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Applications of graph theory have proliferated across the academic spectrum in recent years. Whereas geosciences and landscape ecology have made rich use of graph theory, its use seems limited in physical geography, and particularly in geomorphology. Common applications of graph theory analyses of connectivity, path or transport efficiencies, subnetworks, network structure, system behaviour and dynamics, and network optimization or engineering all have uses or potential uses in geomorphology and closely related fields. In this paper, we give a short introduction to graph theory and review previous geomorphological applications or works in related fields that have been particularly influential. Network-like geomorphic systems can be classified into nonspatial or spatially implicit system components linked by statistical/causal relationships and spatial units linked by some spatial relationship, for example by fluxes of matter and/or energy. We argue that, if geomorphic system properties and behaviour (e.g., complexity, sensitivity, synchronisability, historical contingency, connectivity etc.) depend on system structure and if graph theory is able to quantitatively describe the configuration of system components, then graph theory should provide us with tools that help in quantifying system properties and in inferring system behaviour. (C) 2015 Elsevier B.V. All rights reserved.
To support scientifically sound water management in dryland environments a modelling system has been developed for the quantitative assessment of water and sediment fluxes in catchments, transport in the river system, and retention in reservoirs. The spatial scale of interest is the mesoscale because this is the scale most relevant for management of water and land resources.
This modelling system comprises process-oriented hydrological components tailored for dryland characteristics coupled with components comprising hillslope erosion, sediment transport and reservoir deposition processes. The spatial discretization is hierarchically designed according to a multi-scale concept to account for particular relevant process scales. The non-linear and partly intermittent run-off generation and sediment dynamics are dealt with by accounting for connectivity phenomena at the intersections of landscape compartments. The modelling system has been developed by means of data from nested research catchments in NE-Spain and in NE-Brazil.
In the semi-arid NE of Brazil sediment retention along the topography is the main process for sediment retention at all scales, i.e. the sediment delivery is transport limited. This kind of deposition retains roughly 50 to 60 % of eroded sediment, maintaining a similar deposition proportion in all spatial scales investigated. On the other hand, the sediment retained in reservoirs is clearly related to the scale, increasing with catchment area. With increasing area, there are more reservoirs, increasing the possibility of deposition. Furthermore, the area increase also promotes an increase in flow volume, favouring the construction of larger reservoirs, which generally overflow less frequently and retain higher sediment fractions. The second example comprises a highly dynamic Mediterranean catchment in NE-Spain with nested sub-catchments and reveals the full dynamics of hydrological, erosion and deposition features. The run-off modelling performed well with only some overestimation during low-flow periods due to the neglect of water losses along the river. The simulated peaks in sediment flux are reproduced well, while low-flow sediment transport is less well captured, due to the disregard of sediment remobilization in the riverbed during low flow.
This combined observation and modelling study deepened the understanding of hydro-sedimentological systems characterized by flashy run-off generation and by erosion and sediment transport pulses through the different landscape compartments. The connectivity between the different landscape compartments plays a very relevant role, regarding both the total mass of water and sediment transport and the transport time through the catchment.
In present-day land and marine controlled-source electromagnetic (CSEM) surveys, electromagnetic fields are commonly generated using wires that are hundreds of metres long. Nevertheless, simulations of CSEM data often approximate these sources as point dipoles. Although this is justified for sufficiently large source-receiver distances, many real surveys include frequencies and distances at which the dipole approximation is inaccurate. For 1D layered media, electromagnetic (EM) fields for point dipole sources can be computed using well-known quasi-analytical solutions and fields for sources of finite length can be synthesized by superposing point dipole fields. However, the calculation of numerous point dipole fields is computationally expensive, requiring a large number of numerical integral evaluations. We combine a more efficient representation of finite-length sources in terms of components related to the wire and its end points with very general expressions for EM fields in 1D layered media. We thus obtain a formulation that requires fewer numerical integrations than the superposition of dipole fields, permits source and receiver placement at any depth within the layer stack and can also easily be integrated into 3D modelling algorithms. Complex source geometries, such as wires bent due to surface obstructions, can be simulated by segmenting the wire and computing the responses for each segment separately. We first describe our finite-length wire expressions and then present 1D and 3D examples of EM fields due to finite-length sources for typical land and marine survey geometries and discuss differences to point dipole fields.