Convolutional Neural Network Coupled with a Transfer-Learning Approach for Time-Series Flood Predictions

Abstract

East Asian regions in the North Pacific have recently experienced severe riverine flood disasters. State-of-the-art neural networks are currently utilized as a quick-response flood model. Neural networks typically require ample time in the training process because of the use of numerous datasets. To reduce the computational costs, we introduced a transfer-learning approach to a neural-network-based flood model. For a concept of transfer leaning, once the model is pretrained in a source domain with large datasets, it can be reused in other target domains. After retraining parts of the model with the target domain datasets, the training time can be reduced due to reuse. A convolutional neural network (CNN) was employed because the CNN with transfer learning has numerous successful applications in two-dimensional image classification. However, our flood model predicts time-series variables (e.g., water level). The CNN with transfer learning requires a conversion tool from time-series datasets to image datasets in preprocessing. First, the CNN time-series classification was verified in the source domain with less than 10% errors for the variation in water level. Second, the CNN with transfer learning in the target domain efficiently reduced the training time by 1/5 of and a mean error difference by 15% of those obtained by the CNN without transfer learning, respectively. Our method can provide another novel flood model in addition to physical-based models.

1. Introduction

The East Asian regions along the North Pacific have recently experienced an increase in catastrophic flood disasters due to larger and stronger typhoons. To reduce and mitigate flood disasters, artificial neural network (ANN) models may be a beneficial tool for accurately and quickly forecasting riverine flood events in localized areas [1], in addition to conventional physical models [2]. In Japan, areas vulnerable to strong typhoons and heavy rainfall events have experienced severe riverine flood disasters in the last 3–4 years [3]. An overflow-risk warning system that is based on real-time observed data has been successfully working for most major rivers in Japan. However, a flood warning system that can forecast with a quick response has not been practically implemented in specific locations of rivers. If the specific time and location of inundation were forecasted by the flood warning system before the inundation occurred, most people may have been able to evacuate these locations in past flood disasters. Consequently, the number of victims may have been reduced. When a forecast flood warning system is developed for practical use, an ANN model with deep learning is a candidate due to the model’s features. The ANN model is a data-driven model that does not need physical-based parameter setups unlike physical models. For example, a rainfall-runoff model should be calibrated, using numerous parameters that are based on complex physical laws in a target watershed [4]. Like the rainfall-runoff model, the setup of a physical model requires heavy work. The ANN model can predict a near-future trend that is based only on the learning of past data. ANN prediction usually has a low computational cost, although the learning incurs high computational costs. The major beneficial uses of the ANN-based flood model are related to a quick response to symptoms of a near-future flood event and an easy run using only past data [5].

Numerous studies of ANN models have been performed for flood predictions [6]. ANN models that adopt a deep learning approach have been recently employed in practical flood predictions [7]. As another type of ANN model, the long, short-term memory (LSTM) architecture [8,9] was utilized for water-level predictions during flood events [10,11,12].

In most case studies, ANN models successfully predicted past flood events with numerous datasets. In general, ANN models require high computational costs in the training process due to large datasets. To reduce the high cost of computational runs, our study introduces a transfer-learning approach [13]. The premise of the approach is that a model pretrained by large datasets in a source domain can be reused in other target domains. After retraining the part of the pretrained model with the datasets of the target domains, the retrained model can provide reasonable outputs with a low computational cost.

Our focus on flood events is to predict time-series data, such as water levels. The LSTM architecture implemented in an ANN model is the best tool for the treatment of time-series data. LSTM coupled with transfer learning has been developed. Laptev et al. [14] reported that their multilayer LSTM with transfer learning reduced errors more than LSTM without transfer learning in the long-term trends in electric energy consumption in the U.S. However, LSTM generally has not been successful especially for short-time, rapidly changing, and non-periodical data, such as data on flood wave. This finding can be explained as follows: An unknown value at a subsequent time step is rarely predicted from the present value because numerous temporal trends may exist [15].

A convolutional neural network (CNN) architecture [16] is primarily employed for two-dimensional (2D)-spatial image classification. The implementation of CNN in an ANN model achieved satisfactory performances with transfer learning in a variety of image analysis fields [17,18]. The ImageNet created by VGG16 [19], which uses 150 million images, is often employed to perform image classification for a new image dataset. CNN with transfer learning is successful because a CNN gradually structures from low-level visual features on a previous layer to semantic features that are specific to a dataset on a deeper layer [20,21]. Therefore, we considered that a CNN with transfer learning is more reliable and practical than a LSTM with transfer learning.

A technical challenge is to perform a conversion from time-series data to image data in an ANN model. Several studies have reported how to map time-series trends in a 2D spatial image. For example, stock market predictions in near-future trend employed the image of 31 stocks × 100 time steps [22]. The precipitation predictions utilized an image of spatial information of climates in time series, such as air temperatures at eight locations × eight time steps with a ten-minute interval [23]. If we apply these conversion techniques, the CNN coupled with a transfer-learning approach can predict time-series data for flood events.

This paper proposes a new data-driven-based model for flood modeling. The model consists of a CNN incorporated with transfer learning to efficiently and quickly predict time-series water levels in flood events even in different domains after pretraining the CNN in a certain domain. First, we will show the verification of the CNN-based flood model in large datasets obtained in a certain watershed. Second, we will evaluate the performance of the CNN with a transfer-learning approach in a different watershed. Last, we will evaluate the prediction accuracy for the number of retrainings of the CNN with the transfer learning.

2. Materials and Methods

2.1. Study Site

We selected two watersheds that do not have flood control facilities such as large dams and ponds (Figure 1). The first watershed is a part of the Oyodo River watershed, which is located in Southwest Japan. The watershed has an area of 861 km², a main river with a length of 52 km that flows to the Hiwatashi gauge station near Oyodo River Dam (31.7870° N, 131.2392° E) downstream, and an elevation that ranges from 118 to 1350 m. The area often experiences heavy rainfall events from the summer to early fall due to typhoons. This watershed is named “Domain A” in this study. Another watershed is the Abashiri River watershed toward the northeast of Hokkaido. The watershed has an area of 1380 km², a main river with a length of 115 km that flows to the outlet in the North Pacific, and an elevation that ranges from 0 to 978 m. Heavy rainfall events have seldom occurred due to weak monsoon impacts and few occurrences of typhoon tracks and approaches. We refer to this watershed as “Domain B”.

2.2. Data Acquisition

The hourly datasets for rainfalls and water levels from 1992 to 2017 in Domain A and 2000 to 2019 in Domain B were obtained from the website of the hydrology and water-quality database [24], managed by the Ministry of Land, Infrastructure, Transport, and Tourism in Japan (MLIT Japan) and the meteorological database [25] that belongs to the Japan Meteorological Agency (JMA). The observed datasets in Domain A were obtained from five gauge stations for water level and 11 gauge stations for rainfall. Domain B had four water-level stations and nine rainfall stations. The downstream stations where the model predicts water levels were Hiwatashi for Domain A and Hongou for Domain B (Figure 1). We focused on the historical flood events at each domain. Each flood event has a 123-hour duration, including the time of the flood maximum peak, three days before the peak, and two days after the peak. One maximum peak during the duration of each flood event was identified when the water level exceeded a certain criterion of water levels—approximately 45% to 60% of the highest peak of the observed datasets among all flood events. The quantity of data for each flood event is 123. If multiple peaks exist locally in one flood event, note that only the highest peak is regarded as the maximum value of the event. The datasets in Domain A and Domain B are listed in

Table 1. Flood events in Domain A.

Event Name	Start Time 1	End Time 1	Maximum Water Level (m) During Each Event 2,3	Remarks
8/5/1992	8/5/1992 21:00	8/10/1992 23:00	4.56
7/29/1993	7/29/1993 20:00	8/3/1993 22:00	9.50	3rd position
8/7/1993	8/7/1993 2:00	8/12/1993 4:00	8.04
8/13/1993	8/31/1993 19:00	9/5/1993 21:00	6.99
6/10/1994	6/10/1994 20:00	6/15/1994 22:00	4.80
6/1/1995	6/1/1995 6:00	6/6/1995 8:00	4.66
6/22/1995	6/22/1995 15:00	6/27/1995 17:00	6.90
7/15/1996	7/15/1996 19:00	7/20/1996 21:00	6.84
8/11/1996	8/11/1996 23:00	8/17/1996 1:00	5.18
8/4/1997	8/4/1997 0:00	8/9/1997 2:00	5.05
7/24/1999	7/24/1999 0:00	7/29/1999 2:00	6.72
8/14/1999	8/14/1999 15:00	8/19/1999 17:00	6.03
9/11/1999	9/11/1999 20:00	9/16/1999 22:00	8.26
9/21/1999	9/21/1999 19:00	9/26/1999 21:00	5.42
5/31/2000	5/31/2000 14:00	6/5/2000 16:00	6.47
6/18/2001	6/18/2001 20:00	6/23/2001 22:00	5.30
8/5/2003	8/5/2003 10:00	8/10/2003 12:00	6.79
8/27/2004	8/27/2004 10:00	9/1/2004 12:00	9.80	2nd position
10/17/2004	10/17/2004 9:00	10/22/2004 11:00	7.70
9/3/2005	9/3/2005 8:00	9/8/2005 10:00	10.65	highest peak
6/21/2006	6/21/2006 23:00	6/27/2006 1:00	4.99
7/19/2006	7/19/2006 11:00	7/24/2006 13:00	5.28
8/15/2006	8/15/2006 18:00	8/20/2006 20:00	5.20
7/8/2007	7/8/2007 21:00	7/13/2007 23:00	5.58
7/11/2007	7/11/2007 15:00	7/16/2007 17:00	7.11
9/28/2008	9/28/2008 16:00	10/3/2008 18:00	5.18
6/17/2010	6/17/2010 18:00	6/22/2010 20:00	6.30
6/30/2010	6/30/2010 7:00	7/5/2010 9:00	9.16
6/13/2011	6/13/2011 23:00	6/19/2011 1:00	4.84
6/18/2011	6/18/2011 0:00	6/23/2011 2:00	4.77
6/19/2012	6/19/2012 7:00	6/24/2012 9:00	5.13
6/25/2012	6/25/2012 7:00	6/30/2012 9:00	4.60
7/10/2012	7/10/2012 18:00	7/15/2012 20:00	5.86
6/25/2014	6/25/2014 10:00	6/30/2014 12:00	5.31
7/28/2014	7/28/2014 17:00	8/2/2014 19:00	6.61
8/6/2014	8/6/2014 8:00	8/11/2014 10:00	6.08
7/19/2015	7/19/2015 18:00	7/24/2015 20;00	5.05
8/22/2015	8/22/2015 18:00	8/27/2015 20:00	4.62
6/25/2016	6/25/2016 19:00	6/30/2016 21:00	6.09
7/6/2016	7/6/2016 3:00	7/11/2016 5:00	5.52
7/11/2016	7/11/2016 11:00	7/16/2016 13:00	6.21
9/17/2016	9/17/2016 5:00	9/22/2016 7:00	7.91
8/4/2017	8/4/2017 5:00	8/9/2017 7:00	5.13

¹ Date and time is denoted as month/day/year hour:minute; ² Maximum value at each event was observed at Hiwatashi Station; ³ Risk levels for near flooding occurrence and flooding cautionary exceed 9.20 and 6.00 m, respectively.

and

Table 2. Flood events in Domain B.

Event Name	Start Time 1	End Time 1	Maximum Water Level (m) During Each Event 2,3	Remarks
4/9/2000	4/9/2000 8:00	4/14/2000 10:00	3.81
9/9/2001	9/9/2001 18:00	9/14/2001 20:00	4.84	2nd position
9/30/2002	9/30/2002 2:00	10/5/2002 4:00	3.38
8/7/2003	8/7/2003 21:00	8/12/2003 23:00	4.28
4/18/2006	4/18/2006 22:00	4/24/2006 0:00	3.30
8/17/2006	8/17/2006 1:00	8/22/2006 3:00	4.04
10/6/2006	10/6/2006 2:00	10/11/2006 4:00	4.77	3rd position
10/7/2009	10/7/2009 5:00	10/12/2009 7:00	3.33
9/20/2011	9/20/2011 0:00	9/25/2011 2:00	3.20
4/5/2013	4/5/2013 7:00	4/10/2013 9:00	3.71
9/14/2013	9/14/2013 13:00	9/19/2013 15:00	4.33
10/6/2015	10/6/2015 9:00	10/11/2015 11:00	4.15
8/15/2016	8/15/2016 16:00	8/20/2016 18:00	4.17
8/19/2016	8/19/2016 4:00	8/24/2016 6:00	5.03	highest peak
8/28/2016	8/28/2016 21:00	9/2/2016 23:00	3.46
9/7/2016	9/7/2016 12:00	9/12/2016 14:00	4.15
8/7/2019	8/7/2019 0:00	8/12/2019 2:00	3.22	provisional value

¹ Date and time is denoted as month/day/year hour:minute. ² Maximum value at each event was observed at Hongou Station. ³ Risk levels for near flooding occurrence and flooding cautionary exceed 5.30 and 3.20 m, respectively.

, respectively. The geographical and observational characteristics of both domains are shown in

Table 3. Characteristics of the two domains.

	Domain A	Domain B
Number of events	43	17
Maximum water level (at prediction location)	10.65 m	5.03 m
Number of water level stations	5	4
Number of rainfall stations	11	9
Watershed area	861 km2	1319 km2
Prediction location	Hiwatashi (31.8599° N, 131.1135° E)	Hongou (43.9096° N, 144.1385° E)
Main river name	Oyodo River	Abashiri River

.

2.3. ANN and CNN Features

An ANN model usually consists of three layers—input layer, hidden layer, and output layer—and creates network with neurons. Note that the hidden layer often has multiple layers as a deep learning approach. Each neuron has an activation function that filters input values x with weighted coefficients w into an output value z. If a layer has n neurons, a certain neuron j in a subsequent layer receives n input values. These inputs weighted by coefficients are integrated and added by bias b_j. The activation function f outputs z_j from a neuron. These variables are defined in the following equations. The structure of the ANN model is shown in Figure 2.

$$y_j=b_j+{{\displaystyle \sum }}_{i=1}^n{w}_{i,j}{x}_i,$$

(1)

$$z_j=f\left(y_j\right) .$$

(2)

A CNN is a type of ANN architecture with a deep-learning approach. We created a relatively simple algorithm of a CNN based on past studies [16,23]. The variables in Equations (1) and (2) are mapped to the 2D spatial image in the CNN, which consists of a convolution layer (convolution) and a max-pooling layer (pooling). We consider that the input variable x has L × L 2D source pixels, which is filtered with a H × H small window of convolution with a table of weighted values. The convolution takes the same size of values from the source image, and then multiplies the weighted values of the H × H window to the filtered values of source pixels. The filtering is repeated over the source image by shifting the window. Components of the input and filter are defined as x_i,j (1 ≤ i ≤ L, 1 ≤ j ≤ L) and w_k,l,n (0 ≤ k ≤ H − 1, 0≤ l ≤ H − 1, 1 ≤ n ≤ N), respectively. This process is shown in Figure 3. Note that a zero-padding technique was introduced to ensure that the size of input is equivalent to that of the output. The x_i,j is multiplied by w_k,l,n while separately shifting a grid at (i,j) on the filtering. This equation, including the convolution form and bias b_n in the function, is expressed as follows:

$$y_{i,j,n}={{\displaystyle \sum }}_{k=0}^{H-1}{{\displaystyle \sum }}_{l=0}^{H-1}{w}_{k,l,n}{\widehat{x}}_{i+k,j+l}+b_n,$$

(3)

$$z_{i,j,n}=f\left(y_{i,j,n}\right) .$$

(4)

We use a rectified linear unit (ReLU) as the activation function (f), which can select positive input values due to an improvement in the conversion of a matrix, as expressed in the following equation.

$$f\left(y_{i,j,n}\right)=\max \left(y_{i,j,n},0\right).$$

(5)

By filtering in the convolution, common features among images are extracted when the filter pattern is similar to a portion of each image.

The pooling does not have weighted coefficients and activation functions, is usually utilized to produce 2D data, and is defined in the following equation:

$$z_{p,q}=\max \left(x_{i,j,k}\right), (i, j) \mathsf{ϵ} U_p{,}_q,$$

(6)

where U_p,q is the square unit domain with the size R × R and (p,q) are the horizontal and vertical components. U_p,q is moved on a 2D image with a non-overlap approach. As horizontal and vertical scales are shrunk 1/R times, the maximum value of x_i,j,n in U_p,q provides output with a data size of 1/R² times of the input 2D data. The features extracted by the convolution can satisfy the consistency by means of the pooling even if the same features in reality are recognized as different features due to searching errors. Our CNN algorithm had two convolution layers and two pooling layers.

By performing these processes, smaller-size 2D image data are generated and then passed to a fully connected layer, which has the same function of Equations (1) and (2). These 2D image data are converted into numerous 1D digital datasets that involve information about classification of the original image. A softmax function is a normalized exponential function in Equation (7) that converts outputs to probability quantities in the output layer. It evaluates the binary classification.

$$f\left(y_j\right)=e^{y_j}/{{\displaystyle \sum }}_{r=1}^m{e}^{y_r}.$$

(7)

However, our model prediction requires a specific magnitude of water level, instead of classification. Therefore, we introduced the sigmoid function into the softmax position to assign the magnitude from the normalized value (0 to 1) between the maximum value and the minimum value of the water levels.

2.4. Transfer Learning

We assume that two domains exist separately. When a model is trained in a certain (source) domain with large datasets, it usually takes ample time to have an accurate prediction. If the model is applied to another (target) domain without any connection with the source domain, training it causes ample time. Transfer learning is one of the solution methods for improvement of the efficient prediction (e.g., reduction of run time) in the target domain [13]. The transfer learning can reuse common knowledge obtained from the source domain for the target domain. This overview sketch is shown in Figure 4. The CNN coupled with a transfer-learning approach (CNN transfer learning) is a recently successful method in image classification. As our model should perform time-series predictions, CNN transfer learning was utilized in this study by means of a conversion tool between time-series data and image data. First, the CNN was run in the source domain (Figure 5a). Second, parts of the hidden layers of the CNN were fixed and reused in the target domain. Last, “the fully connected layer 1” and “the fully connected layer 2” in the deep layers were retrained, using the datasets of the target domain (Figure 5b).

2.5. Data Conversion from Time-Series to Image

To perform time-series predictions with the CNN, a conversion method between time-series data and image data is necessary. As shown in Figure 6, our method was a simple way to arrange 16 variables (rainfall and water level) at all gauge stations from upstream to downstream on the vertical, and to arrange the temporal variation of each variable on the horizontal. The digital values were then converted to an image by using a black-and-white gradation that ranges from zero to one and is normalized by the maximum and minimum values of all observed datasets of water level and rainfall. The spacing between two values on the horizontal axis was one hour. The interval of the vertical axis was one for simplicity.

The image in the CNN has to correspond to a value of the water level in the time progress when train and prediction are conducted in the CNN. A 16 × 16 image was selected from the 2D image of a flood event due to the limited number of variables. A square image is used as input data. The information from the input data was associated with a 1 × 1 image (i.e., value) of the output data at the predicted point. We assumed that the flood-related information in a square image generates the value of the predicted point in the next time step (i.e., in an hour). Note that the predicted point indicates a location where water levels are predicted. This treatment was separately repeated in time progress as shifted from the head of the 2D image to the tail. Drawing information is shown in Figure 7. This data treatment was also employed when the LSTM predicts the value in advance using current and 15 past data values provided from 16 variables. The LSTM searches the relationship among plural line-based data; however, the CNN finds spatial patterns among 2D images.

The number of variables (i.e., four for water-level gauges and nine for rain gauges) in Domain B differs from that of Domain A. To make the image size of Domain B equivalent to that of Domain A, as shown in Figure 6, the image size has been expanded from 123 × 13 to 123 × 16, using the interpolation that maintains high-resolution images with the Lanczos algorithm [26].

2.6. Computational Setups in CNN and CNN Transfer Learning

Four cases were selected to evaluate the errors between predicted outputs and observed outputs in Domain A, using the CNN, and those in Domain B, using CNN transfer learning. These cases involved datasets that had the first-to third-position highest peaks in each domain (top three datasets) and two datasets with midlevel peaks, which were chosen among the other events in each domain. The four cases of the top three datasets and one midlevel-peak dataset were used as the datasets of the test process. Note that another midlevel-peak data set remains in the validation data set to evaluate at least one midlevel-peak dataset during the validation process. First, the CNN was trained with the training datasets, excluding the top three datasets and two moderate-peak datasets. Second, the trained CNN was checked to see whether a loss function shows overfitting, using validation datasets, including the top three datasets and the two datasets with moderate peaks as a representative of most datasets. This validation is usually performed to conduct a no-bias evaluation of a model. Last, a test was performed using one of the top three datasets or the moderate-peak dataset. In general, these procedures are usually utilized in machine learning [27,28]. In Domain A, we chose 38 events for training, four events for validation, and one event for testing (

Table 4. Source datasets for training, validation, and testing in Domain A.

Source Case	Training Datasets	Validation Datasets	Test Dataset
A1	8/5/1992, 8/31/1993, 6/10/1994, 6/1/1995, 6/22/1995, 7/15/1996, 8/11/1996, 8/4/1997, 7/24/1999, 9/11/1999, 9/21/1999, 5/31/2000, 5/31/2000, 6/18/2001, 8/5/2003, 10/17/2004, 6/21/2006, 7/19/2006, 8/15/2006, 7/8/2007, 7/11/2007, 9/28/2008, 6/17/2010, 6/30/2010, 6/13/2011, 6/19/2012, 6/25/2012, 7/10/2012, 6/25/2014, 7/28/2014, 8/6/2014, 7/19/2015, 8/22/2015, 6/25/2016, 7/6/2016, 7/11/2016, 9/17/2016, 8/4/2017	8/7/1993, 8/14/1999, 8/27/2004, 9/3/2005	7/29/1993
A2		7/29/1993, 8/7/1993, 8/14/1999, 9/3/2005	8/27/2004
A3		7/29/1993, 8/7/1993, 8/14/1999, 8/27/2004	9/3/2005
A4		7/29/1993, 8/7/1993, 8/27/2004, 9/3/2005	8/14/1999

). Domain B had 12 events for training, four events for validation, and one event for testing (

Table 5. Target datasets for training, validation, and testing in Domain B.

Source Case	Training Datasets	Verification Datasets	Test Dataset
B1	9/30/2002, 8/7/2003, 4/18/2006, 8/17/2006, 10/7/2009, 4/5/2013, 9/14/2013, 10/6/2015, 8/15/2016, 8/28/2016, 9/7/2016, 8/7/2019	4/9/2000, 9/9/2001, 10/6/2006, 9/20/2011	8/19/2016
B2		4/9/2000, 10/6/2006, 9/20/2011, 8/19/2016	9/9/2001
B3		4/9/2000, 9/9/2001, 9/20/2011, 8/19/2016	10/6/2006
B4		4/9/2000, 9/9/2001, 10/6/2006, 8/19/2016	9/20/2011

).

The programs for the flood models (CNN and CNN transfer learning) were created by Python (version 3.6.4) [29], incorporated with Keras libraries [30] on the Window-OS PC that has the Intel(R) Core(TM) i7-4770K CPU @ 3.50GHz. The setups of several parameters, such as batch size, epoch number, and activation functions, are shown in

Table 6. Setups of CNN parameters and functions.

Parameters		Values/Function	Remarks
Convolutional layer	Filter size	3 × 3
	Filter number	5
Pooling layer	Filter size	2 × 2
Fully connected layer 1	Neuron number	16
Fully connected layer 2	Neuron number	1
Learning process	Batch size	100
	Epoch number	100
	Learning rate	0.001
	Optimizer	Adam
Activation function 1 to 3		ReLU	See Figure 5a
Activation function 4		Sigmoid/softmax	See Figure 5a
Loss function		Mean square error = $\frac{1}{N1}{{\displaystyle \sum }}_{i=1}^{N1}{\left(V_{ci}-V_{oi}\right)}^2$	ci = model prediction, oi = observed data, N1 = the number of data
Error evaluation		Root mean square error (RMSE) = $\sqrt{\frac{1}{N1}{{\displaystyle \sum }}_{i=1}^{N1}{\left(V_{ci}-V_{oi}\right)}^2}$	Same as above

.

3. Results

We verified a typical classification by using the CNN as a preliminary examination, which is often used for image analyses based on “true or false” binary classification. The classification in this study was defined as upward or downward trends of water levels. The results showed a satisfactory accuracy rate of 88.8–93.5% for the cases from A1 to A4 (A1–A4) in the selected datasets of Domain A. However, the errors were caused by small up-and-down oscillations that primarily occurred during an early rising phase of a waveform. By this verification of the binary classification, our CNN can capture the upward and downward trends of flood waves. A detailed explanation is shown in Appendix A.

We also evaluated an effect of a pixel-size difference between an original image (123 × 13 pixels) and a resized image (123 × 16 pixels) in Domain B on CNN predictions of water levels. Predicted waveforms of the resized image in test datasets of the cases from B1 to B4 (B1–B4) were similar to those of the original image in another preliminary examination. However, the RMSEs obtained by the resized image are moderately reduced from those by the original image. Therefore, we assumed that the effect of the pixel-size difference could be limited to dramatically modify the CNN predictions of water levels. A detailed explanation is shown in Appendix B.

3.1. Verification of CNN Prediction With Source Datasets

The CNN predicted the water levels of A1–A4 in Domain A after training the CNN among 38 flood events. To use the validation datasets for each case, including the top three datasets that have higher peaks of floods, the RMSEs ranged from 0.14 to 0.73 m, which corresponds to 2.6–6.9% of the variation between the minimum value and maximum value among the validation datasets. These errors can be acceptable because the top three datasets were excluded in the training process. In the test process for A1–A4, the CNN had an acceptable performance with a less than 10% relative error (Figure 8 and

Table 7. Error evaluation of the CNN in Domain A.

Case	RMSE (m)	Relative Error (%) 1
A1	0.464	6.45
A2	0.370	3.79
A3	0.734	6.93
A4	0.136	2.58

¹ Relative error was the RMSE divided by the variation between minimum water level and maximum water level in each test dataset.

), although the higher peak of each A1–A3 prediction did not follow the observed peak. For example, the A3 prediction to capture the highest peak (3 September 2005) of flood wave shows that the RMSE was 0.73 and the relative error was 6.9%, although the peak height could not be captured by an approximately 20% difference (Figure 8c). For the dataset with the moderate peak of the flood wave (14 August 1999), the CNN in A4 predicted a considerably better shape of the water level, whose relative error was only 2.6% to the total variation in the water level during the 14 August 1999 event (Figure 8d). These results indicate that the moderate peak flood of A4 was typical for prepared datasets in the training process. Capturing a higher peak of each dataset of A1–A3 caused poor prediction due to exclusion of the A1–A3 datasets in the training process.

3.2. Verification of CNN Transfer Learning with Target Datasets in Domain B

After the verification of the CNN via the training, validation, and testing processes in Domain A, the transfer learning on the fully connected layers 1 and 2 was conducted in Domain B. The number of retrainings can be an important factor for improving the prediction of the CNN transfer learning. We evaluated how RMSEs are reduced based on the number of retrainings. Figure 9 shows the RMSEs for all cases (B1–B4), which are calculated by the observed and predicted water levels with respect to the number of retrainings. The number zero in the horizontal axis means that the CNN was employed without any retrainings in Domain B. As the number of trainings increased, the RMSEs for B1–B4 were reduced. The retraining converged approximately by approximately 20 times.

Figure 10 shows the comparison between the predicted water level and the observed water level in a time series during flood events in the test datasets of B1–B4 after the 20-time retrainings. These wave shapes tend to rise earlier than the observed wave that actually increased before the peaks. The predicted wave curves had small oscillations or non-smoothness.

In addition, the RMSEs of B1–B4 in the test datasets indicates 0.06–0.15 m, which corresponds to a variation from 3.3% to 4.3% between the minimum value and maximum value of the water level of each dataset (

Table 8. Error evaluation of the CNN transfer learning with 20-time retrainings in Domain B.

Case	RMSE (m)	Relative Error (%) 1	Reference: RMSE (m) of CNN Without Transfer Learning and With Resized Image
B1	0.118	4.24	0.144
B2	0.153	4.30	0.200
B3	0.125	3.52	0.155
B4	0.064	3.34	0.064

¹ Relative error was the same as that in Table 7.

). The RMSEs are approximately equivalent to or reduced by at most 20% from those (0.06–0.20 m) of the CNN prediction with 100 trainings in Domain B, without transfer learning and with resized 123 × 16 pixels (Table 8). The retraining time of the CNN transfer learning was considerably shorter due to retraining the part of the CNN structure compared with the computational cost of the CNN without transfer learning. During the check process of the validation datasets after the 20-time retrainings, the RMSEs of B1–B4 ranged from 0.10 to 0.12 m, which corresponds to reasonable values from 2.6 to 3.2% for the variation between the minimum value and maximum value of the water level for each dataset.

4. Discussion

The time-series water-level predictions of A1–A4 using the CNN in Domain A showed acceptable agreement with the observed data, although the higher peaks of each of A1–A3 were poorly captured. Comparisons with other neural networks, such as the fully connected deep neural network (FCDNN) [7] and recurrent neural network (RNN) [31] indicated that our CNN prediction was poorer than the performance of these models. For example, Hitokoto and Sakuraba [7] reported that their FCDNN provided better predictions of water levels for the top-four largest flood events from 1990 to 2014 in the same watershed. The RMSE in an hour prediction of water level was 0.12 m, which is approximately 1/3 of the mean RMSE of our CNN prediction, due to the use of two different verification methods. The RMSEs of the FCDNN were calculated by the leave-one-out cross-validation method [32], in which three of the top four largest flood events were included as training datasets for each prediction. Our CNN excluded the top three datasets in the training process. Therefore, the accuracy of the CNN may not be worse than that of the FCDNN.

In addition to the flood prediction, the time-series predictions in other fields have been performed utilizing the CNN. Temporal predictions of the precipitation occurrence, as performed by the CNN, showed that the accuracy exceeded 90% in the first lead time based on the quadrant classification, which is based on the combination of yes and no occurrences in prediction and observation [23]. Another example of stock market prediction by the CNN that reported 50% accuracy was achieved in the upward or downward trend of 31 stocks [22]. Although the backgrounds and computational setups of these studies completely differ from those of our study, the preliminary numerical examination of the CNN predictions based on binary classification (i.e., upward or downward value of water level) achieved approximately 90% accuracy. Therefore, our temporal prediction by the CNN can produce high accuracy.

Our method uses the CNN coupled with a transfer-learning approach in time-series predictions. It may be original based on the literature review for machine-learning-based flood models in the latest two decades [33]. The results of the CNN transfer learning after 20-time retrainings show that the RMSEs were less than 5% of each variation in water level in the test dataset in Domain B. These errors are slightly reduced from those of the CNN in Domain A. However, some specific differences exist between the predicted water levels and the observed water levels in Domain B, which were not observed in the CNN predictions in Domain A. For example, the predicted flood peaks were slightly underestimated by only 5%–10% of the variation of observed water levels in B1–B3 (Figure 10). The slight underestimation of wave peaks in B1–B3 may be caused by the genetic tendency of the CNN trained in Domain A. This finding may be attributed to the notion that the CNN was substantially fitted to the flood waveforms that have steeper slopes of peaks.

Quantitative improvement in the CNN transfer learning appeared in the reduction of computational costs. The CNN transfer learning’s RMSEs are slightly reduced from those of the CNN without transfer learning (i.e., a single use of CNN) in Domain B (Table 8). The former had 20-time retrainings of “the fully connected layer 1” and “the fully connected layer 2” of the CNN, which means that the number of parameters of the training process was also reduced (Figure 5b). The latter required full training by 100 times (i.e., epochs = 100) through all layers of the CNN (Figure 5a). Based on our computer resources, the computational cost was reduced to approximately 18% compared with the CNN without transfer learning. Thus, the beneficial aspect from the results of the CNN transfer learning reveal that the computational costs were substantially more reduced than the CNN without transfer learning once the CNN is well verified in Domain A (source domain). The CNN has to first perform the pretraining. The CNN can be applied to other domains once the CNN is pretrained.

A few studies of time-series prediction have been performed by using the LSTM, with a transfer-learning approach. For example, Laptev et al. [14] successfully reduced the prediction errors in the target dataset of time-series electricity loads obtained from the US electric company, using transfer learning with multiple layers of the LSTM. For error evaluation, they reported that the symmetric mean absolute percentage error (SMAPE) in small-size datasets (till the maximum of 20% of the total datasets) in the target domain was improved by approximately 1/3 of the SMAPE for the total datasets. Their LSTM was likely to improve the accuracy even in small-size datasets with transfer learning. Although comparing our results is difficult due to different-types of datasets and different methods of error evaluation, the accuracy improvement in a target domain (Domain B) using transfer learning could be achieved with approximately 15% reduction in a mean error difference between the CNN with transfer learning and that without transfer learning in the first trial of our study. Note that the mean error difference is defined in the following equation:

$$\mathrm{Mean} \mathrm{error} \mathrm{difference} = \frac{1}{n1}{{\displaystyle \sum }}_i^{n1}\left(RMS{E}_{TL,i}-RMS{E}_{NONTL,i}\right)/RMS{E}_{NONTL,i},$$

(8)

where TL is with transfer learning, and NONTL is without transfer learning.

The CNN transfer learning in Domain B can be necessary to further reduce the RMSEs compared with those from a single use of the CNN without the transfer-learning approach. The RMSEs of CNN transfer learning can be smaller because the transfer-learning approach in this study was simple (i.e., retrainings only of the fully connected layers 1 and 2). In general, if some deeper layers close to the end of the CNN is retrained, the transfer learning can be more effective for improving predictions (e.g., Wang et al. [34]). For example, we may perfume the sensitivity tests of retraining the layers, such as the max-pooling 2 and the fully connected layers 1 and 2 (Figure 5a). Therefore, the next step of our study can perform the retrainings of additional layers in the CNN in Domain B.

5. Conclusions

We created a new model that consists of the CNN with a transfer-learning approach and a conversion tool between the image dataset and time-series dataset. The model can predict time-series floods in an hour in the target domain (Domain B) after pretraining the CNN with numerous datasets in the source domain (Domain A). As the first trial of a proposed method with this model, we note the following findings:

• CNN binary classification of upward/downward trends of water levels provided highly accurate predictions for a preliminary examination.
• CNN with time-series predictions in Domain A had less than 10% errors in the total variation of water levels in each test dataset.
• CNN with transfer learning in Domain B reduced the RMSEs as the number of retrainings was increased, and the RMSEs after 20-time retrainings were slightly reduced from those of the CNN without transfer learning in Domain B with a substantially reduced computational cost.

Due to the method of the beginning stage, our future works require some extensions of the CNN-based flood modeling with the transfer-learning approach as follows:

• Lead time in the prediction should be extended from an hour to three to six hours based on the time lags for the watersheds.
• The best retraining process in deep layers should be investigated.