Using remote sensors to predict soil properties: Radiometry and peat depth in Dartmoor, UK

Remote sensors provide high resolution data over large spatial extents that can potentially be used to map soil properties such as the concentration of organic carbon or its moisture content. The sensors rarely measure the property of interest directly but instead measure a related property. There is a need to make ground measurements of the property of interest to calibrate a model or relationship between the soil property and the sensor data. We develop a framework for optimizing the locations and number of ground measurements of a soil property for surveys incorporating sensor data. The data are used to estimate a linear mixed model of the property where the fixed effects are a flexible spline-based function of the sensor measurements. The framework is used to map peat depth across a portion of Dartmoor National Park using radiometric potassium data measurements from an airborne survey. The most accurate maps result from using a geostatistical predictor to combine the relationship with the sensor data and the spatial correlation amongst the peat depth measurements. The optimal sampling designs suggest that ground measurements should be focussed where peat depths are largest and most uncertain. When measurements are made at 25 optimally selected sites, predictions that do not utilise the sensor data have 20% larger root mean square errors than those that do. For 200 ground measurements this benefit is 14%. The maps produced using the sensor data and 25 ground measurements have smaller root mean square errors than those based only upon 200 ground measurements

What can legacy datasets tell us about soil quality trends? Soil acidity in Victoria

Purpose-built soil monitoring networks have been established in many countries to identify where soil functionality is threatened and to target remediation initiatives. An alternative to purpose-built soil monitoring networks is to use legacy soils information. Such information yields almost instant assessments of soil change but the results should be interpreted with caution since the information was not collected with monitoring in mind. We assess the threat of soil acidification in Victoria using two legacy datasets: (i) the Victorian Soils Information System (VSIS) which is a repository of the results of soil analyses conducted for scientific purposes since the 1950s and (ii) a database of 75 000 routine soil test results requested by farmers between 1973 and 1993. We find that the VSIS measurements are clustered in space and time and are therefore suitable for local rather than broad-scale assessments of soil change. The farmers' results have better spatial and temporal coverage and space-time models can be used to quantify the spatial and temporal trends in the pH measurements. However, careful validation of these findings is required since we do not completely understand how the measured paddocks were selected and we cannot be certain that sampling or laboratory protocols have not changed with time

Modelling the electrical conductivity of soil in the Yangtze delta in three dimensions

Numerous processes, past and present, have given rise to lateral and vertical variation in the soil and to its individual properties such as its salinity and electrical conductivity. The resulting patterns of variation are complex and appear to comprise both random and deterministic components. The latter dominates vertically as trends in most soil profiles, and in the situation we describe it is prominent in the horizontal plane, too. Describing this variation requires flexible choice of covariance function. The processes of model estimation and prediction by kriging in three dimensions are similar to those in two dimensions. The extra complexity of the three-dimensional variation requires practitioners to appreciate fully the assumptions that their choices of model imply and to establish ways of testing the validity of these assumptions. We have examined several covariance functions more commonly used to describe simultaneously variation in space and time and adapted them to model three-dimensional variation in soil. We have applied these covariance functions to model the variation in salinity in reclaimed land in the Yangtze delta of China where the apparent electrical conductivity (ECa) has been measured at numerous points down to 1.1 m. The models take into account random and deterministic components in both the horizontal and vertical dimensions. The most suitable mixed model was then used to krige the ECa on a fine grid from which three-dimensional diagrams of the salinity are displayed

Regionalisation of groundwater droughts using hydrograph classification

Groundwater drought is a spatially and temporally variable phenomenon. Here we describe the development and application of a method to regionalize and quantify groundwater drought based on categorisation of Standardised Groundwater level Index (SGI) time series. The categorisation scheme uses non-hierarchical k-means cluster analysis. This has been applied to 74 SGI time series for the period January 1983 to August 2012 for a case study from Lincolnshire, UK. Six SGI time series clusters have been identified. For each cluster a correlation can be established between the mean SGI and a mean Standardised Precipitation Index (SPI) associated with an optimal SPI accumulation period, qmax. Based on a comparison of SPI time series for each cluster and SPI estimated for the whole study area, it is inferred that the clusters are largely independent of heterogeneity in the diving meteorology across the study region and are primarily a function of catchment and hydrogeological factors. This inference is supported by the observation that the majority of sites in each cluster are associated with one of three principal aquifers in the study region. The groundwater drought characteristics of the three largest clusters (CL1, CL2 and CL4 that constitute ~80% of the sites) have been analyzed. There is a common linear relationship between drought magnitude and duration for each of three clusters. However, there are differences in the character of the groundwater drought events between the three clusters as a function of autocorrelation of the mean SGI time series for each cluster. For example, CL1 has a relatively short period of significant SGI autocorrelation compared with CL2 (15 and 23 months respectively); CL1 has more than twice the number of drought episodes (39 episodes) than CL2 (15 episodes), and the average and maximum duration of droughts in CL1 (4.6 and 27 months) are less than half those of CL2 (11.3 and 61 months). The drought characteristics of CL4 are intermediate between those of CL1 and CL2. Differences in characteristics between the three clusters are also seen in their response to three major multi-annual droughts that occurred during the analysis period. For example, sites in CL2 with the longest SGI autocorrelation experience the greatest magnitude droughts and are the slowest to recover from drought, with groundwater drought conditions typically persisting at least six months longer than at sites in the other two clusters. Membership of the clusters reflects differences in the autocorrelation of the SGI time series that in turn is shown to be related to unsaturated zone thickness at individual boreholes. This last observation emphasises the importance of catchment and aquifer characteristics as (non-trivial) controls on groundwater drought hydrographs

Regional analysis of groundwater droughts using hydrograph classification

Groundwater drought is a spatially and temporally variable phenomenon. Here we describe the development of a method to regionally analyse and quantify groundwater drought. The method uses a cluster analysis technique (non-hierarchical k-means) to classify standardised groundwater level hydrographs (the standardised groundwater level index, SGI) prior to analysis of their groundwater drought characteristics, and has been tested using 74 groundwater level time series from Lincolnshire, UK. Using the test data set, six clusters of hydrographs have been identified. For each cluster a correlation can be established between the mean SGI and a mean standardised precipitation index (SPI), where each cluster is associated with a different SPI accumulation period. Based on a comparison of SPI time series for each cluster and for the study area as a whole, it is inferred that the clusters are independent of the driving meteorology and are primarily a function of catchment and hydrogeological factors. This inference is supported by the observation that the majority of sites in each cluster are associated with one of the principal aquifers in the study region. The groundwater drought characteristics of the three largest clusters, which constitute ~ 80 % of the sites, have been analysed. There are differences in the distributions of drought duration, magnitude and intensity of groundwater drought events between the three clusters as a function of autocorrelation of the mean SGI time series for each cluster. In addition, there are differences between the clusters in their response to three major multi-annual droughts that occurred during the analysis period. For example, sites in the cluster with the longest SGI autocorrelation experience the greatest-magnitude droughts and are the slowest to recover from major droughts, with groundwater drought conditions typically persisting at least 6 months longer than at sites in the other clusters. Membership of the clusters is shown to be related to unsaturated zone thickness at individual boreholes. This last observation emphasises the importance of catchment and aquifer characteristics as (non-trivial) controls on groundwater drought hydrographs. The method of analysis is flexible and can be adapted to a wide range of hydrogeological settings while enabling a consistent approach to the quantification of regional differences in response of groundwater to meteorological drought

Modelling the distribution and quality of sand and gravel resources in 3D: a case study in the Thames Basin, UK

Three-dimensional (3D) models are often utilised to assess the presence of sand and gravel deposits. Expanding these models to provide a better indication of the suitability of the deposit as aggregate for use in construction would be advantageous. This, however, leads to statistical challenges. To be effective, models must be able to reflect the interdependencies between different criteria (e.g. depth to deposit, thickness of deposit, ratio of mineral to waste, proportion of ‘fines’) as well as the inherent uncertainty introduced because models are derived from a limited set of boreholes in a study region. Using legacy borehole data collected during a systematic survey of sand and gravel deposits in the UK, we have developed a 3D model for a 2400 km2 region close to Reading, southern England. In developing the model, we have reassessed the borehole grading data to reflect modern extraction criteria and explored the most suitable statistical modelling technique. The additive log-ratio transform and the linear model of coregionalization have been applied, techniques that have been previously used to map soil texture classes in two dimensions, to assess the quality of sand and gravel deposits in the area. The application of these statistical techniques leads to a model which can be used to generate thousands of plausible realisations of the deposit which fully reflect the extent of model uncertainty. The approach offers potential to improve regional-scale mineral planning by providing an enhanced understanding of sand and gravel deposits and the extent to which they meet current extraction criteria

How should a spatial-coverage sample design for a geostatistical soil survey be supplemented to support estimation of spatial covariance parameters?

We use an expression for the error variance of geostatistical predictions, which includes the effect of uncertainty in the spatial covariance parameters, to examine the performance of sample designs in which a proportion of the total number of observations are distributed according to a spatial coverage design, and the remaining observations are added at supplementary close locations. This expression has been used in previous studies on numerical optimization of spatial sampling, the objective of this study was to use it to discover simple rules of thumb for practical geostatistical sampling. Results for a range of sample sizes and contrasting properties of the underlying random variables show that there is an improvement on adding just a few sample points and close pairs, and a rather slower increase in the prediction error variance as the proportion of sample points allocated in this way is increased above 10 to 20% of the total sample size. One may therefore propose a rule of thumb that, for a fixed sample size, 90% of sample sites are distributed according to a spatial coverage design, and 10% are then added at short distances from sites in the larger subset to support estimation of spatial covariance parameters

Spatio-temporal modelling of the status of groundwater droughts

An empirical (geo)statistical modelling scheme is developed to address the challenges of modelling the severity and distribution of groundwater droughts given their spatially and temporally heterogeneous nature and given typically highly irregular groundwater level observations in space and time. The scheme is tested using GWL measurements from 948 observation boreholes across the Chalk aquifer (UK) to estimate monthly groundwater drought status from 1960 to 2013. For each borehole, monthly GWLs are simulated using empirical mixed models where the fixed effects are based on applying an impulse response function to the local monthly precipitation. Modelled GWLs are standardised using the Standardised Groundwater Index (SGI) and the monthly SGI values interpolated across the aquifer to produce spatially distributed monthly maps of SGI drought status for 54 years for the Chalk. The mixed models include fewer parameters than comparable lumped parameter groundwater models while explaining a similar proportion (more than 65%) of GWL variation. In addition, the empirical modelling approach enables confidence bounds on the predicted GWLs and SGI values to be estimated without the need for prior information about catchment or aquifer parameters. The results of the modelling scheme are illustrated for three major episodes of multi-annual drought (1975–1976; 1988–1992; 2011–2012). They agree with previous documented analyses of the groundwater droughts while providing for the first time a systematic, spatially coherent characterisation of the events. The scheme is amenable to use in near real time to provide short term forecasts of groundwater drought status if suitable forecasts of the driving meteorology are available

Quantifying and mapping topsoil inorganic carbon concentrations and stocks: approaches tested in France

Soils act as a sink or a source of atmospheric carbon, and great efforts are made to monitor soil organic carbon stocks, but soil inorganic carbon (SIC) stocks are not measured by many national- and continental-scale soil monitoring networks. Topsoil (0–30 cm) SIC concentrations were determined for > 2000 sites on a regular 16-km grid as part of the French, Réseau de Mesures de la Qualité des Sols (RMQS). We used design-based statistical methods to calculate unbiased estimates of the mean SIC concentration and total stocks across France. Model-based methods were used to determine the uncertainty of these estimates and to map the spatial distribution of these quantities. Observations of inorganic carbon were highly skewed and did not conform to standard statistical models. Data were normalized using a nonparametric transformation. The estimates and predictions of inorganic carbon are baselines against which the results of future phases of the network can be compared. We found that the total topsoil inorganic carbon stocks in France amount to 1070 ± 61 Tg, ca. one-third of the corresponding organic carbon stocks. Spatial distribution of SIC was strongly linked to the underlying geology. We tested the reliability of estimating SIC concentrations and stocks from the French Soil Test Database, which contains the results of 280 000 soil analyses requested by farmers between 1990 and 2004. A biased estimate of soil inorganic carbon concentrations resulted, presumably because soil samples were selected according to concerns of farmers rather than by a statistical design

Exploring the spatial variation in the fertilizer-nitrogen requirement of wheat within fields

The fertilizer-nitrogen (N) requirement for wheat grown in the UK varies from field to field. Differences in the soil type, climate and cropping history result in differences in (i) the crops’ demands for N, (ii) the supply of N from the soil (SNS) and (iii) the recovery of the fertilizer by the crops. These three components generally form the basis of systems for N recommendation. Three field experiments were set out to investigate the variation of the N requirement for wheat within fields and to explore the importance of variation in the crops’ demands for N, SNS and fertilizer recovery in explaining the differences in the economic optima for N. The N optima were found to vary by >100 kg N/ha at two of the sites. At the other site, the yield response to N was small. Yields at the optimum rate of N varied spatially by c. 4 t/ha at each site. Soil N supply, which was estimated by the unfertilized crops’ harvested N, varied spatially by 120, 75 and 60 kg/ha in the three experiments. Fertilizer recovery varied spatially from 30% to >100% at each of the sites. There were clear relationships between the SNS and the N optima at all the three sites. The expected relationship between the crop's demand for N and N optima was evident at only one of the three sites. There was no consistent relationship between the N recovery and the N optima. A consistent relationship emerged, however, between the optimal yield and SNS; areas with a greater yield potential tending to also supply more N from the soil. This moderated the expected effect of the SNS and the crop's demand for N on the N optima