1. Introduction
Floods are the most frequent natural hazards, leaving substantial damages and casualties behind [
1,
2,
3]. The unprecedented climate change as well as population growth and changing land cover are altering the water cycle, with dramatic impacts on natural and built-up/developed lands, which in turn increase the damages associated with floods [
4]. In Canada, flood is known as the most common, widely distributed, and costliest natural disaster [
5]. In the United States, inflation-adjusted damages associated with floods during 1980–2005 were estimated at more than USD 500 billion [
6]. Since 1900, the records for 100 river floods in Europe show human and economic damages of more than the set thresholds (i.e., exceeding 20 deaths and/or USD 1 billion) [
7].
Regardless of the technological advancements, as well as investments, to deal with floods, they still continue to destroy houses and cause fatalities [
7]. Numerous modeling approaches have been developed to understand and forecast flood. These tools and techniques, varying from simple statistical and lumped hydrologic/hydraulic methods to high spatiotemporal resolution models and machine learning approaches [
8], have been improved over the past decades with implications in watershed and river hydrology, water resources planning and management, flood forecasting and flood damage assessment [
9,
10,
11,
12,
13,
14,
15]. They are further integrated into the flood hazard mapping process as an effective measure of flood hazard mitigation [
16,
17].
Uncertainties arising from the modeling structure as well as forcing data and parameters of the models could significantly affect the accuracy of the flood hazard maps. Regardless of recognition of sources of uncertainty [
18,
19], eliminating these uncertainties is not possible due to the constraints associated with financial resources, time and technology, as well as our imperfect knowledge of the flood science [
20]. To address uncertainty in practice, it should be quantified and communicated to planners and decisionmakers for risk assessment [
21].
The effect of different sources of uncertainty on hydrologic, hydraulic and flood inundation modeling has been extensively studied. The models’ inputs and parameter uncertainties can be expressed through ensembles of realizations, which are usually generated from a Monte Carlo (MC)-based sampling method [
22]. Vrugt et al. [
23] demonstrated the application of a Markov Chain Monte Carlo (MCMC) sampler, called differential evolution adaptive Metropolis (DREAM), to analyze parameters and the forcing of data error in watershed hydrologic modeling. Jung and Merwade [
20] analyzed the uncertainty arising from discharge, topography, and roughness based on MC simulations, using HEC-RAS (Hydrologic Engineering Center’s River Analysis System) in developing inundation maps for river basins. Farmakis et al. [
24] investigated the effect of structural, input (upstream flow), and parameter (channel and floodplain gradients and roughness, as well as the channel width) uncertainty on flood mapping, using HEC-RAS, LISFLOOD-FP and FLO-2d models with an MC simulation approach. Other examples to use MC-based approaches for uncertainty estimation include Kalyanapu et al. [
25] who incorporated uncertainties in Flood2D-GPU hydraulic model peak flows; Neal et al. [
26] who generated flood events using a 2D LISFLOODFP hydraulic model; and Nuswantoro et al. [
27] who developed a stochastic rain generator using a Sobek rainfall-runoff model and a 1D–2D hydraulic model. Other alternatives to MC-based simulations for uncertainty analysis of one-dimensional models are the First-Order Second-Moment method, the Moment method, the spectral method, the Mellin transformation and the Point Estimate Method (PEM) [
28]. Issermann and Chang [
28] demonstrated the application of PEMs in the uncertainty analysis of spatiotemporal models to generate probabilistic floodplain maps. Hu et al. [
29] described the development of a framework using long short-term memory (LSTM) and the reduced order model (ROM) to represent the spatiotemporal distribution of floods, considering the uncertainty in flood-induced conditions. Wu et al. [
30], in an attempt to decrease the uncertainty arising from long-time forecasting, integrated LSTM and the spatiotemporal attention module for flood forecasting. Reliable flood mapping could also benefit from remote-sensing data and satellite imageries. LiDAR-derived Digital Elevation Models (DEM)s demonstrate as useful in flood mapping [
31]. Muhadi et al. [
31] provided a review on the use of LiDAR-derived data in flood applications. Nonetheless, the dependency of these data on timely coverage and cloud cover brings uncertainty to real-time flood forecasts. Olthof and Svacina [
32] tested different flood-mapping approaches using numerous sources of data, including Lidar DEMs, water height estimated from nineteen RADARSAT-2 flood maps, and point-based flood perimeter observations, and showed how these data could be combined to generate accurate full flood extents. Several other toolboxes and methods have been developed for uncertainty analysis with applications in the models’ calibration as well as sensitivity analysis. Examples are the Bayesian recursive estimation technique (BaRE) [
33], the Shuffled Complex Evolution Metropolis (SCEM) algorithm [
34], the dynamic identifiability analysis framework (DYNIA) [
35], the maximum likelihood Bayesian model averaging (MLBMA) method [
36], the dual state-parameter estimation methods [
37,
38], the simultaneous optimization and data assimilation algorithm (SODA) [
39], the optimization software toolkit for research in computational heuristics (OSTRICH) [
40], and the Variogram analysis of response surface (VARS) framework [
41].
It is a common practice to incorporate uncertainty in developing probabilistic floodplain maps [
42,
43,
44,
45]. As opposed to probabilistic maps, deterministic maps provide precise (but potentially inaccurate) information on flood depth and extent [
42] by classifying the floodplain into two groups: flooded (wet) and not-flooded (dry) areas. As discussed by Dottori et al. [
21], it is better to be approximately right rather than precisely wrong. To develop deterministic maps, the models are calibrated to obtain a single optimum parameter set. This might result in the incorrect assessment of flood risk [
43]. Therefore, many researchers advocate for the use of probabilistic floodplain mapping [
16,
46,
47,
48,
49,
50,
51,
52].
Probabilistic floodplain mapping uses an ensemble simulation-based approach [
53]. To develop probabilistic maps through the estimation of uncertainties, two main procedures can be employed: Bayesian approaches [
54] and the Generalized Likelihood Uncertainty Estimation (GLUE) methodology [
55]. GLUE is probably the most common method used for uncertainty estimation in hydrological studies [
56]. Di Baldassarre et al. [
43] applied the GLUE procedure to incorporate uncertainties from the LISFLOOD-FP raster-based model parameters (channel’s roughness) in flood inundation. Pedrozo Acua et al. [
57] also used the GLUE method to incorporate input uncertainties in a distributed hydrologic model in developing floodplain maps using the MIKE-21 2D (2 dimensional) hydraulic model. The GLUE-based methods have shown successful application in assessing uncertainties and producing probabilistic flood inundation predictions [
45,
58,
59,
60,
61,
62,
63,
64,
65,
66].
This paper expands upon previous research on probabilistic floodplain mapping by developing a framework to propagate hydrologic and hydraulic uncertainties into flood modeling and delineation. Seven scenarios considering individual and compound sources of uncertainty are defined. A multi-event approach based on the Dynamically Dimensioned Search (DDS) method is employed for the calibration of the hydrologic model to simulate extreme events. DDS has shown successful application for model calibration in watershed hydrology literature [
67,
68]. Input (rainfall) and parameters of the Hydrologic Engineering Center’s Hydrologic Modeling System (HEC-HMS), as well as channel- and floodplain-roughness coefficients of the 1D HEC-RAS hydraulic model are incorporated in the uncertainty analysis. The updated flow from the hydrologic model through modifying the forcing data and the model parameters is used as input to the hydraulic model. Then, with and without the parameters’ uncertainty in hydraulic modeling, thousands of ensembles of water levels at cross sections are built through implementation of the GLUE method. For each scenario, hundreds of floodplain maps are generated by processing the hydraulic model results in the geographical information system (GIS) with the DEM of 1 m resolution for the study region. The maps are finally superimposed to develop probabilistic floodplain maps for a 100-year design storm. With the influence of the changing climate, the flood risk may further increase by increasing the flood magnitude, frequency, and extent [
69,
70]. For example, a recent study showed that the 100-year flood event assessed in the 1970s is now becoming 35-year event across the United Kingdom [
71]. To investigate how floods will evolve for the study watershed in the future under a changing climate, probabilistic floodplain maps are also developed, considering the hydrologic input (major) uncertainty for a 100-year event in the 2050s under high emission Representative Concentration Pathway 8.5 (RCP8.5).
The objectives of the study are as follows: (1) to develop a framework for probabilistic floodplain mapping by incorporating different sources of uncertainty and to assess their effect on flood modeling; (2) to integrate hydrologic modeling and hydraulic modeling for the development of floodplain maps for a 100-year event in a flash-flood-prone watershed; and (3) to predict flood risk potential and assess flood inundation due to hydrologic input uncertainty under climate change impacts.
5. Concluding Remarks
This study provides a methodology to incorporate uncertainties in probabilistic floodplain mapping. HEC-HMS and HEC-RAS models were used for hydrologic and 1D hydraulic modeling. Uncertainty associated with the models inputs and parameters was considered in the analysis through defining several scenarios. The proposed methodology was applied to a flash-flood-prone watershed in the Greater Toronto Area, Canada. The HEC-HMS model was calibrated using the DDS algorithm based on a multi-event calibration process considering more than 40 historical storm events. The HEC-RAS model, previously developed for the watershed, was used for river-flow routing. HEC-RAS RAS-Mapper was used to create floodplain maps with the watershed terrain model (1 m × 1 m resolution). For each scenario, 100-year probabilistic floodplain maps were then created by superimposing the maps generated using the GLUE method to account for the models’ inputs and parameters uncertainty. In addition, to better understand how the floodplain would evolve in future under the changing climate, probabilistic floodplain maps were also developed for the 100-year event in the 2050s under RCP8.5 using the same method but only considering the major source of uncertainty.
Insight into the maps showed that the extent of the floodplain and uncertainty in flood depth for each cell is higher in the existence of hydraulic structures, such as culverts and bridges. To quantify uncertainty at the cross-section scale, the water level obtained for each realization was normalized, taking into account the minimum and maximum water levels considering all realizations and all scenarios. Minimum and maximum generated water levels (based on the base map datum) for a selected cross section upstream of the river were 204.84 m and 207.74 m, respectively; so, the depth of the water due to a 100-year flood event at this cross section could vary up to 2.9 m. Similarly, for a selected cross section downstream of the river, minimum and maximum simulated water levels were 83 m and 86.55 m, respectively, which indicates a difference of up to 3.55 m in the water depth when uncertainties are incorporated in floodplain mapping. Considering all cross sections, minimum and maximum variations in the water depth were observed at 0.54 m and 6.37 m, respectively, with an average value of almost 3 m. Greater water level depth variation was observed downstream of the watershed. In the 2050s, under a high emission scenario, the total area under potential flood risk for this watershed is projected to increase by 1.75 km2 compared to the baseline period, and the water depth for the selected upstream and downstream cross sections are projected to increase by 0.75 m and 1.43 m (average of future projection scenarios), respectively. The flooding probability related to non-stationary IDF is higher for the flood area compared with stationary IDF method, suggesting that flood risk is greater when rainfall non-stationarity is fully accounted for.
These results indicate how uncertain the floodplain maps could be and that to develop reliable floodplain maps, uncertainty associated with the modeling techniques and tools are required to be incorporated. The increasing flood inundation areas and depths also indicate an increasing flood risk for the future under climate change, which will require an improved flood management capacity to enhance the resilience to climate change and long-term sustainable development for the watershed. It is worth mentioning that other sources of uncertainty (such as the uncertainty arising from the models’ structure) could also affect the floodplain maps. Moreover, updating the HEC-RAS model with the recent LiDAR data could potentially enhance the results. Potential studies to extend the current research include communication/presentation of uncertainty and probability with the end-users in the application of floodplain maps, reducing the uncertainty associated with flood modeling, and application of multi-model approaches to account for model structure uncertainty. Further study could also include the use of Radar and LiDAR data to access their potential in terms of reducing the uncertainty in the floodplain mapping.