Sparse pattern representation with application to pattern parameterization in atmosphere and land surface coupled systems

Research Area:
Atmospheric Sciences, Mathematics

We will develop a common theoretical fundament for the unified description of patterns and pattern interactions. This shall be achieved by the development and application of multivariate, vector-valued, location- and possibly time-dependent statistical models with as few parameters as possible, namely sparse representations. Sparse representations are data- and/or model adapted mathematical representations in appropriate bases formulated and encoded with a minimal degrees of freedom. The most important quantities for describing the atmosphere and land-surface exchange patterns are sensible heat, latent heat and CO₂ fluxes, which will be obtained from model simulations and observations. These data will be analyzed with the help of wavelet and curvelet decompositions and, in particular, with empirical mode decompositions (EMDs) for describing patterns. EMDs are specifically adapted to and constructed for the targeted data and computed with numerical tools such as optimizations based on interpolating local extremes by piecewise polynomials. Pattern interactions shall be described by identifying mappings between patterns in their sparse representations. Based on the outcome of these analyses, we will propose methods for the incorporation of pattern interactions in integrated models like TerrSysMP to improve simulations and predictions.

The developed theory and techniques will be applied to pattern and pattern-interaction analysis using the large-eddy simulations performed in D6, as well as to the ground-based remote sensing observations from the TR32 and possibly to satellite data.

Cooperation partner:

C1, C3, C4, D6, D7