Precise calculations of the existence of multiple AMOC equilibria in coupled climate models Part I: equilibrium states

This study examines criteria for the existence of two stable states of the Atlantic Meridional Overturning Circulation (AMOC) using a combination of theory and simulations from a numerical coupled atmosphere–ocean climate model. By formulating a simple collection of state parameters and their relationships, the authors reconstruct the North Atlantic Deep Water (NADW) OFF state behavior under a varying external salt-flux forcing. This part (Part I) of the paper examines the steady-state solution, which gives insight into the mechanisms that sustain the NADW OFF state in this coupled model; Part II deals with the transient behavior predicted by the evolution equation. The nonlinear behavior of the Antarctic Intermediate Water (AAIW) reverse cell is critical to the OFF state. Higher Atlantic salinity leads both to a reduced AAIW reverse cell and to a greater vertical salinity gradient in the South Atlantic. The former tends to reduce Atlantic salt export to the Southern Ocean, while the latter tends to increases it. These competing effects produce a nonlinear response of Atlantic salinity and salt export to salt forcing, and the existence of maxima in these quantities. Thus the authors obtain a natural and accurate analytical saddle-node condition for the maximal surface salt flux for which a NADW OFF state exists. By contrast, the bistability indicator proposed by De Vries and Weber does not generally work in this model. It is applicable only when the effect of the AAIW reverse cell on the Atlantic salt budget is weak.

Non-ergodicity of inviscid two-dimensional flow on a beta-plane and on the surface of a rotating sphere

It is shown that, for a sufficiently large value of β, two-dimensional flow on a doubly-periodic beta-plane cannot be ergodic (phase-space filling) on the phase-space surface of constant energy and enstrophy. A corresponding result holds for flow on the surface of a rotating sphere, for a sufficiently rapid rotation rate Ω. This implies that the higher-order, non-quadratic invariants are exerting a significant influence on the statistical evolution of the flow. The proof relies on the existence of a finite-amplitude Liapunov stability theorem for zonally symmetric basic states with a non-vanishing absolute-vorticity gradient. When the domain size is much larger than the size of a typical eddy, then a sufficient condition for non-ergodicity is that the wave steepness ε < 1, where ε = 2[surd radical]2Z/βU in the planar case and $\epsilon = 2^{\frac{1}{4}} a^{\frac{5}{2}}Z^{\frac{7}{4}}/\Omega U^{\frac{5}{2}}$ in the spherical case, and where Z is the enstrophy, U the r.m.s. velocity, and a the radius of the sphere. This result may help to explain why numerical simulations of unforced beta-plane turbulence (in which ε decreases in time) seem to evolve into a non-ergodic regime at large scales.

The role of oceans and sea ice in abrupt transitions between multiple climate states

The coupled climate dynamics underlying large, rapid, and potentially irreversible changes in ice cover are studied. A global atmosphere–ocean–sea ice general circulation model with idealized aquaplanet geometry is forced by gradual multi-millennial variations in solar luminosity. The model traverses a hysteresis loop between warm ice-free conditions and cold glacial conditions in response to ±5 W m−2 variations in global, annual-mean insolation. Comparison of several model configurations confirms the importance of polar ocean processes in setting the sensitivity and time scales of the transitions. A “sawtooth” character is found with faster warming and slower cooling, reflecting the opposing effects of surface heating and cooling on upper-ocean buoyancy and, thus, effective heat capacity. The transition from a glacial to warm, equable climate occurs in about 200 years. In contrast to the “freshwater hosing” scenario, transitions are driven by radiative forcing and sea ice feedbacks. The ocean circulation, and notably the meridional overturning circulation (MOC), does not drive the climate change. The MOC (and associated heat transport) collapses poleward of the advancing ice edge, but this is a purely passive response to cooling and ice expansion. The MOC does, however, play a key role in setting the time scales of the transition and contributes to the asymmetry between warming and cooling.

Atmospheric and oceanic contributions to irreducible forecast uncertainty of Arctic surface climate

Uncertainty of Arctic seasonal to interannual predictions arising from model errors and initial state uncertainty has been widely discussed in the literature, whereas the irreducible forecast uncertainty (IFU) arising from the chaoticity of the climate system has received less attention. However, IFU provides important insights into the mechanisms through which predictability is lost, and hence can inform prioritization of model development and observations deployment. Here, we characterize how internal oceanic and surface atmospheric heat fluxes contribute to IFU of Arctic sea ice and upper ocean heat content in an Earth system model by analyzing a set of idealized ensemble prediction experiments. We find that atmospheric and oceanic heat flux are often equally important for driving unpredictable Arctic-wide changes in sea ice and surface water temperatures, and hence contribute equally to IFU. Atmospheric surface heat flux tends to dominate Arctic-wide changes for lead times of up to a year, whereas oceanic heat flux tends to dominate regionally and on interannual time scales. There is in general a strong negative covariance between surface heat flux and ocean vertical heat flux at depth, and anomalies of lateral ocean heat transport are wind-driven, which suggests that the unpredictable oceanic heat flux variability is mainly forced by the atmosphere. These results are qualitatively robust across different initial states, but substantial variations in the amplitude of IFU exist. We conclude that both atmospheric variability and the initial state of the upper ocean are key ingredients for predictions of Arctic surface climate on seasonal to interannual time scales.