Technical Notes
Mar 19, 2019

Rescaling Transposed Extreme Rainfall within a Heterogeneous Region

Publication: Journal of Hydrologic Engineering
Volume 24, Issue 6

Abstract

Geospatial transposition of observed storms can be useful for examining potential rainfall and flood hazards, and several recent software packages help facilitate transposition of remote sensing–based rainfall observations from radar or satellites. Two unanswered questions persist, however, in regions that exhibit heterogeneity in extreme rainfall properties: is transposition reasonable, and, if so, how should it be performed? This note posits that the answer to the first question depends on the degree of heterogeneity, and it attempts to answer the second question via “rescaling” transposed rainfall according to the degree of heterogeneity between two locations. General considerations for this rescaling are discussed, and two rescaling methods are introduced. Both methods are illustrated using gauge-corrected radar rainfall data from three locations in the Front Range of the Rocky Mountains in Colorado that exhibit moderate heterogeneity in an extreme rainfall hydroclimate. The second of these methods, termed stochastic distribution ratio rescaling, is presented here for the first time and has the advantage of straightforward uncertainty estimation.

Get full access to this article

View all available purchase options and get full access to this article.

Acknowledgments

The authors are partially supported by the Bureau of Reclamation Research and Development Office Project ID 1735: Development of a Stochastic Storm Transposition Toolkit for Physically-based Rainfall and Flood Hazard Analysis.

References

Alexander, G. N. 1963. “Using the probability of storm transposition for estimating the frequency of rare floods.” J. Hydrol. 1 (1): 46–57. https://doi.org/10.1016/0022-1694(63)90032-5.
Atlas, D., D. Rosenfeld, and D. A. Short. 1990. “The estimation of convective rainfall by area integrals: 1. The theoretical and empirical basis.” J. Geophys. Res. Atmos. 95 (D3): 2153–2160. https://doi.org/10.1029/JD095iD03p02153.
Benson, S. A. 2014. Comparative analysis of flood frequency based on radar-based precipitation data and precipitation trends. Arlington, TX: Univ. of Texas at Arlington.
Bonnin, G. M., D. Martin, B. Lin, T. Parzybok, M. Yekta, and D. Riley. 2006. NOAA Atlas 14: Precipitation-frequency atlas of the United States. Silver Spring, MD: National Weather Service, National Oceanic and Atmospheric Administration.
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.
England, J. F., P. Y. Julien, and M. L. Velleux. 2014. “Physically-based extreme flood frequency with stochastic storm transposition and paleoflood data on large watersheds.” J. Hydrol. 510 (Mar): 228–245. https://doi.org/10.1016/j.jhydrol.2013.12.021.
Fontaine, T. A., and K. W. Potter. 1989. “Estimating probabilities of extreme rainfalls.” J. Hydr. Eng. 115 (11): 1562–1575. https://doi.org/10.1061/(ASCE)0733-9429(1989)115:11(1562).
Foufoula-Georgiou, E. 1989. “A probabilistic storm transposition approach for estimating exceedance probabilities of extreme precipitation depths.” Water Resour. Res. 25 (5): 799–815. https://doi.org/10.1029/WR025i005p00799.
Franchini, M., K. R. Helmlinger, E. Foufoula-Georgiou, and E. Todini. 1996. “Stochastic storm transposition coupled with rainfall—runoff modeling for estimation of exceedance probabilities of design floods.” J. Hydrol. 175 (1–4): 511–532. https://doi.org/10.1016/S0022-1694(96)80022-9.
Friedrich, K., E. A. Kalina, J. Aikins, D. Gochis, and R. Rasmussen. 2016. “Precipitation and cloud structures of intense rain during the 2013 Great Colorado Flood.” J. Hydrometeorol. 17 (1): 27–52. https://doi.org/10.1175/JHM-D-14-0157.1.
Gochis, D., et al. 2015. “The Great Colorado Flood of September 2013.” Bull. Am. Meteorol. Soc. 96 (9): 1461–1487. https://doi.org/10.1175/BAMS-D-13-00241.1.
Gupta, V. K. 1972. Transposition of storms for estimating flood probability distributions. Fort Collins, CO: Colorado State Univ.
Guttman, N. B. 1993. “The use of L-moments in the determination of regional precipitation climates.” J. Clim. 6 (12): 2309–2325. https://doi.org/10.1175/1520-0442(1993)006%3C2309:TUOLMI%3E2.0.CO;2.
Hansen, E. M. 1987. “Probable maximum precipitation for design floods in the United States.” J. Hydrol. 96 (1–4): 267–278. https://doi.org/10.1016/0022-1694(87)90158-2.
Hansen, E. M., L. C. Schreiner, and J. F. Miller. 1978. Application of probable maximum precipitation estimates—United States East of the 105th Meridian. Hydrometeorological Rep. Washington, DC: National Weather Service, National Oceanic and Atmospheric Administration.
Hayden, N. G., K. W. Potter, and D. S. Liebl. 2016. “Evaluating infiltration requirements for new development using extreme storm transposition: A case study from Dane County, WI.” JAWRA J. Am. Water Resour. Assoc. 52 (5): 1170–1178. https://doi.org/10.1111/1752-1688.12441.
HEC (Hydrologic Engineering Center). 2017. Real-time simulation (HEC-RTS) t Version 3. Davis, CA: USACE.
Huff, F. A., and J. L. Vogel. 1978. “Urban, topographic and diurnal effects on rainfall in the St. Louis Region.” J. Appl. Meteorol. 17 (5): 565–577. https://doi.org/10.1175/1520-0450(1978)017%3C0565:UTADEO%3E2.0.CO;2.
Javier, J. R. N., J. A. Smith, J. England, M. L. Baeck, M. Steiner, and A. A. Ntelekos. 2007. “Climatology of extreme rainfall and flooding from orographic thunderstorm systems in the upper Arkansas River basin.” Water Resour. Res. 43 (10): W10410. https://doi.org/10.1029/2006WR005093.
Kavetski, D., G. Kuczera, and S. W. Franks. 2006. “Bayesian analysis of input uncertainty in hydrological modeling: 1.” Theory Water Resour. Res. 42 (3): W03407. https://doi.org/10.1029/2005WR004368.
Kitchen, M., and R. M. Blackall. 1992. “Orographic rainfall over low hills and associated corrections to radar measurements.” J. Hydrol. 139 (1–4): 115–134. https://doi.org/10.1016/0022-1694(92)90198-5.
Lee, R.-Y., B. S. Holland, and J. A. Flueck. 1979. “Distribution of a ratio of correlated gamma random variables.” SIAM J. Appl. Math. 36 (2): 304–320. https://doi.org/10.1137/0136025.
Lin, Y., and K. E. Mitchell. 2005. “The NCEP Stage II/IV hourly precipitation analyses: Development and applications.” In Proc., 19th Conf. on Hydrology, 2–5. Boston: American Meteorological Society.
Nadarajah, S. 2010. “Distribution properties and estimation of the ratio of independent Weibull random variables.” AStA Adv. Stat. Anal. 94 (3): 231–246. https://doi.org/10.1007/s10182-010-0134-1.
Nadarajah, S., and S. Kotz. 2006. “On the product and ratio of gamma and Weibull random variables.” Econ. Theory 22 (02): 338–344. https://doi.org/10.1017/S0266466606060154.
Nathan, R., P. Jordan, M. Scorah, S. Lang, G. Kuczera, M. Schaefer, and E. Weinmann. 2016. “Estimating the exceedance probability of extreme rainfalls up to the probable maximum precipitation.” J. Hydrol. 543 (Part B): 706–720. https://doi.org/10.1016/j.jhydrol.2016.10.044.
Ntelekos, A. A., J. A. Smith, and W. F. Krajewski. 2007. “Climatological analyses of thunderstorms and flash floods in the Baltimore Metropolitan region.” J. Hydrometeorol. 8 (1): 88–101. https://doi.org/10.1175/JHM558.1.
Shepherd, J. M. 2005. “A review of current investigations of urban-induced rainfall and recommendations for the future.” Earth Interact. 9 (12): 1–27. https://doi.org/10.1175/EI156.1.
Shimizu, K. 1993. “A bivariate mixed lognormal distribution with an analysis of rainfall data.” J. Appl. Meteorol. 32 (2): 161–171. https://doi.org/10.1175/1520-0450(1993)032%3C0161:ABMLDW%3E2.0.CO;2.
Smith, J. A., M. L. Baeck, G. Villarini, C. Welty, A. J. Miller, and W. F. Krajewski. 2012. “Analyses of a long-term high-resolution radar rainfall data set for the Baltimore metropolitan region.” Water Resour. Res. 48 (4): W04504–W04504. https://doi.org/10.1029/2011WR010641.
Tian, Y., G. J. Huffman, R. F. Adler, L. Tang, M. Sapiano, V. Maggioni, and H. Wu. 2013. “Modeling errors in daily precipitation measurements: Additive or multiplicative?” Geophys. Res. Lett. 40 (10): 2060–2065. https://doi.org/10.1002/grl.50320.
Vrugt, J. A., C. J. F. ter Braak, M. P. Clark, J. M. Hyman, and B. A. Robinson. 2008. “Treatment of input uncertainty in hydrologic modeling: Doing hydrology backward with Markov chain Monte Carlo simulation.” Water Resour. Res. 44 (12): W00B09. https://doi.org/10.1029/2007WR006720.
WMO (World Meteorological Organization). 2009. Manual on estimation of probable maximum precipitation (PMP). Geneva: WMO.
Wright, D. B., R. Mantilla, and C. D. Peters-Lidard. 2017. “A remote sensing-based tool for assessing rainfall-driven hazards.” Environ. Model. Software 90: 34–54. https://doi.org/10.1016/j.envsoft.2016.12.006.
Wright, D. B., J. A. Smith, and M. L. Baeck. 2014. “Flood frequency analysis using radar rainfall fields and stochastic storm transposition.” Water Resour. Res. 50 (2): 1592–1615. https://doi.org/10.1002/2013WR014224.
Wright, D. B., J. A. Smith, G. Villarini, and M. L. Baeck. 2013. “Estimating the frequency of extreme rainfall using weather radar and stochastic storm transposition.” J. Hydrol. 488 (Apr): 150–165. https://doi.org/10.1016/j.jhydrol.2013.03.003.
Zhang, L., and V. P. Singh. 2007. “Bivariate rainfall frequency distributions using Archimedean copulas.” J. Hydrol. 332 (1–2): 93–109. https://doi.org/10.1016/j.jhydrol.2006.06.033.

Information & Authors

Information

Published In

Go to Journal of Hydrologic Engineering
Journal of Hydrologic Engineering
Volume 24Issue 6June 2019

History

Received: Mar 15, 2018
Accepted: Dec 4, 2018
Published online: Mar 19, 2019
Published in print: Jun 1, 2019
Discussion open until: Aug 19, 2019

Permissions

Request permissions for this article.

Authors

Affiliations

Daniel B. Wright, Ph.D., A.M.ASCE [email protected]
Assistant Professor, Dept. of Civil and Environmental Engineering, Univ. of Wisconsin-Madison, Madison, WI 53706 (corresponding author). Email: [email protected]
Kathleen D. Holman, Ph.D.
Meteorologist, Technical Service Center, Bureau of Reclamation, P.O. Box 25007, 86-68210, Denver, CO 80225-0007.

Metrics & Citations

Metrics

Citations

Download citation

If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.

Cited by

View Options

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Media

Figures

Other

Tables

Share

Share

Copy the content Link

Share with email

Email a colleague

Share