An indicator of the multiple equilibria regime of the Atlantic meridional overturning circulation

Recent model results have suggested that there may be a scalar indicator ? monitoring whether the Atlantic meridional overturning circulation (MOC) is in a multiple equilibrium regime. The quantity ? is based on the net freshwater transport by the MOC into the Atlantic basin. It changes sign as soon as the steady Atlantic MOC enters the multiple equilibrium regime because of an increased freshwater input in the northern North Atlantic. This paper addresses the issue of why the sign of ? is such a good indicator for the multiple equilibrium regime. Changes in the Atlantic freshwater budget over a complete bifurcation diagram and in finite amplitude perturbation experiments are analyzed in a global ocean circulation model. The authors show that the net anomalous freshwater transport into or out of the Atlantic, resulting from the interactions of the velocity perturbations and salinity background field, is coupled to the background (steady state) state freshwater budget and hence to ?. The sign of ? precisely shows whether this net anomalous freshwater transport is stabilizing or destabilizing the MOC. Therefore, it can indicate whether the MOC is in a single or multiple equilibrium regime.<br/

Evolving State Machines as Robot Controllers

Automated generation of robot controllers using an Evolutionary Algorithm(EA) has received increasing attention in the last years as it has the potentialfor a reduction in the development time of a robot. Often these EAs generateNeural Networks (NNs) as robot controllers. Using a NN for automaticallygenerating robot controllers has two important downsides: 1.) A human isnot able to fully understand the inner working of a multi-layer NN, and 2.)a NN has only limited abilities to decompose a complex task into sub tasks.Both of these downsides can be addressed by using a State Machine (SM)instead of a NN as robot controller. Therefore, this thesis introduces an EAcalled Evolving State Machines As Controllers (ESMAC). ESMAC generatesSMs instead of NNs. A SM is understandable for humans because ofits modularity and allows for task decomposition by using a state for eachsub task. Furthermore, two extensions of ESMAC are proposed: adaptiveESMAC and selector ESMAC. Adaptive ESMAC aims to automatically determinesthe number of states with which the best tness for a task canbe achieved. Selector ESMAC replaces the transitions that are used in aSM to switch between states with a NN-based switching mechanism. This switching mechanism allows mutations to make more gradual changes to aSM's behaviours, which improves the performance of the EA. The performance of ESMAC is evaluated on two robotic tasks: come-and-go and phototaxis-with-obstacles. All three variants of ESMAC showequally good performance as a NN-based EA on the evaluated tasks. Thecontrollers generated with standard ESMAC and adaptive ESMAC hardlymake any state transitions and mainly use one state. However, controllers that do use multiple states appear to be more robust to changing scenarios and in noisy environments. Selector ESMAC is able to generate SMs-based controllers that have complementing states and, therefore, shows potentialfor decomposing a task into sub tasks.Zebro projec

Spurious multiple equilibria introduced by convective adjustment

The application of bifurcation analysis to ocean climate models is substantially hampered by difficulties associated with the use of convective adjustment, i.e. a parameterisation of convection in which the vertical diffusion of heat and salt is greatly enhanced whenever the water column becomes statically unstable. When tracking steady solutions of these models in parameter space, problems arise due to the occurrence of a multitude of saddle-node bifurcations, each of which is related to a minor reorganisation of convection. In this paper, we analyse the origin of the multiple steady states in detail using a one-dimensional column model. By analytical evaluation of the eigenvalue problem conditions are formulated under which bifurcations may occur. Using numerical continuation methods a regime of multistability is identified and it is shown that the number of coexisting steady states increases with increasing resolution, while the extent of parameter space in which they occur decreases. A comparison of the numerical results to corresponding analytical solutions reveals that the multiple equilibria are inherent to the discretisation and hence artificial. Apparently, successful application of convective adjustment requires knowledge of subgrid-scale tracer fields. Two alternative convective adjustment schemes are proposed that (partially) overcome these problems. Results from a fully implicit model based on the two-dimensional primitive equations indicate that the physically relevant phenomena due to the nonlinear character of large-scale oceanic flow, notably the bifurcations related to the salt advection feedback, are preserved under the alternative formulations.

Measure characterizations and properties of normal and regular lattices

Various equivalent characterizations of normality are considered and a measure theoretic definition is given for strongly normal lattices. Measure conditions related to the apace of σ-smooth, lattice-regular, 0−1 measures are noted which imply, or are equivalent to, the space being Hausdorff, regular, or prime complete

Effect of Atmospheric Feedbacks on the Stability of the Atlantic Meridional Overturning Circulation

The impact of atmospheric feedbacks on the multiple equilibria (ME) regime of the Atlantic meridional overturning circulation (MOC) is investigated using a fully implicit hybrid coupled model (HCM). The HCM consists of a global ocean model coupled to an empirical atmosphere model that is based on linear regressions of the heat, net evaporative, and momentum fluxes generated by a fully coupled climate model onto local as well as Northern Hemisphere averaged sea surface temperatures. Using numerical continuation techniques, bifurcation diagrams are constructed for the HCM with the strength of an anomalous freshwater flux as the bifurcation parameter, which allows for an efficient first-order estimation of the effect of interactive surface fluxes on the MOC stability. The different components of the atmospheric fluxes are first considered individually and then combined. Heat feedbacks act to destabilize the present-day state of the MOC and to stabilize the collapsed state, thus leaving the size of the ME regime almost unaffected. In contrast, interactive freshwater fluxes cause a destabilization of both the present-day and collapsed states of the MOC. Wind feedbacks are found to have a minor impact. The joint effect of the three interactive fluxes is to narrow the range of ME. The shift of the saddle-node bifurcation that terminates the present-day state of the ocean is further investigated by adjoint sensitivity analysis of the overturning rate to surface fluxes. It is found that heat feedbacks primarily affect the MOC stability when they change the heat fluxes over the North Atlantic subpolar gyre, whereas interactive freshwater fluxes have an effect everywhere in the Atlantic basin

Response of a strongly eddying global ocean to North Atlantic freshwater perturbations

The strongly eddying version of the Parallel Ocean Program (POP) is used in two 45-yr simulations to investigate the response of the Atlantic meridional overturning circulation (AMOC) to strongly enhanced freshwater input due to Greenland melting, with an integrated flux of 0.5 Sverdrups (Sv; 1 Sv ≡ 106m3 s-1). For comparison, a similar set of experiments is performed using a noneddying version of POP. The aim is to identify the signature of the salt advection feedback in the two configurations. For this reason, surface salinity is not restored in these experiments. The freshwater input leads to a quantitatively comparable reduction of the overturning strength in the two models. To examine the importance of transient effects in the relation betweenAMOCstrength and density distribution, the results of the eddy-resolving model are related to water mass transformation theory. The freshwater forcing leads to a reduction of the rate of light to dense water conversion in the North Atlantic, but there is no change in dense to light transformation elsewhere, implying that high density layers are continuously deflating. The main focus of the paper is on the effect of the AMOC reduction on the basinwide advection of freshwater. The low-resolution model results show a change of the net freshwater advection that is consistent with the salt advection feedback. However, for the eddy-resolving model, the net freshwater advection into the Atlantic basin appears to be unaffected, despite the significant change in the large-scale velocity structure

Response of a strongly eddying global ocean to North Atlantic freshwater perturbations

The strongly eddying version of the Parallel Ocean Program (POP) is used in two 45-yr simulations to investigate the response of the Atlantic meridional overturning circulation (AMOC) to strongly enhanced freshwater input due to Greenland melting, with an integrated flux of 0.5 Sverdrups (Sv; 1 Sv ≡ 106m3 s-1). For comparison, a similar set of experiments is performed using a noneddying version of POP. The aim is to identify the signature of the salt advection feedback in the two configurations. For this reason, surface salinity is not restored in these experiments. The freshwater input leads to a quantitatively comparable reduction of the overturning strength in the two models. To examine the importance of transient effects in the relation betweenAMOCstrength and density distribution, the results of the eddy-resolving model are related to water mass transformation theory. The freshwater forcing leads to a reduction of the rate of light to dense water conversion in the North Atlantic, but there is no change in dense to light transformation elsewhere, implying that high density layers are continuously deflating. The main focus of the paper is on the effect of the AMOC reduction on the basinwide advection of freshwater. The low-resolution model results show a change of the net freshwater advection that is consistent with the salt advection feedback. However, for the eddy-resolving model, the net freshwater advection into the Atlantic basin appears to be unaffected, despite the significant change in the large-scale velocity structure

Interaction network based early warning indicators for the Atlantic MOC collapse

[1] Early warning indicators of the collapse of the Atlantic Meridional Overturning Circulation (MOC) have up to now mostly been based on temporal correlations in single time series. Here, we propose new indicators based on spatial correlations in the time series of the Atlantic temperature field. To demonstrate the performance of these indicators, we use a meridional-depth model of the MOC for which the critical conditions for collapse can be explicitly computed. An interaction network approach is used to monitor changes in spatial correlations in the model temperature time series as the critical transition is approached. The new early warning indicators are based on changes in topological properties of the network, in particular changes in the distribution functions of the degree and the clustering coefficient