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Soil analysis is a key practice to increase the efficiency of nutrient management in agriculture. Since the early 20th century, increasingly sophisticated methods have been developed to describe and manipulate the inherent spatial variability in soil chemical properties within the realms of classical and spatial statistics. In this paper, we reviewed design‐based (classical) and model‐based (geostatistical) sampling to suggest field‐scale sampling strategies consistent with common agronomic management goals in annual crop production systems. To assess the relevance of common sampling methods in relation to practice, current extension recommendations across the United States were compared with results from peer‐reviewed literature. Despite decades of research, specific recommendations for sample sizes, sampling depths, numbers of soil cores, and layouts were highly variable for classical and geostatistical approaches. Mobile nutrients, such as NO3, are frequently lacking in spatial structure and rarely are recommended for site‐specific management. Nonmobile nutrients, such as P, are more spatially dependent and exhibit nested spatial structures that are inconsistent across fields. For these reasons, we recommend design‐based sampling in most situations for simplicity, cost, and objectivity. The common design‐based sampling protocol prescribes collection of individual cores in a zig‐zag pattern that are combined to produce a composite sample. This protocol should be amended because it is not sufficiently randomized and is inadequate for log‐normally distributed variables. To facilitate site‐specific management, we recommend structured approaches for delineating management zones or strata and for researchers to systematically enumerate confounding variables while explicitly defining the scope of inference for future soil sampling studies.

The aim of this study is to compare two methods of interpolation, namely Kriging (a standard algorithm), mainly used in geostatistics, and the Experimental Probabilistic Hypersurface (developed by SCM SA). We study several technical points, such as their ability to take uncertainties into account, to return an uncertainty on the interpolation, the quality of the numerical procedures, etc. The Experimental Probabilistic Hypersurface (EPH) is a minimal information model, which only uses the existing data and makes as less artificial hypothesis on the data as possible. The Kriging, on the contrary, relies on an estimation of the variability of the data using a variogram.

Methane (CH4) is one of the most important greenhouse gases causing the global warming effect. The mapping data of atmospheric CH4 concentrations in space and time can help us better to understand the characteristics and driving factors of CH4 variation as to support the actions of CH4 emission reduction for preventing the continuous increase of atmospheric CH4 concentrations. In this study, we applied a spatiotemporal geostatistical analysis and prediction to develop an approach to generate the mapping CH4 dataset (Mapping-XCH4) in 1° grid and three days globally using column averaged dry air mole fraction of CH4 (XCH4) data derived from observations of the Greenhouse Gases Observing Satellite (GOSAT) from April 2009 to April 2020. Cross-validation for the spatiotemporal geostatistical predictions showed better correlation coefficient of 0.97 and a mean absolute prediction error of 7.66 ppb. The standard deviation is 11.42 ppb when comparing the Mapping-XCH4 data with the ground measurements from the total carbon column observing network (TCCON). Moreover, we assessed the performance of this Mapping-XCH4 dataset by comparing with the XCH4 simulations from the CarbonTracker model and primarily investigating the variations of XCH4 from April 2009 to April 2020. The results showed that the mean annual increase in XCH4 was 7.5 ppb/yr derived from Mapping-XCH4, which was slightly greater than 7.3 ppb/yr from the ground observational network during the past 10 years from 2010. XCH4 is larger in South Asia and eastern China than in the other regions, which agrees with the XCH4 simulations. The Mapping-XCH4 shows a significant linear relationship and a correlation coefficient of determination (R2) of 0.66, with EDGAR emission inventories over Monsoon Asia. Moreover, we found that Mapping-XCH4 could detect the reduction of XCH4 in the period of lockdown from January to April 2020 in China, likely due to the COVID-19 pandemic. In conclusion, we can apply GOSAT observations over a long period from 2009 to 2020 to generate a spatiotemporally continuous dataset globally using geostatistical analysis. This long-term Mpping-XCH4 dataset has great potential for understanding the spatiotemporal variations of CH4 concentrations induced by natural processes and anthropogenic emissions at a global and regional scale.

This research aims to determine the current conditions of geographical accessibility to and from healthcare centres in Manizales and Villamaría conurbation through the Enhanced two- step floating catchment area (E2SFCA) method, supported by geographic tools and socioeconomic assessments. The main result is that the average number of beds per 1000 inhabitants in low complexity systems is below the average defined for Colombia and Latin America, thus requiring greater attention in implementing beds to reach the required accessibility levels. These valuations allow concluding that the accessibility of healthcare institutions requires the use of significant calculation tools, such as the E2SFCA method, which has not had great applications within the Colombian territory.

•Geostatistical models showing strong predictive performance are used to produce maps of measles vaccination coverage at 1 × 1 km resolution.•Remoteness, measured as travel time to nearest major settlement, was consistently a key predictor of coverage.•The maps reveal heterogeneities and ‘coldspots’ of low vaccination coverage that are missed using large area summaries.•Aggregated estimates of coverage that do not account for local heterogeneities potentially over-estimate the numbers of children vaccinated by over 10%.•Relating to the WHO GVAP targets of 80% coverage, the integration of high resolution coverage and population maps shows the districts that have attained the threshold in the study countries. The expansion of childhood vaccination programs in low and middle income countries has been a substantial public health success story. Indicators of the performance of intervention programmes such as coverage levels and numbers covered are typically measured through national statistics or at the scale of large regions due to survey design, administrative convenience or operational limitations. These mask heterogeneities and ‘coldspots’ of low coverage that may allow diseases to persist, even if overall coverage is high. Hence, to decrease inequities and accelerate progress towards disease elimination goals, fine-scale variation in coverage should be better characterized. Using measles as an example, cluster-level Demographic and Health Surveys (DHS) data were used to map vaccination coverage at 1 km spatial resolution in Cambodia, Mozambique and Nigeria for varying age-group categories of children under five years, using Bayesian geostatistical techniques built on a suite of publicly available geospatial covariates and implemented via Markov Chain Monte Carlo (MCMC) methods. Measles vaccination coverage was found to be strongly predicted by just 4–5 covariates in geostatistical models, with remoteness consistently selected as a key variable. The output 1 × 1 km maps revealed significant heterogeneities within the three countries that were not captured using province-level summaries. Integration with population data showed that at the time of the surveys, few districts attained the 80% coverage, that is one component of the WHO Global Vaccine Action Plan 2020 targets. The elimination of vaccine-preventable diseases requires a strong evidence base to guide strategies and inform efficient use of limited resources. The approaches outlined here provide a route to moving beyond large area summaries of vaccination coverage that mask epidemiologically-important heterogeneities to detailed maps that capture subnational vulnerabilities. The output datasets are built on open data and methods, and in flexible format that can be aggregated to more operationally-relevant administrative unit levels.

Geostatistics as a subfield of statistics accounts for the spatial correlations encountered in many applications of, for example, earth sciences. Valuable information can be extracted from these correlations, also helping to address the often encountered burden of data scarcity. Despite the value of additional data, the use of geostatistics still falls short of its potential. This problem is often connected to the lack of user-friendly software hampering the use and application of geostatistics. We therefore present GSTools, a Python-based software suite for solving a wide range of geostatistical problems. We chose Python due to its unique balance between usability, flexibility, and efficiency and due to its adoption in the scientific community. GSTools provides methods for generating random fields; it can perform kriging, variogram estimation and much more. We demonstrate its abilities by virtue of a series of example applications detailing their use.

Continuously indexed datasets with multiple variables have become ubiquitous in the geophysical, ecological, environmental and climate sciences, and pose substantial analysis challenges to scientists and statisticians. For many years, scientists developed models that aimed at capturing the spatial behavior for an individual process; only within the last few decades has it become commonplace to model multiple processes jointly. The key difficulty is in specifying the cross-covariance function, that is, the function responsible for the relationship between distinct variables. Indeed, these cross-covariance functions must be chosen to be consistent with marginal covariance functions in such a way that the second-order structure always yields a nonnegative definite covariance matrix. We review the main approaches to building cross-covariance models, including the linear model of coregionalization, convolution methods, the multivariate Matérn and nonstationary and space–time extensions of these among others. We additionally cover specialized constructions, including those designed for asymmetry, compact support and spherical domains, with a review of physics-constrained models. We illustrate select models on a bivariate regional climate model output example for temperature and pressure, along with a bivariate minimum and maximum temperature observational dataset; we compare models by likelihood value as well as via cross-validation co-kriging studies. The article closes with a discussion of unsolved problems.

Spatial process models for analyzing geostatistical data entail computations that become prohibitive as the number of spatial locations become large. This article develops a class of highly scalable nearest-neighbor Gaussian process (NNGP) models to provide fully model-based inference for large geostatistical datasets. We establish that the NNGP is a well-defined spatial process providing legitimate finite-dimensional Gaussian densities with sparse precision matrices. We embed the NNGP as a sparsity-inducing prior within a rich hierarchical modeling framework and outline how computationally efficient Markov chain Monte Carlo (MCMC) algorithms can be executed without storing or decomposing large matrices. The floating point operations (flops) per iteration of this algorithm is linear in the number of spatial locations, thereby rendering substantial scalability. We illustrate the computational and inferential benefits of the NNGP over competing methods using simulation studies and also analyze forest biomass from a massive U.S. Forest Inventory dataset at a scale that precludes alternative dimension-reducing methods. Supplementary materials for this article are available online.