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EN
This study provides an assessment of the current and future changes (in terms of both direction and value) in air temperature, precipitation, snow, wind and their extremes over the territory of Belarus using information from 42 meteorological stations and 92 regional circulation model (RCM) simulations with the highest available horizontal resolution (EUR-11). Three representative concentration pathway scenarios, namely, RCP2.6, RCP4.5 and RCP8.5, are considered. Results demonstrate that in recent decades, temperature has increased over the territory of Belarus by 1.3°C, with the largest increase occurring during the cold season (2.1-2.3°C). Ensemble scenarios project further increases in air temperature in the current century by +0.5-1.5°C, +2.8°C, and +5.2°C under the RCP2.6, RCP4.5 and RCP8.5 scenarios, with the largest increase during the cold season under the RCP8.5 scenario. The annual means were observed to increase (insignificantly) by 5-7% and the summer precipitation extremes exhibited a 20-25% growth in recent decades. Moreover, dry conditions have intensified in Belarus, particularly during the growing season. Further increases in precipitation of 10-15% across Belarus are projected to occur in all seasons under the RCP4.5 and RCP8.5 scenarios. Simulation models predict greater increases in single day rainfall events compared to their multiday precipitation counterparts. The greatest increases in maximal dry period length (by 1-2) are expected to occur in summer and autumn. The models project the general decrease in snowfall across Belarus to continue into the current century, with a reduction in snow precipitation days of 10-30 days. Despite the reduced wind strength (by 0.9-1.0 m·s -1 ) since the 1970s over the territory of Belarus, the ensemble model reveals slight nonsignificant changes in seasonal and annual wind strengths until the end of the century. Significant changes of 1-3 days under varying directions of the wind regime were observed for days with a strong breeze and storms.
2
Content available remote Assessment of climate change and associated impact on selected sectors in Poland
EN
The present paper offers a brief assessment of climate change and associated impact in Poland, based on selected results of the Polish–Norwegian CHASE-PL project. Impacts are examined in selected sectors, such as water resources, natural hazard risk reduction, environment, agriculture and health. Results of change detection in long time series of observed climate and climate impact variables in Poland are presented. Also, projections of climate variability and change are provided for time horizons of 2021–2050 and 2071–2100 for two emission scenarios, RCP4.5 and RCP8.5 in comparison with control period, 1971–2000. Based on climate projections, examination of future impacts on sectors is also carried out. Selected uncertainty issues relevant to observations, understanding and projections are tackled as well.
EN
Heavy and/or long-lasting precipitation events in the Tatra Mountains and their northern foothills may cause floods that propagate downstream in the Vistula River and inundate large areas of Poland. In a warmer climate, future precipitation extremes could be higher than they are today, hence the flood risk potential is likely to grow. Therefore, assessment of these future changes and adaptation to changes in flood risk are of considerable interest and importance. In this study, seven global climate models were used to get insight into a range of changes in the characteristics of mean and heavy precipitation: this was done for two climate scenarios – A1B and A2 of the SRES family. With the help of the so-called delta-change method and based on responses from global climate models, projections were made for 11 precipitation stations in the region. Analyses were made of various indices, such as annual totals, maximum 24 h, 5-day; 10-day, monthly maximum sums of precipitation and also numbers of days with intense precipitation equal or above the thresholds of 30 and 50 mm per day. It was found that all GCM models under examination projected an increase in mean annual precipitation totals as well as in heavy precipitation in the future time horizon studied here (2080-2100).
4
Content available remote Some Decompositions of Matrix Variances
EN
When D is a density matrix and A1, A2 are self-adjoint operators, then the standard variance is a 2 × 2 matrix: VarD(A1, A2)i,j := TrDAiAj − (TrDAi)(TrDAj) (1 ≤ i, j ≤ 2). The main result in this work is that there are projections Pk such that D = Σk λk Pk with 0 < λk and Σk λk = 1 and VarD (A1, A2) = Σk λk VarPk (A1, A2). In a previous paper only the A1 = A2 case was included and the relevance is motivated by the paper [8].
5
Content available A characterization of convex φ-functions
EN
The properties of four elements (LPFE) and (UPFE), introduced by Isac and Persson, have been recently examined in Hilbert spaces, Lp-spaces and modular spaces. In this paper we prove a new theorem showing that a modular of form ρφ(∫)= ∫ Ω φ (t,/∫(t)/)dμ(t) satisfies both (LPFE) and (UPFE) if and only if φ is convex with respect to its second variable. A connection of this result with the study of projections and antiprojections onto latticially closed subsets of the modular space Lφ is also discussed.
6
Content available remote The Order on Projections in C*-Algebras of Real Rank Zero
EN
We prove a number of fundamental facts about the canonical order on projections in C*-algebras of real rank zero. Specifically, we show that this order is separative and that arbitrary countable collections have equivalent (in terms of their lower bounds) decreasing sequences. Under the further assumption that the order is countably downwards closed, we show how to characterize greatest lower bounds of finite collections of projections, and their existence, using the norm and spectrum of simple product expressions of the projections in question. We also characterize the points at which the canonical homomorphism to the Calkin algebra preserves least upper bounds of countable collections of projections, namely that this occurs precisely when the span of the corresponding subspaces is closed.
7
Content available remote Dynamika glebowych zasobów wodnych w Polsce współcześnie i w przyszłości
PL
W pracy przedstawiono wyniki badań nad zmiennością uwilgotnienia strefy aeracji w Polsce w kontekście zmian klimatu oraz możliwych zmian procesów hydrologicznych. Analizowano wieloletnią i sezonową zmienność wilgotności gleb w Polsce na podstawie symulacji uwilgotnienia według modeli ECHAM5 oraz GFDL, w wybranych wieloleciach XX i XXI wieku. Analizowano względną efektywną wilgotność gleby. Dane pozyskano ze Światowego Programu Badania Klimatu WCRP (World Climate Research Programme), z projektu CMIP3 (Coupled Model Intercomparison Project phase 3). Stwierdzono, że w perspektywie najbliższych 50-100 lat może nastąpić wzrost ekstremalnych stanów uwilgotnienia gleby, ze znacznym obniżeniem uwilgotnienia w lecie. Przewiduje się, że okres, w którym występuje wyczerpywanie zapasów dostępnej dla roślin wody, będzie dłuższy.
EN
Special focus of this research is on the variability of soil water storage in Poland in the context of climate change and possible changes in the hydrological processes. In this paper long term variation of soil water storage in Poland is analyzed based on climate models simulations, comprising the ECHAM5 and GFDL models. Long-term mean monthly values of the soil water storage have been evaluated for selected periods of twenty and twenty first century. Index of effective relative soil water storage is calculated and analyzed. Data used in this research were possessed from the World Climate Research Programme, Coupled Model Intercomparison Project phase 3. Projections for second half of the twenty first century show that considerable changes in soil water storage should be expected. Increase of extreme stages is expected and the amount of available water is projected to decrease in summer. Period of decrease in soil moisture is projected to extend
8
Content available remote I-sets and cominimal projections
EN
Let Y [...] be a subspace of codimension two. For n = 4 the formula for cominimal projections will be presented. For n = 5 the complete characterization of I-sets which determined cominimal projections and consequently the manner of finding cominimal projections will be given. This completes the results from [15].
PL
W pracy przedstawiono porównanie niektórych podstawowych relacji geometrycznych w odwzorowaniach złożonych alternatywnie z rzutu prostokątnego i tzw. rzutu okręgowego (inwersyjnego) oraz rzutu prostokątnego i środkowego.
EN
The purpose of the article is the analysis of two typical double-image methods of projection: a representative of quadratic transformations, namely the composition of orthogonal and circular projections and the composition of orthogonal and central projections.
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