Fluctuation Analysis of the Atmospheric Energy Cycle

The atmosphere gains available potential energy by solar radiation and dissipates kinetic energy mainly in the atmospheric boundary layer. We analyze the fluctuations of the global mean energy cycle defined by Lorenz (1955) in a simulation with a simplified hydrostatic model. The energy current densities are well approximated by the generalized Gumbel distribution (Bramwell, Holdsworth and Pinton, 1998) and the Generalized Extreme Value (GEV) distribution. In an attempt to assess the fluctuation relation of Evans, Cohen, and Morriss (1993) we define entropy production by the injected power and use the GEV location parameter as a reference state. The fluctuation ratio reveals a linear behavior in a finite range.Comment: 17 pages, 5 figure

Thermodynamics of climate change: generalized sensitivities

Using a recent theoretical approach, we study how global warming impacts the thermodynamics of the climate system by performing experiments with a simplified yet Earth-like climate model. The intensity of the Lorenz energy cycle, the Carnot efficiency, the material entropy production, and the degree of irreversibility of the system change monotonically with the CO2 concentration. Moreover, these quantities feature an approximately linear behaviour with respect to the logarithm of the CO2 concentration in a relatively wide range. These generalized sensitivities suggest that the climate becomes less efficient, more irreversible, and features higher entropy production as it becomes warmer, with changes in the latent heat fluxes playing a predominant role. These results may be of help for explaining recent findings obtained with state of the art climate models regarding how increases in CO2 concentration impact the vertical stratification of the tropical and extratropical atmosphere and the position of the storm tracks

TheDiaTo (v1.0) – a new diagnostic tool for water, energy and entropy budgets in climate models

This work presents the Thermodynamic Diagnostic Tool (TheDiaTo), a novel diagnostic tool for investigating the thermodynamics of climate systems with a wide range of applications, from sensitivity studies to model tuning. It includes a number of modules for assessing the internal energy budget, the hydrological cycle, the Lorenz energy cycle and the material entropy production. The routine takes as inputs energy fluxes at the surface and at the top of the atmosphere (TOA), which allows for the computation of energy budgets at the TOA, the surface and in the atmosphere as a residual. Meridional enthalpy transports are also computed from the divergence of the zonal mean energy budget from which the location and intensity of the maxima in each hemisphere are calculated. Rainfall, snowfall and latent heat fluxes are received as inputs for computation of the water mass and latent energy budgets. If a land–sea mask is provided, the required quantities are separately computed over continents and oceans. The diagnostic tool also computes the annual Lorenz energy cycle (LEC) and its storage and conversion terms by hemisphere and as a global mean. This is computed from three-dimensional daily fields of horizontal wind velocity and temperature in the troposphere. Two methods have been implemented for the computation of the material entropy production: one relying on the convergence of radiative heat fluxes in the atmosphere (indirect method) and the other combining the irreversible processes occurring in the climate system, particularly heat fluxes in the boundary layer, the hydrological cycle and the kinetic energy dissipation as retrieved from the residuals of the LEC (direct method). A version of these diagnostics has been developed as part of the Earth System Model eValuation Tool (ESMValTool) v2.0a1 in order to assess the performances of CMIP6 model simulations, and it will be available in the next release. The aim of this software is to provide a comprehensive picture of the thermodynamics of the climate system, as reproduced in the state-of-the-art coupled general circulation models. This can prove useful for better understanding anthropogenic and natural climate change, paleoclimatic climate variability, and climatic tipping points

A new framework for climate sensitivity and prediction: a modelling perspective

The sensitivity of climate models to increasing CO2 concentration and the climate response at decadal time-scales are still major factors of uncertainty for the assessment of the long and short term effects of anthropogenic climate change. While the relative slow progress on these issues is partly due to the inherent inaccuracies of numerical climate models, this also hints at the need for stronger theoretical foundations to the problem of studying climate sensitivity and performing climate change predictions with numerical models. Here we demonstrate that it is possible to use Ruelle's response theory to predict the impact of an arbitrary CO2 forcing scenario on the global surface temperature of a general circulation model. Response theory puts the concept of climate sensitivity on firm theoretical grounds, and addresses rigorously the problem of predictability at different time-scales. Conceptually, these results show that performing climate change experiments with general circulation models is a well defined problem from a physical and mathematical point of view. Practically, these results show that considering one single CO2 forcing scenario is enough to construct operators able to predict the response of climatic observables to any other CO2 forcing scenario, without the need to perform additional numerical simulations. We also introduce a general relationship between climate sensitivity and climate response at different time scales, thus providing an explicit definition of the inertia of the system at different time scales. This technique allows also for studying systematically, for a large variety of forcing scenarios, the time horizon at which the climate change signal (in an ensemble sense) becomes statistically significant. While what we report here refers to the linear response, the general theory allows for treating nonlinear effects as well. These results pave the way for redesigning and interpreting climate change experiments from a radically new perspective

Climate sensitivity to ozone and its relevance on the habitability of Earth-like planets

Atmospheric ozone plays an important role on the temperature structure of the atmosphere. However, it has not been included in previous studies on the effect of an increasing solar radiation on the Earth’s climate. Here we study the climate sensitivity to the presence/absence of ozone with an increasing solar forcing for the first time with a global climate model. We show that the warming effect of ozone increases both the humidity of the lower atmosphere and the surface temperature. Under the same solar irradiance, the mean surface temperature is 7 K higher than in an analogue planet without ozone. Therefore, the moist greenhouse threshold, the state at which water vapor becomes abundant in the stratosphere, is reached at a lower solar irradiance (1572 W/m2 with respect to 1647 W/m2 in the case without ozone). Our results imply that ozone reduces the maximum solar irradiance at which Earth-like planets would remain habitable

Climate sensitivity to carbon dioxide and moist greenhouse threshold of earth-like planets under an increasing solar forcing

Carbon dioxide is one of the major contributors to the radiative forcing, increasing both the temperature and the humidity of Earth's atmosphere. If the stellar irradiance increases and water becomes abundant in the stratosphere of an Earth-like planet, it will be dissociated and the resultant hydrogen will escape from the atmosphere. This state is called the moist greenhouse threshold (MGT). Using a global climate model (GCM) of intermediate complexity, we explore how to identify this state for different CO2 concentrations and including the radiative effect of atmospheric ozone for the first time. We show that the MGT correlates with the in ection point in the water vapor mixing ratio in the stratosphere and a peak in the climate sensitivity. For CO2 concentrations between 560 and 200 ppm, the MGT is reached at a surface temperature of 320 K. Despite the higher simplicity of our model, our results are consistent with similar simulations without ozone by complex GCMs, suggesting that they are robust indicators of the MGT. We discuss the implications for the inner edge of the habitable zone as well as the water loss timescales for Earth analog planets

Crisis of the chaotic attractor of a climate model: a transfer operator approach

The destruction of a chaotic attractor leading to rough changes in the dynamics of a dynamical system is studied. Local bifurcations are characterised by a single or a pair of characteristic exponents crossing the imaginary axis. The approach of such bifurcations in the presence of noise can be inferred from the slowing down of the correlation decay. On the other hand, little is known about global bifurcations involving high-dimensional attractors with positive Lyapunov exponents. The global stability of chaotic attractors may be characterised by the spectral properties of the Koopman or the transfer operators governing the evolution of statistical ensembles. It has recently been shown that a boundary crisis in the Lorenz flow coincides with the approach to the unit circle of the eigenvalues of these operators associated with motions about the attractor, the stable resonances. A second type of resonances, the unstable resonances, is responsible for the decay of correlations and mixing on the attractor. In the deterministic case, those cannot be expected to be affected by general boundary crises. Here, however, we give an example of chaotic system in which slowing down of the decay of correlations of some observables does occur at the approach of a boundary crisis. The system considered is a high-dimensional, chaotic climate model of physical relevance. Moreover, coarse-grained approximations of the transfer operators on a reduced space, constructed from a long time series of the system, give evidence that this behaviour is due to the approach of unstable resonances to the unit circle. That the unstable resonances are affected by the crisis can be physically understood from the fact that the process responsible for the instability, the ice-albedo feedback, is also active on the attractor. Implications regarding response theory and the design of early-warning signals are discussed

Stable equatorial ice belts at high obliquity in a coupled atmosphere-ocean model

Various climate states at high obliquity are realized for a range of stellar irradiance using a dynamical atmosphere-ocean-sea ice climate model in an Aquaplanet configuration. Three stable climate states are obtained that differ in the extent of the sea ice cover. For low values of irradiance the model simulates a Cryoplanet that has a perennial global sea ice cover. By increasing stellar irradiance, transitions occur to an Uncapped Cryoplanet with a perennial equatorial sea ice belt, and eventually to an Aquaplanet with no ice. Using an emulator model we find that the Uncapped Cryoplanet is a robust stable state for a range of irradiance and high obliquities and contrast earlier results that high-obliquity climate states with an equatorial ice belt may be unsustainable or unachievable. When the meridional ocean heat flux is strengthened, the parameter range permitting a stable Uncapped Cryoplanet decreases due to melting of equatorial sea ice. Beyond a critical threshold of meridional ocean heat flux, the perennial equatorial ice belt disappears. Therefore, a vigorous ocean circulation may render it unstable. Our results suggest that perennial equatorial ice cover is a viable climate state of a high-obliquity exoplanet. However, due to multiple equilibria, this state is only reached from more glaciated conditions, and not from less glaciated conditions.Comment: 9 pages, 5 figures, ApJ accepte

Can we use linear response theory to assess geoengineering strategies?

Geoengineering can control only some climatic variables but not others, resulting in side-effects. We investigate in an intermediate-complexity climate model the applicability of linear response theory (LRT) to the assessment of a geoengineering method. This application of LRT is twofold. First, our objective (O1) is to assess only the best possible geoengineering scenario by looking for a suitable modulation of solar forcing that can cancel out or otherwise modulate a climate change signal resulting from a rise in CO2 alone. Here we consider only the cancellation of the expected global mean surface air temperature. It is a straightforward inverse problem for this solar forcing, and, considering an infinite time period, we use LRT to provide the solution in the frequency domain in closed form. We provide procedures suitable for numerical implementation that apply to finite time periods too. Second, to be able to use LRT to quantify side-effects, the response with respect to uncontrolled observables, such as regional must be approximately linear. Our objective (O2) here is to assess the linearity of the response. We find that under geoengineering in the sense of (O1) the asymptotic response of the globally averaged temperature is actually not zero. This is due to an inaccurate determination of the linear susceptibilities. The error is due to a significant quadratic nonlinearity of the response. This nonlinear contribution can be easily removed, which results in much better estimates of the linear susceptibility, and, in turn, in a fivefold reduction in the global average surface temperature under geoengineering. This correction dramatically improves also the agreement of the spatial patterns of the predicted and of the true response. However, such an agreement is not perfect and is worse in the case of the precipitation patterns, as a result of greater degree of nonlinearity.Geoengineering can control only some climatic variables but not others, resulting in side-effects. We investigate in an intermediate-complexity climate model the applicability of linear response theory (LRT) to the assessment of a geoengineering method. This application of LRT is twofold. First, our objective (O1) is to assess only the best possible geoengineering scenario by looking for a suitable modulation of solar forcing that can cancel out or otherwise modulate a climate change signal resulting from a rise in CO2 alone. Here we consider only the cancellation of the expected global mean surface air temperature. It is a straightforward inverse problem for this solar forcing, and, considering an infinite time period, we use LRT to provide the solution in the frequency domain in closed form. We provide procedures suitable for numerical implementation that apply to finite time periods too. Second, to be able to use LRT to quantify side-effects, the response with respect to uncontrolled observables, such as regional must be approximately linear. Our objective (O2) here is to assess the linearity of the response. We find that under geoengineering in the sense of (O1) the asymptotic response of the globally averaged temperature is actually not zero. This is due to an inaccurate determination of the linear susceptibilities. The error is due to a significant quadratic nonlinearity of the response. This nonlinear contribution can be easily removed, which results in much better estimates of the linear susceptibility, and, in turn, in a fivefold reduction in the global average surface temperature under geoengineering. This correction dramatically improves also the agreement of the spatial patterns of the predicted and of the true response. However, such an agreement is not perfect and is worse in the case of the precipitation patterns, as a result of greater degree of nonlinearity