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Algorithmic Sensitivity Analysis in the Climate Model Climber 2

Slawig, Thomas

Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin

This report summarizes the results of the project Algosense performed at the Institut für Mathematik, Technische Universität Berlin, from July 2001 to June 2002. Aim of the project was to analyze the applicability of tools for Algorithmic (or Automatic) Differentiation (AD) to two climate models developed at the Potsdam Institute for Climate Impact Research (PIK). These were the so-called Box Model, a small model of the North Atlantic stream, and the more complex model Climber 2 which is a so-called model of intermediate complexity consisting of atmosphere, ocean, ice, and vegetation components. Applications that are considered start from pure sensitivity calculations over uncertainty estimations to optimization runs. First and higher order derivatives are of interest. The outline of this report is the following: In the next section we describe the basic tools and techniques of Algorithmic Differentiation. The following two sections deal with the two models studied in this project. In each of them the corresponding model and its special features important for Algorithmic Differentiation are briefly introduced. Then the used Algorithmic Differentiation tools and technical details of the AD process are presented. At last numerical results are given. Further emphasis is put on the necessary code preparations to apply the AD tools. The last section of the report gives a summary and deals with the perspectives and opportunities of the application of Algorithmic Differentiation to these and maybe other climate models.