# Flood Susceptibility Mapping Using Image-Based 2D-CNN Deep Learning: Overview and Case Study Application Using Multiparametric Spatial Data in Data-Scarce Urban Environments

Authors: Yashon O. Ouma; Lawrence Omai
Journal: International Journal of Intelligent Systems
 (2023)

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## Abstract

This study presents results for urban flood susceptibility mapping (FSM) using image-based 2D-convolutional neural networks (2D-CNN). The model input multiparametric spatial data comprised of land-useland-cover (LULC), digital elevation model (DEM), and the topographic and hydrologic conditioning derivatives, precipitation, and soil types. The implemented dropout regularization 2D-CNN with ReLU activation function, categorical cross-entropy loss function, and AdaGrad optimizer produced the case study area FSM with overall accuracy (OA) of 82.5%. The image-based 2D-CNN outperformed the multilayer perceptron (MLP) neural network by 18.4% in terms of overall accuracy and with corresponding lower MAE and higherF1-measures of 10.9% and 0.989, as compared to 25.6% and 0.877, respectively, for MLP-ANN results. The accuracy of the 2D-CNN that produced FSM map and the model efficiency were evaluated using area under the ROC curve (AUC) with respective success and prediction rates of 0.827 and 0.809. Using image-based 2D-CNN, 27% of the 247.7 km2 of the studied area was mapped with a high risk of flooding, with MLP-ANN overestimating the degree of high flood risk by 4.7%. Based on the gain ratio index analysis of the flood conditioning factors (FCFs), the most significant FCFs were LULC (18.5%), precipitation (14.9%), proximity to river (13.3%), and elevation (12.4%). Soil types contributed 8.6%, slope 9.1%, and the DEM-derived hodological conditioning indicators contributed 23.2%. The study results demonstrate that in urban areas with scarce hydrological monitoring networks, the use of image-based 2D-CNN with multiparametric spatial data can produce high-quality flood susceptibility maps for flood management in urban environments.


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## Body

## 1. Introduction

Compared to other natural disasters such as volcanic eruptions, soil erosion, landslides, earthquakes, and tsunami, flooding is considered to have the highest socio-economic impact in our society. As recently witnessed in several parts of the world, the impacts include damage to infrastructure and shelter, displacement of the population, loss of property and life, as well as damage to the environment. According to Dewan [1] and Guha et al. [2], flooding was reported as the leading contributor to disaster-related deaths between 2005 and 2015 in African countries, South and Central America, and Central, South, and West Asia. In 2016, floods affected approximately 78 million people globally, contributed to 4,731 fatalities, and had a damaging impact equivalent to approximately US$60 billion [2].It is expected that with climate change and growing urban population and related anthropogenic activities, urban flood events and associated risks will increase. In Europe, for example, it is estimated that flooding will affect three-fold more people by 2050 resulting from climate change, and the damage costs are estimated at between 20 and 40 billion Euros [3]. These predictions may represent additional and complicated challenges regarding flood prevention and preparedness for developing countries [4]. To minimize and mitigate the impacts of floods, mapping, prediction, and development of flood early warning systems are necessary. Within urban environments, the prediction of the locations and extent of flood-prone areas under the existing anthropogenic activities and environmental and climate conditions are referred to as flood susceptibility or vulnerability mapping (FSM). For a given area, FSMs provide the qualitative identification and categorization of the flood prone and flood hazard areas and are useful for flood prevention and management measures. However, because of the complex patterns and structures of urban environments, the accurate production of flood prone areas is still a challenging task [5, 6].As summarized in Yang et al. [7], numerous approaches have been proposed towards the assessment of susceptibility of urban areas to flooding. Methods based on numerical modelling and multicriteria decision-analysis (MCDA) that integrate GIS and remote sensing have been proposed for zoning of flood vulnerability or susceptibility maps within urban areas [8, 9]. MCDA approaches, however, have the disadvantage that they rely on subjective expert knowledge and do not apply flood event data, and therefore their outputs are likely to be biased and prone to error [10]. On the other hand, hydrodynamic numerical models are intrinsically limited by the discretization of the physical domain of the watershed and the governing physical equations. They model floods as 1-D point events [11], even though the generation and flow routing of floodwater are highly dependent on the areal 2-D information such as spatially distributed rainfall intensity, land-use/land-cover distribution, and the topographical characteristics of the localized terrain [12, 13]. Additionally, the hydrodynamic models require lengthy hydrological data, and the limited replicability of developed methods at different scales and case studies renders them highly challenging for effective flood modelling, especially in data-scare regions [14–18]. Furthermore, the physically based and MCDA approaches consider flood susceptibility to either fluvial river floods or pluvial urban floods and are not suitable for modelling the combined and complex urban and river flooding scenarios [19–22].To deal with the shortcomings in the numerical models and MCDA approaches, machine learning techniques have been preferred as they are not data intensive and exhibit high predictive ability with superior accuracy [23–25]. Literature survey reveals several machine learning (ML) algorithms that have been formulated for flood susceptibility mapping. The ML algorithms can be categorized as follows: (i) functional algorithms comprising of, e.g., logistic regression (LR) [26], support vector machines (SVM) [16], and artificial neural networks (ANN) [13]; (ii) decision tree-based algorithms, e.g., logistic model trees (LMT) [27], Random Forest (RF) [28], Naïve Bayes Tree (NBT), and Alternating Decision Tree (ADT) [27] etc.; (iii) Bayes-based algorithms, e.g., Bayesian logistic regression (BLR) [28]. The performances of the ML algorithms are, however, reported to vary for different case studies and dependent on the specific input data [27, 29]. The observed differences can also be attributed to the different functional characteristics of the ML algorithms. For example, some of the algorithms such as LR can best explain the influence of the flood conditioning factors with low flood predictive ability. On the other hand, models such as BRT exhibit both high abilities in determining the influence of the flood causative factors as well as high predictive power. ANNs have high prediction ability but cannot determine the influence and role of the flood causative factors [30]. Due to the shortcomings of the standalone algorithms, hybrid ML algorithms have been proposed for improved flood susceptibility mapping [10].In applying hybrid ML algorithms for urban FSM, Khosravi et al. [27] benchmarked weights-of-evidence (WoE) and SVM with hybrid WoE-SVM model and concluded that the hybrid model performed better than the standalone models for case study of Brisbane in Australia. Shafizadeh−Moghadam et al. [30] coupled eight machine learning models with seven ensemble prediction algorithms and determined BRT-EMmedian as the best hybrid model for flood prediction. The ANFIS neuro-fuzzy algorithm has also been integrated with different metaheuristic algorithms for flood susceptibility mapping [26]. Other studies that implemented hybrid models for urban FSM include Darabi et al. [17] and Liu et al. [31]. It is, however, reported that the hybrid models do not always present positive results as concluded by Tien Bui et al. [26]. Besides their complexity in implementation, tendency to generate over generalized results and sensitivity to variable input data, the use of standalone and hybrid machine learning models in urban FSM does not adequately consider the complexity and influence of cell neighborhood spatial conditions in urban environments. The point-to-point-based models also tend not to incorporate nonflood locations and generally consider only the sum weights rather than weights for specific layers [32].To take into account the individual and the interactions of the flood conditioning factors and the spatial characteristics of the cell-to-cell influences in urban flood susceptibility mapping, it is essential to represent the flood conditioning factors in a 2-D structure [12, 13]. The 2-D representation offers a solution to the point-based modelling problem of flooding events by considering the environment in its entirety as an array of 2D urban features. However, simple images-to-arrays reshaping representations may result into the loss of topological structure and information, thus increasing the model computing time due to increased dimensionality and possible model overfitting and poor performance. For this reason, a more efficient image-based classification model for FSM and its assessment in urban environments is required.Since accurate flood prediction requires cell neighborhood condition integration from vast spatial-temporal data, deep learning (DL) algorithms have been recommended as more suitable for flood susceptibility mapping as compared to standalone SVM, RF, ANN, ANFIS, machine learning algorithms, or their hybridization [25, 26, 33, 34]. Deep learning algorithms offer advantages such as enabling adequate training of large datasets, performing unsupervised and semisupervised learning, and the ability to resolve complex and nonlinear relationships. Several investigations have introduced DL-based algorithms for flood susceptibility mapping, with Convolutional Neural Networks (CNN) as the most preferred DL approach [10, 13, 27, 35, 36]. Compared with other DL algorithms, CNN utilizes the information from adjacent pixels of the input image (raster) with much fewer trainable parameters and is, therefore, extremely suitable for solving 2-D image-based problems. Furthermore, due to the spatial inductive bias in CNNs, they are best suited for processing the 2D-raster data used in flood analysis [10]. Wang et al. [35] indicated that CNNs can get rid of the tedious feature engineering steps and extract useful information directly from the original data, and they can play an important role in FSM.For FSM, 1D-CNNs have been employed by e.g., Liu et al. [31], Dong et al. [37], and Guo et al. [38], while 3D-CNNs have been implemented by Wang et al. [35] and Fang et al. [39]. Zhao et al. [13] also compared CNN and RF for FSM with respective AUC accuracies of 0.90 and 0.78, while Lei et al. [36] showed that CNN outperformed RNN with AUCs of 0.84 and 0.82. Lei et al. [36] also mapped flash floods comparing CNN and ANFIS with the later performing at 13.2% higher in accuracy, and Gebrehiwot et al. [33] successfully applied CNN to identify flood ranges using unmanned aerial vehicle data. Although these studies reported CNN to be more accurate in FSM, most of the studies employed the 1D-CNN and 3D-CNN architectures. In their implementations, 1D-CNNs are based on event hydrographs, while 3D-CNNs utilize stacked flood conditioning input raster datasets based on layer sum weights [32]. The implementations of 1D-CNN and 3D-CNN do not, however, consider the area-based (cell-to-cell) influence of the flood conditioning factors as they assume the conditioning factors at a point that sufficiently represents surrounding cells. While this assumption may apply for homogenous land-cover environments, it is not suitable for highly heterogeneous and complex urban environments comprising of integrated natural features and artificial materials.Given the drawbacks of the 1D-CNN and 3D-CNN models and the fact that flood conditioning factors comprise of 2D-spatial images, image-based 2D-CNN is proposed in this study for FSM as it can efficiently capture the spatial relationship between the neighboring environmental parameters. Further to the positive results in 2-D image processing [40], the conventional 2D-CNN has demonstrated superior results as compared to 1D-CNN, LeNet-5, 3D-CNN, and other machine learning methods like SVM and Decision Tree [35]. The other advantage is that 2D-CNN allows different outputs to be run to reach an optimum result and employs a linear or unbiased variable selection model. As opposed to the commonly implemented 1D-CNN for flood susceptibility mapping, the 2D-CNN model can simultaneously utilize the labeled and unlabeled data to increase and maximize the predictive accuracy [34, 35]. This strategy overcomes the flood prediction problem based on learning with labeled inputs and outputs to generate the rules and latent relationships of data for the prediction of unobserved data [33].From the literature survey, most studies implemented 1D-CNNs and 3D-CNNs for FSM studies, with very few studies exploring image-based 2D-CNNs for urban environments [35, 39]. The goal of this study is to improve the accuracy of flood susceptibility mapping in complex urban environments with scarce hydrological monitoring data using image-based 2D-CNN. The objectives of the study are as follows: (1) to determine the significance of flood conditioning factors (FCFs) comprising of hydrological and meteorological factors, land-use and land-cover, geological (soil) factor, and topographic factors in an urban environment, and (2) to implement and evaluate the image-based 2D-CNN deep learning model for the production of high quality FSM for combined urban pluvial and river flooding based on historical flood inventory data for model training and validation. The study implements the image-based hyperparameter optimized 2D-CNN and compares the results with the multilayer perceptron (MLP) neural network.With the intensification of urbanization and climate change effects, seasonal flash flood events continue to be witnessed in most parts of urban areas. For urban flood management in such urban watersheds with scarce or nonexistent hydrological observations and flooding monitoring systems, it is important to develop methods for producing accurate flood susceptibility maps. The proposed approach is applied for the case study of Eldoret municipality in Kenya and can be replicated in other urban environments.


## 2. Study Area

The case study area is Eldoret municipality, located in Uasin Gishu County in Kenya (Figure1). Eldoret town is one of the fastest growing and sixth most populated urban areas in Kenya, with a population of approximately 475,716 inhabitants according to the 2019 national census. The municipality occupies an area of approximately 247.7 km2 with active residential, commercial, and industrial developments. The municipality is situated within the Sosiani River watershed, with the river and its tributaries traversing through the center of the municipality. The land rises from the Sosiani River valley at about 1,950 m to 2,120 m above sea level. Eldoret and the surrounding regions have a warm and temperate climate, characterized by moderate mean annual temperatures of 17.3°C and mean annual precipitation of 2027 mm.Figure 1
Location map of Eldoret municipality (Kenya). Insets are field photographs of flooding events in Eldoret municipality.The municipal area experiences seasonal flash floods that often results into fatalities, damage of property and infrastructure, and disrupts traffic, commerce, and public services [8]. The flash floods are the result of torrential rains and are exacerbated by the rapid urbanization phenomenon characterized by planned and unplanned constructions, deforestation, and the lack of flood control measures due to ineffective drainage infrastructure. The severity of the flood occurrences is compounded by combined urban pluvial floods and the river flooding. Inset in Figure 1 is flood event photographs recorded from previous floods within the study area as recorded between 2016 and 2019.Attributed to climate change, the patterns and intensity of the flash flood events have been unpredictable and increasing in frequency in the recent years. In such regions where early-warning systems are not in place, preparation of up-to-date flood susceptibility maps for flood disaster management tools are essential for informed decision making in urban planning and for continuous monitoring and management of the flooding.


## 3. Data and Methods

### 3.1. Flood Inventory Data (FID)

To develop and validate the urban flood susceptibility maps, the information on past flood events is required for accurate training, prediction, and evaluation of the flood forecasting model results. In this study, the FID was assembled based on previous flood event data observed by the regional Water Resources Authority (WRA) and field surveys. The FID consists of flood points and nonflood points with a maximum dimension of 30 m × 30 m. Both the urban and river flood and nonflood points (Figure2) were combined into a single training and validation database. Flood sample areas comprising of 159 flood points associated with urban and river flooding (Figure 2) were used for model training (70%) and model validation (30%). Figures 2(a) and 2(b), respectively, show the flood inventory data for urban and river flooding events in the study area.Figure 2
Flood inventory maps for flood and nonflood prone areas for (a) urban pluvial flooding and (b) river flooding.
(a)(b)


### 3.2. Multi Parameter Flood Conditioning Spatial Data

The selection of flood conditioning factors is largely dependent on the availability of the primary hydrological, anthropogenic, geological, and topographic factors. In previous studies, different flood conditioning factors have been used, and there are no specific guidelines on the selection of FCFs [41]. In this study, ten (10) urban flood conditioning factors (FCFs) were utilized to generate the FSM based on literature from previous studies [42], the local conditions, and the available data. All the FCFs were resampled to raster image data with spatial resolution of 12.5 m × 12.5 m grid cell sizes, which corresponds to the spatial resolution of the ALOS PALSAR DEM. The data details and sources are summarized in Table 1.Table 1
Case study flood conditioning factors (FCFs), sources, and resolution.
Input rowPrimary input dataData (original) formatSpatial resolution/scaleResampled and processed data formatResolution of resampled dataSource of data1Rainfall intensityPoint dataset11 stationsRaster grid12.5 × 12.5 mWater Resources Authority (WRA), Eldoret2Land-use and land-cover (LULC)Raster grid—Raster grid12.5 × 12.5 mLandsat TM, ETM+ and OLISentinel-2 MSI (https://earthexplorer.usgs.gov/)3DEM and derivativesRaster grid12.5 mRaster grid12.5 × 12.5 mALOS-PALSAR DEM (https://search.asf.alaska.edu/#/)4Soil mapVector1 : 500,000Raster grid12.5 × 12.5 mFAO5Flood inventory map (FIM)Point dataset—Raster grid12.5 × 12.5 mWRA, Google Earth imagery and field surveys


#### 3.2.1. Rainfall Intensity (RI)

In flood susceptibility mapping, rainfall has direct contributions and influence in triggering the occurrence of floods [43]. When the intensity of rainfall (RI) exceeds the capacity of infiltration for a given ground surface, runoff occurs, and the chances are higher if there is lack of adequate flow channels. For this study, 11 rain gauge stations were used to derive the spatial distribution of the RI. RI determines the total average monthly rainfall intensity per station. The RI was determined using the Modified Fournier Index equation (1):(1)MFI=RI=∑i=112ri2Rt,where ri is the monthly precipitation for a given month i and Rt is the annual precipitation. The mean annual rainfall intensity was classified into five categorical classes and reclassified from very low in regions with low precipitation averages and very high for regions receiving higher rainfall amounts with the RI results presented in Figures 3(a)–3(c), respectively, for the years 2000, 2010, and 2019. The RI maps in Figure 3 were spatially interpolated using the Inverse Distance Weighting (IDW) method [44]. Because of the small size of the study area and the sparse distribution of the gauge stations, the IDW interpolation tended to create isolated localized RIs.Figure 3
Rainfall intensity for the years 2000, 2010, and 2019.
(a)(b)(c)


#### 3.2.2. Land-Use and Land-Cover (LULC)

The degree and frequency of flooding within a catchment area are influenced and affected by the land-use and land-cover receptors. This is because the surface water runoff and infiltration depend on the composition and the pattern of the land-cover in addition to the other flood conditioning factors [8]. For example, vegetation density has a negative influence on surface water flow and thus negative correlation with flood occurrence, while impermeable urban surfaces and bare soil will create increased surface water flows due to low infiltrations. LULC was derived using maximum-likelihood supervised classification of 30 m Landsat data, while Google Earth images and field surveys were used for ground-truthing (Figure 4). The overall accuracy for the LULC classification results was greater than 90% for the three study years. The main LULC in the area comprised of agricultural land, water bodies and wetlands, built up areas, and forest cover. Figures 4(a)–4(c) show the LULC, respectively, for 2000, 2010, and 2019. To determine that the contribution of LULC changes towards flooding in the study case area, LULC change analysis was carried out for the three years. The LULC classes were reclassified into five categories in order of their capacity to influence the rate and extent of flooding.Figure 4
LULC for: (a) 2000, (b) 2010, and (c) 2019.
(a)(b)(c)The decadal LULC change from 1990 to 2019 is presented in Table2 and shows that while the water bodies remained largely unchanged, the built-up urban areas increased in areal coverage by nearly 40% from 1990 to 2019. The built-up comprised of residential, commercial, industrial, and paved surfaces by annexed lands from forest, grassland, and agricultural areas. The observed changes in built-up LULC are expected to influence the drainage systems by impacting the surface overflow and the surface infiltration capacity which in turn contributes to higher vulnerability to flooding phenomena.Table 2
LULC change statistics within Eldoret municipality.
Year (decade)LULC change (km2)Water and wetlandUrban built-upForest and grasslandAgricultural land199017.2 (6.9%)121.5 (49.1%)41.7 (16.8%)67.3 (27.2%)200017.1 (6.9%)142.8 (57.7%)30.9 (12.5%)56.9 (23.0%)201017.5 (7.1%)158.7 (64.1%)20.1 (8.1%)51.4 (20.8%)201917.8 (7.2%)170.6 (68.9%)23.2 (9.4%)36.1 (14.6%)


#### 3.2.3. Elevation

The continuous flow of a significant amount of rainwater can result into flash floods, especially in the lower and flat regions. Due to natural flow, lower elevations receive accumulated flow and are more susceptible to flooding events. The grid elevation data were obtained from 12.5 m × 12.5 m ALOS PALSER DEM and classified using natural breaks classification into five-classes with higher elevations (hilly areas) ranked as very low in terms of contributing to flooding phenomena and the low laying areas having very high vulnerability to flooding with the results in Figure5(a).Figure 5
Flood conditioning maps: (a) elevation, (b) slope, (c) flow direction, (d) flow accumulation, (e) SPI, (f) TWI, (g) DTR, and (h) soils.
(a)(b)(c)(d)(e)(f)(g)(h)


#### 3.2.4. Slope

Within a hydrographic catchment area, the direction of steepest descent influences the direction of runoff. This is because that for steeper slopes, the degree of infiltration will be minimal or negligible and thus the excessive runoff in steeper slopes constitutes rapid accumulations which can result into floods [45]. Notably, the elevation and slope topographic parameters contribute inversely to the occurrence of floods. The slope was observed to range from 0° to 22°. Using the Jenks classification method based on natural breaks [46], the slope gradient map was reclassified into five natural breaks as follows: 0°–4.38°, 4.38°–8.96°, 8.96°–13.73°, 13.73°–21.10°, and >21.10° (Figure 5(b)) and were corresponding to very low, low, moderate, high, and very high contributions to flooding.


#### 3.2.5. Flow Direction and Flow Accumulation

Flooding is directly related to the network of the drainage channels and their density within a catchment area. Drainage density results from the accumulation of water flow within the network. Flow accumulation is derived from the flow direction, and the flow direction specifies the direction of outgoing flow from each pixel. With the flow route known, the route with the larger volume of water will be determined as the flow direction. Flow accumulation represents the density of the drainage channels, and the surface water flow accumulation increases from the upstream divides to the catchment outlet. As such, greater accumulated flow will result in greater flood susceptibility. The derived flow direction (Figure5(c)) from the DEM was reclassified into four possible flow directions characterized by low, moderate, high, and very high potential directions of flow. If there is high precipitation and the other flood conditioning factors are invariant, then high flow accumulation (Figure 5(d)) will result into rapid flooding than for low flow accumulation [28]. Using natural breaks, the flow accumulation map was reclassified into the five classes (Figure 5(d)).


#### 3.2.6. SPI and TWI

Stream Power Index (SPI) and Topographic Wetness Index (TWI) are hydrological factors that condition and affect the spatial variation of flood events. Under steady-state conditions and uniform soil properties, Moore et al. [47] proposed that SPI and TWI can, respectively, be calculated according to equations (2) and (3). Areas with very low SPI are the most prone to flooding and are ranked as very high (Figure 5(e)). For TWI, very high floods would be generated in the areas characterized by high TWI, which depicts presence or closeness to drainage channels, and very low floods in the regions further away from the rivers and streams (Figure 5(f)).(2)SPI=As⋅tanβ,(3)TWI=lnAstanβ,where As is the contributing catchment area from the flow accumulation in (m2 m−1) and β is the slope (degrees).SPI tends to be higher for confined channels and often leads to the transformation of the channels and thus higher likelihood of occurrence of flooding. This was the concept applied in the reclassification of the SPI. Therefore, areas with very low SPI are the most prone to flooding and are ranked as very high.


#### 3.2.7. Distance to Rivers (DTR)

Characteristically, the distance to river channels will influence the spatial extent and magnitude of the flood events within an area. Within catchments, the regions adjacent to natural flow channels like rivers and streams are prone to both normal flooding and flash flooding scenarios since they accumulate the flow from higher elevations to lower elevations. Similarly, areas close to water bodies are also likely to be flooded in the event of heavy rains as the terrain within close buffers to these water bodies would be almost flat. Because of the low infiltration rates within the study area, flooding occurrences are common in the lower elevation regions. Based on our previous investigations in [8], only a single buffer of 100 m was selected to represent the influence of DTR in the study area (Figure 5(g)).


#### 3.2.8. Soils

While impermeable soils like clay soil cause more runoff due to slow infiltration thus speeding the possibility of flooding, sandy soils are more permeable and are subject to low runoff due to high infiltration. The soil map for this study was derived from data a 1 : 500,000 soil map of Kenya. The soils were classified into four soil types, namely, clay, clay loam, loam sandy, and sandy soils and reclassified accordingly on the basis of the soil infiltration capacity with the results in Figure5(h).


### 3.3. Framework for Image-Based 2D-CNN Model for Flood Susceptibility Mapping

There exist three architectures for CNN implementation. While 1D-CNN is mainly suited for sentence classification and signal processing [48], 3D-CNN is suited for video processing and the 3-D data form for CNN implementation that contains the attribute and spatial information for the local terrain. Thus 3D-CNN representation contains redundant information that would blur the classification and labeling accuracy [35, 49]. The use of 2D-CNN implies that flood conditioning factors are considered as 2-D feature vectors. This is suitable for overcoming the limitations in multiparametric spatial data processing and slow response to activation and gradient-based learning processes by using the image-based 2D-CNN algorithm, and the convolutional layers are able to automatically extract image features and reduce the dimensionality of the training parameters. Thus, the 2-D data form for FSM modelling simplifies CNN network data construction and correctly displays the attribute information as in the original data.For flood susceptibility modelling, the area comprises of a set of conditioning factors which can be represented as vectors in 1D-data as depicted in Figure6 [28]. Because the flood conditioning factors are 2D-images, the 2D-CNN is chosen as it has not only presented good results in 2-D image processing [49] but also because 2D-CNN has demonstrated superior results than 1D-CNN, LeNet-5, 3D-CNN, and other machine learning methods like SVM and Decision Tree [35]. 2D-CNN can be designed to process multiple arrayed data [48], and the pixels within a predefined neighborhood can be aggregated using a permutation invariant operation such as maximum or mean function. After the network convolutional stream, the regular and fully connected network layers are added, and the weights are independent [50]. Through its convolution and max-pooling layers, CNN is capable of identifying representations with high variability [43]. This characteristic makes CNN well-suited for processing multilayered 2-D raster with pixels arranged regularly. With this approach, 2D-CNN can minimize the complex environmental feature engineering requirements in FSM and can extract the required information from the raw data which is important in flood susceptibility mapping [35].Figure 6
Data representation of flood conditioning factors with input image data conversions to 1-D grid cell vector data and to 2-D matrix array data.The 2-D data form for FSM modelling is considered to be able to simplify the CNN network data construction and correctly display the attribute information as in the original data. The use of 2D-CNN implies that flood conditioning factors are considered as 2-D feature vectors (Figure6). In Figure 6, FSM modelling is considered as a binary task that classifies whether a pixel is a flood point 1 or a nonflood point 0 and predicts the 0,1 occurrence probability. Each pixel grid in the 2D-image is a feature vector containing different flood triggering or conditioning factors, and each image layer represents the flood conditioning or triggering factor which can be applied to 2D-CNN for FSM modelling in heterogeneous urban terrain environments.In flood prediction modelling, the chance of flood occurrence in each raster grid cell is related to the input flood causative or influencing factors. Thus, input data grid cell or pixel contains attributes that influence the chance of flood occurrence. In applying this concept to flood susceptibility mapping, the input attributes that feature grids should be represented in 2-D matrix array. In its implementation, the numbers of flood causing factors are compared with attributes for each factor, and the 2-D matrix size is defined by the larger factors and the attributes. If there are only single factors, the 2-D matrix will default to the single size for each conditioning factor implying 10 × 10 matrix for each cell (Figure6), since there are 10 FCFs in this study.


### 3.4. Evaluation of Significance of the Flood Conditioning Factors

#### 3.4.1. Gain Ratio (GR) Index

Using the information gain decision tree, the Gain Ratio index (GRI) is used to select features on the basis of their significance. From the GRI, the Average Merit Index (AMI) is determined, and the AMI determines the significance of the conditioning factors. IfS is the training set of the flooding factors and n represents the samples, the expected information ES is given as follows:(4)ES=−∑i=1npilogpi,where pi is the probability of belonging to class Ci. The attribute A has m values and its entropy TA and gain GA are given as follows:(5)TA=−∑i=1npiES,(6)GainA=ES−TA.The potential information obtained by splitting the training setS into m parts with corresponding m outcomes on attribute A, is determined by the split information (equation (7)), and the GRI of attribute A is finally obtained (equation Eq. (8)) as given as follows:(7)SplitInfoAS=−∑i=1mXiSiSlog2SiS,(8)GRIA=GainASplitInfoAS.The significance of the conditioning factor to flood occurrence is evaluated such that ifGRIA<0, then the factor is insignificant or irrelevant attribute for prediction.


#### 3.4.2. Multi Collinearity Analysis (MCA) of Flood Conditioning Factors

MCA determines the existence of relationships among the predictive factors. The study employed MCA using the variance inflation factor (VIF) and tolerance (TOL) indices to detect the degree of collinearity within the flood conditioning factors. IfA=A1,A2,…,AN defines a set of independent conditioning factor variables and Rj2 denotes the coefficient of determination for the variable Aj against the predictive factors, the VIF index is determined as in equation (9), and the TOL represents the linear correlation between the variables, that is TOL=1−Rj2 such that(9)VIF=11−Rj2=1TOL.For conditioning factor significance evaluation, ifVIF>10, the corresponding variables are unsuitable for inclusion in the flood model, hence discarded as model inputs.


### 3.5. 2D-Convolutional Neural Network

CNN is characterized by three hierarchical structures, namely, convolution layers, pooling layers, and fully connected layers. The input image is convolved at each convolution layer with a set ofK kernels W=W1,W2,…,Wk and added biases γ=γ1,γ2,…,γk, so as to generate Xk as the output feature map. The Xk features undergo an elementwise nonlinear transformation with σ⋅, such that for every convolutional layer, l:Xkl=σWkl-1∗Xl-1+bkl-1. Successively, the convolutional manipulation extracts different significant features at the input layers for learning and representation of the low-level features. Pooling manipulation in CNN is a down-sampling approach for the reduction of the dimensionality of the feature maps and without altering the depth of the feature maps. Through max-pooling, the feature is divided or decomposed and the maximum element from the feature(s) regions is selected. The feature maps are represented into finite rectangular areas resulting into the reduction of the data dimensionality, lowered computational costs, and the minimization of overfitting problem in neural network data learning process. The extracted features are reorganized by the fully connected layers to minimize any information loses, and the network classification results are finally produced by the output layers. The distinctive feature of CNN is in the ability to accurately represent the discovered features relative to other features.The 2D-CNN structure is a 2 : 2 :1 : 1 configuration, respectively, comprising of convolution layers, max-pooling layers, fully connected layer, and output layer (Figure7). For an input data of n × n image matrix, if the first convolutional layer (CONV1) applies N kernel filters of size a × a, the result will be (n – a + 1) × (n – a + 1) feature maps or N feature maps and the size of output feature maps will be n×n1/2 with the feature depth unaltered after applying a b × b max-pooling operation. Next, applying the dropout, a max-pool of size c × c, results in N matrices of n−a+1/c×n−a+1/c dimensions, which are conveyed to CONV2 with M kernels of a × a dimensions, and follows the second dropout (D2) manipulation. CONV2 comprises of L matrices with dimensions of n−c+1a−1/c×n−c+1a−1/c, which are transferred to D2 max-pooling layer M of a × a dimensions. The resultant M feature maps are n−c+1a−1/c2×n−c+1a−1/c2 in dimensions. The fully connected layer with m neural units reorganizes the extracted features, and the output layer produces the binary classification output comprising of “flooding” 1 and “nonflooding” 0. Figure 7 shows the topological architecture of the adopted 2D-CNN.Figure 7
Topological architecture of the 2D feedforward CNN. (a) represents the feature extraction phase; (b) represents the extracted features; (c) is the flood and nonflood classification processes of an output.In the implementation as shown in Figure7, the size of the images (image.s), size of kernel filters (filter.s), and the number of filters (filter.n) are set to determine the dimensionality of the convolutional layers. Using trial-and-error at the initial phase, the optimal 2D-CNN architecture for the convolutional layer is determined. The parametization features are determined as pooling size (pool.s=2), number of neurons (neurons.n=15), and drop rate (d.rate=0.2). In preliminary testing of the network, the image.s was varied to determine its influence on filter.s and filter.n.


#### 3.5.1. Data Representations for 2D-CNN

The 2D-data representation for CNN is as illustrated in Figure6. The 10 flood causative data layers build a 12.5 m × 12.5 m grid cell imagery, which is the input data that is transformed from 1-D vector array data to 2-D data matrix (Figure 6). For the 1-D data, the pixel vector represents an image with the flood causative attributes in each pixel. The dimension of the 1-D column vectors is equivalent to the number of the input flood causative factors, and each element in the column vector represents the attribute value of its flood causative factor.As depicted in Figure6, the 2-D matrix array data form is derived from the 1-D vector data by converting each into an n × n matrix, with n as the maximum between all the FCFs and total categories for each reclassified FCF. For this case, n = 10, as there are 10 causative factors against 5 maximum categories for each FCF. Each pixel value in the 1-D is expanded to 2-D array matrix of 10 × 10. Finally, for example, the first element of “1” (corresponding to elevation factor attribute) is converted to a row vector from the pixel vector with the output as [1 0 0 0 0 0 0 0 0 0], as depicted in Figure 6, to finally construct the 2-D 10 × 10 matrix input data.


#### 3.5.2. 2D-CNN Model Parametrization

The optimization and setting of the 2D-CNN network hyperparameters significantly impact the prediction performance of model [48]. The critical 2D-CNN hyperparameters are outlined as follows:(i)
Activation function: The Rectified Linear Unit (ReLU) activation was used for fitting the output data through the conversion of linear to nonlinear relationships [51].(ii)
Loss function and learning rate: Categorical cross-entropy function and the AdaGrad (Advanced adaptive Gradient), were respectively, used as the loss function and its optimizer. AdaGrad has the advantage of automatically adjusting the independent learning rates based on the gradient values of the variables in each dimension. For the production of each grid cell posteriori probability classification, the SoftMax function was used [52].(iii)
Dropout regularization: To reduce overfitting and for hidden unit adaptation, dropout integrates the neural and other random units [53]. This study implemented the 2D-CNN with and without the dropout regularization.(iv)
The model output was classified into five quantile ranking values as follows: 1−very low; 2−low; 3−moderate; 4−high; 5−very high. The rankings are applied to numeric data and according to their contribution to flooding.


### 3.6. Multilayer Perceptron (MLP) Neural Network

For comparison with the 2D-CNN, an optimal MLP-ANN with tanh activation function was constructed with the following structural parameters: (a) input neuron layer with range of x∈Rn for FCF = 10 input raster, (b) 3 hidden layers with 10 neurons each, and (c) output neuron layer with yk outputs where y∈Rk and ytk are the target outputs as determined from the flood inventory map.


### 3.7. Model Performance Evaluation Metrics

In addition toR2, the model performance was evaluated using Overall Accuracy (OA), Recall (RC), and Precision (PR), as defined in equations (10)–(14). OA is the ratio of the correctly classified flood pixels to the total training flood grid cells. The F-measure and MAE were also used to compare the results of the 2D-CNN with the MLP neural network.(10)RC=TPTP+FN,(11)PR=TPTP+FP,(12)OA=TP+TNTP+TN+FP+FN,(13)F−measure=2⋅PR⋅RCPR+RC,(14)MAE=1n∑n1pi−ti,where TP = true positives; TN = true negatives; FP = false positives, and FN = false negatives.AUC (equation (15)) and the Matthews correlation coefficient (MCC) (equation (16)) were utilized to deduce the accuracy of the output FSM. The AUC indicates the predictive index of the model by plotting the percentages of the cumulative flood susceptibility and the cumulative flood events within the area [54]. MCC determines the measure of prediction accuracy within candidate classes of different dimensions [55]. MCC represents the observed and output correlation factor, with MCC = 1 indicating perfect prediction and 0 ≤ MCC ≥ −1 representing random prediction results and disagreement between the training (observed) data and predicted results.(15)AUC=∑TP+∑TNTF+TNF,(16)MCC=TP⋅TN−FP⋅FNTP+FPTP+FNTN+FPTN+FN0.5,where TF and TNF are, respectively, the total number of flood and nonflood pixels.


### 3.8. Summary of Methodology Implementation

The schematic workflow for the proposed 2D-CNN model for the prediction of flooding using multiparametric spatial data is presented in Figure8.Figure 8
Framework for implementation of the urban flood susceptibility mapping using multiparametric spatial data with image-based 2D-CNN and MLP-ANN.


## 3.1. Flood Inventory Data (FID)

To develop and validate the urban flood susceptibility maps, the information on past flood events is required for accurate training, prediction, and evaluation of the flood forecasting model results. In this study, the FID was assembled based on previous flood event data observed by the regional Water Resources Authority (WRA) and field surveys. The FID consists of flood points and nonflood points with a maximum dimension of 30 m × 30 m. Both the urban and river flood and nonflood points (Figure2) were combined into a single training and validation database. Flood sample areas comprising of 159 flood points associated with urban and river flooding (Figure 2) were used for model training (70%) and model validation (30%). Figures 2(a) and 2(b), respectively, show the flood inventory data for urban and river flooding events in the study area.Figure 2
Flood inventory maps for flood and nonflood prone areas for (a) urban pluvial flooding and (b) river flooding.
(a)(b)


## 3.2. Multi Parameter Flood Conditioning Spatial Data

The selection of flood conditioning factors is largely dependent on the availability of the primary hydrological, anthropogenic, geological, and topographic factors. In previous studies, different flood conditioning factors have been used, and there are no specific guidelines on the selection of FCFs [41]. In this study, ten (10) urban flood conditioning factors (FCFs) were utilized to generate the FSM based on literature from previous studies [42], the local conditions, and the available data. All the FCFs were resampled to raster image data with spatial resolution of 12.5 m × 12.5 m grid cell sizes, which corresponds to the spatial resolution of the ALOS PALSAR DEM. The data details and sources are summarized in Table 1.Table 1
Case study flood conditioning factors (FCFs), sources, and resolution.
Input rowPrimary input dataData (original) formatSpatial resolution/scaleResampled and processed data formatResolution of resampled dataSource of data1Rainfall intensityPoint dataset11 stationsRaster grid12.5 × 12.5 mWater Resources Authority (WRA), Eldoret2Land-use and land-cover (LULC)Raster grid—Raster grid12.5 × 12.5 mLandsat TM, ETM+ and OLISentinel-2 MSI (https://earthexplorer.usgs.gov/)3DEM and derivativesRaster grid12.5 mRaster grid12.5 × 12.5 mALOS-PALSAR DEM (https://search.asf.alaska.edu/#/)4Soil mapVector1 : 500,000Raster grid12.5 × 12.5 mFAO5Flood inventory map (FIM)Point dataset—Raster grid12.5 × 12.5 mWRA, Google Earth imagery and field surveys


### 3.2.1. Rainfall Intensity (RI)

In flood susceptibility mapping, rainfall has direct contributions and influence in triggering the occurrence of floods [43]. When the intensity of rainfall (RI) exceeds the capacity of infiltration for a given ground surface, runoff occurs, and the chances are higher if there is lack of adequate flow channels. For this study, 11 rain gauge stations were used to derive the spatial distribution of the RI. RI determines the total average monthly rainfall intensity per station. The RI was determined using the Modified Fournier Index equation (1):(1)MFI=RI=∑i=112ri2Rt,where ri is the monthly precipitation for a given month i and Rt is the annual precipitation. The mean annual rainfall intensity was classified into five categorical classes and reclassified from very low in regions with low precipitation averages and very high for regions receiving higher rainfall amounts with the RI results presented in Figures 3(a)–3(c), respectively, for the years 2000, 2010, and 2019. The RI maps in Figure 3 were spatially interpolated using the Inverse Distance Weighting (IDW) method [44]. Because of the small size of the study area and the sparse distribution of the gauge stations, the IDW interpolation tended to create isolated localized RIs.Figure 3
Rainfall intensity for the years 2000, 2010, and 2019.
(a)(b)(c)


### 3.2.2. Land-Use and Land-Cover (LULC)

The degree and frequency of flooding within a catchment area are influenced and affected by the land-use and land-cover receptors. This is because the surface water runoff and infiltration depend on the composition and the pattern of the land-cover in addition to the other flood conditioning factors [8]. For example, vegetation density has a negative influence on surface water flow and thus negative correlation with flood occurrence, while impermeable urban surfaces and bare soil will create increased surface water flows due to low infiltrations. LULC was derived using maximum-likelihood supervised classification of 30 m Landsat data, while Google Earth images and field surveys were used for ground-truthing (Figure 4). The overall accuracy for the LULC classification results was greater than 90% for the three study years. The main LULC in the area comprised of agricultural land, water bodies and wetlands, built up areas, and forest cover. Figures 4(a)–4(c) show the LULC, respectively, for 2000, 2010, and 2019. To determine that the contribution of LULC changes towards flooding in the study case area, LULC change analysis was carried out for the three years. The LULC classes were reclassified into five categories in order of their capacity to influence the rate and extent of flooding.Figure 4
LULC for: (a) 2000, (b) 2010, and (c) 2019.
(a)(b)(c)The decadal LULC change from 1990 to 2019 is presented in Table2 and shows that while the water bodies remained largely unchanged, the built-up urban areas increased in areal coverage by nearly 40% from 1990 to 2019. The built-up comprised of residential, commercial, industrial, and paved surfaces by annexed lands from forest, grassland, and agricultural areas. The observed changes in built-up LULC are expected to influence the drainage systems by impacting the surface overflow and the surface infiltration capacity which in turn contributes to higher vulnerability to flooding phenomena.Table 2
LULC change statistics within Eldoret municipality.
Year (decade)LULC change (km2)Water and wetlandUrban built-upForest and grasslandAgricultural land199017.2 (6.9%)121.5 (49.1%)41.7 (16.8%)67.3 (27.2%)200017.1 (6.9%)142.8 (57.7%)30.9 (12.5%)56.9 (23.0%)201017.5 (7.1%)158.7 (64.1%)20.1 (8.1%)51.4 (20.8%)201917.8 (7.2%)170.6 (68.9%)23.2 (9.4%)36.1 (14.6%)


### 3.2.3. Elevation

The continuous flow of a significant amount of rainwater can result into flash floods, especially in the lower and flat regions. Due to natural flow, lower elevations receive accumulated flow and are more susceptible to flooding events. The grid elevation data were obtained from 12.5 m × 12.5 m ALOS PALSER DEM and classified using natural breaks classification into five-classes with higher elevations (hilly areas) ranked as very low in terms of contributing to flooding phenomena and the low laying areas having very high vulnerability to flooding with the results in Figure5(a).Figure 5
Flood conditioning maps: (a) elevation, (b) slope, (c) flow direction, (d) flow accumulation, (e) SPI, (f) TWI, (g) DTR, and (h) soils.
(a)(b)(c)(d)(e)(f)(g)(h)


### 3.2.4. Slope

Within a hydrographic catchment area, the direction of steepest descent influences the direction of runoff. This is because that for steeper slopes, the degree of infiltration will be minimal or negligible and thus the excessive runoff in steeper slopes constitutes rapid accumulations which can result into floods [45]. Notably, the elevation and slope topographic parameters contribute inversely to the occurrence of floods. The slope was observed to range from 0° to 22°. Using the Jenks classification method based on natural breaks [46], the slope gradient map was reclassified into five natural breaks as follows: 0°–4.38°, 4.38°–8.96°, 8.96°–13.73°, 13.73°–21.10°, and >21.10° (Figure 5(b)) and were corresponding to very low, low, moderate, high, and very high contributions to flooding.


### 3.2.5. Flow Direction and Flow Accumulation

Flooding is directly related to the network of the drainage channels and their density within a catchment area. Drainage density results from the accumulation of water flow within the network. Flow accumulation is derived from the flow direction, and the flow direction specifies the direction of outgoing flow from each pixel. With the flow route known, the route with the larger volume of water will be determined as the flow direction. Flow accumulation represents the density of the drainage channels, and the surface water flow accumulation increases from the upstream divides to the catchment outlet. As such, greater accumulated flow will result in greater flood susceptibility. The derived flow direction (Figure5(c)) from the DEM was reclassified into four possible flow directions characterized by low, moderate, high, and very high potential directions of flow. If there is high precipitation and the other flood conditioning factors are invariant, then high flow accumulation (Figure 5(d)) will result into rapid flooding than for low flow accumulation [28]. Using natural breaks, the flow accumulation map was reclassified into the five classes (Figure 5(d)).


### 3.2.6. SPI and TWI

Stream Power Index (SPI) and Topographic Wetness Index (TWI) are hydrological factors that condition and affect the spatial variation of flood events. Under steady-state conditions and uniform soil properties, Moore et al. [47] proposed that SPI and TWI can, respectively, be calculated according to equations (2) and (3). Areas with very low SPI are the most prone to flooding and are ranked as very high (Figure 5(e)). For TWI, very high floods would be generated in the areas characterized by high TWI, which depicts presence or closeness to drainage channels, and very low floods in the regions further away from the rivers and streams (Figure 5(f)).(2)SPI=As⋅tanβ,(3)TWI=lnAstanβ,where As is the contributing catchment area from the flow accumulation in (m2 m−1) and β is the slope (degrees).SPI tends to be higher for confined channels and often leads to the transformation of the channels and thus higher likelihood of occurrence of flooding. This was the concept applied in the reclassification of the SPI. Therefore, areas with very low SPI are the most prone to flooding and are ranked as very high.


### 3.2.7. Distance to Rivers (DTR)

Characteristically, the distance to river channels will influence the spatial extent and magnitude of the flood events within an area. Within catchments, the regions adjacent to natural flow channels like rivers and streams are prone to both normal flooding and flash flooding scenarios since they accumulate the flow from higher elevations to lower elevations. Similarly, areas close to water bodies are also likely to be flooded in the event of heavy rains as the terrain within close buffers to these water bodies would be almost flat. Because of the low infiltration rates within the study area, flooding occurrences are common in the lower elevation regions. Based on our previous investigations in [8], only a single buffer of 100 m was selected to represent the influence of DTR in the study area (Figure 5(g)).


### 3.2.8. Soils

While impermeable soils like clay soil cause more runoff due to slow infiltration thus speeding the possibility of flooding, sandy soils are more permeable and are subject to low runoff due to high infiltration. The soil map for this study was derived from data a 1 : 500,000 soil map of Kenya. The soils were classified into four soil types, namely, clay, clay loam, loam sandy, and sandy soils and reclassified accordingly on the basis of the soil infiltration capacity with the results in Figure5(h).


## 3.2.1. Rainfall Intensity (RI)

In flood susceptibility mapping, rainfall has direct contributions and influence in triggering the occurrence of floods [43]. When the intensity of rainfall (RI) exceeds the capacity of infiltration for a given ground surface, runoff occurs, and the chances are higher if there is lack of adequate flow channels. For this study, 11 rain gauge stations were used to derive the spatial distribution of the RI. RI determines the total average monthly rainfall intensity per station. The RI was determined using the Modified Fournier Index equation (1):(1)MFI=RI=∑i=112ri2Rt,where ri is the monthly precipitation for a given month i and Rt is the annual precipitation. The mean annual rainfall intensity was classified into five categorical classes and reclassified from very low in regions with low precipitation averages and very high for regions receiving higher rainfall amounts with the RI results presented in Figures 3(a)–3(c), respectively, for the years 2000, 2010, and 2019. The RI maps in Figure 3 were spatially interpolated using the Inverse Distance Weighting (IDW) method [44]. Because of the small size of the study area and the sparse distribution of the gauge stations, the IDW interpolation tended to create isolated localized RIs.Figure 3
Rainfall intensity for the years 2000, 2010, and 2019.
(a)(b)(c)


## 3.2.2. Land-Use and Land-Cover (LULC)

The degree and frequency of flooding within a catchment area are influenced and affected by the land-use and land-cover receptors. This is because the surface water runoff and infiltration depend on the composition and the pattern of the land-cover in addition to the other flood conditioning factors [8]. For example, vegetation density has a negative influence on surface water flow and thus negative correlation with flood occurrence, while impermeable urban surfaces and bare soil will create increased surface water flows due to low infiltrations. LULC was derived using maximum-likelihood supervised classification of 30 m Landsat data, while Google Earth images and field surveys were used for ground-truthing (Figure 4). The overall accuracy for the LULC classification results was greater than 90% for the three study years. The main LULC in the area comprised of agricultural land, water bodies and wetlands, built up areas, and forest cover. Figures 4(a)–4(c) show the LULC, respectively, for 2000, 2010, and 2019. To determine that the contribution of LULC changes towards flooding in the study case area, LULC change analysis was carried out for the three years. The LULC classes were reclassified into five categories in order of their capacity to influence the rate and extent of flooding.Figure 4
LULC for: (a) 2000, (b) 2010, and (c) 2019.
(a)(b)(c)The decadal LULC change from 1990 to 2019 is presented in Table2 and shows that while the water bodies remained largely unchanged, the built-up urban areas increased in areal coverage by nearly 40% from 1990 to 2019. The built-up comprised of residential, commercial, industrial, and paved surfaces by annexed lands from forest, grassland, and agricultural areas. The observed changes in built-up LULC are expected to influence the drainage systems by impacting the surface overflow and the surface infiltration capacity which in turn contributes to higher vulnerability to flooding phenomena.Table 2
LULC change statistics within Eldoret municipality.
Year (decade)LULC change (km2)Water and wetlandUrban built-upForest and grasslandAgricultural land199017.2 (6.9%)121.5 (49.1%)41.7 (16.8%)67.3 (27.2%)200017.1 (6.9%)142.8 (57.7%)30.9 (12.5%)56.9 (23.0%)201017.5 (7.1%)158.7 (64.1%)20.1 (8.1%)51.4 (20.8%)201917.8 (7.2%)170.6 (68.9%)23.2 (9.4%)36.1 (14.6%)


## 3.2.3. Elevation

The continuous flow of a significant amount of rainwater can result into flash floods, especially in the lower and flat regions. Due to natural flow, lower elevations receive accumulated flow and are more susceptible to flooding events. The grid elevation data were obtained from 12.5 m × 12.5 m ALOS PALSER DEM and classified using natural breaks classification into five-classes with higher elevations (hilly areas) ranked as very low in terms of contributing to flooding phenomena and the low laying areas having very high vulnerability to flooding with the results in Figure5(a).Figure 5
Flood conditioning maps: (a) elevation, (b) slope, (c) flow direction, (d) flow accumulation, (e) SPI, (f) TWI, (g) DTR, and (h) soils.
(a)(b)(c)(d)(e)(f)(g)(h)


## 3.2.4. Slope

Within a hydrographic catchment area, the direction of steepest descent influences the direction of runoff. This is because that for steeper slopes, the degree of infiltration will be minimal or negligible and thus the excessive runoff in steeper slopes constitutes rapid accumulations which can result into floods [45]. Notably, the elevation and slope topographic parameters contribute inversely to the occurrence of floods. The slope was observed to range from 0° to 22°. Using the Jenks classification method based on natural breaks [46], the slope gradient map was reclassified into five natural breaks as follows: 0°–4.38°, 4.38°–8.96°, 8.96°–13.73°, 13.73°–21.10°, and >21.10° (Figure 5(b)) and were corresponding to very low, low, moderate, high, and very high contributions to flooding.


## 3.2.5. Flow Direction and Flow Accumulation

Flooding is directly related to the network of the drainage channels and their density within a catchment area. Drainage density results from the accumulation of water flow within the network. Flow accumulation is derived from the flow direction, and the flow direction specifies the direction of outgoing flow from each pixel. With the flow route known, the route with the larger volume of water will be determined as the flow direction. Flow accumulation represents the density of the drainage channels, and the surface water flow accumulation increases from the upstream divides to the catchment outlet. As such, greater accumulated flow will result in greater flood susceptibility. The derived flow direction (Figure5(c)) from the DEM was reclassified into four possible flow directions characterized by low, moderate, high, and very high potential directions of flow. If there is high precipitation and the other flood conditioning factors are invariant, then high flow accumulation (Figure 5(d)) will result into rapid flooding than for low flow accumulation [28]. Using natural breaks, the flow accumulation map was reclassified into the five classes (Figure 5(d)).


## 3.2.6. SPI and TWI

Stream Power Index (SPI) and Topographic Wetness Index (TWI) are hydrological factors that condition and affect the spatial variation of flood events. Under steady-state conditions and uniform soil properties, Moore et al. [47] proposed that SPI and TWI can, respectively, be calculated according to equations (2) and (3). Areas with very low SPI are the most prone to flooding and are ranked as very high (Figure 5(e)). For TWI, very high floods would be generated in the areas characterized by high TWI, which depicts presence or closeness to drainage channels, and very low floods in the regions further away from the rivers and streams (Figure 5(f)).(2)SPI=As⋅tanβ,(3)TWI=lnAstanβ,where As is the contributing catchment area from the flow accumulation in (m2 m−1) and β is the slope (degrees).SPI tends to be higher for confined channels and often leads to the transformation of the channels and thus higher likelihood of occurrence of flooding. This was the concept applied in the reclassification of the SPI. Therefore, areas with very low SPI are the most prone to flooding and are ranked as very high.


## 3.2.7. Distance to Rivers (DTR)

Characteristically, the distance to river channels will influence the spatial extent and magnitude of the flood events within an area. Within catchments, the regions adjacent to natural flow channels like rivers and streams are prone to both normal flooding and flash flooding scenarios since they accumulate the flow from higher elevations to lower elevations. Similarly, areas close to water bodies are also likely to be flooded in the event of heavy rains as the terrain within close buffers to these water bodies would be almost flat. Because of the low infiltration rates within the study area, flooding occurrences are common in the lower elevation regions. Based on our previous investigations in [8], only a single buffer of 100 m was selected to represent the influence of DTR in the study area (Figure 5(g)).


## 3.2.8. Soils

While impermeable soils like clay soil cause more runoff due to slow infiltration thus speeding the possibility of flooding, sandy soils are more permeable and are subject to low runoff due to high infiltration. The soil map for this study was derived from data a 1 : 500,000 soil map of Kenya. The soils were classified into four soil types, namely, clay, clay loam, loam sandy, and sandy soils and reclassified accordingly on the basis of the soil infiltration capacity with the results in Figure5(h).


## 3.3. Framework for Image-Based 2D-CNN Model for Flood Susceptibility Mapping

There exist three architectures for CNN implementation. While 1D-CNN is mainly suited for sentence classification and signal processing [48], 3D-CNN is suited for video processing and the 3-D data form for CNN implementation that contains the attribute and spatial information for the local terrain. Thus 3D-CNN representation contains redundant information that would blur the classification and labeling accuracy [35, 49]. The use of 2D-CNN implies that flood conditioning factors are considered as 2-D feature vectors. This is suitable for overcoming the limitations in multiparametric spatial data processing and slow response to activation and gradient-based learning processes by using the image-based 2D-CNN algorithm, and the convolutional layers are able to automatically extract image features and reduce the dimensionality of the training parameters. Thus, the 2-D data form for FSM modelling simplifies CNN network data construction and correctly displays the attribute information as in the original data.For flood susceptibility modelling, the area comprises of a set of conditioning factors which can be represented as vectors in 1D-data as depicted in Figure6 [28]. Because the flood conditioning factors are 2D-images, the 2D-CNN is chosen as it has not only presented good results in 2-D image processing [49] but also because 2D-CNN has demonstrated superior results than 1D-CNN, LeNet-5, 3D-CNN, and other machine learning methods like SVM and Decision Tree [35]. 2D-CNN can be designed to process multiple arrayed data [48], and the pixels within a predefined neighborhood can be aggregated using a permutation invariant operation such as maximum or mean function. After the network convolutional stream, the regular and fully connected network layers are added, and the weights are independent [50]. Through its convolution and max-pooling layers, CNN is capable of identifying representations with high variability [43]. This characteristic makes CNN well-suited for processing multilayered 2-D raster with pixels arranged regularly. With this approach, 2D-CNN can minimize the complex environmental feature engineering requirements in FSM and can extract the required information from the raw data which is important in flood susceptibility mapping [35].Figure 6
Data representation of flood conditioning factors with input image data conversions to 1-D grid cell vector data and to 2-D matrix array data.The 2-D data form for FSM modelling is considered to be able to simplify the CNN network data construction and correctly display the attribute information as in the original data. The use of 2D-CNN implies that flood conditioning factors are considered as 2-D feature vectors (Figure6). In Figure 6, FSM modelling is considered as a binary task that classifies whether a pixel is a flood point 1 or a nonflood point 0 and predicts the 0,1 occurrence probability. Each pixel grid in the 2D-image is a feature vector containing different flood triggering or conditioning factors, and each image layer represents the flood conditioning or triggering factor which can be applied to 2D-CNN for FSM modelling in heterogeneous urban terrain environments.In flood prediction modelling, the chance of flood occurrence in each raster grid cell is related to the input flood causative or influencing factors. Thus, input data grid cell or pixel contains attributes that influence the chance of flood occurrence. In applying this concept to flood susceptibility mapping, the input attributes that feature grids should be represented in 2-D matrix array. In its implementation, the numbers of flood causing factors are compared with attributes for each factor, and the 2-D matrix size is defined by the larger factors and the attributes. If there are only single factors, the 2-D matrix will default to the single size for each conditioning factor implying 10 × 10 matrix for each cell (Figure6), since there are 10 FCFs in this study.


## 3.4. Evaluation of Significance of the Flood Conditioning Factors

### 3.4.1. Gain Ratio (GR) Index

Using the information gain decision tree, the Gain Ratio index (GRI) is used to select features on the basis of their significance. From the GRI, the Average Merit Index (AMI) is determined, and the AMI determines the significance of the conditioning factors. IfS is the training set of the flooding factors and n represents the samples, the expected information ES is given as follows:(4)ES=−∑i=1npilogpi,where pi is the probability of belonging to class Ci. The attribute A has m values and its entropy TA and gain GA are given as follows:(5)TA=−∑i=1npiES,(6)GainA=ES−TA.The potential information obtained by splitting the training setS into m parts with corresponding m outcomes on attribute A, is determined by the split information (equation (7)), and the GRI of attribute A is finally obtained (equation Eq. (8)) as given as follows:(7)SplitInfoAS=−∑i=1mXiSiSlog2SiS,(8)GRIA=GainASplitInfoAS.The significance of the conditioning factor to flood occurrence is evaluated such that ifGRIA<0, then the factor is insignificant or irrelevant attribute for prediction.


### 3.4.2. Multi Collinearity Analysis (MCA) of Flood Conditioning Factors

MCA determines the existence of relationships among the predictive factors. The study employed MCA using the variance inflation factor (VIF) and tolerance (TOL) indices to detect the degree of collinearity within the flood conditioning factors. IfA=A1,A2,…,AN defines a set of independent conditioning factor variables and Rj2 denotes the coefficient of determination for the variable Aj against the predictive factors, the VIF index is determined as in equation (9), and the TOL represents the linear correlation between the variables, that is TOL=1−Rj2 such that(9)VIF=11−Rj2=1TOL.For conditioning factor significance evaluation, ifVIF>10, the corresponding variables are unsuitable for inclusion in the flood model, hence discarded as model inputs.


## 3.4.1. Gain Ratio (GR) Index

Using the information gain decision tree, the Gain Ratio index (GRI) is used to select features on the basis of their significance. From the GRI, the Average Merit Index (AMI) is determined, and the AMI determines the significance of the conditioning factors. IfS is the training set of the flooding factors and n represents the samples, the expected information ES is given as follows:(4)ES=−∑i=1npilogpi,where pi is the probability of belonging to class Ci. The attribute A has m values and its entropy TA and gain GA are given as follows:(5)TA=−∑i=1npiES,(6)GainA=ES−TA.The potential information obtained by splitting the training setS into m parts with corresponding m outcomes on attribute A, is determined by the split information (equation (7)), and the GRI of attribute A is finally obtained (equation Eq. (8)) as given as follows:(7)SplitInfoAS=−∑i=1mXiSiSlog2SiS,(8)GRIA=GainASplitInfoAS.The significance of the conditioning factor to flood occurrence is evaluated such that ifGRIA<0, then the factor is insignificant or irrelevant attribute for prediction.


## 3.4.2. Multi Collinearity Analysis (MCA) of Flood Conditioning Factors

MCA determines the existence of relationships among the predictive factors. The study employed MCA using the variance inflation factor (VIF) and tolerance (TOL) indices to detect the degree of collinearity within the flood conditioning factors. IfA=A1,A2,…,AN defines a set of independent conditioning factor variables and Rj2 denotes the coefficient of determination for the variable Aj against the predictive factors, the VIF index is determined as in equation (9), and the TOL represents the linear correlation between the variables, that is TOL=1−Rj2 such that(9)VIF=11−Rj2=1TOL.For conditioning factor significance evaluation, ifVIF>10, the corresponding variables are unsuitable for inclusion in the flood model, hence discarded as model inputs.


## 3.5. 2D-Convolutional Neural Network

CNN is characterized by three hierarchical structures, namely, convolution layers, pooling layers, and fully connected layers. The input image is convolved at each convolution layer with a set ofK kernels W=W1,W2,…,Wk and added biases γ=γ1,γ2,…,γk, so as to generate Xk as the output feature map. The Xk features undergo an elementwise nonlinear transformation with σ⋅, such that for every convolutional layer, l:Xkl=σWkl-1∗Xl-1+bkl-1. Successively, the convolutional manipulation extracts different significant features at the input layers for learning and representation of the low-level features. Pooling manipulation in CNN is a down-sampling approach for the reduction of the dimensionality of the feature maps and without altering the depth of the feature maps. Through max-pooling, the feature is divided or decomposed and the maximum element from the feature(s) regions is selected. The feature maps are represented into finite rectangular areas resulting into the reduction of the data dimensionality, lowered computational costs, and the minimization of overfitting problem in neural network data learning process. The extracted features are reorganized by the fully connected layers to minimize any information loses, and the network classification results are finally produced by the output layers. The distinctive feature of CNN is in the ability to accurately represent the discovered features relative to other features.The 2D-CNN structure is a 2 : 2 :1 : 1 configuration, respectively, comprising of convolution layers, max-pooling layers, fully connected layer, and output layer (Figure7). For an input data of n × n image matrix, if the first convolutional layer (CONV1) applies N kernel filters of size a × a, the result will be (n – a + 1) × (n – a + 1) feature maps or N feature maps and the size of output feature maps will be n×n1/2 with the feature depth unaltered after applying a b × b max-pooling operation. Next, applying the dropout, a max-pool of size c × c, results in N matrices of n−a+1/c×n−a+1/c dimensions, which are conveyed to CONV2 with M kernels of a × a dimensions, and follows the second dropout (D2) manipulation. CONV2 comprises of L matrices with dimensions of n−c+1a−1/c×n−c+1a−1/c, which are transferred to D2 max-pooling layer M of a × a dimensions. The resultant M feature maps are n−c+1a−1/c2×n−c+1a−1/c2 in dimensions. The fully connected layer with m neural units reorganizes the extracted features, and the output layer produces the binary classification output comprising of “flooding” 1 and “nonflooding” 0. Figure 7 shows the topological architecture of the adopted 2D-CNN.Figure 7
Topological architecture of the 2D feedforward CNN. (a) represents the feature extraction phase; (b) represents the extracted features; (c) is the flood and nonflood classification processes of an output.In the implementation as shown in Figure7, the size of the images (image.s), size of kernel filters (filter.s), and the number of filters (filter.n) are set to determine the dimensionality of the convolutional layers. Using trial-and-error at the initial phase, the optimal 2D-CNN architecture for the convolutional layer is determined. The parametization features are determined as pooling size (pool.s=2), number of neurons (neurons.n=15), and drop rate (d.rate=0.2). In preliminary testing of the network, the image.s was varied to determine its influence on filter.s and filter.n.


### 3.5.1. Data Representations for 2D-CNN

The 2D-data representation for CNN is as illustrated in Figure6. The 10 flood causative data layers build a 12.5 m × 12.5 m grid cell imagery, which is the input data that is transformed from 1-D vector array data to 2-D data matrix (Figure 6). For the 1-D data, the pixel vector represents an image with the flood causative attributes in each pixel. The dimension of the 1-D column vectors is equivalent to the number of the input flood causative factors, and each element in the column vector represents the attribute value of its flood causative factor.As depicted in Figure6, the 2-D matrix array data form is derived from the 1-D vector data by converting each into an n × n matrix, with n as the maximum between all the FCFs and total categories for each reclassified FCF. For this case, n = 10, as there are 10 causative factors against 5 maximum categories for each FCF. Each pixel value in the 1-D is expanded to 2-D array matrix of 10 × 10. Finally, for example, the first element of “1” (corresponding to elevation factor attribute) is converted to a row vector from the pixel vector with the output as [1 0 0 0 0 0 0 0 0 0], as depicted in Figure 6, to finally construct the 2-D 10 × 10 matrix input data.


### 3.5.2. 2D-CNN Model Parametrization

The optimization and setting of the 2D-CNN network hyperparameters significantly impact the prediction performance of model [48]. The critical 2D-CNN hyperparameters are outlined as follows:(i)
Activation function: The Rectified Linear Unit (ReLU) activation was used for fitting the output data through the conversion of linear to nonlinear relationships [51].(ii)
Loss function and learning rate: Categorical cross-entropy function and the AdaGrad (Advanced adaptive Gradient), were respectively, used as the loss function and its optimizer. AdaGrad has the advantage of automatically adjusting the independent learning rates based on the gradient values of the variables in each dimension. For the production of each grid cell posteriori probability classification, the SoftMax function was used [52].(iii)
Dropout regularization: To reduce overfitting and for hidden unit adaptation, dropout integrates the neural and other random units [53]. This study implemented the 2D-CNN with and without the dropout regularization.(iv)
The model output was classified into five quantile ranking values as follows: 1−very low; 2−low; 3−moderate; 4−high; 5−very high. The rankings are applied to numeric data and according to their contribution to flooding.


## 3.5.1. Data Representations for 2D-CNN

The 2D-data representation for CNN is as illustrated in Figure6. The 10 flood causative data layers build a 12.5 m × 12.5 m grid cell imagery, which is the input data that is transformed from 1-D vector array data to 2-D data matrix (Figure 6). For the 1-D data, the pixel vector represents an image with the flood causative attributes in each pixel. The dimension of the 1-D column vectors is equivalent to the number of the input flood causative factors, and each element in the column vector represents the attribute value of its flood causative factor.As depicted in Figure6, the 2-D matrix array data form is derived from the 1-D vector data by converting each into an n × n matrix, with n as the maximum between all the FCFs and total categories for each reclassified FCF. For this case, n = 10, as there are 10 causative factors against 5 maximum categories for each FCF. Each pixel value in the 1-D is expanded to 2-D array matrix of 10 × 10. Finally, for example, the first element of “1” (corresponding to elevation factor attribute) is converted to a row vector from the pixel vector with the output as [1 0 0 0 0 0 0 0 0 0], as depicted in Figure 6, to finally construct the 2-D 10 × 10 matrix input data.


## 3.5.2. 2D-CNN Model Parametrization

The optimization and setting of the 2D-CNN network hyperparameters significantly impact the prediction performance of model [48]. The critical 2D-CNN hyperparameters are outlined as follows:(i)
Activation function: The Rectified Linear Unit (ReLU) activation was used for fitting the output data through the conversion of linear to nonlinear relationships [51].(ii)
Loss function and learning rate: Categorical cross-entropy function and the AdaGrad (Advanced adaptive Gradient), were respectively, used as the loss function and its optimizer. AdaGrad has the advantage of automatically adjusting the independent learning rates based on the gradient values of the variables in each dimension. For the production of each grid cell posteriori probability classification, the SoftMax function was used [52].(iii)
Dropout regularization: To reduce overfitting and for hidden unit adaptation, dropout integrates the neural and other random units [53]. This study implemented the 2D-CNN with and without the dropout regularization.(iv)
The model output was classified into five quantile ranking values as follows: 1−very low; 2−low; 3−moderate; 4−high; 5−very high. The rankings are applied to numeric data and according to their contribution to flooding.


## 3.6. Multilayer Perceptron (MLP) Neural Network

For comparison with the 2D-CNN, an optimal MLP-ANN with tanh activation function was constructed with the following structural parameters: (a) input neuron layer with range of x∈Rn for FCF = 10 input raster, (b) 3 hidden layers with 10 neurons each, and (c) output neuron layer with yk outputs where y∈Rk and ytk are the target outputs as determined from the flood inventory map.


## 3.7. Model Performance Evaluation Metrics

In addition toR2, the model performance was evaluated using Overall Accuracy (OA), Recall (RC), and Precision (PR), as defined in equations (10)–(14). OA is the ratio of the correctly classified flood pixels to the total training flood grid cells. The F-measure and MAE were also used to compare the results of the 2D-CNN with the MLP neural network.(10)RC=TPTP+FN,(11)PR=TPTP+FP,(12)OA=TP+TNTP+TN+FP+FN,(13)F−measure=2⋅PR⋅RCPR+RC,(14)MAE=1n∑n1pi−ti,where TP = true positives; TN = true negatives; FP = false positives, and FN = false negatives.AUC (equation (15)) and the Matthews correlation coefficient (MCC) (equation (16)) were utilized to deduce the accuracy of the output FSM. The AUC indicates the predictive index of the model by plotting the percentages of the cumulative flood susceptibility and the cumulative flood events within the area [54]. MCC determines the measure of prediction accuracy within candidate classes of different dimensions [55]. MCC represents the observed and output correlation factor, with MCC = 1 indicating perfect prediction and 0 ≤ MCC ≥ −1 representing random prediction results and disagreement between the training (observed) data and predicted results.(15)AUC=∑TP+∑TNTF+TNF,(16)MCC=TP⋅TN−FP⋅FNTP+FPTP+FNTN+FPTN+FN0.5,where TF and TNF are, respectively, the total number of flood and nonflood pixels.


## 3.8. Summary of Methodology Implementation

The schematic workflow for the proposed 2D-CNN model for the prediction of flooding using multiparametric spatial data is presented in Figure8.Figure 8
Framework for implementation of the urban flood susceptibility mapping using multiparametric spatial data with image-based 2D-CNN and MLP-ANN.


## 4. Results

### 4.1. Analysis of Flood Conditioning Factors Using GR and MCA Indices

Using the average measure index (AMI) from the Gain Ratio Index, the conditioning factors with higher weights were considered as the most significant in flood prediction, while the factors with near zero weight can be eliminated from the prediction process. From the GRI results in Figure9, the LULC factor indicated the highest AMI value of 0.067, implying that LULC according to the GRI is the most significant in flood prediction in the case study area. The second most significant factor is rainfall with AMI = 0.054, followed by distance to river and altitude (elevation) with respective AMI values of 0.048 and 0.045. Flow direction, SPI, and TWI had the least contributions to flood susceptibility detection with AMI values ranging between 0.012 and 0.019, while slope, soil, and flow accumulation had moderate influence on FSM detection. For the study area, all the factors are considered as relevant for inclusion in the flood susceptibility modelling as they exhibited GRIA>0.Figure 9
Gain ratio (GR) average measure index (AMI) for flood conditioning factors determination using the GR index.In terms of the contributions of the FCFs in identifying vulnerable areas of flooding in the study area, LULC had the highest significance of 18.5% and consecutively followed by rainfall (14.9%), DFR (13.3%), elevation (12.4%), flow accumulation (10.2%), slope (9.1%), soils (8.6%) TWI (5.3%), SPI (4.4%), and flow direction (3.3%). The contributions of the FCFs imply that the topographic characteristics of the terrain account for the highest influence at 44.7% of the flood conditioning factors. The studied area is characterized by urban and agricultural activities which are most favorable for flash flood occurrences. The flood occurrences are also significantly influenced by the amount of rainfall received, the runoff flow channeling, and the degree of slope. The characteristically uneven topographical landscape with gentle elevation and curvatures with convergent patterns in low slopes results in higher chances of flooding in the studied area. In summary for the flooded area, the flood causing factors show that flood forecasting is influenced by interrelated and spatially distributed hydrologic, topographical, and land-use/cover.Using the MCA statistic for the tolerance and variance inflation factors, results in Table3 reveal that all the FCFs have acceptable tolerance (TOL) values. Tolerance, which is a measure of the degree to which the beta coefficients are influenced by the presence of other predictor variables in a model, is observed to be greater that the threshold of 0.25, implying low levels of multicollinearity between the FCFs. Similarly, since all the VIF values are less than 3, except for flow direction and SPI, the input variables are considered to have a moderate multicollinearity and therefore suitable as independent predictors for FSM in the study area. Both the TOL and VIF results confirm that all the FCFs are suitable as inputs in the FSM with varied degrees of contribution.Table 3
Multicollinearity analysis of flooding influencing factors.
Flood influencing factorMCA statisticsTolerance (TOL)Variance inflation factor (VIF)Rainfall0.6071.65Land-use and land-cover (LULC)0.8241.21Altitude (elevation)0.7431.35Slope0.4012.49Flow direction (FD)0.1178.55Flow accumulation (FA)0.4822.07SPI0.1158.70TWI0.4362.29Distance to river (DTR)0.4882.05Soils0.3982.51The analysis of the FCFs shows that the critical potential factors contributing to the flooding in the area are characterized by rainfall (>1000 mm annually), lower elevations (<2000 m), gentle slopes (<4°), low distance to river (<100 m), built-up and bare/paved surfaces, and soils composed of clay and clay loam aggregates.


### 4.2. 2D-CNN Dropout Regularization and Hyperparameter Analysis

To determine the influence of the dropout manipulation and the activation functions for the 2D-CNN on flood susceptibility mapping, two 2D-CNN architectures with and without dropout manipulations were constructed and trained using the same training dataset. The overall accuracy of the networks is presented in Figure10(a), where two dropout rates of 0.4 (D1) and 0.3 (D2) were used as depicted in Figure 7. The results indicate that as the epochs increase, OA improves with the introduction of the dropout manipulation after each convolutional process. The dropout trained 2D-CNN performed better with an OA index of 0.88 as compared to the OA of 0.62 with the 2D-CNN without dropout regularization. While both 2D-CNN configurations demonstrated variable performances, their optimal epoch was between 210 and 350th, with the nondropout 2D-CNN model diminishing in performance after the optimal epoch as compared to the dropout trained model. The influence of the ReLU activation function was compared with the tanh activation function, with the results in Figure 10(b) showing that the 2D-CNN activated with the ReLU performed better than the tanh activated network. This demonstrates the reliability ReLU in the training of CNN networks [51].Figure 10
2D-CNN overall accuracy OA for: (a) network configuration with and without dropout manipulations, and (b) activation using tanh and ReLU functions.
(a)(b)Based on results mentioned above, the dropout regularization was adopted for implementation with the optimal hyperparameter settings comprising of 3 × 3 convolutional kernel size; 2 × 2 max-pooling kernel size; 335 epochs and learning rate of 0.0015. ReLU was the adopted activation function, with the categorical cross-entropy being used for the loss function and AdaGrad as the network optimizer. The training and validation sets were constructed for the 2D-CNN and carried out per the iterations till the training convergence, and the flood susceptibility index for each pixel was classified using the trained model.


### 4.3. 2D-CNN Model Performance Validation

In flood susceptibility analysis, the accuracy for identifying the flood prone areas is important. The analytical performance of the image-based 2D-CNN for local flood susceptibility modelling was first measured using the correlation coefficientR with results in Figure 11. The model performance shows that at the training phase, the dropout regularized 2D-CNN performed slightly better than the validation phase with respective R values of 0.748 and 0.727. In the testing phase, the model performed better by 0.14% as compared to the training. The overall model performance was higher with R = 0.883. The performance was also validated using known point data from the FIM database to construct the receiver operating chrematistics (ROC) to determine the accuracy of the produced susceptibility map in terms of the success rate and the prediction accuracy curves with results in Figure 12.Figure 11
Flood prediction regression for model training, validation testing and overall output.Figure 12
ROC curve for the 2D-CNN model using the flood prediction verification datasets (CFO is the cumulative probability of flood occurrence and FPI is the flood probability index).The success rate determines how accurate the 2D-CNN model performed with the training data, while the prediction rate shows the model accuracy for predicting the probability of flood occurrence. The model success rate AUC calculated form the training datasets was estimated at 0.827 and corresponding prediction rate curve was determined with AUC = 0.809. Both the correlation and AUC for the model prediction performance not only show the reliability of the performance, but also indicate that the FCFs can be used to generate reliable FSM. The AUC of the ROC results depicts the suitability of the 2D-CNN to calculate the occurrence and nonoccurrence of flooding based on historical flood event data.


### 4.4. Flood Susceptibility Mapping Results

Based on quantile reclassification, the susceptibility model results were classified into very low, low, moderate, high, and very high degrees of vulnerabilities. For the studied area, only regions with very high vulnerability are considered as being prone to significant flood risk (Figure13). Figures 13(a)–13(c) presents the results for FSM for the study area using 2D-CNN with dropout training for 2000, 2010, 2019, and for comparative evaluation Figure 13(d) shows the FSM for 2019 using MLP-ANN. The susceptibility prediction results shows that the highest degree of vulnerability to flooding in the municipality varies between 28.1% and 35.3%. In all the results, most of the highly susceptible areas are located in lower elevations, flat slope and with higher drainage density and are characterized by clay and clay-loam soils. The regions within close proximity to the river channels are observed to be within the highly susceptible flood zones.Figure 13
Flood susceptibility maps and susceptibility index for Eldoret municipality using 2D-CNN for: (a) 2000, (b) 2010, (c) 2019, and (d) 2019 results using MLP-ANN.
(a)(b)(c)(d)Figure14 presents the degrees of flood susceptibility from 2000 to 2019 using the image-based 2D-CNN. The year 2000 had the least area susceptible to flooding with only 28.1% being vulnerable. The degree of vulnerability increased to 35.3% in 2010 and decreased to 27% in 2019. The observed increase in vulnerability between 2000 and 2010 is characterized by geomorphological changes arising from anthropogenic and natural changes. The decrease in vulnerability however is attributed to improvements in drainage systems within the built-up area and better land-use practices such as afforestation from 2010 to 2019 as depicted in Table 2. In terms of temporal variability of susceptibility to flooding, the results from 2D-CNN shows that at least 64.7% of the area is not vulnerable to high flooding risks. Of which, about 35% of the areas laying in the higher elevations have low probability of flooding occurrence.Figure 14
Degree of flood susceptibility in the study area.Comparing the FSM results from 2D-CNN and MLP-ANN for 2019, both models displayed almost the similar spatial distribution patterns for the area under very high vulnerability. However, MLP-ANN with area under very high susceptibility to 32.5% is observed to overestimate the probability of flood extent by 4.7%. Results for the accuracy comparison of the 2D-CNN and MLP-ANN results for 2019 in Figures13(c) and 13(d) using OA, MAE and F-measure are presented in Figure 15. 2D-CNN outperformed the MLP-ANN with the highest OA of 82.5% compared to 64.1% for MLP-ANN, while the F-measure is 0.989 against 0.877 and 2D-CNN also had the least MAE of 10.9% as compared to MLP-ANN with MAE = 25.6%. Using the Wilcoxon signed-rank test, the difference between the 2D-CNN and MLP-ANN FSMs was determined to be different with Z-value of 3.48 and p-value of 0.06, at 95% level of confidence.Figure 15
Performance evaluation of 2D-CNN and MLP-ANN models for flood susceptibility mapping.The results indicate that the image-based 2D-CNN has a more practical outcome can effectively improve the accurate mapping of flood susceptibility as compared to the MLP-ANN. Notably, MLP-ANN results in Figure13(d) overestimated the flood susceptibility extent by mapping the high to very high susceptible areas to constitute approximately 48% of the area, as compared to 2D-CNN with approximately 34% as the level of high and very high susceptibility area. The overestimation of the flood occurrence by MLP-ANN is attributed to the point-based approach in predicting flood occurrence. That is, as compared to the 2D-CNN, MLP-ANN uses a single perceptron or pixel for each input, and because it is fully connected, it uses several parameters that form a dense interconnectivity resulting into redundancy and inefficiency leading to overfitting and low ability for pattern and spatial information generalization.


### 4.5. Discussions

Despite several methods having been developed for flood susceptibility mapping for urban environments [7], the methods remain applicable to the specific case studies, are focused on a single type of flood and gauged areas and they do account for heterogeneity in flood conditioning factors within urban environments [6, 56]. Within urban drainage areas and depending on the urban drainage capacity, there is increased risk of river-based flooding due to the adjacency of the rivers to the city more so as urban rainfall flows into the rivers. Furthermore, in such urban areas, there is the likelihood of compound flooding as the river flooding can interact with the pluvial urban floods. This implies that flood vulnerability in urban areas is often underestimated when considering a single flood-inducing factor as either river or urban pluvial flooding.For urban land-use planning and flood risk management, the determination of critical areas with highest susceptibility to flooding is important. In the current study, the various urban receptors are represented by land-use and land-cover information to adequately represent the complex social-economic urban systems [57–60]. In addition, topographic, geological and hydro-climatic flood conditioning parameters were integrated into the urban flood susceptibility mapping process. As evident from the LULC change results in Table 2, urbanization is a significant factor influencing flood susceptibility due to deforestation and development of buildings and roads which in turn increases the sealed surfaces while reducing permeability. The developed land-cover causes less infiltration with more runoff and consequently increases susceptibility to flooding events within the urban environment. From the susceptibility maps, areas located in higher elevations and covered with agricultural crops, shrubs and forest have the least susceptibility to flooding. Characteristically, vegetation impedes erosion on the high slope areas by buffering the impact of rain falling on the slope, and vegetation roots also increase the shear strength of the slope by increasing the cohesive strength of the soil hence low to very low susceptibility in vegetated areas.From the compound flood susceptibility prediction results in Figure13, the different flood types are taken into consideration. As observed by Reinstaller et al. [61], the proximity of the river to the urban inner areas results in both urban pluvial and river floods, with the inner and suburban areas being the most susceptible to flooding. Based on the slope of the case study area, the residential areas with high population concentrations along the river are the most affected by both the river and urban flooding. The susceptibility results are closely related to the urban patterns such that when flooding occurs, the inner city and the low-laying residential areas are the most susceptible [31, 40]. The susceptibility assessments demonstrate that flood adaptations are required in the case study area. For example, as a mitigation, the authorities should consider constructing dams to protect the surrounding residential areas along the river and improve the drainage infrastructure in the high impact areas while planning low impact development measures in areas that are currently undergoing rapid urbanization.From the model performance, the input image size (image.s) and pixel size (pixel.s) were observed to be more sensitive to the 2D-CNN network performance than the filter size (filter.s=2) and the number of filters (filter.n=6). This is attributed the fact that the image width determines the sample grid information content, thus as the width increases more information is presented for inferring decision. From the results, the accuracy of the 2D-CNN model increased by 13.5% from training to overall prediction. To improve on the impact of the high dimensionality of the input data on the model complexity and the computation time, the optimization of the input factors using metaheuristic schemes should be considered [45]. Notably, because the vulnerable areas are below the elevated terrain, they can only be identified by the surrounding topographical information at suitable pixel sizes pixel.s [12]. Thus, for urban flood mapping, the 2-D image-based CNN model is a more suitable model, as it has the ability to identify the degree of susceptibility at the pixel size defined by the area-based grid terrain units.The study results demonstrate that accurate flood prediction requires the analysis of a broad set of temporal and spatial data. The ability of the image-based 2D-CNN model to convert the raw data into a valuable expression is more suitable for dealing with such datasets compared to the conventional machine learning and MLP neural network models [25, 26, 33–35]. This is because these models are not able to detect the high variations in the neighboring cells due to the lack of inductive bias, that is lack of spatial and temporal equivariance, resulting in the lesser coherent prediction results [10]. Additionally, the 2D-CNN modelling procedure not only offers competitive performance for large datasets, but the automatic factor selection also makes the approach more attractive [62].For the model performance and FSM accuracy assessment, while the metrics as Precision, Recall, OA, MCC andR2 considers the final classification, and the combined ROC curve and AUC index presents the precision and reliability of the FSM prediction results as they tend to be sensitive to flood causative factors [13, 35, 60]. Even though the accuracy of flood prediction may decrease with low proportions of training data due to limited extent of the case study, the current results demonstrate that the image-based 2D-CNN is acceptable with the available data for the study area. Despite the advantages, the deep learning model has some limitations, such as the time-consuming process of training the data.


## 4.1. Analysis of Flood Conditioning Factors Using GR and MCA Indices

Using the average measure index (AMI) from the Gain Ratio Index, the conditioning factors with higher weights were considered as the most significant in flood prediction, while the factors with near zero weight can be eliminated from the prediction process. From the GRI results in Figure9, the LULC factor indicated the highest AMI value of 0.067, implying that LULC according to the GRI is the most significant in flood prediction in the case study area. The second most significant factor is rainfall with AMI = 0.054, followed by distance to river and altitude (elevation) with respective AMI values of 0.048 and 0.045. Flow direction, SPI, and TWI had the least contributions to flood susceptibility detection with AMI values ranging between 0.012 and 0.019, while slope, soil, and flow accumulation had moderate influence on FSM detection. For the study area, all the factors are considered as relevant for inclusion in the flood susceptibility modelling as they exhibited GRIA>0.Figure 9
Gain ratio (GR) average measure index (AMI) for flood conditioning factors determination using the GR index.In terms of the contributions of the FCFs in identifying vulnerable areas of flooding in the study area, LULC had the highest significance of 18.5% and consecutively followed by rainfall (14.9%), DFR (13.3%), elevation (12.4%), flow accumulation (10.2%), slope (9.1%), soils (8.6%) TWI (5.3%), SPI (4.4%), and flow direction (3.3%). The contributions of the FCFs imply that the topographic characteristics of the terrain account for the highest influence at 44.7% of the flood conditioning factors. The studied area is characterized by urban and agricultural activities which are most favorable for flash flood occurrences. The flood occurrences are also significantly influenced by the amount of rainfall received, the runoff flow channeling, and the degree of slope. The characteristically uneven topographical landscape with gentle elevation and curvatures with convergent patterns in low slopes results in higher chances of flooding in the studied area. In summary for the flooded area, the flood causing factors show that flood forecasting is influenced by interrelated and spatially distributed hydrologic, topographical, and land-use/cover.Using the MCA statistic for the tolerance and variance inflation factors, results in Table3 reveal that all the FCFs have acceptable tolerance (TOL) values. Tolerance, which is a measure of the degree to which the beta coefficients are influenced by the presence of other predictor variables in a model, is observed to be greater that the threshold of 0.25, implying low levels of multicollinearity between the FCFs. Similarly, since all the VIF values are less than 3, except for flow direction and SPI, the input variables are considered to have a moderate multicollinearity and therefore suitable as independent predictors for FSM in the study area. Both the TOL and VIF results confirm that all the FCFs are suitable as inputs in the FSM with varied degrees of contribution.Table 3
Multicollinearity analysis of flooding influencing factors.
Flood influencing factorMCA statisticsTolerance (TOL)Variance inflation factor (VIF)Rainfall0.6071.65Land-use and land-cover (LULC)0.8241.21Altitude (elevation)0.7431.35Slope0.4012.49Flow direction (FD)0.1178.55Flow accumulation (FA)0.4822.07SPI0.1158.70TWI0.4362.29Distance to river (DTR)0.4882.05Soils0.3982.51The analysis of the FCFs shows that the critical potential factors contributing to the flooding in the area are characterized by rainfall (>1000 mm annually), lower elevations (<2000 m), gentle slopes (<4°), low distance to river (<100 m), built-up and bare/paved surfaces, and soils composed of clay and clay loam aggregates.


## 4.2. 2D-CNN Dropout Regularization and Hyperparameter Analysis

To determine the influence of the dropout manipulation and the activation functions for the 2D-CNN on flood susceptibility mapping, two 2D-CNN architectures with and without dropout manipulations were constructed and trained using the same training dataset. The overall accuracy of the networks is presented in Figure10(a), where two dropout rates of 0.4 (D1) and 0.3 (D2) were used as depicted in Figure 7. The results indicate that as the epochs increase, OA improves with the introduction of the dropout manipulation after each convolutional process. The dropout trained 2D-CNN performed better with an OA index of 0.88 as compared to the OA of 0.62 with the 2D-CNN without dropout regularization. While both 2D-CNN configurations demonstrated variable performances, their optimal epoch was between 210 and 350th, with the nondropout 2D-CNN model diminishing in performance after the optimal epoch as compared to the dropout trained model. The influence of the ReLU activation function was compared with the tanh activation function, with the results in Figure 10(b) showing that the 2D-CNN activated with the ReLU performed better than the tanh activated network. This demonstrates the reliability ReLU in the training of CNN networks [51].Figure 10
2D-CNN overall accuracy OA for: (a) network configuration with and without dropout manipulations, and (b) activation using tanh and ReLU functions.
(a)(b)Based on results mentioned above, the dropout regularization was adopted for implementation with the optimal hyperparameter settings comprising of 3 × 3 convolutional kernel size; 2 × 2 max-pooling kernel size; 335 epochs and learning rate of 0.0015. ReLU was the adopted activation function, with the categorical cross-entropy being used for the loss function and AdaGrad as the network optimizer. The training and validation sets were constructed for the 2D-CNN and carried out per the iterations till the training convergence, and the flood susceptibility index for each pixel was classified using the trained model.


## 4.3. 2D-CNN Model Performance Validation

In flood susceptibility analysis, the accuracy for identifying the flood prone areas is important. The analytical performance of the image-based 2D-CNN for local flood susceptibility modelling was first measured using the correlation coefficientR with results in Figure 11. The model performance shows that at the training phase, the dropout regularized 2D-CNN performed slightly better than the validation phase with respective R values of 0.748 and 0.727. In the testing phase, the model performed better by 0.14% as compared to the training. The overall model performance was higher with R = 0.883. The performance was also validated using known point data from the FIM database to construct the receiver operating chrematistics (ROC) to determine the accuracy of the produced susceptibility map in terms of the success rate and the prediction accuracy curves with results in Figure 12.Figure 11
Flood prediction regression for model training, validation testing and overall output.Figure 12
ROC curve for the 2D-CNN model using the flood prediction verification datasets (CFO is the cumulative probability of flood occurrence and FPI is the flood probability index).The success rate determines how accurate the 2D-CNN model performed with the training data, while the prediction rate shows the model accuracy for predicting the probability of flood occurrence. The model success rate AUC calculated form the training datasets was estimated at 0.827 and corresponding prediction rate curve was determined with AUC = 0.809. Both the correlation and AUC for the model prediction performance not only show the reliability of the performance, but also indicate that the FCFs can be used to generate reliable FSM. The AUC of the ROC results depicts the suitability of the 2D-CNN to calculate the occurrence and nonoccurrence of flooding based on historical flood event data.


## 4.4. Flood Susceptibility Mapping Results

Based on quantile reclassification, the susceptibility model results were classified into very low, low, moderate, high, and very high degrees of vulnerabilities. For the studied area, only regions with very high vulnerability are considered as being prone to significant flood risk (Figure13). Figures 13(a)–13(c) presents the results for FSM for the study area using 2D-CNN with dropout training for 2000, 2010, 2019, and for comparative evaluation Figure 13(d) shows the FSM for 2019 using MLP-ANN. The susceptibility prediction results shows that the highest degree of vulnerability to flooding in the municipality varies between 28.1% and 35.3%. In all the results, most of the highly susceptible areas are located in lower elevations, flat slope and with higher drainage density and are characterized by clay and clay-loam soils. The regions within close proximity to the river channels are observed to be within the highly susceptible flood zones.Figure 13
Flood susceptibility maps and susceptibility index for Eldoret municipality using 2D-CNN for: (a) 2000, (b) 2010, (c) 2019, and (d) 2019 results using MLP-ANN.
(a)(b)(c)(d)Figure14 presents the degrees of flood susceptibility from 2000 to 2019 using the image-based 2D-CNN. The year 2000 had the least area susceptible to flooding with only 28.1% being vulnerable. The degree of vulnerability increased to 35.3% in 2010 and decreased to 27% in 2019. The observed increase in vulnerability between 2000 and 2010 is characterized by geomorphological changes arising from anthropogenic and natural changes. The decrease in vulnerability however is attributed to improvements in drainage systems within the built-up area and better land-use practices such as afforestation from 2010 to 2019 as depicted in Table 2. In terms of temporal variability of susceptibility to flooding, the results from 2D-CNN shows that at least 64.7% of the area is not vulnerable to high flooding risks. Of which, about 35% of the areas laying in the higher elevations have low probability of flooding occurrence.Figure 14
Degree of flood susceptibility in the study area.Comparing the FSM results from 2D-CNN and MLP-ANN for 2019, both models displayed almost the similar spatial distribution patterns for the area under very high vulnerability. However, MLP-ANN with area under very high susceptibility to 32.5% is observed to overestimate the probability of flood extent by 4.7%. Results for the accuracy comparison of the 2D-CNN and MLP-ANN results for 2019 in Figures13(c) and 13(d) using OA, MAE and F-measure are presented in Figure 15. 2D-CNN outperformed the MLP-ANN with the highest OA of 82.5% compared to 64.1% for MLP-ANN, while the F-measure is 0.989 against 0.877 and 2D-CNN also had the least MAE of 10.9% as compared to MLP-ANN with MAE = 25.6%. Using the Wilcoxon signed-rank test, the difference between the 2D-CNN and MLP-ANN FSMs was determined to be different with Z-value of 3.48 and p-value of 0.06, at 95% level of confidence.Figure 15
Performance evaluation of 2D-CNN and MLP-ANN models for flood susceptibility mapping.The results indicate that the image-based 2D-CNN has a more practical outcome can effectively improve the accurate mapping of flood susceptibility as compared to the MLP-ANN. Notably, MLP-ANN results in Figure13(d) overestimated the flood susceptibility extent by mapping the high to very high susceptible areas to constitute approximately 48% of the area, as compared to 2D-CNN with approximately 34% as the level of high and very high susceptibility area. The overestimation of the flood occurrence by MLP-ANN is attributed to the point-based approach in predicting flood occurrence. That is, as compared to the 2D-CNN, MLP-ANN uses a single perceptron or pixel for each input, and because it is fully connected, it uses several parameters that form a dense interconnectivity resulting into redundancy and inefficiency leading to overfitting and low ability for pattern and spatial information generalization.


## 4.5. Discussions

Despite several methods having been developed for flood susceptibility mapping for urban environments [7], the methods remain applicable to the specific case studies, are focused on a single type of flood and gauged areas and they do account for heterogeneity in flood conditioning factors within urban environments [6, 56]. Within urban drainage areas and depending on the urban drainage capacity, there is increased risk of river-based flooding due to the adjacency of the rivers to the city more so as urban rainfall flows into the rivers. Furthermore, in such urban areas, there is the likelihood of compound flooding as the river flooding can interact with the pluvial urban floods. This implies that flood vulnerability in urban areas is often underestimated when considering a single flood-inducing factor as either river or urban pluvial flooding.For urban land-use planning and flood risk management, the determination of critical areas with highest susceptibility to flooding is important. In the current study, the various urban receptors are represented by land-use and land-cover information to adequately represent the complex social-economic urban systems [57–60]. In addition, topographic, geological and hydro-climatic flood conditioning parameters were integrated into the urban flood susceptibility mapping process. As evident from the LULC change results in Table 2, urbanization is a significant factor influencing flood susceptibility due to deforestation and development of buildings and roads which in turn increases the sealed surfaces while reducing permeability. The developed land-cover causes less infiltration with more runoff and consequently increases susceptibility to flooding events within the urban environment. From the susceptibility maps, areas located in higher elevations and covered with agricultural crops, shrubs and forest have the least susceptibility to flooding. Characteristically, vegetation impedes erosion on the high slope areas by buffering the impact of rain falling on the slope, and vegetation roots also increase the shear strength of the slope by increasing the cohesive strength of the soil hence low to very low susceptibility in vegetated areas.From the compound flood susceptibility prediction results in Figure13, the different flood types are taken into consideration. As observed by Reinstaller et al. [61], the proximity of the river to the urban inner areas results in both urban pluvial and river floods, with the inner and suburban areas being the most susceptible to flooding. Based on the slope of the case study area, the residential areas with high population concentrations along the river are the most affected by both the river and urban flooding. The susceptibility results are closely related to the urban patterns such that when flooding occurs, the inner city and the low-laying residential areas are the most susceptible [31, 40]. The susceptibility assessments demonstrate that flood adaptations are required in the case study area. For example, as a mitigation, the authorities should consider constructing dams to protect the surrounding residential areas along the river and improve the drainage infrastructure in the high impact areas while planning low impact development measures in areas that are currently undergoing rapid urbanization.From the model performance, the input image size (image.s) and pixel size (pixel.s) were observed to be more sensitive to the 2D-CNN network performance than the filter size (filter.s=2) and the number of filters (filter.n=6). This is attributed the fact that the image width determines the sample grid information content, thus as the width increases more information is presented for inferring decision. From the results, the accuracy of the 2D-CNN model increased by 13.5% from training to overall prediction. To improve on the impact of the high dimensionality of the input data on the model complexity and the computation time, the optimization of the input factors using metaheuristic schemes should be considered [45]. Notably, because the vulnerable areas are below the elevated terrain, they can only be identified by the surrounding topographical information at suitable pixel sizes pixel.s [12]. Thus, for urban flood mapping, the 2-D image-based CNN model is a more suitable model, as it has the ability to identify the degree of susceptibility at the pixel size defined by the area-based grid terrain units.The study results demonstrate that accurate flood prediction requires the analysis of a broad set of temporal and spatial data. The ability of the image-based 2D-CNN model to convert the raw data into a valuable expression is more suitable for dealing with such datasets compared to the conventional machine learning and MLP neural network models [25, 26, 33–35]. This is because these models are not able to detect the high variations in the neighboring cells due to the lack of inductive bias, that is lack of spatial and temporal equivariance, resulting in the lesser coherent prediction results [10]. Additionally, the 2D-CNN modelling procedure not only offers competitive performance for large datasets, but the automatic factor selection also makes the approach more attractive [62].For the model performance and FSM accuracy assessment, while the metrics as Precision, Recall, OA, MCC andR2 considers the final classification, and the combined ROC curve and AUC index presents the precision and reliability of the FSM prediction results as they tend to be sensitive to flood causative factors [13, 35, 60]. Even though the accuracy of flood prediction may decrease with low proportions of training data due to limited extent of the case study, the current results demonstrate that the image-based 2D-CNN is acceptable with the available data for the study area. Despite the advantages, the deep learning model has some limitations, such as the time-consuming process of training the data.


## 5. Conclusions

This study presents results on the application of image-based 2D-CNN model in urban flood susceptibility mapping (FSM) using a multiparametric spatial data comprising of ten (10) flood conditioning factors and 159 historical flood sample points. The 2D-CNN was constructed to classify the flood and nonflood points and to extract the flood features. The results using statistical evaluations showed that the 2D-CNN with dropout regularization function was able to accurately predict the FSM with overall accuracy statistic of 82.5%; Matthews correlation coefficient value of 0.574 andR = 0.8826. The 2D-CNN predicted flood susceptibility map showed high convergence with the historical flood inventory map in terms of the AUC index of prediction and success rates of 0.827 and 0.809 respectively. From the FSM results for the case study area, the study recommends the use of the image-based 2D-CNN model with dropout regularization as more suitable for the production of high-quality FSM as compared to the conventional 2D-CNN and the feedforward MLP-ANN. To improve on the significance of the high dimensionality of the input data on the model complexity and the computation time, the optimization of the input factors using metaheuristic schemes should be considered. In terms of the flood conditioning factors, land-use land-cover, rainfall and location from rivers had the highest influence on flooding in the area. Further, the inclusion of additional flood conditioning factors such as lithology in urban flood susceptibility mapping should be explored as they may contribute to more precise FSM results. To improve on the quality of training, validation and testing in case studies with scarce data, investigations on clustering-based data splitting approach that creates data splits where the development or test data differ from the training set is recommended for further investigations.



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*Source: 5672401-2023-03-23.xml*