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The Bergman kernels of monomial polyhedra are explicitly computed. Monomial polyhedra are a class of bounded pseudoconvex Reinhardt domains defined as sublevel sets of Laurent monomials. Their kernels are rational functions and are obtained by an application of Bell's transformation formula.

The Ocean Heat Uptake Efficiency (OHUE) quantifies the ocean's ability to mitigate surface warming through deep heat sequestration. Despite its importance, the main controls on OHUE, as well as its nearly two-fold spread across contemporary climate models, remain unclear. We argue that OHUE is primarily controlled by the strength of mid-latitude ventilation in the background climate, itself related to subtropical pycnocline depth and ocean stratification. This hypothesis is supported by a strong correlation between OHUE and pycnocline depth in the CMIP5 and CMIP6 under RCP85/SSP585, as well as in MITgcm. We explain these results through a regional OHUE decomposition, showing that the mid-latitudes largely account for both: (1) global heat uptake after increased radiative forcing and; (2) the correlation between pycnocline depth and OHUE. Coupled with the nearly equivalent inter-model spreads in OHUE/pycnocline depth, these results imply that mid-latitude ventilation also dominates the ensemble spread in OHUE. Our results provide a pathway towards observationally constraining OHUE, and thus future climate.

Given graphs $G$ and $H$ and a positive integer $k$, the Gallai-Ramsey number $gr_{k}(G : H)$ is the minimum integer $N$ such that for any integer $n \geq N$, every $k$-edge-coloring of $K_{n}$ contains either a rainbow copy of $G$ or a monochromatic copy of $H$. These numbers have recently been studied for the case when $G = K_{3}$, where still only a few precise numbers are known for all $k$. In this paper, we extend the known precise Gallai-Ramsey numbers to include $H = C_{8}$ for all $k$.

The vertical upwelling/diffusion model (VUDM) has historically played a key role in shaping our ideas about how the heat balance is achieved in the ocean. Its has been and is still widely used in many applications ranging from the estimation of transfer coefficients to the parameterisation of ocean heat uptake in Simple Climate Models (SCMs). Its conceptual value as a realistic theoretical model of the ocean heat balance has become increasingly unclear over the years however, because: 1) the different ways in which upwelling has been linked to high-latitude deep water formation and downgradient diffusion linked to vertical/diapycnal mixing have remained imprecise and somewhat ad-hoc so far; 2) other effects such as isopycnal mixing, density-compensated temperature anomalies, meso-scale eddy-induced advection and the depth-varying ocean area have all be demonstrated to affect actual ocean heat uptake as well, but their incorporation into existing VUDM frameworks has been problematic. In this paper, a new process-based vertical advection/diffusion theoretical model of ocean heat uptake is constructed that resolve all above difficulties. This new model is obtained by coarse-graining the full three-dimensional advection/diffusion for potential temperature carried by ocean climate models, by using the same isopycnal analysis as in the theory of ocean water masses. The resulting model describes the temporal evolution of the isopycnally-averaged thickness-weighted potential temperature in terms of an effective velocity that depends uniquely on the surface heating conditionally integrated in density classes, an effective diapycnal diffusivity controlled by isoneutral and dianeutral mixing, and an additional term linked to the meridional transport of density-compensated temperature anomalies by the diabatic residual overturning circulation., Comment: 13 pages, preliminary draft of paper to be submitted to Geoscience Model Development

Ice sheet numerical modeling is an important tool to estimate the dynamic contribution of the Antarctic ice sheet to sea level rise over the coming centuries. The influence of initial conditions on ice sheet model simulations, however, is still unclear. To better understand this influence, an initial state intercomparison exercise (initMIP) has been developed to compare, evaluate, and improve initialization procedures and estimate their impact on century-scale simulations. initMIP is the first set of experiments of the Ice Sheet Model Intercomparison Project for CMIP6 (ISMIP6), which is the primary Coupled Model Intercomparison Project Phase 6 (CMIP6) activity focusing on the Greenland and Antarctic ice sheets. Following initMIP-Greenland, initMIP-Antarctica has been designed to explore uncertainties associated with model initialization and spin-up and to evaluate the impact of changes in external forcings. Starting from the state of the Antarctic ice sheet at the end of the initialization procedure, three forward experiments are each run for 100 years: a control run, a run with a surface mass balance anomaly, and a run with a basal melting anomaly beneath floating ice. This study presents the results of initMIP-Antarctica from 25 simulations performed by 16 international modeling groups. The submitted results use different initial conditions and initialization methods, as well as ice flow model parameters and reference external forcings. We find a good agreement among model responses to the surface mass balance anomaly but large variations in responses to the basal melting anomaly. These variations can be attributed to differences in the extent of ice shelves and their upstream tributaries, the numerical treatment of grounding line, and the initial ocean conditions applied, suggesting that ongoing efforts to better represent ice shelves in continental-scale models should continue.

The Flux-Anomaly-Forced Model Intercomparison Project (FAFMIP) aims to investigate the spread in simulations of sea-level and ocean climate change in response to CO2 forcing by atmosphere-ocean general circulation models (AOGCMs). It is particularly motivated by the uncertainties in projections of ocean heat uptake, global-mean sealevel rise due to thermal expansion and the geographical patterns of sea-level change due to ocean density and circulation change. FAFMIP has three tier-1 experiments, in which prescribed surface flux perturbations of momentum, heat and freshwater respectively are applied to the ocean in separate AOGCM simulations. All other conditions are as in the pre-industrial control. The prescribed fields are typical of pattern and magnitude of changes in these fluxes projected by AOGCMs for doubled CO2 concentration. Five groups have tested the experimental design with existing AOGCMs. Their results show diversity in the pattern and magnitude of changes, with some common qualitative features. Heat and water flux perturbation cause the dipole in sea-level change in the North Atlantic, while momentum and heat flux perturbation cause the gradient across the Antarctic Circumpolar Current. The Atlantic meridional overturning circulation (AMOC) declines in response to the heat flux perturbation, and there is a strong positive feedback on this effect due to the consequent cooling of sea-surface temperature in the North Atlantic, which enhances the local heat input to the ocean. The momentum and water flux perturbations do not substantially affect the AMOC. Heat is taken up largely as a passive tracer in the Southern Ocean, which is the region of greatest heat input, while the weakening of the AMOC causes redistribution of heat towards lower latitudes. Future analysis of these and other phenomena with the wider range of CMIP6 FAFMIP AOGCMs will benefit from new diagnostics of temperature and salinity tendencies, which will enable investigation of the model spread in behaviour in terms of physical processes as formulated in the models.