Wavelets and the Generalization of the Variogram

The experimental variogram computed in the usual way by the method of moments and the Haar wavelet transform are similar in that they filter data and yield informative summaries that may be interpreted. The variogram filters out constant values; wavelets can filter variation at several spatial scales and thereby provide a richer repertoire for analysis and demand no assumptions other than that of finite variance. This paper compares the two functions, identifying that part of the Haar wavelet transform that gives it its advantages. It goes on to show that the generalized variogram of order k=1, 2, and 3 filters linear, quadratic, and cubic polynomials from the data, respectively, which correspond with more complex wavelets in Daubechies's family. The additional filter coefficients of the latter can reveal features of the data that are not evident in its usual form. Three examples in which data recorded at regular intervals on transects are analyzed illustrate the extended form of the variogram. The apparent periodicity of gilgais in Australia seems to be accentuated as filter coefficients are added, but otherwise the analysis provides no new insight. Analysis of hyerpsectral data with a strong linear trend showed that the wavelet-based variograms filtered it out. Adding filter coefficients in the analysis of the topsoil across the Jurassic scarplands of England changed the upper bound of the variogram; it then resembled the within-class variogram computed by the method of moments. To elucidate these results, we simulated several series of data to represent a random process with values fluctuating about a mean, data with long-range linear trend, data with local trend, and data with stepped transitions. The results suggest that the wavelet variogram can filter out the effects of long-range trend, but not local trend, and of transitions from one class to another, as across boundaries.     

The year-long unprecedented European heat and drought of 1540 – a worst case

The heat waves of 2003 in Western Europe and 2010 in Russia, commonly labelled as rare climatic anomalies outside of previous experience, are often taken as harbingers of more frequent extremes in the global warming-influenced future. However, a recent reconstruction of spring–summer temperatures for WE resulted in the likelihood of significantly higher temperatures in 1540. In order to check the plausibility of this result we investigated the severity of the 1540 drought by putting forward the argument of the known soil desiccation-temperature feedback. Based on more than 300 first-hand documentary weather report sources originating from an area of 2 to 3 million km², we show that Europe was affected by an unprecedented 11-month-long Megadrought. The estimated number of precipitation days and precipitation amount for Central and Western Europe in 1540 is significantly lower than the 100-year minima of the instrumental measurement period for spring, summer and autumn. This result is supported by independent documentary evidence about extremely low river flows and Europe-wide wild-, forest- and settlement fires. We found that an event of this severity cannot be simulated by state-of-the-art climate models.     

A two-dimensional model for a solar prominence: Effect of an external magnetic field

Using analytical approximations we study the effects of different external magnetic configurations on the half-width, mass, and internal magnetic structure of a quiescent solar prominence, modelled as a thin vertical sheet of cool plasma. Firstly, we build up a zeroth-order model and analyse the effects produced by a potential coronal field or a constant- force-free field. This model allows us to obtain the half-width and mass of the prominence for different values of the external field, pressure and shear angle. Secondly, the effects of these external magnetic configurations on a two-dimensional model proposed by Ballester and Priest (1987) are studied. The main effects are a change of the half-width with height, an increase of the mass, a decrease of the magnetic field strength with height and a change in the shape of the magnetic field lines.     

Lead distribution on a public shotgun range

. A detailed study has been made of the distribution of lead on a public shotgun range in the George Washington – Jefferson National Forests in southwestern Virginia. Sampling of more than 100 sites has yielded data on the distribution pattern of the lead shot. Since opening in 1993 through 2000, 11.1 metric tons (t) of lead have been accumulated over an area 220쑼 m (66,000 m²) with an average rate of accumulation of 1.4 t/year. More than 85% of the total dispersed lead lies scattered in the forest that surrounds the approximately 60Ꮔ-m cleared shooting surface. Lead is irregularly distributed because of the use of stationary targets and the general trajectory of launched clay targets. Maximum concentrations occur at distances of ~28, ~80, and ~180 m, and reach a maximum value of more than 5,000 g/m². Significant amounts of fine particulate lead, generated during shooting and as a result of impact occur close to the shooting box, but are absent at distances beyond 50 m.     

A multi-objective approach to the design of low thrust space trajectories using optimal control

In this article, we introduce a novel three-step approach for solving optimal control problems in space mission design. We demonstrate its potential by the example task of sending a group of spacecraft to a specific Earth L ₂ halo orbit. In each of the three steps we make use of recently developed optimization methods and the result of one step serves as input data for the subsequent one. Firstly, we perform a global and multi-objective optimization on a restricted class of control functions. The solutions of this problem are (Pareto-)optimal with respect to ΔV and flight time. Based on the solution set, a compromise trajectory can be chosen suited to the mission goals. In the second step, this selected trajectory serves as initial guess for a direct local optimization. We construct a trajectory using a more flexible control law and, hence, the obtained solutions are improved with respect to control effort. Finally, we consider the improved result as a reference trajectory for a formation flight task and compute trajectories for several spacecraft such that these arrive at the halo orbit in a prescribed relative configuration. The strong points of our three-step approach are that the challenging design of good initial guesses is handled numerically by the global optimization tool and afterwards, the last two steps only have to be performed for one reference trajectory.     

Midges of the genus Pseudodiamesa Goetghebuer (Diptera, Chironomidae): current knowledge and palaeoecological perspective

Larvae of the genus Pseudodiamesa Goetghebuer, which includes 12 described valid species and is divided by Makarchenko and Makarchenko (1999) into two species groups, Pseudodiamesa branickii group and Pseudodiamesa nivosa group, are widespread in lakes and running waters of cold, high-latitude and high-altitude areas of the Northern Hemisphere. Larval remains of the genus are often found in subfossil assemblages from these cold regions, but intra-genus morphotypes usually are not distinguished by palaeoecologists. Current knowledge of the ecology of the species indicates that the Pseudodiamesa nivosa group is more cold-adapted than the Pseudodiamesa branickii group and, therefore, these two intra-genus morphotypes cannot be amalgamated into a larger taxonomic unit without losing substantial information. Here we present the morphological characters of head capsules of Pseudodiamesa larvae attributed to the different species-group morphotypes, which are clearly visible in subfossil specimens. The information summarized in this paper will help provide more reliable chironomid-based palaeoclimatic inferences from lake sediment records covering colder phases through the late Quaternary in the Northern Hemisphere.     

How does taxonomic resolution affect chironomid-based temperature reconstruction?

The resolution achievable for chironomid identifications has increased in recent years because of significant improvements in taxonomic literature. However, high taxonomic resolution requires more training for analysts. Furthermore, with greater taxonomic resolution, misidentifications and the number of rare, poorly represented taxa in chironomid calibration datasets may increase. We assessed the effects of various levels of taxonomic resolution on the performance of chironomid-based temperature inference models (transfer functions) and temperature reconstruction. A calibration dataset consisting of chironomid assemblage and temperature data from 100 lakes was examined at four levels of taxonomic detail. The coarsest taxonomic resolution primarily represented identifications to genus or suprageneric level. At the highest level of taxonomic resolution, identification to genus level was possible for 37% of taxa, and identification below genus was possible for 60% of taxa. Transfer functions were obtained using Weighted Averaging (WA) and Weighted Averaging-Partial Least Squares (WA-PLS) regression. Cross-validated performance statistics, such as the root mean square error of prediction (RMSEP) and the coefficient of determination (r ²) between inferred and observed values improved considerably from the lowest taxonomic resolution level (WA: RMSEP 1.91°C, r ² 0.78; WA-PLS: RMSEP 1.59°C, r ² 0.86) to the highest taxonomic resolution level (WA: RMSEP 1.66°C, r ² 0.84; WA-PLS: RMSEP 1.41°C, r ² 0.89). Reconstructed July air temperatures during the Lateglacial period based on fossil chironomid assemblages from Hijkermeer (The Netherlands) were similar for all levels of taxonomic resolution, except the coarsest level. At the coarsest taxonomic level, reconstruction failed to infer one of the known Lateglacial cold episodes in the record. Also, the difference in reconstructed values based on lowest and highest taxonomic resolutions exceeded sample-specific estimated standard errors of prediction in several instances. Our results suggest that chironomid-based transfer functions at the highest taxonomic resolution outperform models based on lower-resolution calibration data. However, transfer functions of intermediate taxonomic resolution produced results very similar to models based on high-resolution taxonomic data. In studies that include analysts with different levels of expertise, inference models based on intermediate taxonomic resolution, therefore, might provide an alternative to transfer functions of maximum taxonomic detail in order to ensure taxonomic consistency between calibration datasets and down-core records produced by different analysts.     

The topology of the IRAS Point Source Catalogue Redshift Survey

We investigate the topology of the new Point Source Catalogue Redshift Survey (PSCz) of IRAS galaxies by means of the genus statistic. The survey maps the local Universe with approximately 15 000 galaxies over 84.1 per cent of the sky, and provides an unprecedented number of resolution elements for the topological analysis. For comparison with the PSCz data we also examine the genus of large N -body simulations of four variants of the cold dark matter (CDM) cosmogony. The simulations are part of the Virgo project to simulate the formation of structure in the Universe. We assume that the statistical properties of the galaxy distribution can be identified with those of the dark matter particles in the simulations. We extend the standard genus analysis by examining the influence of sampling noise on the genus curve and introducing a statistic able to quantify the amount of phase correlation present in the density field, the amplitude drop of the genus compared to a Gaussian field with identical power spectrum. The results for PSCz are consistent with the hypothesis of random-phase initial conditions. In particular, no strong phase correlation is detected on scales ranging from 10 to 32 h ⁻¹ Mpc, whereas there is a positive detection of phase correlation at smaller scales. Among the simulations, phase correlations are detected in all models at small scales, albeit with different strengths. When scaled to a common normalization, the amplitude drop depends primarily on the shape of the power spectrum. We find that the constant-bias standard CDM model can be ruled out at high significance, because the shape of its power spectrum is not consistent with PSCz. The other CDM models with more large-scale power all fit the PSCz data almost equally well, with a slight preference for a high-density τCDM model.