Deep learning model on rates of change for multi-step ahead streamflow forecasting

In recent years, climate change has seriously affected the ecosystem (Han et al. 2022). Climate change in the form of unpredictable precipitation, temperature and evaporation patterns not only affects the surrounding ecosystem but can disrupt the hydrological trait of streamflow. Streamflow is a major element of the hydrological cycle. The attribute of streamflow is highly associated with climate and land-use conditions (Masrur Ahmed et al. 2021). Alterations made by human activities can accelerate instabilities in the temperature and rainfall patterns resulting in adverse conditions such as sea level rise and extreme weather (Adikari et al. 2021). Similarly, one of the critical issues when land cover is being altered is the loss or reduction of allowable areas for infiltration. The change can result in more runoff into the river. Failure to mitigate or adapt this change will cause overflow at the riverbanks and a major flood.

The global threat of urban flooding to water security and the economy is too enormous to be ignored. Major flooding can cause severe damage to the infrastructure. The mudflow often ruins belongings. Thus, a resilient approach is necessary to mitigate this peril. A good and reliable multi-step ahead forecasting model can be a potential risk management solution for better flood management and disaster preparedness to allow sufficient evacuation and asset protection (Kao et al. 2021; Nanditha & Mishra 2021).

There are two approaches to developing a multi-step ahead forecasting model, the process-driven model and the data-driven model (Huang et al. 2021).

The process-driven model, also known as a physically based model, is derived from the physics mass conservation theory and momentum preservation. Physical data, such as precipitation, river alignment and hydraulic structures, such as culverts, weirs and dams, or other geological past evidence are required from physical sites through observation and numerous ground surveys, interviews, satellite and aerial photography. Various assumptions can bring uncertainties to these data (Teng et al. 2017). Specific parameters cannot be obtained directly and must be substituted with default parameters. The watershed in the model will be represented as lumped, semi-distributed or fully distributed (Cai & Yu 2022). It concurrently will be defined under the range of complexity from conceptual to physically specified (Bourdin et al. 2012). Forecasting activity will be developed based on the principle of flood formation, considering physical features, hydrology, hydrodynamics and other theoretical aspects (Chen et al. 2021).

Data-driven model has gained considerable interest in recent years and is regarded as an alternative to the process-based model. Data-driven model does not require the simulation of physical processes. The model employs historical values or multivariate models to forecast the future (Zhao et al. 2021). The model can retrieve information from linear, nonlinear and hydrological systems to map a relationship between observed parameters and target variables (Alizadeh et al. 2021). Artificial neural network (ANN) is the favorite black box model. However, clarity or interpretability has become a concern for machine learning (Kaadoud et al. 2022).

The deep learning model refers to the data-driven model with multiple hidden layers, allowing more feature extraction with higher efficiency. The learning algorithm using enormous computing power delivers better extraction results with more significant amounts of complex data. Thus, a more complex mapping has become possible in hydrological analysis. Long short-term memory (LSTM) is a popular hydrology and water resources model. It can solve issues related to long sequences of training that often will end up with vanishing gradients. Compared with other neural networks, LSTM can perform much better with time-varying time-series data. The model can deliver good results for a single-point short-term forecast. Otherwise, the performance will gradually deteriorate for longer-term forecasting (Lv et al. 2020).

The LSTM model is one of the deep learning models that have been extensively proposed in research as a tool for knowledge extraction (Kaadoud et al. 2022), medical diagnosis (Balaji et al. 2021), electricity prediction (Li & Becker 2021), soil moisture projection (Li et al. 2022), runoff forecasting (Chen et al. 2020) and precipitation nowcasting (Lin et al. 2021).

Alizadeh et al. (2021) successfully concluded a post-processing streamflow simulation using LSTM. A combination of the first order difference (DIFF)-FFNN-LSTM model was considered to solve the limitation of machine learning on nonstationarity data points (Lin et al. 2021). Kilinc & Haznedar (2022) developed the LSTM-genetic algorithm (GA) model for river streamflow modeling using daily flow data. Hayder et al. (2022) employed nonlinear autoregressive with exogenous inputs (NARX) & LSTM models using historical streamflow, weighted rainfall and average evaporation as the input parameters to simulate river streamflow. Watershed et al. (2022) utilized rainfall data in multi-layer perceptron (MLP) to predict river stage. Feng et al. (2022) developed the parallel cooperation search algorithm-extreme learning machine (PCSA-ELM) model from daily runoff to predict streamflow. Guo et al. (2021) used rainfall, river stage and tidal level data to initiate light gradient boosting machine learning regression (LGBMR) for river stage forecast. Jougla & Leconte (2022) experimented with short-term streamflow forecast using ANN models with inputs combinations of observed streamflow, surface, deep and surface soil moisture. Mostaghimzadeh et al. (2022) investigated the MLP-GA model for inflow forecast for a reservoir. Hai Nguyen et al. (2022) addressed urban flooding using the GA-Bayesian additive regression tree (BART) model for river flow forecast. Liu et al. (2022) proposed a directed graph neural network for multi-step streamflow forecast using streamflow and precipitation inputs. Danandeh Mehr et al. (2022) introduced a new genetic programming-seasonal autoregressive integrated moving average (GP-SARIMA) river flow model in streamflow simulation. Kilinc (2022) conducted a streamflow forecast based on the particle swarm optimization (PSO)-LSTM model in the Orontes Basin. Upon detailed observation of the research works performed in recent years, it could be concluded that there was no attempt to use rates of change in the AI model development. The past and current research mainly concentrated on using raw data to forecast streamflow with multiple variations of models.

In this context, the study is motivated to introduce a suitable deep learning model to simulate and forecast streamflow in an early warning system. The outcome will lead to higher accuracy in forecast flow and minimize the potential of progressive accumulation of errors in time-series analysis.

The contributions of this paper can be simplified as follows:

• (1)

  The MLP model, a feed-forward neural network (FFNN) identified as the ANN model in section 2.1.1 of the methodology, will be performed in early analysis and set as the benchmark model of this study.

• (2)

  This study will introduce a novelty approach using rates of change as the state-of-the-art method in a machine learning model to minimize input errors and provide early indicators in flood warning systems.

• (3)

  To evaluate the performance indices of various models for establishing LSTM as the superior deep learning model that generates highly accurate point results.

• (4)

  To achieve higher accuracy for the forecast of peak flow values.

The remainder of the article will be organized as follows: Section 2 will illustrate the model development, the performance indices picked for evaluating the model, the study area and model development. Section 3 will concentrate on the results. Section 4 will further discuss the findings. Finally, section 5 is the conclusion and recommendation for future study.

Abbasi et al. (2021) described the data-driven models as sensitive to input variables. These input variables are subjected to three major uncertainties: data, variable and model uncertainty. Data uncertainty refers to the poor quality of predictors. Variable uncertainty is defined as a poor selection of hyperparameters. A common approach to solve this concern is to introduce preprocessing solution where the techniques of dimensionality reduction and input variables selection are employed. Model uncertainty refers to the inability of the model to capture the actual physical processes. Due to these uncertainties, the selection of appropriate models is important in analyzing the different types of data. In this study, ANN and LSTM are chosen for this effort to process the time-series type of data.

Artificial intelligence (AI) is a common name that was commonly misinterpreted as ANN. ANN is one of the most basic and standard networks in the domain of AI. It has gained substantial attention and increasing popularity for data processing, supported by the growing consistent availability of multiple data variations due to improving technology. One of the ANN applications is to develop a hydrological model. ANN model can estimate, forecast, detect data patterns, optimize and establish relationships of complex variables (Afan et al. 2016). The origin of ANN can be traced back to biological neural networks that resemble how the human brain works.

ANN network architecture comprises at least three layers: the input, the hidden and the output. Input variables, such as the rainfall data, will be fed to the network at the input layer and appear as several neurons. The input layer is often manipulated to improve the deliverance of the modeling. One of the possible methods is to select the parameter that has a direct impact on the outcome of the model. The nodes will link to the next layer, with each link having a weight that represents the strength of the connection. Each node will go through a nonlinear transformation known as the activation function at the hidden layer before continuing to the output layer.

A recurrent neural network (RNN) is a more advanced form of ANN model with an additional feature to memorize information, allowing progressive feedback interaction for generating better understanding simulation. Owing to its ability to handle consecutive inputs, RNN with a self-looped cycle helps store predecessor data outputs of a sequence to solve complex hydrological time series. However, the dynamic structure of RNN is subject to the vulnerability of vanishing or exploding gradient during the backpropagation progression, hampering the learning process. During training, errors can accumulate, leading to further complications (Fang & Yuan 2019). Another issue related to RNN is the long sequence dependency (Kilinc & Haznedar 2022). For solving the issues inherited in RNN, the LSTM network has become the way out.

LSTM is a deep learning network suitable for time-series data (Kim et al. 2022) that consists of a memory cell that can store information over an interval. The ability to store information is made possible with several nonlinear gate units that can regulate information movement into or out of the cell. LSTM network has proven to be more effective than RNN with its ability to keep or eliminate information and thus produce better forecast outputs that outperform FFNN (Ni et al. 2020). This capability gives an advantage to the LSTM, especially in the learning process associated with sequential data. Many benefits of LSTM, including the encoder–decoder building block, can be garnered (Yokoo et al. 2022). A staked multi-layer LSTM can be used for long-term forecasts by extracting sequential temporal information (Cai et al. 2020). To further improve the input sequences selection and semantics encryption in long-term memory, an attention mechanism can be introduced to the LSTM model (Li et al. 2019).

Several simulation combinations are available for LSTM models (Ouyang et al. 2021). Kratzert et al. (2019) applied N-to-1 model to attain streamflow estimates. Under this model, a large sample of hydrological data per multi-time step time series of catchment parameters was attained as the input model. The output of the model was a one-step variable. The second combination was the N-to-M LSTM model or akin to the sequence-to-sequence model. Xiang et al. (2020) demonstrated the seq2seq LSTM learning model for rainfall-runoff to predict multi-time step streamflow. The third formulation is the N-to-N model, where Feng et al. (2020) applied hydrometeorological time series, catchment attributes and streamflow observations to enhance daily streamflow forecasting.

As model uncertainty is inherited in both ANN and LSTM networks, this study will introduce a new preprocessing approach involving rates of change to enhance AI modeling.

By applying the rate of change (⁠⁠, fluctuation can be managed so that the model's accuracy can be improved further.

Modeling conceptualizes the water movement behavior within a catchment by representing empirical idealization and simplification processes. Under this concept, there is a concern about the possibility of errors due to the vague understanding of complex parameter relationships. An effort is required to quantify the errors and objectively assess a model to justify the limitations by comparing the observed with the simulated variables (Liu 2020). For a model to be considered scientifically sound, vigorous and secure, it must undergo sensitivity analysis, model calibration and validation. Sensitivity analysis measures the reaction of a model in response to input parameters, while calibration identifies the differences between the observed and simulated flow. Validation ensures the model accuracy maintains for further extension of the application.

Model performance can be conducted in two ways, namely subjectively or objectively. Subjective assessment implies visual inspection for goodness-of-fit between actual and simulated for underestimation or overestimation or detecting the periodic pattern. Under the objective assessment, a mathematical approach for goodness-of-fit is applied where efficiency increases as the error between actual historical and simulated data decreases. Although there is no universal agreement on performance evaluation standards, it is generally accepted to consider multi-objective indicators (Ritter & Muñoz-carpena 2013). It is an excellent practice to review efficiency levels through dimensionless statistics, absolute error-index and graphical representation (Waseem et al. 2008). The idea of goodness-of-fit is to examine the model's capability to reproduce historical patterns, forecast future events and quantify the improvements with multiple modeling approaches (Althoff & Rodrigues 2021). Optimally, it is crucial to consider both absolute and relative errors in model performance assessment (Jackson et al. 2019).

Under this study, five performance indexes will be assessed to determine the developed models' goodness of fit. These evaluation methods, which take into consideration of the absolute and relative aspects of the errors, are the root-mean-square error (RMSE), mean absolute error (MAE), correlation coefficient (R), Nash–Sutcliffe efficiency (NSE) and peak flow criteria (PFC)/low-flow criteria (LFC).

MAE is a well-recognized absolute error goodness-of-fit indicator that measures the significance of average error in a model. It is unsuitable for comparing two catchments with different hydrological characteristics (Althoff & Rodrigues 2021).

R is a standard regression criterion that describes the fraction of total variance. The range of the R-value lies between 0 and 1, where 1 is the perfect fit.

The value of R with value one signifies better agreement, while the value of zero signifies no co-relation. R has a limitation on measuring only the linear relationship between variables. Like RMSE, R is indifferent to proportional differences between the observed and simulated values (Daren Harmel & Smith 2007). Therefore, achieving a higher R-value is possible even though the gap between the observed and simulated values varies significantly. The correlation is also sensitive to outliers that can result in bias during model assessment.

NSE is the most widely applied goodness-of-fit measurement. It measures the absolute difference between the observed and predicted, followed by normalization with a variance of observed values to remove bias. The range of NSE lies between 1 and −∞, where 1 is the perfect fit. The model accuracy can be translated into very good for 0.75 < NSE ≤ 1, good for 0.65 < NSE ≤ 0.75, satisfactory for 0.50 < NSE ≤ 0.65 or unsatisfactory for NSE ≤ 0.50 (Kim et al. 2021).

The numerator reflects on possible minor errors becoming smaller, while the opposite is true for more significant errors. This trait has become the limitation that can lead to overestimation or underestimation of the model under assessment. Another concern is the existence of a measured mean implies catchment with high variable values will lead to an overestimation of efficiency.

PFC and LFC measure the error of the hydrological model to forecast peak flow values and low-flow values, respectively. A zero PFC and LFC signify a perfect model. This condition exists when no peak flow exceeds one-third of the actual mean peak flow. A similar situation applies to LFC.

Mean-squared error (MSE) measures the amount of error in a statistical model. It gauges the average squared difference between the observed and predicted values. When MSE equals zero, the model does not have an error. As errors increase, MSE values will increase too.

Kuala Lumpur is the capital city of Malaysia, which is situated in Southeast Asia. The main river in the city is the Klang River, with a catchment area of 1,288 km² and flowing through a distance of 120 km (Zabidi et al. 2011). Eleven major tributaries are attached to the river, which flows across Selangor State and the Kuala Lumpur Federal Territory (Othman et al. 2020). The weather of Malaysia is affected mainly by two dominant monsoon seasons, i.e., North-East Monsoon from November to February and South-West Monsoon from May to August. The city receives an average annual rainfall of 2,600 mm. Batu, Gombak and upper Klang Rivers are the tributaries of the Klang River in the upper catchment of Kuala Lumpur (Hanna et al. 2020). Amid massive development and coupled with frequent short and intense duration precipitation, Kuala Lumpur is vulnerable to flash flood occurrence. This setting is particularly true at the confluence of the Klang River and Gombak River, where the well-known historical tourist area of Masjid Jamek is located.

For this reason, another consideration for selecting this study area is the potential risk as the stormwater will be diverted into the tunnel, which has dual functionality primarily for the traffic motorway during regular days. This circumstance warrants high accuracy of river flow forecast at the confluence for flood mitigation purposes and traffic evacuation from the tunnel. The selection of the study location can demonstrate the significance of machine learning as the engineering nonstructural measure in flood mitigation and early warning system.

The SMART catchment of 160 km² is equipped with 28 numbers of hydrological stations. Each station has a combination of rain gauge and Doppler current meter (DCM). Some site has water level sensor in place of DCM. Data on rainfall and flow are collected and constantly transmitted to the main server at the control center through telemetry. However, there are 28 stations and only rainfall data from 11 telemetry stations are selected for this study. The rest of the surrounding stations are for observation and do not contribute to the flow at the Klang River and Ampang River confluence. The historical 30 min of rainfall data interval is collected from January 2008 to August 2021. A data interval of more than 30 min is discouraged, as a major storm can change drastically within that period. Likewise, the data interval of fewer than 30 min is also prevented as a substantial volume of data can cause learning difficulty in a model and delay the forecast.

This section highlighted the results attained during the training of various models for streamflow forecasting. The model training was conducted using the FFNN and LSTM models. At the initial stage, analysis was done without any preprocessing process. This procedure was later followed by introducing a suitable preprocessing step to improve the forecast. The results' assessment was elaborated based on different input parameters and target variables, as mentioned in the following subsections.

Precipitation data of 11 stations at the upper catchment of SMART watershed with intervals of 30 min were used as training input for FFNN and LSTM to predict flows at the confluence of Ampang River and Klang River. For the FFNN model, analysis was carried out with one hidden layer and extended to two hidden layers. The number of neurons varied from 2 to 23 for each hidden layer. The trained models yielded different accuracy under different combinations of algorithms. The model's best accuracy was obtained with 1 hidden layer and 10 neurons with an overall R of 0.4465, MAE of 3.7135, NSE of 0.1994, RMSE of 8.856, PFC of 0.1843 and LFC of 1.1376 as shown in Table 1. However, this result is not satisfactory for flood warning purposes.

Further training and validation were then performed using the LSTM model in MATLAB with the same input parameters and target variables. The performance of the results obtained from the LSTM model was measured and shown in Table 2. The result of LSTM was satisfactory in comparison to the FFNN model.

In the case of section 3.1, it was observed that the input data were repetitive in values, but the target values were inconsistent at different times. For this reason, the training efficiency has been reduced. To overcome this problem, Q_t was introduced as part of the input data besides the 11 existing rainfall stations data. The target value was Q_t+0.5. Hence, this model was to forecast 30 min ahead of streamflow at the confluence. From the results in Table 3, it could be observed that the best output model (R = 0.9359, MAE = 0.7722, NSE = 0.8756, RMSE = 3.4911, PFC = 0.1294 and LFC = 0.9057) was corresponding to two hidden layers with 17 and 8 neurons in the first hidden layer and second hidden layer, respectively. However, there was a trade-off in increased epoch time when the hidden layers were added from single to double layers. Nevertheless, the results improved significantly after introducing Q_t into the input parameters.

The training and validation processes were then performed using LSTM with the same input parameters and target variables. The result of the LSTM model is shown in Table 4. There was a significant improvement to the LSTM model performance, with an increase of 5% for training regression and 10% for validation regression. NSE also improved from 0.8190 to 0.8963.

The training was then performed 1 h ahead of forecast. This step was to test the possibility of achieving higher accuracy or vice versa when forecast time increased. Likewise, the input parameters were maintained as 11 stations of rainfall data with intervals of 30-min and flow Q_t akin to section 3.2; the target variables were replaced with Q_t+1, which were 1 h ahead flows at the confluence of Ampang River and Klang River. From Table 5, the best result came from two hidden layers corresponding to 14 and 5 neurons for each hidden layer, respectively. The R = 0.8671, MAE = 1.1305, NSE = 0.7515, RMSE = 4.9333, PFC = 0.1375 and LFC = 0.8509. When compared to section 3.2, it could be observed that the overall performance started to deteriorate as the forecast time increased progressively.

Similarly, further training and validation were performed using the LSTM model with the same input parameters and target variables. The result of the LSTM model is shown in Table 6.

The second part of the training involved the rate of change as part of the development to see the potential to achieve higher accuracy in the forecast or vice versa. The input parameters were maintained as 11 stations of rainfall data with intervals of 30 min and flow Q_t. At the same time, the target variable changed to rates of change derived from Q_t+0.5 – Q_t divided by the time interval (refer to Equation (2)). The best results were yielded at two hidden layers with neurons of 23 and 10 for each layer, respectively. The best performance with R = 0.7303, MAE = 0.0263, NSE = 0.5334 and RMSE = 0.1297, as shown in Table 7, had a longer epoch time of 0:05:40 at 116 iterations when compared with a single hidden layer of 15 neurons where R = 0.7129, MAE = 0.0279, NSE = 0.5073 and RMSE = 0.1333 with epoch time 0:00:53 with 83 iterations. There was no significant increase in accuracy, although there was a trade-off regarding the computing speed.

The LSTM model was then executed with the same input parameters and target variables to check on the model testing and validation performance accuracy. The result of the LSTM model is shown in Table 8.

This section will further illustrate the results obtained earlier. The study was conducted in two parts. The first part was to evaluate prediction performance with the MLP networks. The algorithm of the MLP networks varied from one hidden layer to two hidden layers. The number of neurons started from 2 and increased to a maximum of 23 for a single hidden layer network. While in the case of two hidden layers, the neurons started from 2 and increased to a maximum of half of the total neurons in the first layer. The results showed better yield as the layer increased from one to two. However, as more layers were added, the results did not reflect better yield. These results were due to the approximation of the ideal function as indicated in the universal approximation theorem (Tang & Yang 2021). There was an optimal number of layers and nodes in the networks to avoid overfitting or vice versa. This procedure would determine the best architecture structure to deliver the best results according to various inputs and target values, as mentioned in sections 3.1–3.3. The predicted and original streamflow was then compared to measure the precision of the forecast results. LSTM networks followed this process for the same input parameters and target values. This first part of the study aims to find the best performance networks under different criteria and compare the achievement between the MLP and LSTM networks. The second part of the study focused on implementing rates of change as a novelty approach and understanding its relationship with the purpose of flood mitigation.

For the stated condition in section 3.1, it could be concluded that the best MLP structure was 1 layer with 10 neurons. Table 1 showed that the results yielded R = 0.4465, MAE = 3.7135, NSE = 0.1994, RMSE = 8.856, PFC = 0.1843 and LFC = 1.1376. The divergence reached within 1:19 min at 190 epochs. As the regression and NSE values were far from reaching value 1, it indicated poor-quality input data and poor-quality forecast of streamflow at the confluence of Klang River and Ampang River. Due to maintenance testing, poor-quality input data could be caused by weak communication signals or data distortion. Similarly, MAE and RMSE were far from 0 value which denoted the forecasts were far from the line of best fit. The model would have few accurate values when tested out of the sample. When comparing the PFC value with the LFC value, the PFC value reflected a better forecast for peak flow than the low-flow forecast. Peak flow was the extreme value of the streamflow series and was typically difficult to model.

As further training and validation were conducted using the LSTM model to simulate streamflow, the deep learning produced significantly better results with R = 0.9055, MSE = 17.8532, MAE = 1.4365, NSE = 0.8190 and RMSE = 5.3695. A better result than the MLP model was expected as the LSTM architecture could remember essential data, making it a superior model. A single forward pass was involved as the training went through the MLP model. However, the operation would have involved three single forward passes in the LSTM network. The memory cells in the LSTM model, as shown in Figure 3, helped to store the final output and used it as the input for the successive step.

For section 3.2, the training was improved by introducing the preprocessing step. The result of the MLP model was very encouraging with R = 0.9359, MAE = 0.7722, NSE = 0.8756, RMSE = 3.4911, PFC = 0.1294 and LFC = 0.9057 for 2 hidden layers MLP with 17 neurons and 8 neurons, respectively. This improvement was made possible as the issue of input parameters redundancy with inconsistent target values was solved after introducing the flow Q_t into the parameter inputs. The target values of Q_t+0.5 denoted the forecast for streamflow 30 min ahead. The value of R and NSE close to 1 indicated higher precision. It could be observed that MAE and RMSE values were also reduced by almost half of the values acquired in section 3.1. These results implied better forecast accuracy for out-of-sample data. PFC value was nearing 0, while the LFC value was almost 1. This value suggested a better forecast for peak flow than low flow, as shown in Figure 9.

The training then proceeded with the LSTM model. The results generated R = 0.9470, MSE = 10.2326, MAE = 0.5640, NSE = 0.8963 and RMSE = 3.1629, as shown in Table 4. And again, a better result than the MLP network was achieved for the LSTM model, consistent with the previous studies. The overall result indicated LSTM model could perform better than MLP and, therefore, a better forecasting model.

Since this was a multi-step ahead study, the analysis was continued with a 1-h ahead streamflow forecast as mentioned in section 3.3. This continuation would allow us to track the trend of the forecast. The MLP yielded the best performance with R = 0.8671, MAE = 1.1305, NSE = 0.7515, RMSE = 4.9333, PFC = 0.1375 and LFC = 0.8509 for 2 hidden layers with neurons of 14 and 5 each layer, respectively, as shown in Table 5. Therefore, there was a drop in performance 1 h ahead MLP forecast. However, the result was still within an acceptable range for an hour ahead of the forecast. A comparable trend was also noticed in the LSTM model that had attained R = 0.8849, MSE = 21.4296, MAE = 0.9397, NSE = 0.7828 and RMSE = 5.0098, as shown in Table 6. Figure 10 revealed an acceptable peak flow forecast, although less accurate than Figure 9. Therefore, this trend was per the theory that the shorter the forward time, the better the forecast would be.

The second part of this study will evaluate the application of the as the target variables in the networks. For the MLP model, the best performance yielded R = 0.7303, MAE = 0.0263, NSE = 0.5334, RMSE = 0.1297, PFC = 0.1386 and LFC = 0.3936 for 2 hidden layers of 23 neurons and 10 neurons, respectively, as shown in Table 7. It could be seen that the performance was poorer compared to models in sections 3.2–3.3. This yield was reflected in lower R and NSE values. However, the MAE and RMSE values were nearer to 0. As the was the subtraction value of two consecutive steps of flows with a division of time interval as mentioned in section 2.3, the potential errors between the steps had been minimized and therefore significantly reduced the MAE and RMSE values. The lower PFC value compared to LFC reflected a better peak flow forecast than the low flow for this model, as plotted in Figure 12. It could be noted that being the lowest LFC value among all models implied a better forecast of low flow in this model.

On the other hand, the results from the LSTM model were superior with which yielded significantly better results with R = 0.8573, MSE = 0.0010, MAE = 0.0181, NSE = 0.7349 and RMSE = 0.1319 as shown in Table 8. The performance was similar to or much better than the streamflow 1-h ahead training outcome in Table 6 of section 3.3. Like the MLP, the MSE and MAE values were also almost reaching 0, suggesting a better forecast for out-of-sample data forecasting.

The forecasted rates of change were then translated to forecasted flow. A graph of actual flow at the confluence vs. forecasted flow derived from rates of change was plotted. Figure 12 showed very high forecasting accuracy and minimal under-forecast compared with the previous output.

Given the results obtained in this study, it could be established that was suitable as an element to detect an early change in streamflow movement. The classification of streamflow variations, such as normal, alert and danger, could be deployed for this reason. This discovery would allow the water managers additional time to take advance precautionary steps to mitigate flood events. Nevertheless, this study was the first effort to utilize in machine learning. Further improvement by applying other techniques in terms of data preprocessing or data mining procedures could be considered in the subsequent study.

Flood forecasting system requires high accuracy to support the water managers in their daily operations, such as handling hydraulic gates to divert river streamflow to ensure and safeguard public safety. This regional case study is to develop the best deep learning model with suitable hyperparameters for the SMART control center in Kuala Lumpur, Malaysia. This study aims to present a novel technique by introducing rates of change in the machine learning models. This study will perform a simulation and deliver a multi-step ahead streamflow forecast.

Several models of ANN were employed to develop and train for the flow forecast at the confluence of the Ampang River and Klang River. The first part of the simulation stage yielded a poor result, possibly below par, caused by a redundancy of input parameters with different target values or the multi-finality issue. However, the LSTM model displayed a significantly better result than ANN, with a 45% improvement in the regression value from 0.4465 to 0.9055. This improvement aligned with Ni et al.'s statement that the LSTM network could deliver better results than ANN due to its memory cells.

Q_t was introduced into the model as the input parameter to solve the redundancy issue, while Q_t + 0.5 was the target variable. This inclusion significantly improved the model performance with values of R = 0.9359, MAE = 0.7722, NSE = 0.8756 and RMSE = 3.4911 for the ANN model. The model was equivalent to making a 30-min ahead forecast. The LSTM model still yielded better results than the ANN model.

The following experiment was to perform an hour ahead of the forecast. Both ANN and LSTM generated less accurate performance than the 30-min ahead forecast. It was confirmed that the Lv et al. (2020) statement suggested the performance model deterioration when the forecast lead time increased, as shown in section 3.3.

As for the core of this study, the rates of change were introduced into the model as the target variables. The R and NSE were unsatisfactory for flood mitigation operations, but the MAE and RMSE values were reduced to near 0. Positive and negative values of variables could be detected as the output results. The forecasted rates of change were then translated to the forecasted flow. The result was awe-inspiring when a graph of observed flow vs. forecasted flow was plotted, as shown in Figure 12. The rates of change could be used as early detection to track a flow pattern change that could assist the water managers in staying alert.

In summary, these findings confirmed the previous theoretical understandings concerning the model performance and led to the discovery of an additional layer of protection in flood mitigation operations. It was beneficial for being the novice step to understand rates of change behavior in model development and could be explored further. The limitation of this study had been restricted to the use of ANN and LSTM models. It was suggested to apply evolutionary computing methods, such as nature-inspired optimization models, for future studies to generate higher-quality data for better outcomes. Other features, such as land condition and evaporation rate, could be considered additional input parameters to provide more information, as hydrological is a highly complex process.

All authors contributed to the study and design. W. Y. T. performed material preparation, data collection, investigation, data curation and analysis. S. H. L. contributed to conceptualization, methodology, software teaching and supervision; K. P. contributed to the software development; F. Y. T. contributed to supervision; A. E.-S. contributed to review, supervision and project administration. W. Y. T. wrote the first draft of the manuscript, and all authors commented on previous versions. All authors have read, approved the final manuscript and agreed to the published version of the manuscript.

This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

Data cannot be made publicly available; readers should contact the corresponding author for details.

The authors declare there is no conflict.