This project addresses energy backscatter from sub-grid scale motion, both theoretically and in the context of state-of-the-art global ocean circulation models at “eddy permitting” or barely eddy resolving resolutions. We systematically explore remedies by quantifying the energy budget near the grid scale in situations close to geostrophic turbulence, evaluating existing closure schemes, investigating new approaches to minimally dissipative sub-grid closures, and transferring the best approaches to full primitive equation ocean and earth system models.
Result I: Ocean kinetic energy backscatter
Ocean kinetic energy backscatter reinjects overdissipated kinetic energy via subgrid energy equation into resolved flow to reduce total (unphysical) energy dissipation via classical viscosity closures.
➢ 10% to 50% reduced SSH mean and variability biases (Fig. 1), as well as temperature and salinity mean biases in global ¼° simulations with the FESOM2 model
Result II: Stochastic atmosphere-ocean coupling for climate models
A stochastic coupling scheme is introduced communicate underestimated surface fluxvariability between the ocean and atmosphere. Fluxes are based on randomly drawn ocean surface fields for meshes with higher resolution in the ocean compared to the atmosphere.
➢ 10% to 50% reduced pricipitation mean and variability biases in the tropical Pacific
Result III: Spurious waves and spectral artifacts on unstructured meshes
Differences in continuous, structured and unstructured models are clearly seen on, e.g., Floquet-Bloch dispersion diagrams for a 1D shallow water model (w, k, ℎ are frequency, wavenumber and discretization step, respectively):
➢ Spectral gaps need to be estimated since they imply absence of normal propagating waves at frequencies lying in the gaps. Such gaps create unwanted directional bias, spurious waves and other undesirable artefacts.
➢ Some structured, e.g., triangular, meshes also lead to spectral gaps.
Next phase outlook:
➢ Spurious interfacial waves on unstructured meshes
Result IV: Local diagnostics of entropy production
Diagnosed rates of entropy production calculated from resolved wind fluctuations take positive or negative signs, with only a slight bias to positive values (part of M4). The dynamics is therefore, on average, thermodynamically consistent.
➢ Restrictions to the dynamic Smagorinsky model arise that also take into account the need for model stability.
Stochastic superparametrization (SSP) for ocean models
We are working on adapting SSP for applying it to ocean primitive equations (PE).
Please download Anton's report here, since we cannot display his equations with our CMS.
Kutsenko, A. (2020). An entire function connected with the approximation of the golden ratio. Am. Math. Monthly, preprint arXiv:1906.01059 (accepted).
Juricke, S., Danilov, S., Koldunov, N., Oliver, M. & Sidorenko, D. (2019). Ocean kinetic energy backscatter parametrization on unstructured grids: Impact on global eddy‐permitting simulations, J. Adv. Model. Earth Sys., https://doi.org/10.1029/2019MS001855.
Danilov, S., & Kutsenko, A. (2019). On the geometric origin of spurious waves in finite-volume discretizations of shallow water equations on triangular meshes. J. Comput. Phys.,https://doi.org/10.1016/j.jcp.2019.108891.
Kutsenko, A. A. (2019). Matrix representations of multidimensional integral and ergodic operators. Appl. Math. Comput., Vol. 369, https://doi.org/10.1016/j.amc.2019.124818.
Rackow, T., & Juricke, S (2019). Flow‐dependent stochastic coupling for climate models with high ocean‐to‐atmosphere resolution ratio. Q. J. Roy. Meteor. Soc., 1-17, https://doi.org/10.1002/qj.3674.
Strommen, K., Christensen, H. M., MacLeod, D., Juricke, S., & Palmer, T. (2019). Progress Towards a Probabilistic Earth System Model: Examining The Impact of Stochasticity in EC-Earth v3. 2. Geosci. Model Dev., 12(7), doi: https://doi.org/10.5194/gmd-12-3099-2019.
Juricke, S., S. Danilov, A. Kutsenko and M. Oliver (2019). Ocean kinetic energy backscatter parametrizations on unstructured grids: Impact on mesoscale turbulence in a channel.Ocean Model., doi: https://doi.org/10.1016/j.ocemod.2019.03.009.
Kutsenko, A. A. (2019). A note on sharp spectral estimates for periodic Jacobi matrices. J. Approx. Theory, Vol. 242, p. 58-63, doi: https://doi.org/10.1016/j.jat.2019.03.003.
Danilov, S., Juricke, S., Kutsenko, A., & Oliver, M. (2019). Toward consistent subgrid momentum closures in ocean models. In Energy Transfers in Atmosphere and Ocean (pp. 145-192). Springer, Cham., doi: https://doi.org/10.1007/978-3-030-05704-6_5.
Juricke, S., MacLeod, D., Weisheimer, A., Zanna, L., & Palmer, T. (2018). Seasonal to annual ocean forecasting skill and the role of model and observational uncertainty. Q. J. Roy. Meteor. Soc., doi: https://doi.org/10.1002/qj.3394.
Mohamad, H. and Oliver, M. (2018). H s-class construction of an almost invariant slow subspace for the Klein-Gordon equation in the non-relativistic limit, J. Math. Phys., 59, 051509, https://doi.org/10.1063/1.5027040.
Wang, Q., Wekerle, C., Danilov, S., Koldunov, N., Sidorenko, D., Sein, D., Rabe, B. & Jung, T. (2018). Arctic Sea Ice Decline Significantly Contributed to the Unprecedented Liquid Freshwater Accumulation in the Beaufort Gyre of the Arctic Ocean, Geophys. Res. Lett., 45, 4956-4964, doi: https://doi.org/10.1029/2018GL077901.
Kutsenko, A. A., Shuvalov, A. L. & Poncelet, O. (2018). Dispersion spectrum of acoustoelectric waves in 1D piezoelectric crystal coupled with 2D infinite network of capacitors , J. Appl. Phys., 123, 044902, https://doi.org/10.1063/1.5005165 .
Kutsenko, A. (2017). Mixed multidimensional integral operators with piecewise constant kernels and their representations. Lin. Multilin. Algebra, 67, 1-10, https://doi.org/10.1080/03081087.2017.1415294.
Kutsenko, A. A. (2017). Application of matrix-valued integral continued fractions to spectral problems on periodic graphs with defect. J. Math. Phys. 58, 063516, doi:10.1063/1.4989987
Kutsenko, A. A., Nagy, A. J., Su, X., Shuvalov, A. L. & Norris, A. N. (2017). Wave Propagation and Homogenization in 2d and 3d Lattices: A Semi-Analytical Approach. Q. J. Mech. Appl. Math. (2017) 70 (2): 131-151. doi: 10.1093/qjmam/hbx002.