Principal component analysis (PCA) is a multivariate data analysis approach commonly used in X-ray absorption spectroscopy to estimate the number of pure compounds in multicomponent mixtures. This approach seeks to describe a large number of multicomponent spectra as weighted sums of a smaller number of component spectra. These component spectra are in turn considered to be linear combinations of the spectra from the actual species present in the system from which the experimental spectra were taken. The dimension of the experimental dataset is given by the number of meaningful abstract components, as estimated by the cascade or variance of the eigenvalues (EVs), the factor indicator function (IND), or the F-test on reduced EVs. It is shown on synthetic and real spectral mixtures that the performance of the IND and F-test critically depends on the amount of noise in the data, and may result in considerable underestimation or overestimation of the number of components even for a signal-to-noise (s/n) ratio of the order of 80 (σ = 20) in a XANES dataset. For a given s/n ratio, the accuracy of the component recovery from a random mixture depends on the size of the dataset and number of components, which is not known in advance, and deteriorates for larger datasets because the analysis picks up more noise components. The scree plot of the EVs for the components yields one or two values close to the significant number of components, but the result can be ambiguous and its uncertainty is unknown. A new estimator, NSS-stat, which includes the experimental error to XANES data analysis, is introduced and tested. It is shown that NSS-stat produces superior results compared with the three traditional forms of PCA-based component-number estimation. A graphical user-friendly interface for the calculation of EVs, IND, F-test and NSS-stat from a XANES dataset has been developed under LabVIEW for Windows and is supplied in the supporting information. Its possible application to EXAFS data is discussed, and several XANES and EXAFS datasets are also included for download.

In the vadose zone, preferential flow and transport are much more common than uniform water flow and solute transport. In recent decades, several models have been developed for preferential water flow and physical nonequilibrium solute transport. Among these models, the dual-permeability approach is an interesting tool for the conceptualization and modeling of preferential flow. However, this approach has been mainly studied from a numerical point of view. In this study, we developed a new analytical model for water infiltration into dual-permeability soils. The model is based on the analytical model originally proposed for single-permeability soils. The proposed model relies on the assumption that the water exchange rate at the interface between the matrix and fast-flow regions does not change cumulative infiltration at the soil surface, so that the total cumulative infiltration can be set equal to the sum of independent cumulative infiltrations into each region. This assumption was investigated using numerically generated data. The proposed analytical model was then used to evaluate the effects of fast-flow region hydraulic properties and hydraulic conditions on total cumulative infiltration for the case of single-and multi-tension water infiltration experiments. Finally, both single-and dual-permeability models were evaluated with respect to their ability to fit experimental data and associated problems of non-uniqueness in optimized parameters. The proposed model could serve as a new tool for modeling and characterizing preferential flow in the vadose zone.Abbreviations: BOF, basic oxygen furnace; CVRMSE, coefficient of variation of the root mean square error;

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