The role of rainfall space–time structure, as well as its complex interactions with land surface properties, in flood response remains an open research issue. This study contributes to this understanding, specifically for small (
Rainfall spatiotemporal structure plays an important role in flood generation in urban watersheds (Saghafian et al., 1995; Smith et al., 2005a; Emmanuel et al., 2012; Nikolopoulos et al., 2014). Spatial heterogeneities in land use and land cover complicate the translation of rainfall spatiotemporal distribution into flood responses (Ogden et al., 2011; Galster et al., 2006; Morin et al., 2006; Ntelekos et al., 2008; ten Veldhuis et al., 2018; Yin et al., 2016), especially for small catchments (Faurès et al., 1995; Smith et al., 2005b; Zhou et al., 2017, 2019; Yang et al., 2020). The influence of rainfall spatial–temporal structure on flood frequency analysis in urban areas remains an open research issue.
Previous studies have demonstrated the sensitivity of hydrological response to rainfall variability in both space and time (Smith et al., 2012; Ochoa-Rodriguez et al., 2015; Rafieeinasab et al., 2015). Following the advent of rainfall measurement using weather radar (Fulton et al., 1998; Krajewski and Smith, 2002), many studies have highlighted the use of high-resolution rainfall data in assessing rainfall variability over a range of spatial and temporal scales (Berne et al., 2004; Gebremichael and Krajewski, 2004; Moreau et al., 2009; Emmanuel et al., 2012) and how their use could improve runoff estimation (Morin et al., 2006; Smith et al., 2007; Schellart et al., 2012; Wright et al., 2014b; Gourley et al., 2017; Rafieeinasab et al., 2015).
There are conflicting findings on the relative importance of rainfall temporal and spatial characteristics. Paschalis et al. (2014), Ochoa-Rodriguez et al. (2015) and Yang et al. (2016) found that “coarsening” temporal resolution has a stronger impact on flood response than coarsening spatial resolution. Adams et al. (2012) found the space–time averaging effects of routing through the catchment notably remove the impact of spatially variable rainfall at a 150 km
Stochastic storm transposition (SST) was developed as a physically based
stochastic rainfall generator for rainfall frequency analysis. Previous studies show that SST with relatively short records (10 or more years) of
high-resolution radar rainfall fields can produce reasonable rainfall
scenarios with realistic spatial–temporal structure, which cannot be provided by conventional design storm methods. In the conventional approach, the idealized assumptions include idealized rainfall temporal structure, uniformed spatial distribution and
Previous studies have demonstrated that the relationship between rainfall
and flood is scale-dependent, varying with rainfall patterns, basin characteristics and runoff generation processes. However, there is still no
clear answer on the relative importance of the temporal and spatial features of
rainfall in flood responses (Cristiano et al., 2017). Moreover, studies focusing on small (
This study contributes to the understanding of the interaction between rainfall variability and flood response over small-scale urbanized watersheds (
The paper is organized as follows. In Sect. 2, we introduce the study region and describe the SST-based methodology, the Gridded Surface Subsurface Hydrologic Analysis (GSSHA) model and the metrics used to characterize rainfall and flood response. In Sect. 3, we present model validation and analyses of flood frequency distributions and rainfall–flood relationships. A summary and conclusions are presented in Sect. 4.
The study focuses on the highly urbanized 14.3 km
Overview of the Dead Run study region including
Characteristics of the Dead Run watershed (Smith et al., 2015).
Note:
High-resolution (15 min temporal resolution, 1 km
Instantaneous discharge data with a resolution of 5 min from the US Geological Survey (USGS) were used for DR-1, DR-2, DR-5 and Franklintown. For DR-3 and DR-4, the discharge data are converted through stage–discharge curves from Lindner and Miller (2012). Streamflow observations for the outlet station at Franklintown extend back to 1960. The subwatersheds have records beginning in 2008.
The distributed physics-based GSSHA model is used to simulate multiscale flood responses. GSSHA is a two-dimensional, distributed-parameter raster-based (i.e. square computational cell-based) hydrologic modeling system. It uses explicit finite difference and finite volume methods in two dimensions on a structured grid to simulate overland flow and in one dimension to simulate channel flow (Downer and Ogden, 2004, 2006). Previous studies of the GSSHA model show that the model with fine grid resolution can produce adequate simulations of flood response, especially when driven by high-resolution radar rainfall fields (Sharif et al., 2010, 2013; Wright et al., 2014a; Cristiano et al., 2019).
In this study, we use the Dead Run model created by Smith et al. (2015). A brief description of the model is provided here; see Smith et al. (2015) for more details. The delineation of the watershed and channel network was based on a 30 m USGS digital elevation model (Gesch et al., 2002). Channel flow overland flow was set with different Manning's roughness coefficients. Additional stream channels were added based on the Baltimore County hydrography geographic information system (GIS) map. Stream cross sections were extracted from a 1 m resolution topography data set for Dead Run developed from lidar. Storm sewers in DR-2 and DR-5 were added using the Baltimore County Stormwater Management GIS map and digitized storm sewer maps. The semicircle's diameter was set to the pipe diameter. Detention basins were represented within the channel with cross sections extracted from the 1 m lidar topographic data.
Several aspects of the model were modified from those used in Smith et al. (2015), primarily to improve computational speed. Infiltration is calculated using Richards' equation (RE) in Smith et al. (2015), while this study uses the three-layer Green–Ampt (GA) scheme. A uniform value of Manning's roughness coefficient of 0.01 is set for all the stream channels for model simplification. Initial soil moisture is approximated to be one-third of the field capacity for each storm event.
The rainfall scenarios in this study are developed using RainyDay, an open-source SST software package (Wright et al., 2017). The steps used are briefly summarized here; the reader is directed to Zhou et al. (2019) and references therein for further details.
The first step is to identify a geospatial “transposition domain” that
contains the watershed of interest. In this study, we use a square 7000 km
The second step is to identify the largest
The third step is to randomly sample a subset of
The fourth step repeats Step 3
Rainfall statistics were computed for each event, based on radar rainfall data at 15 min, 1 km
Rainfall location is given by
For a uniformly distributed rainfall, the mean RWD is
Equations (1)–(3) are typical rainfall characteristics used in conventional rainfall–flood analysis since they reflect the general information of rainfall. Since the basin-averaged index will ignore the potential spatial heterogeneity over the watershed, Eqs. (4)–(8) describe the spatial distribution of rainfall within the area.
Flood peak (
We validated the Dead Run GSSHA model through analyses of the 21 largest warm season (April–September) flood events, with peak discharges ranging from
70.3 to 253 m
Peak discharge difference is calculated as the difference between the modeled peak and measured peak as a percentage of the measured peak (Fig. 2a). The peak discharge is underestimated at DR2, DR4, DR5 and Franklintown. The median peak discharge difference at the downstream Franklintown gage was
Comparison of
The peak time difference is calculated as the time difference between the
simulated peak time and measured peak time (Fig. 2b). The median difference
ranges from
The median Nash–Sutcliffe efficiency (NSE) for the 21 events at Franklintown is 0.77 (Fig. 2c). The best NSE at Franklintown is 0.97, indicating that the match between the model and measured data was nearly exact. For the subwatersheds, the best median NSE is at DR-4 with a value of 0.74, while the least median NSE is at DR-1 with a value of 0.21. The results show that the main tendency of flood response is captured by the model.
The hydrograph of the 14 August 2011 storm event is shown as a representative of flood simulations for the 21 events (Fig. 3). The peak discharge difference is
Hydrographs and rainfall for the 14 August 2011 storm event. Time refers to minutes from the start of the model simulation.
It should be noted that the error in simulated response may be attributable to measurement errors tied to stage–discharge curves and conversions of radar reflectivity to rainfall rate, as well as to the features that were simplified within the model, such as initial soil moisture and some aspects of the storm drain network (Smith et al., 2015). For example, it has been documented that the average error of discharge between USGS direct measurements and stage–discharge curves for Franklintown is 17.4 % between 2008 and 2010 (Lindner and Miller, 2012); this error likely grows for high flow conditions. Furthermore, for the rainfall data set used in this study, the median difference of the storm total rainfall between a rain gage and the bias-corrected radar rainfall data for all the pixel of gages over the 21 storms is 22.6 % (Smith et al., 2015). It may also increase the error in the measurements and modeling results.
Overall, the validation shows that the hydrological model can capture the main shape and timing of the measured response in Dead Run. We conclude, therefore, that the model is suitable for the subsequent flood frequency analysis.
Under the SST framework, 3 h rainfall scenarios for 10-, 50-, 100- and 200-year return periods were generated (Fig. A2). For each rainfall return period, 300 realizations of rainfall events are used as input to drive the hydrological model. Henceforth, for each rainfall return period, 300 flood responses can be simulated for Franklintown and the five DR subwatersheds.
The distribution of maximum discharge at the Franklintown gage for rainfall return periods ranging from 10 to 200 years is illustrated in Fig. 4a. To compare the distributions of rainfall and flood peaks, the values are normalized to range from 0 to 1. The normalization is the ratio of values minus the minimum to the maximum minus minimum. The most striking feature is that the distributions of total rainfall and flood peaks are highly variable across the four return periods. The kernel density distribution of rainfall shows a peak at the position of 50th quantile for four return periods. The distribution of flood peaks is more complex. For the 100-year rainfall return period, the kernel density distribution of flood peaks shows a multimodal trend with two small peaks around the 25th and 75th quantiles, which contrasts with the unimodal distribution of rainfall. The following results will show that the flood peak is highly related to spatial rainfall features, implying that the multimodal distribution of flood peaks is associated with the spatial distribution of rainfall. The pronounced difference in the distributions of total rainfall and flood peaks highlights the complex relationship between rainfall properties and flood response in this relatively small urbanized watershed.
Violin plots of
The flood response time is calculated as the difference between the time of maximum rainfall rate and maximum discharge (Fig. 4b). Median values of response time are similar under all return periods, ranging from 70 to 83 min, which, given the temporal resolution of rainfall is 15 min, can be similar for all four return periods. It can be concluded that although the flood peak magnitude increases with rainfall return period, the response time is consistent for various rainfall scenarios. This implies in this small highly urbanized watershed the response time is more linked to the drainage system rather than to rainfall characteristics.
Figure 5 demonstrates the simulated hydrographs for the four return periods. The upper and lower spread (75th and 25th quantiles) of the hydrograph indicate the range of variability of simulated hydrographs. For the 10-year return period, the hydrograph is relatively smooth, with a smaller spread. With increasing return periods, the hydrograph is peakier, with a shorter duration of high magnitude discharge. The hydrograph for the 50-year return period shows a transitional shape between small (10-year) and large (100- and 200-year) rainfall return periods. For the 100-year return period, the upper spread shows a tendency toward dual peaks, which cannot be revealed from conventional design flood practices. Since in the conventional rainfall flood frequency approach, the design storm is temporally idealized as a unimodal peak process, using these design storms, the flood response is generally simulated as a unimodal peak process. The above results imply the uncertainty and insufficiency of flood frequency analysis using the conventional methods. For the 200-year return period, the hydrograph is peakiest with a large upper spread.
Time series of simulated hydrographs for Franklintown based on the 3 h design storms from 10- to 200-year return periods with spatially uniform (blue) and spatially distributed (red) rainfall. The grey bar indicates the median value of the basin-averaged rainfall rate.
The distribution of flood peaks over the five subwatersheds exhibits contrasting variation with rainfall return periods ranging from 10 to 200 years (Fig. 6). Generally, the basin scale plays an important role in determining the distribution of flood magnitudes. Under the 10-year rainfall return period, DR1 and DR2, with similar basin scales of 1.32 and 1.92 km
Box plots of normalized flood peaks for Franklintown and five subwatersheds.
Results show that sub-basin flood distributions vary significantly with rainfall return periods. DR1, with a 33 % larger impervious area and more
than double the stormwater-detention-controlled area than DR2 (Table 1), has a 26 % larger median flood peak under a small rainfall return period. For large return periods, DR2 has a slightly larger median peak and a larger peak and interquartile range than DR1. The contrasting peaks in DR1 and DR2 imply that flood peaks are less impacted by impervious areas for extreme storms, while for small rainfall events, detention infrastructure may play less of a role in the detention of flood peaks. DR5, with the smallest detention-controlled area, has the smallest flood peaks under a small rainfall return period. Under a large return period, however, it has the largest changes in peak discharges, with comparable flood peaks with subwatersheds larger than 6 km
We further examine the spatial distribution of flood magnitude over the Dead
Run watershed under the 100-year return period of flood at Franklintown (Fig. 7). The dimensionless flood index is used to compare flood peak magnitudes over the watershed (Lu et al., 2017). The flood index is computed
as the maximum flow discharge divided by the computed 10-year flood (
Box plot of flood index across the DR subwatersheds for the 100-year design storms.
We investigate the relationship between the spatial and temporal characteristics of rainfall and flood response for small and large rainfall
return periods based on Spearman's rank correlation (Fig. A3). The peak rainfall rate (
We used random forest regression models to examine the importance of rainfall characteristics to the flood response. Random forests (RF) is an ensemble learning method (Breiman, 2001) that aggregates results from multiple models to achieve better accuracy. RF is one of the most widely used methods for regression and classification. Moreover, it is relatively easy to train and test. In this study, rainfall space–time structure characteristics are used as RF model features. The flood peak is set as the model target. The relationship between rainfall structure and flood peak is then explored under the RF-based regression method. The main parameters of the RF model are tuned by a grid search approach (Probst et al., 2019). The prediction performance is assessed using mean absolute error (MAE), root mean square error (RMSE) and explained variance regression score (
The difference in feature importance is compared between the 10- and
200-year return periods (Fig. 8). For the 10-year return period, peak rainfall rate (
Feature importance analysis of RF model for space–time rainfall structure and 10-year (red) and 200-year (blue) flood peaks.
In conventional design storm/flood practices, the return period of rainfall
and peak discharge is often assumed to be equivalent (Rahman et al., 2002). Under the SST framework, we can examine this assumption (Wright et al., 2014a). At the 14.3 km
Scatterplot comparison return periods for rainfall and peak discharge for individual SST-based simulations.
We also compared the simulated flood response resulting when rainfall is uniform over the watershed, rather than spatially distributed as in previous analyses (Fig. 4 and Table 2). Generally, flood peaks generated from uniform rainfall have lower peaks than from nonuniform rainfall. The difference increases with the return period. Under the 10-year return period, the shapes of the two hydrographs have similar upper and lower bounds (75 % and 25 % quantiles). The median flood peak using nonuniform scenarios is 22 % higher than the uniform scenarios. Under the 200-year return period, the hydrograph resulting from nonuniform rainfall is much peakier than the uniform SST scenarios, with higher upper and lower bounds. The lower bound of hydrograph by nonuniform SST scenarios is close to the median hydrograph of uniform SST scenarios.
The median flood peak reductions using spatially uniform and spatially distributed rainfall.
The impact of rainfall spatial heterogeneity among the five subwatersheds is
different. DR1, with a basin scale of 1.32 km
This paper addresses the problem of the impacts of short-duration rainfall
variability on hydrologic response in the small urbanized watershed. By coupling a high-resolution radar rainfall data set and stochastic storm
transposition (SST) with the GSSHA distributed physics-based model (see also
Wright et al., 2014a; Zhu et al., 2018), the relationships between rainfall spatiotemporal structure and urban flood response are examined. The main findings are as follows:
The flood frequency distributions for subwatersheds within the highly urbanized 14.3 km The spatial heterogeneity of flood frequency over the 14.3 km The relationship between the space–time structure of rainfall and flood response is complex. For smaller and more frequent rainfall events, flood peaks are more closely linked to the temporal features of rainfall (total rainfall and peak rainfall rate). For extreme storms, the maximum discharge is closely linked to the spatial structure of rainfall (storm core coverage). This finding is broadly consistent with Peleg et al. (2017) and Zhu et al. (2018), despite the very different drainage scales considered in those studies. There is no significant correlation between rainfall peak, total rainfall and flood peaks, implying an important role of surface properties in urbanized watersheds. Similar to Wright et al. (2014a), this comparison calls into question the conventional design storm assumption of a The spatial heterogeneity of rainfall is a key driver of flood response across scales. Relative to spatially uniform rainfall, spatially distributed rainfall can increase flood peaks by 50 % on average at the watershed outlet and its subwatersheds for both small and large return periods. This finding is broadly consistent with prior results at much larger scales in an agricultural setting (Zhu et al., 2018) and suggests both spatial and temporal rainfall distributions need to be considered in flood frequency analyses, even in relatively small urban watersheds. This study also implies that the drainage network substantially alters the impact of rainfall characteristics on runoff.
Coupling the GSSHA model and SST-based rainfall frequency analysis, this study provides an effective approach for regional flood frequency analysis
for urban watersheds. Some idealized assumptions used in conventional methods are questioned. The approach can be used to explore the dominant control on the upper tail of urban flood peaks, without many of the limiting assumptions associated with design storm methods. The study area could be extended in future work with larger basin scales and by manipulating the spatial heterogeneity of basin characteristics within GSSHA or other similar modeling systems.
Maps of mean storm total rainfall
Composite map of rainfall distribution for the 10-, 50-, 100- and 200-year return periods.
Correlation between space–time rainfall structure and flood responses at Franklintown under 10- and 200-year return periods.
The parameter tuning process of the RF model (using RMSE as an example).
Radar data are archived at Princeton University and can be downloaded from
The main contributions from each co-author are as follows. ZZ contributed to the computation and organization of the paper. JAS contributed to the supervision and writing. MLB is responsible for generating the radar rainfall data. BKS contributed to the construction of the initial hydrological model. DBW contributed to the writing of the paper. SL contributed to the supervision and writing.
The authors declare that they have no conflict of interest.
Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
The authors would like to thank the anonymous reviewers and editors for insightful comments and suggestions.
This research has been supported by the National Science Foundation of China (grant nos. 51909191 and 52111530045), the US National Science Foundation (grant no. CBET-1444758) and the China National Key R&D Program during the 13th Five-year Plan Period (grant no. 2018YFD1100401).
This paper was edited by Nadia Ursino and reviewed by two anonymous referees.