Using GIS to Generate Spatially Balanced Random Survey Designs for Natural Resource Applications

Sampling of a population is frequently required to understand trends and patterns in natural resource management because financial and time constraints preclude a complete census. A rigorous probability-based survey design specifies where to sample so that inferences from the sample apply to the entire population. Probability survey designs should be used in natural resource and environmental management situations because they provide the mathematical foundation for statistical inference. Development of long-term monitoring designs demand survey designs that achieve statistical rigor and are efficient but remain flexible to inevitable logistical or practical constraints during field data collection. Here we describe an approach to probability-based survey design, called the Reversed Randomized Quadrant-Recursive Raster, based on the concept of spatially balanced sampling and implemented in a geographic information system. This provides environmental managers a practical tool to generate flexible and efficient survey designs for natural resource applications. Factors commonly used to modify sampling intensity, such as categories, gradients, or accessibility, can be readily incorporated into the spatially balanced sample design.     

Estimating Trophic State Proportions of a Regional Lake Population: Are Larger Samples Always Better?

During the summers of 1991–1994, the Environmental Monitoringand Assessment Program (EMAP) sampled 344 lakes throughout thenortheastern United States using a proportional stratified sampling design based on lake size. Approximately one-quarter ofthe 344 lakes were sampled each year (4 years) for totalphosphorus to determine the proportion (and associated95% confidence intervals) of the northeast lake population 1ha (11,076 ± 1,699 lakes) that was in oligotrophic,mesotrophic, eutrophic, or heupereutropic (4 classes) conditionaccording to the total phosphorus criteria of the North AmericaLake Manegement Society. Estimates for the second, third, andfourth yr were developed as cumulative of the previous yrsamples and the current yr samples for the northeast as a wholeand for each of its three ecoregions (4 regions). New confidence intervals were computed for each cumulative yrcondition estimate. This produced a total (4 years × 4classes × 4 regions) of 64 cumulative yr tropic conditionestimates. Confidence intervals for 21% of these estimates didnot shorten with increased sample size. This phenomena raisedquestions about the accuracy of estimates based on cumulativesampling procedures. We explain why and how the phenomenon comesabout with both straight random and proportional randomsampling. Further, we present an example of the effects thisphenomenon has on lake tropic state condition estimates in thenortheastern United States.     

Predicting Water Quality Impaired Stream Segments using Landscape-Scale Data and a Regional Geostatistical Model: A Case Study in Maryland

In the United States, probability-based water quality surveys are typically used to meet the requirements of Section 305(b) of the Clean Water Act. The survey design allows an inference to be generated concerning regional stream condition, but it cannot be used to identify water quality impaired stream segments. Therefore, a rapid and cost-efficient method is needed to locate potentially impaired stream segments throughout large areas. We fit a set of geostatistical models to 312 samples of dissolved organic carbon (DOC) collected in 1996 for the Maryland Biological Stream Survey using coarse-scale watershed characteristics. The models were developed using two distance measures, straight-line distance (SLD) and weighted asymmetric hydrologic distance (WAHD). We used the Corrected Spatial Akaike Information Criterion and the mean square prediction error to compare models. The SLD models predicted more variability in DOC than models based on WAHD for every autocovariance model except the spherical model. The SLD model based on the Mariah autocovariance model showed the best fit (r² = 0.72). DOC demonstrated a positive relationship with the watershed attributes percent water, percent wetlands, and mean minimum temperature, but was negatively correlated to percent felsic rock type. We used universal kriging to generate predictions and prediction variances for 3083 stream segments throughout Maryland. The model predicted that 90.2% of stream kilometers had DOC values less than 5 mg/l, 6.7% were between 5 and 8 mg/l, and 3.1% of streams produced values greater than 8 mg/l. The geostatistical model generated more accurate DOC predictions than previous models, but did not fit the data equally well throughout the state. Consequently, it may be necessary to develop more than one geostatistical model to predict stream DOC throughout Maryland. Our methodology is an improvement over previous methods because additional field sampling is not necessary, inferences about regional stream condition can be made, and it can be used to locate potentially impaired stream segments. Further, the model results can be displayed visually, which allows results to be presented to a wide variety of audiences easily.     

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.     

REGIONAL SCALE TREND MONITORING OF INDICATORS OF TROPHIC CONDITION OF LAKES1

ABSTRACT: The U.S. Environmental Protection Agency has proposed a sample survey design to answer questions about the ecological condition and trends in condition of U.S. ecological resources. To meet the objectives, the design relies on a probability sample of the resource population of interest (e.g., a random sample of lakes) each year on which measurements are made during an index period. Natural spatial and temporal variability and variability in the sampling process all affect the ability to describe the status of a population and the sensitivity for trend detection. We describe the important components of variance and estimate their magnitude for indicators of trophic condition of lakes to illustrate the process. We also describe models for trend detection and use them to demonstrate the sensitivity of the proposed design to detect trends. If the variance structure that develops during the probability surveys is like that synthesized from available databases and the literature, then the trends in common indicators of trophic condition of the specified magnitude should be detectable within about a decade for Secchi disk transparency (0.5–1 percentiyear) and total phosphorus (2–3 percent/year), but not for chlorophyll-a (> 3–4 percent/year), which will take longer.     

The influence of anthropogenic and natural geochemical factors on urban soil quality variability: a comparison between Glasgow, UK and Aveiro, Portugal

As part of a harmonised assessment of urban soils (), we investigated the variability of metal content in soils from Aveiro (Portugal) and Glasgow (UK). Samples were collected from parks and other public open spaces in each city. Metal content (Al, Ca, Cr, Cu, Fe, Mn, Ni, Pb and Zn) and basic soil parameters (texture, CEC, pH, organic matter) were determined and data investigated using principal component analysis (PCA). The two cities differ in absolute levels of metal content reflecting industrial and historical development. Factors identified by PCA included anthropogenic (Cu, Pb, Zn), soil properties and geology, which explain variability when data were assessed based on metal content, soil properties and land use. This study highlights the contribution from geological background even in strongly urbanised environments.     

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.     

The role of sample surveys for monitoring the condition of the nation's lakes

In order to meet a growing need to determine the condition of the nation's ecosystems and how their condition is changing, the U.S. Environmental Protection Agency (EPA) developed EMAP, the Environmental Monitoring and Assessment Program. A common survey design serves as the foundation on which to base monitoring of status and trends among diverse ecosystem types. In this paper, we describe the need for a statistically based survey design, briefly summarize the basic EMAP design, describe how that design is tailored for the selection of a probability sample of lakes on which to make measurements of lake condition, and illustrate the process for selecting a sample of lakes in the northeastern United States. Finally, we illustrate how measurements taken on the sample of lakes can be summarized, with known uncertainty, to describe the condition of a population of lakes.The U.S. Government right to retain a non-exclusive, royalty free licence in and to any copyright is acknowledged.