Complex Earth System Models are widely utilised to make conditional statements about the future climate under some assumptions about changes in future atmospheric greenhouse gas concentrations; these statements are often referred to as climate projections. The models themselves are high-dimensional nonlinear systems and it is common to discuss their behaviour in terms of attractors and low-dimensional nonlinear systems such as the canonical Lorenz `63 system. In a non-autonomous situation, for instance due to anthropogenic climate change, the relevant object is sometimes considered to be the pullback or snapshot attractor. The pullback attractor, however, is a collection of {\em all} plausible states of the system at a given time and therefore does not take into consideration our knowledge of the current state of the Earth System when making climate projections, and are therefore not very informative regarding annual to multi-decadal climate projections. In this article, we approach the problem of measuring and interpreting the mid-term climate of a model by using a low-dimensional, climate-like, nonlinear system with three timescales of variability, and non-periodic forcing. We introduce the concept of an {\em evolution set} which is dependent on the starting state of the system, and explore its links to different types of initial condition uncertainty and the rate of external forcing. We define the {\em convergence time} as the time that it takes for the distribution of one of the dependent variables to lose memory of its initial conditions. We suspect a connection between convergence times and the classical concept of mixing times but the precise nature of this connection needs to be explored. These results have implications for the design of influential climate and Earth System Model ensembles, and raise a number of issues of mathematical interest.
It is shown that, the wavelet regression detrended fluctuations of the monthly global temperature data (land and ocean combined) for the period 1880-2009yy, are completely dominated by one-third subharmonic resonance to annual forcing (both natural and anthropogenically induced). Role of the oceanic Rossby waves and the resonance contribution to the El Nino phenomenon have been discussed in detail.
It is shown that global climate exhibits chaotic response to solar forcing variability in a vast range of timescales: from annual to multi-millennium. Unlike linear systems, where periodic forcing leads to periodic response, nonlinear chaotic response to periodic forcing can result in exponentially decaying broad-band power spectrum with decay rate T_e equal to the period of the forcing. It is shown that power spectrum of a reconstructed time series of Northern Hemisphere temperature anomaly for the past 2,000 years has an exponentially decaying broad-band part with T_e = 11 yr, i.e. the obser…
There is evidence that ice age cycles are paced by astronomical forcing, suggesting some kind of synchronisation phenomenon. Here, we identify the type of such synchronisation and explore systematically its uniqueness and robustness using a simple paleoclimate model akin to the van der Pol relaxation oscillator and dynamical system theory. As the insolation is quite a complex quasiperiodic signal involving different frequencies, the traditional concepts used to define synchronisation to periodic forcing are no longer applicable. Instead, we explore a different concept of generalised synchronis…
The global atmospheric temperature anomalies of Earth reached a maximum in 1998 which has not been exceeded during the subsequent 10 years. The global anomalies are calculated from the average of climate effects occurring in the tropical and the extratropical latitude bands. El Nino/La Nina effects in the tropical band are shown to explain the 1998 maximum while variations in the background of the global anomalies largely come from climate effects in the northern extratropics. These effects do not have the signature associated with CO2 climate forcing. However, the data show a small underlying…
It is shown that the periodic alteration of night and day provides a chaotic dissipation mechanism for the North Atlantic (NAO) and Southern (SOI) climate oscillations. The wavelet regression detrended daily NAO index for last 60 years and daily SOI for last 20 years as well as an analytical continuation in the complex time domain were used for this purpose.
We carry out climate simulations for 1880-2003 with GISS modelE driven by ten measured or estimated climate forcings. An ensemble of climate model runs is carried out for each forcing acting individually and for all forcing mechanisms acting together. We compare side-by-side simulated climate change for each forcing, all forcings, observations, unforced variability among model ensemble members, and, if available, observed variability. Discrepancies between observations and simulations with all forcings are due to model deficiencies, inaccurate or incomplete forcings, and imperfect observations…
Global warming arises from 'temperature forcing', a net imbalance between energy fluxes entering and leaving the climate system and arising within it. Humanity introduces temperature forcing through greenhouse gas emissions, agriculture, and thermal emissions from fuel burning. Up to now climate projections, neglecting thermal emissions, typically foresee maximum forcing around the year 2050, followed by a decline. In this paper we show that, if humanity's energy use grows at 1%/year, slower than in recent history, and if thermal emissions are not controlled through novel energy technology, te…
The last glacial period was punctuated by a series of abrupt climate shifts, the so-called Dansgaard-Oeschger (DO) events. The frequency of DO events varied in time, supposedly because of changes in background climate conditions. Here, the influence of external forcings on DO events is investigated with statistical modelling. We assume two types of simple stochastic dynamical systems models (double-well potential-type and oscillator-type), forced by the northern hemisphere summer insolation change and/or the global ice volume change. The model parameters are estimated by using the maximum like…
Global Climate Models are key tools for predicting the future response of the climate system to a variety of natural and anthropogenic forcings. Here we show how to use statistical mechanics to construct operators able to flexibly predict climate change for a variety of climatic variables of interest. We perform our study on a fully coupled model - MPI-ESM v.1.2 - and for the first time we prove the effectiveness of response theory in predicting future climate response to CO$_2$ increase on a vast range of temporal scales, from inter-annual to centennial, and for very diverse climatic quantiti…
We determine the volcano climate sensitivity and response time for the Mount Pinatubo eruption. This is achieved using observational measurements of the temperature anomalies of the lower troposphere and the aerosol optical density (AOD) in combination with a radiative forcing proxy for AOD. Using standard linear response theory we find sensitivity = 0.18 +- 0.04 K/(W/m2), which implies a negative feedback of -1.0 +- 0.4. The intrinsic response time is 5.8+-1.0 months. Both results are contrary to the conventional paradigm that includes long response times and positive feedback. In addition, w…
A review of the recent refereed literature fails to confirm quantitatively that carbon dioxide (CO2) radiative forcing was the prime mover in the changes in temperature, ice-sheet volume, and related climatic variables in the glacial and interglacial periods of the past 650,000 years, even under the "fast response" framework where the convenient if artificial distinction between forcing and feedback is assumed. Atmospheric CO2 variations generally follow changes in temperature and other climatic variables rather than preceding them. Likewise, there is no confirmation of the often-posited signi…
Although steady, isotropic Darcy flows are inherently laminar and non-mixing, it is well understood that transient forcing via engineered pumping schemes can induce rapid, chaotic mixing in groundwater. In this study we explore the propensity for such mixing to arise in natural groundwater systems subject to cyclical forcings, e.g. tidal or seasonal influences. Using a conventional linear groundwater flow model subject to tidal forcing, we show that under certain conditions these flows generate Lagrangian transport and mixing phenomena (chaotic advection) near the tidal boundary. We show that …
The deposition of varved sedimentary sequences is usually controlled by climate conditions. The study of two Late Miocene evaporite successions (one halite and the other gypsum) consisting of annual varves has been carried out to reconstruct the paleoclimatic and paleoenvironmental conditions existing during the acme of the Messinian salinity crisis, ~ 6 Ma, when thick evaporite deposits accumulated on the floor of the Mediterranean basin. Spectral analyses of these varved evaporitic successions reveal significant periodicity peaks at around 3-5, 9, 11-13, 20-27 and 50-100 yr. A comparison wit…
We investigate the issue of "dangerous human-made interference with climate" using simulations with GISS modelE driven by measured or estimated forcings for 1880-2003 and extended to 2100 for IPCC greenhouse gas scenarios as well as the 'alternative' scenario of Hansen and Sato. Identification of 'dangerous' effects is partly subjective, but we find evidence that added global warming of more than 1 degree C above the level in 2000 has effects that may be highly disruptive. The alternative scenario, with peak added forcing ~1.5 W/m2 in 2100, keeps further global warming under 1 degree C if clim…
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($10^5$) 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…
The three-dimensional baroclinic quasigeostrophic flow model has been widely used to study basic mechanisms in oceanic flows and climate dynamics. In this paper, we consider this flow model under random wind forcing and time-periodic fluctuations on fluid boundary (the interface between the oceans and the atmosphere). The time-periodic fluctuations are due to periodic rotation of the earth and thus periodic exposure of the earth to the solar radiation. After establishing the well-posedness of the baroclinic quasigeostrophic flow model in the state space, we demonstrate the existence of the ran…
As a consequence of greenhouse forcing, all state of the art general circulation models predict a positive temperature trend that is greater for the troposphere than the surface. This predicted positive trend increases in value with altitude until it reaches a maximum ratio with respect to the surface of as much as 1.5 to 2.0 at about 200 to 400 hPa. However, the temperature trends from several independent observational data sets show decreasing as well as mostly negative values. This disparity indicates that the three models examined here fail to account for the effects of greenhouse forcings…
North Atlantic climate during glacial times was characterized by large-amplitude switchings, the Dansgaard-Oeschger (DO) events, with an apparent tendency to recur preferably in multiples of about 1470 years. Recent work interpreted these intervals as resulting from a subharmonic response of a highly nonlinear system to quasi-periodic solar forcing plus noise. This hypothesis was challenged as inconsistent with the observed variability in the phase relation between proxies of solar activity and Greenland climate. Here we reject the claim of inconsistency by showing that this phase variability …
Climate models are critical tools for developing strategies to manage the risks posed by sea-level rise to coastal communities. While these models are necessary for understanding climate risks, there is a level of uncertainty inherent in each parameter in the models. This model parametric uncertainty leads to uncertainty in future climate risks. Consequently, there is a need to understand how those parameter uncertainties impact our assessment of future climate risks and the efficacy of strategies to manage them. Here, we use random forests to examine the parametric drivers of future climate r…
We analyze the stability of a low-order coupled sea ice and climate model and extract the essential physics governing the time scales of response as a function of greenhouse gas forcing. Under present climate conditions the stability is controlled by longwave radiation driven heat conduction. However, as greenhouse gas forcing increases and the ice cover decays, the destabilizing influence of ice-albedo feedback acts on equal footing with longwave stabilization. Both are seasonally out of phase and as the system warms towards a seasonal ice state these effects, which underlie the bifurcations …
This paper is a continuation of a study by Douglass and Clader. We extend the analysis through December 2003 using the latest updates of the observational temperature and solar irradiance data sets in addition to a new volcano proxy data set. We have re-determined the solar effect on the temperature from satellite measurements of the solar irradiance and the temperature of the lower troposphere the sensitivity to solar irradiance. This re-analysis calculates two newly recognized dynamic and non-radiative flux factors which must be applied to the observed sensitivity. The sensitivity is about t…
Early Mars had rivers, but the cause of Mars' wet-to-dry transition remains unknown. Past climate on Mars can be probed using the spatial distribution of climate-sensitive landforms. We analyzed global databases of water-worked landforms and identified changes in the spatial distribution of rivers over time. These changes are simply explained by comparison to a simplified meltwater model driven by an ensemble of global climate model simulations, as the result of $\gtrsim$10 K global cooling, from global average surface temperature (T) $\ge$ 268 K to T $\sim$ 258 K, due to a weaker greenhouse e…
The climate system is a forced, dissipative, nonlinear, complex and heterogeneous system that is out of thermodynamic equilibrium. The system exhibits natural variability on many scales of motion, in time as well as space, and it is subject to various external forcings, natural as well as anthropogenic. This paper reviews the observational evidence on climate phenomena and the governing equations of planetary-scale flow, as well as presenting the key concept of a hierarchy of models as used in the climate sciences. Recent advances in the application of dynamical systems theory, on the one hand…
A linearized energy-balance model for global temperature is formulated, featuring a scale-free long-range memory (LRM) response and stochastic forcing representing the influence on the ocean heat reservoir from atmospheric weather systems. The model is parametrized by an effective response strength, the stochastic forcing strength, and the memory exponent. The instrumental global surface temperature record and the deterministic component of the forcing are used to estimate these parameters by means of the maximum-likelihood method. The residual obtained by subtracting the deterministic solutio…
Solar forcing on climate has been reported in several studies although the evidence so far remains inconclusive. Here, we analyze the stream flow of one of the largest rivers in the world, the Parana in southeastern South America. For the last century, we find a strong correlation with the sunspot number, in multidecadal time scales, and with larger solar activity corresponding to larger stream flow. The correlation coefficient is r=0.78, significant to a 99% level. In shorter time scales we find a strong correlation with El Nino. These results are a step toward flood prediction, which might h…
