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Markus Reichstein

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Machine Learning Applications Artificial Intelligence Computational Engineering, Finance, and Science physics.ao-ph physics.geo-ph

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preprint2026arXiv

FLUXtrapolation: A benchmark on extrapolating ecosystem fluxes

We introduce FLUXtrapolation, a benchmark for extrapolating ecosystem fluxes under progressively harder distribution shifts. Ecosystem fluxes are central to understanding the carbon, water, and energy cycles, yet they can only be measured directly at sparsely located measurement towers. Producing global flux estimates therefore requires training models on observed sites using globally available covariates and predicting in unobserved regions, that is, upscaling. Flux upscaling is a challenging domain generalization problem that is affected by a shift in covariate distribution across climates, ecosystem types, and environmental conditions, as well as by conditional shift: important drivers remain unobserved at global scale. We provide a quantitative analysis of both these shifts in $P_X$ and $P_{Y\mid X}$. FLUXtrapolation is designed based on domain expertise on flux upscaling: it defines temporal, spatial, and temperature-based extrapolation scenarios and evaluates performance across held-out domains, temporal aggregations, and tail errors. In a pilot study, we find that baselines perform similarly under median hourly RMSE, but separate under the proposed tail-focused and multi-scale evaluation. FLUXtrapolation therefore poses a realistic and thus relevant challenge for machine learning methods under distribution shift; at the same time, progress on this benchmark would directly support the scientific goal of improving flux upscaling.

preprint2020arXiv

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.

preprint2016arXiv

Have precipitation extremes and annual totals been increasing in the world's dry regions over the last 60 years?

Daily rainfall extremes and annual totals have increased in large parts of the global land area over the last decades. These observations are consistent with theoretical considerations of a warming climate. However, until recently these global tendencies have not been shown to consistently affect land regions with limited moisture availability. A recent study, published by Donat et al. (2016, Nature Climate Change, doi:10.1038/nclimate2941), now identified rapid increases in globally aggregated dry region daily extreme rainfall and annual rainfall totals. Here, we reassess the respective analysis and find that a) statistical artifacts introduced by the choice of the reference period prior to data standardization lead to an overestimation of the reported trends by up to 40%, and also that b) the definition of `dry regions of the globe' affect the reported globally aggregated trends in extreme rainfall. Using the same observational dataset, but accounting for the statistical artifacts and using alternative, well-established dryness definitions, we find no significant increases in heavy precipitation in the world's dry regions. Adequate data pre-processing approaches and accounting for uncertainties regarding the definition of dryness are crucial to the quantification of spatially aggregated trends in the world's dry regions. In view of the high relevance of the question to many potentially affected stakeholders, we call for a cautionary consideration of specific data processing methods, including issues related to the definition of dry areas, to guarantee robustness of communicated climate change relevant findings.

preprint2016arXiv

Maximally Divergent Intervals for Anomaly Detection

We present new methods for batch anomaly detection in multivariate time series. Our methods are based on maximizing the Kullback-Leibler divergence between the data distribution within and outside an interval of the time series. An empirical analysis shows the benefits of our algorithms compared to methods that treat each time step independently from each other without optimizing with respect to all possible intervals.

preprint2012arXiv

Gap Filling in the Plant Kingdom---Trait Prediction Using Hierarchical Probabilistic Matrix Factorization

Plant traits are a key to understanding and predicting the adaptation of ecosystems to environmental changes, which motivates the TRY project aiming at constructing a global database for plant traits and becoming a standard resource for the ecological community. Despite its unprecedented coverage, a large percentage of missing data substantially constrains joint trait analysis. Meanwhile, the trait data is characterized by the hierarchical phylogenetic structure of the plant kingdom. While factorization based matrix completion techniques have been widely used to address the missing data problem, traditional matrix factorization methods are unable to leverage the phylogenetic structure. We propose hierarchical probabilistic matrix factorization (HPMF), which effectively uses hierarchical phylogenetic information for trait prediction. We demonstrate HPMF's high accuracy, effectiveness of incorporating hierarchical structure and ability to capture trait correlation through experiments.