Large oil refineries emit heat, vapor, and cloud condensation nuclei (CCN), all of which can affect the formation of cloud and precipitation. The Factor Separation (FS) technique is applied to isolate the net contributions of waste heat, vapor, and CCN to the rainfall of a cumulus developing in the industrial plume. The mutualinteractive contributions of two or three of the factors are also computed. The model simulations indicate that the sensible heat provides the major stimulus for cloud development and rain formation. The pure contribution of the industrial CCN is to enhance the condensation causing an increase in the mass of total cloud water. The contributions arising from mutual interactions among two or three factors are quite large and should not be neglected. Particularly, the synergistic interaction of the sensible heat and pollution effects contribute towards the accumulated rainfall.

Introduction

There is considerable interest in the effects of large electrical power plants and oil refineries on meteorological phenomena. Preferential cumulus formation has been observed above electrical power plants and oil refineries (Auer, 1976). Hobbs et al. (1970) reported that in regions adjacent to or downwind of the Port Townsend paper mill (Washington State, USA) the annual rainfall recorded was 30% greater than the rainfall from nearby stations. This dramatic increase in annual precipitation is likely caused by the presence of the paper mill. Hobbs et al. speculated that the enhanced rainfall might be attributed to the large and giant CCN emitted from the paper mill into the pollution plume. Support for this hypothesis came from Eagan et al.'s (1974) study.

Here, we present three examples of the Alpert–Stein Factor Separation Methodology (hereafter, FS in short) on a medium scale in the atmosphere, often referred to as meso-scale or, in general, meso-meteorology. The first example is that of a deep Genoa cyclogenesis (Alpert et al., 1996a, b) that was observed during the Alpine Experiment (ALPEX) in March 1982, and then studied intensively by several research groups. The second example is that of a small-scale shallow short-lived meso-beta-scale – only tens of kilometers in diameter – cyclone over the Gulf of Antalya, Eastern Mediterranean (Alpert et al., 1999). The third example is that of a much smaller scale, of orographic wind, following Alpert and Tsidulko (1994). In each of these three examples, some factors relevant to the specific problem are selected, and special focus is given to the role played by the synergies as revealed by the FS approach.

A multi-stage evolution of an ALPEX cyclone: meso-alpha scale

A relatively large number of studies have been devoted to cyclogenesis, with particular attention given to the processes responsible for the lee cyclone generation. Early studies of lee cyclogenesis (henceforth LC) focused on observations, and indicated the regions with the highest frequencies (Petterssen, 1956).

More recently, several theories have been advanced to explain the LC features, and they are frequently separated for convenience into two groups, as follows: the modified (by the lower boundary layer) baroclinic instability approach, as reviewed by Tibaldi et al. (1990) and Pierrehumbert (1985), and the directional wind shear suggested by Smith (1984).

Software tools

CLN

CLN (Class Library for Numbers, http://www.ginac.de/CLN/) is a library for efficient computations with all kinds of numbers in arbitrary precision. It was written by Bruno Haible, and is currently maintained by Richard Kreckel. It is written in C++ and distributed under the GNU General Public License (GPL). CLN provides some elementary and special functions, and fast arithmetic on large numbers, in particular it implements Schönhage–Strassen multiplication, and the binary splitting algorithm. CLN can be configured to use GMP low-level MPN routines, which improves its performance.

GNU MP (GMP)

The GNU MP library is the main reference for arbitrary-precision arithmetic. It has been developed since 1991 by Torbjörn Granlund and several other contributors. GNU MP (GMP for short) implements several of the algorithms described in this book. In particular, we recommend reading the “Algorithms” chapter of the GMP reference manual.

This is a book about algorithms for performing arithmetic, and their implementation on modern computers. We are concerned with software more than hardware – we do not cover computer architecture or the design of computer hardware since good books are already available on these topics. Instead, we focus on algorithms for efficiently performing arithmetic operations such as addition, multiplication, and division, and their connections to topics such as modular arithmetic, greatest common divisors, the fast Fourier transform (FFT), and the computation of special functions.

The algorithms that we present are mainly intended for arbitrary-precision arithmetic. That is, they are not limited by the computer wordsize of 32 or 64 bits, only by the memory and time available for the computation. We consider both integer and real (floating-point) computations.

The book is divided into four main chapters, plus one short chapter (essentially an appendix). Chapter 1 covers integer arithmetic. This has, of course, been considered in many other books and papers. However, there has been much recent progress, inspired in part by the application to public key cryptography, so most of the published books are now partly out of date or incomplete. Our aim is to present the latest developments in a concise manner. At the same time, we provide a self-contained introduction for the reader who is not an expert in the field.

Chapter 2 is concerned with modular arithmetic and the FFT, and their applications to computer arithmetic.