Transfer function-noise modeling and spatial interpolation to evaluate the risk of extreme (shallow) water-table levels in the Brazilian Cerrados

Water regimes in the Brazilian Cerrados are sensitive to climatological disturbances and human intervention. The risk that critical water-table levels are exceeded over long periods of time can be estimated by applying stochastic methods in modeling the dynamic relationship between water levels and driving forces such as precipitation and evapotranspiration. In this study, a transfer function-noise model, the so called PIRFICT-model, is applied to estimate the dynamic relationship between water-table depth and precipitation surplus/deficit in a watershed with a groundwater monitoring scheme in the Brazilian Cerrados. Critical limits were defined for a period in the Cerrados agricultural calendar, the end of the rainy season, when extremely shallow levels

Spatial statistics and soil mapping: A blossoming partnership under pressure

For the better part of the 20th century pedologists mapped soil by drawing boundaries between different classes of soil which they identified from survey on foot or by vehicle, supplemented by air-photo interpretation, and backed by an understanding of landscape and the processes by which soil is formed. Its limitations for representing gradual spatial variation and predicting conditions at unvisited sites became evident, and in the 1980s the introduction of geostatistics and specifically ordinary kriging revolutionized thinking and to a large extent practice. Ordinary kriging is based solely on sample data of the variable of interest—it takes no account of related covariates. The latter were incorporated from the 1990s onward as fixed effects and incorporated as regression predictors, giving rise to kriging with external drift and regression kriging. Simultaneous estimation of regression coefficients and variogram parameters is best done by residual maximum likelihood estimation. In recent years machine learning has become feasible for predicting soil conditions from huge sets of environmental data obtained from sensors aboard satellites and other sources to produce digital soil maps. The techniques are based on classification and regression, but they take no account of spatial correlations. Further, they are effectively ‘black boxes’; they lack transparency, and their output needs to be validated if they are to be trusted. They undoubtedly have merit; they are here to stay. They too, however, have their shortcomings when applied to spatial data, which spatial statisticians can help overcome. Spatial statisticians and pedometricians still have much to do to incorporate uncertainty into digital predictions, spatial averages and totals over regions, and to take into account errors in measurement and spatial positions of sample data. They must also communicate their understanding of these uncertainties to end users of soil maps, by whatever means they are made

Uncertainty assessment of spatial soil information

Uncertainty is present in our daily lives. It affects our decisions on what to do. The weather forecast might tell us that there is a 60% chance that it will rain: we take umbrellas. If it says that the chance of rain is only 10% we might decide to leave our umbrellas at home and risk getting wet. More seriously, farmers want to know the likelihood of disease in their crops and the deficiencies in plant nutrients in the soil. These are matters that affect profit and loss of farm business. Agencies responsible for public health and environmental protection need to weigh the risk of doing nothing in the face of uncertain threats against the cost of acting unnecessarily to counter them when the threats are almost non-existent. There are many examples of decision making problems involving uncertain soil information. They include the remediation of polluted soil, the prevention of soil erosion, and the mitigation of pesticide leaching. They are practical matters, not purely academic exercises in statistics. All measurements of soil properties (and other environmental variables) contain error in the sense that they depart from the true values. That error arises from imperfections in the analytical instruments, from the people who use them and from errors that occur during the processing of the recorded data to make them suitable for storage in information databases. Short-range spatial variation is another source of error, given that soil samples are never returned to where they were taken and sampling locations have positional error. Soil taken from location s and analysed in the laboratory might differ substantially from the soil at location s + h, even if |h| is as small as a few decimeters. Composite soil sampling can diminish these differences, but some error inevitably persists because even such a composite is still only a sample of all the soil at that site. All this means that we can never be sure about the true state of the soil: we, the producers and users of soil information, are to some extent uncertain. Uncertainty tends to increase when measurements of basic soil properties are used to obtain derived ones via pedotransfer functions or mechanistic models of dynamic soil processes, for example. Interpolation from measurements to create maps of soil properties adds to the errors of measurement and so too increases uncertainties. We must conclude that considerable uncertainty is often associated with the information that is stored in soil databases and presented in various forms, including maps. This does not mean that the information is of no value; uncertainty is not the same as ignorance. In many cases we do know a great deal about the soil, but we must also acknowledge that the information is not perfect. Some numerical expression of the uncertainty is important because it is needed to determine whether the information is sufficiently accurate for the purpose that a user has in mind. Soil data of too poor a quality might lead to flawed decisions with serious undesirable consequences, both economic and environmental. For instance, the European legislation on the use of pesticides in agriculture depends crucially on the leaching potential of these substances to the ground- and surface-water, which in turn depends importantly on soil properties. In these circumstances users should be aware of the quality of the soil information so that they can be sure that it is sufficiently reliable for their purposes. Ideally they should account for the uncertainty of the information when making their decisions. This chapter (i) provides a statistical definition of uncertainty in soil information; (ii) extends this definition to uncertainty in spatial soil information; (iii) reviews methods that are used to quantify uncertainty in soil information, while paying attention to different sources of uncertainty; (iv) shows how uncertainty in soil information propagates through subsequent analyses; and (v) explains how uncertainty information can be used in decision making. It focuses on the quantification of uncertainty of soil properties that are measured and recorded on continuous scales: properties such as pH, particle-size distribution, and soil organic matter content. The chapter also addresses uncertainty of categorical variables, such as soil type and diagnostic properties recorded as present or absent, i.e. binary variables. It begins with defining uncertainty in a single soil measuremen

Estimating nitrogen fluxes at the European scale by upscaling INTEGRATOR model outputs from selected sites

A comparison was made between upscaled model results of nitrogen (N) fluxes to air and water from 450 sites within the EU-27 and results derived for the entire EU-27 area using the model INTEGRATOR. The 450 sites were selected using stratified random sampling, dividing the EU-27 into 150 strata and selecting three sites at random within each stratum. The strata were based on important environmental factors influencing N fluxes. Hierarchical divisive cluster analysis was used to reduce the numerous combinations of environmental factors to the required total of 150, such that the heterogeneity of environmental factors within strata was as small as possible. Modelled NH<sub>3</sub>, N<sub>2</sub>O and NO<sub>x</sub> emissions and N leaching/runoff obtained were scaled up from the 450 sites to the entire EU-27 and were within 10% of results obtained by running the model for the whole of the EU-27 using about 36 500 sites. This implies that a reliable estimate of N fluxes for EU-27 can be made by upscaling results of the 450 selected sites suggesting that dramatic reduction in computation time can be achieved without substantial deterioration of result

Uncertainties in model predictions of nitrogen fluxes from agro-ecosystems in Europe

To assess the responses of nitrogen and greenhouse gas emissions to pan-European changes in land cover, land management and climate, an integrated dynamic model, INTEGRATOR, has been developed. This model includes both simple process-based descriptions and empirical relationships and uses detailed GIS-based environmental and farming data in combination with various downscaling methods. This paper analyses the propagation of uncertainties in model inputs and parameters to outputs of INTEGRATOR, using a Monte Carlo analysis. Uncertain model inputs and parameters were represented by probability distributions, while spatial correlation in these uncertainties was taken into account by assigning correlation coefficients at various spatial scales. The uncertainty propagation was analysed for the emissions of NH<sub>3</sub>, N<sub>2</sub>O and NO<sub>x</sub>, N leaching to groundwater and N runoff to surface water for the entire EU27 and for individual countries. Results show large uncertainties for N leaching and runoff (relative errors of ∼ 19% for Europe as a whole), and smaller uncertainties for emission of N<sub>2</sub>O, NH<sub>3</sub> and NO<sub>x</sub> (relative errors of ∼ 12%). Uncertainties for Europe as a whole were much smaller compared to uncertainties at country level, because errors partly cancelled out due to spatial aggregation

Mapping rootable depth and root zone plant-available water holding capacity of the soil of sub-Saharan Africa

In rainfed crop production, root zone plant-available water holding capacity (RZ-PAWHC) of the soil has a large influence on crop growth and the yield response to management inputs such as improved seeds and fertilisers. However, data are lacking for this parameter in sub-Saharan Africa (SSA). This study produced the first spatially explicit, coherent and complete maps of the rootable depth and RZ-PAWHC of soil in SSA. We compiled georeferenced data from 28,000 soil profiles from SSA, which were used as input for digital soil mapping (DSM) techniques to produce soil property maps of SSA. Based on these soil properties, we developed and parameterised (pedotransfer) functions, rules and criteria to evaluate soil water retention at field capacity and wilting point, the soil fine earth fraction from coarse fragments content and, for maize, the soil rootability (relative to threshold values) and rootable depth. Maps of these secondary soil properties were derived using the primary soil property maps as input for the evaluation rules and the results were aggregated over the rootable depth to obtain a map of RZ-PAWHC, with a spatial resolution of 1 km2. The mean RZ-PAWHC for SSA is 74mm and the associated average root zone depth is 96 cm. Pearson correlation between the two is 0.95. RZ-PAWHC proves most limited by the rootable depth but is also highly sensitive to the definition of field capacity. The total soil volume of SSA potentially rootable by maize is reduced by one third (over 10,500 km3) due to soil conditions restricting root zone depth. Of these, 4800 km3 are due to limited depth of aeration, which is the factor most severely limiting in terms of extent (km2), and 2500 km3 due to sodicity which is most severely limiting in terms of degree (depth in cm). Depth of soil to bedrock reduces the rootable soil volume by 2500 km3, aluminium toxicity by 600 km3, porosity by 120 km3 and alkalinity by 20 km3. The accuracy of the map of rootable depth and thus of RZ-PAWHC could not be validated quantitatively due to absent data on rootability and rootable depth but is limited by the accuracy of the primary soil property maps. The methodological framework is robust and has been operationalised such that the maps can easily be updated as additional data become available

Mapping rootable depth and root zone plant-available water holding capacity of the soil of sub-Saharan Africa

In rainfed crop production, root zone plant-available water holding capacity (RZ-PAWHC) of the soil has a large influence on crop growth and the yield response to management inputs such as improved seeds and fertilisers. However, data are lacking for this parameter in sub-Saharan Africa (SSA). This study produced the first spatially explicit, coherent and complete maps of the rootable depth and RZ-PAWHC of soil in SSA. We compiled georeferenced data from 28,000 soil profiles from SSA, which were used as input for digital soil mapping (DSM) techniques to produce soil property maps of SSA. Based on these soil properties, we developed and parameterised (pedotransfer) functions, rules and criteria to evaluate soil water retention at field capacity and wilting point, the soil fine earth fraction from coarse fragments content and, for maize, the soil rootability (relative to threshold values) and rootable depth. Maps of these secondary soil properties were derived using the primary soil property maps as input for the evaluation rules and the results were aggregated over the rootable depth to obtain a map of RZ-PAWHC, with a spatial resolution of 1 km2. The mean RZ-PAWHC for SSA is 74mm and the associated average root zone depth is 96 cm. Pearson correlation between the two is 0.95. RZ-PAWHC proves most limited by the rootable depth but is also highly sensitive to the definition of field capacity. The total soil volume of SSA potentially rootable by maize is reduced by one third (over 10,500 km3) due to soil conditions restricting root zone depth. Of these, 4800 km3 are due to limited depth of aeration, which is the factor most severely limiting in terms of extent (km2), and 2500 km3 due to sodicity which is most severely limiting in terms of degree (depth in cm). Depth of soil to bedrock reduces the rootable soil volume by 2500 km3, aluminium toxicity by 600 km3, porosity by 120 km3 and alkalinity by 20 km3. The accuracy of the map of rootable depth and thus of RZ-PAWHC could not be validated quantitatively due to absent data on rootability and rootable depth but is limited by the accuracy of the primary soil property maps. The methodological framework is robust and has been operationalised such that the maps can easily be updated as additional data become available