Andreas Papritz

An Empirical Comparison of Kriging Methods for Nonlinear Spatial Point Prediction

Spatial prediction is a problem common to many disciplines. A simple application is the mapping of an attribute recorded at a set of points. Frequently a nonlinear functional of the observed variable is of interest, and this calls for nonlinear approaches to prediction. Nonlinear kriging methods, developed in recent years, endeavour to do so and additionally provide estimates of the distribution of the target quantity conditional on the observations. There are few empirical studies that validate the various forms of nonlinear kriging. This study compares linear and nonlinear kriging methods with respect to precision and their success in modelling prediction uncertainty. The methods were applied to a data set giving measurements of the topsoil concentrations of cobalt and copper at more than 3000 locations in the Border Region of Scotland. The data stem from a survey undertaken to identify places where these trace elements are deficient for livestock. The comparison was carried out by dividing the data set into calibration and validation sets. No clear differences between the precision of ordinary, lognormal, disjunctive, indicator, and model-based kriging were found, neither for linear nor for nonlinear target quantities. Linear kriging, supplemented with the assumption of normally distributed prediction errors, failed to model the conditional distribution of the marginally skewed data, whereas the nonlinear methods modelled the conditional distributions almost equally well. In our study the plug-in methods did not fare any worse than model-based kriging, which takes parameter uncertainty into account.

Fitting a linear model of coregionalization for soil properties using simulated annealing

Abstract It is not simple to model cross and auto-variograms to describe the covariation of two or more soil properties, since the models that are fitted must meet certain constraints. These constraints are most readily met by fitting a linear model of coregionalization (LMCR). This presents practical problems. Not all combinations of authorized variogram functions constitute a LMCR. This paper presents a method for automated fitting of variogram functions to auto and cross-variogram estimates, subject to the constraints of the LMCR. The method uses simulated annealing to minimize a weighted sum of squares between the observed and modelled variograms. The method was applied to some data on soil. It was found to be robust to the initial choice of variogram parameters. Practical methods for setting up a good cooling schedule for the simulated annealing are discussed.

Nitrogen budgets of two small experimental forested catchments at Alptal, Switzerland

Abstract Two small experimental headwater catchments (approx. 1500 m 2 ) were set up in an alpine spruce forest in the Alptal valley (central Switzerland). They are located at an altitude of 1200 m and receive an average of 2300 mm precipitation a year. The site is moderately impacted by atmospheric nitrogen deposition (12 kg N ha −1 yr −1 bulk deposition of inorganic N). Two different gley soils occur as patches atop a Flysch substratum. The spatial heterogeneity of the soil is related with both the microtopography of the site and the vegetation. The catchments were made by digging 80-cm deep trenches into the shallow gleyic soils. Because of the low permeability of the clay-rich subsoil, these trenches collect the lateral water flow generated in the plots. The catchments were equipped with gauging stations (V-notch weirs) and automatic runoff-proportional water samplers. Meteorological parameters, deposition, water and solute discharge were monitored during one year. A correct water balance was obtained from the experimental catchments. The leaching of inorganic nitrogen was estimated to be 4 kg N ha −1 yr −1 , mainly as nitrate. It is, however, not clear if this nitrate is leached because the ecosystem is nitrogen saturated (N in surplus of the maximal ecosystem retention). Quick preferential water flow occurs through the soil, and this may prevent nitrate from rain or snowmelt to be removed by the soil matrix before entering the water runoff pathways. Both mini-catchments showed similar biogeochemical cycles, especially for nitrogen. The time series obtained will be used as reference period for a paired-catchment experiment simulating an increased nitrogen (ammonium nitrate) deposition.

Temporal change of spatially autocorrelated soil properties: optimal estimation by cokriging

Abstract Data on temporal changes of soil properties are required to appraise and to mitigate man-made changes in ecosystems. The spatial distribution of a soil property at any one time may be considered to be a realization of a separate random process. On this assumption change can be estimated optimally by kriging. This results in a set of equations with close resemblance to a bivariate cokriging system. Difficulties arise where soil sampling is destructive, for then measurements cannot be made at identical points on two or more occasions, and experimental cross variograms between times cannot be computed in the usual way. These problems can be overcome by using pseudo cross variograms. Although the stationarity condition required for the existence of the pseudo cross variogram is theoretically more general than second order stationarity, the practical application of this function remains nonetheless limited to second order stationary random processes. The equations for describing temporal change from destructive sampling are derived, and the kriging system with the pseudo cross variogram is given.

On the pseudo cross-variogram

Normal cross-variograms cannot be estimated from data in the usual way when there are only a few points where both variables have been measured. But the experimental pseudo cross-variogram can be computed even where there are no matching sampling points, and this appears as its principal advantage. The pseudo cross-variogram may be unbounded, though for its existence the intrinsic hypothesis alone is not a sufficient stationarity condition. In addition the differences between the two random processes must be second order stationary. Modeling the function by linear coregionalization reflects the more restrictive stationarity condition: the pseudo cross-variogram can be unbounded only if the unbounded correlation structures are the same in all variograms. As an alternative to using the pseudo cross-variogram a new method is presented that allows estimating the normal cross variogram from data where only one variable has been measured at a point.

Grain Zinc, Iron, and Copper Concentrations of Wheat Grown in Central Iran and Their Relationships with Soil and Climate Variables

We performed a survey in central Iran to assess the variability in grain zinc (Zn), iron (Fe), and copper (Cu) concentrations of winter wheat and their relationships with soil and climate variables under field conditions. The goal was to identify factors that should be studied further to improve wheat cultivation in the study area with respect to the nutritional quality of this main Iranian staple crop. Soil and grain samples were collected from 137 randomly selected wheat fields in the provinces of Qom, Isfahan, and Fars. In general, soils were characterized by a high pH. Grain micronutrient concentrations ranged from 11.7 to 64.0 mg kg(-1) (mean, 31.6 mg kg(-1)) for Zn, from 21.1 to 96.6 mg kg(-1) (mean, 42.7 mg kg(-1)) for Fe, and from 2.4 to 9.3 mg kg(-1) (mean, 5.5 mg kg(-1)) for Cu. The grain concentrations of these three metals were positively correlated to each other. DTPA-extractable and total soil micronutrient concentrations alone were very poor predictors of grain micronutrient concentrations. Predictions were slightly improved when other soil and climate variables were taken into account (Zn, R2=0.26; Fe, R2=0.08; and Cu, R2=0.13).

Calcium and magnesium transport in aggregated soils at variable ionic strength

Abstract Miscible displacement experiments were performed under conditions of variable total concentration and saturated steady-state water flow in order to study the transport of CaCl2 and MgCl2 with simultaneous cation exchange through aggregates (diameter: 0.2–0.4 cm) of two soils (Abist loam and Laegern clay loam). Using independently measured parameter values, good predictions of the experimental CaMg breakthrough curves (BTC) were obtained with a transport model based on the classical convection-dispersion equation and on the assumption of local ion exchange equilibrium. The agreement between experimental and model curves was best in the early parts of the BTC. Some tailing was observed in the later parts which was not successfully accounted for by the model. Calculations with an extended model, based on the mobile-immobile water (or two-region) concept, showed that the tailing effect may be partially due to physical non-equilibrium conditions governing the solute transfer between inter- and intra-aggregate solution. In a previous sensitivity analysis, predictions with the two-region model showed great sensitivity to the choice of parameter values determining mass transfer and partitioning of the total cation exchange capacity between mobile and immobile region. Unfortunately, however, no satisfactory methods were found to be available to determine these parameters independently. Estimation of the mass transfer coefficient from BTC of non-reactive tracers (3H2O and 3Cl) failed, because the latter were in perfect agreement with the local equilibrium assumption. In addition to physical non-equilibrium effect, the results suggest that cation exchange capacities during transport were significantly underestimated with the standard NH4OAc method.

Runoff processes in catchments with a small scale topography

Abstract How do runoff processes influence nitrogen export from forested catchments? To support nitrogen balance studies for three experimental catchments (1500m2) in the Northern Swiss prealps water flow processes in the two dominating soil types are monitored. Here we present the results for an experimental wetland catchment (1500m2) and for a delineated sloped soil plot (10m2), both with a muck humus topsoil. Runoff measurements on both the catchment and the soil plot showed fast reactions of surface and subsurface runoff to rainfall inputs, indicating the dominance of fast-flow paths such as cracks and fissures. Three quarters of the runoff from the soil plot can be attributed to water flow in the gleyic, clayey subsoil, 20% to flow in the humic A horizon and only 5% to surface runoff. The water balance for the wetland catchment was closed. The water balance of the soil plot did not close. Due to vertical upward flow from the saturated subsoil into the upper layers, the surface runoff plus subsurface runoff exceeded the input (precipitation) to the plot.

Boron accumulation and tolerance of hybrid poplars grown on a B-laden mixed paper mill waste landfill

Paper mill wastes are a mixture of by-products from pulp production and on-site energy production, consisting of paper mill sludge, ash and cinders. Landfilling of these highly boron (B) and heavy metal laden waste products carries environmental risks. Poplars have been successfully employed in the phytomanagement and hydraulic control of B contaminated sites. Here, we assess the performance of hybrid poplars on a paper-mill waste landfill, investigate the accumulation of B by the trees and explore the relationship between local-scale root growth and substrate properties. Leaf and root tissue samples were collected on three plots and analyzed for their chemical properties and root traits. Additionally, we sampled four soil cores in the vicinity of each of the trees and determined chemical and physical properties. Using a principal component analysis followed by a cluster analysis, we identified three substrate types. This method delineated the soil effects on tree survival and growth, although correlations with individual soil element concentrations were weak. Despite signs of B toxicity in some leaves, B was not the key limiting factor for poplar growth. Instead, Ca deficiency caused by a Mg:Ca imbalance was the primary reason for the poor performance of some trees. Root growth was not limited by toxicity effects of soil contaminants. Our results show that hybrid poplars perform well under the harsh growing conditions on a multi-contaminated, B-laden substrate in a hemiboreal climate. Exploiting the differences in the performance of the four clones in relation to the soil types, could increase the success of revegetation on this and other landfills.

Modelling the risk of Pb and PAH intervention value exceedance in allotment soils by robust logistic regression

Soils of allotments are often contaminated by heavy metals and persistent organic pollutants. In particular, lead (Pb) and polycyclic aromatic hydrocarbons (PAHs) frequently exceed legal intervention values (IVs). Allotments are popular in European countries; cities may own and let several thousand allotment plots. Assessing soil contamination for all the plots would be very costly. Soil contamination in allotments is often linked to gardening practice and historic land use. Hence, we predict the risk of IV exceedance from attributes that characterize the history and management of allotment areas (age, nearby presence of pollutant sources, prior land use). Robust logistic regression analyses of data of Swiss allotments demonstrate that the risk of IV exceedance can be predicted quite precisely without costly soil analyses. Thus, the new method allows screening many allotments at small costs, and it helps to deploy the resources available for soil contamination surveying more efficiently.