Non-parametric kernel density estimation of species sensitivity distributions in developing water quality criteria of metals

Abstract

Due to use of different parametric models for establishing species sensitivity distributions (SSDs), comparison of water quality criteria (WQC) for metals of the same group or period in the periodic table is uncertain and results can be biased. To address this inadequacy, a new probabilistic model, based on non-parametric kernel density estimation was developed and optimal bandwidths and testing methods are proposed. Zinc (Zn), cadmium (Cd), and mercury (Hg) of group IIB of the periodic table are widespread in aquatic environments, mostly at small concentrations, but can exert detrimental effects on aquatic life and human health. With these metals as target compounds, the non-parametric kernel density estimation method and several conventional parametric density estimation methods were used to derive acute WQC of metals for protection of aquatic species in China that were compared and contrasted with WQC for other jurisdictions. HC5 values for protection of different types of species were derived for three metals by use of non-parametric kernel density estimation. The newly developed probabilistic model was superior to conventional parametric density estimations for constructing SSDs and for deriving WQC for these metals. HC5 values for the three metals were inversely proportional to atomic number, which means that the heavier atoms were more potent toxicants. The proposed method provides a novel alternative approach for developing SSDs that could have wide application prospects in deriving WQC and use in assessment of risks to ecosystems.

Comparative study of species sensitivity distributions based on non-parametric kernel density estimation for some transition metals

“…The NPKDE was also verified its natural robustness in development of WQC for Zn, Cd and Hg of group IIB in the periodic table and compare with other jurisdictions (Wang et al, 2015b). The results showed that the NPKDE was better fit, more robustness and better predicted than conventional, parametric density estimations for establishing SSDs and convenient to compare with each other for WQC of same group of the periodic table.…”

“…Acute WQC were calculated based on HC5 by use of an assessment factor of 2.0 to avoid some uncertainties (Equation (6)) (Van Sprang et al, 2004;Wang et al, 2015b).…”

“…Thus, this is one of the reasons that the sample data could not be fit well by use of parametric distributions. However, the strength of NPKDE method is less constraint and without priori data information before fitting, hence it has a good robustness for modeling and can reduce the adverse disturbance from outliers (Wang et al, 2015b).…”

“…SSDs were widely applied to derive WQC for several transition metals, such as Cr (Du, 2012), Cu (Kong et al, 2011;Wu et al, 2011a), Mn (Kong et al, 2011), Ni (Du, 2012), Zn (Wu et al, 2011b), Cd (Kong et al, 2011;Wu et al, 2011c), and Hg (Kong et al, 2011;Wang et al, 2015a;Zhang et al, 2012), to protect freshwater aquatic organisms. SSDs are usually used in deriving HC5 and WQC of single organic pollutant or metal but rarely used to derive WQC for multiple pollutants (Campbell et al, 2000;Giesy et al, 1999;Solomon et al, 1996;TenBrook et al, 2010;Vardy et al, 2011).…”

“…Commonly, parametric models used for developing SSDs and obtaining WQCs mainly include Burr Type III (Shao, 2000), Exponential Growth , Gaussian (Wu et al, 2011b), Gompertz (Newman et al, 2000), log-normal (Van Vlaardingen et al, 2004), log-logistic (Pennington, 2003), Sigmoid Weibull (Van Straalen, 2002). Not only parametric models, various non-parametric or free-distribution methods, such as Bootstrap (Newman et al, 2000), Monte Carlo (Posthuma et al, 2002), Bayesian methods (Hayashi and Kashiwagi, 2010), and non-parametric kernel density estimation (NPKDE) (Wang et al, 2015b) were also applied, which could describe the toxicity data more objectively and accurately since these methods can be processed without making such many assumptions as parametric methods. Bootstrap methods were first used to estimate HC5 values of pesticide by establishing SSDs (Jagoe and Newman, 1997).…”