Use of Radar Quantitative Precipitation Estimates (QPEs) for Improved Hydrological Model Calibration and Flood Forecasting

Dayal Wijayarathne aSchool of Earth, Environment and Society, McMaster University, Hamilton, Ontario, Canada

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Paulin Coulibaly bDepartment of Civil Engineering, McMaster University, Hamilton, Ontario, Canada
aSchool of Earth, Environment and Society, McMaster University, Hamilton, Ontario, Canada

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Sudesh Boodoo cCloud Physics and Severe Weather Research Section, Environment and Climate Change Canada, King City, Ontario, Canada

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David Sills dDepartment of Civil and Environmental Engineering, University of Western Ontario, London, Ontario, Canada

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Abstract

Flood forecasting is essential to minimize the impacts and costs of floods, especially in urbanized watersheds. Radar rainfall estimates are becoming increasingly popular in flood forecasting because they provide the much-needed real-time spatially distributed precipitation information. The current study evaluates the use of radar quantitative precipitation estimates (QPEs) in hydrological model calibration for streamflow simulation and flood mapping in an urban setting. First, S-band and C-band radar QPEs were integrated into event-based hydrological models to improve the calibration of model parameters. Second, rain gauge and radar precipitation estimates’ performances were compared for hydrological modeling in an urban watershed to assess radar QPE’s effects on streamflow simulation accuracy. Third, flood extent maps were produced using coupled hydrological–hydraulic models integrated within the Hydrologic Engineering Center Real-Time Simulation (HEC-RTS) framework. It is shown that the bias correction of radar QPEs can enhance the hydrological model calibration. The radar–gauge merging obtained a Kling–Gupta efficiency, modified peak flow criterion, Nash–Sutcliffe efficiency, and volume error improvement of about +0.42, +0.12, +0.78, and −0.23, respectively, for S-band and +0.64, +0.36, +1.12, and −0.34, respectively, for C-band radar QPEs. Merged radar QPEs are also helpful in running hydrological models calibrated using gauge data. The HEC-RTS framework can be used to produce flood forecast maps using the bias-corrected radar QPEs. Therefore, radar rainfall estimates could be efficiently used to forecast floods in urbanized areas for effective flood management and mitigation. Canadian flood forecasting systems could be efficiently updated by integrating bias-corrected radar QPEs to simulate streamflow and produce flood inundation maps.

© 2021 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Dayal Wijayarathne, wijayard@mcmaster.ca

Abstract

Flood forecasting is essential to minimize the impacts and costs of floods, especially in urbanized watersheds. Radar rainfall estimates are becoming increasingly popular in flood forecasting because they provide the much-needed real-time spatially distributed precipitation information. The current study evaluates the use of radar quantitative precipitation estimates (QPEs) in hydrological model calibration for streamflow simulation and flood mapping in an urban setting. First, S-band and C-band radar QPEs were integrated into event-based hydrological models to improve the calibration of model parameters. Second, rain gauge and radar precipitation estimates’ performances were compared for hydrological modeling in an urban watershed to assess radar QPE’s effects on streamflow simulation accuracy. Third, flood extent maps were produced using coupled hydrological–hydraulic models integrated within the Hydrologic Engineering Center Real-Time Simulation (HEC-RTS) framework. It is shown that the bias correction of radar QPEs can enhance the hydrological model calibration. The radar–gauge merging obtained a Kling–Gupta efficiency, modified peak flow criterion, Nash–Sutcliffe efficiency, and volume error improvement of about +0.42, +0.12, +0.78, and −0.23, respectively, for S-band and +0.64, +0.36, +1.12, and −0.34, respectively, for C-band radar QPEs. Merged radar QPEs are also helpful in running hydrological models calibrated using gauge data. The HEC-RTS framework can be used to produce flood forecast maps using the bias-corrected radar QPEs. Therefore, radar rainfall estimates could be efficiently used to forecast floods in urbanized areas for effective flood management and mitigation. Canadian flood forecasting systems could be efficiently updated by integrating bias-corrected radar QPEs to simulate streamflow and produce flood inundation maps.

© 2021 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Dayal Wijayarathne, wijayard@mcmaster.ca

1. Introduction

Flooding is one of the most significant natural hazards, given its potential for lost lives and catastrophic socioeconomic impacts (Jonkman and Vrijling 2008; Jonkman and Kelman 2005). Over the past decade, the frequency of flooding has increased due to population growth and climate change worldwide (Zhang et al. 2018; Tol 2016; Pagano et al. 2014; Barredo 2009; Jonkman and Vrijling 2008). In Canada, floods are often mentioned as the most frequent natural hazard to life, property, economy, and the environment (Bowering et al. 2014). The estimated total cost of floods in Canada was almost 36 billion Canadian dollars from 1900 to 2016 (Public Safety Canada 2019). During the past few years, significant urban floods such as the flash flood of 8 July 2013 in Toronto (Sills et al. 2016; Boodoo et al. 2015) have increased the demand for flood mitigation measures in Canada to minimize the damage (Han and Coulibaly 2019).

Standard flood mitigation measures are divided into two main categories: structural and nonstructural measures (Thampapillai and Musgrave 1985). Structural measures mainly construct flood control structures that require a significant capital investment (Mays 2010). Nonstructural measures include flood forecasting. These measures are more effective and affordable alternatives to reducing the negative impacts of flooding (WMO 2006). A flood forecasting system that can deliver accurate and reliable forecasts with appropriate lead time is a critical part of nonstructural flood management (Unduche et al. 2018; Reed et al. 2007; Nagai 2003). According to the United Nations, flood damages can be reduced up to 35% if a flood is adequately forecast in advance (Pilon 2002). Various flood forecasting systems with varying complexities are being used worldwide to predict floods in advance. Community Hydrologic Prediction System (CHPS) in the United States, European Flood Forecasting System (EFFS) in Europe, National Flood Forecasting System (NFFS) in England, and Flood Early Warning System (FEWS) in Scotland (Ramos 2016; Cranston and Tavendale 2012; Roe et al. 2010; Werner et al. 2009; de Roo et al. 2003) are some of the examples. Hydrological and hydraulic models are critical parts of such flood forecasting systems (Teal and Allan 2017).

Hydrological and hydraulic modeling approaches were used to forecast river flows and flood extent over decades (Wijayarathne and Coulibaly 2020; Awol et al. 2019; Leach et al. 2018; Han and Coulibaly 2017; Che and Mays 2015; Arduino et al. 2005). These models represent different hydrological processes in the hydrologic cycle, such as precipitation, evapotranspiration, infiltration, interception, and runoff, using a set of model parameters. Hydrological models calculate streamflow using inputs such as precipitation, temperature, soil moisture, and topography (Devia et al. 2015). Hydraulic models that simulate flood extent and inundation levels in flood plain and surrounding areas use the hydrological models’ output (Aksoy et al. 2016). Among all meteorological inputs, precipitation is the primary forcing for hydrological models (Devia et al. 2015). Therefore, the efficiency of flood forecasting systems where hydrological and hydraulic models are embedded is mainly determined by the accuracy and reliability of precipitation inputs (Larson and Peck 1974).

Surface rainfall gauges or weather radar provide precipitation input for the hydrological models (Randall et al. 2014). Rain gauges are believed to be accurate instruments for precipitation point measurements even though they suffer from both random errors (e.g., poor gauge site conditions, human errors, inadequate network density, and exposure to prevailing winds) and systematic errors (e.g., wind-induced undercatch, wetting, and evaporation losses) (Rossa et al. 2011; Sevruk 1982). At present, the calibration of a hydrological model mainly relies on in situ rain gauge data (Moreno et al. 2012; McMillan et al. 2011). However, this approach often fails to adequately capture spatial and temporal variations (Dhiram and Wang 2016). Weather radar produces spatially and temporally continuous data over a large area, including regions with sparse gauge point observation networks (Thorndahl et al. 2017), and its use can help address this shortcoming.

With the worldwide development of radar infrastructure and data processing methods, the interest in real time, spatially distributed precipitation information derived from weather radar over conventional rainfall gauges is notable (Şensoy et al. 2016). The ability to capture the spatial variation of precipitation has contributed to radar playing an essential role in meteorological studies (Doviak 1993). However, radar quantitative precipitation estimates (QPEs) are known to be suffering from errors arising from the measurements and reflectivity–rain intensity conversion process (Dai et al. 2018). Attenuation, miscalibration, ground clutter, anomalous propagation, beam blockage, range degradation, the presence of a bright band, variations in precipitation drop size distribution, radome wetting, etc. can cause errors in reflectivity measurements and eventually radar QPEs (Boodoo et al. 2015; Germann et al. 2009; Borga et al. 2006; Meischner 2005; Borga 2002; Jordan et al. 2000). Therefore, it is not practically possible to obtain error-free radar QPEs when weather radar is used as a precipitation measurement tool.

The first appearance of radar QPEs as precipitation input to hydrological models was reported at the urban storm drainage conference in Sweden in 1984 (Thorndahl et al. 2017). The applications of weather radar from a hydrological perspective have developed considerably since then, especially with the advances in computer power and expansion of new hydrological models (Beneti et al. 2019; Khan et al. 2019; Ran et al. 2018; Thorndahl et al. 2017; Zappa et al. 2011; Meischner 2005). In Canada, research in weather radar began after the Second World War in 1943 under the project Stormy Weather (Sills and Joe 2019; Douglas 1990). Weather radars were subsequently used for various hydrological studies in the Canadian context (Wijayarathne et al. 2020a; Hassan et al. 2019; Sills and Joe 2019; Huang et al. 2010; Hudak et al. 2008, 2002; Brown et al. 2007; Chen and Farrar 2007; Germann and Zawadzki 2004; Germann and Zawadzki 2002; Bellon and Zawadzki 1994; Bellon and Austin 1984, 1978; Bellon et al. 1980; Barge et al. 1979). The main applications of weather radar in Canada include determining the type of precipitation, precipitation features, and structure, operational forecasting such as weather forecasts and snow depth predictions, operational weather warnings, and as a tool to validate atmospheric models (Sills and Joe 2019). However, the use of radar QPEs as an input to hydrological models is not a typical application in Canada, and previous studies were limited to the model University of Waterloo Flood Forecasting System (WATFLOOD) (Wijayarathne and Coulibaly 2020c). Therefore, the use of radar QPEs in operational flood forecasting is not yet implemented widely in Canada, and there are some challenges to overcome (McKee et al. 2018).

For flood forecasting in urban and semiurban watersheds where response time is in hours, radar QPEs with high temporal and spatial resolution are needed to calibrate and run hydrological models. Relatively small-sized urban and semiurban catchments with a high degree of imperviousness respond to rainfall relatively quickly and hence are very sensitive to the spatial and temporal variability of rainfall (Ochoa-Rodriguez et al. 2019; Villarini and Krajewski 2010). Therefore, hydrological models calibrated using selected events (e.g., severe or extreme weather spanning a few hours) are advantageous. Even though radar QPEs produce real-time, spatially, and temporally continuous precipitation data, the intrinsic errors associated with radar measurements and eventually radar QPEs are the main reason for the limited use of radar QPEs in operational flood forecasting (Wang et al. 2015). A significant improvement in radar QPEs was observed after the introduction of dual-polarization technology and prototype algorithms in Canada (Boodoo et al. 2015; Hall et al. 2015; Chandrasekar et al. 2013; Bringi et al. 2011; Sugier et al. 2006; Ryzhkov et al. 2005), with dual-polarized approaches producing more accurate radar QPEs than is possible with single-polarized radar. In addition to dual-polarization, a significant improvement to radar QPEs is possible via adjustment of values to match rain gauge observations (radar–gauge merging) (Wijayarathne et al. 2020b; Ochoa-Rodriguez et al. 2019; Falck et al. 2018; Wang et al. 2015; Goudenhoofdt and Delobbe 2009; Vieux and Bedient 2004). Radar–gauge merging combines the advantages of both gauge and radar QPEs while minimizing their weaknesses to produce accurate and reliable radar QPEs (McKee and Binns 2016). With the invention of methods to retrieve, compute, view, bias-correct, and manage radar QPEs, it is possible to implement Flood Early Warning Systems (FEWS) to issue real-time flood forecasts for operational use (Andres et al. 2016). For that reason, radar QPEs should go through careful selection, a comprehensive evaluation, and corrections where necessary before using them as precipitation forcing for the hydrological model in operational flood forecasting. Further research is essential to fill these niche areas before using radar QPEs for operational flood forecasting in urban and semiurban watersheds with confidence.

The current study involves implementing a flood forecasting framework that allows connecting hydrological and hydraulic models in one platform using both rain gauge and weather radar QPEs derived from U.S. and Canadian weather radar to assess the benefit of radar QPEs in flood forecasting. First, the impact of radar–gauge merging on radar QPE accuracy and reliability, and eventually, streamflow simulations were examined. Then, the use of radar QPEs to improve hydrological model parameters’ calibration was tested by integrating weather radar QPEs to event-based hydrological models focusing on flood forecasting. An intercomparison of rain gauge and radar QPE performance for hydrological modeling in an urban watershed was performed to assess the effects of various precipitation forcing on streamflow simulation accuracy. Hydrological and hydraulic models were integrated within one framework to generate flood inundation maps to examine the impact of radar QPEs on flood forecasting potential in an urban setting.

2. Study area

The Mimico Creek watershed used in this study (Fig. 1) is a part of the Great Lakes basin and lies between the Humber River and Etobicoke Creek watersheds (TRCA 2020c). It is currently managed by the Toronto and Region Conservation Authority (TRCA). The Mimico Creek starts at Brampton and flows through Mississauga and Toronto in the Greater Toronto Area (GTA) of Ontario, Canada (Natural Resources Canada 2016). It flows about 33 km through urban neighborhoods and discharges into Lake Ontario. More than 60% of the creek is artificially channelized, leading to rapid urban stormwater runoff, sometimes resulting in flooding (TRCA 2020c). The watershed covers 77 km2 and is home to over 100 000 people (TRCA 2020a). It is heavily urbanized, with approximately 90% urban area and 10% natural cover (Fig. 1) (Ontario GeoHub 2020). Predominant soil types are poorly drained clays and clay loams (TRCA 2009). The combination of impervious urban areas with poorly drained clay soil makes the watershed particularly susceptible to flooding. Further details on the Mimico Creek watershed can be found on the TRCA Watershed Features Etobicoke and Mimico website (TRCA 2020a). The watershed has excellent coverage from both Canadian King City (WKR) C-band radar and U.S. Buffalo, New York, (KBUF) Next Generation Weather Radar (NEXRAD) S-band radar (Fig. 1).

Fig. 1.
Fig. 1.

Mimico Creek watershed in GTA, and coverages of the Canadian WKR and U.S. KBUF NEXRAD sites.

Citation: Journal of Hydrometeorology 22, 8; 10.1175/JHM-D-20-0267.1

3. Data/hydrological and hydraulic models

a. Hydrometeorological and hydrometric data

Subhourly (5–15 min) rainfall accumulations and temperature reported at fourteen hydrometeorological stations from 2013 to 2018 were gathered from TRCA data archives. All TRCA rain gauges are located within the Doppler range (<180 km) of the KBUF NEXRAD S-band radar and the dual-polarized Doppler range (<120 km) of the WKR C-band radar station (Fig. 1). It is assumed that TRCA rain gauges characterize the precipitation distribution over the entire watershed. This assumption is valid due to the relatively small size of the watershed and relatively high rain gauge density of one gauge per ~75 km2 (Wijayarathne et al. 2020b). Subhourly (5–15 min) streamflow data from 2013 to 2018 recorded by the Water Survey of Canada (compiled at https://wateroffice.ec.gc.ca/search/historical_e.html) were collected from a long-term flow gauge named “Islington” (identifier: 02HC033) (Fig. 1). Both precipitation and streamflow data were aggregated to obtain a 15-min rainfall time series for analysis.

b. Radar QPEs

1) King City (WKR) C-band radar QPEs

The WKR C-band radar station has a conventional reflectivity measurement range of 256 km and a dual-polarization Doppler range of 120 km (Fig. 1). Radar reflectivity data, gathered from Environment and Climate Change Canada (ECCC) archives, include dual-polarization Polarimetric Plan Position Indicator (POLPPI) scans in 10-min cycles at the lowest (0.5°) elevation (Boodoo et al. 2015). The data resolution is 0.25 km by 0.5° in azimuth (Wijayarathne et al. 2020a). The modified “ZPHI” algorithm was used to correct reflectivity values for attenuation (Ryzhkov et al. 2007). The radar estimated precipitation value at the radar grid point nearest to the gauge location was extracted. Wijayarathne et al. (2020a) evaluated the performance of WKR C-band radar QPEs derived using seven reflectivity–rain rate (ZR) relationships to verify the reliability and accuracy for operational use in the GTA and reported the best performance from the relationship R=aKDPb10cZDR. Therefore, in this study, the rainfall rate was calculated for a specific differential phase–differential reflectivity (KDPZDR) rate relationship R=aKDPb10cZDR, where a = 37.9, b = 0.89, and c = −0.072 (Bringi and Chandrasekar 2001). This is applied only if KDP values are greater than 0.1° km−1; otherwise, RZ is used; that is Z = 200R1.6 (Marshall and Palmer 1948). Therefore, in effect, the rates are derived as a composite of these two relationships. To be consistent with the gauge and streamflow data, the 10-min rainfall accumulations were resampled using time interpolation to derive 15-min rainfall accumulations using Hydrologic Engineering Center Data Storage System Visual Utility Engine (HEC-DSSVue).

2) Buffalo (KBUF) NEXRAD S-band radar QPEs

Level III NEXRAD S-band radar QPEs from the KBUF NEXRAD station were downloaded from the archives of the National Centers for Environmental Information (NCEI) (NOAA 2018). The radar QPEs were derived using the Precipitation Processing System (PPS) algorithm R = 0.017Z0.714 (Fulton et al. 1998), and reflectivity values were collected every 5–10 min with resolution 0.25 km in range and 0.5° in azimuth. The Digital Precipitation Array (DPA) QPE accumulation on the 4.7625-km Hydrologic Rainfall Analysis Projection (HRAP) grid was selected for the analysis after a NEXRAD QPE evaluation for GTA watersheds by Wijayarathne et al. (2020a). National Oceanic and Atmospheric Administration (NOAA) Weather and Climate Toolkit (WCT), ArcGIS 10.6.1, MATLAB, and Python scripts were used for further processing of NEXRAD QPEs (Wijayarathne et al. 2020a; Guzman et al. 2013). The first previously recorded value at each 15-min interval was extracted, and rain rates were assumed to be constant across the time of interest.

c. Hydrological and hydraulic models

1) Hydrologic Engineering Center’s Hydrologic Modeling System (HEC-HMS)

The HEC-HMS hydrological model was developed by the Hydrologic Engineering Center of the U.S. Army Corps of Engineers to simulate both continuous and event-based hydrological processes in a dendritic watershed in both space and time (Darbandsari and Coulibaly 2020; Wijayarathne and Coulibaly 2020). It allows users to select from a list of methods that can model different runoff generation components (i.e., rainfall loss, direct runoff, river routing, base flow, and routing processes) (Cunderlik and Simonovic 2004). Precipitation, temperature, and calibrated parameters are the primary input to the HEC-HMS model. For further details on the HEC-HMS model, readers are referred to the HEC-HMS user manual (U.S. Army Corps of Engineers 2020a). In this study, the HEC-HMS, version 4.2.1, model implemented for the Mimico Creek watershed by TRCA (Zahmatkesh et al. 2021) was used. For urban subbasins, the model used the Soil Conservation Service (SCS) curve number and SCS Unit Hydrograph as the loss and transform methods, respectively. Clark Unit Hydrograph method was used as the transform method for subbasins with natural cover (Zahmatkesh et al. 2021). The other parameters such as Manning’s n, curve number, imperviousness, and lag time were considered unspecified to determine during model calibration. To represent prevailing stormwater management facilities, reservoir routing components were also added to the HEC-HMS model (Zahmatkesh et al. 2021). Detention basin routing was performed using the “outflow curve” method. Storage-discharge curves were drawn to express the response of the reservoir to the flood wave. The initial condition of the reservoir was set as “inflow = outflow” of the reservoir.

2) Hydrologic Engineering Center’s River Analysis System (HEC-RAS)

The HEC-RAS hydraulic model was developed by the Hydrologic Engineering Center of the U.S. Army Corps of Engineers to simulate both one- and two-dimensional and combined one-/two-dimensional flow in open channels and floodplains (Ezz 2018; Hicks and Peacock 2005). The model can produce flood extent and water levels using resulting peak flows from hydrological models (Hashemyan et al. 2015). The RAS Mapper portion of the HEC-RAS software performs flood inundation mapping for flood forecasting applications (Brunner et al. 2015). Further details on the HEC-RAS model can be found in the HEC-RAS user manual (U.S. Army Corps of Engineers 2020b). For this study, the HEC-RAS model developed for the Mimico Creek watershed by TRCA was used (Zahmatkesh et al. 2021).

3) Hydrologic Engineering Center’s Real-Time Simulation (HEC-RTS)

The HEC-RTS is a framework that assimilates different HEC products making it possible to develop a flood forecasting system by integrating HEC models in one platform (U.S. Army Corps of Engineers 2020c). HEC-RTS connects the hydrological model HEC-HMS with the hydraulic model HEC-RAS and HEC-RAS mapper to generate flood inundation maps (Charley et al. 2012). Rainfall–runoff processes for a selected watershed are simulated using the HEC-HMS model component. One and two-dimensional, steady, and unsteady flow routing in streams are executed using the HEC-RAS model component. RAS mapper component of the HEC-RTS framework generates flood inundation maps using peak flows from HEC-HMS. Therefore, HEC-RTS can support operational flood forecasting by combining hydrological and hydraulic models in one common framework (Vyas and John 2016). For further details on the HEC-RTS model, readers are referred to the HEC-RTS user manual (U.S. Army Corps of Engineers 2020c).

4. Methods

a. Hydrological model calibration and validation

1) Selection of precipitation events

Since this study focuses on flood forecasting in a fully urbanized catchment, it has been decided to calibrate and validate the hydrological model to simulate extreme events (Awol 2020). Therefore, an event-based model calibration approach was used to calibrate the hydrological model (Awol et al. 2018). Given that the time of concentration of the watershed is relatively low (~4 h), 15-min time steps were used for hydrological simulations (Fang et al. 2008). Consistent with previous storm events reported in the GTA with the potential for flooding, events with rainfall accumulation > 20 mm were considered during the event selection (TRCA 2020b). Other criteria such as precipitation intensity, percent detection, availability of radar and gauge precipitation, missing value percentage, and sufficient discharge at the watershed outlet were also considered during event selection (Wijayarathne et al. 2020a,b). Because ZR relationships for WKR C-band radar QPEs do not account for bright band contamination, precipitation during the winter season was excluded from the study (Wijayarathne et al. 2020a; Boodoo et al. 2015). Consequently, eighteen precipitation events that occurred during spring, summer, and autumn periods from 2013 to 2018 were screened to select significant storm events with the potential of flooding to perform calibration and validation of hydrological models and stormwater runoff simulation (Table 1).

Table 1.

Description of events. Italics indicate –calibration events, and boldface font indicates validation events.

Table 1.

2) Bias correction of radar QPEs

First, radar estimated precipitation data were bias-corrected using the cumulative distribution function matching (CDFM) radar–gauge merging method to increase accuracy and reliability before using them as precipitation input to hydrological and hydraulic models. The CDFM method uses polynomial fitting to match the CDF of radar rainfall (cdfR) to a reference gauge dataset (cdfG) (Kornelsen and Coulibaly 2015; Drusch et al. 2005). The CDF of the nearest grid point for WKR QPEs and radar pixel where the gauge is located for NEXRAD QPEs were rescaled so that the CDFs of both radar and gauge data match. As suggested by Wijayarathne et al. (2020a), a third-degree polynomial model was employed in this study [Eq. (1)]. These polynomials can be applied to other datasets to employ a comparable bias correction (Leach et al. 2018).
Rcor=P1S3+P2S2+P3S+P4,
where Rcor is adjusted radar QPE, P1P4 are coefficients of the polynomial models, and S is raw radar QPE.
The impact of radar–gauge merging on the accuracy and reliability of radar QPEs was assessed by comparing the nearest gauge point for WKR QPEs and radar pixel where the gauge is located for NEXRAD QPEs (Wijayarathne et al. 2020a). The correlation coefficient r [Eq. (2)] (value of 1 for a perfect fit) and root-mean-square error [RMSE (mm); Eq. (3)] (value of 0 for a perfect fit) were calculated between radar–gauge pairs for each event:
r=(PGP¯G)(PRP¯R)(PGP¯G)2(PRP¯R)2and
RMSE=i=1n(PGPR)2n,
where PG is gauge measurement, P¯G is average gauge measurement, PR is radar rainfall, P¯R is average radar rainfall, and n is number of radar–gauge pairs.
Second, to further assess the impact of radar–gauge merging on the accuracy and reliability of radar QPEs, a proxy validation was performed using HEC-HMS hydrological model from TRCA (McKee et al. 2018). The previously calibrated model parameters determined using gauge data were employed during the model run (Chu and Steinman 2009). Precipitation input to the HEC-HMS model was modified according to five different scenarios: (i) gauge data (G-G); (ii) WKR C-band radar QPEs (G-C); (iii) WKR C-band radar QPEs bias-corrected with CDFM (G-C-B); (iv) NEXRAD S-band radar QPEs (G-N); and (v) NEXRAD S-band radar QPEs bias-corrected with CDFM (G-N-B). The agreement between observed and simulated streamflow was evaluated by calculating the correlation coefficient rm [Eq. (4)], root-mean-square error [RMSEm (m3 s−1); Eq. (5)], percent bias [PBIAS; Eq. (6)], mean absolute error [MAE (m3 s−1); Eq. (7)], Kling–Gupta efficiency [KGE; Eq. (8)] (Gupta et al. 2009), Nash–Sutcliffe efficiency [NSE; Eq. (9)] (Nash and Sutcliffe 1970), volume error [VE; Eq. (10)] (Razavi and Coulibaly 2017), and modified peak flow criterion [MPFC; Eq. (11)] (Coulibaly et al. 2001). The optimal value of PBIAS is 0. Positive values indicate model overestimation, whereas negative values show model underestimation (Wijayarathne and Coulibaly 2020). MAE values range from 0 to ∞ where lower values indicate better performances (Willmott and Matsuura 2005). KGE value ranges between −∞ and 1, with one indicating a perfect fit (Gupta et al. 2009). NSE values spanning between −∞ and 1, with 1 being the optimal value. Values between 0 and 1 are considered acceptable (Moriasi et al. 2007; Nash and Sutcliffe 1970). The value of VE ranges from 0 to ∞, and better performances show values close to 0 (Samuel et al. 2011). MPFC focuses on peak flows, and a value of 1 reveals a perfect fit (Coulibaly et al. 2001). The formulas are as follows:
rm=i=1n(QiQ¯)(Qi^Q^¯)i=1n(QiQ¯)2i=1n(Qi^Q^¯)2,
RMSEm=i=1n(Qi^Qi)2n,
PBIAS=[i=1n(Qi^Qi)i=1n(Qi)×100%],
MAE=i=1n|Qi^Qi|n,
KGE=1(r1)2+(α1)2+(β1)2,
NSE=1i=1n(Qi^Qi)2i=1n(QiQ¯)2,
VE=i=1nQi^i=1nQii=1nQi,and
MPFC=1[i=1np(QpiQ^pi)2Qpi2]1/4(i=1npQpi2)1/2,
where Qi is observed flow at the ith data point, Q¯ is mean observed flow, Qi^ is simulated flow at the ith data point, Q^¯ is mean simulated flow, n is the number of data points, np is the number of peak flows that are greater than 75 percentiles of observed flow, Qpi is observed peak flows, Q^pi is simulated peak flows, r is linear correlation coefficient, α is a measure of relative variability, β is bias (ratio between the mean simulated and mean observed values), NSElog is NSE calculated using the logarithmic streamflow values (for low flows), and NSEsqr is NSE found using the squared streamflow values (for high flows).

3) Model recalibration and validation

In the hydrological model run analysis above, the existing HEC-HMS model from TRCA was used to evaluate the impact of radar–gauge merging on streamflow simulation. It is worth noting that the model’s calibrated parameters were determined using historical gauge data, and therefore, the performances can be biased toward gauge data. To address this issue, HEC-HMS hydrological model was recalibrated using both WKR C-band radar QPEs and KBUF S-band radar QPEs to evaluate the effects of different radar QPEs on hydrological model calibration and streamflow simulation. The following scenarios listed in Table 2 were considered during the recalibration. Scenarios 1–5 used gauge data, radar-only QPEs, and merged radar QPEs during calibration and validation. Flood forecasting systems usually encompass hydrological models calibrated and validated using historical gauge data. To examine the advantage of using bias-corrected radar QPEs to run the hydrological models with optimum parameters obtained using gauge data, two additional scenarios (scenarios 6 and 7) were also considered in the study.

Table 2.

HEC-HMS model run scenarios during recalibration and validation.

Table 2.

The HEC-HMS model was recalibrated against observed 15-min steam flow recorded at the Islington flow gauge downstream. Two-thirds of the number of selected events (12) were assigned for model calibration, and the remaining events (6) were used for validation purposes (Table 1). First, historical precipitation events and their corresponding hydrographs at the outlet of the watershed were identified. The HEC-HMS model was calibrated using the rainfall hyetographs corresponding to the events as the input until the observed hydrograph matches the simulated flow at the outlet for each calibration event. Four hydrological model parameters and their ranges (low and upper limits) were used during the calibration: 1) imperviousness (5%–50%), 2) curve number (30–90), 3) lag time (10–80 min), and 4) Manning coefficient (0.01–0.09) (Zahmatkesh et al. 2021). Based on the number of subbasins (70) and channels/reaches (34) in the watershed, a total of 240 parameters were chosen to be optimized via calibration of the HEC-HMS model (Zahmatkesh et al. 2021). The dynamically dimensioned search (DDS) optimization algorithm (Tolson and Shoemaker 2008) was used to determine optimal parameter sets for each calibration event by maximizing the NSE objective function for 1000 generations (Samuel et al. 2011) within Optimization Software Toolkit (OSTRICH) (Matott 2017). The HEC-HMS model was linked to the OSTRICH framework using MATLAB as the model interface. The DDS single objective optimization algorithm is designed to facilitate model calibration with many parameters and scales the search domain, searching for the optimum solution (Tolson and Shoemaker 2008). OSTRICH is a windows-based program that can be used to automate the model calibration without any other supplementary software (Matott 2017). OSTRICH at present supports 36 optimization and calibration algorithms, including DDS. Several scripts were written using MATLAB, Python, and batch files to define the calibration method (DDS), parameter names, initial values, and minimum and maximum amounts (range). The optimized set of model parameters for each calibration event that are correspond to the highest value of objective function (NSE) were obtained. An average value of the parameters resulting after calibration for each event was calculated and used as the calibrated parameter list. Finally, the performances of calibrated model parameters were verified using selected validation events. Model performances were evaluated based on standard model performance statistics during each calibration and validation scenarios, as mentioned above.

b. Flood inundation mapping

This part of the research involved setting up the HEC-RTS platform for the Mimico Creek watershed using both radar QPEs and gauges to assess the benefit of radar-derived rainfall for flood forecasting. First, existing hydrological (HEC-HMS) and hydraulic (HEC-RAS) models were integrated into the HEC-RTS framework using the setup module in HEC-RTS. Hydrometeorological data were transferred from an ArcHydro geo-database time series to Hydrologic Engineering Center Data Storage System (HEC-DSS) software and eventually to HEC-HMS as hydrometeorological inputs. HEC-RTS links HEC-HMS and HEC-RAS, and therefore each model is executed in a coordinated manner. Simulated streamflow from HEC-HMS hydrological model was inputted to HEC-RAS using DSS data exchange software to produce flood inundation maps. Flood inundation depths and extent boundaries were generated through the RAS mapper component of HEC-RAS within the HEC-RTS framework. The HEC-RTS framework was used to produce flood inundation maps that correspond to the seven model run scenarios listed in Table 2 for the 8 July 2013 flash flood event in Toronto. Precipitation input from gauges (G-G), radar-only QPEs (C-C and N-N), and merged radar QPEs (C-C-B, N-N-B, G-C-B, and G-N-B) along with calibrated model parameters from the seven calibration scenarios were used to generate flood inundation maps. The flood extent was mapped using peak flows recorded at each junction of Mimico Creek. A proxy validation of the flood map was performed using the water levels/ depths recorded at the Islington flow gauge during the 8 July 2013 flash flood event. The correlation coefficient rD [Eq. (12)] and root-mean-square error RMSED (m) [Eq. (13)] were calculated between observed water depths and simulated water depths:
rD=(DOD¯O)(DSD¯S)(DOD¯O)2(DSD¯S)2and
RMSED=i=1n(DSDO)2n,
where DO is observed water depth, D¯O is average observed water depth, DS is simulated water depth, D¯S is average simulated water depth, and n is number of observations.
The probability of flooding for each cell on the inundation maps was calculated and flood probability maps were prepared using ArcGIS. The flood extent and inundation levels generated using gauge data as precipitation input to HEC-RTS were considered the reference (observed flood extent) to validate the flood maps. First, the accuracy A [Eq. (14)] of the flood extent was calculated for each radar QPE as the hydrological model input:
A=simulated areaobserved area×100%.
Also, several contingency statistics were calculated by pixel-to-pixel comparison using ArcGIS. The contingency statistics explain whether simulations hit, miss, or lead to false estimates relative to observations (AghaKouchak and Mehran 2013). The probability of detection (POD) corresponds to the fraction of the reference observations identified accurately by the simulations [Eq. (15)] (AghaKouchak and Mehran 2013). The POD varies from 0 to 1; the value of 1 indicates a perfect score, and 0 is for no skill (Everitt 1992). Since contingency statistics do not provide any information on the inundation levels, the rD [Eq. (12)] and RMSED [Eq. (13)] were calculated between inundation levels simulated using gauge and corresponding radar QPEs for detected pixel pairs to compare flood depths. The false-alarm ratio (FAR) describes the fraction of the simulations that are not confirmed by reference observations [Eq. (16)] (AghaKouchak and Mehran 2013). The FAR ranges from 0 to 1; the value of 0 is optimal (Everitt 1992). The critical success index (CSI) combines POD and FAR to provide the overall skill of the simulation with regard to observations [Eq. (17)] (AghaKouchak and Mehran 2013). The value of CSI ranges from 0 to 1, with 1 being the optimal value and 0 for no skill (Schaefer 1990). The formulas are as follows:
POD=H(H+M),
FAR=F(H+F),and
CSI=H(H+M+F),
where H is hit, both reference and simulation detect the flood; M is miss, flood identified by reference but missed by simulation; and F is false, flood area identified by simulation but not observed by reference.

5. Results and discussion

a. Bias-correction of radar QPEs

The correlation r improved for both WKR C-band (+0.44) and KBUF S-band (+0.53) radar QPEs after applying radar–gauge merging (Table 3). The RMSE decreased for both WKR C-band (−4.42) and KBUF S-band radar (−1.33) QPEs after adjusting radar QPEs to match gauge observations. Overall, the accuracy and reliability of both WKR C-band and KBUF S–band radar QPEs improved after applying the CDFM radar–gauge merging method. The random component of the error causes the existing mismatch (Wijayarathne et al. 2020b).

Table 3.

Evaluation results for radar QPEs before and after radar–gauge merging.

Table 3.

A comparison of hydrological model performance statistics of the streamflow simulation at Islington hydrometric station using gauge measurements (G-G), radar-only QPEs (G-C and G-N), and merged radar QPEs (G-C-B and G-N-B) as precipitation input is presented in Figs. 2 and 3 . Overall, the figures show that the radar–gauge merging has a considerable effect on simulated stream flows’ accuracy. According to the previous literature, the uncertainty in the precipitation forcing is the most problematic in hydrological modeling (Her et al. 2019). Since the optimal model parameters in the existing HEC-HMS model were determined using gauge data during its calibration, the model performance statistics calculated between observed and simulated flow using the gauge as precipitation input (G-G) were used as the reference during evaluation.

Fig. 2.
Fig. 2.

Model performance between observed and simulated streamflow using gauges (G-G), radar-only QPEs (G-C and G-N), and merged radar QPEs (G-C-B and G-N-B): (a) correlation coefficient r, (b) root-mean-square error (RMSE), (c) percent bias (PBIAS, here labeled BIAS), and (d) mean absolute error (MAE). (Note: cms = m3 s−1).

Citation: Journal of Hydrometeorology 22, 8; 10.1175/JHM-D-20-0267.1

Fig. 3.
Fig. 3.

Boxplots showing model performance criteria for radar QPEs before (G-C and G-N) and after (G-C-B and G-N-B) radar–gauge merging: (a) Nash–Sutcliffe efficiency (NSE), (b) Kling–Gupta efficiency (KGE), (c) volume error (VE), and (d) modified peak flow criterion (MPFC).

Citation: Journal of Hydrometeorology 22, 8; 10.1175/JHM-D-20-0267.1

Figure 2 shows the average correlation r, RMSE (m3 s−1), PBIAS (%), and MAE (m3 s−1) between observed and simulated streamflow using gauges, radar-only QPEs, and merged radar QPEs as precipitation input to the HEC-HMS model. The streamflow simulations using gauge data appeared to perform best with relatively higher prediction accuracy than radar QPEs (0.91, 5.41 m3 s−1, 20.81%, and 4.04 m3 s−1 for r, RMSE, PBIAS, and MAE, respectively). The intrinsic errors associated with reflectivity measurement and reflectivity– rain intensity conversions cause errors in radar QPEs (Dai et al. 2018). Errors can be induced to the radar estimated precipitation by radome wetting, beam filling, partial beam blocking, radar miscalibration, vertical air motion, evaporation, advection, attenuation, ground clutter, and variability of the drop size distribution (Wijayarathne et al. 2020a; Seo et al. 2015). These biases can propagate through the hydrological model leading to uncertainties in streamflow simulations (Germann et al. 2009; Fornasiero et al. 2005). However, the model performance could be influenced by the gauge data as the model was calibrated using gauge data.

Overall, the model performances were improved using merged radar QPEs relative to that of radar-only QPEs for both WKR C-band and KBUF S-band radar QPEs (Fig. 2). The agreement between observed and simulated streamflow using WKR C-band radar QPEs is relatively low in comparison with the KBUF S-band radar QPEs, according to RMSE, MAE, and PBIAS (Fig. 2). However, the correlation is relatively higher for WKR C-band radar QPEs. Results suggest that both WKR C-band and NEXRAD S-band radar QPEs were improved after the application of radar–gauge merging. Bias correction using radar–gauge merging obtained r, RMSE, PBIAS, and MAE improvements of about +0.22, −8.08 m3 s−1, −47.44%, and −5.28 m3 s−1, respectively for WKR C-band radar QPEs. For NEXRAD S-band radar QPEs, improvement of about +0.28, −3.93 m3 s−1, −33.45%, and −3.34 m3 s−1 were reported for r, RMSE, PBIAS, and MAE, respectively. Interestingly, the C-band radar QPEs overestimated the streamflow both before and after radar–gauge merging while S-band QPEs underestimated the streamflow. In general, radar-only QPEs are known to underestimate precipitation, especially during heavy precipitation events (Smith et al. 2007; Duchon and Essenberg 2001). The significant ground clutter caused by highly developed infrastructure in the fully urbanized Mimico Creek watershed strongly contaminates and inflates the reflectivity values leading to higher radar reflectivity values and consequently QPEs (Torres and Warde 2014). Since C-band radar attenuates more than S-band radar owing to its shorter wavelength, the WKR radar is expected to underestimate precipitation, especially in heavy rain events (Boodoo et al. 2015). The Mimico Creek watershed is located much closer to the WKR radar station (<40-km radius, Fig. 1), and hence detects precipitation closest to the ground and hence the gauge location. Even though path attenuation was addressed during the study, the attenuation correction could be dominated by the extensive ground clutter at WKR, leading to higher reflectivity values and subsequently overestimated stream flows. Also, the season of the year where the precipitation event was recorded can influence the radar QPEs (Prat and Nelson 2015). The brightband contamination could produce significantly high reflectivity values, causing overestimating QPEs especially during early spring and late fall. In contrast to the WKR radar, the KBUF radar detects precipitation over the study area at a distance of more than 100 km away from the radar station. This distance results in rainfall detection at a higher elevation leading to underestimated precipitation (Young and Brunsell 2008).

Figure 3 presents the boxplots of four model efficiency indices for the 18 selected events: NSE, KGE, VE, and MPFC. In comparison with radar-only QPEs, WKR C-band merged-radar QPEs provide more accurate simulated streamflow for all rainfall events (NSE: +1.12, KGE: +0.64, VE: −0.34, and MPFC: +0.36). The NEXRAD radar QPEs also improved model performance considerably relative to radar-only QPEs (NSE: +0.78, KGE: +0.42, VE: −0.23, and MPFC: +0.12). The intrinsic errors associated with radar produce relatively poor radar QPEs leading to less accurate streamflow simulations than with merged-radar QPEs. The medians of the performance indices for both WKR C-band and KBUF S-band radar remained much closer to the medians of the reference gauge and sometimes even within the interquartile range (IQR) after applying the bias correction. The first quartile, median, and third quartile of performance indices calculated for simulated streamflow using both WKR and KBUF radar were the same as gauges after radar–gauge merging as compared with the radar-only QPEs. Also, IQRs of performance indices were reduced after the bias correction of radar QPEs, implying that radar–gauge merging helps enhance predicted streamflow accuracy.

b. Model calibration and validation

Figure 4 presents the average event-based model performance statistics for the streamflow simulation at the Islington flow station downstream of Mimico Creek watershed during the calibration period. The performance matrices calculated between observed and simulated flow using a model calibrated with gauge data (G-G) were used to reference radar QPE performance evaluation. The calculated correlation values varied depending on the event and were relatively higher for all calibration scenarios that involved merged radar QPEs (C-C-B: 0.48–0.95; N-N-B: 0.47–0.96) when compared with scenarios with radar-only QPEs (C-C: 0.03–0.96; N-N: 0.25–0.98). Therefore, in comparison with models calibrated with radar-only QPEs for both WKR C-band and KBUF S-band, models calibrated with merged radar QPEs provided reasonably accurate simulated stream flows. As shown in Fig. 4, RMSE values also varied considerably between both different events and calibration scenarios. Similar to correlation, calibration scenarios involving merged radar QPEs (C-C-B and N-N-B) showed better performances than scenarios with radar-only QPEs (C-C and N-N). The corresponding RMSE values were relatively low and nearly similar for models calibrated using merged radar QPEs (4.39–33.82 m3 s−1 and 5.43–22.08 m3 s−1 for C-C-B and N-N-B, respectively) than the models calibrated with radar-only QPEs (7.35–45.39 m3 s−1and 7.96–33.51 m3 s−1 for C-C and N-N, respectively). The MAE followed the same trend as RMSE with relatively lower values for calibration scenarios with merged radar QPEs (C-C-B: 3.13–22.78 m3 s−1; N-N-B: 3.93–22.06 m3 s−1) and relatively raised errors for scenarios using radar-only QPEs (C-C: 5.60–46.50 m3 s−1; N-N: 6.20–55.71 m3 s−1). Consistent with the correlation, hydrological models calibrated with bias-corrected radar QPEs (C-C-B and N-N-B) performed better than models calibrated with radar-only QPEs (C-C and N-N) concerning error measurements. The average negative and positive bias percentages estimated for scenarios with radar-only QPEs were significantly reduced using the merged radar QPEs for both WKR C-band and KBUF S-band radar during calibration. Hydrological models calibrated with bias-corrected radar QPEs produced results with relatively low bias values (from −40.27% to 141.36% and from −62.82% to 42.05% for C-C-B and N-N-B, respectively) in comparison with results from the models calibrated with radar-only QPEs (2.62%–173.00% and from −66.76% to 122.81% for C-C and N-N, respectively; Fig. 4). Calculated hydrological model performance indices, KGE, NSE, VE, and MPFC, also supported that radar–gauge merging improves the accuracy and reliability of radar QPEs and subsequently calibration of hydrological models. The KGE values were relatively better for models calibrated using merged radar QPEs (C-C-B: from −0.35 to 0.82; N-N-B: from −0.26 to 0.67) in comparison with models calibrated with radar-only QPEs (C-C: from −2.08 to 0.41; N-N: from −2.63 to 0.45). The NSE followed KRE with values range from −2.08 to 0.73, from −1.32 to 0.66, from −22.30 to 0.04, and from −12.37 to 0.24 for C-C-B, N-N-B, C-C, and N-N, respectively, revealing better performance for merged radar QPEs. Reported volume errors also supported the notion that models calibrated with merged radar QPEs perform better than models calibrated with radar-only QPEs with reported VE values of 0.03–0.76, 0.03–0.67, 0.04–1.72, and 0.06–1.71 for C-C-B, N-N-B, C-C, and N-N, respectively. The MPFC values were better for calibrated models with bias-corrected radar QPEs (C-C-B: 0.26–0.72; N-N-B: 0.04–0.69) relative to the models calibrated with radar-only QPEs (C-C: 0.01–0.27; N-N: 0–0.64).

Fig. 4.
Fig. 4.

Average r, RMSE (m3 s−1), PBIAS (%; here labeled BIAS), MAE (m3 s−1), KGE, NSE, VE, and MPFC between observed and simulated streamflow at Islington flow station downstream of Mimico Creek watershed during calibration. (Note: cms = m3 s−1).

Citation: Journal of Hydrometeorology 22, 8; 10.1175/JHM-D-20-0267.1

Figure 5 compares the boxplots of observed and simulated streamflow at Islington flow station downstream of Mimico Creek watershed using gauge data, radar-only QPEs, and merged radar QPEs for seven model run scenarios listed in Table 2 during validation. The median and IQR of simulated flows using gauge data as the precipitation input to the hydrological model calibrated with gauge data (G-G) matched the observed flow relatively well as compared with the radar QPEs. On the contrary, hydrological models calibrated and validated with radar-only QPEs (C-C and N-N) showed the least match with the observed streamflow. The inherent errors associated with radar QPEs during data acquisition and processing can cause errors leading to less accurate radar QPEs and subsequently erroneous simulated stream flows. However, hydrological models calibrated and validated with KBUF S-band radar-only QPEs performed better than the models calibrated with WKR C-band radar-only QPEs. The anomalously high reflectivity values resulted from ground clutter, and bright band contamination during spring and fall might have resulted in overestimated QPEs leading to less accurate streamflow simulations. Even though the hydrological model calibrated with radar-only QPEs showed relatively low performances, the agreement between observed and simulated streamflow increased after applying radar–gauge merging. In comparison with radar-only QPEs scenarios (C-C and N-N), hydrological models calibrated with merged radar QPEs (C-C-B and N-N-B) provided considerably accurate simulated streamflow for all events. Surprisingly, when hydrological models were calibrated with gauge data and then run with bias-corrected radar QPEs (G-C-B and G-N-B), similar or better performance was observed than the models calibrated with merged radar QPEs (C-C-B and N-N-B). The medians of simulated streamflow for both G-C-B and G-N-B calibration scenarios remained much closer to the medians of the observed and G-G and most of the time within the IQR of observed streamflow. The overall performance of model run scenarios varies from best performance to worst as G-G > G-C-B ≅ G-N-B > C-C-B ≅ N-N-B > C-C ≅ N-N.

Fig. 5.
Fig. 5.

Boxplots of observed and simulated streamflow for model run scenarios during validation.

Citation: Journal of Hydrometeorology 22, 8; 10.1175/JHM-D-20-0267.1

Figure 6 visually represents observed and simulated hydrographs for the seven model run scenarios (Table 2) using gauges, radar-only QPEs, and merged radar QPEs as precipitation input to the HEC-HMS model validation events. Several standard metrics for hydrographs were calculated to quantify hydrograph similarity with regard to occurrence, amplitude, and timing (Ehret and Zehe 2011). The widely used time-aggregated average measures of amplitude error [RMSET; Eq. (18)] were calculated along with the shift in peak value (PVS) and time (PTS) (Ehret and Zehe 2011):
RMSET=1Tt=1T(OtSt)2,
where T is number of steps in time series and Ot and St are the observations and simulations at time step t.
Fig. 6.
Fig. 6.

Hydrographs of streamflow for model run scenarios during validation.

Citation: Journal of Hydrometeorology 22, 8; 10.1175/JHM-D-20-0267.1

The simulated peak streamflow’s magnitude and timing closely matched with models calibrated with merged radar QPEs for both WKR C-band and KBUF S-band radar QPEs as compared with the models calibrated with radar-only QPEs (Fig. 6). The average RMSET values along with time and value shifts for different radar QPEs are given in Table 4. The least reported RMSET values for G-C-B and G-N-B imply that hydrological models calibrated with gauge data and run with bias-corrected radar QPEs performed better than the models calibrated and run with merged radar QPEs (C-C-B and N-N-B) and radar-only QPEs (C-C and N-N) (Table 4). The peak value shifts for bias corrected radar QPEs are considerably lower than radar-only QPEs implying that accuracy and reliability of both WKR C-band and KBUF S-band radar QPEs improved after applying radar–gauge merging. The reported average peak time is shifted for bias corrected radar QPEs for about 2 h, which is considerably lower than radar-only QPEs. It is worth noting that relatively high average time shifts are reported because of the relatively high time shift reported for events 10 and 12.

Table 4.

Average RMSET values for time and value shifts for hydrographs in Fig. 6.

Table 4.

The similarity of hydrographs from the HEC-HMS model runs using bias-corrected radar QPEs are further statistically demonstrated in Fig. 7. A comparison of hydrological model performance statistics calculated for seven calibration scenarios listed in Table 2 is shown in Fig. 7. All four indices were significantly improved after the application of radar–gauge merging using the CDFM radar–gauge merging method. Similar to the previous results, G-C-B and G-N-B performed better than C-C-B and N-N-B, implying that merged radar QPEs can be successfully used to run hydrological models that were calibrated using gauge data for flood forecasting purposes.

Fig. 7.
Fig. 7.

Hydrological model performance criteria for validation events: (a) KGE, (b) NSE, (c) VE, and (d) MPFC.

Citation: Journal of Hydrometeorology 22, 8; 10.1175/JHM-D-20-0267.1

To further assess the effect of radar QPEs on hydrological model simulations, Taylor diagrams were drawn using three statistical parameters (standard deviation, correlation coefficient, and centered root-mean-square error) calculated for the validation events (Fig. 8) (Taylor 2001). The simulated streamflow using gauge data as precipitation input to a model calibrated using gauge data (G-G) performed best as they are plotted closest to the black arc and the point “OBS.” The model run scenarios that involved bias-corrected radar QPEs during calibration were plotted relatively closer to the black curve as well as the point OBS, revealing their better performances relative to the models calibrated with radar-only QPEs. Also, hydrological models calibrated with gauge data but validated with merged radar QPEs (G-C-B and G-N-B) performed better, showing the ability to use bias-corrected radar to run existing hydrological models for operational flood forecasting.

Fig. 8.
Fig. 8.

Taylor diagrams showing a statistical comparison between observed and simulated streamflow for all model run scenarios during validation. [Note: the Taylor diagram summarizes standard deviation, correlation coefficient, and centered root-mean-square error for each calibration scenario for validation events. Different colors denote different model run scenarios. The best scenario plots itself closer to the black arc as well as to the point OBS (observed flow)].

Citation: Journal of Hydrometeorology 22, 8; 10.1175/JHM-D-20-0267.1

c. Flood inundation mapping

Figure 9 shows the flood extent maps produced using HEC-HMS and HEC-RAS models within the HEC-RTS framework for the 8 July 2013 Toronto flood. Flood extent maps corresponding to a selected part of the downstream part of the watershed are visually presented in Fig. 9. The area under inundation determined using the bias-corrected radar QPEs (C-C-B, N-N-B, G-C-B, and G-N-B) visually agreed well with the flood extent using gauge data as compared with the radar-only QPEs (C-C and N-N; Fig. 9). For example, a relatively large submerged area in Fig. 9c that resulted from radar-only C-band QPEs reflects the overestimation of precipitation due to excessive ground clutter. The extent of the flood-prone area generated by RAS Mapper using the outflow from the hydrological models calibrated with gauge data but ran with merged radar QPEs (G-C-B and G-N-B) performed better, revealing the ability to use bias-corrected radar to run existing hydrological models for operational flood forecasting.

Fig. 9.
Fig. 9.

Simulated flood inundation corresponding to the model run scenarios using the HEC-RTS framework.

Citation: Journal of Hydrometeorology 22, 8; 10.1175/JHM-D-20-0267.1

The metrics calculated between observed and simulated water levels reported at the Islington flow gauge station during the 8 July 2013 flood event are presented in Table 5. The rD and RMSED values considerably improved after applying bias correction for both WKR C-band and NEXRAD S-band radar QPEs. The highest rD and the least RMSED were reported for gauges (G-G) and can be used as the reference to validate the flood maps with confidence. Similar to the previous results, better performance was observed when hydrological models were calibrated with gauge data and then run with bias corrected radar QPEs (G-C-B and G-N-B) for both C and S band radar QPEs.

Table 5.

Metrics calculated between observed and simulated water levels. (Note: water levels are reported with regard to a datum defined by Environment Canada.)

Table 5.

Table 6 shows the average accuracy of flood extent between simulated streamflow using radar-only QPEs and merged radar QPEs in comparison with gauge simulated flood extent. Overall, the accuracy improved using merged radar QPEs relative to radar-only QPEs for both WKR C-band and KBUF S-band radar. Both C-C and C-C-B overestimated the flood extent while both N-N and N-N-B considerably underestimated the flood extent. The accuracy of the extent of the flood is optimum for simulations from the hydrological models calibrated with gauge data and run with bias-corrected radar QPEs.

Table 6.

The accuracy of flood extent for each radar QPE in comparison with gauges’ simulated flood extent.

Table 6.

The contingency statistics calculated between flood extent maps produced using different radar QPEs and gauges are presented in Table 7. The optimum detection is reported for C-C, C-C-B, and G-C-B. However, relatively high FAR values corresponding to C-C and C-C-B imply that WKR C-band radar QPEs simulate flooding that are not confirmed by the reference leading to significant over estimation. Relatively high POD and relatively low FAR reported for G-C-B collectively indicate that the simulation using G-C-B detects flood extent relatively well in comparison with the reference. The reported CSI values suggest that the flood extent involving merged radar QPEs (C-C-B and N-N-B) showed better performances than scenarios with radar-only QPEs (C-C and N-N) for both WKR C- band and NEXRAD S-band radar QPEs. Moreover, hydrological models calibrated with gauge data and run with bias-corrected radar QPEs (G-C-B and G-N-B) show better overall skill than the models calibrated and run with merged radar QPEs (C-C-B and N-N-B) as well as radar-only QPEs (C-C and N-N).

Table 7.

Contingency statistics between flood extend maps produced using different radar QPEs and gauges.

Table 7.

The r and RMSE calculated between inundation levels using gauge and corresponding radar QPEs for detected pixel pairs are presented in Table 8. According to the results, hydrological models calibrated and validated with radar-only QPEs (C-C and N-N) showed the least match with the gauge simulated flood depths. As compared with radar-only QPEs scenarios (C-C and N-N), hydrological models calibrated with merged radar QPEs (C-C-B and N-N-B) provided considerably accurate simulated inundation levels. Similar to previous results, the best performances are reported when hydrological models were calibrated with gauge data and then run with bias-corrected radar QPEs (G-C-B and G-N-B). Therefore, gauge-calibrated hydrological models can be run effectively using the bias-corrected radar QPEs for operational flood forecasting.

Table 8.

The average r and RMSE calculated between inundation levels for detected pixel pairs.

Table 8.

6. Conclusions

This research integrates the HEC-HMS hydrological model and HEC-RAS hydraulic model into the HEC-RTS framework to assess the potential of radar QPEs for flood forecasting. It is shown that radar–gauge merging enhances the accuracy and reliability of both Canadian WKR C-band and U.S. NEXRAD KBUF S-band dual-polarized radar QPEs and, subsequently, the streamflow simulations’ accuracy. Bias-corrected radar QPEs improved all hydrological model performance indices when compared with radar-only QPEs during model recalibration. This indicates that the radar–gauge merging can enhance the hydrological models’ calibration. Therefore, radar QPEs can be used as precipitation input to hydrometeorological models for the areas where precipitation gauges are sparse. As radar provides real-time spatially distributed precipitation information, it can be used as precipitation input for hydrological and hydraulic models for flood forecasting purposes in small urban watersheds where response time is only a few hours. Furthermore, it is found that bias-corrected radar QPEs can be effectively used to run hydrological models initially calibrated using gauge data. The majority of the Canadian flood forecasting agencies use hydrological models calibrated and validated using gauge data (Zahmatkesh et al. 2019). However, due to lack of long-term radar data archives, and the high cost and the time required to recalibrate existing models, updating the existing hydrological models using bias-corrected radar QPEs is recommended to simulate streamflow input to hydraulic models to produce flood inundation maps. Furthermore, the HEC-RTS framework can be used to produce flood extent maps using bias-corrected radar QPEs for future storm events. These maps could be used to make appropriate decisions and take immediate actions to reduce human and economic losses. In the future, the HEC-RTS framework could be upgraded to an automated Flood Early Warning Systems (FEWS) using methods available in HEC-RTS to retrieve, compute, view, and manage real-time Canadian and NEXRAD radar precipitation data to issue real-time flood forecasts for operational use.

Acknowledgments

The authors thank the Natural Science and Engineering Research Council (NSERC) Canadian FloodNet project for financially support this research (NETGP-451456). The authors thank Dr. Z. Zahmatkesh and Dr. S. Han for providing the recalibrated HEC-HMS model. The authors are also grateful to Mr. Andre D.L. Zanchetta for his NEXRAD radar QPE acquisition and processing assistance. TRCA provided both the HEC-HMS and HEC-RAS model and hydrometeorological data used in this study. The WKR C-band radar QPEs and KBUF NEXRAD S-band radar QPEs were collected from the Observations-Based Research Section, King City, ECCC, and NOAA National Centers for Environmental Information data archives. The authors declare no conflict of interest.

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