Project C1

Project C1 - Michael Hinze and Peter Korn: Model order reduction in variational data assimilation

Scientific Background and Motivation

Any real-world simulation such as a weather- or climate prediction requires an objective synthesis between a dynamical model of the atmosphere/ocean and noisy, incomplete and heterogeneous observations of the real atmosphere/ocean. To provide this synthesis is the purpose of variational data assimilation. Data assimilation allows to use a mathematical atmosphere/ocean model in order to determine uncertain variables (control variables) such as the initial condition or model parameters (e.g. mixing coefficients) from noisy measurements. From the mathematical point of view one has to deal with a very large-scale optimization problem with PDE constraints governed by the atmosphere- and/or ocean model. The computational costs for this optimization problem increase considerably within the trend towards high-resolution simulation. To reduce these costs nonlinear model order reduction (MOR) techniques can be applied.

Aims and Objectives

In this project we combine modern concepts of MOR based on numerical simulations and of PDE constrained optimization with meteorological leading edge approaches to atmosphere-ocean modeling to develop novel concepts for variational data assimilation in a three-dimensional ocean circulation model. MOR opens the perspective for reducing the computational costs of variational data assimilation, it provides a mathematical tool to treat the related optimization problems numerically, and also to analyze the sensitivity of the used atmosphere and/or ocean models with respect to the parameters involved. This research requires the interplay of Meteorology (atmosphere and/or ocean modeling at the MPI), Applied Mathematics (MOR and optimization at the UniHH), Scientific Computing (simulation of atmosphere and/or ocean models at the ZMAW), and Computer Science (treatment of and information extraction from huge data amounts).

Contact: Dr. Peter Korn, KlimaCampus, email: peter.korn@zmaw.de