ABSTRACT
This study aims to develop a smart model for evaluating the spatial density of added IoT sensors (called AIOT grids) to optimize their amount and placements, named SM_ESD_AIOT model; the proposed SM_ESD_AIOT model mainly collaborates cluster analysis with Akaike information criterion (AIC) based on the resulting 2D inundation simulations from the ANN-derived model in comparison with those from the physically based hydrodynamic (SOBEK) model under various sets of AIOT-based sensor networks. Miaoli City in northern Taiwan is selected as the study with the three practical IoT sensors; also, the 1,939 electrical poles are treated as the potential AIOT grids grouped under 5, 10, 15, and 20 clusters. Using a simulated rainfall-induced flood event of 51 h, the five AIOT-based sets, consisting of five added and three practical IoT sensors, could be selected as the optimal one with the minimum AIC (around 1.45). Also, on average, the 2D inundation simulation indices from the optimal five AIOT-based sensor networks are 0.7 better than the results from the three IoT sensors (about 0.495). As a result, the proposed SM_ESD_AIOT is shown to efficiently optimize the amount and placements of the AIOT sensors to enhance the reliability and accuracy of 2D inundation simulation.
HIGHLIGHTS
ANN is applied to develop a smart model for identifying flood-related IoT sensors.
The SM_ESD_AIOT can evaluate the spatial density of added IoT sensors (AIOT).
The cluster analysis with Akaike information criterion (AIC) is used in the proposed SM_ESD_AIOT model.
The demonstration proceeds with comparing results from the hydrodynamic simulation model.
The SM_ESD_AIOT can enhance the reliability of flood simulation.
INTRODUCTION
Recently, climate change and extreme rainstorm events have more frequently triggered rainfall-induced floods that severely damage people's lives and properties (e.g., Hsiao et al. 2021; Khatum et al. 2023; Wu 2023; Zhao et al. 2023) Therefore, real-time detection of water levels plays a vital role in providing relevant information on preventing flood-induced hazards. Thus, the Internet of Thing (IoT)-based sensors are comprehensively adopted in the real-time monitoring of flood-related details, such as the inundation depths (e.g., Langhammer 2023; Chacon-Hurtado et al. 2017; Prakash et al. 2023); also, they make a significant contribution to the flood simulation and forecasts (Arshad et al. 2019; Wu et al. 2021b, 2022; Wu 2023). Therefore, the accuracy and reliability of the flood-related simulation and forecast are significantly impacted by the amount of flood-related IoT sensors with high likelihood (Rose et al. 2023). The hydrological gauge networks are widely and efficiently used in the observation measurement. Hence, designing the optimal flood-related IoT sensor network should be essential in flood prevention and mitigation.
A number of the methods and algorithms for evaluating the spatial distribution of hydrological gauges to achieve the optimal gauge networks of mainly monitoring the rainfall and water level have been introduced, e.g., the genetic algorithm (e.g., Li & Yeh 2005; Hanh et al. 2019), optimization algorithms, such as particle swarm (Aziz et al. 2016) and NSGA-II heuristic (Rose et al. 2023), and geostatistical analysis (e.g., Aziz et al. 2016; Chang et al. 2017) under the given spatial coverage-related objective function. For example, Li & Yeh (2005) demonstrated with the genetic algorithm to figure out spatial optimal problems with several constraints considering the multiple objectives. Rose et al. (2023) developed an NSGA-II-derived model to identify the optimal locations of the limited water-level sensors with the objective functions relying on the spatial coverage under the given constraints. Additionally, to achieve the goal of identifying the optimal gauge number, Chang et al. (2017) applied the Akaike information criterion (AIC), which takes into consideration the effect of the number of model parameters on the parameter calibration, in establishing a framework for detecting the critical rainfall gauges in the watersheds by conducting the cross-validation with the semivariograms calculated using the rainfall characteristics (rainfall depth and storm pattern); in Chang's method, the concerned rain gauges could be first separated into various groups via the cluster analysis under the given cluster number, referred to the WMO's recommendation. As well as the above genetic and optimization algorithms, the probabilistic-based entropy methods could be commonly applied in the design of the optimal hydrological gauges under consideration of uncertainty in the gauge number, especially for the rain gauge networks (e.g., Yeh & Chen 2011; Xu et al. 2015; Chacon-Hurtado et al. 2017; Kwon et al. 2020; Bertini et al. 2021).
In summary, the above optimization-based algorithms could be frequently undertaken by maximizing the spatial coverage of the gauges in terms of the spatial gauge density (WMO 2008; Coulibaly et al. 2013); in detail, the spatial gauge density is given the ratio of the watershed to the gauge amount, inducing the gauge number plays a crucial role in the design of the optimal gauge networks, indicating that the design of the optimal gauge network should be undertaken by finding out the number and associated locations of the gauges of interest. Nevertheless, despite numerous algorithms proposed for optimizing the gauge network, they primarily focus on optimizing the gauge locations without considering the gauge amount, especially for the water-level stations. Instead, the optimal gauge number and location regarding rainfall measurement could be commonly accomplished via the entropy method, AIC index, and geostatistics (i.e., Kriging and inverse distance methods) (e.g., Chang et al. 2017; Shahidi & Abedini 2018; Kwon et al. 2020). Therefore, efficient monitoring of flood-induced inundation should be done by optimizing the number and locations of the flood-related IoT sensors. However, the above researches poorly take into account the impact of the added IoT (AIOT) number and locations on the rainfall-runoff–water level characteristics (e.g., Chacon-Hurtado et al. 2017; Ogie et al. 2017; Arshad et al. 2019; Sikorski et al. 2022). Therefore, an optimization-derived algorithm for effectively achieving the optimal number and placements of flood-related IoT sensors should be needed to monitor inundation depths to delineate the extent of induced flooding in the concerned zones.
It is well known that accurate and reliable flood simulation and forecast could be commonly accomplished by the artificial intelligence (AI)-derived hydrodynamic numerical models efficiently in response to the spatiotemporal changes in the real-time inundation depths detected through IoT sensors with few computation time (e.g., Arshad et al. 2019; Chen et al. 2021; Kwon & Kim 2021; Boulouard et al. 2022; Wu et al. 2022; Langhammer 2023; Wu 2023); the AI-derived flood simulation models are mainly configured based on machine learning (ML) technique with the two types of natural network (NN) structures, the convolutional NN (CNN) and artificial NN (ANN) models. The CNN-based models can estimate the single model output with the gridded model inputs, which are advantageous to the 2D flood simulations to achieve the spatiotemporal flood-related variates of high resolutions in time and space (e.g., the inundation depths and corresponding area) (e.g., Chen et al. 2021; Kwon & Kim 2021; Munawar et al. 2021). Alternatively, the ANN-derived model can emulate temporal-based multi-outputs via the linear multi-layer network with all possible model inputs, especially real-time observations from IoT sensors, such as precipitation, discharge, and water level (Chu et al. 2019; Goyal et al. 2021; Wu et al. 2022; Wu 2023). That is to say, adopted with the resulting real-time observations from the appropriate IoT sensors, the flood-induced simulation could be efficiently and reliably carried out via the AI-derived models with high likelihood; namely, the real-time observations coming from the IoT sensor network could significantly effectively assist the 2D inundations simulation via the AI-derived models (Schumann et al. 2023). Therefore, the high spatial density of the IoT sensor networks, consisting of the optimal gauge amount and placements, is expected to not only usefully contribute to monitoring the flood-induced inundation but also provide essential and efficient real-time flood-related observations for numerically mapping the flooding region via the ANN-derived model. Furthermore, the variation in the amount and locations of the IoT sensor networks might reduce the accuracy and reliability of monitoring, mapping, and emulating floods. In short, it should be known that the effect of the variation in the station amount and placement on the 2D inundation simulation should be considered in optimizing flood-related IoT sensor networks.
Overall, the variation in the spatial density of the water level-related IoT sensors, including the determination of the gauge amount and identification of the corresponding setup locations, probably results in uncertainties in the flood-induced inundation detection and simulation as to what might impact the reliability and accuracy of flood early warning and management. Therefore, this study aims to develop a framework for evaluating the spatial density of the AIOT sensors to identify the optimal gauge amount and placements by collaborating the cluster analysis with the model applicability index (AIC) based on the 2D inundation simulation, named SM_ESD_AIOT model. Additionally, in proceeding with optimizing the IoT sensor networks to reflect the change in the station amount efficiently and locations on 2D inundation simulation, the estimation of the gridded inundation depths, a smart model ANN-derived flood simulation model could be adopted in the proposed SM_ESD_AIOT. It is expected that the appropriate AIOT amount and locations probed by the proposed SM_ESD_AIOT model could be referred to the design of the flood-related IoT sensor networks in the potential inundated zones.
METHODOLOGY
Model concept
This study aims to model a framework for evaluating the spatial density of the AIOT sensors based on the simulations of the gridded inundation depths to identify the appropriate AIOT amount and location in the optimal sensor network, named SM_ESD_AIOT model. Within the SM_ESD_AIOT model, the grids in the digital elevation maps (DEMs) used in the ANN-derived 2D flood simulation model SM_ESD_VIOT (Wu et al. 2022) are regarded as the potential AIOT locations (called AIOT grids). They are classified into numerous groups under given cluster numbers by using the cluster analysis based on the locations and maximum probable inundation depths achieved via the physically based flood simulation model; the potential AIOT grids separated in each group with the maximum inundation depths are specifically defined as the representative AIOT grids. Conducted by the cluster analysis with different cluster numbers, numerous sets of representative AIOT grids could be obtained (described AIOT sets). After that, to respond to the impact of changing the AIOT amount and locations on the 2D inundation simulation, carried out by the SM_EID_VIOT model (Wu et al. 2022), with the inundation depths at the practical IoT sensors and numerous sets representative AIOT grids, the 2D inundation simulation could proceed with being compared with the results from the physically based flood numerical model in terms of the model indices, root mean square (RMSE) and correlation coefficient. Eventually, the appropriate AIOT set could be examined subject to the corresponding minimum AIC indices to the performance indices.
Altogether, the identification of the appropriate AIOT amount and associated locations be accomplished via the proposed SM_ESD_AIOT model through the following steps: the selection and classification of the potential locations of AIOT grids, 2D inundation simulation via the ANN-derived model with the inundation depths at the practical and AIOT sensors (defined AIOT-based sensor network), quantification of the accuracy of the 2D inundation simulations and determination and demonstration of the appropriate AIOT grids in the optimal AIOT-based sensor network. The detailed concepts and methods used in the development of the ANN-derived SM_EID_VIOT model are introduced below.
Classification of the AIOT sensors
serves as the Euclidean distance between variates x and y, being two pairs of data length n. In addition to the clustering method with the distance-calculation equation considered in the K-means clustering algorithm, the classified factors should be defined in advance. Within the proposed SM_ESD_AIOT model, the AIOT grids are designed to accurately and effectively measure the real-time water level near specific spots with high flood risk. Therefore, within the proposed SM_ESD_AIOT model, the separation of AIOT grids under a desired cluster number could be carried out via the K-means method with the Euclidean distance equation based on the corresponding locations and probable maximum inundation depths to the AIOT grids.Configuration of the ANN-derived SM_EID_VIOT model
are estimated in advance by the inverse distance method with the inundation depths at the neighboring IoT sensors:
is the number of the neighboring IoT sensors, and 
stands for the inundation depth at the jth IoT sensor with the distance to the ith virtual IoT grid (VIOTj). Alternatively, the equations of the estimated inundation depths at the VIOT grids are then established based on the ANN-derived model. Namely, the ANN-derived could be regarded as a correction approach for adjusting the estimated spatial averages of the inundation depths at the specific VIOT grids (
) as follows:
serves as the resulting estimated inundation depth at the ith VIOT grid. For the SM_EID_VIOT model, to reduce the variation in the outputs of the ANN-derived models attributed to the uncertainties in the selection of the activation/transform functions, the ANN_GA-SA_MTF model (Wu et al. 2022) is adapted in the SM_EID_VIOT model to establish the relationship between the inundation-depth estimates at the VIOT grids and observations at the practical IoT sensors. The ANN_GA-SA_MTF model was introduced by configuring the network structure of three layers with the multiple transfer functions (see Table 1), and the number of the associated neurons calculated using the equations (see Table 2); the associated ANN weights are optimized by using the genetic-based algorithm under consideration of the sensitivities to the model parameters (called the GA-SA algorithm) (Wu et al. 2012). A variety of transform functions commonly used (Wu et al. 2020)
| Transfer function | Formula | Derivative | |
|---|---|---|---|
| TF1 | Logistic (soft step, Sigmoid) |  |  |
| TF2 | Tanh |  |  |
| TF3 | Arctan |  |  |
| TF4 | Identity | f(x) =  x | f′(x) =  |
| TF5 | Rectified linear unit (ReLU) |  |  |
| TF6 | Parameteric rectified linear unit (PReLU, leaky ReLU) |  |  |
| TF7 | Exponential linear unit (ELU) |  |  |
| TF8 | Inverse abs (IA) |  |  |
| TF9 | Rootsig (RS) |  |  |
| TF10 | Sech function (SF) |  |  |
| Transfer function | Formula | Derivative | |
|---|---|---|---|
| TF1 | Logistic (soft step, Sigmoid) | | |
| TF2 | Tanh | | |
| TF3 | Arctan | | |
| TF4 | Identity | f(x) = x | f′(x) = |
| TF5 | Rectified linear unit (ReLU) | | |
| TF6 | Parameteric rectified linear unit (PReLU, leaky ReLU) | | |
| TF7 | Exponential linear unit (ELU) | | |
| TF8 | Inverse abs (IA) | | |
| TF9 | Rootsig (RS) | | |
| TF10 | Sech function (SF) | | |
Definition of parameters used in the proposed ANN-GA-SA_MTF model (Wu et al. 2022)
| Parameters | Definition | ||
|---|---|---|---|
| Transfer functions used | TF1–TF10 | ||
| Input factors | Resulting areal average of inundation depth from IoT sensors |  | |
| Output factor | Inundation depth at VIOT grids |  | |
| Number of hidden levels | 1 | ||
| Number of neurons | 3 | ||
| Calibration of parameters of transfer function | Number of optimizations | 10 | |
Weights of neurons ( | Mean | 1 | |
| Standard deviation | 3 | ||
Bias of function ( | Mean | 0 | |
| Standard deviation | 1 | ||
Adjusting factor ( | Mean | 1 | |
| Standard deviation | 0.005 | ||
| Parameters | Definition | ||
|---|---|---|---|
| Transfer functions used | TF1–TF10 | ||
| Input factors | Resulting areal average of inundation depth from IoT sensors | | |
| Output factor | Inundation depth at VIOT grids | | |
| Number of hidden levels | 1 | ||
| Number of neurons | 3 | ||
| Calibration of parameters of transfer function | Number of optimizations | 10 | |
| Weights of neurons ( | Mean | 1 | |
| Standard deviation | 3 | ||
| Bias of function ( | Mean | 0 | |
| Standard deviation | 1 | ||
| Adjusting factor ( | Mean | 1 | |
| Standard deviation | 0.005 | ||
serves as the number of transfer functions of interest; 
stand for the observed model inputs and estimated model outputs via the ANN_GA-SA_MTF model with the ith set of the appropriate parameters 
, respectively; and 
accounts for the weighted factor of the ith transfer function with the appropriate parameters 
calculated with the objective-function value 
as:
is the number of observed hydrological estimates.
and 
are the observed and estimated water level at the current time 
, respectively, with the forecast error 
quantified via the time series algorithm and Kalman filtering method, respectively; then, the estimations of the ungauged water-level errors could be achieved via the Kriging equation with the weighted semivariogram functions (Wu et al. 2011a).
represents the corrected inundation-depth estimate at the ith VIOT based on the estimated inundation depth 
with the estimated error 
by the RTEC_2DIS method.Identification of appropriate AIOT grids within the optimal sensor network
Schematic illustration of combining the practical IoT sensors and AIOT grids as the AIOT-based sensor network in the proposed SM_ESD model.
Schematic illustration of combining the practical IoT sensors and AIOT grids as the AIOT-based sensor network in the proposed SM_ESD model.
Where 
, 
, and 
stand for the estimated flooding area, areal maximum inundation depth, and average inundation depths at the time step t-hour via the SOBEK model, respectively; 
, 
, and 
serve as the simulated flooding extent, areal maximum, and average inundation depths at the time step t-hour by the SM_EID_VIOT model with the inundation depths from the kth AIOT-based sensor network with the AIOT grids 
; 
, 
, and 
represent the corresponding RMSEs of the simulated flooding area, areal maximum, and average inundation depths at the time step t-hour for the kth AIOT-based sensor network; and 
is the duration of the inundation event.
is the model performance in terms of the errors of model outputs (e.g., theRMSE); 
and 
account for the amount of model parameters and dataset used in the parameter calibration, respectively. Thus, used to determine the good-of-fit candidate model, the AIC index not only focuses on the model accuracy but also concerns the number of the model parameters in response to the efficiency of the model calibration. By so doing, the candidate model associated with a minimum AIC index could be regarded as the optimal model, which could provide more accurate estimations with high likelihood under an acceptable parameter number.
represent the corresponding AIC values to the errors (
, 
, and 
) for the kth AIOT set and 
serves as the number of the potential locations considered as the AIOT grids; in this study, the number of the potential locations of the AIOT grids 
could be referred to the spatial gauge density (SGD) (WMO 2008) as:
to examine the model applicability of various AIOT sets considered, which would be calculated via the following equation:
is the number of AIOT grids in the kth AIOT-based sensor network and 
stands for the number of AIC values calculated using Equations (17) and (18).In total, within the proposed SM_ESD_AIOT model, the resulting appropriate number of AIOT sensors and associated locations could be determined based on the above weighted average 
.
Model demonstration
) are calculated using the following equations (Wu 2023):
and 
represent the amount of inundated grids and non-inundated identified both by the SM_EID_VIOT and SOBEK models; and NVIOT serves as the number of the available grids (i.e., VIOT-based grids).Among the above 2D inundation simulation indices, 
mainly quantifies the accuracy of the inundated grids recognized by the proposed SM_EID_VIOT model; 
accounts for the reliability of the resulting inundated grids from the proposed SM_EID_VIOT model could also the inundated ones by the SOBEK model; and 
measures the accuracy of the spatial distribution of the resulting inundated and non-inundated grids from the proposed SM_EID_VIOT model.
Therefore, as optimizing the AIOT grids via the proposed SM_ESD_AIOT model, the 2D inundation simulation indices could be utilized to quantify and assess the change in the accuracy and reliability of 2D inundation simulation in time and space with the various amounts and placements of the AIOT grids within the concerned sensor networks.
Model framework
Step [1]: Collect the simulations of rainfall-induced flood events, including the gridded inundation-depth hydrographs and probable maximum inundation depths, the locations of practical IoT sensors, and geometrical data (i.e., DEM) in the study area.
Step [2]: Calibrate the parameters of the ANN-derived 2D inundation simulation (SM_EID_VIOT) model.
Step [3]: Select the DEM grids in the study area as the potential locations of added IoT sensors, named AIOT grids, which are combined with the IoT grids as AIOT-based sensor networks (see Figure 1).
Step [4]: Classify the AIOT grids into the various groups under given cluster numbers via the cluster analysis subject to their locations and associated probable maximum inundation depths; in each group within the AIOT sets concerned, the AIOT grid with the most significant values of the possible maximum inundation depths is treated as the presentative one.
Step [5]: Extract the simulated inundation depths at the IoT and presentative AIOT grids for a number of AIOT sets within the AIOT-based sensor networks from the simulated rainfall-induced flood events.
Step [6]: Carry out 2D inundation simulation via the SM_EID_VIOT model with the inundation depths from the desired AIOT-based sensor networks to achieve the inundation characteristics, including the spatial average and maximum inundation-depth hydrographs and flooding-area hydrographs.
Step [7]: Quantify the differences of the simulated inundation characteristics for various AIOT sets from the results from the physically based hydrodynamic numerical model (SOBEK) in terms of the RMSE using Equations (13)–(15).
Step [8]: Calculate the corresponding AIC values to the resulting performance indices of the inundation characteristics to compute their weighted average
through Equations (17) and (18).Step [9]: Define the AIOT-based sensor network with the minimum
as the optimal one, of which the associated AIOT girds are regarded as the appropriate AIOT grids, i.e., the added IoT sensors.Step [10]: Demonstrate the accuracy and reliability of the resulting appropriate AIOT grids applied in the 2D inundation simulation in terms of 2D inundation performance indices, including the precision of simulated inundated grids, recall, and precision of available grids, using Equations (19)–(21).
Locations of the study area (Miaoli City) (Note: Blue circles are the radar-precipitation grid, and red points are the roadside IoT sensors) (Wu 2023).
Locations of the study area (Miaoli City) (Note: Blue circles are the radar-precipitation grid, and red points are the roadside IoT sensors) (Wu 2023).
STUDY AREA AND DATA
Locations of electric poles located in the study area (Miaoli City).
Development framework of the proposed SM_ESD_AIOT model.
RESULTS AND DISCUSSION
Simulation of rainfall-induced flood events
Observations of gridded rainfall characteristics in the study area (Wu et al. 2021a).
Inundation-depth hydrographs at the practical IoT sensors (IOT1–IOT3) for the validation event in the study area.
Inundation-depth hydrographs at the practical IoT sensors (IOT1–IOT3) for the validation event in the study area.
Flooding map with the maximum possible gridded inundation depths in Miaoli County.
Flooding map with the maximum possible gridded inundation depths in Miaoli County.
Configuration of the ANN-derived model for 2D inundation simulation
Based on the model development framework in Section 2.6, the 2D inundation simulation with various sets of presentative AIOT grids could be accomplished via the three-layer ANN-derived SM_EID_VIOT model with the gridded inundation depths from the various AIOT-based sensor networks under the given conditions, including a hidden layer, associated neurons, and the remaining parameters, as well as transfer functions as listed in Tables 1 and 2. Wu et al. (2022) trained the SM_EID_VIOT model to achieve the corresponding ANN weights to the study area with the inundation depths at the practical IoT sensors and 6,823 VIOT grids extracted from the above 1,000 simulations of rainfall-induced flood events. Table 3 illustrates the results from the parameter calibration of the ANN_GA-SA_MTF model for the 400th VIOT grid, the location (TWD97_X: 232658.5; TWD97_Y: 2729101.0).
Summary of the appropriate calibrated parameters of the ANN_GA-SA_MTF model at the 400th VIOT grid used in the SM_EID_VIOT model for the study area
| Transfer function | No. of optimization | Adjust factor  | 1.00039 | |||||
|---|---|---|---|---|---|---|---|---|
| 1 | OPT1 | Weights of neurons | The 1st hidden layer | Input factors | ||||
| 1 | Bias | |||||||
| Neuron | 1 | 0.614 | −1.143 | |||||
| 2 | −0.592 | −2.719 | ||||||
| 3 | −0.286 | −4.283 | ||||||
| Output layer | The 1st hidden layer | |||||||
| 1 | 2 | 3 | Bias | |||||
| Input factor | 1 | 0.117 | 0.842 | 0.858 | 0.877 | |||
| Transfer function | No. of optimization | Adjust factor | 1.00039 | |||||
|---|---|---|---|---|---|---|---|---|
| 1 | OPT1 | Weights of neurons | The 1st hidden layer | Input factors | ||||
| 1 | Bias | |||||||
| Neuron | 1 | 0.614 | −1.143 | |||||
| 2 | −0.592 | −2.719 | ||||||
| 3 | −0.286 | −4.283 | ||||||
| Output layer | The 1st hidden layer | |||||||
| 1 | 2 | 3 | Bias | |||||
| Input factor | 1 | 0.117 | 0.842 | 0.858 | 0.877 | |||
Consequently, proceeding with the proposed SM_ESD_AIOT model framework (see Figure 5), the 2D inundation simulation could be accomplished via the SM_EID_VIOT model with the inundation depths from the practical IoT sensors and numerous sets of AIOT grids (i.e., AIOT-based sensor networks). The AIOT grids could also be treated as the VIOT grids significantly closer to the electric poles.
Identification of AIOT grids
Electrical poles (red points) located at inundated spots within the study area.
Electrical poles (red points) located at inundated spots within the study area.
resolution; hence, the potential inundation area in the study area would be 10.92 km2. Also, according to the SGD equation (Equation (16)) with a finer gauge density of 0.5 defined in this study, the possible number of the AIOT grids could be roughly given 20 IoT sensors, which could be regarded as the maximum cluster number. Therefore, in the proposed SM_ESD_AIOT model to identify the appropriate AIOT grids, the classification of the 1,783 electrical poles of interest could be then carried out via the cluster analysis based on their locations and maximum probable inundation depths under the given cluster number (i.e., 5, 10, 15, and 20) as shown in Figure 10; also, Figure 11 shows the percentage of the AIOT grids separated into different groups under the four cluster numbers. Observing Figures 11 and 12, regardless of the cluster number, the potential AIOT grids are noticeably primarily located in the southern region with high percentages. For instance, about the 15 clusters, 0.1, 44.8, and 52.7% of all potential AIOT grids could be allocated to the 8th, 9th, and 10th groups, and the remaining groups only have one potential AIOT grids; that is to say, except the 8th–10th groups, the potential AIOT grids in the remaining groups could be directly defined as the presentative AIOT grids possibly relying on their inundation characteristics. 
Classification of potential AIOT grids under various cluster numbers combined with the three practical IoT sensors as the AIOT-based sensor network.
Classification of potential AIOT grids under various cluster numbers combined with the three practical IoT sensors as the AIOT-based sensor network.
Summary of ratios of AIOT grids in various groups under different cluster numbers.
Summary of ratios of AIOT grids in various groups under different cluster numbers.
In total, the practical three IoT sensors and four sets of representative AIOT grids could be combined with the sensor networks as shown in Figure 10, in which the networks only involving the practical IoT sensors consisting of the practical IoT sensors and various AIOT sets are called IOT-based and AIOT sensor networks, respectively. Accordingly, the 2D inundation simulation could be accomplished via the SM_EID_VIOT model with the corresponding inundation depths to the IoT-based and four AIOT-based sensor networks, respectively. Consequently, the resulting inundation characteristics from the above 2D inundation simulation with the four AIOT-based sensor networks could be applied in identifying the optimal sensor network composed of the representative AIOT grids.
2D Inundation simulation via the ANN-derived model
Inundation-depth hydrographs of four sets of representative AIOT grids for the validation event.
Inundation-depth hydrographs of four sets of representative AIOT grids for the validation event.
Simulations of maximum flooding zones under consideration of three practical IoT sensors and four sets of representative AIOT grids.
Simulations of maximum flooding zones under consideration of three practical IoT sensors and four sets of representative AIOT grids.
Comparison of the spatial average and maximum inundation depths via the SM_EID_VIOT model with different sets of representative AIOT grids with those from the SOBEK model.
Comparison of the spatial average and maximum inundation depths via the SM_EID_VIOT model with different sets of representative AIOT grids with those from the SOBEK model.
Comparison of the simulated flooding-area hydrographs via the SM_EID_VIOT model with different sets of representative AIOT grids with those from the SOBEK model.
Comparison of the simulated flooding-area hydrographs via the SM_EID_VIOT model with different sets of representative AIOT grids with those from the SOBEK model.
Overall, adding the potential IoT sensors could considerably influence the inundation characteristics in time and space as to effectively improve the accuracy of 2D inundation simulation. Therefore, to proceed with the identification of the optimal sensor network composed of the practical IoT sensors and appropriate AIOT grids, the resulting 2D inundation simulations under the use of four sets of representative AIOT grids should be used in the proposed SM_ESD_AIOT model.
Determination of appropriate AIOT sensors within the optimal sensor network
To examine the optimal AIOT set comprised of the appropriate AIOT grids through the proposed SM_ESD_AIOT model in the spatial variation and temporal correlation regarding the estimated inundation depths and extents, the performance indices of estimated inundation characteristics should be calculated in terms of the root mean squared errors (RMSE) and correlation coefficient as listed in Table 4. Observing Table 4, nevertheless, the RMSE values of the simulated spatial average inundation depths via the SM_EID_VIOT model with the inundation depths from the four AIOT-based sensor networks (on average, 0.258 m) are slightly over those from the SOBEK model with the water levels from the practical IoT-based sensor network (nearly 0.158); in particular, as mentioned in the above section (see Figure 13), the change of the simulated spatial average inundation depths in time noticeably departure from the results provided by the SOBEK model as to cause the negative correlation coefficient. Regardless, the RMSE values of the simulated maximum inundation depth and flooding extent from the four sets of AIOT-based sensor networks (on average, 0.741 m and1.836 km2) are markedly underestimated as compared with the results from the practical IoT-based sensor network (0.746 m and 2.447 km2); also, they have a more consistent temporal varying trend to the results from the SOBEK model than those for the IoT-based sensor network under the high correlation coefficients of greater than 0.9.
Performance index of estimated inundation characteristics via the SIM_EID_VIOT model with inundation depths in the IOT-based and AIOT-based sensor networks
| Number of AIOT grids | Performance index | Spatial average inundation depth (m) | Spatial maximum inundation depth (m) | Flooding area (km2) |
|---|---|---|---|---|
| 0 (IoT-based sensor network) | RMSE | 0.158 | 0.764 | 2.447 |
| Correlation coefficient | 0.237 | 0.891 | 0.769 | |
| 5 | RMSE | 0.277 | 0.704 | 1.907 |
| Correlation coefficient | −0.470 | 0.944 | 0.892 | |
| 10 | RMSE | 0.229 | 0.702 | 1.721 |
| Correlation coefficient | −0.383 | 0.945 | 0.935 | |
| 15 | RMSE | 0.263 | 0.778 | 1.859 |
| Correlation coefficient | −0.451 | 0.935 | 0.915 | |
| 20 | RMSE | 0.263 | 0.778 | 1.859 |
| Correlation coefficient | −0.451 | 0.935 | 0.915 |
| Number of AIOT grids | Performance index | Spatial average inundation depth (m) | Spatial maximum inundation depth (m) | Flooding area (km2) |
|---|---|---|---|---|
| 0 (IoT-based sensor network) | RMSE | 0.158 | 0.764 | 2.447 |
| Correlation coefficient | 0.237 | 0.891 | 0.769 | |
| 5 | RMSE | 0.277 | 0.704 | 1.907 |
| Correlation coefficient | −0.470 | 0.944 | 0.892 | |
| 10 | RMSE | 0.229 | 0.702 | 1.721 |
| Correlation coefficient | −0.383 | 0.945 | 0.935 | |
| 15 | RMSE | 0.263 | 0.778 | 1.859 |
| Correlation coefficient | −0.451 | 0.935 | 0.915 | |
| 20 | RMSE | 0.263 | 0.778 | 1.859 |
| Correlation coefficient | −0.451 | 0.935 | 0.915 |
) is supposed to be defined in advance as calculating the AIC index. Since the watershed in the study is about38 km2, the number of grids could be estimated via the SGD (Equation (16)) with a finer density of 0.5, i.e., 
. By doing so, the AIC values of the four AIOT-based sensor networks could be achieved as shown in Figure 17, indicating that the optimal set of representative AIOT grids is challenging to be determined according to the AIC values of inundation characteristics. For example, regarding the AIC values calculated with the RMSE values of the spatial average and maximum inundation depths, the five representative AIOT grids could be examined as the appropriate ones with the minimum AIC, about −1.78 and −0.221, respectively; instead, the optimal set comes with the 20 representative AIOT grids under a minimum AIC value (about 0.758) based on the RMSE of the flooding extent. 
Corresponding AIC values to the model performance indices of various inundation characteristics under various AIOT-based sensor networks.
Corresponding AIC values to the model performance indices of various inundation characteristics under various AIOT-based sensor networks.
) is calculated through Equation (17) as shown in Figure 18. Referring to Figure 17, the 
sharply drops from 2.132 (IoT-based sensor network) to nearly 1.377–1.79 (AIOT-based sensor networks). Specifically, in the case of the five AIOT grids, the corresponding 
reaches the minimum (around 1.337), indicating that the five representative AIOT grids could be treated as the appropriate ones, combined with the three practical IoT sensors as the optimal sensor network. 
Weighted average of AIC values under various AIOT-based sensor networks.
Verification of appropriate AIOT grids within the optimal sensor network
To demonstrate the advantage of the appropriate five AIOT grids in the optimal AIOT-based sensor network to 2D inundation simulation, the performance indices regarding 2D inundation simulation (
are utilized by Equations (19)–(21) (Wu 2023) with the results from the IOT-based and four AIOT-based sensor networks.
) calculated with the hourly inundation-depth hydrographs for IOT-based and four sets of AIOT-based sensor networks, indicating that the above performance indices have a considerable change with time; for example, concerning results from the five representative AIOT grids, 
deeply drops from 1.0 to 0 at the 8th hour and gradually rises to 0.4; otherwise, 
first drops from 1.0 to 0.35 at the 13th hour and then gradually rises to 0.608. Since the performance indices noticeably vary with time, the statistical properties (mean and standard deviation) of the three performance indices are computed as listed in Table 5. Observing Table 5, the corresponding averages of 
to the four sets of AIOT sensor network markedly oscillate between 0.517 and 0.521, slightly larger than the results from the SOBEK model with the maximum value (0.468) with a similar standard deviation (about 0.2); this reveals that similar to the graphical comparison, the average of the performance indices from the four sets of AIOT-based sensor network more significantly approach 1.0 closer than those for the IOT-based network. In addition to the gridded hourly inundation depths, the 2D inundation simulation performance indices are calculated in Table 5, indicating that the accuracy and reliability of the 2D inundation simulation with the inundation depths provided from the four sets of AIOT-based sensor networks are superior to those only from the practical IoT sensors as a result of the finer performance indices; for example, 
for the four sets of AIOT-based sensor networks are markedly over 0.7; in contrast, the result from the IoT-based sensor network only approximates 0.446. Statistical properties of 2D inundation simulation model indices for the IOT-based and four sets of AIOT-based sensor networks
| Number of AIOTs in the sensor network | Validation event |  |  |  | |
|---|---|---|---|---|---|
| 0 (IoT-based network) | Gridded inundation depth | Mean | 0.498 | 0.282 | 0.615 |
| Standard deviation | 0.202 | 0.233 | 0.177 | ||
| Maximum inundation depth | 0.566 | 0.345 | 0.446 | ||
| 5 | Gridded inundation depth | Mean | 0.521 | 0.352 | 0.629 |
| Standard deviation | 0.232 | 0.281 | 0.202 | ||
| Maximum inundation depth | 0.566 | 0.814 | 0.687 | ||
| 10 | Gridded inundation depth | Mean | 0.521 | 0.370 | 0.629 |
| Standard deviation | 0.232 | 0.271 | 0.202 | ||
| Maximum inundation depth | 0.586 | 0.811 | 0.730 | ||
| 15 | Gridded inundation depth | Mean | 0.521 | 0.355 | 0.629 |
| Standard deviation | 0.232 | 0.277 | 0.202 | ||
| Maximum inundation depth | 0.579 | 0.816 | 0.701 | ||
| 20 | Gridded inundation depth | Mean | 0.517 | 0.410 | 0.627 |
| Standard deviation | 0.232 | 0.261 | 0.202 | ||
| Maximum inundation depth | 0.585 | 0.807 | 0.728 | ||
| Number of AIOTs in the sensor network | Validation event | | | | |
|---|---|---|---|---|---|
| 0 (IoT-based network) | Gridded inundation depth | Mean | 0.498 | 0.282 | 0.615 |
| Standard deviation | 0.202 | 0.233 | 0.177 | ||
| Maximum inundation depth | 0.566 | 0.345 | 0.446 | ||
| 5 | Gridded inundation depth | Mean | 0.521 | 0.352 | 0.629 |
| Standard deviation | 0.232 | 0.281 | 0.202 | ||
| Maximum inundation depth | 0.566 | 0.814 | 0.687 | ||
| 10 | Gridded inundation depth | Mean | 0.521 | 0.370 | 0.629 |
| Standard deviation | 0.232 | 0.271 | 0.202 | ||
| Maximum inundation depth | 0.586 | 0.811 | 0.730 | ||
| 15 | Gridded inundation depth | Mean | 0.521 | 0.355 | 0.629 |
| Standard deviation | 0.232 | 0.277 | 0.202 | ||
| Maximum inundation depth | 0.579 | 0.816 | 0.701 | ||
| 20 | Gridded inundation depth | Mean | 0.517 | 0.410 | 0.627 |
| Standard deviation | 0.232 | 0.261 | 0.202 | ||
| Maximum inundation depth | 0.585 | 0.807 | 0.728 | ||
Comparison in time series of 2D inundation simulation model indices for the IOT-based and four AIOT-based sensor networks.
Comparison in time series of 2D inundation simulation model indices for the IOT-based and four AIOT-based sensor networks.
The above results from the model validation show that the four sets of AIOT-based sensor networks could effectively improve the accuracy and reliability of the 2D inundation simulation; however, the consistent results from the comparison in the four sets of AIOT-based sensor networks are hardly achieved based on the 2D inundation simulation performance indices calculated from the gridded hourly and maximum inundation depths, respectively, as shown in Table 5. For example, determined using the index 
calculated from the maximum inundation depths, the 15 AIOT grids exhibit a maximum (0.816), but the maximum value (0.410) could be obtained for the 20 AIOT grids from the hourly inundation depths. By doing so, the comparison of the four sets of AIOT-based sensor networks in the 2D inundation simulation could proceed with calculating the average of the performance indices from the average and maximum inundation depths as shown in Figure 20. It can be seen that the 2D inundation simulation performance indices for the resulting five AIOT-based optimal sensor networks hardly significantly exceed those for the remaining AIOT-based network, but with the approximations, including 0.7 (
), 0.6 (
), and 0.65 (
). This implies that the five representative AIOT grids could provide similar inundation characteristics in time and space to the more than five grids of AIOT sets in the 2D inundation simulation. In addition, concerning the locations of the AIOT grids (see Figure 11), the resulting five appropriate AIOT grids are shown to be more uniformly distributed in the study area (Miaoli City).
Comparison of the means of averaged 2D inundation simulation model indices for the IOT-based and four AIOT-based sensor networks.
Comparison of the means of averaged 2D inundation simulation model indices for the IOT-based and four AIOT-based sensor networks.
CONCLUSIONS
This study aims to model a framework for evaluating the spatial distribution of the added roadside water-level IoT sensors (named AIOT grids) based on the 2D inundation simulation via the ANN-derived flood simulation model (SM_EID_VIOT) (Wu et al. 2022), called SM_ESD_AIOT model. The proposed SM_ESD_AIOT model could capitalize on identifying the number of locations of added IoT sensors by using the cluster analysis with the model applicability AIC index. In detail, within the proposed SM_ESD_AIOT model, the appropriate amount and location of added IoT sensor could be determined based on the AIC values of the difference in the simulated inundation characteristics via the SM_EID_VIOT model from the results from the physically based hydrodynamic model (i.e., RMSE); thus, the number of the appreciated added IoT sensors and associated locations could be found out based on the minimum AIC value under consideration of various sets of the desired sensor network composed of the practical and potential added IoT sensors.
In this study, Miaoli City, located in northern Taiwan, is selected as the study area in which the photographic, hydraulic, and hydrological data, including the DEM, hydraulic structures, and gridded rainstorms are applied in the model development and demonstration; additionally, the 1,939 electrical poles are considered as the potential locations of added IoT sensors. The results from the model development reveal that adding IoT sensors could efficiently improve the inundation characteristics (i.e., spatial maximum inundation depths) accuracy nearly by 10%, under consideration of the added IoT sensors of 5, 10, 15, and 20 sets; also, although the precision of the 2D inundation simulation could be slightly improved from 0.6 to 0.7, the accuracy of estimated flooding extent has a significant increase by 25%. Eventually, among the four sets of added IoT sensors, the five added IoT sensors could be defined as the appropriate ones with a minimum AIC value (around 1.337) under a considerably uniform distribution in space. Therefore, increasing the five IoT sensors in the study area can significantly improve the accuracy and reliability of 2D inundation simulations and enhance flood early warning and mitigation performance.
Proceeding with the proposed SM_ESD_AIOT model, the appropriate amount and location of the added IoT sensors could be achieved based on the photographic features and inundation characteristics without considering the settlement cost. Accordingly, as well as identifying the optimal senor network via the cluster analysis with the AIC index, the proposed SM_ESD_AIOT model could capitalize on the cost-benefit analysis (e.g., Rose et al. 2023; Sikorski et al. 2022) to find out the appropriate locations of added IoT sensors. Additionally, it is well-known that existing uncertainties could be found in the rainfall and induced runoff and water levels in time and space due to climate change (e.g., Zhu et al. 2019; Gu et al. 2020; Zou et al. 2021). Therefore, future work would be done by quantifying and evaluating the effect of climate change on the design of the runoff water level-related IoT sensor networks.
ACKNOWLEDGEMENTS
This paper was funded by the National United University Project (Grant No. SM113004).
DATA AVAILABILITY STATEMENT
Data cannot be made publicly available; readers should contact the corresponding author for details.
CONFLICT OF INTEREST
The authors declare there is no conflict.
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