A non-parametric bivariate entropy estimator for spatial processes

In this paper, entropy is presented as an alternative measure to characterize the bivariate distribution of a stationary spatial process. This non-parametric estimator attempts to quantify the concept of spatial ordering, and it provides a measure of how Gaussian the experimental bivariate distribution is. The concept of entropy is explained and the classical definition presented, along with some important results. In particular, the reader is reminded that, for a known mean and covariance, the bivariate Gaussian distribution maximizes entropy. A relative entropy estimator is introduced in order to measure departure of an experimental bivariate distribution from the bivariate Gaussian. Two case studies are presented as examples.     

The Italian Astrophysical Observatory in Antarctica: OASI

OASI (Infrared and Sub-mm Antarctic Observatory) is the first large telescope permanently installed in Antarctica. It is located close to the Italian Base in Antarctica (Terra Nova Bay Station, latitude: 74.39 S, longitude: 164.09 E). The OASI first light was received in December 1990 when the wobbling secondary mirror was mounted. The telescope is planned to be an open facility which can operate in the wavelengths range between 350 m and 3mm. The sky coverage from OASI goes down to a declination of about-35° for a 24 hours/day observing time.     

Geochemical features of rocks,stream sediments,and soils of the Fiume Grande Valley (Calabria,Italy)

The role of both natural weathering and anthropogenic pollution in controlling the distribution of major oxides and several trace elements in soils, stream sediments, and rocks of the Fiume Grande catchment was evaluated. The contents of major oxides and trace elements in soils appear to be governed by weathering and pedogenetic processes, although the use of fertilizers in agriculture could also partly affect K₂O and P₂O₅ contents. Stream sediments have concentrations of major oxides (except CaO) very similar to soils, as relevant amounts of soil materials are supplied to the stream channels by erosive phenomena. In contrast, stream sediments have concentrations of Cr, Co, Ni, Zn, As, and Pb significantly higher than those of soils, probably due to different conditions and rates of mobility of these elements within the three considered matrices and/or disposal of wastes in the drainage network. Comparison of the concentrations of PHEs in soils with the maximum admissible contents established by the Italian law shows that these limits are too restrictive in some cases and too permissive in other ones. The approach of setting these limits with no consideration for the local geological–geochemical framework may lead to improper management of the territory and its resources. Electronic supplementary material Supplementary material is available in the online version of this article at and is accessible for authorized users.     

Impact of different regression frameworks on the estimation of the scaling properties of radar rainfall

Rainfall is characterized by high variability both in space and time. Despite continuous technological progress, the available instruments that are used to measure rainfall across several spatio-temporal scales remain inaccurate. To remedy this situation, scaling relationships of spatial rainfall offer the potential to link the observed or predicted precipitation quantities at one scale to those of interest at other scales. This paper focuses on the estimation of the spatial rainfall scaling functions. Standard scaling analysis constructed by means of the ordinary least squares method often violates such basic assumptions implicit in its use and interpretation as homoschedasticity, independence, and normality of the errors. Consequently, the authors consider alternative regression frameworks i.e. bootstrapping regression, semi parametric linear model, and multilevel normal linear model to show how these different approaches exert a significant impact on the multifractal analysis of radar rainfall. In addition, the uncertainties associated with the construction of the scaling function due solely to the regression procedure are quantified. The radar data come from the polarimetric C-band weather radar located in Rome, Italy, and the scaling properties are computed for a square domain centred on the radar site with a side length of 128 km and a finest resolution of 1 km².     

Genesis and evolution of a curved mountain front: paleomagnetic and geological evidence from the Gran Sasso range (central Apennines, Italy)

The Gran Sasso range is a striking salient formed by two roughly rectilinear E–W and N–S limbs. In the past 90° counterclockwise (CCW) rotations from the eastern Gran Sasso were reported [Tectonophysics 215 (1992) 335], suggesting west–east increase of rotation-related northward shortening along the E–W limb. In this paper, we report on paleomagnetic data from Meso-Cenozoic sedimentary dykes and strata cropping out at Corno Grande (central part of the E–W Gran Sasso limb), the highest summit of the Apennine belt. Predominant northwestward paleomagnetic declinations (in the normal polarity state) from both sedimentary dykes and strata are observed. When compared to the expected declination values for the Adriatic foreland, our data document no thrusting-related rotation at Corno Grande. The overall paleomagnetic data set coupled with the available geological information shows that the Gran Sasso arc is in fact a composite structure, formed by an unrotated-low shortening western (E–W trending) limb and a strongly CCW rotated eastern salient. Late Messinian and post-early Pliocene shortening episodes documented along the Gran Sasso front indicate that belt building and arc formation occurred during two distinct episodes. We suggest that the southern part of a late Messinian N–S front was reactivated during early–middle Pliocene time, forming a tight range salient due to CCW rotations and differential along-front shortening rates. The formation of a northward displacing bulge in an overall NW–SE chain is likely a consequence of the collision between the Latium-Abruzzi and Apulian carbonate platforms during northeastward propagation of the Apennine wedge, inducing lateral northward extrusion of Latium-Abruzzi carbonates towards ductile basinal sediment areas.     

Modelling the evolution of the space debris population

The current space activities are already disturbed and jeopardized by the growing number of orbiting debris. Those planned for the near future, such as the launch of large satellite constellations and the construction of the international space station, are even more sensitive to the evolution of the space environment. Therefore, a clear picture of the present situation in Earth orbit and its future evolution is needed. In this paper we describe in some details the work we have carried out on this problem in the last several years. Starting from the current population and simulating a reasonable scenario for the space activities in the next decades, we have obtained plausible quantitative models of the possible future space environment. We summarize some results concerning the effectiveness of possible mitigation measures and assess the robustness of these results, by checking how sensitively they depend upon the initial conditions and the choice of some model parameters. We also analyze the effect of the launch of a number of satellite constellations, showing the importance of the adoption of some debris prevention measures in their launch policies. Finally, we study the possible problems arising from the recent discovery of a new family of debris composed by drops of NaK coolant, that leaked outside the nuclear reactors of the Soviet RORSAT-class satellites. Our preliminary results indicate that these drops are going to cause an increasing number of small-scale, possible satellite-damaging impacts but, due to their small size, no additional catastrophic collisions; therefore their influence on the long-term evolution of the overall debris population is limited.     

Characterization of natural colloids from a river and spring in a karstic basin

 Colloids are known to transport contaminants over long distances in natural media. Despite this potentially harmful effect, very few studies have been undertaken in subsurface aquifers. This paper presents the first results of a study of natural colloids and particles in a karstic aquifer. The site was chosen for its coverage by clay layers and peat which deliver various and numerous particle types in water. The methodological part describes three methods used for size determination and sample fractionation of surface water and spring water. These methods have been adapted for the treatment of multiple samples due to the rapid discharge variation typical of karstic aquifers. The analysis of many particle size distributions (PSD) shows that they can be described by a Pareto law. The variation of the slope of the PSD at the spring is mainly dependent on discharge. This behavior is interpreted as a washing of the karstic drains during the first phase of high flow events. Fractionation of the samples allowed application of various characterization techniques to particle size classes. X-ray diffraction (XRD) patterns showed that most of the mineral particles originated from Quaternary deposits and limestones. However the use of scanning electron micrsocopy with energy-dispersive spectrometer (SEM-EDS) detailed the composition of individual particles and revealed particles not found by XRD. These techniques also showed the high complexity of the natural particles and the important place of coprecipitation in their formation. Consequences on the fluxes of particulate matter and its potential role as a carrier of contaminants are discussed. Received: 28 October 1996 · Accepted: 7 July 1997     

Note on simulating the size distribution of glacial cirques

The glacial cirques of a mountainous region usually have comparable size. Cirque widths between 400 m and 800 m are relatively common, whereas very large and very small cirques are infrequent. Although the presence of an upper limit is probably a result of the limited time available since the epoch of formation, the absence of very small cirques is more problematic. Simple statistical arguments suggest that this feature can be explained if the formation of cirques is very selective and localized in relatively small areas of the landscape. Copyright © 2002 John Wiley & Sons, Ltd.