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ABSTRACT:As the atmospheric system is characterized by highly complex interactions between a large number of physical variables, it is a challenging task for researchers to break up the complicated structures into a few significant modes of variability.An innovative technique, called Non-negative Matrix Factorization (NMF), developed to provide a reduced-dimensional representation of large-scale non-negative data and to extract underlying features, is introduced as a tool for meteorological applications. The method is used to decompose space-time meteorological fields into spatial patterns and associated time indices in order to advance our knowledge of dominant atmospheric processes. For the Northern Hemisphere the 500 hPa geopotential field together with sea level pressure (SLP) are analysed using an up-to-date NMF algorithm as well as a helpful method of NMF initialization based on Singular Value Decomposition (SVD). Several NMF patterns correspond to the variations identified by traditional EOF analysis, such as the East Atlantic and the Pacific/North American Pattern. For the North Atlantic Oscillation the NMF identifies sub-patterns: The positive phase is associated with systems of pressure variation over the Pacific Ocean and the Arctic, respectively, the negative phase resembles the EOF pattern.As the NMF patterns not only represent variability, like EOF patterns, but also are fractions of the total observed values, we demonstrate for a location near Nikolski, Alaska, the temporal development of the geopotential as a superposition of NMF-factors.

<p><strong>Abstract.</strong> Increasing traffic density and a changing car fleet on the one hand as well as various reduction measures on the other hand may influence the composition of the particle population and, hence, the health risks for residents of megacities like Beijing. A suitable tool for identification and quantification of source group-related particle exposure compositions is desirable in order to derive optimal adaptation and reduction strategies and therefore, is presented in this paper. <br></br> Particle number concentrations have been measured in high time- and space-resolution at an urban background monitoring site in Beijing, China, during 2004–2008. In this study a new pattern recognition procedure based on non-negative matrix factorization (NMF) was introduced to extract characteristic diurnal air pollution patterns of particle number and volume size distributions for the study period. Initialization and weighting strategies for NMF applications were carefully considered and a scaling procedure for ranking of obtained patterns was implemented. In order to account for varying particle sizes in the full diameter range [3 nm; 10 &amp;mu;m] two separate NMF applications (a) for diurnal particle number concentration data (NMF-N) and (b) volume concentration data (NMF-V) have been performed. <br></br> Five particle number concentration-related NMF-N factors were assigned to patterns mainly describing the development of ultrafine (particle diameter <i>D</i>_p < 100 nm instead of <i>D</i>_P) as well as fine particles (<i>D</i>_p < 2.5 &amp;mu;m), since absolute number concentrations are highest in these diameter ranges. The factors are classified into primary and secondary sources. Primary sources mostly involved anthropogenic emission sources such as traffic emissions or emissions of nearby industrial plants, whereas secondary sources involved new particle formation and accumulation (particle growth) processes. For the NMF-V application the five extracted factors mainly described coarse particle (2.5 &amp;mu;m < <i>D</i>_p < 10 &amp;mu;m) variations, generated by processes like dust storm events. Because particle volume depends on particle diameter in a cubic manner, larger particles are emphasized in the latter application. <br></br> In order to gain insight in the day-by-day varying source-associated composition of the particle burden non-negative linear combinations of individual source-associated pollution patterns were used to approximate the original particle data. Consequently, this NMF-based procedure provides a reasonable numerical-statistical tool for the description of daily patterns of particle pollution, source identification and reconstruction of daily patterns by summarizing weighted factors.</p>