General definitions and present status of the landscape ecology basic concepts of landscape ecology different approaches to landscape classifications spatial patterns in natural and cultural landscapes principles of landscape dynamics descriptive and quantitative methods in landscape ecology - analysis and synthesis planning, management, conservation and restoration of cultural landscapes in practice synthesis - practical examples of landscape studies from spatial quantitative analysis to holistic problem-solving procedures.

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Principles and Methods in Landscape Ecology

Porous Materials Water in Porous Materials Flow in Porous Materials Unsaturated Flows Unsaturated Flow in Building Physics Composite Materials Evaporation and Drying Topics in Water Transport Appendices Symbols Used Properties of Water Minerals, Salts and Solutions Other Liquids Other Data

Water Transport in Brick, Stone and Concrete

Received 4 November 2005; revised 15 December 2005; accepted 20 December 2005; published 31 January 2006. [1] The relationship between permeability and porosity is reviewed and investigated. The classical Kozeny-Carman approach and a fractal pore-space geometry assumption are used to derive a new permeability-porosity equation. The equation contains only two fitting parameters: a Kozeny coefficient and a fractal exponent. The strongest features of the model are related to its simplicity and its capability to describe measured permeability values of different non-granular porous media better than other models. Citation: Costa, A. (2006), Permeability-porosity relationship: A reexamination of the Kozeny-Carman equation based on a fractal pore-space geometry assumption, Geophys. Res. Lett., 33, L02318, doi:10.1029/2005GL025134. [2] Estimation of permeability is of pivotal importance for the description of different physical processes, such as hydrocarbon recovery, fluid circulation in geothermal systems and degassing from vesiculating magmas. Mainly due to the intricate geometry of the connected pore space and to the complexity of porous media, it has been very difficult to formulate satisfactory theoretical models for permeability. One of the most largely used methods remains the KozenyCarman approach. [3] In this study we briefly review the Kozeny-Carman model. Then, using the hypothesis of a fractal pore-space geometry and the empirically based Archie law, we reformulate that model without introducing the concept of hydraulic radius and obtain a new simple permeabilityporosity equation. As an application, we used the obtained equation to predict permeability of fiber mat systems and of vesicular rocks.

https://agupubs.onlinelibrary.wiley.com/doi/epdf/10.1029/2005GL025134

Permeability-porosity relationship: a reexamination of the Kozeny-Carman equation based on a fractal pore-space geometry assumption

Heterogeneity can be dealt with by defining homogeneous equivalent properties, known as averaging, or by trying to describe the spatial variability of the rock properties from geologic observations and local measurements. The techniques available for these descriptions are mostly continuous Geostatistical models, or discontinuous facies models such as the Boolean, Indicator or Gaussian-Threshold models and the Markov chain model. These facies models are better suited to treating issues of rock strata connectivity, e.g. buried high permeability channels or low permeability barriers, which greatly affect flow and, above all, transport in aquifers. Genetic models provide new ways to incorporate more geology into the facies description, an approach that has been well developed in the oil industry, but not enough in hydrogeology. The conclusion is that future work should be focused on improving the facies models, comparing them, and designing new in situ testing procedures (including geophysics) that would help identify the facies geometry and properties. A world-wide catalog of aquifer facies geometry and properties, which could combine site genesis and description with methods used to assess the system, would be of great value for practical applications.

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Dealing with spatial heterogeneity

Numerical models of complex Earth systems serve two important purposes First, they embody quantitative hypotheses about those systems and thus help researchers develop insight and generate testable predictions Second, in a more pragmatic context, numerical models are often called upon as quantitative decision-support tools In geomorphology, mathematical and numerical models provide a crucial link between small-scale, measurable processes and their long-term geomorphic implications In recent years, several models have been developed that simulate the structure and evolution of three-dimensional fluvial terrain as a consequence of different process “laws” (eg, Willgoose et al, 1991a; Beaumont et al, 1992; Chase, 1992; Anderson, 1994; Howard, 1994; Tucker and Slingerland, 1994; Moglen and Bras, 1995) By providing the much-needed connection between measurable processes and the dynamics of long-term landscape evolution that these processes drive, mathematical landscape models have posed challenging new hypotheses and have provided the guiding impetus behind new quantitative field studies and Digital Elevation Model (DEM) -based analyses of terrain (eg, Snyder et al, 2000) The current generation of models, however, shares a number of important limitations Most models rely on a highly simplified representation of drainage basin hydrology, treating climate through a simple “perpetual runoff” formulation

The Channel-Hillslope Integrated Landscape Development Model (CHILD)

The relationship between water content and water potential for a soil is termed its water retention curve. This basic hydraulic property is closely related to the soil pore size distribution, for which it serves as a conventional method of measurement. In this paper a general model of the water retention curve is derived for soils whose pore size distribution is fractal in the sense of the Mandelbrot number-size distribution. This model, which contains two adjustable parameters (the fractal dimension and the upper limiting value of the fractal porosity) is shown to include other fractal approaches to the water retention curve as special cases. Application of the general model to a number of published data sets covering a broad range of soil texture indicated that unique, independent values of the two adjustable parameters may be difficult to obtain by statistical analysis of water retention data for a given soil. Discrimination among different fractal approaches thus will require water retention data of high density and precision.

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Models of the water retention curve for soils with a fractal pore size distribution

To study relationships between soil hydraulic properties and soil structural properties, a computer micro model of soil is constructed. We present first a general method of building a two-dimensional porous structure, including both pores and particles, with different levels of aggregation resulting from a fragmentation process. A fractal structure is obtained when self similarity is imposed over the successive scales of fragmentation. Emphasis is put upon the modeling of the retention curve. A classical capillary model and methods taken from percolation theory enable us to simulate qualitatively the primaiy and secondary loops of this hysteretic curve. In the fractal case, theoretical analytical expressions proposed for adjusting retention data are tested. The unsaturated hydraulic conductivity is also calculated on the same simulated soil by analogy with an electrical network. The soil structures are deformable and simulation proves to be a useful tool to investigate the behavior of swelling soils. , I- .

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Computer construction of fractal soil structures: Simulation of their hydraulic and shrinkage properties

A numerical model presented here develops a three-dimensional image of alluvial media on an elementary scale significant for groundwater flow modelling. The model was tested on the alluvial plain of the Rhone River (France), on a scale of several kilometres and, from geomorphological observations and dating, reproduced the construction of this alluvial plain from ≈15 000 years BP to the present. The history of the alluvial plain during the Late Glacial and Holocene periods is summarized. Through most of this time, the River Rhone has maintained a braided pattern, with the exception of two incising phases with a meander pattern. The model does not use any physically based equations or water representation. The main processes governing the construction of the plain are modelled by simple rules chosen according to geometrical or empirical laws taken from the literature or as modelling assumptions. Using multi-agent concepts of distribution and interaction of elementary entities, these sedimentary rules are applied to ‘sediment’ entities or to conceptual ‘erosion’ entities that simulate local deposition and erosion of sediments. The sedimentation model reproduces the various climatic periods during which the sediments were deposited by simulating genetic periods and associated modelled processes. For each period, the model was constrained by quantitative field data such as altitude of ancient channels and deposits or thickness of sediments. The general geometry of the alluvial deposits was satisfactorily reproduced. During the simulation, characteristic large-scale features emerge despite the use of local rules. The model results are discussed with reference to other approaches, such as geostatistical or Boolean models, and the applicability of the model to other less documented alluvial plains is outlined.

Modelling of the construction of the Rhône alluvial plain since 15 000 years BP

This paper reports the development and test, at the scale of 1 m 2 , of an event-based model that aims at simulating the influence of a spatial distribution of large circular macropores on surface runoff. The main originality of this model is that it focuses on the way macropores are supplied with water at the soil surface, by coupling an original model for water interception by individual macropores to a high-resolution spatialized overland flow model. A three-step evaluation of the model was carried out, involving (1) an experimental test of the model for water interception by macropores; (2) a sensitivity analysis of the model to time and space discretization; and (3) a comparison between numerical and field results in the case of runoff on a crusted soil surface with a population of large macropores made by termites in the Sahel. The model was found to accurately simulate the effect of a spatial distribution of large macropores on runoff, and it showed that small heterogeneities, like macropores or areas where a crust has been destroyed, which cover a very limited proportion of the soil surface, can have a high impact on runoff.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2001WR000337

A model for simulating the influence of a spatial distribution of large circular macropores on surface runoff

This article proposes a multi-agent approach to modelling the genesis of alluvial sediments. The aim is to generate a set of sedimentary structures such as channels, point-bars and oxbow lakes by means of sedimentary process simulations. These structures will later be used to study groundwater flow. The major deposition-erosion processes are represented in an approximate and stochastic manner. The behaviour of sedimentary entities is defined by empirical rules derived from the local geometry of the flume. The emphasis of this paper is on the capacity of the model to reproduce stream evolution. The model was tested on the West Fork White River (Indiana), and shows the main trend in the evolution of a meandering system despite the simplicity of imposed rules. Expected future developments of this approach are outlined.

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Edith Perrier

Papers

Models of the water retention curve for soils with a fractal pore size distribution

Computer construction of fractal soil structures: Simulation of their hydraulic and shrinkage properties

Modelling of the construction of the Rhône alluvial plain since 15 000 years BP

A model for simulating the influence of a spatial distribution of large circular macropores on surface runoff

Sur une nouvelle approche de modélisation de la mise en place des sédiments dans une plaine alluviale pour en représenter l'hétérogénéité