A perspective on gaussian processes for earth observation

Earth observation (EO) by airborne and satellite remote sensing and in-situ observations play a fundamental role in monitoring our planet. In the last decade, machine learning and Gaussian processes (GPs) in particular has attained outstanding results in the estimation of bio-geo-physical variables from the acquired images at local and global scales in a time-resolved manner. GPs provide not only accurate estimates but also principled uncertainty estimates for the predictions, can easily accommodate multimodal data coming from different sensors and from multitemporal acquisitions, allow the introduction of physical knowledge, and a formal treatment of uncertainty quantification and error propagation. Despite great advances in forward and inverse modelling, GP models still have to face important challenges that are revised in this perspective paper. GP models should evolve towards data-driven physics-aware models that respect signal characteristics, be consistent with elementary laws of physics, and move from pure regression to observational causal inference.Comment: 1 figur

A Manifesto for the Equifinality Thesis.

This essay discusses some of the issues involved in the identification and predictions of hydrological models given some calibration data. The reasons for the incompleteness of traditional calibration methods are discussed. The argument is made that the potential for multiple acceptable models as representations of hydrological and other environmental systems (the equifinality thesis) should be given more serious consideration than hitherto. It proposes some techniques for an extended GLUE methodology to make it more rigorous and outlines some of the research issues still to be resolved

Recurrence time analysis, long-term correlations, and extreme events

The recurrence times between extreme events have been the central point of statistical analyses in many different areas of science. Simultaneously, the Poincar\'e recurrence time has been extensively used to characterize nonlinear dynamical systems. We compare the main properties of these statistical methods pointing out their consequences for the recurrence analysis performed in time series. In particular, we analyze the dependence of the mean recurrence time and of the recurrence time statistics on the probability density function, on the interval whereto the recurrences are observed, and on the temporal correlations of time series. In the case of long-term correlations, we verify the validity of the stretched exponential distribution, which is uniquely defined by the exponent $\gamma$, at the same time showing that it is restricted to the class of linear long-term correlated processes. Simple transformations are able to modify the correlations of time series leading to stretched exponentials recurrence time statistics with different $\gamma$, which shows a lack of invariance under the change of observables.Comment: 9 pages, 7 figure