Observing extreme events in incomplete state spaces with application to rainfall estimation from satellite images
- 1Department of Mathematical Sciences, Atmospheric Sciences Group, University of Wisconsin-Milwaukee, Milwaukee, WI 53201-0413, USA
- 2Hydrologic Research Center, 12780 High Bluff Drive, Suite 250, San Diego, CA 92130, USA
- 3Scripps Institution of Oceanography, UCSD, La Jolla, CA 92093-0224, USA
Abstract. Reconstructing the dynamics of nonlinear systems from observations requires the complete knowledge of its state space. In most cases, this is either impossible or at best very difficult. Here, by using a toy model, we investigate the possibility of deriving useful insights about the variability of the system from only a part of the complete state vector. We show that while some of the details of the variability might be lost, other details, especially extreme events, are successfully recovered. We then apply these ideas to the problem of rainfall estimation from satellite imagery. We show that, while reducing the number of observables reduces the correlation between actual and inferred precipitation amounts, good estimates for extreme events are still recoverable.