Statistical Analysis of Spatial Pattern: A Comparison of Grid and Hierarchical Sampling Approaches

Previous studies have combined random-site hierarchical sampling designs with analysis of variance techniques, and grid sampling with spatial autocorrelation analysis. We illustrate that analysis techniques and sampling designs are interchangeable using densities of an infaunal bivalve from a study in Poverty Bay, New Zealand. Hierarchical designs allow the estimation of variances associated with each level, but high-level factors are imprecisely estimated, and they are inefficient for describing spatial pattern. Grid designs are efficient for describing spatial pattern, and are amenable to conventional analysis. Our example deals with a continuous spatial habitat, but our conclusions also apply in disjunct or patchy habitats. The influence of errors in positioning is also assessed. The advantages of systematic sampling are reviewed, and more efficient hierarchical approaches are identified. The distinction between biological and statisticalsignificance in all analyses is emphasised.     

Integrating probabalistic and targeted compliance monitoring for comprehensive watershed assessment

Environmental monitoring typically falls into one of two broad categories. Targeted designs, utilizing fixed stations, focus on describing and quantifying impacts, tracking trends, and assessing compliance with regulatory guidelines or limits. Probabilistic designs, in contrast, draw sampling stations at random from an area or region, and the stations are used to describe conditions in the region of interest based on a subpopulation of sites. These two design approaches are usually viewed as mutually exclusive, with randomized designs used for broader regional assessments of overall ambient condition and targeted designs for demonstrating regulatory compliance and/or characterizing specific, localized impacts. Combining elements of both approaches into a single design provides benefits not available from either design alone. Embedding targeted monitoring within the framework of a probabilistic design enables data from targeted stations to be viewed in a more accurate regional context and provides a consistent background against which to identify characteristic regional patterns of contamination and impact. We use the San Gabriel River Regional Monitoring Program, recently implemented in southern California, to illustrate the structure of a hybrid design and how it enables data analyses and assessments that provide a more complete picture of conditions in the watershed. For example, the hybrid design showed that approximately 80% of the metals levels at compliance sites were below the 25th percentile of the overall watershed condition as indicated by the probabilistic sampling.     

Electrofishing in boatable rivers: Does sampling design affect bioassessment metrics?

Data were collected from 60 boatable sites using an electrofishing design that permitted comparisons of the effects of designs and distances on fish assemblage metrics. Sites were classified a priori as Run-of-the-River (ROR) or Restricted Flow (RF). Data representing four different design options (i.e., 1000 and 2000 m for both single and paired banks) were extracted from the dataset and analyzed. Friedman tests comparing metric values among the designs detected significant differences for all richness metrics at both types of sites and for catch per unit effort and percent tolerant species at ROR sites. Richness metrics were generally higher for the two 2000-m designs than for the two 1000-m designs. When plotted against cumulative electrofishing distance, the percent change in metrics declined sharply within approximately 1000 m, after which metrics usually varied by less than 10%. These data demonstrate that designs electrofishing 1000 m of shoreline are sufficient for bioassessments on boatable rivers similar to those in this study, regardless of whether the shoreline is along a single bank or distributed equally among paired banks. However, at sites with depths greater than 4 m, it may be advisable to employ nighttime electrofishing or increase day electrofishing designs to 2000 m.The U.S. Governments right to retain a non-exclusive, royalty free licence in and to any copyright is acknowledged.     

Staggered nested designs to assess scales of variability: the advantages of a spatially explicit analysis

A staggered nested sampling design was used to identify spatial scales of variation in the abundance of an intertidal clam Austrovenus stutchburyi. A georeferenced sampling design permitted assessment of abundance at spatial lags between 0.1 and 87 m. An analysis of variance approach produced imprecise estimates of variability, whereas spatially explicit analyses improved the resolution greatly. A geostatistical model identified the spatial scale of residual variance as 13 m and that of the asymptote of spatial dependence as 17 m. It also permitted mapping of bivalve abundance. Staggered nested designs are highly efficient for comparing hierarchies of scale, but in this study analysis of detailed positional information was required to tease out useful spatial information.     

Effect of imperfect detectability on adaptive and conventional sampling: simulated sampling of freshwater mussels in the upper Mississippi River

Adaptive sampling designs are recommended where, as is typical with freshwater mussels, the outcome of interest is rare and clustered. However, the performance of adaptive designs has not been investigated when outcomes are not only rare and clustered but also imperfectly detected. We address this combination of challenges using data simulated to mimic properties of freshwater mussels from a reach of the upper Mississippi River. Simulations were conducted under a range of sample sizes and detection probabilities. Under perfect detection, efficiency of the adaptive sampling design increased relative to the conventional design as sample size increased and as density decreased. Also, the probability of sampling occupied habitat was four times higher for adaptive than conventional sampling of the lowest density population examined. However, imperfect detection resulted in substantial biases in sample means and variances under both adaptive sampling and conventional designs. The efficiency of adaptive sampling declined with decreasing detectability. Also, the probability of encountering an occupied unit during adaptive sampling, relative to conventional sampling declined with decreasing detectability. Thus, the potential gains in the application of adaptive sampling to rare and clustered populations relative to conventional sampling are reduced when detection is imperfect. The results highlight the need to increase or estimate detection to improve performance of conventional and adaptive sampling designs.     

Trace metal and total suspended solids concentrations in freshwater: the importance of small-scale temporal variation

The temporal variation in the concentrations of particulate trace metals (Cu, Pb and Zn) and total suspended solids (TSS) was examined in three rivers that drain into the Port Jackson estuary, Australia, using a nested, hierarchical sampling design. Sampling was conducted between March and June 1999, under low flow conditions. The sampling design incorporated four temporal scales (hours, days, weeks and months). It was considered that hours, days, weeks and months were representative of such time scales and could be analyzed as random, nested sources of variation in an analysis of variance (ANOVA). Significant variation was found at temporal scales ranging from hours, within the same day, to months. The amount and scales of variation differed between particulate trace metals and TSS concentrations and between rivers. In many cases, differences between small-scale were as important as differences between months. The results suggest that higher anthropogenic influences cause higher variability at small temporal scale. Results indicate the need for nested sampling designs to be incorporated into studies of temporal variation in order to unconfound small-scale temporal variation. The conclusions of this study are likely to be applicable to other water quality variables and pollutants.     

Evaluation of a gradient sampling design for environmental impact assessment

Before-After Control Impact (BACI) sampling designsare commonly used in environmental impact assessmentand are considered the most effective for detectingchanges due to anthropogenic disturbances. Thesedesigns handle local spatial variability throughrandomized placement of samples into a treatmentstratum and a control stratum. When a contaminantdisperses with distance from a point source it issuggested that a gradient design will be moresensitive to change than randomized placement ofsamples. This requires allocating samples according todistance, rather than by random placement withinrandomly placed blocks. In this paper gradient versusrandom sampling designs were compared using data froman oil field in the North Sea. The gradient samplingdesign was more powerful than a randomized CI sampling design.     

Assessment of sampling designs to measure riverine fluxes from the Pearl River Delta, China to the South China Sea

The Pearl River Delta (PRD), located in South China and adjacent to the South China Sea, is comprised of a complicated hydrological system; therefore, it was a great challenge to sample adequately to measure fluxes of organic and inorganic materials to the coastal ocean. In this study, several sampling designs, including five-point (the number of sampling points along the river cross-section and three samples collected at the upper, middle, and bottom parts at each vertical line), three-point (at the middle and two other profiles), one-point (at the middle profile), and single-point (upper, middle, or bottom sub-sampling point at the middle profile) methods, were assessed using total organic carbon (TOC) and suspended particulate matter (SPM) as the measurables. Statistical analysis showed that the three- and five-point designs were consistent with one another for TOC measurements (p > 0.05). The three- and one-point sampling methods also yielded similar TOC results (95% of the differences within 10%). Single-point sampling yielded considerably larger errors than the three- and one-point designs, relative to the results from the five-point design, but sampling at the middle sub-point from the middle profile of a river achieved a relatively smaller error than sampling at the upper or bottom sub-point. Comparison of the sampling frequencies of 12 times a year, four times a year, and twice a year indicated that the frequency of twice a year was sufficient to acquire representative TOC data, but larger sample size and higher sampling frequency were deemed necessary to characterize SPM.     

Patchy distributions: Optimising sample size

A method for estimating sample size which does not require an a priori definition of desired precision, or the assumption that the population is normally distributed with constant variance, has recently been proposed. This paper discusses this method and presents five modifications which make the method easier to use and reduce the probability of estimating a larger sample size than is actually required. The method is extended and used to estimate the mean abundance of patchily distributed benthic organisms. The technique can be used to guide the design of any environmental sampling programme, be it physical, chemical or biological, where comparisons between times and/or locations are required. Trade-offs between numbers of replicates and numbers of levels/sites are discussed.     

Using variance components to estimate power in a hierarchically nested sampling design

We used variance components to assess allocation of sampling effort in a hierarchically nested sampling design for ongoing monitoring of early life history stages of the federally endangered Devils Hole pupfish (DHP) (Cyprinodon diabolis). Sampling design for larval DHP included surveys (5 days each spring 2007–2009), events, and plots. Each survey was comprised of three counting events, where DHP larvae on nine plots were counted plot by plot. Statistical analysis of larval abundance included three components: (1) evaluation of power from various sample size combinations, (2) comparison of power in fixed and random plot designs, and (3) assessment of yearly differences in the power of the survey. Results indicated that increasing the sample size at the lowest level of sampling represented the most realistic option to increase the survey’s power, fixed plot designs had greater power than random plot designs, and the power of the larval survey varied by year. This study provides an example of how monitoring efforts may benefit from coupling variance components estimation with power analysis to assess sampling design.     

Status of the Niagara River point source discharge information: Sampling design and estimation of loading

Two basic requirements, low bias and high precision, are necessary for generating reliable estimates for the load from point and nonpoint sources of pollution. Biases and low precision can be the result of using a bad sampling design and/or inadequate method of estimation. The effects of biases can be reduced at the design stage prior to the data collection or at the data anlysis stage. This paper discusses the statistical issues involved in generating adequate load estimations using recently published point source discharge data from the Niagara River to illustrate these issues.     

Sampling of Sparse Species with Probability Proportional to Prediction

In this article, a 3P sampling (Probability Proportional to Prediction) approach is presented for surveying sparse species connected to certain types of substrates. The method uses the surveyors judgement of the probability of finding the species on a substrate as the base for selection of substrates for species inventories. The method is presented together with estimators, variances and variance estimators. The method is first presented for sampling based on all substrates in a study area and then as a subsampling technique in a two-stage design in which plots or strips are selected in a first stage. The presented approach was evaluated as a subsampling technique in a strip survey of calicioid lichen species associated with coarse broadleaf trees. In comparison with a simple random subsampling without replacement, 3P subsampling was in one study area found to be an improvement with 30–55% in terms of standard errors. The improvement was more modest in the other study area, only between 10–16%. The strip survey with 3P subsampling was more cost-efficient than a strip survey without subsampling except in one case. Based on the results in the test, 3P sampling seems to have a potential for sampling sparse species.     

Seagrass (Posidonia oceanica) monitoring in western Mediterranean: implications for management and conservation

The seagrass Posidonia oceanica is extensively monitored in Mediterranean coastal waters and is an ideal candidate for an eco-regional assessment of the coastal ecosystem. The aim of this study is to evaluate the potential of P. oceanica as eco-regional indicator for its assessment at the scale of Mediterranean basin. For this purpose, regional and national P. oceanica monitoring programmes are identified, and their data and metadata are collected and compared in terms of objectives, strategies, sampling designs and sampling methods. The analysis identifies a number of issues concerning data quality, reliability and comparability. In particular, the adoption of different sampling designs and methods may introduce relevant errors when comparing data. The results of this study stress the necessity of carefully planning monitoring programmes. Moreover, it highlights that the adoption of a number of common tools would facilitate all Mediterranean monitoring activities and allows an optimisation of management efforts at an eco-regional scale.     

Design of on-line river water quality monitoring systems using the entropy theory: a case study

The design of a water quality monitoring network is considered as the main component of water quality management including selection of the water quality variables, location of sampling stations and determination of sampling frequencies. In this study, an entropy-based approach is presented for design of an on-line water quality monitoring network for the Karoon River, which is the largest and the most important river in Iran. In the proposed algorithm of design, the number and location of sampling sites and sampling frequencies are determined by minimizing the redundant information, which is quantified using the entropy theory. A water quality simulation model is also used to generate the time series of the concentration of water quality variables at some potential sites along the river. As several water quality variables are usually considered in the design of water quality monitoring networks, the pair-wise comparison is used to combine the spatial and temporal frequencies calculated for each water quality variable. After selecting the sampling frequencies, different components of a comprehensive monitoring system such as data acquisition, transmission and processing are designed for the study area, and technical characteristics of the on-line and off-line monitoring equipment are presented. Finally, the assessment for the human resources needs, as well as training and quality assurance programs are presented considering the existing resources in the study area. The results show that the proposed approach can be effectively used for the optimal design of the river monitoring systems.     

Estimating means and variances: The comparative efficiency of composite and grab samples

This paper compares the efficiencies of two sampling techniques for estimating a population mean and variance. One procedure, called grab sampling, consists of collecting and analyzing one sample per period. The second procedure, called composite sampling, collectsn samples per period which are then pooled and analyzed as a single sample. We review the well known fact that composite sampling provides a superior estimate of the mean. However, it is somewhat surprising that composite sampling does not always generate a more efficient estimate of the variance. For populations with platykurtic distributions, grab sampling gives a more efficient estimate of the variance, whereas composite sampling is better for leptokurtic distributions. These conditions on kurtosis can be related to peakedness and skewness. For example, a necessary condition for composite sampling to provide a more efficient estimate of the variance is that the population density function evaluated at the mean (i.e.f()) be greater than . If , then a grab sample is more efficient. In spite of this result, however, composite sampling does provide a smaller estimate of standard error than does grab sampling in the context of estimating population means.     

基于SADA的最小(大)化超标区布点方法在环境监测中的应用

二次布点是在已有监测数据基础上增加监测点进行监测,决策者常常需要通过结合二次布点和原有监测数据,使插值估算的浓度超标区域最大化或最小化。较详细地介绍了SADA软件最大(小)化超标区域布点法,结合沈阳市区PM10超标区域研究为实例,验证了该方法的显著效果并与随即布点法进行了分析比较。     

Optimising the sampling effort in riparian surveys

Riparian condition is commonly measured as part of stream health monitoring programs as riparian vegetation provides an intricate linkage between the terrestrial and aquatic ecosystems. Field surveys of a riparian zone provide comprehensive riparian attribute data but can be considerably intensive and onerous on resources and workers. Our objective was to assess the impact of reducing the sampling effort on the variation in key riparian health indicators. Subsequently, we developed a non-parametric approach to calculate an information retained (IR) statistic for comparing several constrained systematic sampling schemes to the original survey. The IR statistic is used to select a scheme that reduces the time taken to undertake riparian surveys (and thus potentially the costs) whilst maximising the IR from the original survey. Approximate bootstrap confidence intervals were calculated to improve the inferential capability of the IR statistic. The approach is demonstrated using riparian vegetation indicators collected as part of an aquatic ecosystem health monitoring program in Queensland, Australia. Of the nine alternative sampling designs considered, the sampling design that reduced the sampling intensity per site by sixfold without significantly comprising the quality of the IR, results in halving the time taken to complete a riparian survey at a site. This approach could also be applied to reducing sampling effort involved in monitoring other ecosystem health indicators, where an intensive systematic sampling scheme was initially employed.     

Assessing benthic community condition in Chesapeake Bay: does the use of different benthic indices matter?

Federal and state environmental agencies conduct several programs to characterize the environmental condition of Chesapeake Bay. These programs use different benthic indices and survey designs, and have produced assessments that differ in the estimate of the extent of benthic community degradation in Chesapeake Bay. Provided that the survey designs are unbiased, differences may exist in the ability of these indices to identify environmental degradation. In this study we compared the results of three indices calculated on the same data, and the assessments of two programs: the Chesapeake Bay Program and the Mid-Atlantic Integrated Assessment (MAIA). We examined the level of agreement of index results using site-based measures of agreement, evaluated sampling designs and statistical estimation methods, and tested for significant differences in assessments. Comparison of ratings of individual sites was done within separate categories of water and sediment quality to identify which indices summarize best pollution problems in Chesapeake Bay. The use of different benthic indices by these programs produced assessments that differed significantly in the estimate of degradation. A larger fraction of poor sites was classified as good by the Environmental Monitoring and Assessment Program’s Virginian Province and MAIA benthic indices compared to the Chesapeake Bay benthic index of biotic integrity, although overall classification efficiencies were similar for all indices. Differences in survey design also contributed to differences in assessments. The relative difference between the indices remained the same when they were applied to an independent dataset, suggesting that the indices can be calibrated to produce consistent results.     

Review of monitoring and assessing ground vegetation biodiversity in national forest inventories

Ground vegetation (GV) is an important component from which many forest biodiversity indicators can be estimated. To formulate policies at European level, taking into account biodiversity, European National Forest Inventories (NFIs) are one of the most important sources of forest information. However, for monitoring GV, there are several definitions, data collection methods, and different possible indicators. Even though it must be considered that natural conditions in different countries form very different understory types, each one has its own cost-efficient monitoring design, and they can hardly be compared. Therefore, the development of general guidelines is a particularly complex issue. This paper is a review of data collection methods and consequently a selection of the best available methods for the set of indicators with an emphasis on GV sampling methodologies in NFIs. As a final result, recommendations on GV definitions and classifications, sampling methodologies, and indicators are formulated for NFIs. Different sampling areas are recommended for each life form (shrubs, herbs, etc.). Inventory cycles and sampling seasons (depending on the phonological stages) should be specially considered and evaluated in the results. The proposed indicators are based on composition at different levels of sampling intensity for each life form and on coverage measurements.