Predicting climate change using response theory: global averages and spatial patterns

The provision of accurate methods for predicting the climate response to anthropogenic and natural forcings is a key contemporary scientific challenge. Using a simplified and efficient open-source general circulation model of the atmosphere featuring O(105105) degrees of freedom, we show how it is possible to approach such a problem using nonequilibrium statistical mechanics. Response theory allows one to practically compute the time-dependent measure supported on the pullback attractor of the climate system, whose dynamics is non-autonomous as a result of time-dependent forcings. We propose a simple yet efficient method for predicting—at any lead time and in an ensemble sense—the change in climate properties resulting from increase in the concentration of CO22 using test perturbation model runs. We assess strengths and limitations of the response theory in predicting the changes in the globally averaged values of surface temperature and of the yearly total precipitation, as well as in their spatial patterns. The quality of the predictions obtained for the surface temperature fields is rather good, while in the case of precipitation a good skill is observed only for the global average. We also show how it is possible to define accurately concepts like the inertia of the climate system or to predict when climate change is detectable given a scenario of forcing. Our analysis can be extended for dealing with more complex portfolios of forcings and can be adapted to treat, in principle, any climate observable. Our conclusion is that climate change is indeed a problem that can be effectively seen through a statistical mechanical lens, and that there is great potential for optimizing the current coordinated modelling exercises run for the preparation of the subsequent reports of the Intergovernmental Panel for Climate Change

Ocean Energy, Fluxes and an Anti-Anti-Turbulence Conjecture

The energy sources for convection and the general circulation are revisited through an analysis of the compressible equations of motion, rather than the Boussinesq equations. We are motivated in this endeavor by a more straightforward connection in the compressible equations between thermodynamics and dynamics, and the continuing debate in the field regarding the suggestion, made first in the form of Sandström’s theorem, that surface buoyancy fluxes can not drive the overturning circulation. While ultimately supporting the Sandström position, the analysis leads to some new insights into ocean energetics and surface energy fluxes. We argue the ultimate role of buoyancy fluxes are to damp the circulation and that ocean energy cycles between internal and kinetic energy. Ocean heating due to the general circulation, geothermal heat flux and the biosphere are evaluated for their roles and we suggest the latter two provide energy to the overturning much more effectively than surface forcing. All three also contribute significantly to net ocean surface energy flux, an effect that influences the interpretation of ocean heat content imbalances

Fixed points, stable manifolds, weather regimes and their predictability

International audienceIn a simple, one-layer atmospheric model, we study the links between low-frequency variability and the model's fixed points in phase space. The model dynamics is characterized by the coexistence of multiple "weather regimes". To investigate the transitions from one regime to another, we focus on the identification of the stable manifolds associated with the fixed points. We show that these manifolds acts as separatrices between regimes. We localize each manifold by making use of several tools arising from the meteorological applications of nonlinear dynamics, namely ``bred vectors" (BVs) and singular vectors (SVs). These results are then verified in the framework of ensemble forecasts issued from ``clouds" (ensembles) of initial states. The divergence of the trajectories allows us to establish the connections between zones of low predictability and the geometry of the stable manifolds

Multiple equilibria and oscillatory modes in a mid-latitude ocean-forced atmospheric model

International audienceAtmospheric response to a mid-latitude sea surface temperature (SST) front is studied, while emphasizing low-frequency modes induced by the presence of such a front. An idealized atmospheric quasi-geostrophic (QG) model is forced by the SST field of an idealized oceanic QG model. First, the equilibria of the oceanic model and the associated SST fronts are computed. Next, these equilibria are used to force the atmospheric model and compute its equilibria when varying the strength of the oceanic forcing. Low-frequency modes of atmospheric variability are identified and associated with successive Hopf bifurcations. The origin of these Hopf bifurcations is studied in detail, and connected to barotropic instability. Finally, a link is established between the model's time integrations and the previously obtained equilibria. © Author(s) 2012

Fixed points, stable manifolds, weather regimes and their predictability

International audienceIn a simple, one-layer atmospheric model, we study the links between low-frequency variability and the model's fixed points in phase space. The model dynamics is characterized by the coexistence of multiple "weather regimes". To investigate the transitions from one regime to another, we focus on the identification of the stable manifolds associated with the fixed points. We show that these manifolds acts as separatrices between regimes. We localize each manifold by making use of several tools arising from the meteorological applications of nonlinear dynamics, namely ``bred vectors" (BVs) and singular vectors (SVs). These results are then verified in the framework of ensemble forecasts issued from ``clouds" (ensembles) of initial states. The divergence of the trajectories allows us to establish the connections between zones of low predictability and the geometry of the stable manifolds

Fixed points, stable manifolds, weather regimes and their predictability

International audienceIn a simple, one-layer atmospheric model, we study the links between low-frequency variability and the model's fixed points in phase space. The model dynamics is characterized by the coexistence of multiple "weather regimes". To investigate the transitions from one regime to another, we focus on the identification of the stable manifolds associated with the fixed points. We show that these manifolds acts as separatrices between regimes. We localize each manifold by making use of several tools arising from the meteorological applications of nonlinear dynamics, namely ``bred vectors" (BVs) and singular vectors (SVs). These results are then verified in the framework of ensemble forecasts issued from ``clouds" (ensembles) of initial states. The divergence of the trajectories allows us to establish the connections between zones of low predictability and the geometry of the stable manifolds

Spatio-temporal patterns of Chaos in the Atlantic Overturning Circulation

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A coupled model of interior balanced and boundary flow

International audienceOcean circulation modeling requires parameterizations of sub-grid scale processes, which in turn involves two separate issues. First, the parameterization should mirror the effect of important sub-grid dynamics and second, constants and boundary conditions as required by the parameterization must be determined. In modern ocean circulation modeling, many parameterizations take the form of viscous operators with poorly known coefficients, and the boundary conditions options are free-slip, partial-slip or no-slip, suitably adjusted for the order of the operator. The extent to which viscous operators are dynamically apt is unclear and there is virtually no dynamical guidance on how to choose between the boundary conditions. Often the decision about the suitability of the parameterizations and the boundary conditions is made based on qualitative characteristics of the solution, which is somewhat subjective. Here, a dynamical boundary layer model is developed that explicitly determines the boundary potential vorticity fluxes resulting from the sub-grid scale interactions of the resolved flow with the boundaries. When applied to a quasi-geostrophic model, comparisons of model evolution with high resolution primitive equation simulations are favorable. The recipe outlined here, while far from a complete parameterization of boundary dynamics, represents a step toward resolving the issues currently surrounding sub-grid scale parameterization. The results also argue that boundary dynamics naturally dissipate balanced energy and are likely to represent a principal means by which the oceanic mesoscale energy budget is balanced

Fast Warming of the Surface Ocean Under a Climatological Scenario

International audienceKey Points: 6 • Weakly varying climatological winds reduce upper ocean vertical mixing, affect-7 ing the redistribution of air-sea fluxes 8 • Coupled to an atmospheric boundary layer, the modeled ocean response to clima-9 tological winds is to warm up considerably at the surface 10 • Results illustrate the pivotal improvements in air-sea interactions achieved by driv-11 ing an ocean model with an atmospheric boundary layer 12 Abstract 13 We examine various strategies for forcing ocean-only models, including an atmospheric 14 boundary layer model. This surface forcing allows air-sea exchanges to affect atmospheric 15 temperature and relative humidity, thus removing the assumption of an infinite atmo-16 spheric heat capacity associated with the prescription of these variables. When exposed 17 to climatological winds, the simulated North Atlantic oceanic temperature warms con-18 siderably at the surface as compared to a model with full atmospheric variability. This 19 warming is mainly explained by a weakened upper ocean vertical mixing in response to 20 the weakly varying climatological winds. Specifying the atmospheric temperatures in-21 hibits this warming, but depends on the unrealistic large atmospheric heat capacity. We 22 thus interpret the simulated warmer ocean as a more physically consistent ocean response. 23 We conclude the use of an atmospheric boundary layer model provides many benefits 24 for ocean only modeling, although a 'normal' year strategy is required for maintaining 25 high frequency winds. 2