Spatial analysis of the error in a model of soil nitrogen

Models of the dynamics of nitrogen in soil (soil-N) can be used to aid the fertilizer management of a crop. The predictions of soil-N models can be validated by comparison with observed data. Validation generally involves calculating non-spatial statistics of the observations and predictions, such as their means, their mean squared-difference, and their correlation. However, when the model predictions are spatially distributed across a landscape the model requires validation with spatial statistics. There are three reasons for this: (i) the model may be more or less successful at reproducing the variance of the observations at different spatial scales; (ii) the correlation of the predictions with the observations may be different at different spatial scales; (iii) the spatial pattern of model error may be informative. In this study we used a model, parameterized with spatially variable input information about the soil, to predict the mineral-N content of soil in an arable field, and compared the results with observed data. We validated the performance of the N model spatially with a linear mixed model of the observations and model predictions, estimated by residual maximum likelihood. This novel approach allowed us to describe the joint variation of the observations and predictions as: (i) independent random variation that occurred at a fine spatial scale; (ii) correlated random variation that occurred at a coarse spatial scale; (iii) systematic variation associated with a spatial trend. The linear mixed model revealed that, in general, the performance of the N model changed depending on the spatial scale of interest. At the scales associated with random variation, the N model underestimated the variance of the observations, and the predictions were correlated poorly with the observations. At the scale of the trend, the predictions and observations shared a common surface. The spatial pattern of the error of the N model suggested that the observations were affected by the local soil condition, but this was not accounted for by the N model. In summary, the N model would be well-suited to field-scale management of soil nitrogen, but suited poorly to management at finer spatial scales. This information was not apparent with a non-spatial validation. (c),2007 Elsevier B.V. All rights reserved.

Behavioral and spatial analysis of extraterritorial movements in red foxes (Vulpes vulpes)

Abstract: Movements away from the natal or home territory are important to many ecological processes, including gene flow, population regulation, and disease epidemiology, yet quantitative data on these behaviors are lacking. Red foxes exhibit 2 periods of extraterritorial movements: when an individual disperses and when males search neighboring territories for extrapair copulations during the breeding season. Using radiotracking data collected at 5-min interfix intervals, we compared movement parameters, including distance moved, speed of movement, and turning angles, of dispersal and reproductive movements to those made during normal territorial movements; the instantaneous separation distances of dispersing and extraterritorial movements to the movements of resident adults; and the frequency of locations of 95%, 60%, and 30% harmonic mean isopleths of adult fox home territories to randomly generated fox movements. Foxes making reproductive movements traveled farther than when undertaking other types of movement, and dispersal movements were straighter. Reproductive and dispersal movements were faster than territorial movements and also differed in intensity of search and thoroughness. Foxes making dispersal movements avoided direct contact with territorial adults and moved through peripheral areas of territories. The converse was true for reproductive movements. Although similar in some basic characteristics, dispersal and reproductive movements are fundamentally different both behaviorally and spatially and are likely to have different ultimate purposes and contrasting effects on spatial processes such as disease transmission

The Representative Soil Sampling Scheme of England and Wales: the spatial variation of topsoil nutrient status and pH between 1971 and 2001

The Representative Soil Sampling Scheme (RSSS) has monitored the soil of agricultural land in England and Wales since 1969. Here we describe the first spatial analysis of the data from these surveys using geostatistics. Four years of data (1971, 1981, 1991 and 2001) were chosen to examine the nutrient (available K, Mg and P) and pH status of the soil. At each farm, four fields were sampled; however, for the earlier years, coordinates were available for the farm only and not for each field. The averaged data for each farm were used for spatial analysis and the variograms showed spatial structure even with the smaller sample size. These variograms provide a reasonable summary of the larger scale of variation identified from the data of the more intensively sampled National Soil Inventory. Maps of kriged predictions of K generally show larger values in the central and southeastern areas (above 200 mg L-1) and an increase in values in the west over time, whereas Mg is fairly stable over time. The kriged predictions of P show a decline over time, particularly in the east, and those of pH show an increase in the east over time. Disjunctive kriging was used to examine temporal changes in available P using probabilities less than given thresholds of this element. The RSSS was not designed for spatial analysis, but the results show that the data from these surveys are suitable for this purpose. The results of the spatial analysis, together with those of the statistical analyses, provide a comprehensive view of the RSSS database as a basis for monitoring the soil. These data should be taken into account when future national soil monitoring schemes are designed.

Spatio-temporal analysis of an invasive plant pathogen (Phytophthora ramorum) in England and Wales

Phytophthora ramorum is a damaging invasive plant pathogen and was first discovered in the UK in 2002. Spatial point analyses were applied to the occurrence of this disease in England and Wales during the period of 2003-2006 in order to assess its spatio-temporal spread. Out of the 4301 garden centres and nurseries (GCN) surveyed, there were 164, 105, 123 and 41 sites with P. ramorum in 2003, 2004, 2005 and 2006, respectively. Spatial analysis of the observed point patterns of GCN outbreaks suggested that these sites were significantly clumped within a radius of ca 60 km in 2003, but not in later years. Further analyses were conducted to determine the relationship of GCN outbreak sites over two consecutive years and thus to infer possible disease spread over time. This analysis suggested that disease spread among GCN sites was most likely to have occurred within a distance of 60 km for 2003-2004, but not for the later years. There were 35, 63, 81 and 58 sites with P. ramorum in the semi-natural environment (SNE). Analyses were carried out to assess whether infected GCN sites could act as an inoculum source of infected SNE plants or vice versa. In all years, there was a significant spatial closeness among GCN and SNE outbreak sites within a distance of 1 km. But a significant relationship over a longer distance (within 60 km) was only observed between cases in 2003 and 2004. These analyses suggest that statutory actions taken so far appear to have reduced the extent of long-distance spread of P. ramorum among garden centres and nurseries, but not the disease spread at a shorter distance between GCN and SNE sites.

Estimating the spatial scales of regionalized variables by nested sampling, hierarchical analysis of variance and residual maximum likelihood

The variogram is essential for local estimation and mapping of any variable by kriging. The variogram itself must usually be estimated from sample data. The sampling density is a compromise between precision and cost, but it must be sufficiently dense to encompass the principal spatial sources of variance. A nested, multi-stage, sampling with separating distances increasing in geometric progression from stage to stage will do that. The data may then be analyzed by a hierarchical analysis of variance to estimate the components of variance for every stage, and hence lag. By accumulating the components starting from the shortest lag one obtains a rough variogram for modest effort. For balanced designs the analysis of variance is optimal; for unbalanced ones, however, these estimators are not necessarily the best, and the analysis by residual maximum likelihood (REML) will usually be preferable. The paper summarizes the underlying theory and illustrates its application with data from three surveys, one in which the design had four stages and was balanced and two implemented with unbalanced designs to economize when there were more stages. A Fortran program is available for the analysis of variance, and code for the REML analysis is listed in the paper. (c) 2005 Elsevier Ltd. All rights reserved.

A geostatistical analysis of the spatial variation of soil mineral nitrogen and potentially available nitrogen within an arable field.

The technology for site-specific applications of nitrogen (N) fertilizer has exposed a gap in our knowledge about the spatial variation of soil mineral N, and that which will become available during the growing season within arable fields. Spring mineral N and potentially available N were measured in an arable field together with gravimetric water content, loss on ignition, crop yield, percentages of sand, silt, and clay, and elevation to describe their spatial variation geostatistically. The areas with a larger clay content had larger values of mineral N, potentially available N, loss on ignition and gravimetric water content, and the converse was true for the areas with more sandy soil. The results suggest that the spatial relations between mineral N and loss on ignition, gravimetric water content, soil texture, elevation and crop yield, and between potentially available N and loss on ignition and silt content could be used to indicate their spatial patterns. Variable-rate nitrogen fertilizer application would be feasible in this field because of the spatial structure and the magnitude of variation of mineral N and potentially available N.

Estimating the spatial scale of herbicide and soil interactions by nested sampling, hierarchical analysis of variance and residual maximum likelihood

An unbalanced nested sampling design was used to investigate the spatial scale of soil and herbicide interactions at the field scale. A hierarchical analysis of variance based on residual maximum likelihood (REML) was used to analyse the data and provide a first estimate of the variogram. Soil samples were taken at 108 locations at a range of separating distances in a 9 ha field to explore small and medium scale spatial variation. Soil organic matter content, pH, particle size distribution, microbial biomass and the degradation and sorption of the herbicide, isoproturon, were determined for each soil sample. A large proportion of the spatial variation in isoproturon degradation and sorption occurred at sampling intervals less than 60 m, however, the sampling design did not resolve the variation present at scales greater than this. A sampling interval of 20-25 m should ensure that the main spatial structures are identified for isoproturon degradation rate and sorption without too great a loss of information in this field.

Estimating the spatial scales of regionalized variables by nested sampling, hierarchical analysis of variance and residual maximum likelihood

The variogram is essential for local estimation and mapping of any variable by kriging. The variogram itself must usually be estimated from sample data. The sampling density is a compromise between precision and cost, but it must be sufficiently dense to encompass the principal spatial sources of variance. A nested, multi-stage, sampling with separating distances increasing in geometric progression from stage to stage will do that. The data may then be analyzed by a hierarchical analysis of variance to estimate the components of variance for every stage, and hence lag. By accumulating the components starting from the shortest lag one obtains a rough variogram for modest effort. For balanced designs the analysis of variance is optimal; for unbalanced ones, however, these estimators are not necessarily the best, and the analysis by residual maximum likelihood (REML) will usually be preferable. The paper summarizes the underlying theory and illustrates its application with data from three surveys, one in which the design had four stages and was balanced and two implemented with unbalanced designs to economize when there were more stages. A Fortran program is available for the analysis of variance, and code for the REML analysis is listed in the paper. (c) 2005 Elsevier Ltd. All rights reserved.

Towards more precise sugar beet management based on geostatistical analysis of spatial variability within fields

Within-field variation in sugar beet yield and quality was investigated in three commercial sugar beet fields in the east of England to identify the main associated variables and to examine the possibility of predicting yield early in the season with a view to spatially variable management of sugar beet crops. Irregular grid sampling with some purposively-located nested samples was applied. It revealed the spatial variability in each sugar beet field efficiently. In geostatistical analyses, most variograms were isotropic with moderate to strong spatial dependency indicating a significant spatial variation in sugar beet yield and associated growth and environmental variables in all directions within each field. The Kriged maps showed spatial patterns of yield variability within each field and visual association with the maps of other variables. This was confirmed by redundancy analyses and Pearson correlation coefficients. The main variables associated with yield variability were soil type, organic matter, soil moisture, weed density and canopy temperature. Kriged maps of final yield variability were strongly related to that in crop canopy cover, LAI and intercepted solar radiation early in the growing season, and the yield maps of previous crops. Therefore, yield maps of previous crops together with early assessment of sugar beet growth may make an early prediction of within-field variability in sugar beet yield possible. The Broom’s Barn sugar beet model failed to account for the spatial variability in sugar yield, but the simulation was greatly improved when corrected for early canopy development cover and when the simulated yield was adjusted for weeds and plant population. Further research to optimize inputs to maximise sugar yield should target the irrigation and fertilizing of areas within fields with low canopy cover early in the season.

Spatial covariation of Azotobacter abundance and soil properties: A case study using the wavelet transform

The soil microflora is very heterogeneous in its spatial distribution. The origins of this heterogeneity and its significance for soil function are not well understood. A problem for understanding spatial variation better is the assumption of statistical stationarity that is made in most of the statistical methods used to assess it. These assumptions are made explicit in geostatistical methods that have been increasingly used by soil biologists in recent years. Geostatistical methods are powerful, particularly for local prediction, but they require the assumption that the variability of a property of interest is spatially uniform, which is not always plausible given what is known about the complexity of the soil microflora and the soil environment. We have used the wavelet transform, a relatively new innovation in mathematical analysis, to investigate the spatial variation of abundance of Azotobacter in the soil of a typical agricultural landscape. The wavelet transform entails no assumptions of stationarity and is well suited to the analysis of variables that show intermittent or transient features at different spatial scales. In this study, we computed cross-variograms of Azotobacter abundance with the pH, water content and loss on ignition of the soil. These revealed scale-dependent covariation in all cases. The wavelet transform also showed that the correlation of Azotobacter abundance with all three soil properties depended on spatial scale, the correlation generally increased with spatial scale and was only significantly different from zero at some scales. However, the wavelet analysis also allowed us to show how the correlation changed across the landscape. For example, at one scale Azotobacter abundance was strongly correlated with pH in part of the transect, and not with soil water content, but this was reversed elsewhere on the transect. The results show how scale-dependent variation of potentially limiting environmental factors can induce a complex spatial pattern of abundance in a soil organism. The geostatistical methods that we used here make assumptions that are not consistent with the spatial changes in the covariation of these properties that our wavelet analysis has shown. This suggests that the wavelet transform is a powerful tool for future investigation of the spatial structure and function of soil biota. (c) 2006 Elsevier Ltd. All rights reserved.

A geomatics-based approach for the derivation of the spatial distribution of sediment transport processes in periglacial mountain environments

Within this paper modern techniques such as satellite image analysis and tools provided by geographic information systems (GIS.) are exploited in order to extend and improve existing techniques for mapping the spatial distribution of sediment transport processes. The processes of interest comprise mass movements such as solifluction, slope wash, dirty avalanches and rock- and boulder falls. They differ considerably in nature and therefore different approaches for the derivation of their spatial extent are required. A major challenge is addressing the differences between the comparably coarse resolution of the available satellite data (Landsat TM/ETM+, 30 in x 30 m) and the actual scale of sediment transport in this environment. A three-stepped approach has been developed which is based on the concept of Geomorphic Process Units (GPUs): parameterization, process area delineation and combination. Parameters include land cover from satellite data and digital elevation model derivatives. Process areas are identified using a hierarchical classification scheme utilizing thresholds and definition of topology. The approach has been developed for the Karkevagge in Sweden and could be successfully transferred to the Rabotsbekken catchment at Okstindan, Norway using similar input data. Copyright (C) 2008 John Wiley & Sons, Ltd.

Sensitivity analysis of a catchment-scale nitrogen model

There are now considerable expectations that semi-distributed models are useful tools for supporting catchment water quality management. However, insufficient attention has been given to evaluating the uncertainties inherent to this type of model, especially those associated with the spatial disaggregation of the catchment. The Integrated Nitrogen in Catchments model (INCA) is subjected to an extensive regionalised sensitivity analysis in application to the River Kennet, part of the groundwater-dominated upper Thames catchment, UK The main results are: (1) model output was generally insensitive to land-phase parameters, very sensitive to groundwater parameters, including initial conditions, and significantly sensitive to in-river parameters; (2) INCA was able to produce good fits simultaneously to the available flow, nitrate and ammonium in-river data sets; (3) representing parameters as heterogeneous over the catchment (206 calibrated parameters) rather than homogeneous (24 calibrated parameters) produced a significant improvement in fit to nitrate but no significant improvement to flow and caused a deterioration in ammonium performance; (4) the analysis indicated that calibrating the flow-related parameters first, then calibrating the remaining parameters (as opposed to calibrating all parameters together) was not a sensible strategy in this case; (5) even the parameters to which the model output was most sensitive suffered from high uncertainty due to spatial inconsistencies in the estimated optimum values, parameter equifinality and the sampling error associated with the calibration method; (6) soil and groundwater nutrient and flow data are needed to reduce. uncertainty in initial conditions, residence times and nitrogen transformation parameters, and long-term historic data are needed so that key responses to changes in land-use management can be assimilated. The results indicate the general, difficulty of reconciling the questions which catchment nutrient models are expected to answer with typically limited data sets and limited knowledge about suitable model structures. The results demonstrate the importance of analysing semi-distributed model uncertainties prior to model application, and illustrate the value and limitations of using Monte Carlo-based methods for doing so. (c) 2005 Elsevier B.V. All rights reserved.

Recent habitat degradation in karstic Lake Uluabat, western Turkey: A coupled limnological-palaeolimnological approach

The Ramsar site of Lake Uluabat, western Turkey, suffers from eutrophication, urban and industrial pollution and water abstraction, and its water levels are managed artificially. Here we combine monitoring and palaeolimnological. techniques to investigate spatial and temporal limnological variability and ecosystem impact, using an ostracod and mollusc survey to strengthen interpretation of the fossil record. A combination of low invertebrate Biological Monitoring Working Party scores (<10) and the dominance of eutrophic diatoms in the modern lake confirms its poor ecological status. Palaeolimnological analysis of recent (last >200 yr) changes in organic and carbonate content, diatoms, stable isotopes, ostracods and molluscs in a lake sediment core (UL20A) indicates a 20th century trend towards increased sediment accumulation rates and eutrophication which was probably initiated by deforestation and agriculture. The most marked ecological shift occurs in the early 1960s, however. A subtle rise in diatom-inferred total phosphorus and an inferred reduction in submerged aquatic macrophyte cover accompanies a major increase in sediment accumulation rate. An associated marked shift in ostracod stable isotope data indicative of reduced seasonality and a change in hydrological input suggests major impact from artificial water management practices, all of which appears to have culminated in the sustained loss of submerged macrophytes since 2000. The study indicates it is vital to take both land-use and water management practices into account in devising restoration strategies. in a wider context, the results have important implications for the conservation of shallow karstic lakes, the functioning of which is still poorly understood. (c) 2008 Elsevier Ltd. All rights reserved.

A geostatistical analysis of soil, vegetation, and image data characterizing land surface variation

The elucidation of spatial variation in the landscape can indicate potential wildlife habitats or breeding sites for vectors, such as ticks or mosquitoes, which cause a range of diseases. Information from remotely sensed data could aid the delineation of vegetation distribution on the ground in areas where local knowledge is limited. The data from digital images are often difficult to interpret because of pixel-to-pixel variation, that is, noise, and complex variation at more than one spatial scale. Landsat Thematic Mapper Plus (ETM+) and Satellite Pour l'Observation de La Terre (SPOT) image data were analyzed for an area close to Douna in Mali, West Africa. The variograms of the normalized difference vegetation index (NDVI) from both types of image data were nested. The parameters of the nested variogram function from the Landsat ETM+ data were used to design the sampling for a ground survey of soil and vegetation data. Variograms of the soil and vegetation data showed that their variation was anisotropic and their scales of variation were similar to those of NDVI from the SPOT data. The short- and long-range components of variation in the SPOT data were filtered out separately by factorial kriging. The map of the short-range component appears to represent the patterns of vegetation and associated shallow slopes and drainage channels of the tiger bush system. The map of the long-range component also appeared to relate to broader patterns in the tiger bush and to gentle undulations in the topography. The results suggest that the types of image data analyzed in this study could be used to identify areas with more moisture in semiarid regions that could support wildlife and also be potential vector breeding sites.