## Assessment methodology for contaminants in biota

### Overview

Time series of contaminant concentrations are assessed in three stages:
1. The concentration measurements each year are summarised by an annual contaminant index.
2. A weighted regression model is fitted to the annual contaminant indices. The type of model depends on the number of years of data:
• 1-2 years: no model
• 3-4 years: mean
• 5-6 years: linear trend
• 7+ years: smoother
3. The fitted models are used to assess environmental status against available assessment criteria and evidence of temporal change in contaminant levels in the last fifteen years

Each stage is described in more detail below for the case when all the concentration measurements are above the detection limit. Other help files describe how the methodology is adapted when there are 'less-than' measurements.

### Calculating annual contaminant indices

Let cti, i = 1 ... nt be the concentrations measured in year t, t = 1 ... T. The annual contaminant index in year t is the median log concentration:

y_t=text{median}{\log(c_{ti}), i=1 ...n_t}

### Modelling the annual contaminant indices

The annual contaminant indices are modelled as:

y_t=f(t)+\epsilon_t

where yt is the annual contaminant index in year t, f(t) is a smooth function of time (possibly linear) describing the underlying trend in contaminant levels, and εt is an error term assumed to be independent and normally distributed with variance σ2.

The form of f(t) depends on the number of years of data:

1-2 years
no model is fitted as there are too few years for formal statistical analysis
3-4 years
mean model f(t) = µ
there are too few years for a formal trend assessment, but the mean level is summarised by µ and is used to assess status
5-6 years
linear model f(t) = µ + βt
the contaminant indices vary linearly with time; the fitted model is used to assess status and evidence of temporal change
7+ years
smooth model f(t) = smooth function of time
the contaminant indices vary smoothly over time; the fitted model is used to assess status and evidence of temporal change

A loess smoother is used to estimate the smooth function of time. The amount of smoothing is controlled by the neighbourhood of contaminant indices that is used to estimate each f(t) as t runs from 1 to T. A neighbourhood of 9, for example, uses the 9 indices that are closest to t to estimate f(t). A sequence of neighbourhoods are considered (7, 9, 11 up to T, if T is odd, or T + 1, if T is even) with the final choice based on Akaike's Information Criterion corrected for small sample size (AICc). However, if there is no evidence of nonlinearity in the data (i.e. if the AICc of the linear model is lower than that of the best smoother) then the linear model f(t) = µ + βt is used instead.

Linear regression is described by e.g. Draper & Smith (1998). Loess smoothers were developed by Cleveland (1979). The application of loess smoothers to contaminant time series is described by Fryer & Nicholson (1999).

Cleveland WS, 1979. Robust locally-weighted regression and smoothing scatterplots. Journal of the American Statistical Association 74: 829-836.

Draper NR & Smith H, 1998. Applied regression analysis, 3rd edition. Wiley

Fryer RJ & Nicholson MD, 1999. Using smoothers for comprehensive assessments of contaminant time series in marine biota. ICES Journal of Marine Science 56: 779-790.

### Assessing environmental status and temporal trends

Environmental status and temporal trends are assessed using the model fitted to the annual contaminant indices.

Environmental status is assessed by comparing the upper one-sided 95% confidence limit on the fitted value in the most recent monitoring year to the available assessment criteria. For example, if the upper confidence limit is below the Background Assessment Concentration (BAC), then the mean contaminant index in the most recent monitoring year is significantly below the BAC and concentrations are said to be 'at background'.

No formal assessment of status is made when there are only 1 or 2 years of data. However, an ad-hoc assessment is made by comparing the contaminant index (1 year) or the larger of the two contaminant indices (2 years) to the assessment criteria.

Temporal trends are assessed for all time series with at least five years of data. When a linear model has been fitted (i.e. when there are 5-6 years of data, or if there are 7+ years of data and no evidence of nonlinearity), there is evidence of a temporal trend if the slope β of the linear regression of yt on t is significant at the 5% level. When a smooth model has been fitted, the fitted smoother is used to test for evidence of any systematic change in contaminant levels over time; this test is also decomposed into both a nonlinear and linear component. The results for each time series can be found in the statistical analysis output on the right hand side of the map under Graphics. Details of the methodology are in Fryer & Nicholson (1999). However, the summary maps focus on changes in contaminant levels between the start and the end of the time series. The fitted value of the smoother at the start of the time series is compared to the fitted value at the end of the time series using a t-test, with significance assessed at the 5% level. The correlation between the two fitted values is accounted for by the t-test. In the statistical analysis output, this is referred to as the change in the last fifteen years, since the longest time series is fifteen years.

Fryer RJ & Nicholson MD, 1999. Using smoothers for comprehensive assessments of contaminant time series in marine biota. ICES Journal of Marine Science 56: 779-790.