scholarly journals Supplementary material to "Evaluation of statistical methods for quantifying fractal scaling in water quality time series with irregular sampling"

2017 ◽  
Author(s):  
Qian Zhang ◽  
Ciaran J. Harman ◽  
James W. Kirchner
Keyword(s):  
Water Quality ◽  
Time Series ◽  
Statistical Methods ◽  
Irregular Sampling ◽  
Fractal Scaling ◽  
Supplementary Material

scholarly journals Evaluation of statistical methods for quantifying fractal scaling in water-quality time series with irregular sampling

2018 ◽  
Vol 22 (2) ◽  
pp. 1175-1192 ◽  
Author(s):  
Qian Zhang ◽  
Ciaran J. Harman ◽  
James W. Kirchner
Keyword(s):  
Water Quality ◽  
Time Series ◽  
Irregular Sampling ◽  
Quality Data ◽  
Sampled Data ◽  
Spectral Slope ◽  
Water Quality Data ◽  
Fractal Scaling ◽  
Wide Range ◽  
Irregularly Sampled Data

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.

scholarly journals Evaluation of statistical methods for quantifying fractal scaling in water quality time series with irregular sampling

2017 ◽  
Author(s):  
Qian Zhang ◽  
Ciaran J. Harman ◽  
James W. Kirchner
Keyword(s):  
Water Quality ◽  
Time Series ◽  
Irregular Sampling ◽  
Quality Data ◽  
Sampled Data ◽  
Spectral Slope ◽  
Water Quality Data ◽  
Fractal Scaling ◽  
Wide Range ◽  
Irregularly Sampled Data

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, but traditional methods for estimating 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 auto-correlation, as the interpolation methods consistently under-estimate or over-estimate β under a wide range of prescribed β values and gap distributions. Second, the long-established Lomb-Scargle spectral method also consistently under-estimates β. A 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.

scholarly journals Statistical validity of water quality time series in urban watersheds

RBRH ◽  
2017 ◽  
Vol 22 (0) ◽  
Author(s):  
Marcelo Coelho ◽  
Cristovão Vicente Scapulatempo Fernandes ◽  
Daniel Henrique Marco Detzel ◽  
Michael Mannich
Keyword(s):  
Water Quality ◽  
Time Series ◽  
Statistical Methods ◽  
Complex Activity ◽  
Quality Literature ◽  
Monitoring Strategies ◽  
Statistical Validity ◽  
Data Assessment ◽  
Strong Relation ◽  
Basin Water

ABSTRACT The water resources quality continuous monitoring is a complex activity. It generates extensive databases with time series of many variables and monitoring points that require the application of statistical methods for the information extraction. The application of statistical methods for frequency analysis of time series is linked to attending of the basic assumptions of randomness, homogeneity, independence, and stationarity. However, despite its importance, the verification of these assumptions in water quality literature is unusual. Therefore, the present study tests the Upper Iguaçu basin water quality time series against the mentioned hypotheses. Rejection was observed in 15%, 26%, 51% e 31% for randomness, homogeneity, independence, and stationarity, respectively. The results evidenced the strong relation between monitoring strategy, data assessment and meeting of basic statistical assumptions for the analysis of water quality time series. Even with the existence of possible solutions for addressing those issues, the standard monitoring strategies, with irregular frequencies and lack of representativeness in relation to other periods, beyond commercial, act as an obstacle to their implementation.

scholarly journals Detecting dominant changes in irregularly sampled multivariate water quality data sets

2018 ◽  
Author(s):  
Christian Lehr ◽  
Ralf Dannowski ◽  
Thomas Kalettka ◽  
Christoph Merz ◽  
Boris Schröder ◽  
...  
Keyword(s):  
Water Quality ◽  
Time Series ◽  
Stream Water ◽  
Shallow Groundwater ◽  
Irregular Sampling ◽  
Quality Data ◽  
Data Sets ◽  
Water Quality Data ◽  
Data Set ◽  
Sampling In Space

Abstract. Time series of catchment water quality often exhibit substantial temporal and spatial variability which can rarely be traced back to single causal factors. Numerous anthropogenic and natural drivers influence groundwater and stream water quality, especially in regions with high land use intensity. In addition, typical existing monitoring data sets, e.g. from environmental agencies, are usually characterized by relatively low sampling frequency and irregular sampling in space and/or time. This complicates the differentiation between anthropogenic influence and natural variability as well as the detection of changes in water quality which indicate changes of single drivers. Detecting such changes is of fundamental interest for water management purposes as well as for scientific analyses. We suggest the new term dominant changes for changes in multivariate water quality data that concern (1) more than a single variable, (2) more than one single site and (3) more than short-term fluctuations or single events and present an exploratory framework for the detection of such dominant changes in multivariate water quality data sets with irregular sampling in space and time. Firstly, we used a non-linear dimension reduction technique to derive multivariate water quality components. The components provide a sparse description of the dominant spatiotemporal dynamics in the multivariate water quality data set. In addition, they can be used to derive hypotheses on the dominant drivers influencing water quality. Secondly, different sampling sites were compared with respect to median component values. Thirdly, time series of the components at single sites were analysed for seasonal patterns and linear and non-linear trends. Spatial and temporal heterogeneities are efficiently used as a source of information rather than being considered as noise. Besides, non-linearities are considered explicitly. The approach is especially recommended for the exploratory assessment of existing long term low frequency multivariate water quality monitoring data. We tested the approach with a large data set of stream water and groundwater quality consisting of sixteen hydrochemical variables sampled with a spatially and temporally irregular sampling scheme at 29 sites in the Uckermark region in northeast Germany from 1998 to 2009. Four components were derived and interpreted as (1) the agriculturally induced enhancement of the natural background level of solute concentration, (2) the redox sequence from reducing conditions in deep groundwater to post oxic conditions in shallow groundwater and oxic conditions in stream water, (3) the mixing ratio of deep and shallow groundwater to the streamflow and (4) sporadic events of slurry application in the agricultural practice. Dominant changes were observed for the first two components. The changing intensity of the 1st component during the course of the observation period was interpreted as response to the temporal variability of the thickness of the unsaturated zone. A steady increase of the 2nd component throughout the monitoring period at most stream water sites pointed towards progressing depletion of the denitrification capacity of the deep aquifer.

Algae Migration Characteristics in Fresh Water Red Tide

1993 ◽  
Vol 28 (7) ◽  
pp. 197-201 ◽  
Author(s):  
Dunchun Wang ◽  
Isao Somiya ◽  
Shigeo Fujii
Keyword(s):  
Water Quality ◽  
Time Series ◽  
Fresh Water ◽  
Field Data ◽  
Field Survey ◽  
Red Tide ◽  
Bottom Layer ◽  
Total Biomass ◽  
Quality Indices ◽  
Vertical Distributions

To understand the algae migration characteristics in the fresh water red tide, we performed a field survey in the Shorenji Reservoir located in Nabari City, Japan. From the analysis of the field data, it is found that the patterns of vertical distributions of the indices representing biomass are very different in the morning and the afternoon. Since some water quality indices have reverse fluctuations between the surface and the bottom layer in respect of the time series changes and the total biomass of the vertical water column is relatively constant, it is concluded that vertical and daily biomass variation of red tide alga is caused by its daily migration, that is the movement from the bottom layer to the surface in the morning and the reverse movement in the afternoon.

scholarly journals Assessment of Automatically Monitored Water Levels and Water Quality Indicators in Rivers with Different Hydromorphological Conditions and Pollution Levels in Greece

Hydrology ◽  
2021 ◽  
Vol 8 (2) ◽  
pp. 86
Author(s):  
Angeliki Mentzafou ◽  
George Varlas ◽  
Anastasios Papadopoulos ◽  
Georgios Poulis ◽  
Elias Dimitriou
Keyword(s):  
Water Quality ◽  
Time Series ◽  
Quality Indicators ◽  
High Frequency ◽  
Automatic Monitoring ◽  
Water Levels ◽  
High Temporal Resolution ◽  
Water Quality Indicators ◽  
Pollution Levels ◽  
Riverine Ecosystems

Water resources, especially riverine ecosystems, are globally under qualitative and quantitative degradation due to human-imposed pressures. High-temporal-resolution data obtained from automatic stations can provide insights into the processes that link catchment hydrology and streamwater chemistry. The scope of this paper was to investigate the statistical behavior of high-frequency measurements at sites with known hydromorphological and pollution pressures. For this purpose, hourly time series of water levels and key water quality indicators (temperature, electric conductivity, and dissolved oxygen concentrations) collected from four automatic monitoring stations under different hydromorphological conditions and pollution pressures were statistically elaborated. Based on the results, the hydromorphological conditions and pollution pressures of each station were confirmed to be reflected in the results of the statistical analysis performed. It was proven that the comparative use of the statistics and patterns of the water level and quality high-frequency time series could be used in the interpretation of the current site status as well as allowing the detection of possible changes. This approach can be used as a tool for the definition of thresholds, and will contribute to the design of management and restoration measures for the most impacted areas.

scholarly journals Assessing Water Quality by Statistical Methods

Water ◽  
2021 ◽  
Vol 13 (8) ◽  
pp. 1026
Author(s):  
Alina Bărbulescu ◽  
Cristian Ștefan Dumitriu
Keyword(s):  
Water Quality ◽  
Natural Resources ◽  
Statistical Methods ◽  
Anthropogenic Activities

Water is one of the natural resources most affected by anthropogenic activities, like industry, agriculture, and traffic [...]

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