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A common objective for a monitoring program is to characterize an environmental resource based on inference from the sites selected to be monitored to the entire target population. The scale of monitoring ranges from local studies, to regional monitoring, to nationwide monitoring programs. Rarely can these monitoring efforts monitor at all locations, or sites, within the study region. Consequently, a major consideration is how to select representative sites from which it is possible to make inferences to the entire study region.
In addition to the different spatial scales of interest across monitoring efforts, these studies may focus on different environmental resources. A state or province may be interested in all small lakes (e.g. < 10 ha) with the objective of classifying the lakes as meeting designated uses (i.e. having values of designated water quality attributes that do not exceed a specified threshold), partially meeting designated uses, or not meeting designated uses. In this case, the elements of the environmental resource are individual lakes and site selection is based on selecting a subset of lakes from the target population. Alternatively, a state may be interested in all perennial streams and rivers within the state to determine the total stream length that meets a nutrient criterion. In this case, the elements of the environmental resource are all possible locations on the stream and river network within the state and site selection is based on selecting sites on the stream network to be monitored. The stream network is the target population and is viewed as a continuous linear network. Finally, a state may be interested in monitoring a single large estuary within the state (e.g. Puget Sound in Washington State, USA) to determine the proportion of the estuarine area that has sediment contamination exceeding a criteria. In this case, the environmental resource, i.e. the target population, is an area and sites are selected from all possible locations within the estuarine surface area. Similar examples can be given for terrestrial environmental resources.
Typical objectives for environmental resource monitoring programs include estimating the current status of the resource, estimating change in status between two time periods, and estimating trends in status over time. For most monitoring programs, status is estimated using multiple indicators (monitoring variables) determined for each sample site that are derived from measurements of biological, chemical, and physical attributes obtained at the site. What is meant by estimating current status? First, the estimate applies to a specified portion of the region included in the monitoring program, typically the entire region. Second, a specific summary measure must be chosen. Common summary measures are estimates of the population mean, the percentage of the population that is less than a particular value (e.g. percentage of water bodies meeting a water quality standard or percentage of a dry forest region that has tree densities < x trees/ha), the population median, the percentage of the population occurring in categories, or the population standard deviation for an indicator.
An additional summary measure is an estimate of the population cumulative distribution for the indicator. The population cumulative distribution is simply the percentage of the population that is less than or equal to each possible value of an indicator. The population cumulative distribution provides complete information about the indicator distribution (Box 14.1). It has the advantage that it can be used for both categorical and continuous data. It is common in statistics to call the cumulative distribution the cumulative distribution function (CDF) and we will adopt that convention in this chapter. Measurements for indicators obtained from a probability survey can be used to estimate these summary measures of status. For complex survey designs that employ stratification or unequal probability of selection, estimation of current status for any of these summary measures must use weights that are derived from the stratification or unequal probability of selection used in the design.
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