A Comparison of Positive Matrix Factorization and the Weighted Multivariate Curve Resolution Method. Application to Environmental Data

Positive Matrix Factorization (PMF) is a multivariate analysis aimed at source identification and apportionment, specifically designed to cope with environmental data and manage their uncertainty and distributions. The aim of this work is to test the effectiveness of PMF as a tool to perform data mining and define hydrochemical features of groundwater and surface water and to understand their relationship. Here PMF is applied to a dataset concerning groundwater, springs, rivers and a lake. Factor contributions to the samples are spatially analysed trough GIS approach and their interpretation is supported by considering the land use and hydrogeological features.The study area is a part of the Oglio River basin (N Italy) and consists in a ~2000 km2 area around the Oglio River part that outflows from Lake Iseo until the confluence with Mella River. The available dataset is the result of four field surveys conducted in February 2016, June 2016, September 2016 and March 2017, for a total amount of 270 samples collected on 68 monitoring points.The first factor represents water with a high content of oxygen, with SO4 and a small content of major ions. In this factor neither nitrate nor trace elements are represented. The profile of this factor overlaps with the characteristics of lake Iseo and surface water bodies directly connected with it. Its spatial variability highlights a contribution of this factor, also in several wells even if they are not close to the river itself. This was related to the channels net collecting water from the Oglio River and spreading it to the nearby fields.The second factor explains the whole chemical variability of As, Fe, P-tot and NH4. Furthermore, it has a significant contribution of Mn and it can be associated to the advanced stages of reducing conditions due to degradation of natural organic matter.The third factor is characterized mainly by Mn and SO4, with a contribution of the major ions. Based on the profile and on the spatial distribution, it is possible to associate this factor to the early stages of the reducing process.The fourth factor represents only major ions. Major ion concentration in groundwater is mainly determined by water &#8211; rock interactions, which increase the concentrations especially with increasing residence times. This factor shows an increasing trend from north to south, which is the flow direction, confirming its relationship with residence time.The fifth factor represents the total variability of the variable NO3 with contributions also in terms of Cl, SO4, Ca and Mg. Higher NO3 concentrations in groundwater are mostly related with the use of organic or synthetic fertilizers; recent studies reported that this kind of anthropogenic impact affects also major ions concentrations such as Cl, SO4, Ca and Mg. Thus, the profile of this fifth factor was associated to the anthropogenic impact related to the agricultural land use, not just in terms of NO3 but also considering the contribution of different elements.

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Positive matrix factorization applied to a curve resolution problem

Journal of Chemometrics ◽

10.1002/(sici)1099-128x(199811/12)12:6<357::aid-cem523>3.0.co;2-s ◽

1998 ◽

Vol 12 (6) ◽

pp. 357-364 ◽

Cited By ~ 39

Author(s):

Yu-Long Xie ◽

Philip K. Hopke ◽

Pentti Paatero

Keyword(s):

Matrix Factorization ◽

Positive Matrix Factorization ◽

Positive Matrix ◽

Curve Resolution ◽

Resolution Problem

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Source apportionment of urban PM2.5 using positive matrix factorization with vertically distributed measurements of trace elements and nonpolar organic compounds

Atmospheric Pollution Research ◽

10.1016/j.apr.2021.03.007 ◽

2021 ◽

Vol 12 (4) ◽

pp. 200-207

Author(s):

Ho‐Tang Liao ◽

Chien‐Lin Lee ◽

Wei‐Cheng Tsai ◽

Jian Zhen Yu ◽

Shih‐Wei Tsai ◽

...

Keyword(s):

Trace Elements ◽

Source Apportionment ◽

Organic Compounds ◽

Matrix Factorization ◽

Positive Matrix Factorization ◽

Positive Matrix ◽

Nonpolar Organic

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Geochemical Mapping, Risk Assessment, and Source Identification of Heavy Metals in Road Dust Using Positive Matrix Factorization (PMF)

Atmosphere ◽

10.3390/atmos12050614 ◽

2021 ◽

Vol 12 (5) ◽

pp. 614

Author(s):

Muhammad Faisal ◽

Zening Wu ◽

Huiliang Wang ◽

Zafar Hussain ◽

Chenyang Shen

Keyword(s):

Heavy Metals ◽

Risk Assessment ◽

Matrix Factorization ◽

Anthropogenic Activities ◽

Contamination Factor ◽

Road Dust ◽

Positive Matrix Factorization ◽

Prevention Measures ◽

Positive Matrix ◽

The City

Heavy metals in road dust pose a significant threat to human health. This study investigated the concentrations, patterns, and sources of eight hazardous heavy metals (Cr, Ni, Cu, Zn, As, Cd, Pb, and Hg) in the street dust of Zhengzhou city of PR China. Fifty-eight samples of road dust were analyzed based on three methods of risk assessment, i.e., Geo-Accumulation Index (Igeo), Potential Ecological Risk Assessment (RI), and Nemerow Synthetic Pollution Index (PIN). The results exhibited higher concentrations of Hg and Cd 14 and 7 times higher than their background values, respectively. Igeo showed the risks of contamination in a range of unpolluted (Cr, Ni) to strongly polluted (Hg and Cd) categories. RI came up with the contamination ranges from low (Cr, Ni, Cu, Zn, As, and Pb) to extreme (Cd and Hg) risk of contamination. The risk of contamination based on PIN was from safe (Cu, As, and Pb) to seriously high (Cd and Hg). The results yielded by PIN indicated the extreme risk of Cd and Hg in the city. Positive Matrix Factorization was used to identify the sources of contamination. Factor 1 (vehicular exhaust), Factor 2 (coal combustion), Factor 3 (metal industry), and Factor 4 (anthropogenic activities), respectively, contributed 14.63%, 35.34%, 36.14%, and 13.87% of total heavy metal pollution. Metal’s presence in the dust is a direct health risk for humans and warrants immediate and effective pollution control and prevention measures in the city.

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Development of a versatile source apportionment analysis based on positive matrix factorization: a case study of the seasonal variation of organic aerosol sources in Estonia

Atmospheric Chemistry and Physics ◽

10.5194/acp-19-7279-2019 ◽

2019 ◽

Vol 19 (11) ◽

pp. 7279-7295 ◽

Cited By ~ 2

Author(s):

Athanasia Vlachou ◽

Anna Tobler ◽

Houssni Lamkaddam ◽

Francesco Canonaco ◽

Kaspar R. Daellenbach ◽

...

Keyword(s):

Matrix Factorization ◽

Organic Aerosol ◽

Positive Matrix Factorization ◽

Water Soluble ◽

Oxidation Products ◽

Positive Matrix ◽

Bootstrap Analysis ◽

Seasonal Behavior ◽

Yearly Cycle ◽

Aerosol Mass

Abstract. Bootstrap analysis is commonly used to capture the uncertainties of a bilinear receptor model such as the positive matrix factorization (PMF) model. This approach can estimate the factor-related uncertainties and partially assess the rotational ambiguity of the model. The selection of the environmentally plausible solutions, though, can be challenging, and a systematic approach to identify and sort the factors is needed. For this, comparison of the factors between each bootstrap run and the initial PMF output, as well as with externally determined markers, is crucial. As a result, certain solutions that exhibit suboptimal factor separation should be discarded. The retained solutions would then be used to test the robustness of the PMF output. Meanwhile, analysis of filter samples with the Aerodyne aerosol mass spectrometer and the application of PMF and bootstrap analysis on the bulk water-soluble organic aerosol mass spectra have provided insight into the source identification and their uncertainties. Here, we investigated a full yearly cycle of the sources of organic aerosol (OA) at three sites in Estonia: Tallinn (urban), Tartu (suburban) and Kohtla-Järve (KJ; industrial). We identified six OA sources and an inorganic dust factor. The primary OA types included biomass burning, dominant in winter in Tartu and accounting for 73 % ± 21 % of the total OA, primary biological OA which was abundant in Tartu and Tallinn in spring (21 % ± 8 % and 11 % ± 5 %, respectively), and two other primary OA types lower in mass. A sulfur-containing OA was related to road dust and tire abrasion which exhibited a rather stable yearly cycle, and an oil OA was connected to the oil shale industries in KJ prevailing at this site that comprises 36 % ± 14 % of the total OA in spring. The secondary OA sources were separated based on their seasonal behavior: a winter oxygenated OA dominated in winter (36 % ± 14 % for KJ, 25 % ± 9 % for Tallinn and 13 % ± 5 % for Tartu) and was correlated with benzoic and phthalic acid, implying an anthropogenic origin. A summer oxygenated OA was the main source of OA in summer at all sites (26 % ± 5 % in KJ, 41 % ± 7 % in Tallinn and 35 % ± 7 % in Tartu) and exhibited high correlations with oxidation products of a-pinene-like pinic acid and 3-methyl-1, 2, 3-butanetricarboxylic acid (MBTCA), suggesting a biogenic origin.

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