## Predictability and Nonlinear Modelling in Natural Sciences and EconomicsResearchers in the natural sciences are faced with problems that require a novel approach to improve the quality of forecasts of processes that are sensitive to environmental conditions. Nonlinearity of a system may significantly complicate the predictability of future states: a small variation of parameters can dramatically change the dynamics, while sensitive dependence of the initial state may severely limit the predictability horizon. Uncertainties also play a role here. This proceedings volume addresses such problems by using tools from chaos theory and systems theory, which are adapted for the analysis of problems in the environmental sciences. Sensitive dependence on the initial state (chaos) and the parameters are analyzed using various methods, for example Lyapunov exponents and Monte Carlo simulation. Uncertainty in the structure and the values of parameters of a model is studied in relation to processes that depend on the environmental conditions. These methods also apply to biology and economics. Audience: Research workers at universities and (semi-) governmental institutes for the environment, agriculture, ecology, meteorology and water management, and theoretical economists. |

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### Contents

Introduction | 1 |

The Liouville equation and prediction of forecast skill | 29 |

An improved formula to describe error growth in meteorological models | 45 |

Copyright | |

32 other sections not shown

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algorithm applied approach approximation assessment assumed attractor average behaviour Bilthoven biomass calculated calibration chaotic chaotic attractor climate coefficient components concentration correlation critical loads denotes density dependence deposition deterministic distribution dynamical systems ecological ecosystems effects emission environmental epidemic equation error growth evaluation example Figure filter fish forecast forest function Hurst exponent identification increase individual Janssen Kleijnen Kooijman Latin hypercube sampling layer linear linear regression Lyapunov exponent marginal variance mathematical mean measures method model inputs model output model parameters model structure Monte Carlo Netherlands nonlinear observed parameter values period pesticide phase space phytoplankton population prediction problem range statistic regression regression analysis rescaled range risk sampling SEIR model sensitivity analysis sensitivity and uncertainty simulation models soil solution sources spatial statistical stochastic techniques temperature theory tropospheric uncertainty analysis uncertainty contribution UNCSAM validation variables variation vector water quality models weather