Comparing Extreme Value Estimation Techniques for Short-Term Snow Accumulations

Pomeyie, Kenneth; Bean, Brennan; Sun, Yan

doi:10.6339/23-JDS1086

Journal of Data Science

Comparing Extreme Value Estimation Techniques for Short-Term Snow Accumulations

Volume 21, Issue 2 (2023): Special Issue: Symposium Data Science and Statistics 2022, pp. 368–390

Kenneth Pomeyie

Brennan Bean Yan Sun

https://doi.org/10.6339/23-JDS1086

Pub. online: 25 January 2023 Type: Statistical Data Science

Open Access

Received
1 August 2022

Accepted
17 January 2023

Published
25 January 2023

Abstract

The potential weight of accumulated snow on the roof of a structure has long been an important consideration in structure design. However, the historical approach of modeling the weight of snow on structures is incompatible for structures with surfaces and geometry where snow is expected to slide off of the structure, such as standalone solar panels. This paper proposes a “storm-level” adaptation of previous structure-related snow studies that is designed to estimate short-term, rather than season-long, accumulations of the snow water equivalent or snow load. One key development associated with this paper includes a climate-driven random forests model to impute missing snow water equivalent values at stations that measure only snow depth in order to produce continuous snow load records. Additionally, the paper compares six different approaches of extreme value estimation on short-term snow accumulations. The results of this study indicate that, when considering the 50-year mean recurrence interval (MRI) for short-term snow accumulations across different weather station types, the traditional block maxima approach, the mean-adjusted quantile method with a gamma distribution approach, and the peak over threshold Bayesian approach tend to most often provide MRI estimates near the median of all six approaches considered in this study. Further, this paper also shows, via bootstrap simulation, that the peak over threshold extreme value estimation using automatic threshold selection approaches tend to have higher variance compared to the other approaches considered. The results suggest that there is no one-size-fits-all option for extreme value estimation of short-term snow accumulations, but highlights the potential value from integrating multiple extreme value estimation approaches.

References

Abatzoglou JT (2011). Development of gridded surface meteorological data for ecological applications and modelling. International Journal of Climatology, 33(1): 121–131.

ASCE (2022). Minimum Design Loads and Associated Criteria for Buildings and Other Structures. American Society of Civil Engineers, ASCE/SEI 7-22 edition.

Balkema AA, De Haan L (1974). Residual life time at great age. The Annals of Probability, 2(5): 792–804.

Bean B, Maguire M, Sun Y, Wagstaff J, Al-Rubaye SA, Wheeler J, et al. (2021). The 2020 national snow load study, Technical Report 276, Utah State University Department of Mathematics and Statistics, Logan, UT.

Beirlant J, Dierckx G, Guillou A (2005). Estimation of the extreme-value index and generalized quantile plots. Bernoulli, 11(6): 949–970.

Bommier E (2014). Peaks-over-threshold modelling of environmental data, Technical report, U.U.D.M. Project Report 2014:33, Department of Mathematics, Uppsala University.

Breiman L (2001). Random forests. Machine Learning, 45(1): 5–32.

Bücher A, Zhou C (2021). A horse race between the block maxima method and the peak–over–threshold approach. Statistical Science, 36(3): 360–378.

Buska J, Greatorex A, Tobiasson W (2020). Site-specific case studies for determining ground snow loads in the United States, Technical Report ERDC/CRREL SR-20-1, U.S. Army Engineer Research and Development Center, Cold Regions Research and Engineering Laboratory, Hanover, NH.

Chamberlain S (2021). rnoaa: ‘NOAA’ Weather Data from R. R package version 1.3.8.

Coles S (2001). An Introduction to Statistical Modeling of Extreme Values. Springer Science & Business Media.

Copland L (2022). 4.04 - Properties of Glacial Ice and Glacier Classification. 52–62. Academic Press, Oxford, second edition.

Curceac S, Atkinson PM, Milne A, Wu L, Harris P (2020). An evaluation of automated GPD threshold selection methods for hydrological extremes across different scales. Journal of Hydrology, 585: 124845.

Deidda R (2010). A multiple threshold method for fitting the generalized Pareto distribution to rainfall time series. Hydrology and Earth System Sciences, 14(12): 2559–2575.

Delignette-Muller ML, Dutang C (2015). fitdistrplus: An R package for fitting distributions. Journal of Statistical Software, 64(4): 1–34.

Donegan B (2019). The Most Extreme 24-Hour Rainfall Records in All 50 States. Accessed: 7-26-2022.

Durrieu G, Grama I, Jaunatre K, Pham QK, Tricot JM (2018). extremefit: A package for extreme quantiles. Journal of Statistical Software, 87(12): 1–20.

Durrieu G, Grama I, Pham QK, Tricot JM (2015). Nonparametric adaptive estimation of conditional probabilities of rare events and extreme quantiles. Extremes, 18(3): 437–478.

Ferreira A, de Haan L (2015). On the block maxima method in extreme value theory: PWM estimators. The Annals of Statistics, 43(1): 276–298.

Fisher RA, Tippett LHC (1928). Limiting forms of the frequency distribution of the largest or smallest member of a sample. In: Mathematical proceedings of the Cambridge philosophical society, volume 24, 180–190. Cambridge University Press.

Gilleland E, Katz RW (2016). extRemes 2.0: An extreme value analysis package in R. Journal of Statistical Software, 72(8): 1–39.

Gnedenko B (1943). Sur la distribution limite du terme maximum d’une serie aleatoire. The Annals of Mathematics, 44(3): 423.

Jonas T, Marty C, Magnusson J (2009). Estimating the snow water equivalent from snow depth measurements in the Swiss Alps. Journal of Hydrology, 378(1–2): 161–167.

Jonathan P, Ewans K (2013). Statistical modelling of extreme ocean environments for marine design: A review. Ocean Engineering, 62: 91–109.

McCreight JL, Small EE (2014). Modeling bulk density and snow water equivalent using daily snow depth observations. The Cryosphere, 8(2): 521–536.

Menne M, Durre I, Korzeniewski B, Vose R, Gleason B, Houston T (2012). Global Historical Climatology Network - Daily. (GHCN-Daily), Version 3.26.

Northrop PJ, Attalides N (2020). threshr: Threshold Selection and Uncertainty for Extreme Value Analysis. R package version 1.0.3.

Northrop PJ, Attalides N, Jonathan P (2016). Cross-validatory extreme value threshold selection and uncertainty with application to ocean storm severity. Journal of the Royal Statistical Society: Series C (Applied Statistics), 66(1): 93–120.

Pickands III J (1975). Statistical inference using extreme order statistics. The Annals of Statistics, 3(1): 119–131.

R Core Team (2022). R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria.

Scarrott C, MacDonald A (2012). A review of extreme value threshold estimation and uncertainty quantification. REVSTAT–Statistical Journal, 10(1): 33–60.

Sievert C (2020). Interactive Web-Based Data Visualization with R, plotly, and shiny. Chapman and Hall/CRC.

Solari S, Egüen M, Polo MJ, Losada MA (2017). Peaks Over Threshold (POT): A methodology for automatic threshold estimation using goodness of fit p-value. Water Resources Research, 53(4): 2833–2849.

Sturm M, Taras B, Liston GE, Derksen C, Jonas T, Lea J (2010). Estimating snow water equivalent using snow depth data and climate classes. Journal of Hydrometeorology, 11(6): 1380–1394.

Thompson P, Cai Y, Reeve D, Stander J (2009). Automated threshold selection methods for extreme wave analysis. Coastal Engineering, 56(10): 1013–1021.

Tobiasson W, Greatorex A (1996). Database and methodology for conducting site specific snow load case studies for the United States. In: Snow engineering: Recent advances: Proceedings of the Third International Conference, Sendai, Japan, volume 2631, 249256Ye.

Wagstaff J (2021). Regionalized models with spatially continuous predictions at the borders, Ms thesis, Utah State University. Document No. 8065.

Wheeler J, Bean B, Maguire M (2022). Creating a universal depth-to-load conversion technique for the conterminous United States using random forests. Journal of Cold Regions Engineering, 36(1): 04021019.

Wickham H, Averick M, Bryan J, Chang W, McGowan LD, François R, et al. (2019). Welcome to the tidyverse. Journal of Open Source Software, 4(43): 1686.

Yang X, Zhang J, Ren WX (2018). Threshold selection for extreme value estimation of vehicle load effect on bridges. International Journal of Distributed Sensor Networks, 14(2): 155014771875769.

Zoglat A, EL Adlouni S, Badaoui F, Amar A, Okou CG (2014). Managing hydrological risks with extreme modeling: Application of peaks over threshold model to the Loukkos Watershed, Morocco. Journal of Hydrologic Engineering, 19(9): 05014010.

2023 The Author(s). Published by the School of Statistics and the Center for Applied Statistics, Renmin University of China.

Open access article under the CC BY license.

Keywords

extreme value theory generalized extreme value distribution mean recurrence interval peak over threshold snow water equivalent

Metrics

since February 2021

634

Article info
views

241

PDF
downloads

RSS

Authors

Abstract

References

Export citation

Copy and paste formatted citation

Download citation in file