A dynamic approach for evaluating coarse scale satellite soil moisture products

Validating coarse scale remote sensing soil moisture products requires a comparison of gridded data to point-like ground measurements. The necessary aggregation of in situ measurements to the footprint scale of a satellite sensor (>100 km<sup>2</sup>) introduces uncertainties in the validation of the satellite soil moisture product. Observed differences between the satellite product and in situ data are therefore partly attributable to these aggregation uncertainties. The present paper investigates different approaches to disentangle the error of the satellite product from the uncertainties associated to the up-scaling of the reference data. A novel approach is proposed, which allows for the quantification of the remote sensing soil moisture error using a temporally adaptive technique. It is shown that the point-to-area sampling error can be estimated within 0.0084 [m<sup>3</sup>/m<sup>3</sup>]

How complex climate networks complement eigen techniques for the statistical analysis of climatological data

Eigen techniques such as empirical orthogonal function (EOF) or coupled pattern (CP) / maximum covariance analysis have been frequently used for detecting patterns in multivariate climatological data sets. Recently, statistical methods originating from the theory of complex networks have been employed for the very same purpose of spatio-temporal analysis. This climate network (CN) analysis is usually based on the same set of similarity matrices as is used in classical EOF or CP analysis, e.g., the correlation matrix of a single climatological field or the cross-correlation matrix between two distinct climatological fields. In this study, formal relationships as well as conceptual differences between both eigen and network approaches are derived and illustrated using exemplary global precipitation, evaporation and surface air temperature data sets. These results allow to pinpoint that CN analysis can complement classical eigen techniques and provides additional information on the higher-order structure of statistical interrelationships in climatological data. Hence, CNs are a valuable supplement to the statistical toolbox of the climatologist, particularly for making sense out of very large data sets such as those generated by satellite observations and climate model intercomparison exercises.Comment: 18 pages, 11 figure

Preparation of ordered states in ultra–cold gases using Bayesian optimization

Ultra-cold atomic gases are unique in terms of the degree of controllability, both for internal and external degrees of freedom. This makes it possible to use them for the study of complex quantum many-body phenomena. However in many scenarios, the prerequisite condition of faithfully preparing a desired quantum state despite decoherence and system imperfections is not always adequately met. To path the way to a specific target state, we explore quantum optimal control framework based on Bayesian optimization. The probabilistic modeling and broad exploration aspects of Bayesian optimization is particularly suitable for quantum experiments where data acquisition can be expensive. Using numerical simulations for the superfluid to Mott- insulator transition for bosons in a lattice as well for the formation of Rydberg crystals as explicit examples, we demonstrate that Bayesian optimization is capable of finding better control solutions with regards to finite and noisy data compared to existing methods of optimal control