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Concerns have been raised that anthropogenic climate change could lead to large-scale singular climate events, i.e., abrupt nonlinear climate changes with repercussions on regional to global scales. One central goal of this thesis is the development of models of two representative components of the climate system that could exhibit singular behavior: the Atlantic thermohaline circulation (THC) and the Indian monsoon. These models are conceived so as to fulfill the main requirements of integrated assessment modeling, i.e., reliability, computational efficiency, transparency and flexibility. The model of the THC is an interhemispheric four-box model calibrated against data generated with a coupled climate model of intermediate complexity. It is designed to be driven by global mean temperature change which is translated into regional fluxes of heat and freshwater through a linear down-scaling procedure. Results of a large number of transient climate change simulations indicate that the reduced-form THC model is able to emulate key features of the behavior of comprehensive climate models such as the sensitivity of the THC to the amount, regional distribution and rate of change in the heat and freshwater fluxes. The Indian monsoon is described by a novel one-dimensional box model of the tropical atmosphere. It includes representations of the radiative and surface fluxes, the hydrological cycle and surface hydrology. Despite its high degree of idealization, the model satisfactorily captures relevant aspects of the observed monsoon dynamics, such as the annual course of precipitation and the onset and withdrawal of the summer monsoon. Also, the model exhibits the sensitivity to changes in greenhouse gas and sulfate aerosol concentrations that are known from comprehensive models. A simplified version of the monsoon model is employed for the identification of changes in the qualitative system behavior against changes in boundary conditions. The most notable result is that under summer conditions a saddle-node bifurcation occurs at critical values of the planetary albedo or insolation. Furthermore, the system exhibits two stable equilibria: besides the wet summer monsoon, a stable state exists which is characterized by a weak hydrological cycle. These results are remarkable insofar, as they indicate that anthropogenic perturbations of the planetary albedo such as sulfur emissions and/or land-use changes could destabilize the Indian summer monsoon. The reduced-form THC model is employed in an exemplary integrated assessment application. Drawing on the conceptual and methodological framework of the tolerable windows approach, emissions corridors (i.e., admissible ranges of CO2- emissions) are derived that limit the risk of a THC collapse while considering expectations about the socio-economically acceptable pace of emissions reductions. Results indicate, for example, a large dependency of the width of the emissions corridor on climate and hydrological sensitivity: for low values of climate and/or hydrological sensitivity, the corridor boundaries are far from being transgressed by any plausible emissions scenario for the 21st century. In contrast, for high values of both quantities low non-intervention scenarios leave the corridor already in the early decades of the 21st century. This implies that if the risk of a THC collapse is to be kept low, business-as-usual paths would need to be abandoned within the next two decades. All in all, this thesis highlights the value of reduced-form modeling by presenting a number of applications of this class of models, ranging from sensitivity and bifurcation analysis to integrated assessment. The results achieved and conclusions drawn provide a useful contribution to the scientific and policy debate about the consequences of anthropogenic climate change and the long-term goals of climate protection. --- Anmerkung: Die Autorin ist Trägerin des von der Mathematisch-Naturwissenschaftlichen Fakultät der Universität Potsdam vergebenen Michelson-Preises für die beste Promotion des Jahres 2003/2004.
We present an application of imprecise probability theory to the quantification of uncertainty in the integrated assessment of climate change. Our work is motivated by the fact that uncertainty about climate change is pervasive, and therefore requires a thorough treatment in the integrated assessment process. Classical probability theory faces some severe difficulties in this respect, since it cannot capture very poor states of information in a satisfactory manner. A more general framework is provided by imprecise probability theory, which offers a similarly firm evidential and behavioural foundation, while at the same time allowing to capture more diverse states of information. An imprecise probability describes the information in terms of lower and upper bounds on probability. For the purpose of our imprecise probability analysis, we construct a diffusion ocean energy balance climate model that parameterises the global mean temperature response to secular trends in the radiative forcing in terms of climate sensitivity and effective vertical ocean heat diffusivity. We compare the model behaviour to the 20th century temperature record in order to derive a likelihood function for these two parameters and the forcing strength of anthropogenic sulphate aerosols. Results show a strong positive correlation between climate sensitivity and ocean heat diffusivity, and between climate sensitivity and absolute strength of the sulphate forcing. We identify two suitable imprecise probability classes for an efficient representation of the uncertainty about the climate model parameters and provide an algorithm to construct a belief function for the prior parameter uncertainty from a set of probability constraints that can be deduced from the literature or observational data. For the purpose of updating the prior with the likelihood function, we establish a methodological framework that allows us to perform the updating procedure efficiently for two different updating rules: Dempster's rule of conditioning and the Generalised Bayes' rule. Dempster's rule yields a posterior belief function in good qualitative agreement with previous studies that tried to constrain climate sensitivity and sulphate aerosol cooling. In contrast, we are not able to produce meaningful imprecise posterior probability bounds from the application of the Generalised Bayes' Rule. We can attribute this result mainly to our choice of representing the prior uncertainty by a belief function. We project the Dempster-updated belief function for the climate model parameters onto estimates of future global mean temperature change under several emissions scenarios for the 21st century, and several long-term stabilisation policies. Within the limitations of our analysis we find that it requires a stringent stabilisation level of around 450 ppm carbon dioxide equivalent concentration to obtain a non-negligible lower probability of limiting the warming to 2 degrees Celsius. We discuss several frameworks of decision-making under ambiguity and show that they can lead to a variety of, possibly imprecise, climate policy recommendations. We find, however, that poor states of information do not necessarily impede a useful policy advice. We conclude that imprecise probabilities constitute indeed a promising candidate for the adequate treatment of uncertainty in the integrated assessment of climate change. We have constructed prior belief functions that allow much weaker assumptions on the prior state of information than a prior probability would require and, nevertheless, can be propagated through the entire assessment process. As a caveat, the updating issue needs further investigation. Belief functions constitute only a sensible choice for the prior uncertainty representation if more restrictive updating rules than the Generalised Bayes'Rule are available.
Stochastic information, to be understood as "information gained by the application of stochastic methods", is proposed as a tool in the assessment of changes in climate. This thesis aims at demonstrating that stochastic information can improve the consideration and reduction of uncertainty in the assessment of changes in climate. The thesis consists of three parts. In part one, an indicator is developed that allows the determination of the proximity to a critical threshold. In part two, the tolerable windows approach (TWA) is extended to a probabilistic TWA. In part three, an integrated assessment of changes in flooding probability due to climate change is conducted within the TWA. The thermohaline circulation (THC) is a circulation system in the North Atlantic, where the circulation may break down in a saddle-node bifurcation under the influence of climate change. Due to uncertainty in ocean models, it is currently very difficult to determine the distance of the THC to the bifurcation point. We propose a new indicator to determine the system's proximity to the bifurcation point by considering the THC as a stochastic system and using the information contained in the fluctuations of the circulation around the mean state. As the system is moved closer to the bifurcation point, the power spectrum of the overturning becomes "redder", i.e. more energy is contained in the low frequencies. Since the spectral changes are a generic property of the saddle-node bifurcation, the method is not limited to the THC, but it could also be applicable to other systems, e.g. transitions in ecosystems. In part two, a probabilistic extension to the tolerable windows approach (TWA) is developed. In the TWA, the aim is to determine the complete set of emission strategies that are compatible with so-called guardrails. Guardrails are limits to impacts of climate change or to climate change itself. Therefore, the TWA determines the "maneuvering space" humanity has, if certain impacts of climate change are to be avoided. Due to uncertainty it is not possible to definitely exclude the impacts of climate change considered, but there will always be a certain probability of violating a guardrail. Therefore the TWA is extended to a probabilistic TWA that is able to consider "probabilistic uncertainty", i.e. uncertainty that can be expressed as a probability distribution or uncertainty that arises through natural variability. As a first application, temperature guardrails are imposed, and the dependence of emission reduction strategies on probability distributions for climate sensitivities is investigated. The analysis suggests that it will be difficult to observe a temperature guardrail of 2°C with high probabilities of actually meeting the target. In part three, an integrated assessment of changes in flooding probability due to climate change is conducted. A simple hydrological model is presented, as well as a downscaling scheme that allows the reconstruction of the spatio-temporal natural variability of temperature and precipitation. These are used to determine a probabilistic climate impact response function (CIRF), a function that allows the assessment of changes in probability of certain flood events under conditions of a changed climate. The assessment of changes in flooding probability is conducted in 83 major river basins. Not all floods can be considered: Events that either happen very fast, or affect only a very small area can not be considered, but large-scale flooding due to strong longer-lasting precipitation events can be considered. Finally, the probabilistic CIRFs obtained are used to determine emission corridors, where the guardrail is a limit to the fraction of world population that is affected by a predefined shift in probability of the 50-year flood event. This latter analysis has two main results. The uncertainty about regional changes in climate is still very high, and even small amounts of further climate change may lead to large changes in flooding probability in some river systems.