Linking climate change to urban storm drainage system design: An innovative approach to modeling of extreme rainfall processes over different spatial and temporal scales
Introduction
The design of urban storm drainage systems requires a “design storm” that represents the time distribution of rainfalls within an extreme storm event. More specifically, in engineering practice, the design storm of a specified exceedance probability and duration is commonly estimated from the extreme rainfall intensity-durationfrequency (IDF) relations (Hershfield, 1961, Chow, 1964, WMO, 2009). However, in recent years, climate change has been recognized as having a profound impact on the hydrologic cycle at different temporal and spatial scales. The temporal scales could vary from a very short time interval of a few minutes (for urban water cycle) to a yearly time scale (for annual water balance computation). The spatial resolutions could be from a few square kilometers (for urban and rural watersheds) to several thousand square kilometers (for large river basins). In particular, the intensity and frequency of extreme precipitation events in most regions will be likely increased in the future (Alexander et al., 2006, Lenderink and van Meijgaard, 2008, Kharin et al., 2013, Shephard et al., 2014, Zhang et al., 2017). Hence, there exists an urgent need to assess the possible impacts of climate variability and climate change on the IDF relations in general and on the design storm in particular for improving the design of urban drainage systems in the context of a changing climate (Willems et al., 2012, CSA, 2012, Madsen et al., 2014, Simonovic et al., 2016).
To achieve this, the projected annual maximum rainfall series for different rainfall durations from short time scales (e.g., a few minutes) to long time intervals (e.g., one day or longer) under different possible climate change scenarios are required. Consequently, global climate models (GCMs) have been extensively used currently to provide projected precipitations for future periods (e.g., next hundred years) based on different Representative Concentration Pathways (RCP) scenarios. These models have been recognized to be able to represent reasonably well the main features of the global distribution of basic climate parameters (Lambert and Boer, 2001), but could not reproduce well details of regional climate conditions at temporal and spatial scales of relevance to hydrological impact studies (Nguyen and Nguyen, 2008). This is because outputs from GCMs are usually at resolutions that are too coarse (generally greater than 200 km and mostly available at a daily time scale) and are not suitable for many climate change impact studies in urban areas. A new rainfall modeling approach is thus needed to establish an accurate linkage between climate projections from GCMs and extreme rainfall (ER) processes at a local site of interest.
To refine the GCM coarse grid resolution climate projection data to much finer spatial resolutions (regional or local scales) for reliable assessment of climate change impacts, different downscaling methods have been proposed (Wilby et al., 2002, Fowler et al., 2007, Maraun et al., 2010, Gooré Bi et al., 2017). These methods can be classified into two broad categories: dynamical downscaling (DD) and statistical downscaling (SD). The DD techniques involve the extraction of regional scale information from large-scale GCM data based on the modeling of regional climate dynamical processes (Laprise, 2008, Xue et al., 2014, Xu et al., 2019). These models use physical principles to reproduce local climates, thus, are comprehensive physical models, but are computationally intensive. Whereas the SD techniques rely on the empirical relationships between observed (or analyzed) large-scale atmospheric variables and observed (or analyzed) surface environment parameters (Wilby et al., 2002, Nguyen and Nguyen, 2008, Bürger et al., 2012, Bürger et al., 2013, Werner and Cannon, 2016). The SD methods are thus flexible to adapt to specific study purposes and inexpensive computing resource requirement (Nguyen and Nguyen, 2007). Both downscaling methods therefore have their strengths and limitations (Wilby et al., 2002, Teutschbein et al., 2011), and both are currently used for downscaling the GCM outputs to the regional scales (approximately 10 to 50 km resolutions) for climate-related studies. There are many different downscaled climate projection data sources available at the national or global level provided by different organizations. For example, in North America, just to list a few, the NA-CORDEX dataset available at roughly 25 or 50 km resolution covering most of North America (NA-CORDEX, 2018), NEX-GDDP dataset available at about 25 km resolution covering the entire globe (NEX-GDDP, 2018), the NEX-DCP30 dataset available at approximately 1 km resolution for the conterminous United States (NEX-DCP30, 2018), PCIC statistically downscaled climate scenarios available at roughly 10 km for Canada (PCIC, 2018). However, downscaled data from these methods are still considered bias when comparing to observed data at a local site in a same grid cell and need to be bias-corrected. A bias-correction method is therefore required to correct the data before it can be used for impact assessments and adaptation studies (Willems et al., 2012).
In addition to the spatial downscaling, the temporal downscaling is also required to derive the distributions of sub-daily extreme rainfalls from that of the daily values since the climate projections are normally available at the daily scale. Several approaches have been developed in the literature, such as the chaotic method, the scale-invariance approach, the point-process model, the neural networks techniques (Sivakumar et al., 2001, Nguyen et al., 2002, Coulibaly et al., 2005, Marani and Zanetti, 2007, Nguyen et al., 2007, Lee and Jeong, 2014, Herath et al., 2016). Among these methods, the scale-invariance (or scaling) concept has increasingly become a new methodology in the analysis and modeling of various extreme hydrological processes across a wide range of temporal scales (Gupta and Waymire, 1990, Sposito, 1998, Hubert, 2001, Veneziano and Furcolo, 2002, Veneziano and Lepore, 2012, Lovejoy and Schertzer, 2012). Scale invariance implies that the distributions and statistical properties of ERs over different time scales are related to each other by an operator involving only the scale ratio and the scaling exponent (Gupta and Waymire, 1990). In particular, the scaling method has been used in the construction of the IDF relations for the current and future climates (Burlando and Rosso, 1996, Nguyen et al., 2002, Yu et al., 2004, Bougadis and Adamowski, 2006, Nguyen et al., 2007, Blanchet et al., 2016, Ghanmi et al., 2016). More specifically, several scaling models have been proposed in the literature, such as the scaling Gumbel (GUM) model based on the non-central moments and the probability weighted moments (Menabde et al., 1999, Yu et al., 2004). The scaling Generalized Extreme Values (GEV) model based on the non-central moments (Nguyen et al., 1998). More recently, a novel scaling probability weighted moments-based GEV model has been shown to outperform other existing scaling models (Nguyen and Nguyen, 2018).
In view of the above issues, the present paper proposes an innovative SD approach that is able to establish the linkage between climate change information to extreme rainfall estimation for urban storm drainage systems design; a difficult and challenging task in current engineering practices. This SD approach was based on a new procedure for modeling the ER processes over different spatial and temporal scales. The feasibility and accuracy of the proposed approach were assessed for a case study in Ontario (Canada) using the IDF data from a network of seven raingauges. These data are provided in Sections 2. Details of the proposed methodology are described in Section 3. Results are presented and discussed further in Section 4. Finally, a summary of the research findings is provided in Section 5.
Section snippets
Study sites and data
The observed IDF data from a network of seven raingauges located in Ontario (Canada) were used for this study. The station information and locations are presented in Table 1 and Fig. 1. Observed IDF data at each site contain annual maximum rainfall series (AMS) of nine different durations (ranging from 5 min to 1440 min). Note that the observed IDF data have been provided by Environment Canada to produce the at-site IDF relations for the various practical engineering application purposes (
A statistical approach to modeling extreme rainfall processes over different spatial and temporal scales
The proposed statistical modeling approach consists of two main steps. The first step is to establish the linkage between projected daily ERs available at a regional scale and daily extreme amounts at a local site of interest; and the second step is to determine the distribution of sub-daily ERs from the estimated daily ERs at the given location. A detailed description of these two steps is given in Fig. 3 and in the following sections.
Estimation of bias-corrected daily extreme rainfalls at a local site
The performance of the two methods for downscaling of daily extreme rainfalls from regional to local scale were first investigated and compared using different graphical displays and numerical criteria. Historical data from the seven raingauges and the “Retrospective Run” data from NASA in the same time period from 1961 to 2005 were used for the result assessments. The split-half sample was employed to compare the two methods. The first half of data were used for estimating the scaling factors
Conclusions
An innovative statistical downscaling (SD) procedure was proposed for estimating short-duration (sub-daily) extreme design rainfalls at a given local site in the context of climate change. The proposed approach involves two steps: (i) the spatial downscaling step using the scaling factors or the bias correction functions to transfer the daily downscaled global climate model (GCM) extreme rainfall projections at a regional scale to a given local site and (ii) the temporal downscaling step using
Acknowledgements
This work was supported by the Natural Science and Engineering Research Council (NSERC) Canadian FloodNet [Grant number NETGP 451456]; and the McGill Engineering Doctoral Award of the Faculty of Engineering at McGill University.
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