# A Review of Hydrodynamic and Machine Learning Approaches for Flood Inundation Modeling

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## Abstract

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## 1. Introduction

## 2. Overview of Methods

#### 2.1. Hydrodynamic Models

#### 2.2. Machine Learning Approaches

_{i}and y

_{i}of X and Y, y

_{i}= Wx

_{i}+ ε, where W is a 6 × 5 element matrix and ε is a 6-element vector containing noise with known statistical properties. The model that a practitioner uses should be selected according to the data. For example, some data targets are real-valued, and regression models are most suitable for this kind of data. Some data targets are categorical variables, and classification models should be used. Note that the usage of the term model in a machine learning context does not necessarily agree with the definition in broader science, machine learning models rarely describe an interpretable data-generating process.

#### 2.2.1. Classification and Regression

_{i}in X to one of k discrete values 1, 2,…, k. In a typical setting, the magnitude and ordering of the values k values is not informative—for example, 2 is not “greater than” 1. For example, we might be interested in deciding whether an input image xi represents a horse, truck or dog takes a value 1, 2 or 3. The problem of regression is to associate every row x

_{i}in X to a value. In a typical setting, unlike in classification, the magnitude and ordering can be important. For example, we might be interested in deciding whether an input spatial coordinate x

_{i}is not flooded, mildly flooded, or severely flooded taking values 1, 2 and 3. As another example, we might be interested in associating to every input spatial coordinate x

_{i}a real-valued number representing the flood level in meters.

#### 2.2.2. Traditional Machine Learning Models

^{T}>. Here n is the number of training examples, d is the dimensionality of each training input, X

^{T}denotes the transpose of X, and XX

^{T}is an n × n matrix. If we instead ran our algorithm over some transformation of the data ϕ(X), where ϕ is a function that maps every d-element row of X to a D-element row, the prediction of the algorithm now depends on the matrix ϕ(X)ϕ(X

^{T}), which is also an n × n matrix. Under minimal assumptions, given ϕ(X)ϕ(X

^{T}), the memory requirements and computational complexity of the algorithm do not depend on D. The data represented in the new space may reveal a structure that was not obvious in the original space. This means that we may lift our original training inputs to a higher dimensional space without incurring additional costs and with potential benefits for the predictor (see Figure 1 for detail). The dimensionality D of the space to which ϕ maps may be very large, or even infinite.

^{T}and replacing it with a kernel matrix ϕ(X)ϕ(X

^{T}) or using the representer theorem is commonly referred to as kernelizing the algorithm. Examples of kernelized algorithms include the support vector machine (SVM) [22], the support vector regression (SVR) machine [23], kernel ridge regression (KRR) [24] and principal component analysis (PCA) [25]. Kernel methods enjoy a rich theory and historical connection with statistical learning theory [26]. As such, mathematically provable generalization guarantees are available for many kernel methods.

#### 2.2.3. Deep Learning Models

^{(L)}by iteratively applying a sequence of L mappings called fully connected layers,

^{(0)}= x. Here the weights and biases ${\left\{\left(w\left(l\right),b\left(l\right)\right)\right\}}_{l=1}^{L}$ are parameters of the model, and the activation functions ${\left\{\sigma \left(l\right)\right\}}_{l=1}^{L}$ are non-linear functions applied coordinate-wise to each vector input. A graphical depiction of an MLP is given in Figure 3.

^{(l)}and biases b

^{(l)}which define an affine transformation. One may constrain the weights w

^{(l)}to reflect certain locality bias in the input data. This is especially important if the input data is an image, where one expects neighboring pixels to be related. This is the principle behind convolutional layers, which may be viewed as a very large, sparse fully connected layer with repeated entries. Convolutional layers are typically followed by nonlinearities, mirroring the structure in MLPs, and by certain aggregation layers. Aggregation layers include maximum pooling and average pooling.

## 3. Application of Machine Learning for Flood Inundation Modeling

#### 3.1. Traditional Machine Learning Approaches

#### 3.1.1. Classification

Authors | Publication Year | Application | Approach |
---|---|---|---|

Avand et al. [48] | 2022 | Effects of DEM resolution | RF, MLP, and GLM |

Yan et al. [53] | 2021 | Estimating flow depth | MGGP |

El-Hedad et al. [47] | 2021 | Flood risk assessment | BRT, FDA, GLM, MDA |

Madhuri et al. [49] | 2021 | Flood risk assessment | Logistic Regression, SVM, KNN |

Ma et al. [51] | 2021 | Flood risk assessment | XGBoost, LSSVM |

Hou et al. [54] | 2021 | Urban flooding | RF, KNN |

Yuan et al. [55] | 2021 | Road flooding | RF, AdaBoost |

Talukdar et al. [50] | 2021 | Wetland inundation | RF, SVM, MLP |

Karimi et al. [52] | 2019 | Wetland inundation | RF |

#### 3.1.2. Regression

#### 3.2. Deep Learning Approaches

#### 3.2.1. Multilayer Perceptron (MLP)

#### 3.2.2. Convolutional Neural Networks

_{river}was a composite image with two bands including the ground elevation and flooding discharge of size 128 × 128 pixel, and the output was water depth. The objective function to train the network was MSE. The application of the U-Net

_{river}for different discharges demonstrated its capability of detecting the river geometry including the river width, shape, curves, and even the river splits around the island. In comparison to traditional ML model [59] applied on the same data, their model not only demonstrated a reduction of 29% in the reported error, but also eliminated the requirement of a separate classifier to classify grids to the wet or dry regions. One of the main weaknesses of this model is its generalizability. While the trained model showed high performances for the lower depth values (lower discharges), it requires an improvement to deal with high discharges or out of training discharge data.

#### 3.2.3. Autoencoder Approaches

#### 3.2.4. Adversarial Approaches

^{6}times faster than 2D hydraulic models). However, FloodGAN trained using only synthetic data and the results compared to a hydraulic model rather than any other deep learning algorithm. In addition, they only focused on predicting maximum inundation extent and water depth for up to 1-h rainfall events and did not include the prediction of flow velocities. Another drawback of the proposed model is that it does not take the serial correlation of time series data of flooding into account and the prediction results are limited to quasi-static flood hazard maps.

#### 3.2.5. Spatio-Temporal Analysis Approaches

^{2}with a total length of 84.6 km.

Authors | Publication Year | Application | Approach |
---|---|---|---|

Guo et al. [66] | 2021 | Urban flood emulation | Autoencoder |

Löwe et al. [64] | 2021 | Urban flood depth (pluvial) | U-Net |

Hosseiny [63] | 2021 | Flood depth | U-Net |

Hosseiny et al. [59] | 2020 | Flood depth | MLP & RF |

Wei [69] | 2020 | Flood depth | LSTM |

Zhou et al. [19] | 2021 | Flood inundation | LSTM |

Zhu et al. [61] | 2021 | Flood Inundation | MLP |

Hofman et al. [67] | 2021 | Flood inundation (pluvial) | GAN |

Tamiru and Wagari [57] | 2021 | Flood inundation | MLP & HEC-RAS [58] |

Chu et al. [60] | 2020 | Flood inundation | GRNN |

Kabir et al. [62] | 2020 | Flood inundation (fluvial) | 1-D CNN & SVR |

Tsakiri et al. [70] | 2018 | Flood inundation | Linear regression, MLP |

Berkhahn et al. [56] | 2019 | Flood inundation (pluvial) | MLP |

#### 3.3. Datasets

^{2}. They used TELEMAC-MASCARET hydrodynamic model [71] simulated water level data to train their MGGP model. They divided the study region into 34 sub-regions and provided around 10,000 data points for each sub-region.

^{2}in the Wadi Qena Basin in Egypt. The data were derived from 342 inundation locations by analyzing satellite imagery and geological and topographical maps. They used 30 × 30 m pixel flood data and considered three flood influencing factors (e.g., distance from main channel, land cover and soil type) for training their data mining/machine learning models About 70% of the data were used for training the model and the remaining 30% data were used for validating.

^{2}and it was divided into 16 zones. They used a geo-spatial database based on ASTER DEM (30 × 30 m spatial resolution) using eight flood factors [74,75]. Their ML models were evaluated against historical flood data of 2000, 2006 and 2016.

^{2}. They used hydrodynamic model simulated inundation data and rainfall characteristic parameters to train ML models. Data from 150 rainfall events were used for training and 30 events for validating ML models.

^{2}in the Sunamganj district of Bangladesh. They used 30 m resolution satellite data acquired from the Landsat imagery. They reported that lack of high-resolution data for wetlands was a major challenge for validating ML models for wetland inundation.

^{2}of Darling River in Australia (1200 km

^{2}) using RF machine learning technique. They used a set of dependent variables (e.g., inundation area) and another set of independent variables (e.g., topographic, climatic), describing hydrological and physical characteristics of the study area to configure and validate the ML models. The dependent variables were 30 m resolution gridded inundation map obtained from Landsat imagery. From the raster data 10,000 points were randomly selected for the ML model.

^{2}in Baro River Basin (Ethiopia). The data was collected and generated for seven years from 1999 to 2005. They also curated test data for three years from 2006 to 2008.

^{2}and the area of the study is 2720 m × 2860 m. This area is represented by 19,448 grid cells of size 20 m by 20 m by using the TUFLOW hydrodynamic model [77]. Their DL models were tested for 10 flood events including three historical events (i.e., year 1971, 2010 and 2013) and seven “design events”.

^{2}area.

^{2}with a 84.6 km river reach.

_{river}) and depth data for validating their U-Net

_{river}model. They investigated an area of 260 × 251 pixel (4.5 km

^{2}) of which 128 × 128 pixels were randomly selected for training the model.

^{2}of the urbanized area of Carlisle city in England. They generated flood depth data for training the CNN deep learning model from eight synthetic hydrographs using LISFLOOD-FP hydrodynamic [82]. They divided the study area into 581,061 grids and used water depth as the controlling parameter for validating the CNN model. In addition to synthetic depth data for training, two sets of measured data for 2005 and 2015 floods were used to validate the CNN model.

## 4. Strength and Limitations of ML/DL Models

#### 4.1. Strength

#### 4.2. Limitations and Open Research Challenges

#### 4.2.1. Generalizability

_{river}[63] and FloodGAN [67] demonstrated better performance. Advanced DL models can cover greater regions for training whereas the ML or basic DL models (e.g., MLP) require to be trained on small grids, this also increases the number of ML models to model flood in a region [61].

#### 4.2.2. Dataset

#### 4.2.3. Embedding Expert Knowledge

#### 4.2.4. Application of Graph Neural Network and Neural Operators

#### 4.2.5. Explainability

## 5. Conclusions

_{river}and FloodGAN demonstrated better performance. Apart from strengths and weaknesses of such methods, challenges and future research avenues related to application of ML/DL models to model inundation events have been discussed.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Nomenclatures

AdaBoost | Adaptive Boosting |

ANN | Artificial neural network |

ASTER | Advanced Space-borne Thermal Emission and Reflection Radiometer |

BRT | Boosted regression tree |

CNN | Convolutional neural network |

DL | Deep learning |

FDA | Functional data analysis |

FPM | Flood probability map |

GAN | Generative adversarial network |

GLM | Generalized linear models |

GPU | Graphics processing unit |

GRNN | Generalized regression neural network |

GRU | Gated recurrent unit |

HD | Hydrodynamic |

HEC-RAS | Hydrological Engineering Center—River Analysis System |

iRIC | International River Interface Cooperative |

KNN | k-nearest neighbour algorithm |

KRR | Kernel ridge regression |

LSSVM | Least squares support vector machine |

LSTM | Long short-term memory |

MAE | Mean absolute error |

MDA | Multivariate discriminant analysis |

MGGP | Multigene genetic programming |

MIFNN | Multiple input functional neural network |

ML | Machine learning |

MLP | Multilayer perceptron |

MLR | Multiple linear regression |

MSE | Mean square error |

NOAA | National Oceanic and Atmospheric Administration |

OLS | Ordinary least squares |

PCA | Principal component analysis |

REG | Conventional regression |

RF | Random Forest |

RKHS | Reproducing Kernel Hilbert Space |

RMSE | Root mean square error |

RNN | Recurrent neural network |

SGD | Stochastic gradient descent |

SNN | Sequential neural network |

SVM | Support vector machine |

SVR | Support vector regression |

USGS | United States Geological Survey |

XGBoost | Extreme gradient boosting |

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**Figure 1.**(

**Left**) Original data X∈R

^{20×2}does not exhibit obvious structure with respect to labels (indicated by color). (

**Right**) After mapping to ϕ(X) ∈ R

^{20×3}given some matrix A, the data is observed to lie on the surface of a quadratic. Kernel methods make use of a mapping ϕ(X) by operating on the kernel matrix ϕ(X)ϕ(X

^{T}) ∈ R

^{N×N}without defining ϕ explicitly but instead in terms of the kernel matrix ϕ(X)ϕ(X

^{T}).

**Figure 2.**Schematic diagram of Random Forest (RF), the final decision inferred from majority voting using results from each decision tree.

**Figure 3.**Schematic of some popular DL models used in flood modeling, MLPs can be used for both classification and regression and consist of input, output and hidden fully connected layers, Autoencoders: these models consist of two main parts to encode and decode the data, Recurrent Neural networks (RNN) are designed to extract best out of time-series data.

Topic | Reference | ||||||
---|---|---|---|---|---|---|---|

[6] | [5] | [2] | [4] | [3] | [1] | Ours | |

Physical based models | √ | √ | √ | ||||

Machine learning models | √ | √ | √ | √ | |||

Deep Learning models | √ | √ | √ | √ | |||

Extension to real-time response | √ | √ | |||||

Model interpretation methods | √ | ||||||

Embedding expert knowledge | √ |

Event & Location | Publicly Available | Coverage Data | Type (Real/Synthetic Events) | Data Quantity | Authors |
---|---|---|---|---|---|

Inundation, USA | Yes | 3.5 km | Syn | 2100 image | Hosseiny [63] |

Urban flood, Unknown | No | 96,233 m^{2} | Syn, real | 9623 cells | Berkhahn et al. [56] |

Flood inundation, AUS | No | 33,000 km^{2} | real | 19,448 grid cells | Chu et al. [60] |

Flood, Ethiopia | Yes | 74,100 km^{2} | Syn, real | 10 years of data | Tamiru and Wagari [57] |

Inundation, UK | Yes | 14.5 km^{2} | Syn, real | 581,061 cells | Kabir et al. [62] |

Fluvial, Germany | No | 2 × 2 km^{2} | Syn | 901 samples | Hofman et al. [67] |

Fluvial, Switzerland, Portugal | No | 10 km^{2} | Syn | 30,000 samples | Guo et al. [66] |

Pluvial, Denmark | Yes | 194 km^{2} | Real | 53 train maps | Löwe et al. [64] |

Flood, Iran | No | 2185 km^{2} | Real | 220 flood locations | Avand et al. [48] |

Flood, Egypt | No | 14.5 km^{2} | Real | 342 flood locations | El-Haddad et al. [47] |

Flood, India | No | 625 km^{2} | Real | 295 flood locations | Madhuri et al. [49] |

Fluvial, Canada | No | 3.2 × 1.40 km^{2} | Syn, real | 340,000 | Yan et al. [53] |

Fluvial, China | No | 2.43 km^{2} | Real | 180 rainfall events | Hou et al. [54] |

Flood wetland, Bangladesh | No | 3669.58 km^{2} | Syn, real | 7 images | Talukdar et al. [50] |

Flash flood, China | No | 390,000 km^{2} | Real | two sets of data, 129 counties | Ma et al. [51] |

Flood plain inundation, AUS | No | 1200 km^{2} | Real | 10,000 points | Karimi et al. [52] |

Flood hazard forecasting, USA | No | 240 km | Real | Discharge for 3 gauges for 2005–2013 | Tsakiri et al. [70] |

Flood depth, Germany | No | 92.7 km^{2} | Syn, Real | 360 flood events | Zhu et al. [61] |

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## Share and Cite

**MDPI and ACS Style**

Karim, F.; Armin, M.A.; Ahmedt-Aristizabal, D.; Tychsen-Smith, L.; Petersson, L. A Review of Hydrodynamic and Machine Learning Approaches for Flood Inundation Modeling. *Water* **2023**, *15*, 566.
https://doi.org/10.3390/w15030566

**AMA Style**

Karim F, Armin MA, Ahmedt-Aristizabal D, Tychsen-Smith L, Petersson L. A Review of Hydrodynamic and Machine Learning Approaches for Flood Inundation Modeling. *Water*. 2023; 15(3):566.
https://doi.org/10.3390/w15030566

**Chicago/Turabian Style**

Karim, Fazlul, Mohammed Ali Armin, David Ahmedt-Aristizabal, Lachlan Tychsen-Smith, and Lars Petersson. 2023. "A Review of Hydrodynamic and Machine Learning Approaches for Flood Inundation Modeling" *Water* 15, no. 3: 566.
https://doi.org/10.3390/w15030566