Coverage probability of bootstrap confidence intervals in heavy-tailed frequency models, with application to precipitation data

Bootstrap, a technique for determining the accuracy of statistics, is a tool widely used in climatological and hydrological applications. The paper compares coverage probabilities of confidence intervals of high quantiles (5- to 200-year return values) constructed by the nonparametric and parametric bootstrap in frequency analysis of heavy-tailed data, typical for maxima of precipitation amounts. The simulation experiments are based on a wide range of models used for precipitation extremes (generalized extreme value, generalized Pareto, generalized logistic, and mixed distributions). The coverage probability of the confidence intervals is quantified for several sample sizes (n?=?20, 40, 60, and 100) and tail behaviors. We show that both bootstrap methods underestimate the width of the confidence intervals but that the parametric bootstrap is clearly superior to the nonparametric one. Even a misspecification of the parametric model—often unavoidable in practice—does not prevent the parametric bootstrap from performing better in most cases. A tendency to narrower confidence intervals from the nonparametric than parametric bootstrap is demonstrated in the application to high quantiles of distributions of observed maxima of 1- and 5-day precipitation amounts; the differences increase with the return level. The results show that estimation of uncertainty based on nonparametric bootstrap is highly unreliable, especially for small and moderate sample sizes and for very heavy-tailed data.     

Drought episodes in the Czech Republic and their potential effects in agriculture

This paper presents the methodology for assessment of drought episodes and their potential effects on winter and spring cereal crops in the Czech Republic (in the text referred to as Czechia). Historical climate and crop yields data for the period of 47 years (1961–2007) have been integrated into an agrometeorological database. The drought episodes were determined by three methods: according to the values of the standardized precipitation index (SPI), percentage of long-term precipitations (r), and on the basis of the Ped drought index (S _i). Consequently, the combined SPI, S _i, and r indices have been used as tools in identification of the severity, frequency, and extent of drought episodes. Additionally, the paper also presents the S _i drought index and its potential use for real-time monitoring of spatial extension and severity of droughts in Czechia. The drought risk to crops was analyzed by identifying the relationships between the fluctuation of crop yields and drought index (S _i) based on the multiple regression analysis with stepwise selection. In general, models explain that a high percentage of the variability of the yield is due to drought (more than 45% of yield variance).     

The Lateglacial and Holocene in Central Europe: a multi‐proxy environmental record from the Bohemian Forest,Czech Republic

The Hercynian mountain ranges were islands of mountain glaciation and alpine tundra in a Central European ice‐free corridor during the Late Pleistocene. Today they are notable areas of glacial landforms, alpine‐forest free areas, peatlands and woodlands. However, our knowledge of the Lateglacial and early Holocene environmental changes in this region is limited. We present a new multi‐proxy reconstruction of a mid‐altitude environment in the Bohemian Forest spanning this period. A core (5.2 m length) in the ?erné Lake cirque (1028 m a.s.l.) was subjected to lithological, geochemical, pollen and macrofossil analysis supplemented by two optically stimulated luminescence (OSL) and 10 AMS radiocarbon dates. We determined the impact of regional and supraregional climate changes on the environment. The two most significant changes in sedimentation during the Lateglacial (17.6 and 15.8–15.5 cal. ka BP) were synchronous with regional glacial chronostratigraphy. Unlike Central European mountain ranges, in the Bohemian Forest the Younger Dryas was not coincident with glacier re‐advance, but was a dry, cold episode with low lake levels, which prevailed until the early Preboreal. Plant macrofossils indicate local establishment of Betula nana and Betula pendula/pubescens at 15.4–13.4 cal. ka BP. Comparison with Holocene records from Central Europe shows a similar immigration history of vegetation at mid and higher altitudes. The tree line exceeded an altitude of ~1000 m a.s.l. around 10.5 cal. ka BP and coincided with rapid geochemical changes in the sediment. The 8.2 ka BP event did not have any response in the sedimentary record, but corresponded to stabilization of the Picea abies population and expansion of Fagus. Fagus colonized the Bohemian Forest earlier than other Hercynian mid‐mountains, but never predominated in the composition of the forest at higher elevations. Abies alba was the last tree species that immigrated to the study area.     

Depositional rates and dating techniques of modern deposits in the Brno reservoir (Czech Republic) during the last 70 years

Facies analysis, magnetic susceptibility, and analysis of grain size, TOC content and isotopes (¹³⁷Cs, ²¹⁰Pb, ²²⁶Ra, ²²⁸Ra, and ²³⁸U concentrations) were used to determine the history of the modern deposits of the Brno reservoir. The sedimentary succession can be subdivided into two main units. The lower unit is formed predominantly by medium- to coarse-grained silty sands and is interpreted as a fluvial succession deposited before the Svratka River was dammed. The upper unit consists of brownish planar laminated silts and rarely of clayey or sandy silts and is interpreted as a product of the reservoir deposition. The concentrations of ²³⁸U reflect the history of uranium mining in the upper part of the Svratka River catchment. As a consequence, ²¹⁰Pb radionuclide concentrations cannot be used for establishing a sediment chronology. Concentrations of ¹³⁷Cs show two marked peaks, the upper of which is attributed to the Chernobyl reactor accident in 1986, and the lower one is attributed to the maximum rate of atomic weapons testing in 1963. From these peaks, mean depositional rates of 3.2 cm year⁻¹ for the time period of 1986–2007 and of 3.4 cm year⁻¹ between 1963 and 1986 are calculated. Based on the known age of the reservoir, which was constructed in 1939, we can also calculate mean depositional rate for the time period of 1939–1963, which is 3.1 cm year⁻¹.     

Cosmogenic nuclides in the Košice meteorite: Experimental investigations and Monte Carlo simulations

Results of nondestructive gamma‐ray analyses of cosmogenic radionuclides (⁷Be, ²²Na, ²⁶Al, ⁴⁶Sc, ⁴⁸V, ⁵⁴Mn, ⁵⁶Co, ⁵⁷Co, ⁵⁸Co, and ⁶⁰Co) in 19 fragments of the Ko?ice meteorite are presented and discussed. The activities varied mainly with position of fragments in the meteoroid body, and with fluxes of cosmic‐ray particles in the space affecting radionuclides with different half‐lives. Monte Carlo simulations of the production rates of ⁶⁰Co and ²⁶Al compared with experimental data indicate that the pre‐atmospheric radius of the meteoroid was 50 ± 5 cm. In two Ko?ice fragments, He, Ne, and Ar concentrations and isotopic compositions were also analyzed. The noble‐gas cosmic‐ray exposure age of the Ko?ice meteorite is 5–7 Myr, consistent with the conspicuous peak (or doublet peak) in the exposure age histogram of H chondrites. One sample likely contains traces of implanted solar wind Ne, suggesting that Ko?ice is a regolith breccia. The agreement between the simulated and observed ²⁶Al activities indicate that the meteoroid was mostly irradiated by a long‐term average flux of galactic cosmic rays of 4.8 particles cm^?2 s^?1, whereas the short‐lived radionuclide activities are more consistent with a flux of 7.0 protons cm^?2 s^?1 as a result of the low solar modulation of the galactic cosmic rays during the last few years before the meteorite fall.     

Expected changes in agroclimatic conditions in Central Europe

During the past few decades, the basic assumption of agroclimatic zoning, i.e., that agroclimatic conditions remain relatively stable, has been shattered by ongoing climate change. The first aim of this study was to develop a tool that would allow for effective analysis of various agroclimatic indicators and their dynamics under climate change conditions for a particular region. The results of this effort were summarized in the AgriClim software package, which provides users with a wide range of parameters essential for the evaluation of climate-related stress factors in agricultural crop production. The software was then tested over an area of 114,000 km² in Central Europe. We have found that by 2020, the combination of increased air temperature and changes in the amount and distribution of precipitation will lead to a prolonged growing season and significant shifts in the agroclimatic zones in Central Europe; in particular, the areas that are currently most productive will be reduced and replaced by warmer but drier conditions in the same time the higher elevations will most likely experience improvement in their agroclimatic conditions. This positive effect might be short-lived, as by 2050, even these areas might experience much drier conditions than observed currently. Both the rate and the scale of the shift are amazing as by 2020 (assuming upper range of the climate change projections) only 20?C38% of agriculture land in the evaluated region will remain in the same agroclimatic and by 2050 it might be less than 2%. On the other hand farmers will be able to take advantage of an earlier start to the growing season, at least in the lowland areas, as the proportion of days suitable for sowing increases. As all of these changes might occur within less than four decades, these issues could pose serious adaptation challenges for farmers and governmental policies. The presented results also suggest that the rate of change might be so rapid that the concept of static agroclimatic zoning itself might lose relevance due to perpetual change.     

Reproducing kernel and Galerkin��s matrix for the exterior of an ellipsoid: Application in gravity field studies

In the introductory part of the paper the importance of the topic for gravity field studies is outlined. Some concepts and tools often used for the representation of the solution of the respective boundary-value problems are mentioned. Subsequently a weak formulation of Neumann??s problem is considered with emphasis on a particular choice of function basis generated by the reproducing kernel of the respective Hilbert space of functions. The paper then focuses on the construction of the reproducing kernel for the solution domain given by the exterior of an oblate ellipsoid of revolution. First its exact structure is derived by means of the apparatus of ellipsoidal harmonics. In this case the structure of the kernel, similarly as of the entries of Galerkin??s matrix, becomes rather complex. Therefore, an approximation of ellipsoidal harmonics (limit layer approach), based on an approximation version of Legendre??s ordinary differential equation, resulting from the method of separation of variables in solving Laplace??s equation, is used. The kernel thus obtained shows some similar features, which the reproducing kernel has in the spherical case, i.e. for the solution domain represented by the exterior of a sphere. A numerical implementation of the exact structure of the reproducing kernel is mentioned as a driving impulse of running investigations.     

Numerical behaviour of the downward continuation of gravity anomalies

The numerical results of downward continuation (DWC) of point and mean gravity anomalies by the Poisson integral using point, single mean, and doubly averaged kernel are examined. Correct evaluation of the integral in its innermost zone is a challenging task. To avoid instabilities, an analytical planar approximation is used in the innermost integration zone. In addition it is shown that the single mean mode has the minimum discretization error. Downward continuation of point and mean anomalies by singly and doubly averaged kernel are the same mean anomalies on the geoid.     

Blue, complexly zoned, (Na,Mg,Fe,Li)-rich beryl from quartz-calcite veins in low-grade metamorphosed Fe-deposit Sk��ly near Ryma?ov, Czech Republic

Syn-tectonic quartz-calcite veins containing blue beryl are enclosed in hematite > magnetite-rich portions of the low-grade metamorphosed Fe-deposit Skály near Ryma?ov, Czech Republic. Aggregates of pale to deep blue beryl, up to 2?cm in diameter, are associated with euclase, clinochlore, hematite, albite and dravite. Complexly zoned beryl crystals consist of skeletal aggregates of beryl I randomly distributed within volumetrically dominant beryl II with narrow rims of beryl III. All types of beryl have similar contents of Na (0.32?C0.49 apfu) and Mg (0.31?C0.41 apfu) but variable contents of Fe_tot (0.05?C0.34 apfu) and Al (1.20?C1.62 apfu). The LA-ICP-MS study yielded elevated contents of Li, up 1,314?ppm (0.28?wt.% Li₂O) in beryl I. The quartz-calcite veins represent an unusual type of low-T metamorphic-hydrothermal vein related to Fe-ore deposit characterized by single-stage fracturing and mobilization in a closed system at T~200?C300°C and CO ₃ ^2- as a major complexing agent for the mobility of Be.     

Simultaneous determination of the source mechanism and the seismic wave energy

Summary It is necessary to know the source mechanism for the determination of the seismic energy of seismic waves from the seismogram recorded at one station. For sparse data (selected events of the 1985/86 Western-Bohemia earthquake swarm) the source mechanisms cannot be determined fromP-wave first motions. Therefore, a new method of determining the source mechanism simultaneously with the energy calculated from observations at two stations has been developed. The method is described and tested. Advantages, disadvantages and the stability of the method are discussed.