Application of Optimal Nonstationary Time Series Analysis to Water Quality Data and Pollutant Transport Modelling

Abstract. River water-quality time series often exhibit fractal scaling, which here refers to autocorrelation that decays as a power law over some range of scales. Fractal scaling presents challenges to the identification of deterministic trends because (1) fractal scaling has the potential to lead to false inference about the statistical significance of trends and (2) the abundance of irregularly spaced data in water-quality monitoring networks complicates efforts to quantify fractal scaling. Traditional methods for estimating fractal scaling – in the form of spectral slope (β) or other equivalent scaling parameters (e.g., Hurst exponent) – are generally inapplicable to irregularly sampled data. Here we consider two types of estimation approaches for irregularly sampled data and evaluate their performance using synthetic time series. These time series were generated such that (1) they exhibit a wide range of prescribed fractal scaling behaviors, ranging from white noise (β  =  0) to Brown noise (β  =  2) and (2) their sampling gap intervals mimic the sampling irregularity (as quantified by both the skewness and mean of gap-interval lengths) in real water-quality data. The results suggest that none of the existing methods fully account for the effects of sampling irregularity on β estimation. First, the results illustrate the danger of using interpolation for gap filling when examining autocorrelation, as the interpolation methods consistently underestimate or overestimate β under a wide range of prescribed β values and gap distributions. Second, the widely used Lomb–Scargle spectral method also consistently underestimates β. A previously published modified form, using only the lowest 5 % of the frequencies for spectral slope estimation, has very poor precision, although the overall bias is small. Third, a recent wavelet-based method, coupled with an aliasing filter, generally has the smallest bias and root-mean-squared error among all methods for a wide range of prescribed β values and gap distributions. The aliasing method, however, does not itself account for sampling irregularity, and this introduces some bias in the result. Nonetheless, the wavelet method is recommended for estimating β in irregular time series until improved methods are developed. Finally, all methods' performances depend strongly on the sampling irregularity, highlighting that the accuracy and precision of each method are data specific. Accurately quantifying the strength of fractal scaling in irregular water-quality time series remains an unresolved challenge for the hydrologic community and for other disciplines that must grapple with irregular sampling.

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Time series modeling of biochemical oxygen demand at the upstream catchment of Feitsui Reservoir, Taiwan

Hydrology Research ◽

10.2166/nh.2016.136 ◽

2016 ◽

Vol 47 (5) ◽

pp. 1069-1085 ◽

Cited By ~ 1

Author(s):

Yung-Chia Chiu ◽

Chih-Wei Chiang ◽

Tsung-Yu Lee

Keyword(s):

Water Quality ◽

Time Series ◽

Biochemical Oxygen Demand ◽

Oxygen Demand ◽

Quality Data ◽

Series Data ◽

Water Quality Data ◽

Inference System ◽

Feitsui Reservoir ◽

Upstream Catchment

The adaptive neuro fuzzy inference system (ANFIS) has been proposed to model the time series of water quality data in this study. The biochemical oxygen demand data collected at the upstream catchment of Feitsui Reservoir in Taiwan for more than 20 years are selected as the target water quality variable. The classical statistical technique of the Box-Jenkins method is applied for the selection of appropriate input variables and data pre-processing of using differencing is implemented during the model development. The time series data obtained by ANFIS models are compared to those obtained by autoregressive integrated moving average (ARIMA) and artificial neural networks (ANNs). The results show that the ANFIS model identified at each sampling station is superior to the respective ARIMA and ANN models. The R values at all sampling stations of the training and testing datasets are 0.83–0.98 and 0.81–0.89, respectively, except at Huang-ju-pi-liao station. ANFIS models can provide accurate predictions for complex hydrological processes, and can be extended to other areas to improve the understanding of river pollution trends. The procedure of input selection and the pre-processing of input data proposed in this study can stimulate the usage of ANFIS in other related studies.

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