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32. Climate system models — a brief introduction
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32. Climate System Models – A Brief Introduction Martin Claussen Meteorological Institute, University Hamburg, and Max Planck Institute for Meteorology, Bundesstr. 53, D-20146 Hamburg, Germany
Models are, generally speaking, descriptions of nature. There are several possibilities to describe nature. There is the artist’s point of view, there are narrative models and there are physical and mathematical models. The artist’s point of view is often helpful as it brings specific aspects of nature to the attention of scientists. The history of cloud paintings is an illustrative example (Wehry and Ossing, 1997). Narrative models, or story lines, are written concepts to qualitatively reconstruct causal relationships. Such narrative, conceptual models are often used in geology (e.g. Haug and Tiedemann, 1998). Examples of physical models are wind tunnels which simulate atmospheric boundary-layer flow or rotating tanks (e.g. Greenspan, 1980) in which rotating flows as proxy for atmospheric and oceanic motion are investigated. Physical models allow performing well-defined control experiments which, in nature, are impossible to do. So far, physical models only highlight specific processes in the climate system. In this part of the book, only mathematical models of the climate system are discussed. Mathematical models are a set of differential and diagnostic equations. These equations describe the dynamics of components of the climate system with varying degree of approximation. Most equations can be derived from the fundamental laws of conservation of energy, momentum and mass, and such a set of equations is referred to as deductive model. Climate models are generally quasi-deductive (Saltzman, 1985), because they include some empirical parameterisation of processes which cannot be deduced from fundamental laws such as
the so-called subgrid-scale motion discussed below. In parameterisation, only the effect of a process on the system is mathematically described. In contrast to deductive models, inductive models are not derived from first principles. Instead, the dynamics of climate processes, which are assumed to be important, are formulated in mathematical terms without explicit consideration of fundamental physical constraints – such as the models by Calder, Imbrie, Paillard, Paul and Berger discussed in Chapter 3. Inductive models are used to demonstrate the plausibility of climate processes and to explore the consequences of assumptions imposed on the system. There are several ways to classify climate system models according to their complexity and degree of approximation. For example, McGuffie and HenderssonSellers (1997) chose the picture of a pyramid in which the vertices represent mainly atmospheric components which are then coupled together to form the apex of a comprehensive model of atmospheric, oceanic and, in some cases, biospheric dynamics, a so-called general circulation model. Claussen et al. (2002) proposed an alternative view on this ‘classical’ hierarchy by introducing an indicator which characterises the number of interacting components of the climate system being explicitly described in a climate system model (see Fig. 32.1). In the following chapters, mainly general circulation models (in Chapters 33, 34, 35, 37) and the so-called Earth system models of intermediate complexity (EMICs – in chapters 36, 38, 39) are discussed.
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I “Simple” Box-M.
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Fig. 32.1 The three-dimensional spectrum of climate system models. The coordinates are: I, integration, i.e., the number of interacting components of the climate system (see Chapter 1.1) explicitly described in a model; G, geographical detail of description, here defined as the order of magnitude of the number of grid cells when counting atmosphere and ocean modules only; D, dynamic processes considered, here taken as the spatial dimension of atmospheric and of the oceanic modules (some models, for example, predict the atmospheric temperature on average over the depth of the atmosphere, or on average over a latitudinal band; hence their atmospheric module is considered two-dimensional in which the dynamics of atmospheric circulation is described in a more parameterised way than is the case in three-dimensional models). The numbers refer to several models of intermediate complexity, or so-called Earth system models of intermediate complexity (EMICs), while CSM, AO-GCM, A-GCM represent typical general circulation models (GCM) referred to as climate system model (CSM) or atmosphere–ocean GCMs (AOGCM) or atmospheric GCMs (A-GCM). For details see Claussen et al. (2002). This figure is taken from Claussen et al. (2002) with the permission of Springer-Verlag.
In relation to data, mathematical models can be used in two ways. Firstly, mathematical models are used in a prognostic, or predictive, mode. In this mode, models are driven by forcing (by changes in the Earth’s orbit, for example; see Chapter 1), and the results of the model are compared with data or proxy data to (a) interpret data and (b) to validate the model. Secondly, mathematical models can be run in an assimilation mode, i.e. they are ‘tuned to data’. Such tuning can
be done by nudging, for example, which means that some terms are added to the equations of energy, momentum and mass conservation which push the model towards observed data. Other methods require that models in an assimilation mode minimise the distance between model results and data points which are scattered in time and space. In the assimilation mode, models do not predict climate variations, but they are meant to interpolate sparse data in space and time in a physically consistent manner. Moreover, by means of assimilation, it is possible to explore the relative importance of processes in the observed climate variations. In this chapter, all models are used in the prognostic mode. When comparing data and model results, it is important to realise that climate is regarded as a stochastic process. Motion in the climate system consists of many scales ranging from the formation of cloud droplets, wind gusts, drift of pollen, to swirling ocean currents and the waxing and waning of ice sheets. Therefore, it is not possible to predict all this motion in a deterministic way. Instead, the complexity of the problem is reduced by averaging the variables which characterise the state of the system (such as wind speed, temperature, concentration of carbon in plants, etc.) over some region and some period in time. This averaging procedure introduces some degree of randomness, firstly, because the deviation from the average, the so-called subgrid-scale motion is not predictable deterministically and, hence, it is treated as a stochastic variable, and secondly, because subgrid-scale motion affects the averaged, grid-scale motion. Most differences between models can be attributed to the differences in parameterising subgrid-scale processes, i.e. in describing the effect of the subgrid-scale motion on the grid-scale motion. To explore the uncertainty of model results, it is useful to perform multimodel simulations. Therefore, the results of not just one model, but of a suite of models will be presented in Section 5.
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Climate System Models
But even if the subgrid-scale motion were precisely known, the dynamics of the averaged climate variables are still hard to describe; in order to forecast any climate change, the state of the climate system in the past from which the forecast is started has to be reconstructed – which, of course, can be done only to some limited extent. Also the forcing of the climate system is known more or less accurately. In this situation, the averaged quantities are predicted by starting the simulations many times from a number of equally likely, but not precisely known, initial states and by using a number of equally likely, or plausible, external forcing. The former situation is referred to as an initial-value problem and the latter, a boundary-value problem. Actually, the separation between these problems depends on the memory of the system. Weather forecast is a typical initial-value problem, while future scenarios of climate change due to a hypothesised increase in atmospheric CO2 concentration are a sort of boundary-value problem. In some cases, a well-known, strong external forcing dominates climate dynamics such that all simulations yield similar results. In fact, often only one simulation is done, and it is implicitly assumed that other simulations would yield similar results – an assumption that will be critically assessed in Chapter 39. The randomness of climate motion has an important implication for simulations of interglacials and glacial inceptions which will be discussed in the following chapters. Some processes, like the calving of icebergs and subsequent flushing of fresh water into the ocean, depend on small-scale processes
497
which appear to be random. Therefore, it is impossible to precisely predict the occurrence of the first Heinrich event or first stadial at the last glacial inception. Instead, one can only explore the conditions which favour the occurrence of such events, and one can only expect to simulate the gross features seen in palaeoclimate reconstructions. ACKNOWLEDGEMENT The author thanks Susanne Weber, KNMI and Claudia Kubatzki, AWI-Bremerhaven, for constructive comments. REFERENCES Claussen, M., Mysak, L.A., Weaver, A.J., Crucifix, M., Fichefet, T., Loutre, M.-F., Weber, S.L., Alcamo, J., Alexeev, V.A., Berger, A., Calov, R., Ganopolski, A., Goosse, H., Lohman, G., Lunkeit, F, Mokhov, I. I., Petoukhov, V., Stone, P., Wang, Zh., 2002. Earth system models of intermediate complexity: Closing the gap in the spectrum of climate system models, Climate Dynamics 18, 579–586. Greenspan, H.P., 1980. The theory of rotating fluids. Cambridge University Press, 328 pp. Haug, G.H., Tiedemann, R., 1998. Effect of the formation of the isthmus of Panama on Atlantic Ocean thermohaline circulation. Nature 393, 673–676. McGuffie, K., Henderson-Sellers, A., 1997. A climate modelling primer. Wiley, Chichester, 253 pp. Wehry, W., Ossing, F.J. (eds.), 1997. Wolken – Malerei – Klima. Deutsche Meteorologische Gesellschaft, Berlin, 191 pp. Saltzman B., 1985. Paleoclimatic modeling. In: Hecht AD (ed), Paleoclimate analysis and modeling. Wiley , Chichester, 341–396.
32. Climate System Models – A Brief Introduction Martin Claussen Meteorological Institute, University Hamburg, and Max Planck Institute for Meteorology, Bundesstr. 53, D-20146 Hamburg, Germany
Models are, generally speaking, descriptions of nature. There are several possibilities to describe nature. There is the artist’s point of view, there are narrative models and there are physical and mathematical models. The artist’s point of view is often helpful as it brings specific aspects of nature to the attention of scientists. The history of cloud paintings is an illustrative example (Wehry and Ossing, 1997). Narrative models, or story lines, are written concepts to qualitatively reconstruct causal relationships. Such narrative, conceptual models are often used in geology (e.g. Haug and Tiedemann, 1998). Examples of physical models are wind tunnels which simulate atmospheric boundary-layer flow or rotating tanks (e.g. Greenspan, 1980) in which rotating flows as proxy for atmospheric and oceanic motion are investigated. Physical models allow performing well-defined control experiments which, in nature, are impossible to do. So far, physical models only highlight specific processes in the climate system. In this part of the book, only mathematical models of the climate system are discussed. Mathematical models are a set of differential and diagnostic equations. These equations describe the dynamics of components of the climate system with varying degree of approximation. Most equations can be derived from the fundamental laws of conservation of energy, momentum and mass, and such a set of equations is referred to as deductive model. Climate models are generally quasi-deductive (Saltzman, 1985), because they include some empirical parameterisation of processes which cannot be deduced from fundamental laws such as
the so-called subgrid-scale motion discussed below. In parameterisation, only the effect of a process on the system is mathematically described. In contrast to deductive models, inductive models are not derived from first principles. Instead, the dynamics of climate processes, which are assumed to be important, are formulated in mathematical terms without explicit consideration of fundamental physical constraints – such as the models by Calder, Imbrie, Paillard, Paul and Berger discussed in Chapter 3. Inductive models are used to demonstrate the plausibility of climate processes and to explore the consequences of assumptions imposed on the system. There are several ways to classify climate system models according to their complexity and degree of approximation. For example, McGuffie and HenderssonSellers (1997) chose the picture of a pyramid in which the vertices represent mainly atmospheric components which are then coupled together to form the apex of a comprehensive model of atmospheric, oceanic and, in some cases, biospheric dynamics, a so-called general circulation model. Claussen et al. (2002) proposed an alternative view on this ‘classical’ hierarchy by introducing an indicator which characterises the number of interacting components of the climate system being explicitly described in a climate system model (see Fig. 32.1). In the following chapters, mainly general circulation models (in Chapters 33, 34, 35, 37) and the so-called Earth system models of intermediate complexity (EMICs – in chapters 36, 38, 39) are discussed.
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Fig. 32.1 The three-dimensional spectrum of climate system models. The coordinates are: I, integration, i.e., the number of interacting components of the climate system (see Chapter 1.1) explicitly described in a model; G, geographical detail of description, here defined as the order of magnitude of the number of grid cells when counting atmosphere and ocean modules only; D, dynamic processes considered, here taken as the spatial dimension of atmospheric and of the oceanic modules (some models, for example, predict the atmospheric temperature on average over the depth of the atmosphere, or on average over a latitudinal band; hence their atmospheric module is considered two-dimensional in which the dynamics of atmospheric circulation is described in a more parameterised way than is the case in three-dimensional models). The numbers refer to several models of intermediate complexity, or so-called Earth system models of intermediate complexity (EMICs), while CSM, AO-GCM, A-GCM represent typical general circulation models (GCM) referred to as climate system model (CSM) or atmosphere–ocean GCMs (AOGCM) or atmospheric GCMs (A-GCM). For details see Claussen et al. (2002). This figure is taken from Claussen et al. (2002) with the permission of Springer-Verlag.
In relation to data, mathematical models can be used in two ways. Firstly, mathematical models are used in a prognostic, or predictive, mode. In this mode, models are driven by forcing (by changes in the Earth’s orbit, for example; see Chapter 1), and the results of the model are compared with data or proxy data to (a) interpret data and (b) to validate the model. Secondly, mathematical models can be run in an assimilation mode, i.e. they are ‘tuned to data’. Such tuning can
be done by nudging, for example, which means that some terms are added to the equations of energy, momentum and mass conservation which push the model towards observed data. Other methods require that models in an assimilation mode minimise the distance between model results and data points which are scattered in time and space. In the assimilation mode, models do not predict climate variations, but they are meant to interpolate sparse data in space and time in a physically consistent manner. Moreover, by means of assimilation, it is possible to explore the relative importance of processes in the observed climate variations. In this chapter, all models are used in the prognostic mode. When comparing data and model results, it is important to realise that climate is regarded as a stochastic process. Motion in the climate system consists of many scales ranging from the formation of cloud droplets, wind gusts, drift of pollen, to swirling ocean currents and the waxing and waning of ice sheets. Therefore, it is not possible to predict all this motion in a deterministic way. Instead, the complexity of the problem is reduced by averaging the variables which characterise the state of the system (such as wind speed, temperature, concentration of carbon in plants, etc.) over some region and some period in time. This averaging procedure introduces some degree of randomness, firstly, because the deviation from the average, the so-called subgrid-scale motion is not predictable deterministically and, hence, it is treated as a stochastic variable, and secondly, because subgrid-scale motion affects the averaged, grid-scale motion. Most differences between models can be attributed to the differences in parameterising subgrid-scale processes, i.e. in describing the effect of the subgrid-scale motion on the grid-scale motion. To explore the uncertainty of model results, it is useful to perform multimodel simulations. Therefore, the results of not just one model, but of a suite of models will be presented in Section 5.
//FS/ELS/PAGINATION/ELSEVIER AMS/STPS/3B2/CH32-N2955.3D – 493 – [493–498/6] 28.10.2006 12:43PM
Climate System Models
But even if the subgrid-scale motion were precisely known, the dynamics of the averaged climate variables are still hard to describe; in order to forecast any climate change, the state of the climate system in the past from which the forecast is started has to be reconstructed – which, of course, can be done only to some limited extent. Also the forcing of the climate system is known more or less accurately. In this situation, the averaged quantities are predicted by starting the simulations many times from a number of equally likely, but not precisely known, initial states and by using a number of equally likely, or plausible, external forcing. The former situation is referred to as an initial-value problem and the latter, a boundary-value problem. Actually, the separation between these problems depends on the memory of the system. Weather forecast is a typical initial-value problem, while future scenarios of climate change due to a hypothesised increase in atmospheric CO2 concentration are a sort of boundary-value problem. In some cases, a well-known, strong external forcing dominates climate dynamics such that all simulations yield similar results. In fact, often only one simulation is done, and it is implicitly assumed that other simulations would yield similar results – an assumption that will be critically assessed in Chapter 39. The randomness of climate motion has an important implication for simulations of interglacials and glacial inceptions which will be discussed in the following chapters. Some processes, like the calving of icebergs and subsequent flushing of fresh water into the ocean, depend on small-scale processes
497
which appear to be random. Therefore, it is impossible to precisely predict the occurrence of the first Heinrich event or first stadial at the last glacial inception. Instead, one can only explore the conditions which favour the occurrence of such events, and one can only expect to simulate the gross features seen in palaeoclimate reconstructions. ACKNOWLEDGEMENT The author thanks Susanne Weber, KNMI and Claudia Kubatzki, AWI-Bremerhaven, for constructive comments. REFERENCES Claussen, M., Mysak, L.A., Weaver, A.J., Crucifix, M., Fichefet, T., Loutre, M.-F., Weber, S.L., Alcamo, J., Alexeev, V.A., Berger, A., Calov, R., Ganopolski, A., Goosse, H., Lohman, G., Lunkeit, F, Mokhov, I. I., Petoukhov, V., Stone, P., Wang, Zh., 2002. Earth system models of intermediate complexity: Closing the gap in the spectrum of climate system models, Climate Dynamics 18, 579–586. Greenspan, H.P., 1980. The theory of rotating fluids. Cambridge University Press, 328 pp. Haug, G.H., Tiedemann, R., 1998. Effect of the formation of the isthmus of Panama on Atlantic Ocean thermohaline circulation. Nature 393, 673–676. McGuffie, K., Henderson-Sellers, A., 1997. A climate modelling primer. Wiley, Chichester, 253 pp. Wehry, W., Ossing, F.J. (eds.), 1997. Wolken – Malerei – Klima. Deutsche Meteorologische Gesellschaft, Berlin, 191 pp. Saltzman B., 1985. Paleoclimatic modeling. In: Hecht AD (ed), Paleoclimate analysis and modeling. Wiley , Chichester, 341–396.