Increasing extreme hourly precipitation risk for New York City after Hurricane Ida

Abstract

The remnants of Hurricane Ida caused major damage and death in the United States on September 1st, 2021, and 11 people drowned in flooded basement apartments within New York City (NYC). It was catastrophic because the maximum hourly precipitation intensity, recorded as 3.47 inches (88.1 mm) per hour at Central Park, was unprecedentedly high for the NYC region. The stormwater infrastructure in NYC is built for 1.75 inches (44.5 mm) per hour, and so understanding the dynamic risk associated with Ida can inform city planning efforts for climate change’s impact on short duration extreme precipitation events. We contextualize this storm’s record-breaking hourly intensity within the historical record as well as project its risk in the near- to medium-term future using nonstationary stochastic models. These models are conditioned on average temperature (T_avg) and cooling degree day (CDD) projections from three climate models as a covariate, each with a SSP 126 and SSP 370 scenario. The likelihood of such a storm was slowly increasing even before Ida happened, but the projected aggregate reoccurrence risk of an event of Ida’s magnitude over time from the non-stationary models ranges from 4 to 52 times higher than the risk given by the stationary model. Using CDD as a covariate resulted in risks that were more than twice the magnitude than when using T_avg. Presenting both covariates provides a broader envelope of uncertainty, which highlights the importance and nuances in the choice of a regionally appropriate covariate for non-stationary risk analysis.

Supplementary Information

The online version contains supplementary material available at 10.1038/s41598-024-78704-9.

Introduction

In the late summer of 2021 in New York City (NYC), the remnants of Hurricane Ida swept through the Northeast United States on September 1st with a maximum intensity of 3.47 inches (88.1 mm) per hour at Central Park in New York. It was the wettest hour in history for the Central Park rain gauge (which has publicly available records of hourly precipitation since 1948^1,2, and daily precipitation since 1869) as well as for other local rain gauges in New Jersey such as Newark Airport³. The wide-ranging impact of this event is shown in Fig. 1. NYC was put under a Flash Flood Emergency for the first time⁴. Initial National Weather Service damage reports estimate 360 million dollars of damage incurred to NYC specifically⁵, and 75–100 million dollars of damage to the MTA subway⁶. Tragically, 10 people died in flooded basement apartments in the borough of Queens and one in Brooklyn. These buildings were primarily built in low-lying areas and in some cases, upon or adjacent to filled-in historical water bodies within NYC (Fig. 1b and panels 1–4). The uniqueness of these impacts are likely directly tied to the record breaking rain that fell within an hour.

Fig. 1.

Several metrics showing the deadly intensity and duration of the flooding during Ida overlaid on two topographic maps of NYC (A is current topography above sea level and B is historical (1900) topography). (A) Indicates the topography of NYC when it flooded during and after Ida. Grey indicates below sea-level elevation. The historical map, (B) Shows the many water bodies and former coastline that have since been buried, engineered and obscured in relation to present day flooding. The insets (1–4) are highlighted on the zoomed-out map in red. These insets show the detail in occurrences of flood reports and deaths and their proximity to specific water bodies that have since been developed over and no longer function as natural drainage areas. The marker scale in the legend applies to all panels, and the map was made in QGIS⁷³.

Hourly precipitation intensities are predicted to increase with global warming^7–10, especially in places that are already wet^11,12. Via the Clausius-Clapeyron (C-C) relationship, the maximum amount of water vapor an air parcel can hold before the vapor saturates is set almost entirely by its temperature, and at Earth-like temperatures this increases at roughly 7% per degree Celsius. This relationship is a fundamental reason for the expected increase in rainfall intensity with anthropogenic climate change. However, the year-to-year changes can be highly variable¹³, and changes in precipitation due to climate change will also manifest as shifts in the frequency of events¹⁴.

In the midlatitudes, the precipitation-temperature scaling varies due to factors such as latitude and convergence during storms^8,12. There are theoretical approximations linking precipitation and temperature at global scales¹⁵. However, at city or sub-kilometer scales for extreme precipitation, global scaling does not apply. For the tropics, scaling related to convection dynamics and/or column water vapor have been established for extreme precipitation (e.g.¹²). For the midlatitudes, it is useful to consider daily and hourly projection studies separately. On a daily scale, some scaling is seen seasonally between extreme precipitation and dewpoint temperature in the Northeast United States, but observed results are not captured by Global Climate Models (GCMs)¹⁶. Studies on hourly extreme precipitation, especially those using Extreme Value Theory, tend to be local^17,18, or involve numerical downscaling techniques of climate model simulations¹⁹.

NYC is one of the wet regions predicted to get wetter²⁰, but how the short duration extreme precipitation events are changing over urban areas and how they will be further modified in a warming climate is still not well understood. Hourly rainfall intensity research and projections under climate change are being called for increasingly in synthesis studies, such as the 5th National Climate Assessment and the 3rd and 4th (interim) articles of the New York City Panel on Climate Change (NPCC). Their synthesis mainly present the available research on daily extreme precipitation for the Northeast/NYC region^20–23 and only the 3rd NPCC report²⁰ presents analysis on sub-daily rainfall durations (the shortest being 3 h). The 3rd report specifically emphasizes the need for research on appropriate statistical methods for predicting short term trends in hourly rainfall intensity, and the 4th report adds that Ida heightened the need to fill this research gap. Thus, exploring if any scaling of average temperature ( or other related variables like Cooling Degree Days (CDD) and hourly extreme rainfall intensity is observable on a regional level is vital. We highlight both in our results.

Extreme precipitation can be categorized in more than one way, but our focus on the metric of hourly rainfall intensity not only addresses the research gaps identified above but is connected to local stormwater infrastructure design. In NYC, sewers built after 1970 can accommodate 1.75 inches (44.5 mm) per hour²⁴. An hourly intensity of 1.75 inches or greater was not recorded in NYC until 1991, and has only occurred since in 1995, 2004, 2006, 2021, and 2023 (This is discussed more in detail in the “Results” section, see Fig. 2a). Our intention with this choice is to highlight the dynamic future risk of the deadliest aspect of the post-tropical cyclone from Hurricane Ida for the NYC area, with the acknowledgement that a similar analysis of different rainfall durations and/or locations would produce variable results.

Fig. 2.

Historical Extreme rainfall intensity (R) trends. Panel (A) shows three linear trend lines which correspond to the period that they extend on the x-axis. Panel (B) indicates the significance of the trend over time, with significant trends highlighted. The linear trends in (A) correspond to the first time a significant trend is seen in the dataset (in 1990s), the year when the trend is least significant (2000s), and the entire dataset (up to more recent 2023), respectively. Panel (C) presents an iteratively calculated return period using at least 31 datapoints (1948–1979, 1948–1980, 1948–1981, …, 1948–2022, 1948–2023) to show how the risk of Ida has changed under stationary assumptions.

Hurricane Ida moved northwest from its landfall in Louisiana and generated clusters of supercells in the Northeast United States³ as a post-tropical cyclone. The maximum hourly intensities for Central Park (3.47 inches per hour, or 88.1 mm) and Newark Airport (3.62 inches per hour, or 92 mm) far exceeded the NOAA Atlas-14 based 100-year, 1 h storm estimates of 2.82 inches per hour (71.6 mm) and 2.91 inches per hour (74 mm), respectively. Supercell convection and squall lines were observed as associated with the most extreme rainfall rates in the northeast during the storm^3,25. The highest hourly rainfall intensities were not captured by most of the ensemble members in a study by Menemenlis et al.²⁵, which used a 3 km resolution model. The phenomena of supercell clusters coinciding with nearby tornadoes (10 occurred in the Northeast during Ida) has not been focused on historically as an extreme-precipitation causing storm type, but is gaining more recognition and deeper study in recent years²⁶.

Ida can be seen as a harbinger of severe storms to come. It is not entirely alone in the recent record, but it is unusual in terms of storm type as a post-tropical cyclone. For example, Ida did not cause coastal flooding like Superstorm Sandy did in 2012. Additionally, in the week prior to Ida, the hourly intensity record at the Central Park rain gauge had been broken by Hurricane Henri, recording just under 2 inches (50.8 mm) per hour. Two years after Ida occurred, another notable precipitation event occurred on September 29th, 2023, with a maximum hourly precipitation intensity of 1.87 inches (47.5 mm) at Central Park, and a new daily accumulation record at JFK Airport. While not as severe as Ida, this 2023 storm (a coastal extratropical cyclone) is included in our analysis and highlights the recent increased frequency of precipitation events that cause damage and disruption to the city. It is worth noting that no one died in the NYC region as a result of this more recent storm, however, most subway lines were flooded and delayed passengers during rush hour on a weekday, leading to public outrage and renewed concern with the city’s response to worsening urban flooding and extreme precipitation. In response to the September 29th event, the New York City comptroller launched a public-private investigative study, Rainproof NYC, to assess ongoing and planned flood infrastructure projects and make recommendations²⁷. It is under this backdrop and emerging need from a city planning perspective that we developed the following framework- one that shows how stationary risk has evolved over time and how non-stationary models can convey future risk over time through a dynamic lens.

For NYC agencies like the DEP (Department of Environmental Protection), efforts to manage extreme precipitation focus on reducing pluvial flooding and limiting polluted water discharge to New York Harbor. Storms much less severe than Ida or 1.75 inches (44.5 mm) per hour rainfall intensity cause sewer backups and overflow on a regular basis, especially in certain neighborhoods. Compliance with EPA regulations that limit river pollution via Combined Sewer Overflows (CSOs)²⁸ is the main motivation for the DEP’s current stormwater infrastructure improvement, targeting these neighborhoods with recurring flood issues²⁹. Although the DEP is already working towards these massive necessary improvements^24,30, stormwater infrastructure expansion will need to further accommodate the evolving precipitation Intensity-Duration-Frequency (IDF) curves and design exceedance probabilities associated with climate change over the infrastructure lifecycle^31–34. The magnitude of infrastructure work needed to adequately handle high rates of runoff will likely mean that solutions will also come from a range of stormwater management methods. This can range from nature-based, green and blue infrastructure like Bluebelts, Daylighting streams, and rain gardens to gray infrastructure like sewers, retention tanks, and surface cover changes and implementing “cloudburst” management infrastructure²⁷. Our results are thus targeted at different design planning periods of 10, 25, and 50 years.

In this paper we aim to contextualize Ida’s precipitation intensity within the historical record by showing how the risk of an event of this magnitude would have changed year to year in the decades prior to its occurrence. We use a suite of traditional statistical tests to show how the significance of the extreme precipitation trend and the return period of Ida change with each year in the historical dataset. To complement existing climate modeling endeavors, we take a stochastic modeling approach to calculate nonstationary risk. We present a climate change-informed nonstationary method based on the Generalized Extreme Value distribution to project the risk of exceedance of another event of Ida’s magnitude and compare these values to a stationary one. Our results can be translated to potential future damage costs and encourage planning for such events that would be expected under climate change, reinforcing the pressing need for improved urban stormwater management systems that can handle higher intensity rainfall.

Results

Contextualizing Ida historically

The annual maximum warm-season (May 1st to October 31st) hourly rainfall time series for the Central Park rain gauge, or extreme rainfall intensity (R hereafter), is first examined in Fig. 2a. This figure shows that the extreme precipitation of 2021 associated with Hurricane Ida (3.47 inches (88.1 mm) per hour) was about 75% greater than the previous highest annual warm season intensity of 1.95 inches (49.5 mm) per hour in 1995. It is also twice the magnitude of the design rainfall of 1.75 inches (44.5 mm) per hour used by NYC to size its drainage system. An evident trend (0.05 in/hr/decade, or 1.3 mm/hr/decade) over 1948–2023 is statistically significant at the 5% rejection rate. There is no significant auto-correlation in the time series, and the statistical significance of the trend is also tested using a bootstrap resampling approach that considered Ida-like event occurrence in any year between 1948 and 2023 (see “Methods” section and Supplemental Figure S1).

A time-evolving Mann-Kendall trend test is conducted to investigate this trend more systematically. Mann-Kendall trend test’s p-value is estimated beginning with the first 31 years (1948–1979). Subsequently, the dataset is updated by adding one year each time (e.g., 1948–1980, 1948–1981, …, 1948–2022, 1948–2023) and the Mann-Kendall trend test’s p-value is re-estimated. The temporal tendency of this p-value (computed each time based on an updated time series of extreme rainfall intensity) indicates the variable nature of the trend in extreme rainfall intensity. Figure 2b presents these results and shows how the trend significance has evolved since record-keeping began at Central Park. A statistically significant increase in extreme rainfall intensity (as determined by p-value < 0.10) was seen in the early to mid-1990s and from 2018 to the present. The years with a statistically significant trend are labeled on Fig. 2b. A conjunction of the time series of extreme rainfall intensities (Fig. 2a) and the tendency of the Mann-Kendall trend significance (Fig. 2b) indicates that the extreme rainfall intensity has been trending post-2000s upwards and amplified since 2018 (overall, 0.05 in/hr/decade as seen in 2a, or 1.3 mm/hr/decade), highlighting the already-changing nature of extreme rainfall intensity in NYC. Figure 2a also presents three regression lines over varying periods of 1948–2023, 1948–2000, and 1948–1992 to gauge the range of the trend amongst high variability. The blue and red lines show a significant trend; 1948–1992 (blue) is the period of the first significant trend, and 1948–2023 (red) capturing the overall trend. The third yellow line (1948–2000) shows the year with the most statistically insignificant trend, primarily due to a multi-year period of low rainfall intensities that followed the 1990s.

Figure 2c presents the temporal evolution of the return period (or mean recurrence interval) of Ida’s rainfall intensity of 3.47 inches (88.1 mm) per hour. After significance testing of parameters, Gumbel distribution (Type I Extreme Value Distribution as a natural distribution for block maxima³⁵) was chosen to represent extreme rainfall intensity data best. Like the analysis conducted in Fig. 2b, the return period of Ida’s rainfall intensity is estimated using yearly-updated rainfall intensity. When the return period of Ida’s rainfall intensity is estimated using a Gumbel distribution fit to extreme rainfall intensity data from 1948 to 1979, it is approximately a 7,500 year-storm. Subsequently, the Gumbel distribution parameters are re-estimated using updated rainfall intensity data each year, and the return period is computed to obtain the tendency of the return period of Ida’s rainfall intensity of 3.47 inches (88.1 mm) per hour. When the full data record, which includes the 2021 Ida event, is used (1948–2023), the return period is approximately 2500 years. Figure 2c also shows a locally-weighted polynomial trend line using a smoothing span of 0.5³⁶ to highlight the tendency of the return period of Ida. The extreme rainfall intensity already had a significant uptrend before the 2021 Ida event (Fig. 2b), and the return period of an Ida-like event has been decreasing (or the likelihood of the event was increasing) even before Ida happened (Fig. 2c). It is to be noted that even with the return period dropping by half, the Ida event still has an extremely low probability of occurrence. The changing likelihood or probability of an Ida-like event further motivates the need for a formal nonstationary modeling framework to project the risk due to such extremely low-probability high-impact events in the future.

Non-stationary and stationary approaches for risk assessment

Traditional precipitation frequency analysis assumes stationarity of the parameters of the probability distributions, resulting in static estimates for hazards or the probability of extreme events. However, since precipitation frequency, accumulation, and intensity are increasing (or changing over time), the magnitude and likelihood of any n-year storm would also vary dynamically. A lack of adequately long data records to correctly estimate the time-varying parameters in a nonstationary realm and an understanding of how the climate will evolve under global warming limits nonstationary usage. Given the temporal evolution of the trend and the likelihood of an Ida-like event observed in Fig. 2c, stationary and nonstationary modeling approaches were developed to project the probability of a storm of Ida’s magnitude. This framework also enables comparisons between stationary and nonstationary approaches for extreme rainfall intensity prediction and subsequent stormwater management for urban areas.

We use Gumbel-based models to quantify the future probability of an Ida-like event under stationary and nonstationary assumptions (model formulation details are presented in the “Methods” section). Under a stationary assumption, extreme rainfall intensity is modeled as a Gumbel distribution with time-invariant parameters. The future probability of an Ida-like event is a fixed annual exceedance probability estimated from the model and, hence, static for any future planning phase. This model’s location and scale parameters are 0.958 and 0.326, respectively (in units of inches per hour, or 2.43 and 0.83 mm per hour), and the static probability of an Ida-like event () is 0.045%.

The nonstationary models are distinguished by the time varying parameters for the Gumbel distribution. Each model’s parameters are estimated respectively each year using covariates of time for non-stationary model 1 (Eq. 8), and higher (SSP 370) and lower (SSP 126) emission scenario model simulations^37–41 of and it’s integral over 65 ℉ (Cooling Degree Days, or CDD – see Eq. 1) for non-stationary models 2 and 3 (Eqs. 9 and 10). Such non-stationary methods have been applied to precipitation in other regions^17,18,33,42 including an evaluation of regionally appropriate covariates⁴³. Its value and application as a tool for extreme precipitation under climate change is now well established (see for example, review articles by Yuan et al., Wright et al., Slater et al., and Schlef et. al^44–47).

To project the future probability of an Ida-like event, we have developed two versions of the model: one that uses projections and one that uses CDD projections. These are obtained by using the air temperature data from two warming scenarios from a single grid cell covering NYC from three models: GFDL-ESM4.1³⁷, CESM2³⁸, and MPI-ESML1-2-HR^40,41. Each of the models have: (1) a nominal resolution of 100 km, (2) historical simulations that go back to the start of central park’s hourly precipitation observations, and, (3) future projections that are at least 50 years past 2023. The projections are adjusted for grid-to-point resolution based on the difference between historical simulations and observations (see “Methods” section and Table 1 for details).

Table 1.

Summary of the CMIP6 models used for and CDD in the non-stationary model.

	Institution	Reference for model	Equilibrium climate sensitivity (K)
Summary of CMIP6 models used
GFDL-ESM4.1	National Oceanic and Atmospheric Administration, Geophysical Fluid Dynamics Laboratory	Dunne et al.37	2.7
MPI-ESM1-2-HR	Deutsches Klimarechenzentrum	Mauritsen et al. 201940 and Mueller et al.41	2.98
CESM2	National Center for Atmospheric Research	Danabasoglu et al.38	5.15

Equilibrium climate sensitivity is taken from Dunne³⁷ for GFDL-ESM4.1 and from Zelinka et al.⁵² for CESM2 and MPI-ESM1-2-HR.

The observational and projected data is seen in Fig. 3. The observational data is seen to have a modest positive correlation with extreme rainfall intensity, R, (panel A). A similar correlation is found with CDD (see Supplemental Figure S2 and S3). In 3b, we can see the historical observations over time in relation to all 6 model projections for . The projections are noisy, and divergences between SSP 126 and SSP 370 are not clearly seen until after roughly the 25-year design period.

Fig. 3.

Overview of data used for analysis. The relationship between and R (A) is a mildly positive relationship. The historical and future for the warm season are shown in (B). The historical observations (1948–2023) are in green, and the resolution-adjusted simulations are shown on the right side of the dotted line.

and CDD are very similar in the historical period in terms of linear trend, correlation with extreme rainfall intensity, and appear visually similar (See Supplemental Fig. 2). However, the nonstationary model coefficients of the location and scale parameters of the Gumbel distribution fit to extreme rainfall intensity, R, conditioned on and CDD in the historical period pick up on the differences, and the divergence between these model-dependent time-varying location and scale parameters grow in the future period (see Supplemental Figure S4 and S5). Supplemental Table T1 contains the model coefficients of the parameters from Eqs. (9) and (10) when both covariates are normalized (i.e., converted to standardized anomalies), and this unitless comparison shows that CDD has a larger slope in the scale parameter, and has a larger slope in the location term. The difference in the parameters combined with the future projections induce differences in the future probabilities of an Ida-like event. This difference is illustrated in Supplemental Figure S6, where the distribution of simulated extreme rainfall intensity is compared between covariates for one scenario.

The stationary and nonstationary future probabilities of an Ida-like event are used in a decision tree framework (see Eqs. 11–15 in the “Methods” section and Supplemental Figure S7) to derive the expected future risk of such extreme rainfall intensities over three specific planning phases that the city planners and engineers often consider for operation and design of hydraulic infrastructure – a 10-year immediate timeframe risk, a 25-year intermediate timeframe risk, and a 50-year long-term risk. Figure 4 presents these results for all the developed models (M0, M1, M2, M3, respectively Eqs. 7, 8, 9, 10), with each climate model’s high and low scenario run with M2 and M3 (Eqs. 9 and 10). The risk presented is aggregated over time, but it is important to note the and CDD driven models (M2 and M3) show non-linear risk change with time. Yearly probabilities for future 10 years from select models are shown in Supplemental Table T2.

Fig. 4.

The range of the number of expected Ida-like events in the next 10, 25, and 50 years. All probabilities are calculated yearly for the 3 design periods onwards from 2024, and then aggregated using a decision tree. Analysis is the same for both panels with the exception of covariate choice. Stationary refers to M0, Time refers to M1, and the rest use the climate covariate-specific M2/3 (see methods for details). Asides from the stationary line, all the results are non-stationary models.

Substantial differences are realized between stationary future risk and nonstationary future risk across the three planning phases, as well as between models with and CDD as covariates. For a 10-year immediate timeframe, the expected risk of an Ida-like event is 0.4% under a stationary climate assumption. However, the anticipated risk under nonstationary assumptions ranges from 4 to 13 times when using and 7–26 times the stationary risk for the same 10-year design period when using CDD. These risk ratios are higher for the 25- and 50-year timeframes, with the 50-year long-term risk being as high as 115% under the CDD-driven high-emission (SSP 370) scenario of the CESM2 climate model, or 52 times greater than the stationary estimate (2% over 50 years). In the most extreme case, the expected number of Ida-like extreme rainfall intensity events over the next 50 years is more than 1 occurrence (115%) if one uses the CESM2 high-emission scenario-based CDD to project extreme rainfall intensities, and 52% when using . The 50-year planning phase shows a great deal of variability in the probabilities, depending on which climate model, scenario, and covariate is used, indicating that there is large uncertainty in these risk ratio estimates. However, even when variability across the model is accounted for, all the non-stationary models return results much larger than the stationary risk.

That the CESM2 model provided the highest probabilities is consistent with its relatively higher Equilibrium Climate Sensitivity compared to the other two models. At the 25-year planning phase, each climate model shows a different relationship between their high and low scenario predictions. For example, the GFDL ESM4.1 low emission scenario indicates a higher risk than its high emission counterpart because the CDD from both scenarios is relatively similar at that point. This reflects the variability of (and CDD) projections in Fig. 3b (and Supplemental Figure S3), and that a large divergence in scenarios is not seen for decades after the projection initialization.

These expected risk estimates can readily translate into equivalent annualized costs or damages the city might incur. While the nonstationary models clearly project a greater number of Ida-like events than the stationary assumption, it is to be noted that these are based on stochastic projection models that factor in the observed trends in extreme precipitation. These trends do not differentiate between storm type nor do they incorporate specific knowledge about the underlying atmospheric dynamics. Hence, the results must be viewed from a risk assessment lens, not a deterministic viewpoint.

Discussion

The characteristics of extreme rainfall are changing around the world, and our results show that the risk of hazards from precipitation is increasing in NYC. These changes need to be modelled to update the anticipated risk and future designs of stormwater infrastructure, and the framework we present is one way to inform mitigation measures and design alternatives adaptively on the decadal to multi-decadal time scales. The framework is also one of dynamic risk; our models show a non-linear change in risk year to year. Results like these provide a broader and more nuanced lens with which to predict and plan for the erratic response of regional precipitation trends to a warming climate.

Precipitation extremes depend on other factors besides temperature, however the other factors (like convergence of moisture in the atmosphere, vertical stability, and dynamics of non-buoyant vertical motion) have more uncertainty than temperature. In this study, we focused on examining how changes in the distribution of temperature might impact probability of precipitation extremes. Our use of CDD and as covariates was motivated by their similarity in trend to precipitation extremes in the historical record (see Supplemental Figure S2). Although the two datasets were very similar in the historical observation period, small differences in variation translated to differences in the Gumbel distribution’s location and scale parameters. This, combined with a faster rate of change for CDD in the future, led to risks that differed by more than a factor of 2. The non-stationary model does not assert causality between the covariates and the predicant (rainfall), but rather use the covariates to capture the time-varying trend in the model parameters. While shifts and increases in rainfall intensity and frequency as a result of climate change are statistically documented¹⁴, there is not a proven physical explanation yet, and so no way to tie this to a climactic causality outlook. Still, by including both and CDD, we present a larger envelope of risk and a body of work that may prompt others to robustly establish more methods to determine a “regionally appropriate covariate” for such statistical models.

It is known from observations and simulations that “the scaling rates between extreme precipitation and temperature are strongly dependent on the region, temperature, and moisture availability, which inhibits simple extrapolation of the scaling rate from past climate data into the future”⁸. Non-stationary methods have been used before for storm attribution studies, like in the case of Hurricane Harvey in Texas⁴⁸ where the authors assume a linear relationship between the Generalized Extreme Value (GEV) parameters and CO2 and Niño3.4. GEV-based models like theirs, as well as Steinschneider & Najibi’s linear nonstationary model between precipitation and dew point temperature¹⁶. However, there is still a lack in studies using climate models to predict and characterize scaling climactic variables with extreme hourly precipitation risk, especially on a local or urban scale.

Thus, there is still a need to better resolve climate models at the urban scale to capture and improve the projections of tail events and shorter duration extreme events. Stochastic alternatives for extreme rainfall projections like the one presented in this study need to be explored jointly while Global Climate Models improve at these scales. The variability in the results produced by the climate models presented here can be used to better characterize uncertainty from climate model projections when used for the urban environment. These results can also be used in risk thresholds to inform safety factors for new designs and failure risks for current assets.

The spatial effects of frontal-scale dynamics means that the impacts of floods on residents and the City’s built environment does not necessarily translate to any one dimensional metric like hourly precipitation intensity or accumulation. For example, schedules and locations of human life plays a role- residents of basement apartments are more likely to be prone to injury or death from flooding if they are home when the rain is occurring and if they live in low lying areas⁴⁹ that may have been swamps, rivers, or other natural drainage areas prior to human urban development of the environment (Fig. 1b). This was the case of Ida, whose maximum precipitation intensity happened on a weekday evening between 9 and 10 pm. Residents are likely to be inconvenienced and subsequently upset if rain causes delays to their commute, either by flash flooding on streets and highways or flooding of the subways⁵⁰, which are complex systems that are difficult to predict. That was the case in the recent event on September 29th, 2023, and other times in the past few years like Hurricane Henri a week before Ida, or Hurricane Elsa previously that summer in 2021.

The higher emission (SSP 370) risk projection ranges from 42% to 115% over the next 50 years, which is significantly higher than the stationary risk of 2%. Despite the one projection that would indicate more than one Ida-like event in the future, the spread in the results do not indicate a sure chance of an event of Ida’s magnitude recurring in that time period. However, there have been impactful events of lesser magnitude in the two years since (e.g., the Sep 29th, 2023 coastal extratropical cyclone), once again challenging the city’s sewers hydraulic capacity, transportation infrastructure, and housing infrastructure. These events highlight the urgency in the work of the city to mitigate flash flooding. Future work on this topic could include a spatial analysis of several rain gauges (or high-resolution gridded rainfall products such as stage IV radar rainfall estimates or Multi-Radar/Multi-Sensor (MRMS)) in the region to assess risk of current and proposed mitigation infrastructure under the types of high intensity storms expected under climate change on a finer scale. Many types of promising infrastructure are being considered and studied for funding in the city, some of which could work in parallel to provide both small scale and sewershed scale strategy. This includes future sewer expansion for CSO Long-Term Control Plans, nature-based solutions like the bluebelt drainage program, and green infrastructure such as rain gardens, infiltration basins, and green roofs^24,30,51. Ultimately, managing more intense rainfalls and mitigating damage will require a significant and adaptive building process that is regionally appropriate for NYC and informed by non-stationary extreme precipitation risk.

Methods

Annual maximum warm season rainfall (R)

Hourly rain gauge data for Central Park was obtained from the National Centers for Environmental Information (NCEI) from two datasets. Central Park is the rain gauge which the city uses for its IDF design curves and remains the basis of drainage design. Hourly Precipitation Data (HPD) is used for 1948–2013². This data is appended with the Integrated Surface Database (ISD) hourly global data set from 2014 until 2023¹. Annual Maximum Warm Season Rainfall, R, is the maximum hourly rainfall from May 1 to October 31 for each year from 1948 to 2023. The 8 years of overlap between these two datasets were examined and the difference proved to be negligible for R, but overall, ISD has a slight positive bias as compared to HPD for the Central Park station.

Temperature (T_avg) and cooling degree days

Observed daily average temperature for Central Park from 1948 to 2023 was also obtained from NCEI to estimate the Warm Season Cooling Degree Days, CDD, which is the warm season sum of the positive difference between the average daily temperature and 65 F°. The average temperature ( used in the analysis is the average of the average daily temperature over the warm period. CDD is a metric used traditionally for building energy consumption prediction as it can be closely related to fuel consumption.

1

For the future and CDD projections that are calculated from GCM data to run the non-stationary models, we account for variability inherent to climate projections by developing our statistical models using three different GCMs from the CMIP6 archive. To capture a range of differences in the model predictions, we selected three models. We chose three earth system models (ESMs) that all have the same resolution, which is nominally 100 km. Each model includes a SSP 126 and SSP 370 scenario. We also note two of the models have relatively low Equilibrium Climate Sensitivity (ECS) and the other model has a relatively high ECS, as compared to the full set of CMIP6⁵². All are freely available online via https://aims2.llnl.gov/. The details on the CMIP6 models used is as follows:

To normalize the immutable differences between a grid cell climate model estimate and a point observation, an adjustment was made on the projections using each climate model’s historical simulation of the grid point and the observational CDD or from Central Park from 1948 to 2014. This adjustment () shifted the projections by the difference of the means of the historical observations ( from the historical simulation (, scaled by the ratio of standard deviations of the observations to the simulation. The adjustment is as follows:

2

Nonparametric trend analysis

The nonparametric rank-based Mann–Kendall (MK) test is widely applied to detect the monotonic trend in climatic or environmental time series^53,54. The MK test’s null hypothesis (H₀) is that there is no monotonic trend in the time series. A failure to reject H₀ at a specified confidence level indicates that the observed sample data is insufficient to conclude that a trend might exist⁵⁵. The MK test is based on the S statistic defined as:

3

where is the total number of observations and and are the data values in the time series and (), respectively. Three cases can be associated with : (a) it is a large positive number indicating an upward trend since the later-measured values tend to be larger than earlier one, (b) it is a large negative number indicating a downward trend since the later values tend to be smaller than the earlier ones, and (c) it is a small number indicating no trend. Further, can be approximated to a normal distribution to derive a standard normal null distribution as:

4

The null hypothesis cannot be rejected if for a chosen level of rejection rate . Along with the hypothesis test, Sen’s slope (), the rate of change⁵⁶ can be computed. An initial block size of 31 was chosen in line with NOAA NCEI’s climate normals⁵⁷.

Stationary and nonstationary models based on type I extreme value distribution

Gumbel-based models were used to quantify the future probability of an Ida-like event under stationary and nonstationary assumptions. Leveraging the current recognized practice on stationary and nonstationary models for extreme events^35,58–60, Type I extreme value distribution (Gumbel distribution) is chosen for parsimony to model the annual maximum warm season rainfall (R).

Accordingly, under stationary assumption, R is modeled as a Gumbel distribution () with time-invariant location () and scale () parameters.

5

The cumulative distribution function of g can be written as:

6

Given the observed time series record of R, the location and scale parameters, u₀ and β₀ for the stationary model can be estimated using standard procedures of maximum likelihood estimation³⁵. The future probability of Ida-like event () under a stationary assumption is then:

7

This stationary probability is static or is the fixed annual exceedance probability for any future planning phase.

Three nonstationary models were also developed for R where the location and scale parameters change over time and its values are modeled as a linear function of time, the temperature covariate CDD, or . A linear function is assumed for the sake of a simple and parsimonious model. However, a quadratic model was tested and found to be an overfit when comparing the AIC. In the case of the scale parameter (), a log-link function is used to guarantee . Given that the location and scale trend functions can be estimated using historically observed time series of R, the future probability of Ida-like event ( and ) under nonstationary assumption can be derived using the projected location and scale parameters which are, in turn, estimated using future time (t) or projected CDD for a future planning phase or time frame. This nonstationary probability is dynamic and changes each year according to the projected value of the predictor (t, (t) or ) over the next n years of the planning phase. Accordingly, , , and are defined as:

8

9

10

For , the nonstationary future probability of Ida-like event ( and ) for various planning phases are derived separately for a low emission scenario and a high emission scenario. All the models are fit using the ExtRemes library in the RStudio integrated development environment^61,62.

Expected future risk of Ida-like event

The stationary and nonstationary future probability of an Ida-like event are used in an influence diagram/decision tree framework⁶³ to derive the expected future cost or risk over a specified n-year planning phase. The future n-years can be structured into an outcome tree where an Ida-like event can occur each year with the specified probability, and, when it materializes, an inflation-adjusted equivalent uniform annualized cost of damage is incurred by the City. Consequently, a branching tree with branches at the end of a specified n-year planning phase can be pictured with a compounded damage cost at the end of each branch. Supplemental Figure S7 presents an example of such a branching tree for three years where , , and are the respective future probabilities of an Ida-like event in 2024, 2025, and 2026, and C is the inflation-adjusted equivalent uniform annualized cost of damage that could be incurred by the City when an Ida-like event occurs. Consequently, for a three-year planning phase, if an Ida-like event occurs in each of the next three years, the compounded cost of damage is 3C; if it occurs in two of the next three years, the compounded cost of damage is 2C; if it occurs in only one of the next three years, the compounded cost of damage is C; and if it does not occur in the next three year, the compounded cost of damage is 0. For this example eight-branch tree, backward induction logic can be applied to derive the expected cost of future damage due to an Ida-like event as:

11

which, under a stationary assumption of , becomes , and under a nonstationary assumption becomes

More generally, for a specified n-year planning phase

12

13

14

15

Electronic supplementary material

Below is the link to the electronic supplementary material.

Author contributions

CM, ND, JB, and SH developed the methodological framework. CM and ND conducted the analysis. CM wrote the original draft. All authors (CM, JB, ND, SH, and NS) participated in the discussion of result and analysis and edited the paper.

Data availability

Data AvailabilityMeteorological DataHourly Precipitation Data (HPD) is used for 1948-2013². This data is appended with the Integrated Surface Database (ISD) hourly global data set from 2014 until 2023¹. Both HPD and ISD are available from NCEI, which also archives the temperature data used for observed CDD. The GCM simulation data, being part of the CMIP6 archive, is freely available for download via the Earth System Grid Federation, https://aims2.llnl.gov/search.Flood Impact Data The sources of flood impact data seen in Fig. 1 include National Weather Service (NWS) Flash Flood location and duration reports during the event (available upon request)⁶⁴, USGS surveys of high water marks after the event[⁶⁵ (using indicators like mud on walls⁶⁶), and real time sensor measurements from Floodnet⁶⁷ by request, a cooperative-based flood data collection system recently established in NYC. Floodnet only had 5 sensors providing real time flood level information in Gowanus and JFK airport that captured Ida’s flooding but has since grown. The addresses of basement deaths were reported in a local newspaper⁶⁸. NOAA Atlas-14 data⁶⁹ is available online from https://hdsc.nws.noaa.gov/pfds/. The current topographic data and basemap is available from NYC OpenData⁷⁰ The historical topographic map is 2 geo-rectified 1900 USGS map quadrants, which are highly accurate maps of the Brooklyn and Queens region. While it does not show a landscape unaltered by human development, it does capture NYC’s water bodies before significant major land and tributary changes occurred in the areas where people drowned in their basements⁷¹. The map is available online from the USGS Historical Topo Map Collection⁷². The map was created in QGIS⁷³, an open-source program. Code Availability RStudio and Python code for analysis and plots is available by request to the corresponding author.

Declarations

Competing interests

The authors declare no competing interests.