[1] In many applications of geostatistical methods, the dependence structure of the investigated parameter is described solely with the variogram or covariance functions, which are susceptible to measurement anomalies and implies the assumption of Gaussian dependence. Moreover the kriging variance respects only observation density, data geometry and the variogram model. To address these problems, we borrow the idea from copulas, to depict the dependence structure without the influence of the marginal distribution. The methodology and basic hypotheses for application of copulas as geostatistical methods are discussed and the Gaussian copula as well as a non-Gaussian copula are used in this paper. Copula parameters are estimated using a division of the observations into multipoint subsets and a subsequent maximization of the corresponding likelihood function. The interpolation is carried out with two different copulas, where the expected and median values are calculated from the copulas conditioned with the nearby observations. The full conditional copulas provide the estimation distributions for the unobserved locations and can be used to define confidence intervals which depend on both the observation geometry and values. Observations of a large scale groundwater quality measurement network in Baden-Württemberg are used to demonstrate the methodology. Five groundwater quality parameters: chloride, nitrate, pH, sulfate and dissolved oxygen are investigated. All five parameters show non-Gaussian dependence. The copula-based interpolation results of the five parameters are compared to the results of conventional ordinary and indicator kriging. Different statistical measures including mean squared error, relative differences and probability scores are used to compare cross validation and split sampling results of the interpolation methods. The non-Gaussian copulas give better results than the geostatistical interpolations. Validation of the confidence intervals shows that they are more realistic than the estimation variances obtained by ordinary kriging.

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Photocatalytic reduction of CO2 to value‐added fuel has been considered to be a promising strategy to reduce global warming and shortage of energy. Rational design and synthesis of catalysts to maximumly expose the active sites is the key to activate CO2 molecules and determine the reaction selectivity. Herein, we synthesize a well‐defined copper‐based boron imidazolate cage (BIF‐29) with six exposed mononuclear copper centers for the photocatalytic reduction of CO2. Theoretical calculations show a single Cu site including weak coordinated water delivers a new state in the conduction band near the Fermi level and stabilizes the *COOH intermediate. Steady‐state and time‐resolved fluorescence spectra show these Cu sites promote the separation of electron–hole pairs and electron transfer. As a result, the cage achieves solar‐driven reduction of CO2 to CO with an evolution rate of 3334 μmol g−1 h−1 and a high selectivity of 82.6 %.

We have proposed a simple method to synthesize asymmetric Janus polymer particles at an emulsion interface. Morphological evolution of the particles with polymerization and their dependence on some key variables reveal that both cross-linking degree of the particles and interfacial tension difference play key roles in achieving the asymmetric shapes. By selective growth of functional materials onto the desired sides, composition and microstructure of the Janus particles can be controlled. The representative PS/PAM Janus particles are amphiphilic and can be used as solid surfactants to stabilize emulsions, which preferentially orientate at the interface.