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.

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 (r(2) = 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.

Patterns of spatial autocorrelation in stream water chemistry.

Geostatistical models are typically based on symmetric straight-line distance, which fails to represent the spatial configuration, connectivity, directionality, and relative position of sites in a stream network. Freshwater ecologists have explored spatial patterns in stream networks using hydrologic distance measures and new geostatistical methodologies have recently been developed that enable directional hydrologic distance measures to be considered. The purpose of this study was to quantify patterns of spatial correlation in stream water chemistry using three distance measures: straight-line distance, symmetric hydrologic distance, and weighted asymmetric hydrologic distance. We used a dataset collected in Maryland, USA to develop both general linear models and geostatistical models (based on the three distance measures) for acid neutralizing capacity, conductivity, pH, nitrate, sulfate, temperature, dissolved oxygen, and dissolved organic carbon. The spatial AICC methodology allowed us to fit the autocorrelation and covariate parameters simultaneously and to select the model with the most support in the data. We used the universal kriging algorithm to generate geostatistical model predictions. We found that spatial correlation exists in stream chemistry data at a relatively coarse scale and that geostatistical models consistently improved the accuracy of model predictions. More than one distance measure performed well for most chemical response variables, but straight-line distance appears to be the most suitable distance measure for regional geostatistical modeling. It may be necessary to develop new survey designs that more fully capture spatial correlation at a variety of scales to improve the use of weighted asymmetric hydrologic distance measures in regional geostatistical models.

The structure of variation and its influence on the estimation of status: indicators of condition of lakes in the Northeast, U.S.A.

One goal of regional-scale sample surveys is to estimate the status of a resource of interest from a statistically drawn representative sample of that resource. An expression of status is the frequency distribution of indicator scores capturing variability of attributes of interest. However, extraneous variability interferes with the status description by introducing bias into the frequency distributions. To examine this issue, we used data from a regional survey of lakes in the Northeast U.S. collected by the U.S. Environmental Protection Agency's Environmental Monitoring and Assessment Program (EMAP). We employ a components of variance model to identify sources of extraneous variance pertinent to status descriptions of physical, chemical, and biological attributes of the population of lakes in the NE. We summarize the relative magnitude of four components of variance (lake-to-lake, year, interaction, and residual) for each indicator and illustrate how extraneous variance biases the status descriptions. We describe a procedure that removes this bias from the status descriptions to produce unbiased estimates and introduce a novel method for estimating the 'cost' of removing the bias (expressed as either increased sampling uncertainty or additional samples needed to achieve the target precision in the absence of bias). We compare the relative magnitude of the four variance components across the array of indicators, finding in general that conservative chemical indicators are least affected by extraneous variance, followed by some nonconservative indicators, with nutrient indicators most affected by extraneous variance. Intermediate were trophic condition indicators (including sediment diatoms), fish species richness and individuals indicators, and zooplankton taxa richness and individuals indicators. We found no clear patterns in the relative magnitude of variance components as a function of several methods of aggregating fish and zooplankton indicators (e.g., level of taxonomy, or species richness vs. numbers of individuals).