Exponential sum approximations for t−βt^{-\beta}

Given $\beta>0$ and $\delta>0$, the function $t^{-\beta}$ may be approximated for $t$ in a compact interval $[\delta,T]$ by a sum of terms of the form $we^{-at}$, with parameters $w>0$ and $a>0$. One such an approximation, studied by Beylkin and Monz\'on, is obtained by applying the trapezoidal rule to an integral representation of $t^{-\beta}$, after which Prony's method is applied to reduce the number of terms in the sum with essentially no loss of accuracy. We review this method, and then describe a similar approach based on an alternative integral representation. The main difference is that the new approach achieves much better results before the application of Prony's method; after applying Prony's method the performance of both is much the same.Comment: 18 pages, 5 figures. I have completely rewritten this paper because after uploading the previous version I realised that there is a much better approach. Note the change to the title. Have included minor corrections following revie

The Hurricane : March-Two Step

https://digitalcommons.library.umaine.edu/mmb-ps/2347/thumbnail.jp

A southeastern Mediterranean PV streamer and its role in December 2001 case with torrential rains in Israel

A precipitation event of unprecedented intensity took place over northern part of Israel during 4 December 2001–5 December 2001. The case was associated with formation of a Cyprus Low cyclone over the Asia Minor. In the current study the synoptic developments over the eastern part of the Mediterranean region are simulated with the MM5 nonhydrostatic model and analyzed based on dynamic tropopause patterns calculated from the simulation results. According to the results, a powerful potential vorticity (PV) streamer system played a major role in the process over the southeastern Mediterranean region. The PV streamer created conditions for seclusion of moist air masses from the equatorial East Africa and Atlantics during the cyclone development. Condensation of the moisture, associated with the latent heat release processes have contributed to the intense thunderstorm activity and heavy precipitation of the event

The surface climatology of the eastern Mediterranean region obtained in a three-member ensemble climate change simulation experiment

International audienceTwo configurations of RegCM3 regional climate model (RCM) have been used to downscale results of two atmosphere-ocean global climate model (AOGCM) simulations of the current (1961?1990) and future climates (2071?2100) over the eastern Mediterranean (EM) region. The RCM domain covering the EM region from northern Africa to central part of Asia Minor with grid spacing of 50 km was used. Three sets of RCM simulations were completed. Results of the RCM experiment support earlier projections of a temperature (annual precipitation) increase (decrease) to the end of 21st century over the EM. The roles of several major factors in controlling uncertainty of the climate change estimates are evaluated. The main uncertainty factors appear to be associated with possible inadequacies in RCM description of the EM-climate-controlling developments over remotely located areas as well as those in the simulations of the global climate and its trends by the AOGCMs