Influence of Spatial Scales on the Performance of Saturated Subsurface Flow and Transport Models

Numerical modeling of saturated subsurface flow and transport has been widely used in the past using different numerical schemes such as finite difference and finite element methods. Such modeling often involves discretization of the problem in spatial and temporal scales. The choice of the spatial and temporal scales for a modeling scenario is often not straightforward. For example, a basin-scale saturated flow and transport analysis demands larger spatial and temporal scales than a meso-scale study, which in turn has larger scales compared to a pore-scale study. The choice of spatial-scale is often dictated by the computational capabilities of the modeler as well as the availability of fine-scale data. In this study, we analyze the impact of different spatial scales and scaling procedures on saturated subsurface flow and transport simulations.

Critical Sensitivity and Trans-Scale Fluctuations in Catastrophic Rupture

Rupture in the heterogeneous crust appears to be a catastrophe transition. Catastrophic rupture sensitively depends on the details of heterogeneity and stress transfer on multiple scales. These are difficult to identify and deal with. As a result, the threshold of earthquake-like rupture presents uncertainty. This may be the root of the difficulty of earthquake prediction. Based on a coupled pattern mapping model, we represent critical sensitivity and trans-scale fluctuations associated with catastrophic rupture. Critical sensitivity means that a system may become significantly sensitive near catastrophe transition. Trans-scale fluctuations mean that the level of stress fluctuations increases strongly and the spatial scale of stress and damage fluctuations evolves from the mesoscopic heterogeneity scale to the macroscopic scale as the catastrophe regime is approached. The underlying mechanism behind critical sensitivity and trans-scale fluctuations is the coupling effect between heterogeneity and dynamical nonlinearity. Such features may provide clues for prediction of catastrophic rupture, like material failure and great earthquakes. Critical sensitivity may be the physical mechanism underlying a promising earthquake forecasting method, the load-unload response ratio (LURR).

Scale-Dependent Habitat Selection of Nesting Great Egrets and Snowy Egrets

Foraging habitat selection of nesting Great Egrets ( Ardea alba ) and Snowy Egrets ( Egretta thula ) was investigated within an estuary with extensive impounded salt marsh habitat. Using a geographic information system, available habitat was partitioned into concentric bands at five, ten, and 15 km radius from nesting colonies to assess the relative effects of habitat composition and distance on habitat selection. Snowy Egrets were more likely than Great Egrets to depart colonies and travel to foraging sites in groups, but both species usually arrived at sites that were occupied by other wading birds. Mean flight distances were 6.2 km (SE = 0.4, N = 28, range 1.8-10.7 km) for Great Egrets and 4.7 km (SE = 0.48, N = 31, range 0.7-12.5 km) for Snowy Egrets. At the broadest spatial scale both species used impounded (mostly salt marsh) and estuarine edge habitat more than expected based on availability while avoiding unimpounded (mostly fresh water wetland) habitat. At more local scales habitat use matched availability. Interpretation of habitat preference differed with the types of habitat that were included and the maximum distance that habitat was considered available. These results illustrate that caution is needed when interpreting the results of habitat preference studies when individuals are constrained in their choice of habitats, such as for central place foragers.

Integrating remote sensing products and GIS tools to support marine spatial management in West Hawai'i

Marine protected areas (MPAs) represent a form of spatial management, and geospatial information on living marine resources and associated habitat is extremely important to support best management practices in a spatially discrete MPA. Benthic habitat maps provide georeferenced information on the geomorphic structure and biological cover types in the marine environment. This information supports an enhanced understanding of ecosystem function and species habitat utilization patterns. Benthic habitat maps are most useful for marine management and spatial planning purposes when they are created at a scale that is relevant to management actions. We sought to improve the resolution of existing benthic habitat maps created during a regional mapping effort in Hawai`i. Our results complemented these existing regional maps and provided more detailed, finer-scale habitat maps for a network of MPAs in West Hawai`i. The map products created during this study allow local planners and managers to extract information at a spatial scale relevant to the discrete management units, and appropriate for local marine management efforts on the Kona Coast. The resultant benthic habitat maps were integrated in a geographic information system (GIS) that also included aerial imagery, underwater video, MPA regulations, summarized ecological data and other relevant and spatially explicit information. The integration of the benthic habitat maps with additional “value added” geospatial information into a dynamic GIS provide a decision support tool with pertinent marine resource information available in one central location and support the application of a spatial approach to the management of marine resources. Further, this work can serve as a case study to demonstrate the integration of remote sensing products and GIS tools at a fine spatial scale relevant to local-level marine spatial planning and management efforts.

Spatial distribution of upland beetles in relation to landform, vegetation and grazing management

Dennis, P., Aspinall, R. J., Gordon, I. J. (2002). Spatial distribution of upland beetles in relation to landform vegetation and grazing management. Basic and Applied Ecology, 3 (2), 183?193. Sponsorship: SEERAD RAE2008

Soft sediment ecology of Lough Hyne Marine Reserve - spatial and temporal patterns

Distribution of soft sediment benthic fauna and the environmental factors affecting them were studied, to investigate changes across spatial and temporal scales. Investigations took place at Lough Hyne Marine Reserve using a range of methods. Data on the sedimentation rates of organic and inorganic matter were collected at monthly intervals for one year at a number of sites around the Lough, by use of vertical midwater-column sediment traps. Sedimentation of these two fractions were not coupled; inorganic matter sedimentation depended on hydrodynamic and weather factors, while the organic matter sedimentation was more complex, being dependent on biological and chemical processes in the water column. The effects of regular hypoxic episodes on benthic fauna due to a natural seasonal thermocline were studied in the deep Western Trough, using camera-equipped remotely-operated vehicle to follow transects, on a three-monthly basis over one year. In late summer, the area below the thermocline of the Western Trough was devoid of visible fauna. Decapod crustaceans were the first taxon to make use of ameliorating oxygen conditions in autumn, by darting below the thermocline depth, most likely to scavenge. This was indicated by tracks that they left on the surface of the Trough floor. Some species, most noticeably Fries’ goby Lesueurigobius friesii, migrated below the thermocline depth when conditions were normoxic and established semi-permanent burrows. Their population encompassed all size classes, indicating that this habitat was not limited to juveniles of this territorial species. Recolonisation by macrofauna and burrowing megafauna was studied during normoxic conditions, from November 2009 to May 2010. Macrofauna displayed a typical post-disturbance pattern of recolonisation with one species, the polychaete Scalibregma inflatum, occurring at high abundance levels in March 2010. In May, this population had become significantly reduced and a more diverse community was established. The abundance of burrowing infauna comprising decapods crabs and Fries’ gobies, was estimated by identifying and counting their distinctive burrow structures. While above the summer thermocline depth, burrow abundance increased in a linear fashion, below the thermocline depth a slight reduction of burrow abundance occurred in May, when oxygen conditions deteriorated again. The majority of the burrows occurring in May were made by Fries’ gobies, which are thought to encounter low oxygen concentrations in their burrows. Reduction in burrow abundance of burrowing shrimps Calocaris macandreae and Callianassa subterranea (based on descriptions of burrow structures from the literature), from March to May, might be related to their reduced activity in hypoxia, leading to loss of structural burrow maintenance. Spatial and temporal changes to macrofaunal assemblage structures were studied seasonally for one year across 5 sites in the Lough and subject to multivariate statistical analysis. Assemblage structures were significantly correlated with organic matter levels in the sediment, the amounts of organic matter settling out of the water column one month before macrofaunal sampling took place as well as current speed and temperature. This study was the first to investigate patterns and processes in the Lough soft sediment ecology across all 3 basins on a temporal and spatial scale. An investigation into the oceanographic aspects of the development, behaviour and break-down of the summer thermocline of Lough Hyne was performed in collaboration with researchers from other Irish institutions.

Variability in north temperate dung beetle assemblages at different spatial and temporal scales

This study examined the spatial and temporal variability of dung beetle assemblages across a variety of scales e.g. from the between-pad scale (examining the effects of dung size and type) to larger spatial scales encompassing southern Ireland. Dung beetle assemblage structure as sampled by dung pad cohort samples and dung baited pitfall trapping were compared. Generally, the rank order of abundance of dung beetle species was significantly correlated between pitfall catches and cohort pad samples. Across different dung sizes, in both pitfall catches and cohort pad samples, the relative abundance of species was frequently significantly different, but the rank order of abundance of dung beetle was usually significantly correlated. Considerable variations in pitfall catches at temporal scales of a few days appeared to be closely related to weather conditions and rotational grazing. However, despite considerable variation in absolute abundances between consecutive days of sampling, assemblage structure typically remained very similar. The relationship between dung pad size and dung beetle colonisation was investigated. In field experiments in which pads of different sizes (0.25 L, 0.5 L, 1.0 L and 1.5 L) were artificially deposited, there was a positive relationship between pad size and both biomass and number of beetles colonising dung pads and pitfall traps. In addition, with one exception, the field experiments indicated a general positive relationship between dung pad size and biomass density (dung beetle biomass per unit dung volume). A laboratory experiment indicated that pat residence times of A. rufipes were significantly correlated with dung pad size. Investigation of naturally-deposited cow dung pads in the field also indicated that both larval numbers and densities were significantly correlated with dung pad size. These results were discussed in the context of theory related to aggregation and coexistence of species, and resource utilisation by organisms in ephemeral, patchy resources. The colonisation by dung beetles of dung types from native herbivores (sheep, horse and cow) was investigated in field experiments. There were significant differences between the dung types in the chemical parameters measured, and there were significant differences in abundances of dung beetles colonising the dung types. Sheep dung was typically the preferred dung type. Data from these field experiments, and from published literature, indicated that dung beetle species can display dung type preferences, in terms of comparisons of both absolute and relative abundances. In addition, data from laboratory experiments indicate that both Aphodius larval production and pat residence times tended to be higher in those dung types which were preferred by adult Aphodius in the colonisation experiments. Data from dung-baited pitfall trapping (from this and another study) at several sites (up to 180 km distant) and over a number of years (between 1991 and 1996) were used to investigate spatial and temporal variation in dung beetle assemblage structure and composition (Aphodius, Sphaeridium and Geotrupes) across a range of scales in southern Ireland. Species richness levels, species composition and rank order of abundances were very similar between the assemblages. The temporal variability between seasons within any year exceeded temporal variability between years. DCA ordinations indicated that there was a similar level of variability between assemblage structure from the between-field (~1km) to regional (~180 km) spatial scales, and between year (6 years) temporal scales. At the biogeographical spatial scale, analysis of data from the literature indicated that there was considerable variability at this scale, largely due to species turnover.

Algal epiphytes of Zostera marina: Variation in assemblage structure from individual leaves to regional scale

Data from a hierarchical study of four Zostera marina beds in Wales were used to identify the spatial scales of variation in epiphyte assemblages. There were significant within and among bed differences in assemblage structure. The differences in assemblage structure with spatial scale generally persisted when species identifications were aggregated into functional groups. There was also significant within and among bed variability in Zostera density and average length. Local variations in Zostera canopy variables at the quadrat scale (total leaf length, average leaf length and leaf density per quadrat) were not related to epiphyte species richness nor to the structure of the assemblage. In contrast, individual leaf length was significantly related to species richness in two of the beds and the structure of epiphyte assemblages was always related to individual leaf lengths. The absence of links between quadrat scale measurements of canopy variables and assemblage structure may reflect the high turnover of individual Zostera leaves. Experimental work is required to discriminate further between the potential causes of epiphyte assemblage variation within and between beds. No bed represented a refuge where a rare species was abundant. If a species was uncommon at the bed scale, it was also uncommon in beds where it occurred. The heterogeneous assemblages found in this study suggest that a precautionary approach to conservation is advisable.

Plant community assembly at small scales: spatial versus environmental factors in a central European grassland

Dispersal limitation and environmental conditions are crucial drivers of plant species distribution and establishment. As these factors operate at different spatial scales, we asked: Do the environmental factors known to determine community assembly at broad scales operate at fine scales (few meters)? How much do these factors account for community variation at fine scales? In which way do biotic and abiotic interactions drive changes in species composition? We surveyed the plant community within a dry grassland along a very steep gradient of soil characteristics like pH and nutrients. We used a spatially explicit sampling design, based on three replicated macroplots of 15x15, 12x12 and 12x12 meters in extent. Soil samples were taken to quantify several soil properties (carbon, nitrogen, plant available phosphorus, pH, water content and dehydrogenase activity as a proxy for overall microbial activity). We performed variance partitioning to assess the effect of these variables on plant composition and statistically controlled for spatial autocorrelation via eigenvector mapping. We also applied null model analysis to test for non-random patterns in species co-occurrence using randomization schemes that account for patterns expected under species interactions. At a fine spatial scale, environmental factors explained 18% of variation when controlling for spatial autocorrelation in the distribution of plant species, whereas purely spatial processes accounted for 14% variation. Null model analysis showed that species spatially segregated in a non-random way and these spatial patterns could be due to a combination of environmental filtering and biotic interactions. Our grassland study suggests that environmental factors found to be directly relevant in broad scale studies are present also at small scales, but are supplemented by spatial processes and more direct interactions like competition.

Multi-scale support vector algorithms for hot spot detection and modelling

The algorithmic approach to data modelling has developed rapidly these last years, in particular methods based on data mining and machine learning have been used in a growing number of applications. These methods follow a data-driven methodology, aiming at providing the best possible generalization and predictive abilities instead of concentrating on the properties of the data model. One of the most successful groups of such methods is known as Support Vector algorithms. Following the fruitful developments in applying Support Vector algorithms to spatial data, this paper introduces a new extension of the traditional support vector regression (SVR) algorithm. This extension allows for the simultaneous modelling of environmental data at several spatial scales. The joint influence of environmental processes presenting different patterns at different scales is here learned automatically from data, providing the optimum mixture of short and large-scale models. The method is adaptive to the spatial scale of the data. With this advantage, it can provide efficient means to model local anomalies that may typically arise in situations at an early phase of an environmental emergency. However, the proposed approach still requires some prior knowledge on the possible existence of such short-scale patterns. This is a possible limitation of the method for its implementation in early warning systems. The purpose of this paper is to present the multi-scale SVR model and to illustrate its use with an application to the mapping of Cs137 activity given the measurements taken in the region of Briansk following the Chernobyl accident.

The relationship between diffuse spectral reflectance of the soil and its cation exchange capacity is scale-dependent

Diffuse reflectance spectroscopy (DRS) is increasingly being used to predict numerous soil physical, chemical and biochemical properties. However, soil properties and processes vary at different scales and, as a result, relationships between soil properties often depend on scale. In this paper we report on how the relationship between one such property, cation exchange capacity (CEC), and the DRS of the soil depends on spatial scale. We show this by means of a nested analysis of covariance of soils sampled on a balanced nested design in a 16 km × 16 km area in eastern England. We used principal components analysis on the DRS to obtain a reduced number of variables while retaining key variation. The first principal component accounted for 99.8% of the total variance, the second for 0.14%. Nested analysis of the variation in the CEC and the two principal components showed that the substantial variance components are at the > 2000-m scale. This is probably the result of differences in soil composition due to parent material. We then developed a model to predict CEC from the DRS and used partial least squares (PLS) regression do to so. Leave-one-out cross-validation results suggested a reasonable predictive capability (R2 = 0.71 and RMSE = 0.048 molc kg− 1). However, the results from the independent validation were not as good, with R2 = 0.27, RMSE = 0.056 molc kg− 1 and an overall correlation of 0.52. This would indicate that DRS may not be useful for predictions of CEC. When we applied the analysis of covariance between predicted and observed we found significant scale-dependent correlations at scales of 50 and 500 m (0.82 and 0.73 respectively). DRS measurements can therefore be useful to predict CEC if predictions are required, for example, at the field scale (50 m). This study illustrates that the relationship between DRS and soil properties is scale-dependent and that this scale dependency has important consequences for prediction of soil properties from DRS data

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.

Exploring the spatial relations between soil physical properties and apparent electrical conductivity

Relations between the apparent electrical conductivity of the soil (ECa) and top- and sub-soil physical properties were examined for two arable fields in southern England (Crowmarsh Battle Farms and the Yattendon Estate). The spatial variation of ECa and the soil properties was explored geostatistically. The variogram ranges showed that ECa varied on a similar spatial scale to many of the soil physical properties in both fields. Several features in the map of kriged predictions of ECa were also evident in maps of the soil properties. In addition, the correlation coefficients showed a strong relation between ECa and several soil properties. A moving correlation analysis enabled differences in the relations between ECa and the soil properties to be examined within the fields. The results indicated that relations were inconsistent; they were stronger in some areas than others. A regression of ECa on the principal component scores of the leading components for both fields showed that the first two components accounted for a large proportion of the variance in ECa, whereas the others accounted for little or none. For Crowmarsh topsoil sand and clay, loss on ignition and volumetric water measured in the autumn had large correlations on the first component, and for Yattendon they were large for topsoil sand and clay, and autumn and spring volumetric water. The cross-variograms suggested strong coregionalization between ECa and several soil physical properties; in particular subsoil sand and silt at Crowmarsh, and subsoil sand and clay at Yattendon. The structural correlations from the linear model of coregionalization confirmed the strength of the relations between ECa and the subsoil properties. Nevertheless, no one property was consistently important for both fields. Although a map of ECa can indicate the general patterns of spatial variation in the soil, it is not a substitute for information on soil properties obtained by sampling and analysing the soil. Nevertheless, it could be used to guide further sampling. (c) 2005 Elsevier B.V. All rights reserved.

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.