An Efficient Statistical Approach to Develop Intensity-Duration-Frequency Curves for Precipitation and Runoff under Future Climate

Abstract

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 precipitation intensity-duration-frequency (IDF) curves based on extreme value analysis. General Circulation Models (GCMs) project increases in future average temperature but are less clear on changes in precipitation. In many areas, climate projections suggest relatively small changes in total precipitation volume, but also suggest increased magnitude of extreme events. Model skill in predicting extreme precipitation events, however, is limited. We develop an approach for estimating future IDF curves that is efficient, uses widely available statistically downscaled GCM output, and is consistent with published IDF curves for the United States that are often incorporated into local stormwater regulations and design guides (and are GCM model agnostic). The method 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 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 is efficient because it requires only annual maxima and is readily automated, allowing rapid examination of results across projections. We estimate future IDF curves at locations throughout the United States 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.

1. Introduction

Engineering design for stormwater management is largely based on empirical evidence obtained from past data with the assumption that the frequency of extreme events that is likely to be seen in the future can be inferred from the historical record. This implies that climate is stationary; however, in many regions of the United States (US), the intensity and frequency of heavy precipitation events is projected to increase even where total precipitation volume may decrease (Hayhoe et al. 2018). There is growing concern about the effects of these changes on the planning, design, and operation of water infrastructure (Arnbjerg-Nielsen 2012; Arnbjerg-Nielsen et al. 2013), and a need to provide information and tools to those in the field to help manage climate risk (Galloway 2011).

Design of urban stormwater best management practices (BMPs) typically begins with consideration of rainfall recurrence intervals, which may be translated into design storm specifications or runoff depth. Practices are designed to achieve a level of service or performance associated with controlling a certain design storm, combination of design storms, and/or runoff depth to reduce flooding, stream erosion, and pollutant loading. In most cases, design standards for gray infrastructure base sizing requirements on storms of a specified intensity, duration, and frequency (IDF analysis). The performance of stormwater practices is dictated primarily by rainfall IDF, impervious surface area, and soils, along with life cycle maintenance (Berndtsson 2010; Claytor and Schueler 1996; Gallo et al. 2012; Hunt et al. 2012; Kadlec and Knight 1996; Khan et al. 2012; Roseen et al. 2009). IDF curves summarize the relationship between precipitation intensity and the duration of precipitation events for a given frequency or recurrence interval. If the IDF relationships change, the design standards for gray and green infrastructure components should change as well to preserve retention and treatment contact times.

Anticipated future changes in climate in the US include regionally variable changes in rainfall amount and timing. In most locations, a greater proportion of precipitation will occur in larger magnitude events. If realized, these changes will alter IDF relationships used for engineering design and planning purposes. Direct calculation of IDF curves for future climate is complicated by the limited skill of GCMs in predicting individual precipitation events at the necessary spatial and temporal scales for BMP design, especially for convective storm events that can include intense microbursts with extreme rainfall, yet occur at spatial scales smaller than the resolution of GCMs. In addition, for light precipitation, GCM models tend to overestimate the frequency but reproduce the observed patterns of intensity relatively well. For heavy precipitation, GCMs roughly reproduce the observed frequency, but underestimate the intensity (Sun et al. 2006; Sillmann et al. 2013; Mehran et al. 2014).

In the US, IDF curves and tables for specific geographic locations are provided in NOAA’s Atlas 14 (e.g., Perica et al. 2013). Developing future IDF scenarios using a consistent approach has the advantage of being relatively simple, and familiar to practitioners in the field. Use of a statistical approach also allows the development of IDF scenario information based on a wide range of GCM and/or regional climate model (RCM) output. In this paper, we develop and demonstrate an efficient method to adjust Atlas 14 IDF curves to reflect potential future changes in local climate that can be readily applied by practitioners in the field. We first describe the approach for developing IDF curves, followed by a case study demonstration for stormwater management.

For consistency with engineering practice, our approach adheres as closely as possible to the way in which the Atlas 14 estimates are created. Specifically, precipitation frequency estimates in the Atlas are based on fitting an extreme value distribution (in most cases, a generalized extreme value [GEV] distribution) to the time series of annual maximum precipitation (AMP) amounts at a station for seventeen event durations ranging from 15 minutes to 60 days. The AMP series consists of one measurement per year, and does not account for the possibility of more than one event in a year exceeding a threshold of interest. The true probability of occurrence of events of a given intensity and duration should be derived from the partial duration series, which includes all events of a specified duration and above a pre-defined volume threshold. Frequency estimates for partial duration series were developed by NOAA for Atlas 14 from the series of AMPs using Langbein’s conversion formula, which transforms a partial duration series-based average recurrence interval (ARI) to an annual exceedance probability (AEP):

$$AEP=1-\exp \left(-\frac{1}{ARI}\right)$$ Equation 1

Selected partial duration ARIs are first converted to AEPs using this formula, and frequency estimates are then calculated for the AEP using the GEV fit to annual maxima.

For Atlas 14, NOAA fit the GEV for each station using the method of L-moments (Hosking and Wallis 1997), incorporating regionalization across approximately the 10 nearest stations for higher order L-moments. The annual maximum series are provided via NOAA ftp server. Because the NOAA method is ultimately based only on annual maxima (the AMP series), only AMPs are needed to adjust IDF estimates for future climate conditions and not the complete time series; thus an update to the Atlas 14 statistics need only consider the AMP series.

2. Approach for Developing Future IDF Curves

Adjusting the IDF curves from Atlas 14 to consider future climate requires understanding how the extreme value distribution fit to annual maximum precipitation series may change. Previous studies have explored methods for estimating future changes in extreme precipitation and IDF relationships including use of conditional probability weather generators (Fowler et al.,2005; Kilsby et al. 2007; Prodanovic and Simonovic 2007; Onof and Arnbjerg-Nielsen 2009; Shrestha et al. 2017), empirical transfer functions (Willems and Vrac 2011; Dahm et al. 2019), empirical change factor approaches (Zhu 2012; Cook et al 2017), and direct dynamical downscaling with regional or local climate models (Rosenberg et al. 2010; Castellano and DeGaetano 2017; Li et al. 2017; Krstvik et al. 2019; Cannon and Innocenti 2019; Cook et al. 2020). Some authors have also suggested that the whole framework of IDF curves, with assumption of constant or stationary parameters (conditional on climate) is misguided and that a better approach is to use an extreme value distribution with non-stationary parameters that could be derived either empirically (based on observations) or in reference to climate models. This type of approach is combined with Bayesian conditioning and uncertainty analysis by Cheng and AghaKouchak (2014), and Ragno et al. (2018); see also Huard et al. (2010).

Many of the existing methods for climate-modified IDF analysis are complex and difficult to apply, while the simpler methods do not preserve important information from the climate models.. Here, we develop a method that is efficient, uses and preservers information from widely available statistically downscaled GCM output, and is consistent with Atlas 14 procedures and results that are already incorporated into many local regulations and design guides (and are GCM model agnostic).

A simple and computationally efficient approach to adjusting IDF curves in Canada was proposed by Srivastav et al. (2014a, 2014b). Their insight was that the essence of the problem was the need to update extreme value distributions for future conditions, and that this could be done through a direct analysis of the distributions. The general concept of the approach of Srivastav et al. (2014a) is described as “…quantile-mapping functions can be directly applied to establish the statistical relationship between the AMPs of a GCM and sub-daily observed data rather than using complete records.”

Quantile mapping (QM) methods, otherwise known as cumulative distribution function (CDF) matching methods, have long been used as a method to correct for local biases in GCM output. The method first establishes a statistical relationship or transfer function between model outputs and historical observations, then applies the transfer function to future model projections (Panofsky and Brier 1968).

Using the notation of Li et al. (2010), for a climate variable x, the QM method for finding the bias-adjusted future value of a climate variable, ${\widehat{x}}_{m-p}$ can be written as:

$${\widehat{x}}_{m-p\ast }=F_{o-c}^{-1}\left(F_{m-c}(x_{m-p})\right)$$ Equation 2

where F is the CDF of either the observations (o) or model (m) for observed climate (c) or future projected climate (p), and $F^{-1}$ is the inverse of the cumulative distribution function. The bias correction for a future period is thus done by finding the corresponding percentile values for these future projection points in the CDF of the model for current observations, then locating the percentile in the CDF of the observations.

A significant weakness of the QM method is that it assumes that the climate CDF does not change much over time, and that, as the mean changes, the variance and skew do not change, which is unlikely (e.g., Milly et al. 2008; USGCRP 2017). To address these issues, Li et al. (2010) proposed the equidistant quantile mapping (EQM) method, which incorporates additional information from the CDF of the model projection. The method assumes that the difference between the model and observed value during the current calibration period also applies to the future period; however, the difference between the shape of the CDFs for the future and historic periods is also taken into account. This is written as:

$${\widehat{x}}_{m-p^{\ast }}=x_{m-p}+F_{o-c}^{-1}\left(F_{m-p}(x_{m-p})\right)-F_{m-c}^{-1}\left(F_{m-p}(x_{m-p})\right)$$ Equation 3

where the form and parameters of the CDF are not yet specified. Srivastav et al. (2014a) argue for using EQM to update IDF curves; however, the specific method of Srivastav et al. (2014b) developed for Canada is not directly applicable to adjusting Atlas 14 IDF curves in the US. First, Canada assumes that the AMP series follows a Gumbel, rather than a GEV distribution. Bias-corrected statistically downscaled climate model output was not widely available for Canada in 2014, therefore the Srivastav method also incorporated a spatial downscaling step from the coarse scale of GCMs, whereas output that is already spatially downscaled to a fine resolution grid is now readily available for the US. Finally, the method of Srivastav et al. justifies use of EQM, but largely consists of a multi-step QM procedure, without the additional EQM corrections.

To address these issues this paper re-derives an EQM method that is consistent with US design guidelines and makes use of readily available, statistically downscaled GCM output.

Our approach uses a combination of EQM and QM to update IDF curves for any location conditional on output of GCMs for future climate conditions, implemented in Python code. The EQM approach can be used to update IDF curves for any location conditional on downscaled output of GCMs for future climate conditions. The process begins with GCM output that has already been subject to spatial bias correction and downscaling to a finer (e.g., 25×25 km) spatial scale and daily time step. The calculation step consists of additional spatial downscaling from the climate output grid to the specific point location of the first-order weather station used by Atlas 14 along with bias correction for the AMP series (as distinct from the general bias correction of the complete precipitation series) using the EQM method for different time durations from sub-hourly to daily.

The historical data are the historical AMP series used by Atlas 14 ($X_{amp}^{STN}$). Model data include the predicted AMP series from the historical climate forcing (ending in 2005) ($X_{amp}^{GCM}$) and future period of interest ($X_{amp}^{GC{M}_{FUT}}$). A GEV (or alternative extreme value) distribution is fit to each of these series, using the L-moments method (Hosking and Wallis 1997; implemented in Python in lmoments3 v1.0.4 at https://pypi.org/project/lmoments3/), consistent with Atlas 14 methods.

To apply the EQM method, quantiles of modeled future AMP series are matched to the distribution for historical AMPs. For a given percentile, we assume that the difference between the model and observed value also applies to the future period. There are two EQM factors. The first is:

$$Y_{amp}^{adj1}=F_{o-c}^{-1}\left(F_{m-p}(x_{m-p})\right)=F^{-1}((F\left(X_{amp}^{GC{M}_{FUT}}\mid {\theta }^{GC{M}_{FUT}}\right))\mid {\theta }^{STN}),$$ Equation 4

where the vertical bar “|” indicates conditional dependence, i.e., $F\left(X_{amp}^{GC{M}_{FUT}}\mid {\theta }^{GC{M}_{FUT}}\right)$ indicates the cumulative distribution function (e.g., GEV) of the future GCM AMP series calculated at the cumulative probability corresponding to $X_{amp}^{GC{M}_{FUT}}$ using the parameter set ${\theta }^{GC{M}_{FUT}}$ calculated for that future series, while ${\theta }^{STN}$ is the parameter set for the GEV fit to the Atlas 14 AMPs. To account for the difference between the CDFs for the model outputs of future and current periods, a second adjustment factor is calculated:

$$Y_{amp}^{adj2}=F_{m-c}^{-1}\left(F_{m-p}(x_{m-p})\right)=F^{-1}((F\left(X_{amp}^{GC{M}_{FUT}}\mid {\theta }^{GC{M}_{FUT}}\right))\mid {\theta }^{GCM})$$ Equation 5

The projected AMP series is then calculated as:

$$Y_{amp}^{ST{N}_{-}FUT}=X_{amp}^{GC{M}_{-}FUT}+Y_{amp}^{adj1}-Y_{amp}^{adj2}$$ Equation 6

We include corrections for constrained data (i.e., results for a given duration that are artificially truncated by crossing over the midnight boundary) using the Atlas 14 factors at this step. Once the $Y_{amp}^{ST{N}_{-}FUT}$ series is calculated, a GEV fit is applied to estimate the full distribution of the future extreme events for the local station. This EQM step is applied to daily data to update the 24-hour IDF curves.

The second step in adjusting the IDF curves is temporal downscaling to convert future daily extremes into sub-daily extremes. The QM method was used for this purpose: First find the corresponding percentile values for these future projection points in the CDF of the model for the historical period, then locate the observed values for the same CDF values of the sub-daily observations. For rainfall duration i:

$$Y_{amp,i}^{GC{M}_{-}FU{T}_{-}sub24}=F^{-1}\left((F(Y_{amp}^{GC{M}_{-}FU{T}_{-}24h}\mid {\theta }^{ST{N}_{-}24h})\mid {\theta }_i^{ST{N}_{sub24}})\right)$$ Equation 7

As noted in Atlas 14 (Perica et al. 2013), estimates for shorter durations can be noisy due to limited data availability and are improved by smoothing. To account for the short modeling simulation period, the modeled extreme values with less than 24 hours’ duration are thus smoothed by fitting them to a linear regression relative to the daily maximum series before fitting them to the GEV distribution:

$$Y_{amp}^{GC{M}_{-}sub24}=a_1\ast Y_{amp}^{GC{M}_{-}24h}+b_1$$ Equation 8

$$Y_{amp}^{GC{M}_{-}FU{T}_{-}sub24}=a_2\ast Y_{amp}^{GC{M}_{-}FU{T}_{-}24h}+b_2$$ Equation 9

The adjusted model predictions ($Y_{amp}^{GC{M}_{-}FUT}$) are then used to fit the GEV distribution with the L-moments method, and the model predicted partial duration series (PDS) were retrieved from the derived GEV distribution at given annual exceedance probability (AEP).

$$Y_{pds}^{GC{M}_{-}FUT}=F^{-1}((F\left(Y_{amp}^{GC{M}_{FUT}}\mid {\theta }_Y^{GC{M}_{FUT}}\right))\mid AEP)$$ Equation 10

The final future 1 to 24-hour IDF ordinates are estimated by multiplying the Atlas 14 published values by the ratio of fitted GEV PDS results for climate-adjusted future conditions to the fitted GEV PDS results obtained for the Atlas 14 observed AMP series:

$$ID{F}_{FUT}=ID{F}_{Atlas}\ast \frac{ID{F}^{GC{M}_{-}FUT}}{ID{F}^{STN}}$$ Equation 11

This last step adjusts for the regional representation of higher L moments that is incorporated in the original Atlas 14 calculations but not explicitly documented.

The relationships between the various equations and data sources are summarized schematically in Figure 1.

Figure 1.

Schematic of IDF Update Process

3. Case Study Applications

The use of the approach described in Section 2 is demonstrated by developing IDF curves based on downscaled output from multiple GCMs at 20 stations throughout the Atlas 14 area of the contiguous US (excluding the Pacific Northwest, where Atlas 14 results have not been published). We then apply IDF scenarios to assess potential effects on performance of stormwater BMPs.

3.1. DEVELOPMENT OF FUTURE IDF CURVES

GCMs generate output at a large spatial scale (typically about 1°x1° or coarser) that does not take into account details of local geography and topography. To be useful at a scale relevant to stormwater management such as the drainage area of a management practice, spatial downscaling is necessary. Downscaling can be done either through the use of a small-scale regional climate model (RCM) or through statistical methods. RCMs are computationally expensive to run, so only a limited number of GCMs have been downscaled in this way. In contrast, there are many different varieties of statistically downscaled GCM output products now available. Most statistically downscaled products apply spatial statistical corrections of GCM monthly output to local spatial scales with bias correction based on analysis of GCM ability to replicate historical climatology, followed by temporal downscaling to a daily time step.

We selected 20 locations covered by Atlas 14, and representative of different hydroclimatic conditions to demonstrate the proposed methods. These locations (Figure 2) are all first-order airport weather stations from the Automated Surface Observing System (ASOS) to help ensure the availability of quality-controlled sub-daily precipitation data.

Figure 2.

Airport Stations for IDF Tool Demonstration

Adjusting the IDF curves for future conditions is based on the relative difference between historic and future conditions in spatially and temporally downscaled and bias corrected GCM (DCM) output. We use the Localized Constructed Analogs (LOCA) statistically downscaled data (Pierce et al. 2014), although output from any DCM could be used. The LOCA downscaling approach was developed to address some shortcomings of the bias-correction constructed analogue and other constructed analog approaches to downscaling that avoids damping localized precipitation extremes. LOCA output is available from https://cida.usgs.gov. We focus on Representative Concentration Pathway (RCP) 8.5 and RCP 4.5 in a future period of 2050–2080 (centered at 2065) relative to the hindcast period (1950–2005). The full hindcast period is used because the constructed analog method maps the statistics of that period to the training data and using a subset can introduce artificial variability between DCMs, DCMs in the LOCA archive show a range of projected future changes in temperature and precipitation for 2050–2080 at each of the 20 study locations (e.g., see Figure 3). Temperature is expected to increase under RCP 8.5 and RCP 4.5 in most locations, but results suggest precipitation may increase or decrease. For this study, because the focus is on storm events, selection of central and bounding cases is based on projected precipitation changes only.

Figure 3.

Example Biplot of Forecast Changes in Average Annual Precipitation and Air Temperature for Durham, North Carolina for 2050 – 2080 vs. 1950 – 2005

Climate model projections are typically used to describe an envelope of potential future conditions. In this study, we selected DCMs from the joint distribution of RCP 4.5 and RCP 8.5 Coupled Model Intercomparison Project 5 (CMIP5) simulations near the 10^th, 50^th, and 90^th percentiles of the distribution of projected annual precipitation volume ca. the year 2065. Use of such an upper percentile is generally considered appropriate for engineering design planning purposes; however, in some cases consideration of the full ensemble range (e.g., greater than 90^th percentile) may also be of interest. Table 1 summarizes the sites and selected climate scenarios.

Table 1.

Test Sites and Selected CMIP5 Downscaled Scenarios from the LOCA Archive (Pierce et al., 2014)

City	Code	Lat.	Long.	Region	10th %le	Median	90th %le	Rainfall Type
Bismarck, ND	BIS	46.77	−100.75	Great Plains North	RCP 8.5 CCSM4	RCP 4.5 NorESM1-M	RCP 8.5 GFDLESM2M	II
Sioux Falls, SD	FSD	43.58	−96.74	Great Plains North	RCP 8.5 CCSM4	RCP 4.5 NorESM1-M	RCP 8.5 GFDLESM2M	II
Houston, TX	IAH	29.99	−95.34	Great Plains South	RCP 4.5 bcc-csm1-1-m	RCP 8.5 GFDLESM2M	RCP 4.5 CSIROMk3-6-0	III
Oklahoma City, OK	OKC	35.39	−97.60	Great Plains South	RCP 4.5 bcc-csm1-1-m	RCP 8.5 GFDLESM2M	RCP 4.5 CSIRO-Mk3-6-0	II
San Antonio, TX	SAT	29.53	−98.47	Great Plains South	RCP 4.5 bcc-csm1-1-m	RCP 8.5 GFDLESM2M	RCP 4.5 CSIRO-Mk3-6-0	II
Minneapolis, MN	MSP	44.88	−93.22	Midwest	RCP 8.5 CCSM4	RCP 8.5 HadGEM2-CC365	RCP 4.5 GFDLESM2M	II
St. Louis, MO	STL	38.75	−90.35	Midwest	RCP 8.5 CCSM4	RCP 8.5 HadGEM2-CC365	RCP 4.5 GFDLESM2M	II
Chicago, IL	ORD	41.98	−87.91	Midwest	RCP 8.5 CCSM4	RCP 8.5 HadGEM2-CC365	RCP 4.5 GFDLESM2M	II
Cleveland, OH	CLE	41.41	−81.85	Midwest	RCP 8.5 CCSM4	RCP 8.5 HadGEM2-CC365	RCP 4.5 GFDLESM2M	II
Philadelphia, PA	PHL	39.87	−75.24	Northeast	RCP 4.5 HadGEM2-ES365	RCP 4.5 GFDLESM2G	RCP 4.5 HadGEM2-CC365	III
Burlington, VT	BTV	44.93	−73.05	Northeast	RCP 4.5 HadGEM2-ES365	RCP 4.5 GFDLESM2G	RCP 4.5 HadGEM2-CC365	II
Boston, MA	BOS	42.36	−71.01	Northeast	RCP 4.5 HadGEM2-ES365	RCP 4.5 GFDLESM2G	RCP 4.5 HadGEM2-CC365	III
New Orleans, LA	MSY	29.99	−90.26	Southeast	RCP 4.5 IPSLCM5A-MR	RCP 4.5 GFDLESM2M	RCP 4.5 GFDLESM2G	III
Tampa, FL	TPA	27.98	−82.53	Southeast	RCP 4.5 IPSLCM5A-MR	RCP 4.5 GFDLESM2M	RCP 4.5 GFDLESM2G	II
Durham, NC	RDU	35.90	−78.79	Southeast	RCP 4.5 IPSLCM5A-MR	RCP 4.5 GFDLESM2M	RCP 4.5 GFDLESM2G	II
San Francisco, CA	SFO	37.66	−122.44	Southwest	RCP 4.5 IPSLCM5A-MR	RCP 4.5 GFDLESM2M	RCP 8.5 CNRM-CM5	I
Los Angeles, CA	LAX	34.05	−118.24	Southwest	RCP 4.5 IPSLCM5A-MR	RCP 4.5 GFDLESM2M	8.5 RCP CNRM-CM5	I
Las Vegas, NV	LAS	36.55	−114.46	Southwest	RCP 4.5 IPSLCM5A-MR	RCP 4.5 GFDLESM2M	RCP 8.5 CNRM-CM5	II
Phoenix, AZ	PHX	33.43	−112.01	Southwest	RCP 4.5 IPSLCM5A-MR	RCP 4.5 GFDLESM2M	RCP 8.5 CNRM-CM5	II
Salt Lake City, UT	SLC	40.79	−111.98	Southwest	RCP 4.5 IPSLCM5A-MR	RCP 4.5 GFDLESM2M	RCP 8.5 CNRM-CM5	II

Note: Rainfall distribution types are as defined in SCS (1986). 10^th, median (50^th), and 90^th percentile rankings are based on total annual precipitation volume predictions for 2050–2075.

Future IDF curves were developed for four climate scenarios (historical baseline and three DCMs centered around the year 2065) for nine recurrence intervals at 20 stations. Figure 4 shows an example of results for the 100-year recurrence event at one location, Los Angeles International Airport. For this site, two DCMs predict that the 24-hour 100-year event will increase by up to 23%, from 7.09 to 8.75 inches, while a third DCM predicts a decrease in this event to 5.12 inches. Differences among DCMs are common at most sites, reflecting the uncertainty in prediction of future extreme precipitation events.

Figure 4.

Precipitation IDF Results for 100-year Recurrence at Los Angeles (LAX), ca. 2065 Compared to Historical

3.2. APPLICATION OF IDF CURVES TO STORMWATER MANAGEMENT

The design of many stormwater BMPs relies on IDF curves. To demonstrate the implications of adjusted IDF curves for stormwater management, we combine the statistical adjustment procedure for IDF curves with EPA’s Storm Water Management Model version 5.1.013 (SWMM5; Rossman 2015) to convert rainfall to runoff and to evaluate the potential changes in performance of urban stormwater BMPs.

Both the IDF curve analysis and the linked SWMM model are implemented in Python 3 (http://python.org). In addition to standard Python libraries such as numpy and scipy, we implement the statistical fitting and adjustment described in Section 2 using the lmoments3 package (Hollebrandse et al. 2015), available at https://pypi.org/project/lmoments3/.

The general structure of the tool is shown in Figure 5. The IDF analysis portion of the tool appears on the right side. After selection of bounding climate scenarios, the program queries various data servers and retrieves historic and future climate model output for a user-identified location of interest, along with the AMP series for the NOAA Atlas 14 station closest to the user location.

Figure 5.

Schematic of IDF Analysis Tool

The IDF curves are converted into design storm precipitation events for use by SWMM by applying the appropriate 24-hr rainfall distribution type identified for the Soil Conservation Service TR-55 method (SCS, 1986). Other, more sophisticated methods of rainfall disaggregation could be used, but we chose the TR-55 method because it remains the approach of choice for many state and local stormwater design manuals (e.g., VA DCR 1999; MDOT 2006; MDE 2009).

To evaluate potential runoff depth on a unit-area basis we route the future storms implied by the IDF curves through the EPA SWMM code, packaged in a Python wrapper with a graphical user interface that controls input and output. Example Python wrappers to automate SWMM runs are freely available on the web (e.g., https://pypi.org/project/SWMM5). The actual SWMM subbasin layout needed to accomplish this task is quite simple. We specify a single BMP catchment (≤10 acres and thus not requiring time of concentration adjustments) for which the user can specify impervious and pervious acreage, roughness, depression storage, and soil/slope properties. The resulting runoff timeseries can be routed through a variety of stormwater BMPs, including gray and green infrastructure, which can be explicitly set up using SWMM input templates. For this demonstration, we focus on routing the flow through a simple detention basin to provide a consistent indicator of how existing design standards may fare under potential future climate relative to sizing based on historic climate.

The detention basin is designed to perform peak matching to undeveloped conditions for the 10-yr 24-hr storm event. In practice, detention basins are frequently designed to manage multiple storm event return periods but working with a single design target makes for an easier comparison between sites in different locations.) An orifice is used for the 10-yr storm outflow. In addition, an emergency spillway weir is added to safety pass the 100-yr 24-hr event.

The detention basin volume is calculated using the TR-55 formula (NRCS 1986) for approximate sizing for 10-yr event inputs. The basin is assumed to be 5 ft deep to the spillway invert; vertical walls are assumed to simplify calculations. The 10-yr event orifice is set at a depth of 0 with the diameter calculated from a standard orifice equation, assuming 5 ft of head and a Q equal to the 10-yr undeveloped flow. Simulations are conducted at a 6-minute time step.

4. Results

Potential increases in precipitation intensity result in increased runoff and lower BMP performance. For the Los Angeles International Airport station mentioned earlier (for which IDF curve adjustments are shown in Figure 4), the amount of event runoff volume that bypasses a detention basin designed for historic climate during a 100-yr storm event is likely to increase under future climate conditions – by as much as 1.65 in/ac (25%) for the GFDL-ESM2M, RCP 4.5 scenario for ca. 2065 (Figure 6). However, the lower-bound scenario for total annual volume (IPSL-CM5A-MR, RCP 4.5) also predicts a decrease in the size and amount of flow bypassed during the 100-yr event. This result is typical of many of the test sites, with the future IDF curves across DCM scenarios spanning the current IDF curve. Thus, for many locations there is not a consensus that large storm events of a given recurrence will increase; rather, the results reveal a risk that such events may increase.

Figure 6.

Detention Basin Performance under Historic and ca. 2065 Climate, Los Angeles, Captured versus Bypassed Flow Volume for 24-hr Event, 85% Impervious

The range of projected changes in precipitation and runoff across scenarios/DCMs evaluated at each of the 20 study locations are summarized in Figures 7 - 8. Results suggest that the 100-yr 24-hr precipitation event volume may increase by up to 67%, while the 10-yr 24-hr precipitation event may increase by up to 30%. The range among DCMs is generally greater for the 100-yr event than for the 10-yr event, reflecting greater uncertainty in predicting the more infrequent events. Simulated flow that bypasses a detention basin designed for historic climate also shows a risk of increasing (Figure 8). While some DCMs predict decreases in precipitation intensity the preponderance of scenarios indicate that increases are likely.

Figure 7.

Ensemble Range of Projected Changes in 10 and 100-yr 24-hr Precipitation from Historic to ca. 2065 Conditions across All Study Locations

Figure 8.

Ensemble range of projected Change in Runoff Volume Bypassing a Detention Basin Designed for the Historic 100-yr Recurrence Event under ca. 2065 Climate Conditions, 85% Impervious

As a check on the plausibility of the calculations, Kao and Ganguly (2011) suggest that change in precipitation extremes should reflect change in the potential saturated water content of the atmosphere in response to temperature change. Based on the ideal gas law and the Clausius-Clapeyron relationship, saturated water content and change in potential precipitation extremes from climate scenario 1 to climate scenario 2 should scale approximately as:

$$\frac{T_1+273}{T_2+273}xexp\left[\frac{17.27T_2}{237.3+T_2}-\frac{17.27T_1}{237.3+T_1}\right],$$ Equation 12

where T_i is air temperature in Celsius at time i.

Equation 12 suggests a nonlinear relationship to temperature in which there is a greater effect of a given amount of temperature increase for sites with colder baseline temperatures, with the largest increases (based solely on potential saturated water content) predicted for stations in the Great Plains North and Midwest regions. Across all 20 stations, Equation 12 suggests a median increase in the potential magnitude of larger precipitation events of 15%, consistent with the model-predicted median increase of 12% for the 10-year event.

5. Discussion and Conclusions

Changes in the climate system are anticipated to include warming temperatures, with regionally variable and less certain changes in the amount and seasonal distribution of precipitation (USGCRP 2017). In all regions of the US, increases in the frequency and severity of heavy precipitation events are likely, even in areas where total annual precipitation volume is predicted to decline. This study provides methods for efficient calculation of future IDF curves based on the transformation from DCM simulations of historic to future climate annual maximum series. The method provides a relatively simple way to develop scenarios of future changes in precipitation in a format directly useful to assessing risk to stormwater management. We illustrate the approach by application to a range of DCM output at 20 cities throughout the contiguous US. Results suggest variable changes regionally in the US, with greater increases in the larger magnitude events. Significant variability also occurs in IDF characteristics estimated from different DCMs. However, specific results are dependent on the LOCA downscaling archive as well as the selection of the future period (see Fadhel et al., 2017).

Effective, cost-efficient urban BMP strategies will need to encompass practices that reduce vulnerabilities across a wide range of potential future climatic conditions. Changes in precipitation intensity, duration, and frequency can affect stormwater BMPs in a variety of ways:

• If intensity increases for a storm of a given duration and recurrence, a larger amount of runoff will be generated and storage BMPs will be undersized relative to the intended ability to retain stormwater.

• If the duration of a storm of a given intensity and recurrence increases, the total volume of runoff generated by typical storms can increases, resulting in shortened retention and treatment times.

• If the recurrence interval of the specified design storm decreases the risk of larger storms that achieve insufficient treatment or bypass the BMP entirely will increase.

Uncertainty in future IDF relationships introduces uncertainty into assessment of risk and vulnerability associated with engineering designs. One approach used to minimize potential future risk is conservative design criteria. For instance, New York City’s climate resiliency guidelines suggest that the current 50-year IDF curve should be used as a proxy for the future 5-year storm for the 2080s and on-site detention/retention systems should be designed to retain the volume associated with the current 50-year curve (NYC MORR 2019). The Federal Highway Administration (FHWA) has proposed a tiered framework with five levels of analysis depending on the analysis of the risks of a project and its hydrologic service life (Kilgore et al. 2016). Where risk is high (based on asset criticality, vulnerability, and cost) and anticipated service life is long, an analysis of potential hydrologic responses to changes in both land use and climate with associated confidence intervals is needed (e.g., 68% confidence interval for service life between 30 and 75 years). Multiple types of model and data uncertainty contribute to uncertainty in estimating runoff; however, a key source of uncertainty for prospective analysis is the difference between different climate models and greenhouse gas emission scenarios. FHWA recommends evaluation over multiple climate models/scenarios to address this source of uncertainty, focusing on the potential change in the NOAA Atlas 14 analysis of 24-hour duration precipitation amounts (and associated confidence bounds) for appropriate recurrence intervals.

IDF curves are most relevant to design requirements for volumetric control during larger storm events with a recurrence interval of 2 years or more. Design of BMPs for water quality, including green infrastructure, is widely based on the 90^th percentile 24-hour event (or similar event), which is by definition an event that is likely to occur multiple times per year. Analysis of changes in this event is not amenable to direct analysis using an IDF curve based on AMPs; however, a statistical analysis can also be developed for more frequently occurring events used in BMP water quality design (e.g., the 85^th, 90^th, or 95th percentile 24-hr event). The primary difference relative to the IDF analysis is that the distribution of an event that is likely to recur more than once per year is described by a Peaks-over-Threshold (POT) approach, which characterizes the frequency of events greater than a specified magnitude (Serinaldi and Kilsby 2014), rather than a GEV. As the value of the threshold (u) increases, the distribution of the POT (prob $Y=(X-u)\mid \text{X}>u$) converges to a generalized Pareto distribution (GPD; Pickands 1985; Balkema and de Haan 1974):

$$H(y)=1-{\left(1+\xi \frac{y}{\tilde{\sigma }}\right)}^{-1/\xi },$$ Equation 13

in which {$y:y>0$ and $1+\xi \frac{y}{\tilde{\sigma }}>0$} and $\tilde{\sigma }=\sigma +\xi (u-\mu )$, $\mu$ is the location parameter, $\sigma >0$ is the scale parameter, and $\xi$ is the shape parameter. An updating procedure for the GPD, similar to that described above for the IDF analysis using the GEV distribution, can be readily applied to estimate the distribution of future 90^th percentile events and will be presented in future work.

The methods described in this paper provide an efficient approach to estimate future IDF relationships that is consistent with both downscaled climate model output and NOAA Atlas 14 calculation methods. The methods can be applied to any location for which historic IDF curves have been calculated and the results can readily be updated as new GCM experiments are released. The results are anticipated to help planners, designers, and engineers evaluate the range of potential future conditions for which adaptation may be needed.