Efficient statistical approach to develop intensity-duration-frequency curves for precipitation and runoff under future climate


Ongoing and potential future changes in precipitation will affect water management infrastructure. Urban drainage systems are particularly vulnerable. Design standards for many stormwater practices rely on design storms based on precipitation intensity-duration-frequency (IDF) curves. In many locations, climate projections suggest relatively small changes in total precipitation volume, but increased magnitude of extreme events. We develop an approach for estimating future IDF curves that is efficient, can use widely available downscaled GCM output, and is consistent with published IDF curves for the USA that are used in local stormwater regulations and design guides. The method is GCM-agnostic and provides a relatively simple way to develop scenarios in a format directly useful to assessing risk to stormwater management infrastructure. Model biases are addressed through equidistant quantile mapping, in which the modeled change in both the location and scale of the cumulative distribution of storm events from historical to future conditions is used to adjust the extreme value fit used for IDF curve development. The approach requires only precipitation annual maxima, is readily automated, and hits a mid-point between theoretical rigor and ease of application that will be of practical use for the rapid screening of vulnerabilities across projections. We demonstrate estimation of future IDF curves at locations throughout the USA and link IDF-derived design storms to a rainfall-runoff model to evaluate the potential change in storage volume requirements for capture-based stormwater management practices by 2065.

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Data availability

All data are available from the corresponding author upon request.


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We acknowledge the World Climate Research Programme’s Working Group on Coupled Modeling, which is responsible for CMIP5, and we thank these modeling groups for producing and making available their model output. For CMIP5, the US Department of Energy’s Program for Climate Model Diagnosis and Intercomparison provides coordinating support and led development of software infrastructure in partnership with the Global Organization for Earth System Science Portals.


Funding for this research was provided by the US Environmental Protection Agency Office of Research and Development.

Author information




J. Butcher and T. Zi developed the theoretical approach. J. Butcher wrote the paper. T. Zi, B. Groza, B. Pickard, and S. Job developed and implemented the Python code. T. Johnson provided funding, guidance, and editorial review.

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Correspondence to Jonathan B. Butcher.

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The authors declare that they have no conflict of interest.


The views expressed in this paper represent those of the authors and do not necessarily reflect the views or policies of the US Environmental Protection Agency.

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Python scripts for implementing the methods described in this paper are available upon request from the corresponding author.

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Butcher, J.B., Zi, T., Pickard, B.R. et al. Efficient statistical approach to develop intensity-duration-frequency curves for precipitation and runoff under future climate. Climatic Change 164, 3 (2021). https://doi.org/10.1007/s10584-021-02963-y

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  • Future precipitation
  • Intensity-duration-frequency
  • Stormwater infrastructure sizing
  • Resilience