Abstract
The Air Pollutants Exposure Model (APEX) is a stochastic population-based inhalation exposure model which (along with its earlier version called pNEM) has been used by the U.S. Environmental Protection Agency (EPA) for over 30 years for assessment of human exposure to airborne pollutants. This study describes the application of a variance decomposition-based sensitivity analysis using the Sobol method to elucidate the key APEX inputs and processes that affect variability in exposure and dose for the simulated population. Understanding APEX’s sensitivities to these inputs helps not only the model user but also the EPA in prioritizing limited resources towards data-collection and analysis efforts for the most influential variables, in order to maintain the quality and defensibility of the simulation results. This analysis examines exposure to ozone of children ages 5–18 years. The results show that selection of activity diaries and microenvironmental parameters (including air-exchange rate and decay rate) are the most influential to estimated exposure and dose, their aggregate main-effect indices (MEIs) equaling 0.818 (out of a maximum of 1.0) for daily-average ozone exposure and 0.469 for daily-average inhaled ozone dose. The modeled person’s home location, sampled from national Census data, has a modest influence on exposure (MEI = 0.079 for daily averages), while age, sex, and body mass, also sampled from Census and other survey data, have modest influences on inhaled dose (aggregate MEI = 0.307). The sensitivity analysis also plays a quality-assurance role by evaluating the sensitivities against our knowledge of the physical properties of the model.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Data availability
The APEX model, documentation, and default input files are in the “APEX52 installer”, at https://www.epa.gov/fera/download-trimexpo-inhalation-apex. The additional files needed to run the Sobol simulations discussed in the paper can be found in “APEX5.2 input files for Sobol sensitivity analysis” at the same location.
Code availability
The APEX model is written in Fortran and freely available for download and use as an executable (.exe) file from EPA: https://www.epa.gov/fera/download-trimexpo-inhalation-apex. Model inputs are text files, and default inputs as well as an example case study are available at the same website. These files, along with the source code, are packaged up in a simple installer approximately 100 MB in size. APEX has been tested on Windows and Linux operating systems, and modern computers typically easily satisfy the RAM and processor requirements of the model. Detailed documentation of APEX also is available at the same site.
Notes
Every combination of profile and random variable is assigned two “seeds” (32-bit integers) which are derived from an overall run seed using a special random generator with a period of (2^32) − 2. When one or more random values are required for a modeling variable, the standard Fortran uniform random generator is used. This generator uses two 32-bit seeds, so if the sample value is desired the two 32-bit seeds allotted to this profile-variable combination are used in the order AB, but if the resample value is desired the BA order is used. Exhaustive testing has confirmed that the values A and B are always different until the entire period of length (2^32) − 2 has been sampled.
References
Douglas-Smith D, Iwanaga T, Croke BFW, Jakeman AJ (2020) Certain trends in uncertainty and sensitivity analysis: an overview of software tools and techniques. Environ Model Softw 124:104588. https://doi.org/10.1016/j.envsoft.2019.104588
Gatel L, Lauvernet C, Carluer N, Weill S, Paniconi C (2020) Sobol global sensitivity analysis of a coupled surface/subsurface water flow and reactive solute transfer model on a real hillslope. Water 12:121. https://doi.org/10.3390/w12010121
Glen G, Isaacs K (2012) Estimating Sobol indices using correlations. Environ Model Softw 37:157–166. https://doi.org/10.1016/j.envsoft.2012.03.014
Helton J, Davis F (2002) Illustration of sampling-based methods for uncertainty and sensitivity analysis. Risk Anal 22(3):591–622. https://doi.org/10.1111/0272-4332.00041
Holder C, Hader J, Avanasi R, Hong T, Carr E, Mendez B, Wignall J, Glen G, Guelden B, Wei Y (2019) Evaluating potential human health risks from modeled inhalation exposures to volatile organic compounds emitted from oil and gas operations. J Air Waste Manag Assoc 69:1503–1524. https://doi.org/10.1080/10962247.2019.1680459
Isaacs K, Smith L (2005) New values for physiological parameters for the exposure model input file physiology.txt. Memorandum submitted to the U.S. Environmental Protection Agency under EPA Contract EP-D-05-065. NERL WA 10. Alion Science and Technology
Karunanidhi D, Aravinthasamy P, Subramani T, Kumar D, Setia R (2021) Investigation of health risks related with multipath entry of groundwater nitrate using Sobol sensitivity indicators in an urban-industrial sector of south India. Environ Res 200:111726. https://doi.org/10.1016/j.envres.2021.111726
Kumar D, Singh A, Kumar P, Jha RK, Sahoo SK, Jha V (2020) Sobol sensitivity analysis for risk assessment of uranium in groundwater. Environ Geochem Health 42:1789–1801. https://doi.org/10.1007/s10653-020-00522-5
McCurdy T, Glen G, Smith L, Lakkadi Y (2000) The national exposure research laboratory’s consolidated human activity database. J Expo Sci Environ Epidemiol 10:566–578. https://doi.org/10.1038/sj.jea.7500114
Mokhtari A, Frey HC, Zheng J (2006) Evaluation and recommendation of sensitivity analysis methods for application to Stochastic Human Exposure and Dose Simulation models. J Expo Sci Environ Epidemiol 16:491–506. https://doi.org/10.1038/sj.jes.7500472
Nossent J, Elsen P, Bauwens W (2011) Sobol’ sensitivity analysis of a complex environmental model. Environ Model Softw 26:1515–1525. https://doi.org/10.1016/j.envsoft.2011.08.010
Pianosi F, Beven K, Freer J, Hall JW, Rougier J, Stephenson DB, Wagener T (2016) Sensitivity analysis of environmental models: a systematic review with practical workflow. Environ Model Softw 79:214–232. https://doi.org/10.1016/j.envsoft.2016.02.008
Razavi S, Jakeman A, Saltelli A, Prieur C, Iooss B, Borgonovo E, Plischke E, Lo Piano S, Iwanaga T, Becker W et al (2021) The future of sensitivity analysis: an essential discipline for systems modeling and policy support. Environ Model Softw 137:104954. https://doi.org/10.1016/j.envsoft.2020.104954
Saltelli A, Chan K, Scott M (eds) (2000) Sensitivity analysis. Wiley, New York
Saltelli A, Tarantola S, Campolongo F, Ratto M (2004) Sensitivity analysis in practice: a guide to assessing scientific models. John Wiley & Sons Ltd, Chichester
Saltelli A, Ratto M, Andres T, Campolongo F, Cariboni J, Gatelli D, Saisana M, Tarantola S (2008) Global sensitivity analysis. A primer. John Wiley & Sons Ltd, Chichester
Saman R, Jakeman A, Saltelli A et al (2021) The future of sensitivity analysis: an essential discipline for systems modeling and policy support. Environ Model Softw 137:104954. https://doi.org/10.1016/j.envsoft.2020.104954
Sobol’ IM (1990) On sensitivity estimates for nonlinear mathematical models (in Russian). Matematicheskoe Modelirovanie 2:112–118
Sobol’ IM (1993) Sensitivity estimates for nonlinear mathematical models. Math Model Comput Exp 1:407–414
US Census Bureau 2010 (2014) US Census Bureau/American FactFinder. “P12: sex by age.” 2010 Census. http://factfinder2.census.gov. Accessed 14 January 2014
US Census Bureau 2011 (2014) US Census Bureau/American FactFinder. “B23001: sex and age by employment status for the population 16 years and over.” 2005–2010 American Community Survey. http://factfinder2.census.gov. Accessed 14 January 2014
U.S. EPA (2007) Ozone population exposure analysis for selected urban areas. Office of Air Quality Planning and Standards. U.S. Environmental Protection Agency, Research Triangle Park, NC, 27711. EPA-452/R-07-010 https://www3.epa.gov/ttn/naaqs/standards/ozone/s_o3_cr_td.html
U.S. EPA (2008) Risk and exposure assessment to support the review of the NO2 primary national ambient air quality standard. Office of Air Quality Planning and Standards, U.S. Environmental Protection Agency, Research Triangle Park, NC, 27711. EPA-452/R-08-008a http://www3.epa.gov/ttn/naaqs/standards/nox/s_nox_cr_rea.html
U.S. EPA (2010) Quantitative risk and exposure assessment for carbon monoxide—Amended. Office of Air Quality Planning and Standards, U.S. Environmental Protection Agency, Research Triangle Park, NC, 27711. EPA-452/R-10-006 https://www.epa.gov/naaqs/carbon-monoxide-co-standards-risk-and-exposure-assessments-current-review
U.S. EPA (2014) Health risk and exposure assessment for ozone. (Final Report). Office of Air Quality Planning and Standards. Research Triangle Park, NC. U.S. EPA. EPA-452/R-14-004a https://nepis.epa.gov/Exe/ZyPURL.cgi?Dockey=P100KBUF.txt
U.S. EPA (2018) Risk and exposure assessment for the review of the primary national ambient air quality standard for sulfur oxides. Office of Air Quality Planning and Standards, U.S. Environmental Protection Agency, Research Triangle Park, NC, 27711. EPA-452/R-18-003 https://www.epa.gov/naaqs/sulfur-dioxide-so2-standards-risk-and-exposure-assessments-current-review
U.S. EPA (2019a) Air pollutants exposure model documentation (APEX, Version 5.2) Volume I: User’s Guide. Office of Air Quality Planning and Standards, U.S. Environmental Protection Agency, Research Triangle Park, NC, 27711. EPA-452/R-19–005a. https://www.epa.gov/fera/apex-user-guides
U.S. EPA (2019b) Air pollutants exposure model documentation (APEX, Version 5.2) Volume II: Technical Support Document. Office of Air Quality Planning and Standards, U.S. Environmental Protection Agency, Research Triangle Park, NC, 27711. EPA-452/R-17-001b https://www.epa.gov/fera/apex-user-guides
U.S. EPA (2019c) The consolidated human activity database (CHAD) Documentation and Users’ Guide. U.S. Environmental Protection Agency, Research Triangle Park, NC, 27711. EPA-452/B-19-001 https://www.epa.gov/fera/consolidated-human-activity-database-chad-documentation-chad-master
U.S. EPA (2020) Policy assessment for the review of the ozone national ambient air quality standards. U.S. Environmental Protection Agency, Research Triangle Park, NC, 27711.EPA-452/R-20-001 https://www.epa.gov/sites/default/files/2020-05/documents/o3-final_pa-05-29-20compressed.pdf
Wei S, Li Y, Gao X, Lee KY, Sun L (2020) Multi-stage sensitivity analysis of distributed energy systems: a variance-based Sobol method. J Mod Power Sys Clean Energy 8(5):895–905. https://doi.org/10.35833/MPCE.2020.000134
Zartarian V, Ozkaynak H, Burke J, Zufall M, Rigas M, Furtaw E (2000) A modeling framework for estimating children’s residential exposure and dose to chlorpyrifos via dermal residue contact and non-dietary ingestion. Environ Health Perspect 108(6):505–514. https://doi.org/10.1289/ehp.00108505
Zhang X-Y, Trame M, Lesko L, Schmidt S (2015) Sobol sensitivity analysis: a tool to guide the development and evaluation of systems pharmacology models. CPT: Pharmacomet Syst Pharmacol 4:69–79. https://doi.org/10.1002/psp4.6
Acknowledgements
The authors extend special thanks to ICF staff Samuel Kovach and Madison Lee for verifying and packaging the model runs, Wren Tracy for assisting in formatting, and Lauren Fitzharris for additional formatting, ensuring compliance with author guidelines, and assisting with manuscript submission. U.S. Environmental Protection Agency Contract No. EP-W-12-010 provided funding to ICF for this work. Although the manuscript was reviewed by the U.S. Environmental Protection Agency and approved for publication, it may not necessarily reflect official Agency policy. Mention of trade names or commercial products does not constitute endorsement or recommendation for use. The data used in this study may be obtained at: https://www.epa.gov/fera/download-trimexpo-inhalation-apex.
Funding
U.S. Environmental Protection Agency Contract No. EP-W-12-010 provided funding to ICF for this work.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors have no conflicts of interest to declare that are relevant to the content of this article.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Supplementary Information
Below is the link to the electronic supplementary material.
Rights and permissions
About this article
Cite this article
Langstaff, J., Glen, G., Holder, C. et al. A sensitivity analysis of a human exposure model using the Sobol method. Stoch Environ Res Risk Assess 36, 3945–3960 (2022). https://doi.org/10.1007/s00477-022-02238-7
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00477-022-02238-7