Boundary line models for soil nutrient concentrations and wheat yield in national-scale datasets.

In boundary line analysis a biological response (e.g., crop yield) is assumed to be a function of a variable (e.g., soil nutrient concentration), which limits the response in only some subset of observations because other limiting factors also apply. The response function is therefore expressed by an upper boundary of the plot of the response against the variable. This model has been used in various branches of soil science. In this paper we apply it to the analysis of some large datasets, originating from commercial farms in England and Wales, on the recorded yield of wheat and measured concentrations of soil nutrients in within-field soil management zones. We considered boundary line models for the effects of potassium (K), phosphorus (P) and magnesium (Mg) on yield, comparing the model with a simple bivariate normal distribution or a bivariate normal censored at a constant maximum yield. We were able to show, using likelihood-based methods, that the boundary line model was preferable in most cases. The boundary line model suggested that the standard RB209 soil nutrient index values (Agriculture and Horticulture Development Board, nutrient management guide (RB209), 2017) are robust and apply at the within-field scale. However, there was evidence that wheat yield could respond to additional Mg at concentrations above index 0, contrary to RB209 guidelines. Furthermore, there was evidence that the boundary line model for yield and P differs between soils at different pH and depth intervals, suggesting that shallow soils with larger pH require a larger target P index than others. HIGHLIGHTS: Boundary line analysis is one way to examine how soil variables influence crop yield in large datasets.We showed that boundary line models could be applied to large datasets on soil nutrients and crop yield.The resulting models are consistent with current practice for P and K, but not for Mg.Models suggest that more refined recommendations for P requirement could be based on soil pH and depth.

Provenance of drinking water revealed through compliance sampling.

Understanding drinking water hydrochemistry is essential for maintaining safe drinking water supplies. Whilst targeted research surveys have characterised drinking water hydrochemistry, vast compliance datasets are routinely collected but are not interrogated amidst concerns regarding the impact of mixed water sources, treatment, the distribution network and customer pipework. In this paper, we examine whether compliance samples retain hydrochemical signatures of their provenance. We first created and subsequently undertook the first hydrochemical analysis of a novel national database of publically available drinking water compliance analyses (n = 3 873 941) reported for 2015 across England and Wales. k-means cluster analysis revealed three spatially coherent clusters. Cluster 1 is dominated by groundwater sources, with high nitrate concentrations and mineralisation, and lower organic carbon, residual chlorine and THM formation. Cluster 2 was dominated by surface water sources and characterised by low mineralisation (low conductivity and major ion concentrations), low nitrate and high organic carbon concentrations (and hence residual chlorine and THM formation). Cluster 3 shows a mixture of groundwater overlain by confining layers and superficial deposits (resulting in higher trace metal concentrations and mineralisation) and surface water sources. These analyses demonstrate that, despite extensive processing of drinking water, at the national scale signatures of the provenance of drinking water remain. Analysis of compliance samples is therefore likely to be a helpful tool in the characterisation of processes that may affect drinking water chemistry. The methodology used is generic and can be applied in any area where drinking water chemistry samples are taken.

A methodological framework for identifying potential sources of soil heavy metal pollution based on machine learning: A case study in the Yangtze Delta, China.

It is a great challenge to identify the many and varied sources of soil heavy metal pollution. Often little information is available regarding the anthropogenic factors and enterprises that could potentially pollute soils. In this study we use freely available geographical data from a search engine in conjunction with machine learning methodologies to identify and classify potentially polluting enterprises in the Yangtze Delta, China. The data were classified into 31 separate and four integrated industry types by five different machine learning approaches. Multinomial naive Bayesian (NB) methods achieved an accuracy of 87% and Kappa coefficient of 0.82 and were used to classify the geographic data from more than 260,000 enterprises. The relationship between the different industry classes and measurements of soil cadmium (Cd) and mercury (Hg) concentrations was explored using bivariate local Moran's I analysis. The analysis revealed areas where different industry classes had led to soil pollution. In the case of Cd, elevated concentrations also occurred in some areas because of excessive fertilization and coal mining. This study provides a new approach to investigate the interaction between anthropogenic pollution and natural sources of soil heavy metals to inform pollution control and planning decisions regarding the location of industrial sites.

Analyzing the spatial distribution of PCB concentrations in soils using below-quantification limit data.

Polychlorinated biphenyls (PCBs) are highly toxic environmental pollutants that can accumulate in soils. We consider the problem of explaining and mapping the spatial distribution of PCBs using a spatial data set of 105 PCB-187 measurements from a region in the north of France. A large proportion of our data (35%) fell below a quantification limit (QL), meaning that their concentrations could not be determined to a sufficient degree of precision. Where a measurement fell below this QL, the inequality information was all that we were presented with. In this work, we demonstrate a full geostatistical analysis-bringing together the various components, including model selection, cross-validation, and mapping-using censored data to represent the uncertainty that results from below-QL observations. We implement a Monte Carlo maximum likelihood approach to estimate the geostatistical model parameters. To select the best set of explanatory variables for explaining and mapping the spatial distribution of PCB-187 concentrations, we apply the Akaike Information Criterion (AIC). The AIC provides a trade-off between the goodness-of-fit of a model and its complexity (i.e., the number of covariates). We then use the best set of explanatory variables to help interpolate the measurements via a Bayesian approach, and produce maps of the predictions. We calculate predictions of the probability of exceeding a concentration threshold, above which the land could be considered as contaminated. The work demonstrates some differences between approaches based on censored data and on imputed data (in which the below-QL data are replaced by a value of half of the QL). Cross-validation results demonstrate better predictions based on the censored data approach, and we should therefore have confidence in the information provided by predictions from this method.

Disaggregation of legacy soil data using area to point kriging for mapping soil organic carbon at the regional scale.

Legacy data in the form of soil maps, which often have typical property measurements associated with each polygon, can be an important source of information for digital soil mapping (DSM). Methods of disaggregating such information and using it for quantitative estimation of soil properties by methods such as regression kriging (RK) are needed. Several disaggregation processes have been investigated; preferred methods include those which include consideration of scorpan factors and those which are mass preserving (pycnophylactic) making transitions between different scales of investigation more theoretically sound. Area to point kriging (AtoP kriging) is pycnophylactic and here we investigate its merits for disaggregating legacy data from soil polygon maps. Area to point regression kriging (AtoP RK) which incorporates ancillary data into the disaggre-gation process was also applied. The AtoP kriging and AtoP RK approaches do not involve collection of new soil measurements and are compared with disaggregation by simple rasterization. Of the disaggregation methods investigated, AtoP RK gave the most accurate predictions of soil organic carbon (SOC) concentrations (smaller mean absolute errors (MAEs) of cross-validation) for disaggregation of soil polygon data across the whole of Northern Ireland. Legacy soil polygon data disaggregated by AtoP kriging and simple rasterization were used in a RK framework for estimating soil organic carbon (SOC) concentrations across the whole of Northern Ireland, using soil sample data from the Tellus survey of Northern Ireland and with other covariates (altitude and airborne radiometric potassium). This allowed direct comparison with previous analysis of the Tellus survey data. Incorporating the legacy data, whether from simple rasterization of the polygons or AtoP kriging, substantially reduced the MAEs of RK compared with previous analyses of the Tellus data. However, using legacy data disaggregated by AtoP kriging in RK resulted in a greater reduction in MAEs. A jack-knife procedure was also performed to determine a suitable number of additional soil samples that would need to be collected for RK of SOC for the whole of Northern Ireland depending on the availability of ancillary data. We recommend i) if only legacy soil polygon map data are available, they should be disaggregated using AtoP kriging, ii) if ancillary data are also available legacy data should be disaggregated using AtoP RK and iii) if new soil measurements are available in addition to ancillary and legacy soil map data, the legacy soil map data should be first disaggregated using AtoP kriging and these data used along with ancillary data as the fixed effects for RK of the new soil measurements.

Which persistent organic pollutants can we map in soil using a large spacing systematic soil monitoring design? A case study in Northern France.

Persistent organic pollutants (POPs) impact upon human and animal health and the wider environment. It is important to determine where POPs are found and the spatial pattern of POP variation. The concentrations of 90 molecules which are members of four families of POPs and two families of herbicides were measured within a region of Northern France as part of the French National Soil Monitoring Network (RMQS: Réseau de Mesures de la Qualité des Sols). We also gather information on five covariates (elevation, soil organic carbon content, road density, land cover and population density) which might influence POP concentrations. The study region contains 105 RMQS observation sites arranged on a regular square grid with spacing of 16 km. The observations include hot-spots at sites of POP application, smaller concentrations where POPs have been dispersed and observations less than the limit of quantification (LOQ) where the soil has not been impacted by POPs. Fifty nine of the molecules were detected at less than 50 sites and hence the data were unsuitable for spatial analyses. We represent the variation of the remaining 31 molecules by various linear mixed models which can include fixed effects (i.e. linear relationships between the molecule concentrations and covariates) and spatially correlated random effects. The best model for each molecule is selected by the Akaike Information Criterion. For nine of the molecules, spatial correlation is evident and hence they can potentially be mapped. For four of these molecules, the spatial correlation cannot be wholly explained by fixed effects. It appears that these molecules have been transported away from their application sites and are now dispersed across the study region with the largest concentrations found in a heavily populated depression. More complicated statistical models and sampling designs are required to explain the distribution of the less dispersed molecules.

Biphasic behaviour in malignant invasion.

Invasion is an important facet of malignant growth that enables tumour cells to colonise adjacent regions of normal tissue. Factors known to influence such invasion include the rate at which the tumour cells produce tissue-degrading molecules, or proteases, and the composition of the surrounding tissue matrix. A common feature of experimental studies is the biphasic dependence of the speed at which the tumour cells invade on properties such as protease production rates and the density of the normal tissue. For example, tumour cells may invade dense tissues at the same speed as they invade less dense tissue, with maximal invasion seen for intermediate tissue densities. In this paper, a theoretical model of malignant invasion is developed. The model consists of two coupled partial differential equations describing the behaviour of the tumour cells and the surrounding normal tissue. Numerical methods show that the model exhibits steady travelling wave solutions that are stable and may be smooth or discontinuous. Attention focuses on the more biologically relevant, discontinuous solutions which are characterised by a jump in the tumour cell concentration. The model also reproduces the biphasic dependence of the tumour cell invasion speed on the density of the surrounding normal tissue. We explain how this arises by seeking constant-form travelling wave solutions and applying non-standard phase plane methods to the resulting system of ordinary differential equations. In the phase plane, the system possesses a singular curve. Discontinuous solutions may be constructed by connecting trajectories that pass through particular points on the singular curve and recross it via a shock. For certain parameter values, there are two points at which trajectories may cross the singular curve and, as a result, two distinct discontinuous solutions may arise.