Alessandro Marani

Energy Dissipation, Runoff Production, and the Three-Dimensional Structure of River Basins

Three principles of optimal energy expenditure are used to derive the most important structural characteristics observed in drainage networks: (1) the principle of minimum energy expenditure in any link of the network, (2) the principle of equal energy expenditure per unit area of channel anywhere in the network, and (3) the principle of minimum total energy expenditure in the network as a whole. Their joint application results in a unified picture of the most important empirical facts which have been observed in the dynamics of the network and its three-dimensional structure. They also link the process of runoff production in the basin with the characteristics of the network.

MINIMUM ENERGY AND FRACTAL STRUCTURES OF DRAINAGE NETWORKS

This paper explores the similarities of digital elevation maps (DEMs) of natural river basins and optimal channel network (OCN) configurations obtained minimizing the total rate of energy expenditure in the system as a whole and in its parts. Striking similarities are observed for natural and optimal networks in their fractal aggregation structure and in certain multifractal structures found to be characteristic of river basins. Our results suggest, upon critical assessment of the reliability of the identification of the attractor of the underlying dynamics implied by our optimality concepts, that fractal structures are indeed possibly a product of least energy dissipation. Power laws emerging in the description of the distribution of aggregated quantities from both DEMs and OCNs suggest a link with the framework of self-organized criticality in the dynamics of natural channel network formation. Also, the geomorphological description of OCNs reveals surprising analogies with well-known empirical or experimental results. A comparison of Peanos basins with OCNs suggests that nature seems to reject the type of strict self-similarity exhibited by Peanos construct in favor of different shapes implying statistical self-similarity not only because of chance acting through random conditions but also because of necessity as reflected by least energy expenditure considerations.

A Note on Fractal Channel Networks

This paper studies the relation between the structure of river networks and the features of their geomorphologic hydrologic response. A mathematical formulation of connectivity of a drainage network is proposed to relate contributing areas and the network geometry. In view of the connectivity conjecture, Hortons bifurcation ratio R(B) tends, for high values of Strahlers order OMEGA of the basin, to the area ratio R(A), and Hortons length ratio R(L) equals, in the limit, the single-order contributing area ratio R(a). The relevance of these arguments is examined by reference to data from real basins. Well-known empirical results from the geomorphological literature (Meltons law, Hacks relation, Moons conjecture) are viewed as a consequence of connectivity. It is found that in Hortonian networks the time evolution of contributing areas exhibits a multifractal behavior generated by a multiplicative process of parameter 1/R(B). The application of the method of the most probable distribution in view of connectivity contributes new inroads toward a general formulation of the geomorphologic unit hydrograph, in particular generalizing its width function formulation. A quantitative example of multifractal hydrologic response of idealized networks based on Peanos construct (for which R(B) = R(A) = 4, R(L) = 2) closes the paper.

Fractal Structures as Least Energy Patterns - the Case of River Networks

Natural drainage networks, like river basins, exhibit fractal and multifractal properties. This work shows that these properties evolve from arbitrary initial conditions by minimizing the local and global rates of energy expenditure in the system. This suggests that many fractal structures may arise as a natural consequence of least energy dissipation requirements.

Hyperspectral remote sensing of salt marsh vegetation, morphology and soil topography

Abstract The present paper deals with the relationship between vegetation patterns and salt marsh morphology in the Venice lagoon and with the use of remote sensing to infer salt marsh morphologic characteristics from vegetation mapping. Field measurements indicate that salt marsh vegetation species (halophytes) are reliable indicators of ground elevation and live within typical elevation ranges characterised by standard deviations of less than 5 cm. A model is then developed which uses vegetation as a morphological indicator of soil topography to estimate ground elevation from fractional cover values of each vegetation type. The use of data from an airborne remote hyperspectral sensor is presented as a means of discriminating between different salt marsh vegetation communities. Vegetation maps obtained from unmixing techniques have then been used to produce digital elevation maps (DEM) of salt marsh areas. The DEM based on halophytes cover estimates and extracted from high spatial and spectral resolution data allows a high estimation accuracy, with an error standard deviation of a few centimetres in the considered study area within the Venice lagoon. The accuracy and resolution attainable through this method are comparable and often superior to those obtained through state of the art laser altimetry.

Salt Marsh Vegetation Radiometry: Data Analysis and Scaling

This paper aims to determine the optimal procedure for classifying salt marsh vegetation from hyperspectral data and to establish relationships between airborne and ground measurement properties. The study is carried out on data collected in the Lagoon of Venice (Italy). Spectral angle mapping proves to be a reliable classification procedure, and spectral differentiation is seen to improve separability of vegetation types. Further, scaling relationships are derived to link the value of the variance of data aggregated at different scales, allowing the determination of data variability at coarse resolution on the basis of ground measurements. The comparison between the theoretical, up-scaled, values of standard deviation and those computed from remote sensing data shows a good agreement supporting the derived relations. Finally, a scaling relationship is established for spectral angles, which may be useful in determining an optimal threshold angle from ground data.

A study on solute NO3-N transport in the hydrologic response by an MRF model

Abstract The results of field studies on solute transport over basin-scale distances are analyzed using the Mass-Response Function (MRF) model and its generalization proposed in this paper. The generalization proposed concerns reversible production/removal processes of solute. It is assumed that equilibrium concentrations in the mobile phase are proportional to the instantaneous fraction of solute mass sorbed in the fixed phase. Such assumption, which is thought of as representative of large-scale transport volumes, is derived from the theory of two-component convection-dispersion in soils and is aimed at endowing the model with predictive characters. It is seen that the use of generalized MRFs poses serious computational problems, which are partly related to the conditional behavior of the instantaneous response of solutes on the impulse time. The conditionality of the transfer functions on the injection time is related in a rational manner to the combined effects of convection-dispersion during the hydrological cycle and of sorption processes that occur between fixed and mobile phases. The relevance of the problem addressed lies in the ability of solute generation and movement over large scales to predict the dominant modes of the phenomena on the basis of the knowledge of parameters with a clear physical significance. In this paper, this ability is tested with reference to suitable field experiments. The results show that a number of characteristic residence times are the most important properties for basin-scale transport processes and for the evolution of resident and flux solute concentrations. An MRF model of solute NO 3 N concentrations in river waters is constructed, the architecture of which is tailored to solute generation and transport processes occurring in a gauged watershed. The theoretical results are compared with the experimental observations and are found to agree with them well. It is argued that MRFs are rational models of the complex chain of events occurring in large-sclae solute sorption and transport, and may be validly employed for quantitative studies of environmental impacts due to the release of chemical species in surface or subsurface waters.

Patterns in tidal environments: salt-marsh channel networks and vegetation

Salt marshes in tidal environments are characterised by complex patterns both in their geomorphic and ecological features. Such patterns arise through the elaboration of a network structure driven by the tidal forcing and through the interaction between hydrodynamical, geophysical and ecological components (e.g. microphytobenthos and vegetation). This contribution introduces observations of tidal environments from remote sensing and ancillary data collected in the field. In particular, CASI airborne data and Quick-Bird satellite data collected on the lagoon of Venice (Italy) have been acquired within the European RTD project TIDE. The remotely sensed data are used to map salt marsh vegetation and channel morphology and to study their spatial structure.

Runoff and Receiving Water Models for NPS Discharge into the Venice Lagoon

Abstract The paper deals with selection and application of runoff and receiving water models for nonpoint source pollution (NPSP) of the Venice Lagoon (Italy). Annual average nutrient loadings (either in dissolved or solid-phase form) are recognized together with source areas and spatial location of delivery. Novel theoretical grounds for mathematical modeling aimed at simulation of water quality within the Lagoon are presented. The approach, which focuses on long-term NPS impacts, yields a critical discussion concerning the features of NPSP models suitable to comprehensive simulations. The models consist of multiple-box mass balances of water and pollutants at nonconstant flow rates portraying the tidal hydraulic behavior of the water body. Spectral analyses of calculated and measured tidal elevation data have been performed and comparison of the hydraulic regime of the proposed model with transfer functions of static models (successfully used to evaluate water volumes exchanged by the sea with lagoon) is carried out. The nonnegligible effects of propagation are also discussed and modeled. The chemical behavior of the storages in Lagoon is assimilated to that of a continuous stirred tank reactor. Sample runs of the model for pollutant propagation throucfi the multiple-box net are also presented. Limits and validity of the modeling approaches, a review of noteworthy references and comparison with features of analogous models available in the literature are discussed.

The Structure of Mass-Response Functions of Dissolved Species in Hydrologic Transport Volumes

Abstract Field solute transport of reactive solute species is investigated through a class of stochastic models termed as mass-response functions, which constitute a new and interesting way of solving large scale transport problems. Upon brief description of the major theoretical constraints and strengths implied by the computational schemes, a complete modelling example is given with reference to basinwide circulation of solutes. This is justified by the possibility of comparing the theoretical results with data collected in an experimental watershed in Japan yielding an unique reference for this approach for the accuracy of the experimental procedures and the refinement of the sampling procedures.