Long-term density evolution through semi-analytical and differential algebra techniques

This paper introduces and combines for the first time two techniques to allow long-term density propagation in astrodynamics. First, we introduce an efficient method for the propagation of phase space densities based on differential algebra (DA) techniques. Second, this DA density propagator is used in combination with a DA implementation of the averaged orbital dynamics through semi-analytical methods. This approach combines the power of orbit averaging with the efficiency of DA techniques. While the DA-based method for the propagation of densities introduced in this paper is independent of the dynamical system under consideration, the particular combination of DA techniques with averaged equations of motion yields a fast and accurate technique to propagate large clouds of initial conditions and their associated probability density functions very efficiently for long time. This enables the study of the long-term behavior of particles subjected to the given dynamics. To demonstrate the effectiveness of the proposed approach, the evolution of a cloud of high area-to-mass objects in Medium Earth Orbit is reproduced considering the effects of solar radiation pressure, the Earth’s oblateness and luni-solar perturbations. The method can propagate 10,000 random fragments and their density for 1 year within a few seconds on a common desktop PC.     

Holocene climate changes in southern Greenland: evidence from lake sediments

A Holocene lake sediment record is presented from Lake N14 situated on Angissoq Island 15 km off the main coast of southern Greenland. The palaeoclimatic development has been interpreted on the basis of flux and percentage content of biogenic silica, clastic material, organic material and sulphur as well as sedimentation rate, moss content and magnetic susceptibility. A total of 43 radiocarbon dates has ensured a reliable chronology. It is argued that varying sediment composition mainly reflects changing precipitation. By analogy with the present meteorological conditions in southern Greenland, Holocene climate development is inferred. Between 11 550 and 9300 cal. yr BP temperature and precipitation increase markedly, but this period is climatically unstable. From 9300 yr BP conditions become more stable and a Holocene climatic optimum, characterised by warm and humid conditions, is observed from 8000 to 5000 cal. yr BP. From 4700 cal. yr BP the first signs of a climatic deterioration are observed, and from 3700 cal. yr BP the climate has become more dry and cold. Superimposed on the climatic long‐term trend is climate variability on a centennial time‐scale that increases in amplitude after 3700 cal. yr BP. A climatic scenario related to the strength and position of the Greenland high‐pressure cell and the Iceland low‐pressure cell is proposed to explain the Holocene centennial climate variability. A comparison of the Lake N14 record with a terrestrial as well as a marine record from the eastern North Atlantic Ocean suggests that the centennial climate variability was uniform over large areas at certain times. Copyright © 2004 John Wiley & Sons, Ltd.     

Approval of Wolves in Scandinavia: A Comparison Between Norway and Sweden

Based on Norwegian and Swedish representative national samples, and samples from areas with large mammalian carnivores present, we investigated whether well-known predictors for approval of wolves may explain between-country differences. Swedes were in general more positive than Norwegians were, while respondents in large carnivore areas, regardless of nationality, were less positive. The profile of those who approved wolf presence was the same in all samples. The difference between the samples was greater in Sweden, indicating that the relationship between urbanized and rural areas is more polarized in Sweden compared to Norway. We suggest this to be an effect of the fact that Norway’s large carnivore and agriculture policies favor the rural population, and of a higher degree of urbanization in Sweden. We recommend future studies to look into the different power relations between people living in urban and rural areas, comparing countries with different degree of urbanization.     

Cost-sensitive rainfall thresholds for shallow landslides

The risk management of rainfall-induced landslides requires reliable rainfall thresholds to issue early warning alerts. The practical application of these thresholds often leads to misclassifications, either false negative or false positive, which induce costs for the society. Since missed-alarm (false negative) and false-alarm (false positive) cost may be significantly different, it is necessary to find an optimal threshold that accounts for and minimises such costs, tuning the false-alarm and missed-alarm rates. In this paper, we propose a new methodology to develop cost-sensitive rainfall thresholds, and we also analyse several factors that produce uncertainty, such as the accuracy of rainfall intensity values at landslide location, the time of occurrence, the minimum rainfall amount to define the non-triggering event, and the variability of cost scenarios. Starting from a detailed mapping of landslides that occurred during five large-scale rainfall events in the Italian Central Alps, we first developed rainfall threshold curves with a ROC-based approach by using both rain gauge and bias-adjusted weather radar data. Then, based on a reference cost scenario in which we quantified several cost items for both missed alarms and false alarms, we developed cost-sensitive rainfall threshold curves by using cost-curve approach (Drummond and Holte 2000). Finally, we studied the sensitivity of cost items. The study confirms how important is the information regarding rainfall intensity at the landslide site for the development of rainfall thresholds. Although the use of bias-corrected radar strongly improves these values, a large uncertainty related to the exact time of landslide occurrence still remains, negatively affecting the analysis. Accounting for the different missed-alarm and false-alarm misclassification costs is important because different combinations of these costs make an increase or decrease of the rainfall thresholds convenient. In our reference cost scenario, the most convenient threshold is lower than ROC-based thresholds because it seeks to minimise the number of missed alarms, whereas the missed-alarm costs are almost seven times greater than false-alarm costs. However, for different cost scenarios, threshold may vary significantly, as much as half an order of magnitude.

     

Minimum/maximum autocorrelation factors applied to grade estimation

There are many situations in the mining industry where grade estimation of multiple correlated variables is required. The resulting model is expected to reproduce the data correlation, but there is no guarantee that the correlation observed among data will be reproduced by the model if the variables are independently estimated by kriging, and the correlation is not explicitly taken into account. The best geostatistical approach to address this estimation problem is to use co-kriging, which requires both cross and direct covariance modeling of all variables. However, the co-kriging method is labor-intensive when the problem involves more than three attributes. An alternative is to decorrelate the variables and estimate each one independently, using, for instance, the minimum/maximum autocorrelation factors (MAF) approach. This method involves the application of a linear transformation to the correlated variables, transforming the original data into a space where they are uncorrelated. The resulting transformed data can be individually estimated using kriging, avoiding the use of the linear model of coregionalization. Once the kriging has been performed, the MAF estimates are back-transformed to the original data space, re-establishing their correlation.The methodology is illustrated in a case study where there are two variables with correlation coefficient, ρ = ?0.98. The MAF transformation was applied in combination with ordinary kriging (herein denoted as KMAF). Co-kriging was performed to provide a benchmark for comparing the results obtained through KMAF. The results obtained by co-kriging and KMAF showed less than 1 % average deviation between the two block models.