Assessing positive matrix factorization model fit: a new method to estimate uncertainty and bias in factor contributions at the measurement time scale J. G. Hemann1, G. L. Brinkman2, S. J. Dutton2, M. P. Hannigan2, J. B. Milford2, and S. L. Miller2 1Department of Applied Mathematics, University of Colorado, Boulder, USA 2Department of Mechanical Engineering, University of Colorado, Boulder, USA
Abstract. A Positive Matrix Factorization receptor model for aerosol pollution source
apportionment was fit to a synthetic dataset simulating one year of daily
measurements of ambient PM2.5 concentrations, comprised of 39 chemical
species from nine pollutant sources. A novel method was developed to
estimate model fit uncertainty and bias at the daily time scale, as related
to factor contributions. A circular block bootstrap is used to create
replicate datasets, with the same receptor model then fit to the data.
Neural networks are trained to classify factors based upon chemical
profiles, as opposed to correlating contribution time series, and this
classification is used to align factor orderings across the model results
associated with the replicate datasets. Factor contribution uncertainty is
assessed from the distribution of results associated with each factor.
Comparing modeled factors with input factors used to create the synthetic
data assesses bias. The results indicate that variability in factor
contribution estimates does not necessarily encompass model error:
contribution estimates can have small associated variability across results
yet also be very biased. These findings are likely dependent on
characteristics of the data.
Citation: Hemann, J. G., Brinkman, G. L., Dutton, S. J., Hannigan, M. P., Milford, J. B., and Miller, S. L.: Assessing positive matrix factorization model fit: a new method to estimate uncertainty and bias in factor contributions at the measurement time scale, Atmos. Chem. Phys., 9, 497-513, doi:10.5194/acp-9-497-2009, 2009.