Three-way compositional analysis of water quality monitoring data

Abstract

Water quality monitoring data typically consist of J parameters and constituents measured at I number of static locations at K sets of seasonal occurrences. The resulting I x J x K three-way array can be difficult to interpret. Additionally, the constituent portion of the dataset (e.g., major ion and trace element concentration, pH, etc.) is compositional in that it sums to a constant (e.g., 1 kg/L) and is mathematically confined to the simplex, the sample space for compositional data. Here we apply a Tucker3 model on centered log-ratio data to find low dimensional representation of latent variables as a means to simplify data processing\ud and interpretation of three years of seasonal compositional groundwater chemistry data for 14 wells at a study\ud site in Wyoming, USA. The study site has been amended with treated coalbed methane produced water, using a subsurface drip irrigation system, to allow for irrigation of forage crops. Results from three-way\ud compositional data analysis indicate that primary controls on water quality at the study site include: solutes concentration by evapotranspiration, cation exchange, and dissolution of native salts. These findings agree well with results from more detailed investigations of the site. In addition, the model identified Ba uptake during gypsum precipitation in some portions of the site during the final 6–9 months of investigation, a process for which the timing and extent had not previously been identified. These results suggest that multi-way compositional analyses hold promise as a means to more easily interpret water quality monitoring data

Bidimensional and Multidimensional Principal Component Analysis in Long Term Atmospheric Monitoring

“…Multiway methods gained a lot of attention in recent years in the environmental data analysis field (see [8][9][10][11][12] and references therein) as they represent a more appropriate choice when compared to bidimensional alternatives.…”

Tensor-based anomaly detection: An interdisciplinary survey

“…Identification of locations or time periods related to abnormal measurement is the main goal of this application. Tensors have recently been applied in water quality monitoring [2,[48][49][50][51][52] , air pollution control [18,53] and monitoring of soil quality [54,55] .…”

Normalization techniques for PARAFAC modeling of urine metabolomic data

“…In practice, three-way data are of primary interest, specially also in form of three-way compositions. Let's have I Â J Â K data array (cube): we have I samples and J variables (compositional parts), every sample is measured K times (Engle et al 2014). Consequently, each of K tables of dimension I Â J (slices of the cube) can be considered as a compositional data matrix, ready to be processed using the logratio methodology.…”

“…We will apply this approach on data which can be arranged in a three-way array. Although for statistical processing of three-way observations well established tools like PARAFAC (Carroll and Chang 1970;Harshman 1970) or Tucker3 (Tucker 1966) exist, they are still rarely used in the compositional context (Gallo 2013;Engle et al 2014;Di Palma et al 2015) with no metabolomic application known so far to us.…”