Fast NFFT based summation of radial functions

This paper is concerned with the fast summation of radial functions by the fast Fourier transform for nonequispaced data. We enhance the fast summation algorithm proposed in [20] by introducing a new regularization procedure based on the two-point Taylor interpolation by algebraic polynomials and estimate the corresponding approximation error. Our error estimates are more sophisticated than those in [20]. Beyond the kernels Kβ(χ

FMM and H-matrices: A Short Introduction to the Basic Idea

The aim of this paper is a short introduction to a fundamental algorithm for the fast multiplication of vectors with fully populated, special matrices arising in various applications. The basic idea is known as fast multipole method, fast multiplication by H-matrices or by mosaic-skeleton matrices. We prefer a linear algebraic approach which may serve as a basis for student seminars in Mathematics, Computer Science or Engineering. Our introduction is accompanied by a broad, but far away from complete, list of references, where the reader may find more sophisticated material

Robust local approximation of scattered data

In this paper, we modify the robust local image estimation method of R. van den Boomgaard and J. van de Weijer for the approximation of scattered data. The derivation of our knot and data dependent approximation method is based on the relation between the Gaussian facet model in image processing and the moving least square technique known from approximation theory. Numerical examples demonstrate the advantages of our robust scattered data approximation

Meteorological, impact and climate perspectives of the 29 June 2017 heavy precipitation event in the Berlin metropolitan area

Extreme precipitation is a weather phenomenon with tremendous damaging potential for property and human life. As the intensity and frequency of such events is projected to increase in a warming climate, there is an urgent need to advance the existing knowledge on extreme precipitation processes, statistics and impacts across scales. To this end, a working group within the Germany-based project, ClimXtreme, has been established to carry out multidisciplinary analyses of high-impact events. In this work, we provide a comprehensive assessment of the 29 June 2017 heavy precipitation event (HPE) affecting the Berlin metropolitan region (Germany), from the meteorological, impacts and climate perspectives, including climate change attribution. Our analysis showed that this event occurred under the influence of a mid-tropospheric trough over western Europe and two shortwave surface lows over Britain and Poland (Rasmund and Rasmund II), inducing relevant low-level wind convergence along the German–Polish border. Over 11 000 convective cells were triggered, starting early morning 29 June, displacing northwards slowly under the influence of a weak tropospheric flow (10 m s−1 at 500 hPa). The quasi-stationary situation led to totals up to 196 mm d−1, making this event the 29 June most severe in the 1951–2021 climatology, ranked by means of a precipitation-based index. Regarding impacts, it incurred the largest insured losses in the period 2002 to 2017 (EUR 60 million) in the greater Berlin area. We provide further insights on flood attributes (inundation, depth, duration) based on a unique household-level survey data set. The major moisture source for this event was the Alpine–Slovenian region (63 % of identified sources) due to recycling of precipitation falling over that region 1 d earlier. Implementing three different generalised extreme value (GEV) models, we quantified the return periods for this case to be above 100 years for daily aggregated precipitation, and up to 100 and 10 years for 8 and 1 h aggregations, respectively. The conditional attribution demonstrated that warming since the pre-industrial era caused a small but significant increase of 4 % in total precipitation and 10 % for extreme intensities. The possibility that not just greenhouse-gas-induced warming, but also anthropogenic aerosols affected the intensity of precipitation is investigated through aerosol sensitivity experiments. Our multi-disciplinary approach allowed us to relate interconnected aspects of extreme precipitation. For instance, the link between the unique meteorological conditions of this case and its very large return periods, or the extent to which it is attributable to already-observed anthropogenic climate change.</p

Meteorological, impact and climate perspectives of the 29 June 2017 heavy precipitation event in the Berlin metropolitan area

Extreme precipitation is a weather phenomenon with tremendous damaging potential for property and human life. As the intensity and frequency of such events is projected to increase in a warming climate, there is an urgent need to advance the existing knowledge on extreme precipitation processes, statistics and impacts across scales. To this end, a working group within the Germany-based project, ClimXtreme, has been established to carry out multidisciplinary analyses of high-impact events. In this work, we provide a comprehensive assessment of the 29 June 2017 heavy precipitation event (HPE) affecting the Berlin metropolitan region (Germany), from the meteorological, impacts and climate perspectives, including climate change attribution. Our analysis showed that this event occurred under the influence of a mid-tropospheric trough over western Europe and two shortwave surface lows over Britain and Poland (Rasmund and Rasmund II), inducing relevant low-level wind convergence along the German–Polish border. Over 11 000 convective cells were triggered, starting early morning 29 June, displacing northwards slowly under the influence of a weak tropospheric flow (10 m s$^{−1}$ at 500 hPa). The quasi-stationary situation led to totals up to 196 mm d$^{−1}$, making this event the 29 June most severe in the 1951–2021 climatology, ranked by means of a precipitation-based index. Regarding impacts, it incurred the largest insured losses in the period 2002 to 2017 (EUR 60 million) in the greater Berlin area. We provide further insights on flood attributes (inundation, depth, duration) based on a unique household-level survey data set. The major moisture source for this event was the Alpine–Slovenian region (63 % of identified sources) due to recycling of precipitation falling over that region 1 d earlier. Implementing three different generalised extreme value (GEV) models, we quantified the return periods for this case to be above 100 years for daily aggregated precipitation, and up to 100 and 10 years for 8 and 1 h aggregations, respectively. The conditional attribution demonstrated that warming since the pre-industrial era caused a small but significant increase of 4 % in total precipitation and 10 % for extreme intensities. The possibility that not just greenhouse-gas-induced warming, but also anthropogenic aerosols affected the intensity of precipitation is investigated through aerosol sensitivity experiments. Our multi-disciplinary approach allowed us to relate interconnected aspects of extreme precipitation. For instance, the link between the unique meteorological conditions of this case and its very large return periods, or the extent to which it is attributable to already-observed anthropogenic climate change