Article

Vanishing point: Scale independence in geomorphological hierarchies

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Abstract

Scale linkage problems in geosciences are often associated with a hierarchy of components. Both dynamical systems perspectives and intuition suggest that processes or relationships operating at fundamentally different scales are independent with respect to influences on system dynamics. But how far apart is “fundamentally different”—that is, what is the “vanishing point” at which scales are no longer interdependent? And how do we reconcile that with the idea (again, supported by both theory and intuition) that we can work our way along scale hierarchies from microscale to planetary (and vice-versa)? Graph and network theory are employed here to address these questions. Analysis of two archetypal hierarchical networks shows low algebraic connectivity, indicating low levels of inferential synchronization. This explains the apparent paradox between scale independence and hierarchical linkages. Incorporating more hierarchical levels results in an increase in complexity or entropy of the network as a whole, but at a nonlinear rate. Complexity increases as a power α of the number of levels in the hierarchy, with α and usually ≤ 0.6. However, algebraic connectivity decreases at a more rapid rate. Thus, the ability to infer one part of the hierarchical network from other level decays rapidly as more levels are added. Relatedness among system components decreases with differences in scale or resolution, analogous to distance decay in the spatial domain. These findings suggest a strategy of identifying and focusing on the most important or interesting scale levels, rather than attempting to identify the smallest or largest scale levels and work top-down or bottom-up from there. Examples are given from soil geomorphology and karst flow networks.

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... Operational problems involve identifying characteristic scales, determining conditions of scale independence, decisions as to what phenomena to represent at a given scale, and tools for transferring information and representations between scales. Theoretical issues of scale linkage involve fundamental questions of whether any single rules, relationships, or representations are even potentially valid across all relevant scale ranges; bottom-up versus top-down influences, and multiple scale causality (see, e.g., Phillips, 2005Phillips, , 2016. ...
... Graph theory is used in this section to explore changes in overall system complexity as the range of scales considered is broadened. In particular, the goal is to determine the rate at which relatedness of landscape system components decreases as additional hierarchical scale levels are addeddthe "vanishing point" (Phillips, 2016) where scale independence obtains. ...
... Some hierarchies are based on conceptual models and may have fuzzy or arbitrary boundaries, but even some of these are generally agreed upon and not controversial, such as the often used pedological hierarchy first presented by Dijkerman (1974). Phillips (2016) treated distance in scale hierarchies as analogous to geographical distances. Hierarchy theory (HT) formalizes the notion that phenomena that operate or vary over similar scales are more closely related than those manifested at different scales. ...
Chapter
Landscapes are influenced by processes operating at scales from molecules to planets, and over time spans ranging from instantaneous to billions of years. Thus scale contingency is an innate, unavoidable aspect of landscape evolution, and is common in landscapes. The laws, place, and history factors relevant to landscape evolution may vary with spatial and temporal scale. Scale contingency is epistemological or ontological and leads to issues with scale linkage—transferring relationships and representations across a range of scales. Space/time ratios are useful in determining the range of scales over which landscape phenomena may be (in)dependent, and thus as practical tools in studying landscape evolution. Several different arguments or analyses show that processes or relationships that operate over distinctly different (by at least two orders of magnitude) scales are independent in terms of their effects on system-level dynamics of landscapes.
... Where the fundamental assumptions of HT hold true, scale independence between scales >2 levels apart exists. Phillips (2016) was concerned with determining how relatedness varies with distance in a scale hierarchy, in a way analogous to spatial distance decay. Algebraic graph theory methods, which can be used more broadly to assess scale independence in geographical networks, were applied as discussed in the next section. ...
... These measures are discussed in more detail in texts on algebraic or spectral graph theory (e.g. Biggs 1994), and elsewhere in a geographical and geoscience context by Phillips (2013Phillips ( , 2016. ...
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Geography and geosciences deal with phenomena that span spatial scales from the molecular to the planetary, and temporal scales from instantaneous to billions of years. A strong reductionist tradition in geosciences and spatial sciences tempts us to seek to apply similar representations and process-based explanations across these vast-scale ranges, usually from a bottom-up perspective. However, the law of scale independence (LSI) states that for any phenomenon that exists across a sufficiently large range of scales, there exists a scale separation distance at which the scales are independent with respect to system dynamics and explanation. The LSI is evaluated here from five independent perspectives: geographic intuition, dynamical systems theory, Kolmogorov entropy, hierarchy theory, and algebraic graph theory. All of these support the LSI. Results indicate that rather than attempting to identify the largest or smallest relevant scales and work down or up from there, the LSI dictates a strategy of focusing directly on the most important or interesting scales. An example is given from a hierarchical state factor model of ecosystem responses to climate change. ARTICLE HISTORY
... A broad class of nonlinear physical problems, primarily consisting of complex geological processes or self-organized critical behavior, also invariably yields fractal behavior for natural landscape (Phillips, 2016). Nonlinearity in a dynamical system primarily arises from self-organized criticality or complexity. ...
... When there exists a strong feedback between the geomorphic components, such as climate-tectonics feedback (Molnar and England 1990), the dynamical system can move toward a chaotic state, giving rise to strange attractor with fractal scaling (e.g., Baas 2002). Conversely, a dominant effect of any autogenic control, such as lithology or catchment shape, in landscape evolution can result in a self-organized critical system (e.g., Phillips, 2016). In such scenarios, the system always evolves toward a finite number of critically stable state(s) and is primarily controlled by some form of threshold. ...
Chapter
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... An additional standard is provided by the scale independence criterion, which states that system components which operate at distinctly different spatial or temporal scales are independent with respect to system dynamics (Schaffer, 1981;Phillips, 1986Phillips, , 2016c. With respect to evaluating ecosystems as putative supraorganisms, this means that graph models should not include components with operate at distinctly different temporal scales (by definition, factors in ecosystems operate at comparable spatial scales), with the latter term generally interpreted as being at least an order of magnitude in difference (Schaffer, 1981;Phillips, 1986Phillips, , 2016Phillips, , 2016c. ...
... An additional standard is provided by the scale independence criterion, which states that system components which operate at distinctly different spatial or temporal scales are independent with respect to system dynamics (Schaffer, 1981;Phillips, 1986Phillips, , 2016c. With respect to evaluating ecosystems as putative supraorganisms, this means that graph models should not include components with operate at distinctly different temporal scales (by definition, factors in ecosystems operate at comparable spatial scales), with the latter term generally interpreted as being at least an order of magnitude in difference (Schaffer, 1981;Phillips, 1986Phillips, , 2016Phillips, , 2016c. ...
Chapter
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... İndirgemecilik, biri iyi diğeri kötü olarak kabul edilen kolesterole benzer (Phillips, 2016). İster iyi ister kötü olsun yedili bir Matruşka gibi giderek içinden yeni sorular ve yeni cevaplar çıkan indirgemeci yaklaşım, belirsiz bir boyuta doğru küçülür. ...
... İndirgemecilik ile bütüncül bakış arasında kendine konum arayan bir coğrafyacı her iki uca mesafeli bir tahterevalli üzerinde olduğunu görecektir. Bugün gelinen noktada Coğrafyanın yüzyıllara dayanan indirgemeci yaklaşımının dünyayı anlamak için yetersiz olduğu (Phillips, 2016) görüşü ağır basmaktadır. ...
... Davis and Sims 2013;Phillips 2016;Zhao et al. 2017;Arora et al. 2021; ...
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Combining the basic criteria to build a taxonomic system with the hierarchic arrangement of the geomorphic environment determines a structure of nested categorial levels. Five of these levels are essentially deduced from the epigeal physiographic expression of the geoforms. To substantiate the relationship between geoform and soil, it is necessary to introduce in the system information on the internal hypogeal component of the geoforms, namely the constituent material, which is in turn the parent material of the soils. As a result of the foregoing, an additional level is needed to document the lithology in the case of bedrock substratum or the facies in the case of unconsolidated cover materials. This leads finally to a system with six categorial levels, identified by their respective generic concepts, including from upper to lower level: geostructure, morphogenic environment, geomorphic landscape, relief/molding, lithology/facies, and the basic landform or terrain form. Such a system with six categories complies with Miller’s Law, which postulates that the capacity of the human mind to process information covers a range of seven plus or minus two elements.
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The main aim is to identify those papers and treatises which have significantly affected some fields of study within the earth sciences, as a result of their incorporation of soil formation theory set out in H. Jenny's Factors of soil formation and in a contemporaneous paper by J. Thorp (1941). Firstly, the intellectual ambience that existed at this time is examined. The impacts of formation theory on these five fields and more recent contributions by scientists in these areas are then briefly reviewed. Influences on terminology and definitions in palaeopedology are noted. Lastly, the pros and cons and principal impacts of the soil formation theory framework are summarised. -J.W.Cooper
Article
A holon is any stable sub-whole in a hierarchy. It is a self-creating, open system, governed by a set of laws which regulate its coherence, stability, structure and functioning. It also possesses the potential of adaptation to the challenge of environmental change. It examines interactions between levels in the landscape 'holarchy'. These are evaluated in terms of scale, communication, stability and evolution in a fluctuating energy stream. -from Author
Chapter
The Old Kentucky River system was a major contributor to the Teays River, draining southwestern Ohio and much of eastern Kentucky. The trunk river flowed northward from southeastern Kentucky throughout Frankfort and Carrollton, and then past Cincinnati and Dayton, joining the Teays River near Springfield, Ohio. North of the glacial boundary, which lies along the modern Ohio River, the course of the Old Kentucky River has been modified, and is today largely buried by drift. Although dissection is extensive to the south, there are many remnants of this entrenched and broadly meandering Teays-age valley system and of its sub-upland predecessors. These valleys contain areas of upward-fining, deeply weathered gravel, composed mainly of rounded quartz, chert, and silicified limestone pebbles derived from the headwaters of the system. Modern rivers have been entrenched 30 to 100 m below the Old Kentucky River valley and its main tributaries, the Old Licking and South Fork. The Old Kentucky River system was severed from the Teays when glaciation dammed its downstream reaches, forcing a reversal in flow direction between its junction with the Teays in west-central Ohio and Carrollton, Kentucky, and causing westward overflow into the Old Ohio River system. Piracy by the Old Ohio may also have contributed to the integration of the Old Kentucky and Old Ohio River basins. Ponded sediment is present in some of the now-abandoned valley remnants east of Cincinnati. As a result of glacial damming, the headwaters of the Teays River in southeastern Ohio and West Virginia overflowed westward across the Manchester divide into the Old Kentucky River drainage basin. All of these events led to establishment of the modern Ohio River system.
Article
Whilst understanding and predicting the effects of coastal change are primarily modelling problems, it is essential that we have appropriate conceptual frameworks for (1) the formalisation of existing knowledge; (2) the formulation of relevant scientific questions and management issues; (3) the implementation and deployment of predictive models; and (4) meaningful engagement involvement of stakeholders. Important progress continues to be made on the modelling front, but our conceptual frameworks have not evolved at a similar pace. Accordingly, this paper presents a new approach that re-engages with formal systems analysis and provides a mesoscale geomorphological context within which the coastal management challenges of the 21st century can be more effectively addressed. Coastal and Estuarine System Mapping (CESM) is founded on an ontology of landforms and human interventions that is partly inspired by the coastal tract concept and its temporal hierarchy of sediment sharing systems, but places greater emphasis on a hierarchy of spatial scales. This extends from coastal regions, through landform complexes, to landforms, the morphological adjustment of which is constrained by diverse forms of human intervention. Crucially, CESM integrates open coastal environments with estuaries and relevant portions of the inner shelf that have previously been treated separately. In contrast to the simple nesting of littoral cells that has hitherto framed shoreline management planning, CESM charts a complex web of interactions, of which a sub-set of mass transfer pathways defines the sediment budget, and a multitude of human interventions constrains natural landform behaviour. Conducted within a geospatial framework, CESM constitutes a form of knowledge formalisation in which disparate sources of information (published research, imagery, mapping, raw data etc.) are generalised into usable knowledge. The resulting system maps provide a framework for the development and application of predictive models and a repository for the outputs they generate (not least, flux estimates for the major sediment system pathways). They also permit comparative analyses of the relative abundance of landforms and the multi-scale interactions between them. Finally, they articulate scientific understanding of the structure and function of complex geomorphological systems in a way that is transparent and accessible to diverse stakeholder audiences. As our models of mesoscale landform evolution increase in sophistication, CESM provides a platform for a more participatory approach to their application to coastal and estuarine management.
Article
Karst plateaus often have a complex geological and geomorphological history. It is widely accepted that their development requires a long period of karst denudation. This study reconstructs the palaeodrainage network of a karst plateau, analyses its properties and establishes its geomorphological significance. The main purpose of this research was to deepen our understanding of a key stage in the evolution of karst plateaus - the transition from a fluvial landsurface to one dominated by karst surface processes. The study was conducted on a large part of the Una-Korana Plateau, the largest plateau in the Dinaric karst. The majority of the plateau is made of carbonate rocks of Triassic, Jurassic and Cretaceous age that set the conditions for the development of the karst. We have reconstructed the palaeodrainage network based on 1:25,000 topographic maps with 10 m contours. The transition of the surface drainage network to the underground karst drainage network is still in progress, so, depending on the degree of karstification, the drainage network was divided into three categories: active, dry and relict. It was found that 90.5% of the pre-existing drainage network has undergone some degree of karstification. The active surface drainage network gradually shifted to a dry network, then to a relict network. The surface drainage network is gradually replaced by a dense network of dolines. Today, the flat and karstified inter-fluvial area is drained underground towards the main watercourses and these drain the entire region over the surface towards the Pannonian basin. This is the largest known karst palaeodrainage network in the Dinaric karst that has been reconstructed in this way.
Article
The principal karst region of south-central Kentucky encompasses an area of some two hundred square miles, including a segment of doline karst, the Sinkhole plain, and a karst plateau. The plateau lies mainly within Mammoth Cave National Park and is underlain by the Flint Ridge cave system, the largest known cave in the world, and by Mammoth Cave, the third largest. The plateau is ringed with a complex of vertical shafts that are an integral part of the drainage from the perched groundwater body in the protective cap rock. The development of the karst area can be interpreted in terms of the unique relationship between the stratigraphic sequence of thick, bedded limestones and of clastic rocks and the location of recharge and discharge areas. Lateral flow from the Sinkhole plain beneath the protected plateau has generated a cave complex of long tubular conduits connected by shafts, shaft drains, and piracy routes. Enough of the system is preserved to permit a fairly complete interpretation of the physiographic development of the region.
Article
Real world ecosystems (as opposed to their mathematical counterparts) are often enormously complex associations of species which interact in diverse ways. As a matter of practical necessity, field ecologists can rarely specify, much less quantify, all of the interactions. Consequently, empirically derived equations purporting to describe the dynamics of such systems generally consider fewer than the total number of interacting species. The present paper calls attention to this reduction in dimensionality and explores some of its consequences. In particular, attention is called to what are termed the Abstracted Growth Equations, those of reduced dimensionality, and to the way that these expressions derive from the underlying n-variable equations. The degree to which the Abstracted Equations accurately describe the dynamics of the species of interest is shown to depend on the time scale of these species relative to that of the species which are omitted. A general result relating the product of the eigenvalues of the Abstracted Equations to the corresponding product for the n-variable equations is proved. It is further pointed out that the distinction between Abstracted and n-variable equations suggests experiments which at least in principle should enable the empiricist to estimate the importance of species and interactions which are omitted. The relationship between Abstracted and n-variable equations is also discussed with regard to measuring competition coefficients and related parameters, and also to the problem of determining whether or not higher order interactions are present in laboratory microcosms. The analysis concludes by comparing the stability properties of several simplified models of community interactions with those of the corresponding one-species Abstracted Equations. It is shown, for the case of difference equations, in particular, that analysis of the one-species models may often lead one to conclude that the system is stable, whereas in fact it is unstable due to overdamping. The final Discussion relates the results of the present paper to previous studies that anticipate the view presented here, and comments on the quarrel that has developed between those ecologists who believe in the existence of community-wide patterns of body size and the like and those who reject this view. It is suggested that the resolution of this dispute may depend on our ability to classify subsystems of species (i.e., guilds) with regard to the extent to which their internal organization is influenced by variation in the larger communities in which they are embedded. Finally, it is shown that Roughgarden's principal results for community coevolution can be deduced from the Abstracted Growth Equations of a particular subset of the entire community.
Article
A high degree of soil variability over short distances and small areas is common, particularly in forest soils. This variability is sometimes, but not always, related to readily apparent variations in the environmental factors that control soil formation. This study examines the potential role of biomechanical effects of trees and of lithological variations within the parent material in explaining soil diversity in the Ouachita Mountains of Arkansas. The diversity of soils on Ouachita sideslopes is high, and the soil series vary primarily with respect to morphological properties such as soil thickness and rock fragment content. Soils vary considerably within small more-or-less homogeneous areas, and richness–area analysis shows that the overall pattern of pedodiversity is dominated by local, intrinsic (within-plot) variability as opposed to between-plot variability. This is consistent with variation controlled mainly by individual trees and local lithological variations. Given the criteria used to distinguish among soil types, biomechanical as opposed to chemical and hydrological effects of trees are indicated. Results also suggest divergent evolution whereby the pedologic effects of trees are large and long-lived relative to the magnitude of the initial effects and lifespan of the plants.
Article
The archetypal badass is individualistic, non-conformist, and able to produce disproportionate results. The badass concept is applied here to geomorphology. The individualistic concept of landscape evolution (ICLE) is introduced, based on three propositions: excess evolution space, capacity of all landforms to change, and variable selection pressure from environmental factors within and encompassing landscapes. ICLE indicates that geomorphic systems are idiosyncratic to some extent, and that even where two systems are similar, this is a happenstance of similar environmental selection, not an attractor state. As geomorphic systems are all individualistic, those that are also non-conformist with respect to conventional wisdoms and have amplifier effects are considered badass. Development of meander bends on a section of the Kentucky River illustrates these ideas. The divergence of karst and fluvial forms on the inner and outer bends represents unstable amplifying effects. The divergence is also individualistic, as it can be explained only by combining general laws governing surface and subsurface flow partitioning with a specific geographical and environmental setting and the history of Quaternary downcutting of the Kentucky River. Landscape evolution there does not conform to any conventional theories or conceptual frameworks of geomorphology. The badass traits of many geomorphic systems have implications for the systems themselves, attitudes toward geomorphic practice, and appreciation of landforms. Badass geomorphology and the ICLE reflect a view, and approach to the study of, landforms as the outcome of the interplay of general laws, place-specific controls, and history. Badass geomorphology also implies a research style receptive to contraventional wisdoms. Aesthetically, amplifier effects and individualism guarantee an essentially infinite variety of landforms and landscapes that geoscientists can appreciate both artistically and scientifically. Non-conformity makes the interpretation and understanding of this variety more challenging—and while that increases the degree of difficulty, it also makes for more interesting and compelling professional challenges. This article is protected by copyright. All rights reserved.
Article
We consider a problem in Mathematical Biology that leads to a question in Graph Theory, which can be solved using an old but not widely known upper estimate of the spectral radius of a nonnegative matrix. We provide a new proof of this estimate. 1.
Book
This book investigates the structure and function of geoecosystems. It does so using a simple dynamic systems model, the "brash' equation, as a conceptual and analytical tool. In brief, the "brash' equation is a set of equations describing the dynamics of the geoecosphere. The geoecosphere is defined as interacting terrestrial life and life support systems - the biosphere, toposphere, atmosphere, pedosphere, and hydrosphere. The rate of change of each component depends on the state of all the others, plus the effect of cosmic, geological, and other forcing factors. The book is divided into three parts. Part one introduces geoecosystems, describing their nature, hierarchical structure, and ideas about their interdependence and integrity. Part two explores the internal (ecological) interactions between geoecosystems and their near-surface environment. Chapters deal with the environmental factors listed in the "brash' equation.: climate and soils; climate and life; altitude; substrate; topography; and insularity. Part three prospects the role of external factors (ecological, geological, and cosmic) as agencies disturbing the dynamics of geoecosystems. -from Author
Book
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Article
We describe a framework called Regional Hydrologic Modeling for Environmental Evaluation (RHyME2) for hydrologic modeling across scales. Rooted from hierarchy theory, RHyME2 acknowledges the rate-based hierarchical structure of hydrological systems. Operationally, hierarchical constraints are accounted for and explicitly described in models put together into RHyME2. We illustrate RHyME2with a two-module model to quantify annual nutrient loads in stream networks and watersheds at regional and subregional levels. High values of R2 (>0.95) and the Nash–Sutcliffe model efficiency coefficient (>0.85) and a systematic connection between the two modules show that the hierarchy theory-based RHyME2 framework can be used effectively for developing and connecting hydrologic models to analyze the dynamics of hydrologic systems.
Article
The primary goal of this project is to develop a relative chronology of events in the geologic history of the Kentucky River, and to consider the geologic controls on those events. This study utilized published geologic and topographic data, as well as field observations and extensive compilation and comparison of digital data, to examine the fluvial record preserved in the Kentucky River valley in central Kentucky. Numerous fluvial features including abandoned paleovalleys, fluvial terraces and deposits, bedrock benches, and relict spillways between adjacent river valleys were identified during the course of the study. The morphology of the modern valley coincides with bedrock lithology and can be used to describe the distribution and preservation of modern and ancient fluvial deposits and features in the study area. Bedrock lithology is the dominant control on valley morphology and on the distribution and preservation of fluvial deposits and features in the study area. Some stream trends are inherited from the late Paleozoic drainage of the Alleghanian orogeny. More recent inheritance of valley morphology has resulted from the erosion of the river from one lithology down into another lithology with differing erosional susceptibility, thus superposing the meander patterns of the overlying valley style onto the underlying lithology. One major drainage reorganization related to a pre-Illinoisan glacial advance disrupted the northward flow of the Old Kentucky River toward the Teays River system and led to organization of the early Ohio River. This greatly reduced the distance to baselevel, and led to abrupt incision and a change in erosional style for the Kentucky River. The successful projection of valley morphologies on the basis of bedrock stratigraphy, the history of erosion suggested by fission track data and the results of this study, as well as soil thickness and development, all argue against the existence of a midto late-Tertiary, low-relief, regional erosional surface. This study instead hypothesizes that the apparent accordance of ridge-top elevations in the study area is a reflection of a fluvially downwasted late Paleozoic depositional surface.
Article
Subsurface solutional pathways make limestone terrains sensitive to changes in soil properties that regulate flows to the epikarst. This study examines biogeomorphic factors responsible for changed water movements and erosion in fluviokarst slopes deforested 200 years ago along the Kentucky River, Kentucky. In this project, infiltration and water content data from forest and fescue grass soil profiles were analyzed within a detailed overview of system factors regulating hillslope hydrology. Results show that grass has growth and rooting characteristics that tend to create a larger volume of lateral water movement in upper soil layers than occurs under forests. This sets up the current emergent pattern of erosion in which water perches at grass slope bases and overwhelms pre-existing epikarst drainage. Tree roots are able to cause solution at multiple discrete points of entry into fractures and bedding planes, increasing storage capacity and releasing sediment over time. Grass roots do not enter bedrock, and their rooting depth limits diffuse vertical preferential flow in root channels to above one meter. In the areas dense clay soils, flow under grass is conducted sideways either through the regolith or at the bedrock surface. Rapid flow along rock faces in hillslope benches likely moves fines via subsurface routes from the hillslope shoulders, causing the exposure of flat outcrops under grass. Lower growing season evapotranspiration also promotes higher grass summer flow volumes. Gullying occurs at sensitive points where cutters pass from the uphill grassed area into the forest, or where flow across the bedrock surface crosses grass/forest boundaries oriented vertical to the slope. At these locations, loss of the protective grass root mat, coupled with instigation of tree root preferential flow in saturated soils, causes soil pipes to develop. Fluviokarst land management decisions should be based on site-specific slope, soil depth, and epkarst drainage conditions, since zones sensitive to erosion are formed by spatial and temporal conjunctions of a large number of lithologic, karst, soil, climate, and vegetation factors. This study shows that it is the composite of differing influences created by forest and grass that make forests critical for soil retention in high-energy limestone terrains.
Article
Earth System Science (ESS) refers to the integrated study of physical, biological, chemical, and social processes that define the conditions on Earth. The Earth is viewed as a series of overlapping spheres, including the atmosphere, the hydrosphere, the geosphere, the biosphere, and the pedosphere. According to ESS none of these spheres occur in isolation; rather, each interacts to produce the Earth's dynamic systems in a “grand symphony of the spheres.” ESS has been recognized as an emerging and strengthening paradigm primarily within the disciplines of geology, geography, and hydrology. Although soils are recognized as a key component of ESS, this linkage has not been widely and directly recognized in the soils community. Herein, we summarize the role that soil science, and especially pedology, plays in the Earth's dynamic systems. The benefits of the earth-system science approach to studying pedology are described, including (i) a better understanding of complex systems, (ii) a greater ability to model global and the pedosphere systems, (iii) improved prescriptions for sustainable environmental management, and (iv) holistic programs of instruction in soil science.
Article
The notion of sets of fractional dimension is applied to the spatial variation of soil-pH values collected from a transect of Iping Common. The soil is a well developed humo-ferric podsol. A preliminary estimation gives a value for the Hausdorff dimension of 1.7–1.9 corresponding to the highly erratic variation. A second set of samples were collected and tested under improved and standardised conditions. The incremental values follow a Gaussian distribution but fail to show the martingale property of equal liklihood of a positive or negative increment at each sample interval and therefore indicate the presence of some dependence. Thus the line graph approximates to a fractional Brownian process of dimension 1.8. This implies a surface of values of dimension 2.8 and the consequences of such a high value for measurement, mapping and experiment are detailed.
Article
The study of pedodiversity and soil richness depends on the notion of soils as discrete entities. Soil classifications are often criticized in this regard because they depend in part on arbitrary or subjective criteria. In this study soils were categorized on the basis of the presence or absence of six lithological and morphological characteristics. Richness vs. area relationships, and the general pattern of soil variability and diversity, were then compared to analyses of pedodiversity based on Soil Taxonomy. The study area consists of sixteen 0.13-ha plots on forested sideslopes of the Ouachita Mountains, Arkansas, with a minimum of 20 classified soil pits per plot. An ad hoc classification was developed, from the standpoint of soil geomorphology and studies of the coevolution of soils and landscapes, and based on the regional environmental framework. Soils were classified based on (1) underlying geology (shale, sandstone bedrock, or transported sandstone rock fragments), and on the presence or absence of (2) texture contrast subsoils, (3) eluvial horizons, (4) surface and/or subsurface stone lines or zones, (5) lithological contrasts between soil and underlying geology, and (6) redoximorphic features. The soil geomorphic classification (SGC) yielded 40 different soil types (out of 288 possible different combinations of the criteria), compared to 19 different series or taxadjuncts identified by standard soil classification. However, 21 of the SGC soil types had only one or two representatives. Individual plots contained five to 11 different SGC soil types with extensive local variability. A standard power-function relationship between soil richness (S) and area or number of samples (A) provided the best fit for most plots (S=cAb). The exponent b was slightly higher than for the taxonomy-based analysis, but in general the analyses lead to similar conclusions with respect to the relationship between richness and area, and the relative importance of local, within-plot versus regional, between-plot variability. Results support the view that soils can be viewed and treated as discrete entities, that richness assessments are not necessarily extremely sensitive to the classification used, and that highly localized variability may be critical to pedodiversity. The suggested criteria for identifying discrete soil types are given, based on qualitative morphological differences and state factor relations, contiguity, and connectivity.
Article
It has been 10 years since publication of the first edition of Soils of the Past. In that time the subject of paleopedology has grown rapidly, and established itself within the mainstream of geological research. Ancient soils contain vital mineralogical, geochemical, textural, and paleontological information about the continental environments in which they formed. Advances in isotope geochemistry and sequence-stratigraphic models allow more detailed reconstructions of environmental change from paleosols and new insights into diverse topics like atmospheric chemistry, global change, palaeoecology, geobiology and mass extinction. This fully updated second edition of soils of the past gives describes the main types of ancient soil, procedures for their recognition and study, their classification and, most significantly, a wide array of examples of how paleosols have been used for paleoenvironmental reconstruction. Soils of the Past is written for advanced undergraduates studying paleopedology as part of a degree in geology, environmental science, or physical geography, and for interested professional earth scientists. In the last few years however palaeopedology has become an established discipline in its own right, so the time is ripe for a new edition. This new book will be a good reflection of the current state of knowledge and be widely adopted. First edition was very well received and sold over 1500 copies when the subject was relatively new. The field has now grown enormously and the second edition should do considerably better. The new edition covers new developments in the field such as: Soils and Climate, stable isotope analysis of soils, soils and sequence stratigraphy. This edition represents the only available overview of the subject at this level.
Article
The difficulty to spatially link the process levels of organizing agricultural management with those of investigating biodiversity preservation creates a spatial scale mismatch which affects the effectiveness of agri-environmental policies. Starting from a literature review this study offers a panorama of the ways authors approach spatial scale mismatch and the solutions they propose to resolve it. We made the hypothesis that the authors rely, sometimes implicitly, on theoretical frameworks to propose their solutions.
Article
The Ardesen area is prone to landslides because of the climate conditions, geologic, and geomorphologic characteristics of the region. As in previous years, in 2001 due to heavy rainfall there were many landslides resulting in damage and human casualties. There is still a great danger of further landslides in the region. Therefore, it is vitally important to prepare a landslide susceptibility map of the region. In this study, the analytical hierarchy process (AHP), the statistical index (Wi), and weighting factor (Wf) methods were used to produce and later compare three susceptibility maps. For this purpose, thematic layers including landslide inventory, lithology-weathering, slope, aspect, land cover, distance to stream, drainage density, and distance to road were used. In this study area, 98% of landslides occurred in highly or completely weathered units. Lithology-weathering, land cover, and slope data layers were found to be important factors in the study area. To confirm the practicality of the three susceptibility maps were compared with a landslide activity map containing 16 active landslide zones. The outcome was that the active landslide zones do not completely fit into the high and very high susceptibility classes. But 81.3% of these landslide zones fall into the high and very high susceptibility zones of the AHP method while this is 62.5% in the case of Wi method, and 68.8% with the Wf method. In spite of the results obtained in this study, the development of a susceptibility map is usually determined by the needs and available resources. The results showed that the AHP method gave a more realistic picture of the actual distribution of landslide susceptibility, than the Wi and Wf methods.
Article
In this paper, the relationship between network synchronizability and the edge-addition of its associated graph is investigated. First, it is shown that adding one edge to a cycle definitely decreases the network synchronizability. Then, since sometimes the synchronizability can be enhanced by changing the network structure, the question of whether the networks with more edges are easier to synchronize is addressed. Based on a subgraph and complementary graph method, it is shown by examples that the answer is negative even if the network structure is arbitrarily optimized. This reveals that generally there are redundant edges in a network, which not only make no contributions to synchronization but actually may reduce the synchronizability. Moreover, a simple example shows that the node betweenness centrality is not always a good indicator for the network synchronizability. Finally, some more examples are presented to illustrate how the network synchronizability varies following the addition of edges, where all the examples show that the network synchronizability globally increases but locally fluctuates as the number of added edges increases.
Article
Spatial systems are typically characterized by multiple controlling factors and processes operating at different spatial and temporal scales (multiple scale causality [MSC]). An entropy decomposition-based approach to MSC is presented here in two contexts. First, given maps or distributions of an observed phenomenon at two or more scales, the contribution at more local or global (relative to the primary scale of observation) controls to the observed entropy can be estimated. Second, a theoretical treatment of the entropy decomposition equations shows that as the range of scale is increased by broadening or narrowing resolutions or by incorporating more controls, the influence of larger or smaller-scale influences not only changes, but may change qualitatively, e.g., in terms of having positive (entropy-increasing) or negative (information-increasing) effects. Such qualitative causal shifts have implications for efforts to use any single causal explanation across the molecular to planetary spatial and instantaneous to geological range of scales relevant to physical geography. The entropy decomposition method is illustrated with an application to soil landscapes in the Ouachita Mountains, Arkansas.*Dan Marion of the U.S. Forest Service, and other personnel of the USDA Forest Service, Southern Research Station, and Ouachita National Forest assisted in innumerable aspects of the Ouachita Mountains soil research. Linda Martin and Zach Musselman provided comments on an earlier draft of this paper. Two anonymous reviewers made insightful comments that improved the paper substantially. Mistakes and wild-eyed, arm-waving speculations are not their fault.