Abstract
A particle size distribution (PSD) of particulate matter (PM) is a primary metric to examine PM transport and fate, as well as PM-bound chemicals and pathogens in urban waters. To facilitate physical interpretation and data sharing, a series of concise analytical models are examined to reproduce unit operation (UO) influent and effluent PSD data and indices. The models are a (1) single-parameter exponential and two-parameter (2) gamma, (3) lognormal, and (4) Rosin-Rammler distributions. Two-parameter models provide physical interpretations for the central tendency of PM diameters, and shape as an index of PSD hetero-dispersivity. Goodness-of-fit is used to test models and PSDs. For influent data from two disparate areas, a paved source area and a larger watershed delivering unique PSDs, lognormal and gamma models provide consistent representation of influent and effluent complexity. In these areas, contrasting UOs (a clarification basin and a volumetric filter), subject to type I settling, scour, and filter PM elution, are differentiated based on flow, surface area, volume, and residence time. Surface overflow rate (SOR) as a common heuristic design tool for only type I settling is used to further test PSD models by simulating effluent PSDs for a scaled basin design. Lognormal and gamma models of SOR-generated effluent PSDs were not statistically different. In conclusion, two-parameter PSD models have physical interpretations and lower errors compared to an exponential model. Gamma and lognormal distributions are physically-based models that reproduce actual complex influent or effluent or through SOR as a tool for PSD transformation. Results indicate that PSD models and parameters can be applied to evaluate behavior of common UOs.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Akaike, H. (1998). Information theory and an extension of the maximum likelihood principle. In Selected papers of hirotugu akaike (pp. 199–213). Springer. https://doi.org/10.1007/978-1-4612-1694-0_15.
Allen, T. (2013). Particle size measurement. Dordrecht: Springer. https://doi.org/10.1007/978-94-009-0417-0.
ASTM (2013). American Society for Testing and Materials. Standard test methods for determining sediment concentration in water samples. ASTM D3977–97 (Reapproved 2013). West Conshohocken, Pa. https://doi.org/10.1520/D3977-97R13.
Bao, W., Zhu, S., Guo, S., Wang, L., Huang, S., Fu, J., & Ye, Z. (2018). Particle size distribution mathematical models and properties of suspended solids in a typical freshwater pond. Environmental Pollution, 241, 164–171. https://doi.org/10.1016/j.envpol.2018.05.063.
Bolognesi, A., Ciccarello, A., Maglionico, M., Kim, J. Y., Ciccarello, A., Maglionico, M., et al. (2012). Can surface overflow rate predict particulate matter load capture for common urban drainage appurtenances? Journal of Environmental Engineering, 138(7), 723–733. https://doi.org/10.1061/(ASCE)EE.1943-7870.0000512.
CAETVP (2014). Canadian environmental technology verification program. The CAETVP procedure for laboratory testing of oil-grit separators. http://etvcanada.ca/wp-content/uploads/2014/06/ETV-OGS-Procedure_final_revised-June_2014.pdf. Accessed 30 May 2019.
Charters, F. J., Cochrane, T. A., & O’Sullivan, A. D. (2015). Particle size distribution variance in untreated urban runoff and its implication on treatment selection. Water Research, 85, 337–345. https://doi.org/10.1016/j.watres.2015.08.029.
Cristina, C. M., Tramonte, J., & Sansalone, J. J. (2002). A granulometry-based selection methodology for separation of traffic-generated particles in urban highway snowmelt runoff. Water, Air, and Soil Pollution, 136(1–4), 33–53. https://doi.org/10.1023/A:1015239831619.
Dickenson, J. A., & Sansalone, J. J. (2009). Discrete phase model representation of Particulate Matter (PM) for simulating PM separation by hydrodynamic unit operations. Environmental Science and Technology, 43(21), 8220–8226. https://doi.org/10.1021/es901527r.
Draper, N. R., & Smith, H. (1998). Applied regression analysis (Vol. 326). John Wiley & Sons.
FDOT (2016). Florida Department of Transportation. Technical report on the water management performance of the FAA pond at Naples municipal airport. Aviation and Spaceports Office, FDOT, Tallahassee, FL. https://www.florida-aviation-database.com/library/filedownload.aspx%3Fguid%3D1edf132e-6c5c-4774-9045-faccb850e305+&cd=2&hl=en&ct=clnk&gl=us. Accessed 30 May 2019.
Fowler, G. D., Roseen, R. M., Ballestero, T. P., Guo, Q., & Houle, J. (2009). Sediment monitoring bias by autosampler in comparison with whole volume sampling for parking lot runoff. In Proceedings of World Environmental and Water Resources Congress 2009 - World Environmental and Water Resources Congress 2009: Great Rivers (Vol. 342, pp. 1514–1522). https://doi.org/10.1061/41036(342)150.
González-Tello, P., Camacho, F., Vicaria, J. M., & González, P. A. (2008). A modified Nukiyama-Tanasawa distribution function and a Rosin-Rammler model for the particle-size-distribution analysis. Powder Technology, 186(3), 278–281. https://doi.org/10.1016/j.powtec.2007.12.011.
Grant, S., Rekhi, N., Pise, N., Reeves, R., Matsumoto, M., Wistrom, A., et al. (2003). A review of the contaminants and toxicity associated with particles in stormwater runoff. Report No. CTSW-RT-03-059. California Department of Transportation, Sacramento, CA. https://doi.org/10.13140/RG.2.1.4847.1526.
Gray, J. R., Glysson, G. D., Turcios, L. M., Schwarz, G. E., Gray, B. J. R., Glysson, G. D., et al. (2000). Comparability of suspended-sediment concentration and total suspended solids data, (August). https://doi.org/10.3133/wri004191.
Gupta, A., & Yan, D. S. (2016). Mineral processing design and operations: an introduction. Elsevier.
Herr, C., & Sansalone, J. J. (2015). In situ volumetric filtration physical model to separate particulate matter from stormwater. Journal of Environmental Engineering, 141(9), 04015017. https://doi.org/10.1061/(ASCE)EE.1943-7870.0000946.
Janke, B. D., Finlay, J. C., & Hobbie, S. E. (2017). Trees and streets as drivers of urban stormwater nutrient pollution. Environmental Science and Technology, 51(17), 9569–9579. https://doi.org/10.1021/acs.est.7b02225.
Kim, J. Y., & Sansalone, J. J. (2010). Significance of using different particulate matter indices on representing particulate-bound metals load and BMP performance during stormwater events. In Proceedings of the World Environmental and Water Resources Congress 2010, Providence, Rhode Island, USA, 16-20 May, 2010 (pp. 3181–3187). Reston: American Society of Civil Engineers (ASCE).
Kvålseth, T. O. (1985). Cautionary note about R2. The American Statistician, 39(4), 279–285. https://doi.org/10.1080/00031305.1985.10479448.
Lambert, S., & Wagner, M. (2016). Formation of microscopic particles during the degradation of different polymers. Chemosphere, 161, 510–517. https://doi.org/10.1016/j.chemosphere.2016.07.042.
Li, H., & Sansalone, J. J. (2020). CFD model of PM sedimentation and resuspension in urban water clarification. Journal of Environmental Engineering, 146(3), 04019118. https://doi.org/10.1061/(ASCE)EE.1943-7870.0001649.
Liu, H., & Sansalone, J. J. (2019). CFD and physical models of PM separation for urban drainage hydrodynamic unit operations. Water Research, 154, 258–266. https://doi.org/10.1016/j.watres.2019.01.057.
Malcom, H. R. (1989). Elements of urban stormwater design. Raleigh, NC: North Carolina State University.
Malvern Instruments (2007). Mastersizer 2000 user manual. https://www.malvernpanalytical.com/en/assets/Mastersizer-2000-user-manual-English-MAN0384-1-0_tcm50-11674.pdf. Accessed 30 May 2019.
Mazin, I. P., Khrgian, A. K., & Imyanitov, I. M. (1989). Clouds and cloudy atmosphere handbook. Leningrad: Gidrometeoizdat.
Mie, G. (1908). Beitra¨ge zur Optik tru¨ ber Medien, speziell kolloidaler Metallösungen. Ann. der Physik, 3(25), 377–445.
Mugele, R. A., & Evans, H. D. (1951). Droplet size distribution in sprays. Industrial & Engineering Chemistry, 43(6), 1317–1324. https://doi.org/10.1021/ie50498a023.
Nichols, P., Lucke, T., & Drapper, D. (2015). Field and evaluation methods used to test the performance of a stormceptor® class 1 stormwater treatment device in Australia. Sustainability (Switzerland), 7(12), 16311–16323. https://doi.org/10.3390/su71215817.
NJDEP (2013). New Jersey Department of Environmental Protection. NJDEP Laboratory protocol to assess total suspended solids removal by a hydrodynamic sedimentation manufactured treatment device. https://www.njstormwater.org/pdf/hds-protocol-1-25-13.pdf. Accessed 30 May 2019.
NRC (2008). National Research Council. Urban stormwater management in the United States. Committee on reducing stormwater discharge contributions to water pollution. The National Academies Press, Washington, D. C. https://www.epa.gov/sites/production/files/2015-10/documents/nrc_stormwaterreport1.pdf. Accessed 30 May 2019.
Nukiyama, S., & Tanasawa, Y. (1939). Experiments on the atomization of liquids in an air stream. Report 3: on the droplet-size distribution in an atomized jet. Trans. Soc. Mech. Eng. Japan, 5, 62–67.
Olding, D. D. (2000). Algal communities as a biological indicator of stormwater management pond performance and function. Water Quality Research Journal of Canada, 35(3), 489–503. https://doi.org/10.2166/wqrj.2000.029.
Olthoff, L. W., Van Der Bilt, A., Bosman, F., & Kleizen, H. H. (1984). Distribution of particle sizes in food comminuted by human mastication. Archives of Oral Biology, 29(11), 899–903. https://doi.org/10.1016/0003-9969(84)90089-X.
Rosin, P., & Rammler, E. (1933). Laws governing the fineness of powdered coal. Journal of Institute of Fuel, 7, 29–36.
Sansalone, J. J., & Cristina, C. M. (2004). Prediction of gradation-based heavy metal mass using granulometric indices of snowmelt particles. Journal of Environmental Engineering, 130(12), 1488–1497. https://doi.org/10.1061/(ASCE)0733-9372(2004)130:12(1488).
Sansalone, J. J., & Kim, J. Y. (2008a). Transport of particulate matter fractions in urban source area pavement surface runoff. Journal of Environmental Quality, 37(5), 1883–1893. https://doi.org/10.2134/jeq2007.0495.
Sansalone, J. J., & Kim, J. Y. (2008b). Suspended particle destabilization in retained urban stormwater as a function of coagulant dosage and redox conditions. Water Research, 42(4–5), 909–922. https://doi.org/10.1016/j.watres.2007.08.037.
Sansalone, J. J., & Pathapati, S. S. (2009). Particle dynamics in a hydrodynamic separator subject to transient rainfall-runoff. Water Resources Research, 45(9). https://doi.org/10.1029/2008WR007661.
Sansalone, J. J., & Ying, G. (2008). Partitioning and granulometric distribution of metal leachate from urban traffic dry deposition particulate matter subject to acidic rainfall and runoff retention. Water Research, 42(15), 4146–4162. https://doi.org/10.1016/j.watres.2008.06.013.
Sansalone, J. J., Koran, J. M., Smithson, J. A., & Buchberger, S. G. (1998). Physical characteristics of urban roadway solids transported during rain events. Journal of Environmental Engineering, 124(5), 427–440. https://doi.org/10.1061/(ASCE)0733-9372(1998)124:5(427).
Sansalone, J. J., Lin, H., & Ying, G. (2009). Experimental and field studies of type i settling for particulate matter transported by urban runoff. Journal of Environmental Engineering, 135(10), 953–963. https://doi.org/10.1061/(ASCE)EE.1943-7870.0000078.
Sapra, R. L. (2014). Using R2 with caution. Current Medicine Research and Practice, 4(3), 130–134. https://doi.org/10.1016/J.CMRP.2014.06.002.
Selbig, W. R., & Fienen, M. N. (2012). Regression modeling of particle size distributions in urban storm water: advancements through improved sample collection methods. Journal of Environmental Engineering, 138(12), 1186–1193. https://doi.org/10.1061/(ASCE)EE.1943-7870.0000612.
Selbig, W. R., Fienen, M. N., Horwatich, J. A., & Bannerman, R. T. (2016). The effect of particle size distribution on the design of urban stormwater control measures. Water, 8(1), 17. https://doi.org/10.3390/w8010017.
Spelman, D., & Sansalone, J. J. (2017). Methods to model particulate matter clarification of unit operations subject to unsteady loadings. Water Research, 115, 347–359. https://doi.org/10.1016/j.watres.2017.02.053.
Spiess, A. N., & Neumeyer, N. (2010). An evaluation of R2 as an inadequate measure for nonlinear models in pharmacological and biochemical research: a Monte Carlo approach. BMC Pharmacology, 10(1), 6. https://doi.org/10.1186/1471-2210-10-6.
Tran, N. H., Ngo, H. H., Urase, T., & Gin, K. Y. H. (2015). A critical review on characterization strategies of organic matter for wastewater and water treatment processes. Bioresource Technology, 193, 523–533. https://doi.org/10.1016/j.biortech.2015.06.091.
US EPA (2016). United States Environmental Protection Agency. National Summary of State Information. Office of Water, Office of Wetlands, Oceans and Watersheds, Washington, DC. https://ofmpub.epa.gov/waters10/attains_nation_cy.control. Accessed 30 May 2019.
Vahabzadeh Bozorg, M., Bidabadi, M., & Bordbar, V. (2019). Numerical investigation of flame behavior and quenching distance in randomly distributed poly-dispersed iron dust cloud combustion within a narrow channel. Journal of Hazardous Materials, 367, 482–491. https://doi.org/10.1016/j.jhazmat.2019.01.002.
Van Buren, M. A. A., Watt, W. E. E., & Marsalek, J. (1997). Application of the log-normal and normal distributions to stormwater quality parameters. Water Research, 31(1), 95–104. https://doi.org/10.1016/S0043-1354(96)00246-1.
Vesilind, P. A. (1980). The Rosin-Rammler particle size distribution. Resource Recovery and Conservation, 5(3), 275–277. https://doi.org/10.1016/0304-3967(80)90007-4.
Weibull, W. (1951). A statistical distribution function of wide applicability. Journal of Applied Mechanics, 18(3), 293–297.
Wijesiri, B., Liu, A., Gunawardana, C., Hong, N., Zhu, P., Guan, Y., & Goonetilleke, A. (2018). Influence of urbanisation characteristics on the variability of particle-bound heavy metals build-up: a comparative study between China and Australia. Environmental Pollution, 242, 1067–1077. https://doi.org/10.1016/j.envpol.2018.07.123.
Willett, J. B., & Singer, J. D. (1988). Another cautionary note about R2: its use in weighted least-squares regression analysis. The American Statistician, 42(3), 236–238. https://doi.org/10.1080/00031305.1988.10475573.
Yang, X., Lee, J., Barker, D. E., Wang, X., & Zhang, Y. (2012). Comparison of six particle size distribution models on the goodness-of-fit to particulate matter sampled from animal buildings. Journal of the Air and Waste Management Association, 62(6), 725–735. https://doi.org/10.1080/10962247.2012.671148.
Ying, G., & Sansalone, J. J. (2011). Gravitational settling velocity regimes for heterodisperse urban drainage particulate matter. Journal of Environmental Engineering, 137(1), 15–27. https://doi.org/10.1061/(ASCE)EE.1943-7870.0000298.
Zhang, Y. (2004). Indoor air quality engineering. Boca Raton: CRC Press. https://doi.org/10.1201/b12485.
Zhang, H., & Sansalone, J. J. (2014). Partitioning and first-flush of nitrogen in rainfall-runoff from an urban source area. Journal of Environmental Engineering, 140(8), 04014027. https://doi.org/10.1061/(ASCE)EE.1943-7870.0000832.
Zhao, H., Jiang, Q., Xie, W., Li, X., & Yin, C. (2018). Role of urban surface roughness in road-deposited sediment build-up and wash-off. Journal of Hydrology, 560, 75–85. https://doi.org/10.1016/j.jhydrol.2018.03.016.
Acknowledgments
The databases developed herein were generated from prior studies funded by the Florida Department of Transportation and Hydro-International.
Funding
This research was funded through Florida Department of Environmental Protection and Florida Department of Transportation.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of Interest
The authors declare that they have no conflict of interest.
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Supplementary Information
ESM 1
Supplemental data for this article can be found in the supplemental information document (SI) (DOCX 1600 kb)
Rights and permissions
About this article
Cite this article
Liu, Y., Sansalone, J.J. Physically-Based Particle Size Distribution Models of Urban Water Particulate Matter. Water Air Soil Pollut 231, 555 (2020). https://doi.org/10.1007/s11270-020-04925-z
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s11270-020-04925-z