea ice, Phys. Rev. E, 85 (2012), 016703. |
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