Assessing local and spatial uncertainty with nonparametric geostatistics

Uncertainty quantification is an important topic for many environmental studies, such as identifying zones where potentially toxic materials exist in the soil. In this work, the nonparametric geostatistical framework of histogram via entropy reduction (HER) is adapted to address local and spatial uncertainty in the context of risk of soil contamination. HER works with empirical probability distributions, coupling information theory and probability aggregation methods to estimate conditional distributions, which gives it the flexibility to be tailored for different data and application purposes. To explore how HER can be used for estimating threshold-exceeding probabilities, it is applied to map the risk of soil contamination by lead in the well-known dataset of the region of Swiss Jura. Its results are compared to indicator kriging (IK) and to an ordinary kriging (OK) model available in the literature. For the analyzed dataset, IK and HER predictions achieve the best performance and exhibit comparable accuracy and precision. Compared to IK, advantages of HER for uncertainty estimation in a fine resolution are that it does not require modeling of multiple indicator variograms, correcting order-relation violations, or defining interpolation/extrapolation of distributions. Finally, to avoid the well-known smoothing effect when using point estimations (as is the case with both kriging and HER), and to provide maps that reflect the spatial fluctuation of the observed reality, we demonstrate how HER can be used in combination with sequential simulation to assess spatial uncertainty (uncertainty jointly over several locations).

Assessing local and spatial uncertainty with nonparametric geostatistics

Uncertainty quantification is an important topic for many environmental studies, such as identifying zones where potentially toxic materials exist in the soil. In this work, the nonparametric geostatistical framework of histogram via entropy reduction (HER) is adapted to address local and spatial uncertainty in the context of risk of soil contamination. HER works with empirical probability distributions, coupling information theory and probability aggregation methods to estimate conditional distributions, which gives it the flexibility to be tailored for different data and application purposes. To explore the method adaptation for handling estimations of threshold-exceeding probabilities, it is used to map the risk of soil contamination by lead in the well-known dataset of the region of Swiss Jura. Its results are compared to indicator kriging (IK) and to an ordinary kriging (OK) model available in literature. For the analyzed dataset, IK and HER achieved the best performance and exhibited comparable accuracy and precision of their predictions. When compared to IK, HER has shown to be a unique approach for dealing with uncertainty estimation in a fine resolution, without the need of modeling multiple indicator variograms, correcting order-relation violations, or defining interpolation/extrapolation of distribution. Finally, to avoid the well-known smoothing effect when using point estimations (this is the case with kriging, but also with HER) and to provide maps that reflect the spatial fluctuation of the revealed reality, we demonstrate how HER can be used in combination with sequential simulation to assess spatial uncertainty (uncertainty jointly over several locations).

Three dimensional soil organic matter distribution, accessibility and microbial respiration in macro-aggregates using osmium staining and synchrotron X-ray CT

The spatial distribution and accessibility of organic matter (OM) to soil microbes in aggregates – determined by the fine-scale, 3-D distribution of organic matter, pores and mineral phases – may be an important control on the magnitude of soil heterotrophic respiration (SHR). Attempts to model SHR at fine scales requires data on the transition probabilities between adjacent pore space and soil OM, a measure of microbial accessibility to the latter. We used a combination of osmium staining and synchrotron X-ray CT to determine the 3-D (voxel) distribution of these three phases (scale 6.6 μm) throughout nine aggregates taken from a single soil core (range of organic carbon (OC) concentrations 4.2–7.7 %). Prior to the synchrotron analyses we had measured the magnitude of SHR for each aggregate over 24 hours under controlled conditions (moisture content and temperature). We test the hypothesis that larger magnitudes of SHR will be observed in aggregates with shorter length scales of OM variation (i.e. more frequent, and possibly more finely disseminated, OM and a larger number of aerobic microsites). After scaling to their OC concentrations, there was a six-fold variation in the magnitude of SHR for the nine aggregates. The distribution of pore volumes, pore shape and volume normalised surface area were similar for each of the nine aggregates. The overall transition probabilities between OM and pore voxels were between 0.02 and 0.03, significantly smaller than those used in previous simulation studies. We computed the length scales over which OM, pore and mineral phases vary within each aggregate using indicator variograms. The median range of models fitted to variograms of OM varied between 178 and 487 μm. The linear correlation between these median length scales of OM variation and the magnitudes of SHR for each aggregate was −0.42, providing some evidence to support our hypothesis. We require a larger number of observations to make a statistical inference. There was no evidence to suggest a statistical relationship between OM:pore transition probabilities and the magnitudes of aggregate SHR. The solid-phase volume proportions (45–63 %) of OM we report for our aggregates were surprisingly large by comparison to those assumed in previous modelling approaches. We suggest this requires further assessment using accurate measurements of OM bulk density in a range of soil types.

Small-scale seed-bank patterns in a forest soil

The forest seed bank has been demonstrated to vary spatially at scales from 2 to 10 m. To our knowledge, the fine-scale spatial structure, i.e. < 2 m, has not been studied before. This study aims to make a thorough investigation of fine-scale spatial structure. Soil samples (128) were collected from each of five 2.1 m × 2.1 m plots, using a combined systematic (64) and random design (64). This allowed investigation of the fine-scale spatial structure of individual species–plot combinations using indicator-variograms. Our results indicated that over half of all species recorded in a particular plot were spatially structured. Remarkably, the presence of spatial structure seemed independent of species frequency. Visualization of the spatial structure showed an irregular spatial pattern, i.e. seed clusters that were randomly distributed in space. Spatial dependence occurred over small distances, possibly suggesting that a significant proportion of seeds was deposited near the mother plant. We conclude by presenting the relevance and implications of small-scale spatial seed-bank patterning for seed-bank sampling.