Extension and application of multivariate curve resolution-alternating least squares to four-way quadrilinear data-obtained in the investigation of pollution patterns on Yamuna River, India—A case study

• This study presents a new development of the MCR-ALS method introducing a quadrilinear constraint.
• A long term four-way environmental dataset is presented as a case of study.
• MCR-ALS resolved dominant pollution patterns for the Yamuna River (India) during the years (1999–2005).
• The MCR-ALS proves to be a powerful tool to summarize and resolve large multi-dimensional datasets.

This study focuses on the development and extension of Multivariate Curve Resolution-Alternating Least Squares (MCR-ALS) to the analysis of four-way datasets. The proposed extension of the MCR-ALS method with non-negativity and the newly developed quadrilinear constraints can be exploited to summarize and manage huge multidimensional datasets and resolve their four way component profiles. In this study, its application is demonstrated by analyzing a four-way data set obtained in a long term environmental monitoring study (15 sampling sites × 9 variables × 12 months × 7 years) belonging to the Yamuna River, one of the most polluted rivers of India and the largest tributary of the Ganges river. MCR-ALS resolved pollution profiles described appropriately the major observed changes on pH, organic pollution, bacteriological pollution and temperature, along with their spatial and temporal distribution patterns for the studied stretch of Yamuna River. Results obtained by MCR-ALS have also been compared with those obtained by another multi-way method, PARAFAC. The methodology used in this study is completely general and it can be applied to other multi-way datasets.

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