- The concentration measurements each year are summarised by an annual contaminant index.
- A 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

- The fitted models are used to assess environmental status against available assessment criteria and evidence of temporal change in contaminant levels in the last ten years

Let *c _{ti}, i = *1

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

The annual contaminant indices are modelled as:

`y_t=f(t)+\epsilon_t`

where *y _{t}* is the annual contaminant index in year

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*) = ¦ - there are too few years for a formal trend assessment, but the mean level is summarised by ¦ and is used to assess status
- 5-6 years
- linear trend
*f*(*t*) = ¦ + β*t* - the contaminant indices vary linearly with time; the fitted model is used to assess status and evidence of temporal change
- 7+ years
- smoother
function of time*f*(*t*) = smooth - a loess smoother is fitted to the contaminant indices with a fixed window width (Fryer & Nicholson, 1999) of either 7, 9 or 11 years; the choice of window width is based on Akaike's Information Criteron (AIC); the fitted model is used to assess status and evidence of temporal change

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.

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 there are
5-6 years, there is evidence of a temporal trend if the slope β of the linear regression of *y _{t}* on

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.