Structures in the phase space of a four dimensional symplectic map

We numerically investigate the projections of non periodic orbits in a 4-dimensional (4-D) symplectic map composed of two coupled 2-dimensional (2-D) maps. We describe in detail the structures that are produced in different planes of projection and we find how the morphology of the 4-D orbits is influenced by the features of the 2-D maps as the coupling parameter increases. We give an empirical law that describes this influence.     

Frequency analysis of a dynamical system

Frequency analysis is a new method for analyzing the stability of orbits in a conservative dynamical system. It was first devised in order to study the stability of the solar system (Laskar, Icarus, 88, 1990). It is a powerful method for analyzing weakly chaotic motion in hamiltonian systems or symplectic maps. For regular motions, it yields an analytical representation of the solutions. In cases of 2 degrees of freedom system with monotonous torsion, precise numerical criterions for the destruction of KAM tori can be found. For a 4D symplectic map, plotting the frequency map in the frequency plane provides a clear representation of the global dynamics and describes the actual Arnold web of the system.     

Hydrogeochemical investigations and groundwater provinces of the Friuli Venezia Giulia Plain aquifers,northeastern Italy

Water resources are a key factor, particularly for the planning of the sustainable regional development of agriculture, as well as for socio-economic development in general. A hydrochemical investigation was conducted in the Friuli Venezia Giulia aquifer systems to identify groundwater evolution, recharge and extent of pollution. Temperature, pH, electric conductivity, total dissolved solids, alkalinity, total hardness, SAR, Ca²⁺, Na⁺, K⁺, Mg²⁺, Cl⁻, SO₄ ²⁻, NO₃ ⁻, HCO₃ ⁻ _, water quality and type, saturation indexes and the environmental stable isotope δ¹⁸O were determined in 149 sampling stations. The pattern of geochemical and oxygen stable isotope variations suggests that the sub-surface groundwater (from phreatic and shallow confined aquifers) is being recharged by modern precipitations and local river infiltrations. Four hydrogeological provinces have been recognised and mapped in the Friuli Venezia Giulia Plain having similar geochemical signatures. These provinces have different degrees of vulnerability to contamination. The deep confined groundwater samples are significantly less impacted by surface activities; and it appears that these important water resources have very low recharge rates and would, therefore, be severely impacted by overabstraction.     

Evaluation of approaches to calculate debris-flow parameters for hazard assessment

Many different runout prediction methods can be applied to estimate the mobility of future debris flows during hazard assessment. The present article reviews the empirical, analytical, simple flow routing and numerical techniques. All these techniques were applied to back-calculate a debris flow, which occurred in 1982 at La Guingueta catchment, in the Eastern Pyrenees. A sensitivity analysis of input parameters was carried out, while special attention was paid to the influence of rheological parameters. We used the Voellmy fluid rheology for our analytical and numerical modelling, since this flow resistance law coincided best with field observations. The simulation results indicated that the “basal” friction coefficients rather affect the runout distance, while the “turbulence” terms mainly influence flow velocity. A comparison of the velocity computed on the fan showed that the analytical model calculated values similar to the numerical ones. The values of our rheological parameters calibrated at La Guingueta agree with data back-calculated for other debris flows. Empirical relationships represent another method to estimate total runout distance. The results confirmed that they contain an important uncertainty and they are strictly valid only for the conditions, which were the basis for their development. With regards to the simple flow routing algorithm, this methods could satisfactorily simulate the total area affected by the 1982 debris flow, but it was not able to directly calculate total runout distance and velocity. Finally, a suggestion on how different runout prediction methods can be applied to generate debris-flow hazard maps is presented. Taking into account the definition of hazard and intensity, the best choice would be to divide the resulting hazard maps into two types: “final hazard maps” and “preliminary hazard maps”. Only the use of numerical models provided final hazard maps, because they could incorporate different event magnitudes and they supplied output-values for intensity calculation. In contrast, empirical relationships and flow routing algorithms, or a combination of both, could be applied to create preliminary hazard maps. The present study only focussed on runout prediction methods. Other necessary tasks to complete the hazard assessment can be looked up in the “Guidelines for landslide susceptibility, hazard and risk zoning” included in this Special Issue.     

Risk assessment strategies for the reactivation of earth flows in the Northern Apennines (Italy)

The aim of this paper is to analyze the reactivation mechanism of ancient earth flows, with a view to gleaning information that can subsequently be utilized to formulate a risk-reduction strategy. All considerations made herein are the result of direct experience and observation of actual events which have occurred over the past few decades in the Northern Apennines. Particular attention has been paid to the analysis of the evolution of landslides during actual reactivation, acknowledging a typical, recurring succession of events that precede the failure of the slope. The hazard assessment of these large landslide bodies, which are of slope scale, constitutes a thorny problem, especially in view of the inapplicability of traditional deterministic models such as limit equilibrium stability analysis. Nevertheless, a site-specific assessment of probability of reactivation of these large and ancient earth flows is fundamental to effective land-use planning.     

Landslide susceptibility and hazard mapping in Australia for land-use planning — with reference to challenges in metropolitan suburbia

This paper provides an overview of the history and current status of landslide susceptibility and hazard mapping for land-use zoning in Australia. It also describes a case study of landslide hazard mapping in a medium density, coastal, suburban residential area of metropolitan Sydney, New South Wales, Australia, with relatively steep terrain. Issues covered include identification and mapping of existing and potential landslides, and susceptibility and hazard zoning for regulatory management and land-use planning. The method involves application of the principles contained within the AGS (2000) guideline, and as updated by the AGS (2007 a,b,c,d,e) suite of guidelines.     

Development and morphometry of sinkholes in coastal plains of Apulia, southern Italy. Preliminary sinkhole susceptibility assessment

Evolution of coastlines in karst areas may be strongly controlled by dissolution processes which favour the development of surface and subsurface landforms. The generation of caves in these environments is commonly favoured by the mixing between fresh and brackish waters. The sinkholes resulting from the upward propagation of the caves may interfere with the anthropogenic environment and cause damage to human elements (property and activities). To highlight the often underestimated importance of karst phenomena in coastal areas, we have analyzed a coastal stretch of Apulia, in southern Italy. The study area, covering an extension of about 6 km², is situated in the Ionian coast, and presents several interesting karst landforms that are generally connected to caves. Tens of sinkholes were mapped through field surveys, multi-year aerial-photographs (dating back to the 1940s) and archival research. We have performed a morphometric analysis of the sinkholes. The analysis describes the main parameters of the sinkholes (area, length, width, and depth), and the control exerted by the main discontinuity systems in the area. The detrimental effects derived from interaction between human environment and these karst landforms is also under consideration. A sinkhole susceptibility map, which may provide useful information for planners, developers and the insurance industry has eventually been produced through application of a decision tree model.     

National flood discharge mapping in Austria

This article presents the approach and the results of a study in which 30, 100 and 200 year return period flood discharges were estimated for 26,000 km of Austrian streams. Three guiding principles were adopted: combination of automatic methods and manual assessments by hydrologists to allow speedy processing and account for the local hydrological situation; combination of various sources of information including flood peak samples, rainfall data, runoff coefficients and historical flood data; and involvement of the Hydrographic Services to increase the accuracy and enhance the acceptance of results. The flood discharges for ungauged catchments were estimated by the Top-kriging approach with manual adjustment to the local flood characteristics. The adopted combination approach proved to be very efficient both in terms of the project time required and in terms of the accuracy and acceptability of the estimated flood discharges of given return periods.     

Integrating Uncertainty Theories with GIS for Modeling Coastal Hazards of Climate Change

Prediction of coastal hazards due to climate change is fraught with uncertainty that stems from complexity of coastal systems, estimation of sea level rise, and limitation of available data. In-depth research on coastal modeling is hampered by lack of techniques for handling uncertainty, and the available commercial geographical information systems (GIS) packages have only limited capability of handling uncertain information. Therefore, integrating uncertainty theory with GIS is of practical and theoretical significance. This article presents a GIS-based model that integrates an existing predictive model using a differential approach, random simulation, and fuzzy set theory for predicting geomorphic hazards subject to uncertainty. Coastal hazard is modeled as the combined effects of sea-level induced recession and storm erosion, using grid modeling techniques. The method is described with a case study of Fingal Bay Beach, SE Australia, for which predicted responses to an IPCC standard sea-level rise of 0.86 m and superimposed storm erosion averaged 12 m and 90 m, respectively, with analysis of uncertainty yielding maximum of 52 m and 120 m, respectively. Paradoxically, output uncertainty reduces slightly with simulated increase in random error in the digital elevation model (DEM). This trend implies that the magnitude of modeled uncertainty is not necessarily increased with the uncertainties in the input parameters. Built as a generic tool, the model can be used not only to predict different scenarios of coastal hazard under uncertainties for coastal management, but is also applicable to other fields that involve predictive modeling under uncertainty.     

The fate of dumped sediments monitored by a high-resolution multibeam echosounder system,Weser Estuary,German Bight

With the development of high-resolution multibeam echosounder systems (MBES) for surveying shallow-water areas a new tool is available to monitor rapid changes in seabed morphology as, e.g., caused by the dumping of dredge spoil in coastal waters. In this study, four data sets of repeated bathymetric surveys with a MBES were processed and analyzed. The data were collected in a 1.94-km² dumping site in the outer Weser Estuary (German Bight). Between June and December 1998, 2.6 million m³ of dredged sediment were deposited there. The bathymetric maps generated in the course of this study reveal features such as subaqueous dunes, scour holes, and mounds of dumped dredge spoil. The mean water depth decreased by about 1 m during the dumping period. Furthermore, difference grids showing changes in sediment volume allowed a calculation of the sediment budget for the monitored area. After a time period of only 5 months, 0.5 million m³ of the originally dumped 2.6 million m³ of dredge spoil had already been removed from the dumping site.