Periodic multivariate normal hidden markov models for the analysis of water quality time series

Abstract

a SUMMARYThe modelling of multivariate riverine water quality time series poses some challenging problems including: weak dependency between observations; nonlinearity; non-Normality; seasonality and missing data. We demonstrate that periodic multivariate Normal hidden Markov models (MNHMMs) are appropriate tools to analyse riverine water quality time series. We introduce a fully Bayesian inference procedure for this class of models, where the number of hidden states of the Markov process is unknown and reversible jump Markov chain Monte Carlo (RJMCMC) methods are developed. We present a case study using long-term dissolved inorganic nitrogen time series measured in three Scottish rivers. Our results show the strength of the hidden Markov multistate approach for analysing long-term multivariate riverine water quality time series.

An anisotropic and inhomogeneous hidden Markov model for the classification of water quality spatio‐temporal series on a national scale: The case of Scotland

“…The original prior on γ was based on the results obtained in Spezia et al () for Rivers Ayr, Garnock, and Lochy, for ammonia, nitrate, and nitrite, that is, where is a vector of ones of dimension three. This prior was too informative, based on information from three rivers analysed in isolation (with two rivers from southern agricultural catchments and one from upland catchments), also considering the nitrite instead of the phosphorus.…”

“…So a hyperprior over M was placed and robustness obtained. The original prior on was based on the results obtained in Spezia et al (2010) for Rivers Ayr, Garnock, and Lochy, for ammonia, nitrate, and nitrite, that is,…”

“…HMMs form a class of stochastic processes which have received a lot of attention in the last 25 years, with many interesting applications in hydrology, where they have been used mostly to analyse rainfall data (e.g., Zucchini & Guttorp, 1991;Samson, 1998;Hughes, Guttorp, & Charles, 1999;Bellone, Hughes, & Guttorp, 2000;Thyer & Kuczera, 2000;Betrò, Bodini, & Cossu, 2008;Ailliot, Thompson, & Thomson, 2009;Carey-Smith, Sansom, & Thomson, 2014;Heaps, Boys, & Farrow, 2015). Spezia, Futter, and Brewer (2010) was the first application of HMMs to water quality time series, and the methodology is extended here to a spatio-temporal framework.…”

Processos condicionantes de alterações em variáveis limnológicas: uma abordagem estatística na Represa de São Pedro, Juiz de Fora (MG)

“…Abordagens multivariadas, como a análise fatorial (AF) e a análise de componentes principais (ACP), são úteis para extrair informações significativas de grandes quantidades de dados de difícil análise e interpretação, pois promovem a redução do número de variá-veis com o mínimo de perdas das informações (AKBAR; HASSAN; ACHARI, 2011;ANDRADE et al, 2007;AUTIN & EDWARDS, 2010;BABOROWSKI;SIMEONOV;EINAX, 2012;GUEDES et al, 2012;LIAO et al, 2008;MENDONÇA & SOUZA, 2011;FREITAS;SILVA, 2014;ROCHA & COSTA, 2015;SHEELA et al, 2012;SPEZIA;FUTTER;BREWER, 2011).…”

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“…Tal monitoramento visa o controle da qualidade da água e busca avaliar diversos parâmetros, os quais muitas vezes são difíceis de analisar e interpretar devido à grande quantidade de dados, principalmente se as coletas e as análises de água ocorrerem por muitos anos. A fim de suplantar esse obstáculo é feita a utilização de abordagens multivariadas como a Análise Fatorial (AF) e a Análise de Componentes Principais (ACP) que são úteis para obter informações significativas, promovendo a redução do número de variáveis com o mínimo de perdas das informações (Liao et al, 2008;Bernardi et al, 2009;Autin e Edwards, 2010;Vanzela et al, 2010;Akbar et al, 2011;Mendonça e Souza, 2011;Spezia et al, 2011;Tu, 2011;Baborowski et al, 2012;Guedes et al, 2012;Sheela et al, 2012;Rocha et al, 2014).…”