Towards a Soil Information System with quantified accuracy : a prototype for mapping continuous soil properties

This report describes the potential and functionality of software for spatial analysis, prediction and stochastic simulation of continuous soil properties using data from the Dutch Soil Information System (BIS). A geostatistical framework and R codes were developed. The geostatistical model of a soil property has a deterministic component representing the mean value within a soil category, and a stochastic component of standardized residuals. The standardized residuals are interpolated or simulated based on the simple kriging system. The software was tested in four case studies: exchangeable soil pH, clay content, organic matter content and Mean Spring Water table depth (MSW). It is concluded that the geostatistical framework and R codes developed in this study enable to predict values of continuous soil properties spatially, and to quantify the inaccuracy of these predictions. The inaccuracy of a spatial prediction at a certain location is quantified by the kriging variance, which can be interpreted as an indication of the uncertainty about the true value

Evaluation of modelling approaches for predicting the spatial distribution of soil organic carbon stocks at the national scale

Soil organic carbon (SOC) plays a major role in the global carbon budget. It can act as a source or a sink of atmospheric carbon, thereby possibly influencing the course of climate change. Improving the tools that model the spatial distributions of SOC stocks at national scales is a priority, both for monitoring changes in SOC and as an input for global carbon cycles studies. In this paper, we compare and evaluate two recent and promising modelling approaches. First, we considered several increasingly complex boosted regression trees (BRT), a convenient and efficient multiple regression model from the statistical learning field. Further, we considered a robust geostatistical approach coupled to the BRT models. Testing the different approaches was performed on the dataset from the French Soil Monitoring Network, with a consistent cross-validation procedure. We showed that when a limited number of predictors were included in the BRT model, the standalone BRT predictions were significantly improved by robust geostatistical modelling of the residuals. However, when data for several SOC drivers were included, the standalone BRT model predictions were not significantly improved by geostatistical modelling. Therefore, in this latter situation, the BRT predictions might be considered adequate without the need for geostatistical modelling, provided that i) care is exercised in model fitting and validating, and ii) the dataset does not allow for modelling of local spatial autocorrelations, as is the case for many national systematic sampling schemes

Geostatistical modeling in the presence of interaction between the measuring instruments, with an application to the estimation of spatial market potentials

This paper addresses the problem of recovering the spatial market potential of a retail product from spatially distributed sales data. In order to tackle the problem in a general way, the concept of spatial potential is introduced. The potential is concurrently measured at different spatial locations and the measurements are analyzed in order to recover the spatial potential. The measuring instruments used to collect the data interact with each other, that is, the measurement at a given spatial location is affected by the concurrent measurements at other locations. An approach based on a novel geostatistical model is developed. In particular, the model is able to handle both the measuring instrument interaction and the missing data. A model estimation procedure based on the expectation-maximization algorithm is provided as well as standard inferential tools. The model is applied to the estimation of the spatial market potential of a newspaper for the city of Bergamo, Italy. The estimated spatial market potential is eventually analyzed in order to identify the areas with the highest potential, to identify the areas where it is profitable to open additional newsstands and to evaluate the newspaper total market volume of the city.Comment: Published in at http://dx.doi.org/10.1214/12-AOAS588 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Model-Based Geostatistics for Prevalence Mapping in Low-Resource Settings

In low-resource settings, prevalence mapping relies on empirical prevalence data from a finite, often spatially sparse, set of surveys of communities within the region of interest, possibly supplemented by remotely sensed images that can act as proxies for environmental risk factors. A standard geostatistical model for data of this kind is a generalized linear mixed model with binomial error distribution, logistic link and a combination of explanatory variables and a Gaussian spatial stochastic process in the linear predictor. In this paper, we first review statistical methods and software associated with this standard model, then consider several methodological extensions whose development has been motivated by the requirements of specific applications. These include: methods for combining randomised survey data with data from non-randomised, and therefore potentially biased, surveys; spatio-temporal extensions; spatially structured zero-inflation. Throughout, we illustrate the methods with disease mapping applications that have arisen through our involvement with a range of African public health programmes.Comment: Submitte

An example of aquifer heterogeneity simulation to modeling well-head protection areas

Groundwater management requires the definition of Well-Head Protection Areas (WHPA) for water supply wells. Italian law uses geometrical, chronological and hydrogeological criteria for WHPA identification, providing a groundwater travel time of 60 days for the definition of the Zone of Travel (ZOT). An exhaustive ZOT delineation must involve numerical modeling of groundwater flow together with simulation of the advective component of the transport process. In this context, the spatial variability of hydrogeological and transport parameters has to be critically estimated during numerical modeling implementation. In the present article, geostatistical simulation using a transition probability approach and groundwater numerical modeling were performed to delineate WHPAs for several supply wells in the middle Venetian Plain, taking into account the lithologic heterogeneity of the aquifer. The transition probability approach for the lithologic data was developed by T-PROGS software, while MODDLOW-2005 and PEST-ASP were used, respectively, to reproduce and calibrate site-specific hydraulic head data. Finally, a backward particle tracking analysis was performed with MODPATH to outline the 60-day ZOT

A geostatistical model based on Brownian motion to Krige regions in R2 with irregular boundaries and holes

Master's Project (M.S.) University of Alaska Fairbanks, 2019Kriging is a geostatistical interpolation method that produces predictions and prediction intervals. Classical kriging models use Euclidean (straight line) distance when modeling spatial autocorrelation. However, for estuaries, inlets, and bays, shortest-in-water distance may capture the system’s proximity dependencies better than Euclidean distance when boundary constraints are present. Shortest-in-water distance has been used to krige such regions (Little et al., 1997; Rathbun, 1998); however, the variance-covariance matrices used in these models have not been shown to be mathematically valid. In this project, a new kriging model is developed for irregularly shaped regions in R 2 . This model incorporates the notion of flow connected distance into a valid variance-covariance matrix through the use of a random walk on a lattice, process convolutions, and the non-stationary kriging equations. The model developed in this paper is compared to existing methods of spatial prediction over irregularly shaped regions using water quality data from Puget Sound

Use of Kriging Technique to Study Roundabout Performance

Road intersections are dangerous places because of the many conflicting points between motorized and nonmotorized vehicles. In the case of defined traffic volume, several research groups have proved that roundabouts reduced the number of injuries and fatal accident cases. In recent years, many countries have adopted roundabouts as a standard design solution for both urban and rural roads. Several recent studies have investigated the performance of roundabouts, including some with models that calculated the entering flow (Q sub e) as a function of the circulating flow (Q sub c). Most existing models have been constructed with the use of linear or exponential statistical regression. The interpolative techniques in classical statistics are based on the use of canonical forms (linear or polynomial) that completely ignore the correlation law between collected data. As such, the determined interpolation stems from the assumption that the data represent a random sample. In the research reported in this paper, a geostatistical approach was considered: the relationship Q sub e versus Q sub c is supposed to be a regionalized phenomenon. According to that supposition, collected data do not represent a random sample of values but are supposed to be related to each other with a defined law. This recognition allows the realization of interpolation on the basis of the real law of the phenomenon. This paper discusses the fundamental theories, the applied operating procedures, and the first results obtained in modeling the Q sub e versus Q sub c relationship with the application of geostatistics

Identification and characterization of nursery areas of red mullet Mullus barbatus in the Central Tyrrhenian Sea

Red Mullet Mullus barbatus is an important target of fishing activities in the central Tyrrhenian Sea, so it is essential to identify its critical habitats in order to manage this resource efficiently. Our research specifically focused on the identification and characterization of nursery areas. The use of spatial interpolation techniques enabled us to identify five nurseries that were highly persistent through time. Moreover, the estimate of juvenile density confirmed the strong aggregation effect of these nursery grounds, as a great portion of young individuals were concentrated in a relatively small surface of the study area. The environmental characterization of these areas showed that juveniles were mainly distributed on bottoms with a relatively high percentage of sand (>70%; P <0.05). Shannon biodiversity index analysis indicated that the southern nurseries reached the highest values of habitat quality (P < 0.0001). Multivariate analysis showed that nursery grounds were divided into three main groups, and analysis of spatial dynamics showed that two different strategies characterized Red Mullet juveniles when density changes over time. In particular, in some areas young individuals selected habitats in a density-dependent way following the basin model scheme, while in other zones they selected habitats in a density-independent way according to the proportional density model. Results also showed that juveniles followed the proportional density model strategy into nursery areas with the highest Shannon biodiversity index values