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Encyclopedia of Complexity and Systems Science pp 1–30Cite as

Abrupt Climate Change Modeling

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Definition of the Subject and Its Importance

The occurrence of abrupt change of climate at various time scales has attracted a great deal of interest for its theoretical and practical significance (Berger and Labeyrie 1987; Alley et al. 2002; Alverson and Oldfield 2000). To some extent, a definition of what constitutes an abrupt climatic change depends on the sampling interval of the data being examined (Fu et al. 1999). For the instrumental period covering approximately the last 100 years of annually or seasonally sampled data, an abrupt change in a particular climate variable will be taken to mean a statistically highly significant difference between adjacent 10-year sample means. In the paleoclimate context (i.e., on long time scales), an abrupt climate change can be in the order of decades to thousands of years. Since the climate dynamics can be often projected onto a limited number of modes or patterns of climate variability (e.g., Dima and Lohmann 2002, 2007), the definition of...

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Abbreviations

Abrupt climate change:

One can define abrupt climate change in the time and frequency domain. (a) In the time domain, abrupt climate change refers to a large shift in climate that persists for years or longer, such as marked changes in average temperature or altered patterns of storms, floods, or droughts, over a widespread area that takes place so rapidly that the natural system has difficulty adapting to it. In the context of past abrupt climate change, “rapidly” typically means on the order of a decade. (b) In the frequency domain, an abrupt change means that the characteristic periodicity changes. Also the phase relation between certain climate variables may change in a relatively short time. For both types of changes, examples will be provided.

Anthropogenic climate change:

Beginning with the industrial revolution in the 1850s and accelerating ever since, the human consumption of fossil fuels has elevated CO2 levels from a concentration of ~280 ppm to more than 380 ppm today. These increases are projected to reach more than 560 ppm before the end of the twenty-first century. As an example, a concomitant shift of ocean circulation would have serious consequences for both agriculture and fishing.

Atmosphere:

The atmosphere is involved in many processes of abrupt climate change, providing a strong nonlinearity in the climate system and propagating the influence of any climate forcing from one part of the globe to another. Atmospheric temperature, composition, humidity, cloudiness, and wind determine the Earth’s energy fluxes. Wind affects the ocean’s surface circulation and upwelling patterns. Atmospheric moisture transport determines the freshwater balance for the oceans, overall water circulation, and the dynamics of glaciers.

Climate models:

are based on balances of energy, momentum, and mass, as well as radiation laws. There are several model categories, full circulation models, low-order models, and models of intermediate complexity. Climate models simulate the interactions of the atmosphere, oceans, land surface, and ice. They are used for a variety of purposes from study of the dynamics of the weather and climate system, past climate to projections of future climate.

Climate simulation:

A climate simulation is the output of a computer program that attempts to simulate the climate evolution under appropriate boundary conditions. Simulations have become a useful part of climate science to gain insight into the sensitivity of the system.

Climate time scales:

The climate system is a composite system consisting of five major interactive components: the atmosphere; the hydrosphere, including the oceans; the cryosphere; the lithosphere; and the biosphere. All subsystems are open and non-isolated, as the atmosphere, hydrosphere, cryosphere, and biosphere act as cascading systems linked by complex feedback processes. Climate refers to the average conditions in the Earth system that generally occur over periods of time, usually several decades or longer. This time scale is longer than the typical response time of the atmosphere. Parts of the other components of the Earth system (ice, ocean, continents) have much slower response times (decadal to millennial).

Climate variability pattern:

Climate variability is defined as changes in integral properties of the climate system. True understanding of climate dynamics and prediction of future changes will come only with an understanding of the Earth system as a whole and over past and present climate. Such understanding requires identification of the patterns of climate variability and their relationships to known forcing. Examples for climate variability patterns are the North Atlantic Oscillation (NAO) or the El Niño Southern Oscillation (ENSO).

Climate variables and forcing:

State variables are temperature, rainfall, wind, ocean currents, and many other variables in the Earth system. In our notation, the variables are described by a finite set of real variables in a vector x(t) ∈ Rn. The climate system is subject to two main external forcings F(x,t) that condition its behavior, solar radiation, and the action of gravity. Since F(x,t) has usually a spatial dependence, F is also a vector ∈ Rn. Solar radiation must be regarded as the primary forcing mechanism, as it provides almost all the energy that drives the climate system. The whole climate system can be regarded as continuously evolving, as solar radiation changes on diurnal, seasonal, and longer time scales, with parts of the system leading or lagging in time. Therefore, the subsystems of the climate system are not always in equilibrium with each other. Indeed, the climate system is a dissipative, highly nonlinear system, with many instabilities.

Cryosphere:

The portion of the Earth covered with ice and snow, the cryosphere, greatly affects temperature. When sea ice forms, it increases the planetary reflective capacity, thereby enhancing cooling. Sea ice also insulates the atmosphere from the relatively warm ocean, allowing winter air temperatures to steeply decline and reduce the supply of moisture to the atmosphere. Glaciers and snow cover on land can also provide abrupt-change mechanisms. The water frozen in a glacier can melt if warmed sufficiently, leading to possibly rapid discharge, with consequent effects on sea level and ocean circulation. Meanwhile, snow-covered lands of all types maintain cold conditions because of their high reflectivity and because surface temperatures cannot rise above freezing until the snow completely melts.

Earth system models of intermediate complexity (EMICs):

Depending on the nature of questions asked and the pertinent time scales, different types of models are used. There are, on the one extreme, conceptual models and, on the other extreme, comprehensive models (GCMs) operating at a high spatial and temporal resolution. Models of intermediate complexity bridge the gap (Claussen et al. 2002). These models are successful in describing the Earth system dynamics including a large number of Earth system components. This approach is especially useful when considering long time scales where the complex models are computationally too expensive, e.g., Lohmann and Gerdes (1998). Improvements in the development of coupled models of intermediate complexity have led to a situation where modeling a glacial cycle, even with prognostic atmospheric CO2, is becoming possible.

External factors:

Phenomena external to the climate system can also be agents of abrupt climate change. For example, the orbital parameters of the Earth vary over time, affecting the latitudinal distribution of solar energy. Furthermore, fluctuations in solar output, prompted by sunspot activity or the effects of solar wind, as well as volcanoes, may cause climate fluctuations.

Feedbacks:

A perturbation in a system with a negative feedback mechanism will be reduced, whereas in a system with positive feedback mechanisms, the perturbation will grow. Quite often, the system dynamics can be reduced to a low-order description. Then, the growth or decay of perturbations can be classified by the systems’ eigenvalues or the pseudospectrum. Consider the stochastic dynamical system

$$ \frac{d}{dt}x(t)=f(x)+g(x)\xi +F\left(x,t\right), $$
(1)

where ξ is a stochastic process. The functions f, g describe the climate dynamics, in this case without explicit time dependence. The external forcing F(x, t) is generally time, variable, and space dependent. In his theoretical approach, Hasselmann (1976) formulated a linear stochastic climate model

$$ \frac{d}{dt}x(t)=A(x)+\sigma \xi +F(t), $$
(2)

with system matrix A ∈ Rn×n, constant noise term σ, and stochastic process ξ. Interestingly, many features of the climate system can be well described by (2), which is analogous to the Ornstein–Uhlenbeck process in statistical physics (Uhlenbeck and Ornstein 1930). In the climate system, linear and nonlinear feedbacks are essential for abrupt climate changes.

Global climate models or general circulation models (GCMs):

The balances of energy, momentum, and mass are formulated in the framework of fluid dynamics on the rotating Earth. GCMs discretize the equations for fluid motion and energy transfer and integrate these forward in time. They also contain parameterizations for processes – such as convection – that occur on scales too small to be resolved directly. The dimension of the state vector is in the order of n ~ 105 − 108 depending on the resolution and complexity of the model.

Land surface:

The reflective capacity of the land can change greatly, with snow or ice sheets reflecting up to 90 % of the sunlight while dense forests absorb more than 90 %. Changes in surface characteristics can also affect solar heating, cloud formation, rainfall, and surface-water flow to the oceans, thus feeding back strongly on climate.

Long-term climate statistics:

Starting with a given initial state, the solutions x(t) of the equations that govern the dynamics of a nonlinear system, such as the atmosphere, result in a set of long-term statistics. If all initial states ultimately lead to the same set of statistical properties, the system is ergodic or transitive. If, instead, there are two or more different sets of statistical properties, where some initial states lead to one set, while the other initial states lead to another, the system is called intransitive (one may call the different states regimes). If there are different sets of statistics that a system may assume in its evolution from different initial states through a long, but finite, period of time, the system is called almost intransitive (Lorenz 1963, 1976). In the transitive case, the equilibrium climate statistics are both stable and unique. Long-term climate statistics will give a good description of the climate. In the almost intransitive case, the system in the course of its evolution will show finite periods during which distinctly different climatic regimes prevail. The almost intransitive case arises because of internal feedbacks or instabilities involving the different components of the climatic system. The climatic record can show rapid steplike shifts in climate variability that occur over decades or less, including climatic extremes (e.g., drought) that persist for decades.

Model categories:

In addition to complex numerical climate models, it can be of great utility to reduce the system to low-order, box, and conceptual models. This complementary approach has been successfully applied to a number of questions regarding feedback mechanisms and the basic dynamical behavior, e.g., Lohmann and Schneider (1999) and Timmermann and Lohmann (2000). In some cases, e.g., the stochastic climate model of Hasselmann (1976), such models can provide a null hypothesis for the complex system. The transition from highly complex dynamical equations to a low-order description of climate is an important topic of research. In his book Dynamical Paleoclimatology, Saltzman (2002) formulated a dynamical system approach in order to differentiate between fast-response and slow-response variables. As an alternative to this method, one can try to derive phenomenologically based concepts of climate variability, e.g., Dima and Lohmann (2002) and Kwasniok and Lohmann (2009). In between the comprehensive models and conceptual models, a wide class of “models of intermediate complexity” were defined (Claussen et al. 2002).

Multiple equilibria:

Fossil evidence and computer models demonstrate that the Earth’s complex and dynamic climate system has more than one mode of operation. Each mode produces different climate patterns. The evidence of models and data analysis shows that the Earth’s climate system has sensitive thresholds. Pushed past a threshold, the system can jump from one stable operating mode to a completely different one.

Oceans:

Because water has enormous heat capacity, oceans typically store 10–100 times more heat than equivalent land surfaces. The oceans exert a profound influence on climate through their ability to transport heat from one location to another. Changes in ocean circulation have been implicated in abrupt climate change of the past. Deglacial meltwater has freshened the North Atlantic and reduced the ability of the water to sink, inducing long-term coolings.

Paleoclimate:

Abrupt climate change is evident in model results and in instrumental records of the climate system. Much interest in the subject is motivated by the evidence in archives of extreme changes. Proxy records of paleoclimate are central to the subject of abrupt climate change. Available paleoclimate records provide information on many environmental variables, such as temperature, moisture, wind, currents, and isotopic compositions.

Regime shifts:

are defined as rapid transitions from one state to another. In the marine environment, regimes may last for several decades, and shifts often appear to be associated with changes in the climate system. If the shifts occur regularly, they are often referred as an oscillation (e.g., Atlantic Multidecadal Oscillation, Pacific Decadal Oscillation). Similarly, one can define a regime shift in the frequency domain.

Thermohaline circulation:

stems from the Greek words “thermos” (heat) and “halos” (salt). The ocean is driven to a large extent by surface heat and freshwater fluxes. As the ocean is nonlinear, it cannot be strictly separated from the wind-driven circulation. The expressions thermohaline circulation (THC) and meridional overturning circulation (MOC) in the ocean are quite often used as synonyms although the latter includes all effects (wind, thermal, haline forcing) and describes the ocean transport in meridional direction. Another related expression is the ocean conveyor belt. This metaphor is motivated by the fact that the North Atlantic is the source of the deep limb of a global ocean circulation system (Broecker et al. 1985). If North Atlantic surface waters did not sink, the global ocean circulation would cease and currents would weaken or be redirected. The resulting reorganization would reconfigure climate patterns, especially in the Atlantic Ocean. One fundamental aspect of this circulation is the balance of two processes: cooling of the deep ocean at high latitudes and heating of deeper levels from the surface through vertical mixing.

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  1. Alfred Wegener Institute for Polar and Marine Research Bussestr. 24, D-27570, Bremerhaven, Germany

    Gerrit Lohmann

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  1. Gerrit Lohmann
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Correspondence to Gerrit Lohmann .

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  1. Ramtech Ltd., Larkspur, California, USA

    Robert A. Meyers

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Lohmann, G. (2014). Abrupt Climate Change Modeling. In: Meyers, R. (eds) Encyclopedia of Complexity and Systems Science. Springer, New York, NY. https://doi.org/10.1007/978-3-642-27737-5_1-5

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