Application of Change-Point Detection to a Structural Component of Water Quality Variables

Abstract

Abstract. In this study, methodologies were developed in statistical time series models, such as multivariate state-space models, to be applied to water quality variables in a river basin. In the modelling process it is considered a latent variable that allows incorporating a structural component, such as seasonality, in a dynamic way and a change-point detection method is applied to the structural component in order to identify possible changes in the water quality variables in consideration.

Time series analysis by state space models applied to a water quality data in Portugal

“…The analysis performed in this study shows that the structural time series models (the state space models associated to the Kalman filter) are suitable to model DO concentration series at the FER water monitoring site, and they allow to obtain pertinent findings concerning water surface quality interpretation and change point of view [2] and [4], thus highlighting the potential value of this type of analysis. In addition, the state-space approach allows doing an online monitoring procedure to detect DO concentration values that are statistically unexpected.…”

“…They allow a natural interpretation of a time series as the combination of several components, such as trend, seasonal or regressive components [7]. A structural model can therefore not only provide forecasts, but also, through estimates of the components, present a set of stylised facts and this formulation will allow making some useful interpretations [2], [3] and [4]. In this study, it is proposed a dynamic modeling procedure based on the state space approach (associated to the Kalman filter) in time series of water quality variables.…”

A Time Series Model Comparison for Monitoring and Forecasting Water Quality Variables

“…In fact, the Lunj-Box test for the non-correlation hypothesis does not reject, using up to 30 different lags in all the locations under study, and Figure 4 presents the histograms of the residuals that resemble the normal curve. 9.599 0.00 0.00 9.983 0.00 0.00 9.673 0.00 0.00 9.559 0.00 0.00 9.532 0.00 0.00 β 3 9.212 0.00 0.00 9.546 0.00 0.00 9.138 0.00 0.00 9.504 0.00 0.00 9.737 0.00 0.00 β 4 8.753 0.00 0.00 9.001 0.00 0.00 9.356 0.00 0.00 9.134 0.00 0.00 9.014 0.00 0.00 β 5 8.313 0.00 0.00 9.262 0.00 0.00 8.555 0.00 0.00 8.688 0.00 0.00 8.753 0.00 0.00 β 6 8.362 0.00 0.00 7.771 0.00 0.00 7.270 0.00 0.00 7.847 0.00 0.00 7.939 0.00 0.00 β 7 7.273 0.00 0.00 8.164 0.00 0.00 7.271 0.00 0.00 8.576 0.00 0.00 8.376 0.00 0.00 β 8 7.087 0.00 0.00 8.844 0.00 0.00 6.556 0.00 0.00 7.668 0.00 0.00 8.260 0.00 0.00 β 9 7.971 0.00 0.00 7.941 0.00 0.00 5.800 0.00 0.00 7.166 0.00 0.00 7.319 0.00 0.00 β 10 7.410 0.00 0.00 7.844 0.00 0.00 7.673 0.00 0.00 7.561 0.00 0.00 8.477 0.00 0.00 β 11 8.030 0.00 0.00 8.968 0.00 0.00 9.737 0.00 0.00 9.673 0.00 0.00 9.408 0.00 0.00 β 12 9.859 0.00 0.00 9.946 0.00 0.00 9.418 0.00 0.00 9.025 0.00 0.00 9.207 0.00 0.00 Furthermore, with the exception of the CAR location, the residuals of the calibration model do not reject (at a 1% significance level) the normality assumption using the Jarque-Bera test or the Kolmogorov-Smirnov test; the K-S p-values are presented in Table 5.…”

“…In [10], a time series analysis approach was applied to model and predict univariate dissolved oxygen and temperature time series for four water quality assessment stations at Stillaguamish River located in the state of Washington. Cluster analysis and linear models were used by [11,12] to describe a hydrological space-time series of quality variables and to detect changes in surface water quality data collected in the River Ave hydrological basin, located in the northwest region of Portugal. In [1], the case study of the hydrological basin of the river Vouga, in Portugal was presented.…”

Statistical Modelling of Water Quality Time Series – The River Vouga Basin Case Study

“…To do so, we used maximum type test statistics, referred in [31], alongside their correct adaptation to an autoregressive process. The basic test evaluates the existence of a change point in the mean of independent and identically distributed Gaussian variables in an unknown time.…”