# Using Convolutional Neural Networks to Build a Lightweight Flood Height Prediction Model with Grad-Cam for the Selection of Key Grid Cells in Radar Echo Maps

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Related Works

#### 2.1. Flood Prediction

#### 2.2. Related Research on Grad-Cam

## 3. Algorithms

#### 3.1. Collection, Cleaning, and Integration of Flood-Related Data and Radar Echo Maps

_{1}, and a value is returned after every interval t. We then represent the flood height value of n consecutive returns as H

_{A}= [h

_{A}(t

_{1}), h

_{A}(t

_{2}), …, h

_{A}(t

_{n})], where t

_{i}= t

_{i}

_{−1}+ t. The value of t ranges from 10 min to 12 h. Due to network instability, external sensors are prone to missing H

_{A}values. Cleaning and augmenting H

_{A}values involves two sub-steps. The first sub-step involves obtaining a reasonable range of flood heights for grid cell A, based on historical data from the weather bureau. We then check whether the H

_{A}values fall within that range, and mark any missing values or values outside that range. The second sub-step involves determining whether to change or discard the marked values, based on the timespan to the previous sub-step. If the duration of the marked value is less than 24 h, then Equation (1) is used to fill in the value in accordance with the situation at that time of day.

_{2}and t

_{3}in area A are h

_{A}(t

_{2})′ and h

_{A}(t

_{3})′, and the values within t

_{20}to t

_{40}are discarded, then the new H

_{A}can be expressed as H

_{A}′ = [h

_{A}(t

_{1}), h

_{A}(t

_{2})′, h

_{A}(t

_{3})′, h

_{A}(t

_{4}), …, h

_{A}(t

_{19}), h

_{A}(t

_{41}), …, h

_{A}(t

_{n})].

_{1}, and the interval between each image is k, then we can represent m continuous radar echo maps as P

_{A}= [p

_{A}(k

_{1}), p

_{A}(k

_{2}), …, p

_{A}(k

_{m})], where k

_{i}= k

_{i}

_{−1}+ k. The value of k usually ranges from 10 min to one hour. The k

_{i}th radar echo map p

_{A}(k

_{i}) in P

_{A}can be expressed as p

_{A}(k

_{i}) = [v

_{a}

_{,ki}(1, 1), v

_{a}

_{,ki}(1, 2), …, v

_{a}

_{,ki}(1, y), v

_{a}

_{,ki}(2, 1), …, v

_{a}

_{,ki}(2, y), …, v

_{a}

_{,ki}(x, 1), …, v

_{a}

_{,ki}(x, y)]. Note that A will not be in the center of the radar echo map when A is located at the edge of the map. In this situation, making A the center would limit the range of the radar echo map, as shown in Figure 4. Note also that the radar echo map grid is actually a rectangle, due to the limited the range of the radar echo map obtained from the government and limitations due to terrain and other factors. We must assume that the radar echo map obtained from the weather bureau is accurate and reasonable. The grid used for radar echo maps should be adjusted to the specifics of the intended application. The additional information provided by grids of high resolution can significantly increase CNN prediction accuracy, and our lightweight model based on the CNN architecture would also benefit from grid of higher resolution. Nonetheless, any improvement in accuracy would come at the cost of higher computational overhead. In other words, selecting the resolution of radar echo maps involves a trade-off between accuracy and computational capacity or efficiency. In fact, the computational demands of large-scale CNNs are likely to exceed the capacity of all but the most highly enabled computer systems.

_{A}′ are 0 (i.e., only rare flood events are greater than 0). Inputting H

_{A}′ directly into the CNN for training would result in data imbalance and corresponding inaccuracies. This situation can be avoided by balancing the ratio of non-flood events against flood events. We begin by recording the number of times the flood height value exceeded σ, where σ is the threshold value indicating a flood event, as defined by the government. We estimate the distribution of flood height levels, randomly select φ data points from the remaining non-flood events, and record when those data points occurred. For convenience, we assume that w pieces of data in H

_{A}′ are retrieved. Note that the newly retrieved data are expressed as H

_{A}″ = [h

_{A}(tr

_{1})″, h

_{A}(tr

_{2})″, …, h

_{A}(tr

_{w})″]. The times associated with these data points are Time

_{A}= {tr

_{1}, tr

_{2}, …, tr

_{w}}, where tr

_{1}, tr

_{2}, …, tr

_{w}are sorted chronologically but may be discontinuous.

_{A}= [p

_{A}(k

_{1}), p

_{A}(k

_{2}), …, p

_{A}(k

_{m})], where k

_{1}, k

_{2}, …, k

_{m}are continuous points in time, and the intervals between each point in time are k. We perform the following checks for the ith time point tr

_{i}of Time

_{A}.

_{j}in k

_{1}, k

_{2}, …, k

_{m}that precisely matches tr

_{i}, then we combine the k

_{j}th radar echo map p

_{A}(k

_{j}) with flood height h

_{A}(tr

_{i})″ as a single set of inputs and outputs.

_{1}, k

_{2}, …, k

_{m}that matches tr

_{i}, and the time interval between tr

_{i}and tr

_{i}

_{+1}is greater than k, then we find k

_{j}, the point in k

_{1}, k

_{2}, …, k

_{m}closest to tr

_{i.}We take the radar echo map p

_{A}(k

_{j}) of k

_{j}and flood height h

_{A}(tr

_{i})″ and combine them into a single set of inputs and outputs.

_{1}, k

_{2}, …, k

_{m}that matches tr

_{i}, and the time interval between tr

_{i}and tr

_{i}

_{+1}is less than k, we find k

_{j}, the point in k

_{1}, k

_{2}, …, k

_{m}closest to tr

_{i.}We take the radar echo map p

_{A}(k

_{j}) of k

_{j}and flood height h

_{A}(tr

_{i})’’ and combine them into a single set of inputs and outputs. Note that tr

_{i}

_{+1}and h

_{A}(tr

_{i}

_{+1})’’ are not considered in subsequent calculations.

_{A}, we obtain a set that can be used as the input and output for the subsequent CNN [(p

_{A}(tcnn

_{1}), h

_{A}(tcnn

_{1})″), (p

_{A}(tcnn

_{2}), h

_{A}(tcnn

_{2})″), …, (p

_{A}(tcnn

_{w′}), h

_{A}(tcnn

_{w}

_{′})″)], where tcnn

_{i}represents the ith data in this set, and w′ is the total number of data points in the set (i.e., w′ < w).

#### 3.2. CNN Architecture Used in Target Framework

_{A}(tcnn

_{i}) in CNN_IO, which represents a radar echo map with a grid size of α × β × γ, where β and γ represent the size of the radar echo map, and α indicates the number of characteristics of the radar echo map. The ith output data of the CNN is h

_{A}(tcnn

_{i}) in CNN_IO, which represents the flood height. As for the selection of CNN training, testing, and validation datasets, we recommend that the ratio should be set at 70%, 15%, 15% or 70%, 10%, 20% to meet most CNN training procedures. In addition, in order to maintain the independence of the three datasets, we suggest that the training, testing, and validation datasets be divided into different flooding events or into different flood years when the user has enough data.

_{z,x,y}= p

_{A}(tcnn

_{t})

_{z,x,y,}

_{z}

_{,x,y}is the output value of the neuron with the zth feature located at (x, y). The multi-layer convolutional layer is used mainly to extract features from the radar echo map. Assuming that the size of the radar echo map received by the CNN is x × y and the CNN uses a total of n convolutional layers, we recommend setting the filter size of the first convolutional layer in accordance with the ratio of x to y. We do this because the rectangular data input of this CNN should be transformed into a square to facilitate subsequent processing. The filter size in the second convolutional layer is based on the output size of the previous layer. The number of convolutional layers depends on the size of the input radar echo map. Regardless of the convolutional layer in which a neuron is located, it can be expressed using the following mathematical formula:

^{i}

_{(z,x,y)}is the output value of the ith neuron whose zth feature is located at (x, y). b

^{i}

_{k}and l

^{i}

_{k}are, respectively, the corresponding bias vector and kernel in the layer. I

_{(•,•,•)}is the input for this layer, and act(•)is the Relu activation function.

_{i}, R

_{i}, H

_{i}), then the output result is (C

_{0}, R

_{0}, H

_{0}), the pool size of this layer is (p, p), and stride is s, such that the mathematical formula of the neuron can be written as

_{0}= H

_{i}

_{i}, R

_{i}, H

_{i}), then the input of the first fully connected layer will be a vector of length C

_{i}× R

_{i}× H

_{i}. Each neuron in these fully connected layers can be expressed using the following formula:

_{i}represents the output of the ith node, D represents the number of input features, I

_{j}represents the feature input value from the jth node, w

_{ij}is the weight from the jth node of the input to the ith node of the output, bias

_{i}is the the offset vector of the ith node of the output, and σ(•) is a sigmoid function.

_{j}represents the output of a given node, σ(•) is the sigmoid function, and w

_{ij}and b

_{j}, respectively, indicate the corresponding weights and bias vectors.

#### 3.3. Using Grad-Cam to Identify Key Grid Cells

_{f}and n

_{f}, the channel size is s

_{c}, and the output result of the CNN is ô. We can calculate the weight w

_{c}of the cth channel of the feature map f

_{c}as follows:

_{f}× n

_{f}) is the term used to calculate global average pooling, and ∂ô/∂f

_{c}are gradients obtained via back propagation. We then combine the degree of importance of all feature maps to derive the degree to which each input grid cell influences the CNN output:

_{k}(i,j) indicates the importance of grid cell (i,j) calculated by Grad-Cam for the kth input data (1 ≤ k ≤ n), Fimp(i,j) is the final importance calculation for grid cell (i,j), w

_{k}is the weight value given by the user, indicating the degree of importance assigned by the user to each input. If the user believes that each piece of input data is of equal importance in prediction, then w

_{k}is set to 1. Finally, Equation (11) can be used to rank the importance of all grid cells from large to small, whereupon the top-ranking cells are selected as key grid cells.

#### 3.4. Lightweight Deep Neural Networks (LDNNs)

_{2}n) neurons in this layer, where ceiling(•) represents the unconditional roundup function. The number of neurons after the second fully connected layer decreases by a multiple of 2 or 4 until reaching 1, and the last layer is the output layer. Without a loss of generality, the formula in each neuron of fully connected layers can be written as follows:

_{j}represent the output of a given node, tanh(•) is the tangent sigmoid function, w

_{ij}is the corresponding weight, and b

_{i}is the bias vector corresponding to the jth neuron.

## 4. Simulation Experiments

#### 4.1. Data Sets and Experiment Parameters

#### 4.2. Selection of CNN Time Delay Parameter Indicating the Difference between the Radar Echo Map Input and Flood Height Output

#### 4.3. Effectiveness of LDNN

#### 4.4. Key Grid Cell Selection: Rationale

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

- Mecklenburg, S.; Bell, V.A.; Moore, R.J.; Joss, J. Interfacing an enhanced radar echo tracking algorithm with a rainfall-runoff model for real-time flood forecasting. Phys. Chem. Earth Part B Hydrol. Ocean. Atmos.
**2000**, 25, 1329–1333. [Google Scholar] [CrossRef] - Šálek, M.; Brezková, L.; Novák, P. The use of radar in hydrological modeling in the Czech Republic—Case studies of flash floods. Nat. Hazards Earth Syst. Sci.
**2006**, 6, 229–236. [Google Scholar] [CrossRef] - Novák, P.; Březková, L.; Frolík, P. Quantitative precipitation forecast using radar echo extrapolation. Atmos. Res.
**2009**, 93, 328–334. [Google Scholar] [CrossRef] - Yoon, S.S. Adaptive blending method of radar-based and numerical weather prediction QPFs for urban flood forecasting. Remote Sens.
**2019**, 11, 642. [Google Scholar] [CrossRef][Green Version] - Chen, L.; Cao, Y.; Ma, L.; Zhang, J. A Deep Learning-Based Methodology for Precipitation Nowcasting with Radar. Earth Space Sci.
**2020**, 7, e2019EA000812. [Google Scholar] [CrossRef][Green Version] - Yin, X.; Hu, Z.; Zheng, J.; Li, B.; Zuo, Y. Study on Radar Echo-Filling in an Occlusion Area by a Deep Learning Algorithm. Remote Sens.
**2021**, 13, 1779. [Google Scholar] [CrossRef] - Singh, S.; Sarkar, S.; Mitra, P. A deep learning based approach with adversarial regularization for Doppler weather radar ECHO prediction. In Proceedings of the 37th IEEE International Geoscience and Remote Sensing Symposium (IGARSS 2017), Fort Worth, TX, USA, 23–28 July 2017; pp. 5205–5208. [Google Scholar]
- Yin, J.; Gao, Z.; Han, W. Application of a Radar Echo Extrapolation-Based Deep Learning Method in Strong Convection Nowcasting. Earth Space Sci.
**2021**, 8, e2020EA001621. [Google Scholar] [CrossRef] - Yan, Q.; Ji, F.; Miao, K.; Wu, Q.; Xia, Y.; Li, T. Convolutional residual-attention: A deep learning approach for precipitation nowcasting. Adv. Meteorol.
**2020**, 2020. Available online: https://www.hindawi.com/journals/amete/2020/6484812/ (accessed on 2 December 2021). [CrossRef] - Han, S.; Mao, H.; Dally, W.J. Deep compression: Compressing deep neural networks with pruning, trained quantization and huffman coding. In Proceedings of the 4th International Conference on Learning Representations (ICLR 2016), San Juan, Puerto Rico, 2–4 May 2016; pp. 1–14. [Google Scholar]
- Li, H.; Kadav, A.; Durdanovic, I.; Samet, H.; Graf, H.P. Pruning filters for efficient ConvNets. In Proceedings of the 5th International Conference on Learning Representations (ICLR 2017), Toulon, France, 24–26 April 2017; pp. 1–13. [Google Scholar]
- Molchanov, P.; Mallya, A.; Tyree, S.; Frosio, I.; Kautz, J. Importance estimation for neural network pruning. In Proceedings of the 32th IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR 2019), Long Beach, CA, USA, 15–20 June 2019; pp. 11264–11272. [Google Scholar]
- Luo, J.H.; Wu, J.; Lin, W. Thinet: A filter level pruning method for deep neural network compression. In Proceedings of the 16th IEEE International Conference on Computer Vision (ICCV 2017), Venice, Italy, 22–26 October 2017; pp. 5058–5066. [Google Scholar]
- Sani, S.; Wiratunga, N.; Massie, S. Learning deep features for knn based human activity recognition. In Proceedings of the 25th International Conference on Case-Based Reasoning Workshops (ICCBR 2017), Trondheim, Norway, 26–28 June 2017; pp. 95–103. [Google Scholar]
- Mohammad, Y.; Matsumoto, K.; Hoashi, K. Deep feature learning and selection for activity recognition. In Proceedings of the 33rd Annual ACM Symposium on Applied Computing (SAC 2018), Pau, France, 9–13 April 2018; pp. 930–939. [Google Scholar]
- Chen, Y.C.; Li, D.C. Selection of key features for PM2.5 prediction using a wavelet model and RBF-LSTM. Appl. Intell.
**2021**, 51, 2534–2555. [Google Scholar] [CrossRef] - He, T.; Guo, J.; Chen, N.; Xu, X.; Wang, Z.; Fu, K.; Yi, Z. MediMLP: Using grad-CAM to extract crucial variables for lung cancer postoperative complication prediction. IEEE J. Biomed. Health Inform.
**2019**, 24, 1762–1771. [Google Scholar] [CrossRef] - Li, Y.; Yang, H.; Li, J.; Chen, D.; Du, M. EEG-based intention recognition with deep recurrent-convolution neural network: Performance and channel selection by Grad-CAM. Neurocomputing
**2020**, 415, 225–233. [Google Scholar] [CrossRef] - Marsot, M.; Mei, J.; Shan, X.; Ye, L.; Feng, P.; Yan, X.; Zhao, Y. An adaptive pig face recognition approach using Convolutional Neural Networks. Comput. Electron. Agric.
**2020**, 173, 105386. [Google Scholar] [CrossRef] - Thorndahl, S.; Nielsen, J.E.; Jensen, D.G. Urban pluvial flood prediction: A case study evaluating radar rainfall nowcasts and numerical weather prediction models as model inputs. Water Sci. Technol.
**2016**, 74, 2599–2610. [Google Scholar] [CrossRef] - Wang, X.; Kinsland, G.; Poudel, D.; Fenech, A. Urban flood prediction under heavy precipitation. J. Hydrol.
**2019**, 577, 123984. [Google Scholar] [CrossRef] - Jati, M.I.H.; Santoso, P.B. Prediction of flood areas using the logistic regression method (case study of the provinces Banten, DKI Jakarta, and West Java). J. Phys. Conf. Ser.
**2019**, 1367, 012087. [Google Scholar] [CrossRef] - Berkhahn, S.; Fuchs, L.; Neuweiler, I. An ensemble neural network model for real-time prediction of urban floods. J. Hydrol.
**2019**, 575, 743–754. [Google Scholar] [CrossRef] - Arora, A.; Arabameri, A.; Pandey, M.; Siddiqui, M.A.; Shukla, U.K.; Bui, D.T.; Bhardwaj, A. Optimization of state-of-the-art fuzzy-metaheuristic ANFIS-based machine learning models for flood susceptibility prediction mapping in the Middle Ganga Plain, India. Sci. Total Environ.
**2021**, 750, 141565. [Google Scholar] [CrossRef] - Kabir, S.; Patidar, S.; Xia, X.; Liang, Q.; Neal, J.; Pender, G. A deep convolutional neural network model for rapid prediction of fluvial flood inundation. J. Hydrol.
**2020**, 590, 125481. [Google Scholar] [CrossRef] - Hsu, S.Y.; Chen, T.B.; Du, W.C.; Wu, J.H.; Chen, S.C. Integrate weather radar and monitoring devices for urban flooding surveillance. Sensors
**2019**, 19, 825. [Google Scholar] [CrossRef][Green Version] - Ichim, L.; Popescu, D. Flooded areas evaluation from aerial images based on convolutional neural network. In Proceedings of the 37th IEEE International Geoscience and Remote Sensing Symposium (IGARSS 2017), Fort Worth, TX, USA, 23–28 July 2017; pp. 9756–9759. [Google Scholar]
- Hata, E.; Seo, C.; Nakayama, M.; Iwasaki, K.; Ohkawauchi, T.; Ohya, J. Classification of aortic stenosis using ECG by deep learning and its analysis using grad-CAM. In Proceedings of the 42nd Annual International Conference of the IEEE Engineering in Medicine & Biology Society (EMBC 2020), Montréal, QC, Canada, 20–24 July 2020; pp. 1548–1551. [Google Scholar]
- Chueh, K.M.; Hsieh, Y.T.; Ma, I.H.; Chen, H.H.; Huang, S.L. Differentiation of gender from macular optical coherence tomography using deep learning. In Proceedings of the 25th Opto-Electronics and Communications Conference (OECC 2020), Taipei, Taiwan, 4–8 October 2020; pp. 1–3. [Google Scholar]
- Panwar, H.; Gupta, P.K.; Siddiqui, M.K.; Morales-Menendez, R.; Bhardwaj, P.; Singh, V. A deep learning and grad-CAM based color visualization approach for fast detection of COVID-19 cases using chest X-ray and CT-Scan images. Chaos Solitons Fractals
**2020**, 140, 110190. [Google Scholar] [CrossRef] - Seerala, P.K.; Krishnan, S. Grad-CAM-based classification of chest X-Ray images of pneumonia patients. In Proceedings of the 6th International Symposium on Signal Processing and Intelligent Recognition Systems (SIRS 2020), Chennai, India, 14–17 October 2020; pp. 161–174. [Google Scholar]
- Zhang, J.; Teng, Y.F.; Chen, W. Support vector regression with modified firefly algorithm for stock price forecasting. Appl. Intell.
**2019**, 49, 1658–1674. [Google Scholar] [CrossRef] - Smola, A.J.; Schölkopf, B. A tutorial on support vector regression. Stat. Comput.
**2004**, 14, 199–222. [Google Scholar] [CrossRef][Green Version] - Xu, Y.; Wang, L. K-nearest neighbor-based weighted twin support vector regression. Appl. Intell.
**2014**, 41, 299–309. [Google Scholar] [CrossRef] - Ohmori, S. A Predictive Prescription Using Minimum Volume k-Nearest Neighbor Enclosing Ellipsoid and Robust Optimization. Mathematics
**2021**, 9, 119. [Google Scholar] [CrossRef] - Malazi, H.T.; Davari, M. Combining emerging patterns with random forest for complex activity recognition in smart homes. Appl. Intell.
**2018**, 48, 315–330. [Google Scholar] [CrossRef] - Kim, S.; Jeong, M.; Ko, B.C. Lightweight surrogate random forest support for model simplification and feature relevance. Appl. Intell.
**2021**, 1–11. [Google Scholar] [CrossRef] - Wang, M.; Yue, L.; Cui, X.; Chen, C.; Zhou, H.; Ma, Q.; Yu, B. Prediction of extracellular matrix proteins by fusing multiple feature information, elastic net, and random forest algorithm. Mathematics
**2020**, 8, 169. [Google Scholar] [CrossRef][Green Version] - Civil IoT Taiwan-Establishing IoT-Based Intelligent Environment Monitoring System. Available online: https://ci.taiwan.gov.tw/dsp/en/index.aspx (accessed on 2 December 2021).
- Li, M.; Soltanolkotabi, M.; Oymak, S. Gradient descent with early stopping is provably robust to label noise for overparameterized neural networks. In Proceedings of the International conference on artificial intelligence and statistics, online, 26–28 August 2020; pp. 4313–4324. [Google Scholar]
- Hazra, A.; Choudhary, P.; Inunganbi, S.; Adhikari, M. Bangla-Meitei Mayek scripts handwritten character recognition using Convolutional Neural Network. Appl. Intell.
**2021**, 51, 2291–2311. [Google Scholar] [CrossRef] - Prechelt, L. Early Stopping—But When? In Neural Networks: Tricks of the Trade. Lecture Notes in Computer Science; Springer: Berlin/Heidelberg, Germany, 1998; Volume 1524, pp. 55–69. [Google Scholar]
- Chen, Y.C.; Lei, T.C.; Yao, S.; Wang, H.P. PM2.5 Prediction Model Based on Combinational Hammerstein Recurrent Neural Networks. Mathematics
**2020**, 8, 2178. [Google Scholar] [CrossRef]

**Figure 5.**Example illustrating the outcomes of time differences (time points and intervals) between flood sensors and the radar echo map.

**Figure 9.**Map of study regions: (

**a**) Location of Yilan and Yunlin within Taiwan; (

**b**) detailed map of Yilan; (

**c**) detailed map of Yunlin.

**Figure 10.**Flood height indicator along public road: (

**a**) Photographs of installation. (

**b**) Photograph of water level gauges.

**Figure 12.**The time series of flood heights in five monitoring locations. (

**a**) Yilan place 1. (

**b**) Yilan place 2. (

**c**) Yilan place 3. (

**d**) Yunlin place 1. (

**e**) Yunlin place 2.

**Figure 15.**Key grid cells selected from among Grad-Cam results in Yilan area. (

**a**) Key grid cells of place 1. (

**b**) Key grid cells of place 2. (

**c**) Key grid cells of place 3.

**Figure 16.**Radar echo maps of the actual flood event 1 in Yilan (26 June 2020, A.M. 04:40~05:10): (

**a**) 04:40. (

**b**) 04:50. (

**c**) 05:00. (

**d**) 05:10.

**Figure 17.**Radar echo maps of the actual flood event 2 in Yilan (30 June 2020, A.M. 07:50~08:20): (

**a**) 07:50. (

**b**) 08:00. (

**c**) 08:10. (

**d**) 08:20.

**Figure 18.**Key grid cells selected from the Grad-Cam results in Yunlin area. (

**a**) Key grid cells of place 1. (

**b**) Key grid cells of place 2.

Yilan | Yunlin | ||||
---|---|---|---|---|---|

Place 1 | Place 2 | Place 3 | Place 1 | Place 2 | |

Average | 0.645 | 0.598 | 0.363 | 1.332 | 0.595 |

Standard Deviation | 4.565 | 1.187 | 1.896 | 1.083 | 0.997 |

Number of data in the dataset | 4320 | 4320 | 4320 | 4464 | 4464 |

Number of flooded data in the dataset | 526 | 658 | 834 | 1143 | 2761 |

Number of data used in the experiment | 1052 | 1316 | 1668 | 2286 | 4464 |

Time Delay | Yilan | Yunlin | |||
---|---|---|---|---|---|

Place 1 | Place 2 | Place 3 | Place 1 | Place 2 | |

30 min | 4.309 | 0.192 | 2.203 | 1.775 | 0.706 |

60 min | 4.514 | 1.873 | 2.348 | 2.688 | 1.641 |

90 min | 5.023 | 1.932 | 2.614 | 2.83 | 1.549 |

120 min | 5.314 | 2.306 | 3.431 | 3.691 | 1.978 |

150 min | 5.967 | 2.684 | 3.739 | 5.034 | 2.261 |

Number of Key Grid Cells | Yilan | Yunlin | |||
---|---|---|---|---|---|

Place 1 | Place 2 | Place 3 | Place 1 | Place 2 | |

10 | 4.286 | 0.401 | 2.203 | 1.23 | 0.947 |

20 | 4.351 | 0.359 | 2.231 | 1.175 | 1.252 |

30 | 4.215 | 0.293 | 2.468 | 1.16 | 1.303 |

40 | 3.948 | 0.285 | 2.649 | 1.169 | 1.342 |

50 | 3.907 | 0.296 | 2.591 | 1.194 | 1.353 |

60 | 3.97 | 0.281 | 2.672 | 1.189 | 1.369 |

70 | 4.621 | 0.21 | 2.73 | 1.206 | 1.368 |

80 | 5.296 | 0.192 | 2.794 | 1.214 | 1.376 |

90 | 5.684 | 0.275 | 2.943 | 1.218 | 1.393 |

100 | 6.102 | 0.33 | 2.926 | 1.23 | 1.405 |

Model | Yilan | Yunlin | |||
---|---|---|---|---|---|

Location 1 | Location 2 | Location 3 | Location 1 | Location 2 | |

CNN | 4.309 | 0.192 | 2.203 | 1.775 | 0.706 |

LDNN (all) | 4.738 | 0.3 | 2.702 | 1.945 | 1.336 |

LDNN (n) | 3.907 | 0.192 | 2.203 | 1.16 | 0.947 |

Type of Costs | Yilan | Yunlin | |||
---|---|---|---|---|---|

Location 1 | Location 2 | Location 3 | Location 1 | Location 2 | |

Time-CNN | 1920 s | 1884 s | 1936 s | 2316 s | 2340 s |

Time-LDNN | 105 s | 173 s | 68 s | 142 s | 120 s |

Time-Reduced ratio | 94.5% | 90.8% | 96.4% | 93.9% | 94.9% |

Memory-CNN | 814 MB | 821 MB | 817 MB | 930 MB | 926 MB |

Memory-LDNN | 64 MB | 92 MB | 50 MB | 92 MB | 79 MB |

Memory-Reduced ratio | 92.1% | 88.8% | 93.9% | 90.1% | 91.5% |

Type of Costs | Yilan | Yunlin | |||
---|---|---|---|---|---|

Location 1 | Location 2 | Location 3 | Location 1 | Location 2 | |

Time-CNN | 58 s | 56 s | 58 s | 94 s | 96 s |

Time-LDNN | 9 s | 11 s | 6 s | 10 s | 8 s |

Time-Reduced ratio | 84.5% | 80.3% | 89.6% | 89.4% | 91.7% |

Memory-CNN | 68 MB | 71 MB | 70 MB | 97 MB | 94 MB |

Memory-LDNN | 20 MB | 24 MB | 15 MB | 33 MB | 30 MB |

Memory-Reduced ratio | 70.5% | 66.2% | 78.5% | 66.0% | 68.1% |

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Chen, Y.-C.; Chang, T.-Y.; Chow, H.-Y.; Li, S.-L.; Ou, C.-Y.
Using Convolutional Neural Networks to Build a Lightweight Flood Height Prediction Model with Grad-Cam for the Selection of Key Grid Cells in Radar Echo Maps. *Water* **2022**, *14*, 155.
https://doi.org/10.3390/w14020155

**AMA Style**

Chen Y-C, Chang T-Y, Chow H-Y, Li S-L, Ou C-Y.
Using Convolutional Neural Networks to Build a Lightweight Flood Height Prediction Model with Grad-Cam for the Selection of Key Grid Cells in Radar Echo Maps. *Water*. 2022; 14(2):155.
https://doi.org/10.3390/w14020155

**Chicago/Turabian Style**

Chen, Yi-Chung, Tzu-Yin Chang, Heng-Yi Chow, Siang-Lan Li, and Chin-Yu Ou.
2022. "Using Convolutional Neural Networks to Build a Lightweight Flood Height Prediction Model with Grad-Cam for the Selection of Key Grid Cells in Radar Echo Maps" *Water* 14, no. 2: 155.
https://doi.org/10.3390/w14020155