Abstract
Recent studies have provided explicit analytical equations that can be used to quantify directly the hydrologic performance statistics of green roofs, such as runoff-reduction ratios. These equations were obtained based on simplified representations of the hydrologic and hydraulic processes occurring on and inside green roofs, as well as stochastic models describing local rainfall characteristics. To simplify derivations, these studies considered only saturation-excess runoff and neglected infiltration-excess runoff that may be generated from green roofs. We develop a method for considering both saturation- and infiltration-excess runoff; the proposed analytical equations can be used to directly quantify the performance statistics of any type of green roof. Systematic comparisons of analytical and numerical simulation results were also conducted to demonstrate the accuracy of the analytical equations. As an alternative to numerical simulations, the analytical equations can be used by engineers to more conveniently quantify the performances of alternative green roof configurations.
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Data Availability Statement
All data and models used during the study are available from the corresponding author upon request.
Acknowledgments
This work has been supported by the Natural Sciences and Engineering Research Council of Canada. The comments made by the four anonymous reviewers and the editor helped a lot in improving this paper. The hand-written annotations provided by one of the reviewers helped greatly and are very much appreciated.
References
Adams, B. J., and F. Papa. 2000. Urban stormwater management planning with analytical probabilistic models. New York: Wiley.
Ahiablame, L. M., B. A. Engel, and I. Chaubey. 2012. “Effectiveness of low impact development practices: Literature review and suggestions for future research.” Water Air Soil Pollut. 223 (7): 4253–4273. https://doi.org/10.1007/s11270-012-1189-2.
Alfredo, K., F. Montalto, and A. Goldstein. 2010. “Observed and modeled performances of prototype green roof test plots subjected to simulated low- and high-intensity precipitations in a laboratory experiment.” J. Hydrol. Eng. 15 (6): 444–457. https://doi.org/10.1061/(ASCE)HE.1943-5584.0000135.
ASCE. 1996. Hydrology handbook. 2nd ed. New York: ASCE.
Bartlett, M., A. Parolari, J. McDonnell, and A. Porporato. 2016. “Beyond the SCS-CN method: A theoretical framework for spatially lumped rainfall-runoff response.” Water Resour. Res. 52 (6): 4608–4627. https://doi.org/10.1002/2015WR018439.
Bengtsson, L., L. Grahn, and J. Olsson. 2005. “Hydrological function of a thin extensive green roof in southern Sweden.” Hydrol. Res. 36 (3): 259–268. https://doi.org/10.2166/nh.2005.0019.
Berndtsson, J. C. 2010. “Green roof performance towards management of runoff water quantity and quality: A review.” Ecol. Eng. 36 (4): 351–360. https://doi.org/10.1016/j.ecoleng.2009.12.014.
Budyko, M. I., D. H. Miller, and D. H. Miller. 1974. Vol. 508 of Climate and life. New York: Academic Press.
Cahill, T. H. 2012. Low impact development and sustainable stormwater management. New York: Wiley.
Cox, D., and V. Isham. 1986. “The virtual waiting-time and related processes.” Adv. Appl. Probab. 18 (2): 558–573. https://doi.org/10.2307/1427312.
Eagleson, P. S. 1972. “Dynamics of flood frequency.” Water Resour. Res. 8 (4): 878–898. https://doi.org/10.1029/WR008i004p00878.
Eagleson, P. S. 1978. “Climate, soil, and vegetation: 2. The distribution of annual precipitation derived from observed storm sequences.” Water Resour. Res. 14 (5): 713–721. https://doi.org/10.1029/WR014i005p00713.
Gardiner, C. W. 2004. Handbook of stochastic methods for physics, chemistry and the natural sciences. 3rd ed. Berlin: Springer.
Guo, R., and Y. Guo. 2018. “Analytical equations for use in the planning of infiltration facilities.” J. Sustainable Water Built Environ. 4 (2): 06018001. https://doi.org/10.1061/JSWBAY.0000849.
Guo, R., Y. Guo, S. Zhang, and D. Z. Zhu. 2020. “A tool for water balance analysis of bioretention cells.” J. Sustainable Water Built Environ. 6 (3): 04020013. https://doi.org/10.1061/JSWBAY.0000920.
Guo, Y. 2016. “Stochastic analysis of hydrologic operation of green roofs.” J. Hydrol. Eng. 21 (7): 04016016. https://doi.org/10.1061/(ASCE)HE.1943-5584.0001371.
Guo, Y., and B. J. Adams. 1998. “Hydrologic analysis of urban catchments with event-based probabilistic models: 1. Runoff volume.” Water Resour. Res. 34 (12): 3421–3431. https://doi.org/10.1029/98WR02449.
Guo, Y., and B. W. Baetz. 2007. “Sizing of rainwater storage units for green building applications.” J. Hydrol. Eng. 12 (2): 197–205. https://doi.org/10.1061/(ASCE)1084-0699(2007)12:2(197).
Guo, Y., and T. Gao. 2016. “Analytical equations for estimating the total runoff reduction efficiency of infiltration trenches.” J. Sustainable Water Built Environ. 2 (3): 06016001. https://doi.org/10.1061/JSWBAY.0000809.
Guo, Y., S. Zhang, and S. Liu. 2014. “Runoff reduction capabilities and irrigation requirements of green roofs.” Water Resour. Manage. 28 (5): 1363–1378. https://doi.org/10.1007/s11269-014-0555-9.
Hakimdavar, R., P. J. Culligan, M. Finazzi, S. Barontini, and R. Ranzi. 2014. “Scale dynamics of extensive green roofs: Quantifying the effect of drainage area and rainfall characteristics on observed and modeled green roof hydrologic performance.” Ecol. Eng. 73 (Dec): 494–508. https://doi.org/10.1016/j.ecoleng.2014.09.080.
Hamouz, V., and T. M. Muthanna. 2019. “Hydrological modelling of green and grey roofs in cold climate with the SWMM model.” J. Environ. Manage. 249 (Nov): 109350. https://doi.org/10.1016/j.jenvman.2019.109350.
Hassini, S., and Y. Guo. 2016. “Exponentiality test procedures for large samples of rainfall event characteristics.” J. Hydrol. Eng. 21 (4): 04016003. https://doi.org/10.1061/(ASCE)HE.1943-5584.0001352.
Hilten, R. N., T. M. Lawrence, and E. W. Tollner. 2008. “Modeling storm water runoff from green roofs with HYDRUS-1D.” J. Hydrol. 358 (3–4): 288–293. https://doi.org/10.1016/j.jhydrol.2008.06.010.
Kasmin, H., V. R. Stovin, and E. A. Hathway. 2010. “Towards a generic rainfall-runoff model for green roofs.” Water Sci. Technol. 62 (4): 898–905. https://doi.org/10.2166/wst.2010.352.
Locatelli, L., O. Mark, P. S. Mikkelsen, K. Arnbjerg-Nielsen, M. B. Jensen, and P. J. Binning. 2014. “Modelling of green roof hydrological performance for urban drainage applications.” J. Hydrol. 519 (Nov): 3237–3248. https://doi.org/10.1016/j.jhydrol.2014.10.030.
Mentens, J., D. Raes, and M. Hermy. 2006. “Green roofs as a tool for solving the rainwater runoff problem in the urbanized 21st century?” Landscape Urban Plann. 77 (3): 217–226. https://doi.org/10.1016/j.landurbplan.2005.02.010.
Milly, P. C. D. 1993. “An analytic solution of the stochastic storage problem applicable to soil water.” Water Resour. Res. 29 (11): 3755–3758. https://doi.org/10.1029/93WR01934.
NOAA (National Oceanic and Atmospheric Administration). 2011. “1981-2010 United States climate normals.” Accessed July 1, 2020. http://www.ncdc.noaa.gov/cdo-web/datatools/normals.
Palla, A., I. Gnecco, and L. G. Lanza. 2009. “Unsaturated 2D modelling of subsurface water flow in the coarse-grained porous matrix of a green roof.” J. Hydrol. 379 (1–2): 193–204. https://doi.org/10.1016/j.jhydrol.2009.10.008.
Peng, Z., and V. Stovin. 2017. “Independent validation of the SWMM Green roof module.” J. Hydrol. Eng. 22 (9): 04017037. https://doi.org/10.1061/(ASCE)HE.1943-5584.0001558.
Raghunath, H. M. 2006. Hydrology: Principles, analysis and design. 2nd ed. New Delhi, India: New Age International.
Restrepo-Posada, P. J., and P. S. Eagleson. 1982. “Identification of independent rainstorms.” J. Hydrol. 55 (1–4): 303–319. https://doi.org/10.1016/0022-1694(82)90136-6.
Rodríguez-Iturbe, I., and A. Porporato. 2005. Ecohydrology of water-controlled ecosystems: Soil moisture and plant dynamics. Cambridge, UK: Cambridge University Press.
Rodríguez-Iturbe, I., A. Porporato, L. Ridolfi, V. Isham, and D. Coxi. 1999. “Probabilistic modelling of water balance at a point: The role of climate, soil and vegetation.” Proc. R. Soc. London, Ser. A. 455 (1990): 3789–3805. https://doi.org/10.1098/rspa.1999.0477.
Rossman, L. A. 2015. Storm water management model user’s manual, version 5.1. Washington, DC: USEPA.
Rossman, L. A., and W. C. Huber. 2016. Storm water management model reference manual, Volume—Hydrology (revised). Washington, DC: USEPA.
She, N., and J. Pang. 2009. “Physically based green roof model.” J. Hydrol. Eng. 15 (6): 458–464. https://doi.org/10.1061/(ASCE)HE.1943-5584.0000138.
Stovin, V., S. Poë, and C. Berretta. 2013. “A modelling study of long term green roof retention performance.” J. Environ. Manage. 131 (Dec): 206–215. https://doi.org/10.1016/j.jenvman.2013.09.026.
Stovin, V., G. Vesuviano, and S. De-Ville. 2015. “Defining green roof detention performance.” Urban Water J. 14 (6): 574–588. https://doi.org/10.1080/1573062X.2015.1049279.
Stovin, V., G. Vesuviano, and H. Kasmin. 2012. “The hydrological performance of a green roof test bed under UK climatic conditions.” J. Hydrol. 74 (1): 148–161. https://doi.org/10.1016/j.jhydrol.2011.10.022.
Teegavarapu, R. S. V., J. D. Salas, and J. R. Stedinger. 2019. Statistical analysis of hydrologic variables: Methods and applications. Reston, VA: ASCE.
Thompson, S. A. 1999. Hydrology for water management. Rotterdam, Netherlands: A. A. Balkema.
Voyde, E., E. Fassman, R. Simcock, and J. Wells. 2010. “Quantifying evapotranspiration rates for New Zealand green roofs.” J. Hydrol. Eng. 15 (6): 395–403. https://doi.org/10.1061/(ASCE)HE.1943-5584.0000141.
Wanielista, M. P., and Y. A. Yousef. 1993. Stormwater management. New York: Wiley.
Yang, W. Y., D. Li, T. Sun, and G. H. Ni. 2015. “Saturation-excess and infiltration-excess runoff on green roofs.” Ecol. Eng. 74 (1): 327–336. https://doi.org/10.1016/j.ecoleng.2014.10.023.
Zhang, S., and Y. Guo. 2013a. “Analytical probabilistic model for evaluating the hydrologic performance of green roofs.” J. Hydrol. Eng. 18 (1): 19–28. https://doi.org/10.1061/(ASCE)HE.1943-5584.0000593.
Zhang, S., and Y. Guo. 2013b. “Explicit equation for estimating storm-water capture efficiency of rain gardens.” J. Hydrol. Eng. 18 (12): 1739–1748. https://doi.org/10.1061/(ASCE)HE.1943-5584.0000734.
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Journal of Hydrologic Engineering
Volume 27 • Issue 4 • April 2022
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© 2022 American Society of Civil Engineers.
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Received: Apr 7, 2021
Accepted: Jan 11, 2022
Published online: Feb 15, 2022
Published in print: Apr 1, 2022
Discussion open until: Jul 15, 2022
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