Groth, Andreas, Patrice Dumas, Michael Ghil, and Stéphane Hallegatte
. “Impacts of natural disasters on a dynamic economy
.” In Extreme Events : Observations, Modeling, and Economics
, edited by Eric Chavez, Michael Ghil, and Jaime Urrutia-Fucugauchi
, 343–360. American Geophysical Union and Wiley-Blackwell, 2015. Abstract
This chapter presents a modeling framework for macroeconomic growth dynamics; it is motivated by recent attempts to formulate and study “integrated models” of the coupling between natural and socioeconomic phe nomena. The challenge is to describe the interfaces between human activities and the functioning of the earth system. We examine the way in which this interface works in the presence of endogenous business cycle dynam ics, based on a nonequilibrium dynamic model. Recent findings about the macroeconomic response to natural disasters in such a nonequilibrium setting have shown a more severe response to natural disasters during expan sions than during recessions. These findings raise questions about the assessment of climate change damages or natural disaster losses that are based purely on long-term growth models. In order to compare the theoretical findings with observational data, we analyze cyclic behavior in the U.S. economy, based on multivariate singular spectrum analysis. We analyze a total of nine aggregate indicators in a 52 year interval (1954–2005) and demon strate that the behavior of the U.S. economy changes significantly between intervals of growth and recession, with higher volatility during expansions.
Recent estimates of climate evolution over the coming century still differ by several degrees. This uncertainty motivates the work presented here. There are two basic approaches to apprehend the complexity of climate change: deterministically nonlinear and stochastically linear, i.e., the Lorenz and the Hasselmann approach. The grand unification of these two approaches relies on the theory of random dynamical systems. We apply this theory to study the random attractors of nonlinear, stochastically perturbed climate models. Doing so allows one to examine the interaction of internal climate variability with the forcing, whether natural or anthropogenic, and to take into account the climate system's non-equilibrium behavior in determining climate sensitivity. This non-equilibrium behavior is due to a combination of nonlinear and random effects. We give here a unified treatment of such effects from the point of view of the theory of dynamical systems and of their bifurcations. Energy balance models are used to illustrate multiple equilibria, while multi-decadal oscillations in the thermohaline circulation illustrate the transition from steady states to periodic behavior. Random effects are introduced in the setting of random dynamical systems, which permit a unified treatment of both nonlinearity and stochasticity. The combined treatment of nonlinear and random effects is applied to a stochastically perturbed version of the classical Lorenz convection model. Climate sensitivity is then defined mathematically as the derivative of an appropriate functional or other function of the system’s state with respect to the bifurcation parameter. This definition is illustrated by using numerical results for a model of the El Niño–Southern Oscillation. The concept of a hierarchy of models is the thread that runs across this chapter, and the robustness of elementary bifurcations across such a hierarchy is emphasized.
The El-Nino/Southern-Oscillation (ENSO) phenomenon is the most prominent signal of seasonal-to-interannual climate variability. The past 30 years of research have shown that ENSO dynamics is governed, by and large, by the interplay of the nonlinear mechanisms, and that their simplest version can be studied in autonomous or forced delay differential equation (DDE) models. This chapter briefly reviews the results of Ghil et al., Zaliapin and Ghil, and Ghil and Zaliapin and pursues their DDE model analysis by focusing on multiple model solutions for the same parameter values and the dynamics of local extrema. It first introduces the DDE model of ENSO variability, reviews the main theoretical results concerning its solutions, and comments on the appropriate numerical integration methods. Novel results on multiple solutions and their extrema are reported and illustrated. After discussing the model's pullback attractor, the chapter explores parameter dependence in the model over its entire 3D parameter space.