Spatial Sampling Design Research Articles

Well-spread samples with dynamic sample sizes.

A spatial sampling design determines where sample locations are placed in a study area so that population parameters can be estimated with relatively high precision. If the response variable has spatial trends, spatially balanced or well-spread designs give precise results for commonly used estimators. This article proposes a new method that draws well-spread samples over arbitrary auxiliary spaces and can be used for master sampling applications. All we require is a measure of the distance between population units. Numerical results show that the method generates well-spread samples and compares favorably with existing designs. We provide an example application using several auxiliary variables to estimate total aboveground biomass over a large study area in Eastern Amazonia, Brazil. Multipurpose surveys are also considered, where the totals of aboveground biomass, primary production, and clay content (3 responses) are estimated from a single well-spread sample over the auxiliary space.

Six Steps towards a Spatial Design for Large-Scale Pollinator Surveillance Monitoring.

Despite the importance of pollinators to ecosystem functioning and human food production, comprehensive pollinator monitoring data are still lacking across most regions of the world. Policy-makers have recently prioritised the development of large-scale monitoring programmes for pollinators to better understand how populations respond to land use, environmental change and restoration measures in the long term. Designing such a monitoring programme is challenging, partly because it requires both ecological knowledge and advanced knowledge in sampling design. This study aims to develop a conceptual framework to facilitate the spatial sampling design of large-scale surveillance monitoring. The system is designed to detect changes in pollinator species abundances and richness, focusing on temperate agroecosystems. The sampling design needs to be scientifically robust to address questions of agri-environmental policy at the scales of interest. To this end, we followed a six-step procedure as follows: (1) defining the spatial sampling units, (2) defining and delimiting the monitoring area, (3) deciding on the general sampling strategy, (4) determining the sample size, (5) specifying the sampling units per sampling interval, and (6) specifying the pollinator survey plots within each sampling unit. As a case study, we apply this framework to the "Wild bee monitoring in agricultural landscapes of Germany" programme. We suggest this six-step procedure as a conceptual guideline for the spatial sampling design of future large-scale pollinator monitoring initiatives.

Comparing Spatial Sampling Designs for Estimating Effectively Maize Crop Traits in Experimental Plots

The current study investigates the performance of various sampling designs in providing accurate estimates for crucial maize yield traits (intended for silage) including plant height, fresh/dry/ear weight, number of maize ears per plant, and total ear weight per plant, using spatial maize data. The experiment took place in an experimental field area at Aristotle University (AUTH) farm during the 2016 growing season. Nine sampling designs were statistically analyzed and compared with spatial data from an Italian maize hybrid (AGN720) to identify the most suitable and effective sampling design for dependable maize yield estimates. The study’s results indicate that, among the different sampling techniques, Stratified Random Sampling is the most effective and reliable method for obtaining accurate maize yield estimates. This new approach not only provides precise estimates but also requires fewer measurements, making it suitable for experiments where not all plants have emerged. These findings suggest that Stratified Random Sampling can be employed effectively as an alternative to harvesting the entire plot for effectively estimating maize crop traits in experimental plots.

Development and deployment of an improved Anopheles gambiae s.l. field surveillance by adaptive spatial sampling design

IntroductionAccurate assessments of vector occurrence and abundance, particularly in widespread vector-borne diseases such as malaria, are crucial for the efficient deployment of disease surveillance and control interventions. Although previous studies have explored the benefits of adaptive sampling for identifying disease hotspots (mostly through simulations), limited research has been conducted on field surveillance of malaria vectors.MethodsWe developed and implemented an adaptive spatial sampling design in southwestern Benin, specifically targeting potential and uncertain Anopheles gambiae hotspots, a major malaria vector in sub-Saharan Africa. The first phase of our proposed design involved delineating ecological zones and employing a proportional lattice with close pairs sampling design to maximize spatial coverage, representativeness of ecological zones, and account for spatial dependence in mosquito counts. In the second phase, we employed a spatial adaptive sampling design focusing on high-risk areas with the greatest uncertainty.ResultsThe adaptive spatial sampling design resulted in a reduced sample size from the first phase, leading to improved predictions for both out-of-sample and training data. Collections of Anopheles gambiae in high-risk and low-uncertainty areas were nearly tripled compared to those in high-risk and high-uncertainty areas. However, the overall model uncertainty increased.DiscussionWhile the adaptive sampling design allowed for increased collections of Anopheles gambiae mosquitoes with a reduced sample size, it also led to a general increase in uncertainty, highlighting the potential trade-offs in multi-criteria adaptive sampling designs. It is imperative that future research focuses on understanding these trade-offs to expedite effective malaria control and elimination efforts.

Maximising the informativeness of new records in spatial sampling design

Abstract In building a robust knowledge base or validating existing models for use in ecological spatial modelling, having plentiful high‐quality data is paramount. Careful survey design helps attain that goal and, in part due to financial constraints, such design requires the balancing of hard monetary costs and the intangible benefit of improved ecological models. We propose a framework that quantifies a location's value to the modeller by accounting for both the probability of obtaining new samples and their expected contribution to the model. The approach is illustrated on a citizen science database of roadkills in Taiwan, modelled as a Poisson point process on a linear road network. Our method has revealed some valuable locations that were not self‐evident, for example, highlighting the possibility of sending volunteers to mountainous areas that despite being hard to reach, would provide valuable samples. We have also highlighted some ex situ sampling opportunities to avoid wasting resources by over‐sampling hard to access locations. Our technique is not restricted to presence‐only data, and in fact we present a general framework that can be applied to a wide range of settings by tuning its formulation. Our method is quite flexible and allows for more elaborate value functions, enabling managers to precisely quantify varied goals within the same framework.

One point per cluster spatially balanced sampling

A spatial sampling design determines where sample locations are placed in a study area so that population parameters can be estimated with relatively high precision. Spatially balanced designs have good spatial spread and give precise results for commonly used estimators when surveying natural resources. A new design is proposed which draws spatially balanced samples from stratified and unstratified populations. The method is two-fold. First, the population is partitioned into n compact geographic clusters. Then, a one point per cluster sample is drawn using a linear assignment strategy that optimises the spatial spread of the sample. Numerical results on several simulated populations show that the method generates well-spread samples and compares favourably with existing designs. An example application is also provided, where soil organic matter concentrations are estimated over a study area in Voorst, Netherlands.

Optimal two-stage spatial sampling design for estimating critical parameters of SARS-CoV-2 epidemic: Efficiency versus feasibility

The COVID-19 pandemic presents an unprecedented clinical and healthcare challenge for the many medical researchers who are attempting to prevent its worldwide spread. It also presents a challenge for statisticians involved in designing appropriate sampling plans to estimate the crucial parameters of the pandemic. These plans are necessary for monitoring and surveillance of the phenomenon and evaluating health policies. In this respect, we can use spatial information and aggregate data regarding the number of verified infections (either hospitalized or in compulsory quarantine) to improve the standard two-stage sampling design broadly adopted for studying human populations. We present an optimal spatial sampling design based on spatially balanced sampling techniques. We prove its relative performance analytically in comparison to other competing sampling plans, and we also study its properties through a series of Monte Carlo experiments. Considering the optimal theoretical properties of the proposed sampling plan and its feasibility, we discuss suboptimal designs that approximate well optimality and are more readily applicable.

Efficiency of spatial sampling designs in estimating abundance and species richness of carabids at the landscape level

ContextDeclining biodiversity in agricultural landscapes has increased the need for research and monitoring of insect abundance and diversity at the landscape level.ObjectivesWe investigated the accuracy of different spatial sampling designs in estimating landscape-level abundance and species richness of carabids in agricultural landscapes and, further, which sample size per landscape section was required and whether dominating land use or landscape subdivision affected accuracy and required sample size.MethodsWe developed a simulation model that created raster maps of agricultural landscapes, compiled local carabid communities (species composition and abundances) within raster cells and simulated the sampling of carabids with pitfall traps using different spatial sampling designs and sample sizes between 4 and 49 sampling points per landscape section. Spatial sampling designs included random, systematic grid-based, stratified and clustered schemes.ResultsTo estimate landscape-level abundance, area-proportional stratified random sampling was most accurate followed by systematic grid-based designs. A sample size of 25 appeared to be the best trade-off between accuracy and sampling cost. Accuracy was not affected substantially by landscape characteristics in most cases. With respect to species richness, all designs except for clustered sampling had comparable accuracies, but even 49 samples were not sufficient to detect 80% of the species.ConclusionSystematic grid-based designs are generally recommendable for sampling of carabids in agricultural landscapes and, in case a carabid-specific habitat classification is available, area-proportional stratified random sampling provides optimal accuracy for estimating landscape-level abundance. For assessment of species richness, large sample size is more important than spatial sampling design.

Spsurvey: Spatial Sampling Design and Analysis in R.

spsurvey is an R package for design-based statistical inference, with a focus on spatial data. spsurvey provides the generalized random-tessellation stratified (GRTS) algorithm to select spatially balanced samples via the grts() function. The grts() function flexibly accommodates several sampling design features, including stratification, varying inclusion probabilities, legacy (or historical) sites, minimum distances between sites, and two options for replacement sites. spsurvey also provides a suite of data analysis options, including categorical variable analysis (cat_analysis()), continuous variable analysis cont_analysis()), relative risk analysis (relrisk_analysis()), attributable risk analysis (attrisk_analysis()), difference in risk analysis (diffrisk_analysis()), change analysis (change_analysis()), and trend analysis (trend_analysis()). In this manuscript, we first provide background for the GRTS algorithm and the analysis approaches and then show how to implement them in spsurvey. We find that the spatially balanced GRTS algorithm yields more precise parameter estimates than simple random sampling, which ignores spatial information.

Status of the geogenic radon potential investigations in Bulgaria

Radon (222Rn) is a radioactive gas and formed as a result of the radioactive decay of radium. 222Rn relieved from the ground could accumulate in the building and contribute to human exposure. Exposure to indoor radon and its decay products contributes to half of the annual dose received by the public from all natural radioactive sources. Radon is recognized as a carcinogenic agent by the WHO and is the second leading cause of lung cancer after tobacco smoke. The radon concentration in buildings and the exposure to radon depend on many factors, but it can be assumed that geology is the main factor influencing the variation of indoor radon. In this regard, the geogenic radon potential (GRP) of the terrain is the probability of the presence of high radon concentration in a building, the genesis of which is directly related to the influence of the earth's surface, and not e.g. from building materials. In addition, there is a concept “radon index”, which is used to characterize GRP. One of the approaches for quantifying the radon index is based on a multivariate cross-tabulation, which includes two parameters – radon concentration in soil gas and gas permeability of the earth layer. Till 2019, complex studies concerning correlation between the measured radon concentrations and bedrock geology in Bulgaria are only scarce and quite general. In the last three years, there are attempts for detailed investigations for evaluation of the bedrock and superficial geology associating with radon potential or/and radon index determinations. Therefore, research works on geogenic radon so far in Bulgaria can be divided into two main groups: regional research works related to the "radon-rock" relationship and local research aimed at determining the radon index at specific sites. In the first group appertain investigations about defining the rock formations in Bulgaria, in their outcrop presence, with possible high radon potential based on geological and published more general “radon–rock correlations” data. Based on that, a GIS based map for the spatial distribution of the particular rock types in accordance with the expected radon potential is made. Also to this group belongs a study concerning spatial sampling design for the use of the polygons (Sliven Province) as the unit of sampling, data collection, and analysis and reduces the number of observations, as well as would optimize the gathering, analysis and systematization of the data for the preparation of a methodology for the preparation of geogenic radon potential map. In the second group appertain investigations of the radon index determination at the two pilot sites affected by fault systems in Sofia.

Adaptive spatial designs minimizing the integrated Bernoulli variance in spatial logistic regression models - with an application to benthic habitat mapping

Constructing efficient spatial sampling designs is important for monitoring, understanding and characterizing environmental processes acting over large-scale spatial domain. Multiple types of devices can accomplish informative sampling in various ways, and time and computational limitations should be considered too. In-situ sampling is often accurate, but it tends to be very sparse in the vast spatial areas considered for mapping purposes, and careful constructions of experimental sampling designs are needed. A criterion for mapping spatial presence-absence variables is presented. The expected integrated Bernoulli variance criterion is used in order to explore regions with more uncertainty about the binary outcomes. This approach uses a hierarchical Bayesian logistic regression model for the binary variable and develops approximate closed form expressions for the expected integrated Bernoulli variance. The approximations are fast to compute for many designs. The expressions are extended to find adaptive designs in the setting of sequential spatial exploration, where there are limited computation resources and operational time restrictions. In simulation studies the approximations are compared with tedious Monte Carlo sampling methods. Approximations are shown to be accurate and to work for a large spatial grid. An application in benthic habitat mapping is presented. It considers a coral dataset from Australia to demonstrate the suggested sampling design approach.

Kryging: geostatistical analysis of large-scale datasets using Krylov subspace methods

Analyzing massive spatial datasets using a Gaussian process model poses computational challenges. This is a problem prevailing heavily in applications such as environmental modeling, ecology, forestry and environmental health. We present a novel approximate inference methodology that uses profile likelihood and Krylov subspace methods to estimate the spatial covariance parameters and makes spatial predictions with uncertainty quantification for point-referenced spatial data. “Kryging” combines Kriging and Krylov subspace methods and applies for both observations on regular grid and irregularly spaced observations, and for any Gaussian process with a stationary isotropic (and certain geometrically anisotropic) covariance function, including the popular Matérn covariance family. We make use of the block Toeplitz structure with Toeplitz blocks of the covariance matrix and use fast Fourier transform methods to bypass the computational and memory bottlenecks of approximating log-determinant and matrix-vector products. We perform extensive simulation studies to show the effectiveness of our model by varying sample sizes, spatial parameter values and sampling designs. A real data application is also performed on a dataset consisting of land surface temperature readings taken by the MODIS satellite. Compared to existing methods, the proposed method performs satisfactorily with much less computation time and better scalability.

Evaluating sample sizes and design for monitoring and characterizing the spatial variations of potentially toxic elements in the soil

Cost-effective, representative and spatial coverage sampling designs are required to monitor the effects of potentially toxic elements (PTEs) in the soil. This study aims to evaluate the minimum sample sizes and placement of soil sampling designs to monitor and characterize the spatial variation of the PTEs (Cu, Zn, Cd, Cr, Pb, and Ni) in the soils. However, there is no standardized approach for evaluating the optimum soil sample size and monitoring location because of the spatial heterogeneity of PTEs in the soil. As a result, three broad techniques were applied. The first step was to use Global Moran's I and q-statistic values to describe the variability of soil PTEs and select appropriate evaluation methods. Second, using simple random sampling (SRS), ordinary kriging (OK), and Mean of Surface with Non-homogeneity (MSN), we estimated and evaluated soil PTEs in the current soil sampling schemes. Finally, MSN and spatial simulated annealing (SSA) optimization techniques were used to assess the required sample sizes and placements in the existing designs. Method performance was evaluated using a standard error (SE) and a relative standard error of the mean (RSE). Except for Zn and Cd, all PTEs tested showed heterogeneous distributions over the area. The MSN lowered the predicted SE by 79–86 % compared with SRS. The OK approach also outperformed the SRS method regarding mean estimated values of soil PTEs by 42–57 %. After SSA refined the initial design, the predicted SE by MSN of Cr and Zn was lowered by 13 % and 39 %, respectively. The MSN was effective with small sample sizes, reducing sample sizes and surveying costs by 39 % after SSA optimized the existing sample numbers. Thus, integrating various sampling strategies may be efficient for building optimal sample designs to monitor PTEs in the soil.

Spatial sampling design optimization of monitoring network for terrestrial ecosystem in China

The rapid socioeconomic development leads to the deterioration of ecological environment. Ecosystem assessment has been conducted worldwide, e.g. the Millennium Ecosystem Assessment to assess consequences of ecosystem change for human well-being. To enhance ecosystem assessment in China, this study proposes the design of a monitoring network for the terrestrial ecosystem consisting of core stations and localized points. With focus on ecosystem services of NPP, water conservation, soil retention and sandstorm prevention, core stations of the monitoring network for observing all four services are first selected by assessing and improving spatial representativeness in ecoregions of forest, grassland and desert ecosystems. Then a spatial sampling method is applied to choose localized points for observing each specific service. Eventually expert's knowledge is used to make final decisions of added stations and points by utilizing existing networks and considering factors such as topography, spatial coverage. Combining both aforementioned approaches and experts knowledge, 60 core stations and 176 localized points are finally determined for the monitoring network. For the forest ecosystem, 39 core stations are decided with 31 selected from existing networks and eight newly added core stations improve spatial representativeness by 51.58 %, 68.11 % and 75.55 % in Temperate grasslands, Temperate desert and Alpine vegetation in Tibet Plateau respectively. For the grassland and desert ecosystem, 21 core stations are chosen with 18 from existing networks and three newly added core stations improve the representativeness by 21.60 % and 44.88 % in Tibet alpine grassland and Grassland in southern mountain areas respectively. Priorities in the implementation phase should be given to instruments installation for monitoring all four services in core stations from existing networks and setting up new stations in regions where representativeness are significantly improved.

Spatially Balanced Sampling with Local Ranking

A spatial sampling design determines where sample locations are placed in a study area so that population parameters can be estimated with good precision. Spatially balanced designs draw samples with good spatial spread and provide precise results for commonly used estimators when surveying natural resources. In this article, we propose a new sampling strategy that incorporates ranking information from nearby locations into a spatially balanced sample. If the population exhibits spatial trends, our simple local ranking strategy can improve the precision of commonly used estimators. Numerical results on several test populations with different spatial structures show that local ranking can improve the performance of a spatially balanced design. To show that local ranking is simple and effective in practice, we provide an example application for the health and productivity assessment of a Shiraz vineyard in South Australia.Supplementary materials accompanying this paper appear online.

Optimization of the sampling design for multiobjective soil mapping using the multiple path SSA (MP-SSA) method

Spatial sampling is important for soil surveys and mapping, and the optimization of the sampling design is a hot topic. Most often in soil sampling, multiple purposes are usually involved and corresponding objectives need to be optimized as much as possible. In such cases, balanced optimization is needed to produce the best compromised solutions that reach the maximum common interest, but not to generate a well-spread Pareto front. To solve this problem, the multiple path spatial simulated annealing (MP-SSA) was developed by extending the classic SSA. It can synchronously optimize multiobjective functions of different types and magnitudes by setting one annealing path for each objective, and designing a voting and annealing mechanism. To illustrate the difference and performance for MP-SSA, it was compared with the archived multiobjective simulated annealing (AMOSA) and Non-dominated Sorting Genetic Algorithm II (NSGA-II), both aiming at generating well-spread Pareto front, in two case studies with hypothetical data and actual soil heavy metal data. The results show that the MP-SSA is more efficient in generating the best compromised solutions, and is an efficient and promising tool for balanced multiobjective optimization for spatial sampling design when all objectives need to be optimized as much as possible.

Spatial Sampling Design to Improve the Efficiency of the Estimation of the Critical Parameters of the SARS-CoV-2 Epidemic

Abstract Given the urgent informational needs connected with the diffusion of infection with regard to the COVID-19 pandemic, in this article, we propose a sampling design for building a continuous-time surveillance system. Compared with other observational strategies, the proposed method has three important elements of strength and originality: (1) it aims to provide a snapshot of the phenomenon at a single moment in time, and it is designed to be a continuous survey that is repeated in several waves over time, taking different target variables during different stages of the development of the epidemic into account; (2) the statistical optimality properties of the proposed estimators are formally derived and tested with a Monte Carlo experiment; and (3) it is rapidly operational as this property is required by the emergency connected with the diffusion of the virus. The sampling design is thought to be designed with the diffusion of SAR-CoV-2 in Italy during the spring of 2020 in mind. However, it is very general, and we are confident that it can be easily extended to other geographical areas and to possible future epidemic outbreaks. Formal proofs and a Monte Carlo exercise highlight that the estimators are unbiased and have higher efficiency than the simple random sampling scheme.

Spatial Sampling Design for the Geogenic Radon Potential Survey in Sliven Province, Bulgaria

The development of a methodology for the geogenic radon potential (GRP) mapping based on soil gas radon and soil gas permeability field measurements is among the main objectives in the determination of “radon priority areas” in Bulgaria. One of the key elements of the methodology is to define as accurately as possible, areas of risk for the presence of radon gas (222Rn) on the map. This study presents an approach to spatial sampling for the geogenic radon potential survey in Sliven Province, Bulgaria. The district is characterised by its very complex geological settings, represented by rocks of different age and mineral and chemical compositions. The proposed methodology defined a sampling frame of province radon map, prepared on the base of indoor radon measurement and the complex sampling scheme of random points. The parcel-level GIS was used for establishing the sample frame of 5×5 km polygons on the territory of the province. The IBM SPSS Complex Samples Module was applied for planning the survey’s polygons by drawing sample units according to the spatial design. The spatial relationship between indoor radon concentration and geological information was analysed for the sampling scheme construction by the polygons. The latter serve as sampling units, allowing both indoor radon concentration and geological data to be linked. The results show that the applied spatial sampling approach allows controlling the specific environmental conditions, in terms of their specificity, variability, and distribution.

Spatial Stratification Method for the Sampling Design of LULC Classification Accuracy Assessment: A Case Study in Beijing, China

Spatial sampling design is important for accurately assessing land use and land cover (LULC) classification results from remote sensing data. Spatial stratification can dramatically improve spatial sampling efficiency by dividing the study area into several strata when classification correctness is spatially stratified heterogeneous. By integrating the LULC classification results from different sources and spatial resolutions, a spatial stratification method for spatial sampling of accuracy assessment is presented in this paper. Its efficiency is demonstrated in the case study using LULC data of Beijing, China, in the following steps. First, we standardized and reclassified multiresolution remote sensing data, including China’s land use/cover datasets (CLUDs) from 2017 (resolution: 30 m), 500 m MCD12Q1, and 10 m FROM-GLC10 data, into six classes. Second, we customized stratification rules, formulated a technical specification to realize 11 strata using CLUDs and MCD12Q1, and employed FROM-GLC10 as the reference data for accuracy assessment. Furthermore, six sample sets with sizes of 16,417; 1821; 652; 337; 198; and 142 were drawn using different methods, and their overall accuracy (OA), deviation accuracy (DA), root-mean-square error (RMSE), and standard deviation (STDEV) values were also evaluated to demonstrate the efficiency brought by spatial stratification. Compared with the spatial even sampling method, the OAs of the stratified even sampling method adopting the proposed stratification method was much closer to the true OA, and the corresponding RMSE and STDEV results decreased from 2.097% and 2.127% to 0.914% and 0.713%, respectively, due to the contribution of spatial stratification in the sampling scheme. The method can be used to distinguish the differences and improve the representativeness of samples, and it can be employed to select validation samples for LULC classification.

Multivariate Spatial Sampling Design Using Copulas with an Environmental Application

Multivariate Spatial Sampling Design Using Copulas with an Environmental Application