# Synchronization-Enhanced Deep Learning Early Flood Risk Predictions: The Core of Data-Driven City Digital Twins for Climate Resilience Planning

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

#### 2.1. Synchronization Module

_{t}is the size of the set [t

_{1}:Δt:T], t

_{1}is the initial recording time, Δt is the time step at which both rainfall and inundation depth are recorded, T is the maximum recording time, N

_{j}is the number of weather stations employed, and N

_{i}is the number of locations where inundation depth observations are available. ${R}_{j}\left(t\right)$ and ${d}_{i}\left(t\right)$ represent lagged, yet related, metrics characterizing the flood events under consideration. As such, for fluvial flooding conditions, ${d}_{i}\left(t\right)$ records assume that urban drainage systems do not exist (or completely malfunction) in the study area. In contrast, the capacity and operability of drainage systems and other flood control measures are inherently present within ${d}_{i}\left(t\right)$ records under pluvial or combined fluvial-pluvial flooding conditions. It should be noted that ${d}_{i}\left(t\right)$ records can be acquired from a flood monitoring station at location i or can represent the output of a well-calibrated hydraulic or hydrologic-hydraulic model at such location. It should be also noted that when the timeseries of rainfall and inundation depth do not have the same Δt, a data imputation method should be applied. The application of SES starts with selecting peak rainfall [R

_{j}(t

_{R})] and inundation depth [d

_{i}(t

_{d})] events from R

_{j}(t) and d

_{i}(t), respectively, with t

_{R}and t

_{d}being the peak times of rainfall and inundation depth, respectively. It should be noted that other events may be selected (e.g., minimum or specific quantile values) depending on the study objective [63]. For instance, zero rainfall events may be employed to associate dry periods to drought occurrence, whereas a specified percentile of inundated areas may be related to poor dam operation conditions. Events selected from the two series (i.e., [R

_{j}(t

_{R})] and [d

_{i}(t

_{d})]) are subsequently aligned such that a rainfall event at time t

_{R}is associated with a depth event between t

_{R}− δ and t

_{R}+ δ, where δ is a pre-defined time window [62]. In contrast to the event synchronization approach developed by Quiroga et al., 2002 [62] that evaluates the synchronization between two timeseries based on reliability only, the SES quantifies both the reliability and precision aspects of synchronization [64]. Within the SES approach, the synchronization reliability is quantified through the coincidence ratio (ρ[d

_{i},R

_{j}]) that indicates the fraction of events paired at a specific time lag t

_{s}.

_{s}, an average time lag [L(d

_{i},R

_{j})] is selected as the optimal lag and an average time jitter [τ(d

_{i},R

_{j})] is utilized to reflect the synchronization precision (i.e., the average deviation between t

_{s}and L). Rainfall amounts at station j is thus synchronized with inundation depths at location i at L(d

_{i},R

_{j}) when ρ(d

_{i},R

_{j}) is sufficiently high and τ(d

_{i},R

_{j}) is notably low. It should be emphasized that the fact of causality between rainfall and flooding leads the rainfall events to always precedes inundation depth events. As such, negative L(d

_{i},R

_{j}) values indicates that while j and i may be within the same hydrological system, the two locations are hydraulically disconnected and therefore rainfall-depth synchronization cannot be confirmed even for high values of ρ[d

_{i},R

_{j}]. It should be also noted that while higher ρ(d

_{i},R

_{j}) values reveal the synchronization between rainfall and depth processes at locations i and j, such synchronization should be physically confirmed as locations i and j may not be hydraulically connected in nature.

_{j}(t

_{R}) and d

_{i}(t

_{d}) pairs, an integrated database of lagged rainfall records ${R}_{j}\left({t}_{lag}^{d}\right)\in {\mathbb{R}}^{{N}_{L}\times {N}_{W}}$, inundation depth values ${d}_{i}\left({t}_{lag}^{d}\right)\in {\mathbb{R}}^{{N}_{L}\times {N}_{i}}$, and flooding status ${I}_{i}\left({t}_{lag}^{d}\right)\in {\mathbb{R}}^{{N}_{L}\times {N}_{i}}$ is prepared as shown in Figure 2, where ${t}_{lag}^{d}=\left[max\left\{L\left({d}_{i},{R}_{j}\right)\right\}:\mathsf{\Delta}t:T\right]$, N

_{L}is the length of the vector ${t}_{lag}^{d}$, ${N}_{w}={N}_{i}\times \left[max\left\{L\left({d}_{i},{R}_{j}\right)\right\}-min\left\{L\left({d}_{i},{R}_{j}\right)\right\}\right]$, and ${R}_{j}\left({t}_{lag}^{d}\right)$ is the rainfall records (i.e., [R

_{j}(t)]) shifted by time lags in the set $\left[max\left\{L\left({d}_{i},{R}_{j}\right)\right\}:\mathsf{\Delta}t:min\{L\left({d}_{i},{R}_{j}\right)\right]$. It should be highlighted that both of ${d}_{i}\left({t}_{lag}^{R}\right)$ and ${I}_{i}\left({t}_{lag}^{R}\right)$ represent the output of the deep learning model whereas ${R}_{j}\left({t}_{lag}^{d}\right)$ is used as the model input. It should also be emphasized that the synchronization analysis module of the FPM can be used on its own as an early flood warning system as L(d

_{i},R

_{j}) can reflect the time at which a peak inundation depth occurs at location i shortly after observing a peak rainfall event at weather station j, given that locations i and j are within the same hydraulic system. However, when synchronization is mathematically confirmed between rainfall and inundation depth at locations i and j that are within the same hydrologic system but are hydraulically disconnected, a homogenous rainfall regime can be suggested within the system (i.e., rainfall patterns, rather that intensities, are nearly the same over the watershed). Such information can guide the decisionmakers to devise prompt preparedness, mitigation, and evacuation plans prior to the occurrence of a flood event, which can boost community resilience under such type of hazard. It should be noted that the synchronization module described herein is considered a preprocessing step within the FPM through which the number of rainfall days required to estimate the flood characteristics is determined.

#### 2.2. Deep Learning Module

_{f}) to convert the input images into feature maps with reduced dimensions, nonlinear function (e.g., sigmoid function or rectified linear unit) to constraint the pixel values within the feature maps to a specific range, sub-sampling (i.e., pooling) layer to spatially integrate distinct pixels of each feature map, and an output layer [65]. The convolution kernel and nonlinear function together with the subsampling layer are referred to as the convolution layer (CL). A convolution block (CB) of multiple CLs connected in series, as shown in Figure 3, introduce more trainable parameters to the network to effectively explore complex input-output relationships [65]. However, the training of CNNs with several connected CBs may be computationally expensive [65], most often results in only locally optimized trainable parameters [70], and increases the likelihood of overfitting [71,72]. Enhanced performance can be achieved through employing a batch normalization directly after applying the convolution kernels and/or a dropout layer following the subsampling layer [53,73]. It should be highlighted that CNNs can integrate the spatial information within individual 2D images that are temporally related without capturing the time-interdependence between them.

_{L}2D images, each with entries $x\left(t\right)\in {\mathbb{R}}^{{N}_{i}\times \raisebox{1ex}{${N}_{w}$}\!\left/ \!\raisebox{-1ex}{${N}_{i}$}\right.}$, and are subsequently used to train a M + 1 set of parallelly connected DL models (of which M are regression models used for inundation depth estimation and a single classification model utilized for flood extent prediction). Such reformulation implies that the DL models are used to estimate the flood extent and the spatial distribution of inundation depth at a specified time t due to a rainfall sequence within the time interval $\left[min\left\{L\left({d}_{i},{R}_{j}\right)\right\},max\left\{L\left({d}_{i},{R}_{j}\right)\right\}\right]$. In addition, estimating the flood extent is conceptualized as a classification problem, where locations are labelled as flooded/unflooded. Each of the DL models within this module consists of a number of CBs connected in series, followed by a LSTM network with N

_{h}hidden unites. As the typical output from a CB is a 2D image, a flatten layer is added between the last CB and the LSTM network to collapse the spatial dimension of such images (i.e., converting 2D datasets into vectors). Finally, a fully connected network is used to map the output from the LSTM network into the output of interest (i.e., inundation depth or flooding status). Figure 5 shows a schematic of the DL module of the FPM. It should be noted that model parameters of such coupled CNN-LSTM architecture include values within each convolution kernel, weights and biases associated with inputs of each cell within the LSTM block, and neuron’s weights and biases in the fully connected network. Such parameters are typically obtained following a feedforward backpropagation optimization procedure (e.g., stochastic gradient descent [75] or adaptive moment estimation [76] approaches).

#### 2.3. Averaging and Testing Module

_{m}) to each candidate model m based on the corresponding contribution to the ensemble posterior distribution [93]. A normality assumption is typically employed, where estimates from each model m should follow a Gaussian distribution. Such assumption is most often violated, and thus model estimates should be transformed into Gaussian latent variables [83,94]. An expectation-maximization (EM) algorithm is subsequently applied with the objective of maximizing the following likelihood function:

_{m}and σ

_{m}, y|m is the estimates from model m after mapping into Gaussian space, and $g\left(y,y|m,{\sigma}_{m}^{2}\right)$ is the normal probability density of y using a mean value of y|m and a standard deviation of σ

_{m}. In the context of this study, the BMA is applied to the M regression DL models only in order to produce highly reliable inundation depth maps at time t. Inundation depth estimates from the M regression models, $\widehat{{d}_{i}^{m}}\left(t\right)$, are therefore combined into ${d}_{i}^{BMA}\left(t\right)$ using the W

_{m}values obtained through the application of the EM algorithm to Equation (1), as follows:

_{i}locations at time t. On the other hand, for classification models, the precision is defined as the fraction of accurately classified instances among the total estimates of a specific class (i.e., flooded/unflooded) [58]. The recall, in contrast, is the fraction of accurately classified instances among the total observations of a specific class. The precision and recall thus reflect the ability of a classification model to accurately predict the different classes, albeit from different perspectives [58]. Therefore, there is a consensus to combine both metrics harmonically into a F-score, where higher values indicate the significant predictability of the classification model (i.e., the model’s ability to estimate the flood extent for a sequence of rainfall events, in the context of the present study). It should be reminded that a single prediction of the classification and BMA-based DL models indicates the flood extent and the spatial distribution of inundation depth, respectively, at a specific instance of time t.

#### 2.4. Prediction Module

## 3. Study Area and Data Description

^{2}. Bow River contributes a higher flow compared to that of Elbow River as it has larger tributaries that covey more surface runoff volume. Two flow gauges, 05BH005 and 05BJ004, locate at the city entrance on Bow and Elbow Rivers, respectively, as shown in Figure 6a. Such gauges provide flow measurements between March and October only when the river is not frozen. Flow records from 2010 to 2015 and from 2018 to 2020 at 05BH005 and 05BJ004 are obtained from the City of Calgary’s Open Data Portal (https://data.calgary.ca/ (accessed on 25 April 2022)). It is also noteworthy that flow records in 2016 and 2017 are not available at 05BH005 and 05BJ004 due to gauge maintenance. Available flow records are employed within the calibrated HEC-RAS model developed by Ghaith et al. [24] for the same study area to estimate actual flood extent and inundation depth maps during the aforementioned time intervals (referred to as observations hereafter). In contrast to the 1D/2D modelling approach that rely on representing the main rivers as 1D channels divided into multiple reaches with cross sections defined at different locations over the reaches, the 2D/3D hydraulic model developed by Ghaith et al. [24] adopts a 2D grid with 250 m square cells to overlay the study area (similar to that shown in Figure 6b). Such grid was subsequently partitioned into two regions, with the corresponding Manning’s roughness coefficients being calibrated based on the inundation depth measured at stations 05BM015, 05BJ001, and 05BH004 (Figure 6a) in 2013 as well as the maximum flood extent. Upstream boundary conditions were represented by flow measurements at stations 05BH001, 05BJ004, and 05BK001, whereas a normal depth based on the ground slope was assumed as the downstream boundary condition at station 05BM002 (Figure 6a). While HEC-RAS models do not intrinsically consider the interactions between fluvial and pluvial flood conditions as well as the capacity and operability of man-made flood control measures (e.g., basement spaces, drainage systems, flood protection structures), model calibration based on locations within both the river and overland flow areas enables capturing such interactions. Thus, fluvial flooding conditions are only assumed in this demonstration as all stations used by Ghaith et al. [24] for model calibration (i.e., 05BM015, 05BJ001, and 05BH004) locate within the rivers as shown in Figure 6a. It should be noted that actual flood extent and depths can be alternatively acquired through either spatially interpolating observations from a dense flood monitoring network or processing satellite images for the study area over time. However, such approaches are not applied in this FPM demonstration study due to data limitations. As the application of the FPM requires rainfall records and corresponding flood extent and inundation depths, four weather stations (Banff, Bow Valley, and Kananaskis stations on Bow River, and Elbow Ranger Station on Elbow River) are selected as shown in Figure 6a. These stations contain daily rainfall records which are acquired from the open portal of the province of Alberta (https://www.alberta.ca/ (accessed on 25 April 2022)). A study area is selected within the City of Calgary to demonstrate the utility of the FPM, and is subsequently divided into a mesh of 500 m × 500 m grid cells. Rainfall records at the four weather stations and corresponding flood hazard (i.e., extent and depth) maps over the selected study area are divided into training (from 2010 to 2015) and testing (from 2018 to 2020) subsets. Rainfall-flood characteristics pairs in the training interval were used within the first two modules of the FPM for input-output preparation and DL model development, whereas those in the testing interval were used for model testing within the third module. It should be highlighted that while a smaller cell size (i.e., 250 m × 250 m) was used within the hydraulic model developed by Ghaith et al. [24], larger grid cells are used when the FPM is applied for demonstration purposes only. It should be also noted that finer grids can be utilized to capture the flood characteristics at higher spatial resolutions (e.g., at the building scale); however, this could be associated with exorbitant computational costs. Thus, when the FPM is applied based on outputs from a hydrodynamic model, a sensitivity analysis should be carried out during the model development stage to evaluate the impact of cell size on the stability of numerical simulations as well as its suitability for flood resilience assessment and mapping purposes. Alternatively, when the FPM is applied using ground-truth observations from a flood monitoring network with sufficient control locations, spatial interpolation techniques can be used to calculate corresponding observations at the required resolution. It should be also noted that the Bow and Elbow rivers are distinct hydraulic systems that are supplied by different tributaries. However, the two rivers are joined near the City of Calgary’s downtown, forming a single flow route beyond their confluence. As a result, rainfall recorded at weather stations on the Bow river’s tributaries (i.e., Banff, Bow Valley, and Kananaskis) do not contribute to the discharge in the Elbow River at locations upstream the confluence of the two rivers. Similarly, weather stations on the Elbow river’s tributaries (i.e., Elbow Ranger Station) are not hydraulically connected to locations on the Bow River upstream the confluence of the two rivers.

## 4. Results and Discussion

#### 4.1. Synchronization Analysis Results

_{i},R

_{j}] and the optimal time lag L[d

_{i},R

_{j}] using the rainfall records from the weather stations shown in Figure 6a and inundation depth values observed at the center of grid cells shown in Figure 6b between 2010 and 2015. The high ρ[d

_{i},R

_{j}] values at the majority of cells, as shown in Figure 7a–d, highlight the synchronization between the rainfall records and inundation depth at the different grid cells at the corresponding optimal lags (Figure 7e–h). Even though some of the employed weather stations are not connected hydraulically to grid cells within different parts of the system as described earlier, the synchronization analysis results presented in Figure 7 support that respective rainfall observations and inundation depth estimates can still be related mathematically rather than physically. The L[d

_{i},R

_{j}] values range between 3 to 16 days and are consistently smaller within the Bow River compared to those within the Elbow River, highlighting the higher water velocity in the former. In addition, the nearly constant L[d

_{i},R

_{j}] values within both river basins suggest the lower routing effect and the consistent strength of propagating flood waves in both basins. These results support the utility of the synchronization analysis module of the FPM as a stand-alone flood warning system that can be used to estimate the lead time between peak rainfall occurrence and flood realization.

#### 4.2. Deep Learning Model Development and Performance Evaluation

_{i},R

_{j}]) shown in Figure 7 are subsequently employed for the preparation of the DL model inputs and outputs in the training and testing intervals as described in the DL module section (i.e., rainfall events in days t − 16 through t − 3 are used to estimate flood characteristics in day t). Rainfall records at the Banff, Bow Valley, Elbow Ranger, and Kananaskis stations between 2010 and 2015 (1362 instances) were used for model training, whereas corresponding records between 2018 and 2020 (681 instances) were used for model testing. Such records were reformulated as described in the Materials and Methods Section and classification- and BMA-based DL models are subsequently developed. Both models could efficiently replicate the flood extent (Table 1) and inundation depth (Figure 8) observations at most of the time instances in both the training and testing intervals. For the classification model, the overall precision, recall, and F-score were higher than 95% during approximately 99% and 96% of the time instances in the training and testing intervals, respectively. Grid cells overlaying the river (shown in Figure 6b) were falsely classified as flooded/unflooded less than 6% and 10% during the training and testing intervals, respectively, whereas those within overland flow areas were falsely classified around 9% and 5% within the training and testing intervals, respectively. In addition, F-score was consistently higher for locations within the river boundaries during both the training and testing intervals as shown in Table 1. This highlights the ability of the FPM to accurately allocate flooded and unflooded cells, and therefore inferring the flood extent. For the BMA-based model, 240 candidate DL models were trained and subsequently weighted using the BMA technique as described earlier. All of the candidate models efficiently reproduced the flood depth observations with average NSE values ranging between 0.84 and 0.97 and between 0.61 and 0.88 for the training and testing intervals, respectively. Such average NSE values were calculated based on all grid cells and all time instances within the training and testing intervals. More specifically, the DL models replicated the flood depth estimates across all grid cells with a NSE value that is larger than 0.8 for more than 98% of the time instances within the training interval. Within the testing interval and based on all of the 240 DL models, the NSE values were larger than 0.8 for approximately 74% to 92% of the time instances. On the other hand, within the ensemble BMA model, only 25% of the candidate DL models (i.e., 60 models) have relatively higher BMA weights that range between 0.0041 and 0.15. In addition, the NSE values were higher than 0.8 for approximately 99% and 92% of the time instances in the training and testing intervals, respectively, with most of the errors are less than 1.0 m (approximately 99% of the training errors and 94% of the testing errors are within ±0.5 m) as shown in Figure 9. For grid cells overlaying the river, the 95th percentile of depth prediction errors was 0.07 m and 0.61 m for the training and testing intervals, respectively. The same measure was 0.05 m and 0.41 m in overland flow areas during the training and testing intervals, respectively. Such results support the capability of the FPM to accurately predict the spatial distribution of inundation depth due to fluvial floods at different instances of time within both the training and testing intervals. It should be emphasized that the use of the FPM to predict the flood extent and inundation depth over a single year is 200 times faster than using a corresponding HEC-RAS model (i.e., computational time of using the FPM is 0.5% less that of using HEC-RAS).

#### 4.3. Example of Model Predictions

## 5. Insights for City Digital Twin Development and Climate Resilience Planning

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 6.**The City of Calgary Study Area: (

**a**) catchment boundary and hydrometeorological Station; (

**b**) model boundary and grid (Base map from Esri, HERE, Garmin, Intermap, increment P Corp., GEBCO, USGS, FAO, NPS, NRCAN, GeoBase, IGN, Kadaster NL, Ordnance Survey, Esri Japan, METI, Esri China (Hong Kong), ©OpenStreetMap contributors, and the GIS User Community).

**Figure 7.**The coincidence ratio, ρ[d

_{i},R

_{j}], and optimal time lag in days, L[d

_{i},R

_{j}], using rainfall records between 2010 and 2015 at (

**a**,

**e**) Banff, (

**b**,

**f**) Bow Valley, (

**c**,

**g**) Kananaskis, and (

**d**,

**h**) Elbow Ranger weather stations.

**Figure 8.**Comparison between FPM-predicted inundation depth, ${d}_{i}^{BMA}\left(t\right)$, and HECRAS-predicted inundation depth for all locations N

_{i}at all time instances of the (

**a**) training and (

**b**) testing intervals.

**Figure 9.**A violin plot of the difference between the FPM-predicted inundation depth, ${d}_{i}^{BMA}\left(t\right)$, and HECRAS-predicted inundation depth over the training and testing intervals.

**Figure 11.**The spatial distribution of (

**a**) inundation depth and (

**b**) prediction errors on 3 July 2020, obtained using the FPM developed in this study.

**Figure 12.**City Digital Twin simulation results: (

**a**) The City of Calgary downtown area during 3 July 2020 flood event; (

**b**) Sheration Suites Calagry Eau Claire building information; (

**c**) historical and future prediction water depth timeseries at Sheration Suites Calagry Eau Claire building.

**Table 1.**Ranges of the precision, recall and F-score for the training and testing intervals for the overall study area, grid cells overlaying the river, and overland flow areas.

Time Interval | Precision | Recall | F-Score | |
---|---|---|---|---|

Overall | Training | [0.94–1.0] | [0.90–1.0] | [0.92–1.0] |

Testing | [0.91–1.0] | [0.94–1.0] | [0.93–1.0] | |

River | Training | [0.86–1.0] | [0.92–1.0] | [0.91–1.0] |

Testing | [0.92–1.0] | [0.85–1.0] | [0.90–1.0] | |

Overland flow areas | Training | [0.90–1.0] | [0.79–1.0] | [0.86–1.0] |

Testing | [0.80–1.0] | [0.87–1.0] | [0.88–1.0] |

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**MDPI and ACS Style**

Ghaith, M.; Yosri, A.; El-Dakhakhni, W.
Synchronization-Enhanced Deep Learning Early Flood Risk Predictions: The Core of Data-Driven City Digital Twins for Climate Resilience Planning. *Water* **2022**, *14*, 3619.
https://doi.org/10.3390/w14223619

**AMA Style**

Ghaith M, Yosri A, El-Dakhakhni W.
Synchronization-Enhanced Deep Learning Early Flood Risk Predictions: The Core of Data-Driven City Digital Twins for Climate Resilience Planning. *Water*. 2022; 14(22):3619.
https://doi.org/10.3390/w14223619

**Chicago/Turabian Style**

Ghaith, Maysara, Ahmed Yosri, and Wael El-Dakhakhni.
2022. "Synchronization-Enhanced Deep Learning Early Flood Risk Predictions: The Core of Data-Driven City Digital Twins for Climate Resilience Planning" *Water* 14, no. 22: 3619.
https://doi.org/10.3390/w14223619