Continuous Rainfall Generation for a Warmer Climate Using Observed Temperature Sensitivities

Introduction

The design of most hydraulic engineering infrastructures is based on local intensity–duration–frequency (IDF) curves, which provide extreme rainfall intensity (mm/h) values for various durations (minutes to days) and return periods (years). Typically, IDF curves cover rainstorm durations from 5 min to 24 h, with return periods from 2 to 100 years . These are normally sufficient to cover the needs of most applications dealing with streamflow, runoff routing, and floods and, therefore, help design infrastructures resilient to extreme rainfalls. Indeed, IDF curves are widely employed in stormwater management and engineering applications across the world (e.g., Akan 1993; Ferguson 1998; Seybert 2006).

IDF curves are best suited for hydrological studies in urban and small rural catchments. They can also be used for larger catchments with concentration times exceeding 24 h. However, when dealing with catchments in mountainous or cold areas, snowmelt and rain-on-snow events can become the driving processes that generate design flood events, requiring different methods such as continuous hydrological modeling and flood frequency analyses. This paper does not address such cases but focuses exclusively on rainfall-generated flood events, for which IDF curves are the main design tool.

These curves are typically developed by using an extreme value distribution locally, which is fitted to historical annual maxima series of accumulated rainfall data of various durations. Most countries have their own governmental bodies or agencies responsible for producing IDF curves at the national level through standard procedures [e.g., Environment and Climate Change Canada (ECCC 2019) and the National Oceanic and Atmospheric Administration (NOAA) Atlas 14 in the United States (Perica et al. 2018)]. An example of IDF curves from ECCC is provided in Fig. 1.

Most IDF curves used operationally rely on a stationarity assumption, in which the climate remains stable over time. This implies a stationary spatial and temporal structure of rainfall (Cheng and AghaKouchak 2014; Myhre et al. 2019). This hypothesis has long been challenged, given the impact of low-frequency internal climate variability (natural variations in climate due to sea surfaces temperature anomalies, such as the Atlantic Multidecadal Oscillation and El Nino Southern Oscillation) on rainfall and temperature patterns (Milly et al. 2008; Ouarda et al. 2019). In addition, the intensity and frequency of extreme rainfalls are affected by the anthropogenic forcing resulting from greenhouse gas (GHG) emissions (Fadhel et al. 2017; Mamoon et al. 2019; Myhre et al. 2019). Indeed, robust increases in the magnitude of daily rainfall were identified in both observations and climate models over the last half of the 20th century (Min et al. 2011; Westra et al. 2013), with an expected intensification of rainfall extremes in the decades to come (Donat et al. 2016). There is also considerable evidence that short-duration (subdaily) rainfall extremes are becoming more intense, as highlighted by Westra et al. (2014) and Fowler et al. (2021a, b), resulting in increased flood risk (Fowler et al. 2021c). This increase in rainfall intensity will potentially lead to a reduction in water security, as water will not redistribute from the soil to the surface reservoirs, leading to plant water stress and issues in agriculture (Eekhout et al. 2018).

The observed and projected intensification of daily and subdaily extreme rainfall calls into question the applicability of historical IDF curves, which do not explicitly consider extreme rainfall nonstationarity, in designing infrastructure that will operate in future climate conditions. This is especially true for many engineering structures, which, for the most part, will still be in operation by the end of the 21st century (Arnbjerg-Nielsen 2012; Cheng and AghaKouchak 2014; Mailhot and Duchesne 2010; Yilmaz et al. 2014). For instance, Cheng and AghaKouchak (2014) suggest that a stationary climate assumption might lead to an underestimation of extreme rainfalls by as much as 60%, increasing flood risk and failure risk in infrastructure systems. We can affirm that most existing stormwater runoff infrastructures are ill-adapted, and design strategies, including climate change adaptation, need to be implemented (Lopez-Cantu and Samaras 2018; Myhre et al. 2019). IDF curves are a critical part of the design process and require updating to account for an evolving climate and reduce infrastructure vulnerability (ASCE 2018; Watt and Marsalek 2013; Yan et al. 2021).

Fig. 2 shows a typical conceptualization (Kind 2012; Merisalu et al. 2021) of the tradeoff between investment and risk that optimizes the total cost of infrastructure, such as stormwater drainage systems. Infrastructure design attempts to balance construction costs (solid blue curve) against damages if the designed return period flow is exceeded during the lifespan of the element (dashed red curve). There is a theoretical optimum of the total cost (dashed black curve) upon which the return period flow is selected, as shown by the orange arrow in the current climate.

The science (as reviewed in this work) shows, with a high level of certainty, that the projected increases in extreme rainfall lead to an increased likelihood of exceeding the return period design flow, therefore increasing the damage risk. This can be seen in Fig. 2, with the shift of the damage curve to the right (solid red curve), which in turn moves the optimal total cost to the right (green arrow). The theoretical cost of the underdesigned infrastructure element is outlined by the difference in height between the orange and green arrows. Thus, building climate-resilient infrastructure through a larger investment in the initial construction cost (blue curve) could ultimately lead to a lower total cost (black curve) over the lifespan of the infrastructure elements, considering their typical long service life. For stormwater drainage infrastructure, the challenge is to quantify the expected impacts of climate change on the red curve, in other words, the projected changes in IDF curves.

A simple illustration of the cost-benefit of adapting to climate change consists in oversizing a culvert by choosing a larger diameter to provide more conveyance. While this oversizing generates a larger initial cost (blue curve), the replacement of a whole section of a washed-away road following an extreme storm event (exceeding the culvert's design capacity) will be more expensive overall.

The importance of larger initial investments is clearly illustrated with the current state of most infrastructures in North America. For instance, the latest ASCEs' Infrastructure Report Card (ASCE 2017) gave the overall infrastructure of the United States a D+ rating (i.e., poor, at-risk). Similarly, the latest Canadian Infrastructure Report Card (CIRC 2019) underlines that about 30% of Canada's water infrastructure [e.g., drinking water, wastewater, stormwater, and, to some extent, roads (culverts), and bridges] is in very poor, poor, or fair conditions. A large part of existing infrastructures is so scheduled for renewal in the short term, and replacements are expected to have a lifespan of between 50 and 100 years . Climate change adaptation must therefore be incorporated in planning and designing new infrastructure projects in order to handle the upcoming increases in rainfall extremes during the projects' lifespan. This means that new infrastructure projects require investing more capital in the short term for future-proofing, which implies that difficult financial decisions will have to be made. However, the cost of not adapting to climate change is more expensive than the cost of adapting to climate change (Chambwera et al. 2014). This should compel stakeholders to integrate climate change considerations into water and infrastructure management (Wasko et al. 2021).

The aim of this study is threefold: (1) provide a critical review of recent studies on the evolutive trends of extreme rainfall under a warmer climate; (2) assess how these findings will influence the IDF curves in the future; and then (3) propose a nonstationarity model of IDF curves that is easily accessible for different regions of the world for design and operational purposes. An overview of the science on the expected impacts of climate change on rainfall extremes is provided in the next section. A discussion on current scientific gaps, current governmental agency guidelines, and new technical recommendations from an operational perspective is then presented, followed by a conclusion and our final remarks. The overarching motivation of this work is to introduce technological support for adaptation in the area of infrastructure design by providing key findings on how to adapt IDF curves in the context of climate change.

Discussion

This discussion begins with a summary of the current knowledge on rainfall extremes based on a recent literature review, followed by an analysis of current guidelines to adapt the IDF curves under a warmer climate. Afterward, some adapted guidelines for practitioners and stakeholders are suggested to fill the scientific gap in the existing resources. Finally, key concerns regarding the detection of the climate change signal and its limitations for decision-making are provided.

What We Know

Since the 1950s, extreme rainfall events have become more intense and more frequent in many regions of the world (Westra et al. 2013, 2014). Scientists expect this trend in rainfall extremes to continue with global warming due to the association with the CC relationship (Li et al. 2021), leading to heavier rainfall events.

However, caution is required when applying the 7 % / ° C rate regionally because there is some evidence of an increase in the CC rate for shorter-duration (hourly or subdaily) extremes when the temperature is in the range of approximately 12°C–22°C. Cases of super CC scaling are noted in North America (e.g., Nie et al. 2018), Europe (e.g., Lenderink et al. 2017; Wood and Ludwig 2020), and Australia (e.g., Bao et al. 2017; Mantegna et al. 2017). This is partly attributable to (1) an increase in the likelihood of convective versus stratiform rainfall occurrence as the temperature increases and (2) to the properties of convective rainfall itself (Westra et al. 2014).

There is also evidence of a limitation to the rate of increase (even a decrease) in rainfall intensities with increasing temperatures above 24 ° C in some regions (Ghausi and Ghosh 2020; Pendergrass 2018). This appears to be associated with a decrease in moisture availability at high temperatures, even though the mechanism(s) leading to the moisture deficits are not fully understood to date (Westra et al. 2014).

There is an overwhelming consensus that extreme rainfall will intensify at the global and regional scales (e.g., Collins et al. 2013; Field et al. 2012; IPCC 2013; Kendon et al. 2019; Martel et al. 2020; Sillmann et al. 2013). The occurrence of extreme rainfall events in many regions (particularly in Europe and North America) has contributed to an increase in the number of related studies over the last few years [Fig. 3(a)]. These studies aim to assess projected changes in rainfall extremes better and to understand better the driving processes (e.g., Innocenti et al. 2019; Kirchmeier-Young and Zhang 2020; Myhre et al. 2019; Wood and Ludwig 2020). Many international initiatives have also emerged to improve the understanding regarding the relationships between global warming, atmospheric circulation, and extreme rainfall events, such as the INTElligent use of climate models for adaptatioN to nonStationary hydrological Extremes (INTENSE) project (Blenkinsop et al. 2018).

As discussed previously, many studies have projected increases in extreme rainfall statistics for the coming decades (Table S1), with an increasing trend correlated with the frequency of occurrence, as well as with the occurrence of the shortest-duration rainfall events [Fig. 3(c)]. A large number of the referenced studies are primarily based on GCM and RCM simulations [Fig. 3(b)] and on the use of more than one climate model [83%; Fig. 3(d)]; however, only a few integrate a multimember ensemble of the same climate model [26%; Fig. 3(d)]. Greater changes in rainfall extremes are projected for the subdaily timescale than for the daily timescale, especially for shorter durations [Fig. 3(b)] (Cannon and Innocenti 2019; Forestieri et al. 2018; Fowler et al. 2021a; Huo et al. 2021; Martel et al. 2020; Rajczak and Schär 2017; Westra et al. 2014; Wood and Ludwig 2020). More significant changes are projected in rare extreme rainfall events when compared to the common rainfall extreme indices, such as the daily annual maximum rainfall (Rx1day) [Fig. 3(b)] (Butcher and Zi 2019; Cannon and Innocenti 2019; Hosseinzadehtalaei et al. 2020; Huo et al. 2021; Kharin et al. 2018; Li et al. 2021). In particular, the 20-year daily rainfall event is projected to become 3–4 times more frequent (Kharin et al. 2013; Martel et al. 2020), while the 100-year daily rainfall event will be between 4 and 5 times more frequent (Martel et al. 2020), indicating a stronger amplification of rainfall extremes over longer return periods.

Analysis of Current Guidelines for Adaptation

The need to adapt IDF curves is now well recognized by many organizations. For example, the guidelines for Canadian water resources practitioners (CSA 2019) highlight the necessity to update the IDF curves more frequently than in the past because climate change is expected to induce an increased intensity and frequency of rainfall extremes in most areas over the next decades.

However, a more frequent update of IDF curves only accounts for changes over the recent past and does not cover the projected future changes in rainfall intensity. The uncertainties around the projected future climate are the main reason why projected changes in rainfall extremes are not included in IDF curves. The following subsections give local, regional, and national examples of guidelines, as well as standards for the modification of IDF curves to account for the future climate. Although these adaptation strategies might be imperfect (based on the current state of scientific knowledge previously discussed), they constitute an interesting step as they cover the lifespan of new infrastructure while improving its resilience.

Simple Constant Percentage Increase

The simplest adaptation strategy is the constant percentage increase, in which the same safety factor is used for all extreme rainfall design values. This method is currently used by some countries and regions. For instance, Belgium and the United Kingdom respectively apply an increase of 30% (Madsen et al. 2014; Willems 2011) and 20% (UK Department for Infrastructure 2020) on all rainfall extremes. Similar factors are also enforced by Canada's provincial governmental bodies, such as in the Province of Quebec (18%; MDDELCC 2017) and in the City of Moncton, New Brunswick (20%; EPWDR 2011).

Adaptive Percentage Increase

The adaptive percentage increase approach recognizes that future increases in rainfall extremes are not uniform and depend on various factors, such as temperature increases (as represented by future time horizons) and rainfall frequency. Different adaptive percentage increase strategies have been identified in different countries. One strategy that is used at the national level by Denmark for rainfall design (Arnbjerg-Nielsen 2008; Gregersen et al. 2014) is to implement different safety factors based on the frequency of the event selected in the design (i.e., 20%, 30%, and 40% increases are added to the 2-, 10-, and 100-year return periods, respectively). The Swedish Water and Wastewater Association (Madsen et al. 2014; Svenskt Vatten 2011) recommends a fixed percentage increase, with an adaptive variation between 5% and 30%, depending on the region. The UK Department for Infrastructure (2020) has selected a unique factor of 20% at the national level with incremental safety factors for rainfall design across all of England based on the time horizon (i.e., up to 10%, 20%, and 40% by 2040, 2070, and 2115, respectively; Defra 2020).

Percentage Increases Based on the Clausius-Clapeyron Relationship

The third approach is to apply a percentage increase based on the projected increase in warming. This follows the rationale behind the Clausius-Clapeyron relationship by providing correction factors based on the most likely local or regional increase in temperature. The future rainfall intensity can be computed as Eq. (1)

I f u t = I r e f × [ 100 + R s c 100 ] Δ T

where I r e f and I f u t = reference and future rainfall intensities, respectively; R s c = rainfall scaling factor (%) based on the CC relationship; and Δ T = projected change in local temperature. The Australian Rainfall-Runoff guidelines (ARR; Ball et al. 2019) recommends a 5% increase per degree Celsius of warming while the Canadian Standard Association (CSA 2019) recommends a value of 7 % / ° C . However, CSA (2019) acknowledges that shorter-duration events could follow a super CC relationship, implying that a larger rate than 7 % / ° C of warming may be applied, depending on the area. This is also supported by multiple studies, as previously discussed.

Future IDF Curves

Some cities (e.g., NYC 2017; City of Vancouver 2018) or regions [e.g., Ontario (MTO 2016) and Newfoundland and Labrador (Finnis and Daraio 2018) in Canada] have already adopted future IDF curves for different time horizons (e.g., 2040 and 2070). The future IDF curves are usually an updated version of historical curves (obtained through standard methods) but upscaled based on the increase in rainfall extremes projected by the climate models. While it allows providing an adaptive percentage increase for both of the different durations and return periods, this approach often relies on GCM spatio-temporal resolutions, which are too coarse to produce reliable regional IDF curves.

Many studies attempt to provide regional future IDF curves by using either GCM [e.g., Canada (Srivastav et al. 2014); India (Chandra et al. 2015); Iran (Khazaei 2021); and the United States (Butcher and Zi 2019; Ragno et al. 2018)], or RCM/CPM [Australia (Mantegna et al. 2017); Belgium (Hosseinzadehtalaei et al. 2018); Canada (Ganguli and Coulibaly 2019); England (Fadhel et al. 2017); Italy (Forestieri et al. 2018); South Korea (Lima et al. 2016); and Spain (Fluixá-Sanmartín et al. 2019)] simulations. However, these future IDF curves are rarely adopted by governmental agencies and remain unused by practitioners.

Overall, most of the currently adopted guidelines fail to recognize the larger projected increases in extreme rainfall toward shorter and less frequent events. Climate model outputs can be used to explore rainfall characteristics/statistics; CPMs are particularly suited to investigate subdaily and subhourly extreme rainfall events. Furthermore, it is recommended to use multimember ensembles of climate models to reduce uncertainty (i.e., climate models and internal variability) in the projected values of rainfall extremes.

Suggested Adapted Guidelines for Practice

First, IDF curves based on past observations should be computed using the latest historical records. IDF curves are often decades-old [e.g., see the ECCC (2019) and NOAA's Atlas 14 (Bonnin et al. 2006)], and so do not even account for recent climate trends. Multiple guidelines thoroughly explain how to perform a rainfall frequency analysis from historical records to produce IDF curves (e.g., CSA 2019). Practitioners thus have some resources at their disposal to ensure that the IDF curves they use are up to date (e.g., less than 2 years old could serve as a general rule of thumb) before using them in any new design applications.

Then, for IDF curves covering the future climate, it is necessary to account for the intensification of rainfall extremes of shorter duration and of longer return periods. From our literature review, we found that the approach based on the CC relationship has strong potential but requires some modifications to integrate the expectation of intensification of projected rainfall extremes with frequency (as the return period increases) and with shorter durations (subdaily). Therefore, we propose to adapt Eq. (1) as follows

I f u t , D , T = I r e f , D , T × F T × F D × ( 100 + R s c , 24 , 2 100 ) Δ T

where I f u t , D , T = projected future rainfall intensity of duration D and return period T ; I r e f , D , T = reference period rainfall intensity of duration D and return period T ; F T = adjustment factor for return period T ( T > 2 years , F T 1 ) ; F D = adjustment factor for duration D shorter than 24 h ( D < 24 h , F D 1 ) ; R s c 24 , 2 = rainfall scaling (%/°C) for the 24-h 2-year return period rainfall event; and Δ T = projected change in seasonal mean temperature (°C).

This equation is based on the expected rainfall scaling ( % / ° C ) of the 24-h 2-year return period rainfall ( R s c , 24 , 2 ), which has the smallest intensity in typical IDF curves. This value is equal to the median Rx1day value, which is one of the most common extreme rainfall indices studied in climate science (Table S1). Local Rx1day values can be computed easily and reliably using climate model outputs.

Because Rx1day is generally well represented in GCMs (Alexander and Arblaster 2017), we computed worldwide R s c , 24 , 2 factors based on 26 CMIP5 GCM simulations (see Table S2 for the list of GCMs used). Only the first member (r1i1p1) of each GCM ensemble simulation was selected for the reference (1981–2000) and future (2081–2100) periods. The seasonal (December-January-February, DJF; March-April-May, MAM; June-July-August, JJA; and September-October-November, SON) Rx1day and mean temperature were calculated for both the reference and future periods and then remapped on a common 2.5 ° × 2.5 ° grid to compute the multimodel ensemble mean. The R s c , 24 , 2 scaling rates were obtained through the ratio of the projected changes of Rx1day (Fig. 4) and mean temperature (Fig. 5). The R s c , 24 , 2 scaling rate for the RCP8.5 scenario is shown in Fig. 6 (the scaling rate of the RCP4.5 scenario is shown in Fig. S1). Similar to those by Seneviratne et al. (2016), the scaling ratios are found to be roughly similar for both the RCP4.5 and RCP8.5 emission scenarios.

The projected change in mean seasonal temperature ( Δ T ), needed to compute Eq. (2), is shown for the RCP8.5 scenario over the 2081–2100 period in Fig. 5. Results for other future time horizons (2021–2040, 2041–2060, and 2061–2080) are available in Figs. S2–S4. By specifying a projected change in mean seasonal temperature ( Δ T ), the practitioner can determine the horizon of interest-based on the infrastructure's expected lifespan (e.g., up to the middle or the end of the 21st century). As discussed previously, the RCP8.5 business-as-usual scenario was preferred over the more optimistic RCP scenarios (e.g., RCP4.5) because it matches the current emissions (Sanford et al. 2014; Schwalm et al. 2020) and provides more conservative design criteria.

The seasonal and spatial heterogeneity of the changes in maximum daily rainfall presented (Fig. 4) and in the scaling rates (Fig. 6) are the consequence of multiple factors, which include large-scale atmospheric circulation changes that drive moisture convergence and local changes of near-surface air temperature and atmospheric conditions that affect convection (O'Gorman and Schneider 2009; Donat et al. 2016). Generally, extreme precipitation increases with temperature in moist, energy-limited environments and decreases in dry, moisture-limited environments (Prein et al. 2017b). Moreover, during the wet season, when there is a moisture surplus, extreme precipitation increases close to or above the Clausius-Clapeyron rate, while the increase is smaller during the dry season (Tabari 2020).

Fig. 6 presents the scaling of the median Rx1day corresponding to the 24-h 2-year return period rainfall. A strong worldwide seasonal variation is found in the scaling rates, depending on the time of occurrence of the annual daily maximum rainfall. We recommend selecting a scaling rate based on the season that displays the largest annual daily maximum rainfall (Fig. 7). Most regions project positive scaling factors, with some level of regional variability. For instance, the scaling rates of most regions in Eastern North America vary between 4%/°C and 6%/°C for the winter (DJF) and autumn (SON). Warm regions with less available moisture (e.g., Southern Spain, the Maghreb, South Africa, and Australia) exhibit negative rates.

For Eq. (2), we recommend using the Δ T and R s c , 24 , 2 scaling provided in Figs. 5 and 6, respectively, or to recompute local scaling factors using RCM and CPM ensembles according to the data availability and the practitioner's level of climate expertise.

Based on the literature review reported previously, it is currently not feasible to compute precise and reliable estimates of the duration ( F D ) and frequency ( F T ) factors. This is especially true for subhourly durations, for which high-resolution CPMs are required. The use of CPM ensembles, such as the one presented by Pichelli et al. (2021) over a domain centered over the Alps, will eventually allow estimating these two factors more accurately at the local scale. Considering the rate at which more and longer CPM simulations are being generated, reliable estimations of both factors are expected to be possible in the next decade. While a single CPM simulation could still be used to provide an initial estimation for these factors, it should be done with precaution, considering the different sources of uncertainties previously discussed. However, even an uncertain estimation would prove to be a better alternative than the status quo when it comes to building resilient infrastructure.

We can nonetheless provide the range of plausible values for each factor. Both factors are positive and equal to or greater than 1. The value of each factor will progressively increase above 1 as the rainfall duration decreases (from the 24-h reference duration) or as the rainfall return period increases (from the 2-year reference return period). The upper limit of both factors is given by their physical interpretation: coefficient values larger than 1.5 are unlikely as they would lead to an improbable super CC as compared to observations and climate model projections. Just as is the case for the scaling rate, these values will be region-dependent. A value of 1 indicates no amplification of rainfall extremes for durations shorter than 24 h ( F D ) and return periods longer than 2 years ( F T ).

Improvements will continue to be made in climate modeling, and it is expected that better spatial and temporal resolutions of climate models will lead to lower uncertainty in their simulations as the 21st century progresses. For these reasons, we strongly recommend that all the Eq. (2) components be periodically revisited (e.g., every 5 years ) by using state-of-the-art climate models and ensemble simulations. Similar to the updating of IDF curves based on historical observations, the nonstationarity of the future climate must be considered, which will ultimately lead to a reduction of the overall uncertainty in infrastructure design.

Finally, the practitioner should keep in mind that no-regret strategies are likely a good option when dealing with climate uncertainty, as their excess adaptation cost can be relatively small when compared to potential consequences. Using the same analogy as before, choosing a culvert that can convey a 20-year flow or a 100-year flow is only a matter of choosing a slightly larger diameter. This is a much smaller cost than having to rebuild a section of road that has been washed away due to an underdesigned culvert.

Detection of the Climate Change Signal

Various trend detection methods were explored to determine if an anthropogenic climate change signal can be detected by using the observation networks of rain gauges. Globally, approximately two-thirds of daily rainfall stations display increasing trends for the latter half of the 20th century (Min et al. 2011; Westra et al. 2013). There is also considerable evidence of greater increases in subdaily rainfall extremes (Fowler et al. 2021a; Westra et al. 2014).

However, natural variability can represent a considerable source of uncertainty and could mask the climate change signal at both the local and regional scales (Deser et al. 2012; Fischer et al. 2013; Martel et al. 2018). Martel et al. (2018) show that the detection of a significant trend at the regional scale could be delayed until the middle of the 21st century in many parts of the world. In the case of local trends, the role of natural variability is even greater, and the detection of a significant trend could be further delayed until the end of the century.

The studies used in this paper lead to an overwhelming consensus: extreme daily and subdaily rainfall events are expected to increase significantly in response to a warmer climate (Fig. 3 and Table S1). Thus, for regions where no trend is observed in rainfall data, a seemingly absent trend should not prevent the implementation of adaptation measures against climate change, especially for infrastructures with a long service life.

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