Modeling multivariable hydrological series: Principal component analysis or independent component analysis?

Abstract

[1] The generation of synthetic multivariate rainfall and/or streamflow time series that accurately simulate both the spatial and temporal dependence of the original multivariate series remains a challenging problem in hydrology and frequently requires either the estimation of a large number of model parameters or significant simplifying assumptions on the model structure. As an alternative, we propose a relatively parsimonious two-step approach to generating synthetic multivariate time series at monthly or longer timescales, by first transforming the data to a set of statistically independent univariate time series and then applying a univariate time series model to the transformed data. The transformation is achieved through a technique known as independent component analysis (ICA), which uses an approximation of mutual information to maximize the independence between the transformed series. We compare this with principal component analysis (PCA), which merely removes the covariance (or spatial correlation) of the multivariate time series, without necessarily ensuring complete independence. Both methods are tested using a monthly multivariate data set of reservoir inflows from Colombia. We show that the discrepancy between the synthetically generated data and the original data, measured as the mean integrated squared bias, is reduced by 25% when using ICA compared with PCA for the full joint distribution and by 28% when considering marginal densities in isolation. These results suggest that there may be significant benefits to maximizing statistical independence, rather than merely removing correlation, when developing models for the synthetic generation of multivariate time series.

Spatiotemporal Variability of Extreme Summer Precipitation over the Yangtze River Basin and the Associations with Climate Patterns

“…Here, we used archetypal analysis (AA) to identify the spatiotemporal structure of seasonal extreme precipitation, similar to Steinschneider and Lall's [15] analysis. Unlike the principle component analysis (PCA), which is typically used for dimension reduction and analysis of the spatiotemporal variability of hydrological variables based on principle components through orthogonal transformation [16], AA represents an individual in a dataset as a convex combination of pure patterns (i.e., archetypes) or, equivalently, the extremal points. Archetypal patterns represent a set of extremal points, thus making AA widely used for extreme event analysis.…”

“…Here, we used archetypal analysis (AA) to identify the spatiotemporal structure of seasonal extreme precipitation, similar to Steinschneider and Lall's [15] analysis. Unlike the principle component analysis (PCA), which is typically used for dimension reduction and analysis of the spatiotemporal variability of hydrological variables based on principle components through orthogonal transformation [16], AA represents an individual in a dataset as a convex combination of pure Many studies have investigated the characteristics of seasonal precipitation over the basin. Gemmer et al [7] demonstrated that during the period of 1960-2004, the precipitation increased significantly in the lower Yangtze region in summer, while a statistically significant negative trend was found in September at the middle reach.…”

Identification of prominent spatio-temporal signals in GRACE derived terrestrial water storage for India

“…where x is aparticular time series (columns of X) E is the expectation function For our time series with a length of more than 90 months, a kurtosis greater than 0.5 indicates a non-Gaussian distribution (Westra et al, 2007). PCA is considered as a pre-processing of ICA, where the first few orthogonal components are analyzed to obtain independent components.…”

Developing a Complex Independent Component Analysis (CICA) Technique to Extract Non-stationary Patterns from Geophysical Time Series

“…More recently, the higher-order statistical technique of independent component analysis (ICA, Cardoso and Souloumiac 1993;Hyvärinen 1999a, classified here as (b)) has been introduced in order to decompose these data into statistically independent components (e.g., Aires et al 2002;Westra et al 2007;Hannachi et al 2009;Frappart et al 2010Frappart et al , 2011. Forootan andKusche (2012, 2013) argue that different physical processes generate statistically independent source signals that are superimposed in geophysical time series; thus, application of ICA likely helps separating (extracting) their contribution from the total signal.…”