Positive Matrix Factorization Model for Environmental Data Analyses

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PMF Overview

The version of PMF available for download was originally developed and tested for the Windows versions 7 to 10. This tool is no longer being updated for newer operating systems, nor can EPA provide troubleshooting support. We continue to have this tool available for download to support users who may have compatible operating systems.

Please send EPA PMF questions to:
PMF_Model@epa.gov

What is the Positive Matrix Factorization (PMF) Model?

EPA’s Positive Matrix Factorization (PMF) Model is a mathematical receptor model developed by EPA scientists that provides scientific support for the development and implementation of air and water quality standards, and environmental forensics. The PMF Model can analyze a wide range of environmental sample data: sediments, wet deposition, surface water, and ambient air. EPA’s PMF Model reduces the large number of variables in complex analytical data sets to combinations of species called source types and source contributions. The source types are identified by comparing them to measured profiles. Source contributions are used to determine how much each source contributed to a sample. In addition, PMF provides robust uncertainty estimates and diagnostics.

How does the model work?

PMF users provide files of sample species concentrations and uncertainties and the number of sources. The model calculates source profiles or fingerprints, source contributions, and source profile uncertainties. PMF Model results are constrained to provide positive source contributions, and the uncertainty weighted difference between the observed and predicted species concentration is minimized.

PMF Model software uses graphical user interfaces that ease data input, visualization of model diagnostics, and exporting of results. The model is free of charge and does not require a license or other software to use. Algorithms used in the PMF Model have been peer reviewed by leading air and water quality management scientists.

Examples of PMF Model applications and how to report results:

System requirements

Version 5.0 of EPA’s Positive Matrix Factorization Model works on Windows versions 7 to 10. The computer should have at least a 2.0 GHz processor, 1 GB of memory, and a 1024x768 pixel display. Users will need to have permissions to write to the computer’s C:\ drive to install and run the PMF Model as this may not be the default setting for some users. Since files will be written to a user’s C:\ drive, the PMF Model needs to be run in Administrator mode. No further updates to the PMF Model are planned.

How can I get help?

  • PMF Frequently Asked Questions
  • PMF 5.0 Fundamentals and User Guide
    The EPA Positive Matrix Factorization (PMF) 5.0 Fundamentals & User Guide provides references and details on how to use PMF. EPA no longer provides technical support for EPA Positive Matrix Factorization (PMF). The User Guide and a large number of publications provide examples of how to apply the model for air, water, sediment, and other data analyses.

PMF Version 5.0 reported issues

The PMF Model suggests the block size for the Bootstrap Error Estimation. The block size calculation in EPA PMF 5.0 is based on a Politis and White publication (2004). The algorithm in the 2004 paper was updated in a 2009 correction (Patton et al., 2009)1 and the revised algorithm is not part of EPA PMF 5.0. Patton has developed MATLAB code that includes the 2009 changes and application the revised bootstrap discussed in Bhandari et al. 2022.2 The Patton MATLAB code can be used to generate a block size and the number can be entered in the Base Model Runs screen.

Multiple users have noted problems with EPA PMF when dealing with large datasets. Large datasets may use all the available computer memory, causing the program to run slowly or even cause an error. Recent testing also indicates that large datasets may cause the PMF Model to stall due to a graphical user interface issue after the completion of the Multilinear Engine computations. EPA is investigating solutions to this problem and suggests reducing the number of Base Model runs to one, gradually increasing the number of runs before a memory or user interface error. Base Model Displacement Method error estimation may take over an hour to run for large datasets. When reporting results, list the number of runs as described in Brown et al.3 Multiple single runs can be evaluated if the Base Model Runs random seed has changed between runs.

Citations

  1. Patton, A., Politis, D. N., and White, H.: Correction to automatic block-length selection for the dependent bootstrap by D. Politis and H. White, Econometric Reviews, 28, 372–375, URL, 2009.
  2. Source apportionment resolved by time-of-day for improved deconvolution of primary source contributions to air pollution, (preprint, March 2022) Bhandari, S., Arub, Z., Habib, G., Apte, J.S., and Ruiz, L.H., doi.org/10.5194/amt-2022-76
  3. Brown, S.G., Eberly, S., Paatero, P. and Norris, G.A., 2015. Methods for Estimating Uncertainty in PMF Solutions: Examples with Ambient Air and Water Quality Data and Guidance on Reporting PMF Results. Science of the Total Environment, 518, pp.626-635.
     

Please share EPA PMF problems and suggestions using the following form:

  • Submit EPA PMF Problems and Suggestions
    PLEASE NOTE: EPA is tracking PMF issues and will post suggestions if many users have similar program or dataset issues. EPA does not have the ability to provide user support and many publications provide EPA PMF application examples.

Downloads & Registration

Technical Contact

Please send EPA PMF questions and comments to PMF_Model@epa.gov.

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Last updated on April 15, 2024