Adaptive Mapping of Design Ground Snow Loads in the Conterminous United States
Publication: Journal of Structural Engineering
Volume 150, Issue 1
Abstract
Recent amendments to design ground snow load requirements in current US standards have reduced the size of case-study regions by 91% from what they were in previous standards, primarily in western states. This reduction is made possible through the development of highly accurate regional generalized additive models (RGAMs), stitched together with a novel smoothing scheme implemented in the R software package remap, to produce the continental-scale maps of reliability-targeted design ground snow loads available in current standards. This approach allows for better characterizations of the changing relationship between temperature, elevation, and ground snow loads across the conterminous US (CONUS). RGAMs are shown to have 10% or better improvement in mean absolute mapping error in two independently created data sets when compared with traditional mapping techniques.
Practical Applications
Structures must be able to withstand environmental stresses without collapsing, including snow. Design ground snow loads are estimated using snow measurements taken at weather stations throughout the US. Mapping techniques allow design ground snow loads to be estimated at regions between weather stations. This paper describes a regional approach for mapping design ground snow loads in CONUS and demonstrates the improved accuracy of the approach, relative to previous methods, on two independently created national data sets.
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Data Availability Statement
Some or all data, models, or code generated or used during the study are available in a repository online in accordance with funder data retention policies. Mapped RTSLs are available at https://asce7hazardtool.online/. Site-specific RC II RTSLs and reproduction data and code for Table 1 are available from Wagstaff et al. (2023). Climate data are available from PRISM Climate Group (2014). The remap smoothing framework is also freely available on the Comprehensive R Archive Network (CRAN) Wagstaff and Bean (2023) as well as GitHub (https://github.com/jadonwagstaff/remap).
Acknowledgments
This research was made possible through funding led by ASCE and the Structural Engineering Institute in collaboration with funding from several organizations. The groups that provided significant monetary support to this effort were (in alphabetical order): Factory Mutual, Metal Building Manufacturer’s Association, National Council of Structural Engineering Associations, Nucor, Simpson Gumpertz and Heger, the State of Montana, the Steel Deck Institute, the Steel Joist Institute, Structural Engineers Association of Montana, Wiss Janney, and Elstner Associates. Further help from the Snow and Rain Load Subcommittee and the steering committee overseeing this research went above and beyond expectations. Many long hours were spent exchanging expertise on national and local concerns resulting in the work contained in this paper and the forthcoming updates to the ASCE 7 Chapter 7 specifications. Thanks to Abbie Liel and Scott Russell for chairing the task group and steering committee overseeing this work. Special thanks to Jim Harris, Mike O’Rourke, Jim Buska, David Thompson, and Jerry Stephens for their boundless time, effort, knowledge, experience, and aid. Additionally, committee members John Duntemann, Richard Nielson, Jared DeBock, Johnn Judd, Hossein Mostafaei, John Corless, John-Paul Cardin, Sean Homem, Gary Ehrlich, Sterling Strait, Vince Sagan, and Thomas DiBlasi all provided time, expertise, local knowledge, review, and support to this work. Graduate student Salam Al-Rubaye at the University of Nebraska-Lincoln was instrumental in the development of the site-specific reliability-targeted snow loads. Undergraduates Miranda Rogers and Scout Jarman were also very helpful and provided much needed support in data processing. Lastly, the authors would like to thank the associate editor and two anonymous reviewers for their time and efforts reviewing this manuscript.
References
Al Hatailah, H., B. R. Godfrey, R. J. Nielsen, and R. L. Sack. 2015. Ground snow loads for Idaho–2015 edition. Moscow, ID: Univ. of Idaho.
Allen, C., and B. Peter. 1963. Snow loads on roofs 1962–63: Seventh progress report. Rep. No. DBR-IR-279. Ottawa: National Research Council, Division of Building Research.
Allen, D. E. 1956. Snow loads on roofs. The present requirements and a proposal for a survey of snow loads on roofs. Rep. No. DBR-IR-106. Rockville, MD: National Research Council, Division of Building Research.
Allen, D. E. 1958. Snow loads on roofs 1956–57: A progress report. Rep. No. DBR-IR-134. Ottawa: National Research Council, Division of Building Research.
Al-Rubaye, S., M. Maguire, and B. Bean. 2022. “Design ground snow loads: Historical perspective and state of the art.” J. Struct. Eng. 148 (6): 03122001. https://doi.org/10.1061/(ASCE)ST.1943-541X.0003339.
ANSI (American National Standards Institute). 1982. Minimum design loads for buildings and other structures. New York: ANSI.
ASCE. 2017. Minimum design loads and associated criteria for buildings and other structures. ASCE 7-16. Washington, DC: ASEE.
ASCE. 2021. Minimum design loads and associated criteria for buildings and other structures. ASCE 7-22. Washington, DC: ASEE.
ASCE. 2023. “ASCE 7 Hazard Tool.” Accessed September 27, 2023. https://asce7hazardtool.online/.
Auguie, B. 2017. “gridExtra: Miscellaneous functions for ‘Grid’ graphics.” Accessed May 8, 2023. https://CRAN.R-project.org/package=gridExtra.
Bean, B., M. Maguire, and Y. Sun. 2017. “Predicting Utah ground snow loads with prism.” J. Struct. Eng. 143 (9): 04017126. https://doi.org/10.1061/(ASCE)ST.1943-541X.0001870.
Bean, B., M. Maguire, and Y. Sun. 2019. “Comparing design ground snow load prediction in Utah and Idaho.” J. Cold Reg. Eng. 33 (3): 04019010. https://doi.org/10.1061/(ASCE)CR.1943-5495.0000190.
Bean, B., M. Maguire, Y. Sun, J. Wagstaff, S. A. Al-Rubaye, J. Wheeler, S. Jarman, and M. Rogers. 2021. The 2020 national snow load study. Rep. No. 276. Logan, UT: Utah State Univ.
Bean, B., Y. Sun, and M. Maguire. 2022. “Interval-valued kriging for geostatistical mapping with imprecise inputs.” Int. J. Approximate Reasoning 140 (Mar): 31–51. https://doi.org/10.1016/j.ijar.2021.10.003.
Becker, R. A., A. R. Wilks, R. Brownrigg, T. P. Minka, and A. Deckmyn. 2021. “Maps: Draw geographical maps.” Accessed May 8, 2023. https://CRAN.R-project.org/package=maps.
Burn, D. 1990. “An appraisal of the ‘region of influence’ approach to flood frequency analysis.” Hydrol. Sci. J. 35 (2): 149–165. https://doi.org/10.1080/02626669009492415.
Buska, J. S., A. Greatorex, and W. Tobiasson. 2020. Site specific case studies for determining ground snow loads in the United States. Rep. No. ERDC/CRREL SR-20-1. Hanover, NH: Engineer Research and Development Center.
CEC (Commission for Environmental Cooperation). 1997. Ecological regions of North America: Toward a common perspective. Montréal: Commission for Environmental Cooperation.
Cho, E., and J. M. Jacobs. 2020. “Extreme value snow water equivalent and snowmelt for infrastructure design over the contiguous United States.” Water Resour. Res. 56 (10): e2020WR028126. https://doi.org/10.1029/2020WR028126.
Daly, C., W. P. Gibson, G. H. Taylor, G. L. Johnson, and P. Pasteris. 2002. “A knowledge-based approach to the statistical mapping of climate.” Clim. Res. 22 (2): 99–113. https://doi.org/10.3354/cr022099.
Daly, C., M. Halbleib, J. I. Smith, W. P. Gibson, M. K. Doggett, G. H. Taylor, J. Curtis, and P. P. Pasteris. 2008. “Physiographically sensitive mapping of climatological temperature and precipitation across the conterminous United States.” Int. J. Climatol. 28 (15): 2031–2064. https://doi.org/10.1002/joc.1688.
DeBock, D. J., A. B. Liel, J. R. Harris, B. R. Ellingwood, and J. M. Torrents. 2017. “Reliability-based design snow loads. I: Site-specific probability models for ground snow loads.” J. Struct. Eng. 143 (7): 04017046. https://doi.org/10.1061/(ASCE)ST.1943-541X.0001731.
Ellingwood, B., T. V. Galambos, J. G. MacGregor, and C. A. Cornell. 1980. Vol. 13 of Development of a probability based load criterion for American National Standard A58: Building code requirements for minimum design loads in buildings and other structures. Gaithersburg, MD: US Department of Commerce, National Bureau of Standards.
Ellingwood, B., J. G. MacGregor, T. V. Galambos, and C. A. Cornell. 1982. “Probability based load criteria: Load factors and load combinations.” J. Struct. Div. 108 (5): 978–997. https://doi.org/10.1061/JSDEAG.0005959.
Ellingwood, B., and R. Redfield. 1983. “Ground snow loads for structural design.” J. Struct. Eng. 109 (4): 950–964. https://doi.org/10.1061/(ASCE)0733-9445(1983)109:4(950).
Faucher, Y. 1967. Snow loads on roofs 1964–65: Ninth progress report. Rep. No. DBR-IR-339. Ottawa: National Research Council of Canada, Division of Building Research.
Galambos, T. V., B. Ellingwood, J. G. MacGregor, and C. A. Cornell. 1982. “Probability based load criteria: Assessment of current design practice.” J. Struct. Div. 108 (5): 959–977. https://doi.org/10.1061/JSDEAG.0005958.
Goovaerts, P. 1997. Geostatistics for natural resources evaluation. Oxford, UK: Oxford University Press.
Gräler, B., E. Pebesma, and G. Heuvelink. 2016. “Spatio-temporal interpolation using gstat.” R J. 8 (1): 204–218. https://doi.org/10.32614/RJ-2016-014.
Hastie, T., and R. Tibshirani. 1986. “Generalized additive models.” Stat. Sci. 1 (3): 297–310. https://doi.org/10.1214/ss/1177013604.
Hastie, T., R. Tibshirani, and J. Friedman. 2009. The elements of statistical learning. 2nd ed. New York: Springer.
Hebert, P., and B. Peter. 1963. Snow loads on roofs 1961–62: Sixth progress report with an appendix on roof to ground load ratios. Rep. No. DBR-IR-228. Ottawa: National Research Council, Division of Building Research.
Hiemstra, P., E. Pebesma, C. Twenhöfel, and G. Heuvelink. 2009. “Real-time automatic interpolation of ambient gamma dose rates from the Dutch radioactivity monitoring network.” Comput. Geosci. 35 (8): 1711–1721. https://doi.org/10.1016/j.cageo.2008.10.011.
Hill, D. F., E. A. Burakowski, R. L. Crumley, J. Keon, J. M. Hu, A. A. Arendt, K. Wikstrom Jones, and G. J. Wolken. 2019. “Converting snow depth to snow water equivalent using climatological variables.” Cryosphere 13 (7): 1767–1784. https://doi.org/10.5194/tc-13-1767-2019.
Ho, M., and D. A. Lutes. 1968. Snow loads on roofs 1965–66: Tenth progress report. Rep. No. DBR-IR-358. Ottawa: National Research Council of Canada, Division of Building Research.
Kennedy, I., and D. Lutes. 1968. Snow loads on roofs 1966–67: Eleventh progress report. Rep. No. DBR-IR-364. Ottawa: National Research Council, Division of Building Research.
Liel, A. B., D. J. DeBock, J. R. Harris, B. R. Ellingwood, and J. M. Torrents. 2017. “Reliability-based design snow loads. II: Reliability assessment and mapping procedures.” J. Struct. Eng. 143 (7): 04017047. https://doi.org/10.1061/(ASCE)ST.1943-541X.0001732.
Lu, G. Y., and D. W. Wong. 2008. “An adaptive inverse-distance weighting spatial interpolation technique.” Comput. Geosci. 34 (9): 1044–1055. https://doi.org/10.1016/j.cageo.2007.07.010.
Marx, B. D., and P. H. C. Eilers. 1998. “Direct generalized additive modeling with penalized likelihood.” Comput. Stat. Data Anal. 28 (2): 193–209. https://doi.org/10.1016/S0167-9473(98)00033-4.
McAllister, T. P., N. Wang, and B. R. Ellingwood. 2018. “Risk-informed mean recurrence intervals for updated wind maps in ASCE 7-16.” J. Struct. Eng. 144 (5): 06018001. https://doi.org/10.1061/(ASCE)ST.1943-541X.0002011.
Menne, M., I. Durre, B. Korzeniewski, R. Vose, B. Gleason, and T. Houston. 2012. “Global historical climatology network–daily, version 3.26.” Accessed June 4, 2020. https://doi.org/10.7289/V5D21VHZ.
Meyer, H., C. Reudenbach, S. Wöllauer, and T. Nauss. 2019. “Importance of spatial predictor variable selection in machine learning applications–moving from data reproduction to spatial prediction.” Ecol. Modell. 411 (Nov): 108815. https://doi.org/10.1016/j.ecolmodel.2019.108815.
Mo, H., L. Dai, F. Fan, T. Che, and H. Hong. 2016. “Extreme snow hazard and ground snow load for China.” Nat. Hazards 84 (Jun): 2095–2120. https://doi.org/10.1007/s11069-016-2536-1.
Mo, H., W. Ye, and H. Hong. 2022. “Estimating and mapping snow hazard based on at-site analysis and regional approaches.” Nat. Hazards 111 (3): 2459–2485. https://doi.org/10.1007/s11069-021-05144-3.
O’Rourke, M., P. Koch, and R. Redfield. 1983. Analysis of roof snow load case studies. CRREL Rep. No. 83-1. Hanover, NH: US Army Cold Regions Research and Engineering Laboratory.
O’Rourke, M. J., R. Redfield, and P. von Bradsky. 1982. “Uniform snow loads on structures.” J. Struct. Div. 108 (12): 2781–2798. https://doi.org/10.1061/JSDEAG.0006105.
O’Rourke, M. J., and U. Stiefel. 1983. “Roof snow loads for structural design.” J. Struct. Eng. 109 (7): 1527–1537. https://doi.org/10.1061/(ASCE)0733-9445(1983)109:7(1527).
Pebesma, E. 2018. “Simple features for R: Standardized support for spatial vector data.” R J. 10 (1): 439–446. https://doi.org/10.32614/RJ-2018-009.
Pebesma, E. J. 2004. “Multivariable geostatistics in S: The gstat package.” Comput. Geosci. 30 (Apr): 683–691. https://doi.org/10.1016/j.cageo.2004.03.012.
Pedersen, T. L., and F. Crameri. 2022. “Scico: Colour palettes based on the scientific colour-maps.” Accessed May 8, 2023. https://CRAN.R-project.org/package=scico.
Pernica, G., and B. Peter. 1966. Snow loads on roofs 1963–64: Eighth progress report. Rep. No. DBR-IR-324. Ottawa: National Research Council Canada, Division of Building Research.
PRISM Climate Group. 2014. “PRISM climate data.” Accessed October 5, 2023. https://prism.oregonstate.edu.
R Core Team. 2022. R: A language and environment for statistical computing. Vienna, Austria: R Foundation for Statistical Computing.
Sack, R. L. 2015. “Ground snow loads for the western United States: State of the art.” J. Struct. Eng. 142 (1): 04015082. https://doi.org/10.1061/(ASCE)ST.1943-541X.0001343.
Sack, R. L., R. J. Nielsen, and B. R. Godfrey. 2016. “Evolving studies of ground snow loads for several western US States.” J. Struct. Eng. 143 (3): 04016187. https://doi.org/10.1061/(ASCE)ST.1943-541X.0001679.
Sack, R. L., and A. Sheikh-Taheri. 1986. Ground and roof snow loads for Idaho. Moscow, ID: Univ. of Idaho.
Scott, J., and B. Peter. 1961. Snow loads on roofs 1960–61: Fifth progress report. Rep. No. DBR-IR-228. Ottawa: National Research Council, Division of Building Research.
SEAO (Structural Engineers Association of Oregon) Snow Load Committee. 2007. Snow load analysis for Oregon. Portland, OR: SEAO.
Shepard, D. 1968. “A two-dimensional interpolation function for irregularly-spaced data.” In Proc., 1968 23rd ACM National Conf., 517–524. New York: Association for Computing Machinery.
Theisen, G. P., M. J. Keller, J. E. Stephens, F. F. Videon, and J. P. Schilke. 2004. Snow loads for structural design in Montana. Bozeman, MT: Montana State Univ.
Thom, H. 1966. “Distribution of maximum annual water equivalent of snow on the ground.” Mon. Weather Rev. 94 (4): 265–271. https://doi.org/10.1175/1520-0493(1966)094%3C0265:DOMAWE%3E2.3.CO;2.
Tobiasson, W., J. Buska, A. Greatorex, J. Tirey, and J. Fisher. 2002. Ground snow loads for New Hampshire. Rep. No. ERDC/CRREL TR-02-6. Hanover, NH: Cold Regions Research and Engineering Laboratory.
Tobiasson, W., and A. Greatorex. 1997. “Database and methodology for conducting site specific snow load case studies for the United States.” In Proc., 3rd Int. Conf. on Snow Engineering, edited by I. Izumi, T. Nakamura, and R. L. Sack, 249–256. Rotterdam, Netherlands: A. A. Balkema.
Tobiasson, W., and R. Redfield. 1980. Snow loads for the United States, parts I and II. Hanover, NH: Cold Regions Research and Engineering Laboratory.
Wagstaff, J. 2021. “Regionalized models with spatially continuous predictions at the borders.” M.S. thesis, Dept. of Mathematics and Statistics, Utah State Univ.
Wagstaff, J., and B. Bean. 2023. “Remap: Regionalized models with spatially smooth predictions.” R J. 14 (4): 160–178. https://doi.org/10.32614/RJ-2023-004.
Wagstaff, J., B. Bean, J. Wheeler, M. Maguire, and Y. Sun. 2023. Supplementary files for “adaptive mapping of design ground snow loads in the conterminous United States. Logan, UT: Utah State Univ.
Wahba, G. 1981. “Spline interpolation and smoothing on the sphere.” SIAM J. Sci. Stat. Comput. 2 (1): 5–16. https://doi.org/10.1137/0902002.
Watt, W., and H. J. Thorburn. 1960. Snow loads on roofs 1959–60: Fourth progress report. Rep. No. DBR-IR-204. Ottawa: National Research Council, Division of Building Research.
Wheeler, J., B. Bean, and M. Maguire. 2022. “Creating a universal depth-to-load conversion technique for the conterminous United States using random forests.” J. Cold Reg. Eng. 36 (1): 04021019. https://doi.org/10.1061/(ASCE)CR.1943-5495.0000270.
Wickham, H. 2016. ggplot2: Elegant graphics for data analysis. New York: Springer.
Wickham, H., et al. 2019. “Welcome to the Tidyverse.” J. Open Source Software 4 (43): 1686. https://doi.org/10.21105/joss.01686.
Wood, S. N. 2003. “Thin plate regression splines.” J. R. Stat. Soc. B 65 (1): 95–114. https://doi.org/10.1111/1467-9868.00374.
Wood, S. N. 2011. “Fast stable restricted maximum likelihood and marginal likelihood estimation of semiparametric generalized linear models.” J. R. Stat. Soc. B 73 (1): 3–36. https://doi.org/10.1111/j.1467-9868.2010.00749.x.
Zeng, X., P. Broxton, and N. Dawson. 2018. “Snowpack change from 1982 to 2016 over conterminous United States.” Geophys. Res. Lett. 45 (23): 940–947. https://doi.org/10.1029/2018GL079621.
Information & Authors
Information
Published In
Journal of Structural Engineering
Volume 150 • Issue 1 • January 2024
Copyright
© 2023 American Society of Civil Engineers.
History
Received: Jan 18, 2023
Accepted: Aug 17, 2023
Published online: Oct 20, 2023
Published in print: Jan 1, 2024
Discussion open until: Mar 20, 2024
ASCE Technical Topics:
- Adaptive systems
- Case studies
- Construction engineering
- Construction management
- Design (by type)
- Engineering fundamentals
- Engineering mechanics
- Geomatics
- Load and resistance factor design
- Load factors
- Mapping
- Methodology (by type)
- Model accuracy
- Models (by type)
- Research methods (by type)
- Snow loads
- Standards and codes
- Static loads
- Statics (mechanics)
- Structural design
- Surveying methods
- Systems engineering
- Systems management
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