N. Scott Urquhart

MONITORING FOR POLICY‐RELEVANT REGIONALTRENDS OVER TIME

The term trend describes the continuing directional change in the value of an indicator, generally upward or generally downward. Many policy questions concern trend across a number of sites, such as lakes in a region, rather than trend at a single site. Power to detect regional trend seldom is discussed, and monitoring designs suitable for detecting such trends rarely are explored. Components of variance and temporal sampling designs play central roles in characterizing trend detection. We present relative numerical values of important components of variance, developed from the Surface Waters component of U.S. EPA’s Environmental Monitoring and Assessment Program (EMAP) field data, and use them as a basis for further assumptions of values. We discuss power curves in general and present them in relation to temporal designs, years of field observation, components of variance, and the level of trend detected. Revisit designs give adequate power for moderate trend in 10–15 yr, even when revisits are less frequent than annually.

Designing a Spatially Balanced, Randomized Site Selection Process for Regional Stream Surveys: The EMAP Mid-Atlantic Pilot Study

In 1993, the U.S. Environmental Protection Agency (EPA), as part of the Environmental Monitoring and Assessment Program (EMAP), initiated a sample survey of streams in the mid-Atlantic. A major objective of the survey was to quantify ecological condition in wadeable streams across the region. To accomplish this goal, we selected 615 stream sites using a randomized sampling design with some restrictions. The design utilized the digitized stream network taken from 1:100,000-scale USGS topographic maps as the sample frame. Using a GIS, first- through third-order (wadeable) stream segments in the sample frame were randomly laid out in a line and sampled at fixed intervals after a random start. We used a variable probability approach so that roughly equal numbers of first-, second-, and third-order stream sites would appear in the sample. The sample design allows inference from the sample data to the status of the entire 230,400 km of wadeable stream length in the mid-Atlantic study area. Of this mapped stream length, 10% was not in the target population because no stream channel existed (4%), the stream channel was dry (5%), or the stream was not wadeable (1%). We were unable to collect field data from another 10% of the mapped stream length due to lack of access (mostly landowner denials). Thus, the field data we collected at 509 sites allows inference to the ecological condition for 184,600 km of the mapped stream length in the region.

Designs for Detecting Trend From Repeated Surveys of Ecological Resources

We report investigations on trend detection capability (power for linear trend) from repeated surveys of the same regional resource population. The temporal sampling plans range from periodic revisits using panel designs to independent surveys at each point in time; the latter have only random revisits. We view the resource of interest as a finite population but characterize several features of the situation with components of variance. The results show how components of variance for site, year, and residual and sampling fraction impact power to detect a specific trend. The panel designs turn out to be far superior to independent surveys for detecting trend and have other desirable features.

A Mixed Model with Both Fixed and Random Trend Components Across Time

The use of longitudinal data is common in environmental and agricultural applications where interest lies in trends in a response variable through time. Various methodologies have been applied in the analysis of such data. Although many methods allow for correlation among the repeated measurements taken on the same experimental unit, nearly all assume independence of those units. Additionally, in mixed model settings, where trends are random, interest has often focused on Best Linear Unbiased Predictors (BLUPs), rather than on variance components, and on techniques for large unbalanced datasets, rather than for relatively small balanced datasets. We present a model that incorporates random trends through time and also allows correlations to exist among observations taken at the same time from the different units. The analysis (for the balanced case) focuses on variance components and an overall fixed trend through time, and is based on intuitively reasonable sums of squares that, under the usual normality assumptions, can be shown to possess desirable distributional properties.

Response designs and support regions in sampling continuous domains

In many environmental samples, the target population is distributed over space in a more or less continuous manner, e.g., the waters of a lake or the trees in a forest. Attributes of such a population can be conceptualized as a continuous function defined on the spatial domain of the population. Some attributes (e.g., water temperature) can be observed at a point; others (e.g., species diversity) can only be determined over a finite extent or support region. A fixed-shape support with uniform weights leads to an unbiased estimator of the population total; however, it may be impossible to maintain a fixed shape near domain boundaries. From a purely formal standpoint, unbiasedness can be maintained by using differential weights or by changing the shape of the support region near the boundary. Both of these procedures raise some issues of interpretation that often are overlooked. We derive estimators that account for edge effects under several support strategies, and identify some interpretation issues, using examples from forestry and limnology. Copyright

Regional Lake Trophic Patterns in the Northeastern United States: Three Approaches

N = 11,076). Results were compared to a large, nonrandomly sampled data set for the same area compiled by Rohm and others and contrasted with lake trophic state information published in the National Water Quality Inventory: 1994 Report to Congress [305(b) report. Lakes across the entire Northeast were identified by EMAP data as 37.9% (±8.4%) oligotrophic, 40.1% (±9.7%) mesotrophic, 12.6% (±7.9%) eutrophic, and 9.3% (±6.3%) hypereutrophic. Lakes in the ADI and NEU generally are at a low, nearly identical trophic state (96% oligotrophic/mesotrophic), while those in the CLP are much richer (45% eutrophic). EMAP results are similar to results of the Rohm data set across the entire region. In the CLP, however, EMAP identified approximately 45% of the lakes as eutrophic/hypereutrophic, while the Rohm data set identified only 21% in these categories. Across the entire Northeast, the 305(b) report identified a much higher proportion (32.2%) of lakes in eutrophic condition and a much smaller proportion (19.8%) in oligotrophic condition than did the EMAP survey data (12.5% ± 7.9% and 37.9% ± 8.5%, respectively). Probability sampling has several advantages over nonrandom sampling when regional resource condition assessment is the goal.

The Temporally Integrated Monitoring of Ecosystems (TIME) Project Design: 2. Detection of Regional Acidification Trends

The Temporally Integrated Monitoring of Ecosystems (TIME) project utilizes a hybrid sampling approach to achieve its goal of assessing whether emissions controls, mandated by the Clean Air Act Amendments of 1990, have had their intended effect on lakes and streams. A randomly placed triangular grid is used to select, with known probability, lakes and streams for sampling on either an annual basis (in the case of acid-sensitive sites) or on a 4-year rotation. Data from these sites will be used to detect trends in regional characteristics of the target populations. The ability of TIME to detect trends in acid-neutralizing capacity (ANC) and SO42− is dependent on the amount of variability (year-to-year, site-to-site, within-season, and site-by-year interaction) exhibited by the sites. In particular, high levels of year-to-year variability lead to very low power to detect trends. One method to minimize year-to-year variability is to group together sites with similar characteristics. By performing trends tests on seven separate subpopulations the TIME design for northeastern U.S. lakes is predicted to be able to detect trends of the expected magnitudes in ANC (0.5 μeq L−1 yr−1) and SO42− (1.2 μeq L−1 yr−1 with power at or above the 0.90 level and α=0.10.

Obtaining species: sample size considerations

Suppose fish are to be sampled from a stream. A fisheries biologist might ask one of the following three questions: ‘How many fish do I need to catch in order to see all of the species?’, ‘How many fish do I need to catch in order to see all species whose relative frequency is more than 5%?’, or ‘How many fish do I need to catch in order to see a member from each of the species A, B, and C?’. This paper offers a practical solution to such questions by setting a target sample size designed to achieve desired results with known probability. We present three sample size methods, one we call ‘exact’ and the others approximate. Each method is derived under assumed multinomial sampling, and requires (at least approximate) independence of draws and (usually) a large population. The minimum information needed to compute one of the approximate methods is the estimated relative frequency of the rarest species of interest. Total number of species is not needed. Choice of a sample size method depends largely on available computer resources. One approximation (called the ‘Monte Carlo approximation’) gets within ±6 units of exact sample size, but usually requires 20–30 minutes of computer time to compute. The second approximation (called the ‘ratio approximation’) can be computed manually and has relative error under 5% when all species are desired, but can be as much as 50% or more too high when exact sample size is small. Statistically, this problem is an application of the ‘sequential occupancy problem’. Three examples are given which illustrate the calculations so that a reader not interested in technical details can apply our results.

Evaluation of US EPA Environmental Monitoring and Assessment Program's (EMAP)-Wetlands sampling design and classification

The United States Environmental Protection Agencys Environmental Monitoring and Assessment Program (EMAP) will monitor the nations resources by evaluating the status and trends of selected indicators of condition using a probability-based sampling design. The EMAP-Wetlands program will monitor the condition of the nations wetlands. The EMAP classification system is an aggregation of the many subclasses of the US Fish and Wildlife Services National Wetlands Inventory (NWI) classification system. This aggregation results in fewer wetland classes with more wetlands per class than the NWI system. Aggregation of the NWI classification was based primarily on dominant vegetation cover, flooding regimes, dominant water source, and adjacency to rivers and lakes. We evaluated the EMAP classification system and sampling design using NWI digital wetlands data for portions of Illinois, Washington, North Dakota, and South Dakata. Relative numbers of wetlands, total areas, average areas, and common versus rare classes were compared between the EMAP and NWI classification systems. As expected, the EMAP classification provided fewer wetland polygons, each with larger areas, without altering total wetland area. Summary statistics comparing sample estimates to true population parameters (represented by the NWI data) demonstrated the effectiveness of the EMAP sampling design with the exception of rare EMAP classes in the selected regions. Although simple random sampling is inadequate for both large and small wetlands, the EMAP sampling design is readily adapted to provide better estimates for these categories. Aggregating the NWI classification to the EMAP classification provides fewer wetland classes, with more wetlands per class, for EMAPs annual reports and statistical summaries.

Comparison of survey estimates of the finite population variance

The Environmental Monitoring and Assessment Program (EMAP) of the U.S. Environmental Protection Agency has conducted several probability surveys of aquatic resources. Such surveys usually have unequal probability of including population elements in the sample. The Northeast lakes survey, which motivated this study of variance estimation, was such a survey. We examine ten estimators for the finite population variance using a Monte Carlo factorial experiment that considers three population characteristics. The results show that the correlation between the inclusion probabilities and the response is the most important factor that differentiates the estimators. Under conditions of low correlation (approximately <0.4), a common feature in environmental surveys, the sample variance is best, elsewhere, two ratio estimators, one based on consistency and the Horvitz-Thompson Theorem (HT) and the other based on the Yates-Grundy form, behave similarly and best.