Runoff Estimation Using Advanced Soft Computing Techniques: A Case Study of Mangla Watershed Pakistan

: A precise rainfall-runoff prediction is crucial for hydrology and the management of water resources. Rainfall-runoff prediction is a nonlinear method inﬂuenced by simulation model inputs. Previously employed methods have some limitations in predicting rainfall-runoff, such as low learning speed, overﬁtting issues, stopping criteria, and back-propagation issues. Therefore, this study uses distinctive soft computing approaches to overcome these issues for modeling rainfall-runoff for the Mangla watershed in Pakistan. Rainfall-runoff data for 29 years from 1978–2007 is used in the study to estimate runoff. The soft computing approaches used in the study are Tree Boost (TB), decision tree forests (DTFs), and single decision trees (SDTs). Using various combinations of past rainfall datasets, these soft computing techniques are validated and tested for the security of efﬁcient results. The evaluation criteria for the models are some statistical measures consisting of root means square error (RMSE), mean absolute error (MAE), coefﬁcient of determination (R 2 ), and Nash–Sutcliffe efﬁciency (NSE). The outcomes of these computing techniques were evaluated with the multilayer perceptron (MLP). DTF was found to be a more accurate soft computing approach with the average evaluation parameters R 2 , NSE, RMSE, and MAE being 0.9, 0.8, 1000, and 7000 cumecs. Regarding R 2 and RMSE, there are about 57% and 17% of improvement in the results of DTF compared to other techniques. Flow duration curves (FDCs) were employed and revealed that DTF performed better than other techniques. This assessment revealed that DTF has potential; researchers may consider it an alternative approach for rainfall-runoff estimations in the Mangla watershed.


Introduction
Rainfall is the most prominent feature among all variables while dealing with hydrological issues because it varies temporally and spatially [1]. It is the primary source of runoff that helps mitigate the impact of droughts and floods on the water resource system. Pakistan and all other developing countries are facing drought and flooding more frequently [2]. So, to address these drought and flood issues, the estimation of runoff generated from the rainfall event is vital. In the transition of precipitation into a runoff, precipitation finally transforms into a runoff after fulfilling various losses such as interception, depression storage, infiltration, and evaporation [3,4]. Runoff is a complex and nonlinear outcome of rainfall and watershed properties. There are numerous modeling methodologies for the rainfall-runoff process [5]. This complicated and nonlinear relationship between rainfall As far as the authors are aware, no work has been performed on the SDTs, DTFs, and TB to simulate the rainfall-runoff process in the Mangla watershed. This study is designed and executed to evaluate SDTs, DTFs, and TB approaches for rainfall-runoff modeling capability. This study seeks to compute the runoff resulting from recent and past precipitation in the Mangla basin of Pakistan. The main objective of this study is to estimate the potential of data mining approaches to estimate runoff and compare SDTs, DTFs, and TB with the MLP.

Materials and Methods
DTREG [42] is used as the predictive software in this study. DTREG (pronounced D-T-Reg) develops neural networks, classification, and regression decision trees. DTREG receives a data set with any number of rows and one column per variable. The "target variable," whose value is to be modeled and forecasted as a function of the "predictor variables," is one of the variables. DTREG examines the information and develops a model that predicts the target variable's values based on the predictor variable's values. DTREG can generate traditional SDTs and TB and DTF models comprised of ensembles of many trees [43].

Single Decision Trees (SDTs)
There are three main components of SDTs: edges, leaves, and terminals. Edges proceed toward the child node. Leaves entail connecting nodes to another node; the terminal node represents the output value following tree construction [43]. SDTs comprise two phases for tree generation. The first phase involves tree growth, whereas the second part involves tree pruning. The data will be constructed in ascending order during tree construction. Tree trimming eliminates or adjusts data that cause noise or have a high entropy level; after pruning the data tree, a regression or classification tree is constructed depending on the given data (continuous or categorical). DTREG [42] will use a variety of variables in a class of variables, including target, predicted, and weight variables. The association between the goal and predicted variables is created in tree building; the weight variable establishes the weight between nodes via edges. The data variables are assigned equal weights if no weight variable is supplied to the data row. If the data variables are continuous, DTREG separates the data based on petal length after randomly selecting data. If the data variables are categorical, the petal width will be used to split the data. The node represents the predicted and desired variables. The splitting variable will be shifted to the child node to continue building the tree. Random data will be separated using regression analysis and the tree technique, as well as misclassification error and probability [22]. Figure 1 depicts the complete schematic diagram of SDTs.

Decision Tree Forests (DTFs)
The DTFs assign data of desired continuous or categorical variables to the

Decision Tree Forests (DTFs)
The DTFs assign data of desired continuous or categorical variables to the model. Numeric values represent continuous data and alphabetic or character variables represent categorical data. The data are going to be partitioned according to the misclassification error. A misunderstanding of the classification led to the initiation of the investigation into structural dependability. The Monte Carlo simulation, the simplified order reliability method (SORM), and the first-order reliability method (FORM) are examples of strategies or approaches that can be used to estimate the likelihood of a failure occurring. These methods are utilized to determine how successful reliability analysis truly is. A tree will be built for each attribute to show how the attributes are related to one another. The node with the lowest rate of incorrect classification will be the root node, and logarithms incorporating the C 4.5 algorithm will be used to produce splitting from the note node [36].
In Figure 2, the data splitting and error elimination process will continue until either the terminal node is reached or the data misclassification error (ME) at the end of the terminal node becomes zero, at which time further data splitting will end. The output value can be seen on the terminal node generation's display.

Decision Tree Forests (DTFs)
The DTFs assign data of desired continuous or categorical variables to the mo Numeric values represent continuous data and alphabetic or character variables repre categorical data. The data are going to be partitioned according to the misclassifica error. A misunderstanding of the classification led to the initiation of the investiga into structural dependability. The Monte Carlo simulation, the simplified order reliab method (SORM), and the first-order reliability method (FORM) are examples of strate or approaches that can be used to estimate the likelihood of a failure occurring. Th methods are utilized to determine how successful reliability analysis truly is. A tree be built for each attribute to show how the attributes are related to one another. The n with the lowest rate of incorrect classification will be the root node, and logarithms in porating the C 4.5 algorithm will be used to produce splitting from the note node [36 In Figure 2, the data splitting and error elimination process will continue until ei the terminal node is reached or the data misclassification error (ME) at the end of the minal node becomes zero, at which time further data splitting will end. The output v can be seen on the terminal node generation's display.

Decision Tree Forests (DTFs)
The DTFs assign data of desired continuous or categorical variables to Numeric values represent continuous data and alphabetic or character variabl categorical data. The data are going to be partitioned according to the misc error. A misunderstanding of the classification led to the initiation of the in into structural dependability. The Monte Carlo simulation, the simplified orde method (SORM), and the first-order reliability method (FORM) are examples or approaches that can be used to estimate the likelihood of a failure occur methods are utilized to determine how successful reliability analysis truly is be built for each attribute to show how the attributes are related to one anothe with the lowest rate of incorrect classification will be the root node, and logar porating the C 4.5 algorithm will be used to produce splitting from the note n In Figure 2, the data splitting and error elimination process will continue the terminal node is reached or the data misclassification error (ME) at the en minal node becomes zero, at which time further data splitting will end. The o can be seen on the terminal node generation's display.

Tree Boost (TB)
Jerome H. Friedman is the pioneer stakeholder of this technique [44]. Another name for TB is stochastic gradient boosting and multiple regression trees. The algorithm or working principle is the same as tree forests. The only difference between TB and DTFs is the mode of construction. TB generates trees in a series pattern, whereas DTFs consist of a forest of trees in parallel. It is a technique that enhances accuracy by weighing output values to reduce total prediction error. The general working mechanism of the is shown in Figure 4.
working principle is the same as tree forests. The only difference between T the mode of construction. TB generates trees in a series pattern, whereas D a forest of trees in parallel. It is a technique that enhances accuracy by we values to reduce total prediction error. The general working mechanism o in Figure 4.

Multi-Layer Perceptron (MLP)
Most hydrologists and researchers compute rainfall and runoff using a networks, the most well-known method. ANN consists of three layers: the i hidden layer, and the output layer. The input layer receives the informatio quent layer generates a beautiful link between rainfall data using algorith and other mathematical techniques. The final layer provides the output val duced ANFIS in 1993 [11], consisting of five output interpretation layers. membership function is used to associate variables with membership whi sists of nodes that establish a relationship with incoming signals. The thi every node, the fourth layer computes each node's contribution to the outp the last layer provides the result. There are numerous varieties of ANN. M layer perceptron neural network) is utilized in hydrology [45]. In Figures 5 a is depicted as a network of input; hidden and neuronal output layers are layer comprises many neurons, each in the preceding layer linked to tho layer. Consider the input layer's output value as the hidden layer's input v

Multi-Layer Perceptron (MLP)
Most hydrologists and researchers compute rainfall and runoff using artificial neural networks, the most well-known method. ANN consists of three layers: the input layer, the hidden layer, and the output layer. The input layer receives the information. The subsequent layer generates a beautiful link between rainfall data using algorithmic functions and other mathematical techniques. The final layer provides the output value. Jang introduced ANFIS in 1993 [11], consisting of five output interpretation layers. In layer 1, the membership function is used to associate variables with membership while layer 2 consists of nodes that establish a relationship with incoming signals. The third layer locks every node, the fourth layer computes each node's contribution to the output value, and the last layer provides the result. There are numerous varieties of ANN. MLPNN (multi-layer perceptron neural network) is utilized in hydrology [45]. In Figures 5 and 6, MLPNN is depicted as a network of input; hidden and neuronal output layers are all present. A layer comprises many neurons, each in the preceding layer linked to those in the next layer. Consider the input layer's output value as the hidden layer's input value.
in Figure 4.

Multi-Layer Perceptron (MLP)
Most hydrologists and researchers compute rainfall and runoff using networks, the most well-known method. ANN consists of three layers: the hidden layer, and the output layer. The input layer receives the informati quent layer generates a beautiful link between rainfall data using algorit and other mathematical techniques. The final layer provides the output va duced ANFIS in 1993 [11], consisting of five output interpretation layers. membership function is used to associate variables with membership wh sists of nodes that establish a relationship with incoming signals. The th every node, the fourth layer computes each node's contribution to the out the last layer provides the result. There are numerous varieties of ANN. M layer perceptron neural network) is utilized in hydrology [45]. In Figures 5 is depicted as a network of input; hidden and neuronal output layers are layer comprises many neurons, each in the preceding layer linked to th layer. Consider the input layer's output value as the hidden layer's input v  Similarly, the hidden layer's output value will be the outpu neuron transfer function sends neurons between the hidden an no point link between the input and output layers.
The input layer receives the data. All neurons in this layer ematical functions to process data in the buried layer. The ou from the concealed layer and returns the anticipated value [22,3 supplied in the input layer of Figure 6. Each neuron in the input rons in the layers beneath it. These values can be transmitted u tions, with the output layer being responsible for interpreting th

Study Area
This study focused on daily precipitation and runoff in the M watershed is located at a latitude 33-35 °N and longitude 73.62 °E Mangla catchment's demographical borders are in Pakistan and area of 165,499.15 km 2 , making it the second-largest tributary in basin [22]. The Mangla watershed is situated on the Jhelum Riv pacity of 7.475 MAF and a drainage area of 33,333.15 km 2 . The ru basin drains into the Mangla watershed. This catchment suppl power with water. Six million hectares of land are irrigated from a 1000 MW hydroelectric power-producing capability. The Jh Neelam, Poonch, Kanshi, and Naran, make up the Mangla wat area, precipitation and snowmelt generated runoff, representin The water stored in various basins, such as the Neelam, Poonch, ran basin, will flow to the river Jhelum as runoff at the Mangla c Similarly, the hidden layer's output value will be the output layer's input value. The neuron transfer function sends neurons between the hidden and output layers. There is no point link between the input and output layers.
The input layer receives the data. All neurons in this layer are linked and use mathematical functions to process data in the buried layer. The output layer receives input from the concealed layer and returns the anticipated value [22,35]. Six external inputs are supplied in the input layer of Figure 6. Each neuron in the input layer interacts with neurons in the layers beneath it. These values can be transmitted using mathematical functions, with the output layer being responsible for interpreting the resulting value.

Study Area
This study focused on daily precipitation and runoff in the Mangla basin. The Mangla watershed is located at a latitude 33-35 • N and longitude 73.62 • E. As seen in Figure 7, the Mangla catchment's demographical borders are in Pakistan and India. It has a drainage area of 165,499.15 km 2 , making it the second-largest tributary in the world after the Indus basin [22]. The Mangla watershed is situated on the Jhelum River and has a storage capacity of 7.475 MAF and a drainage area of 33,333.15 km 2 . The runoff of the Jhelum River basin drains into the Mangla watershed. This catchment supplies irrigation and hydropower with water. Six million hectares of land are irrigated from this reservoir as part of a 1000 MW hydroelectric power-producing capability. The Jhelum and its tributaries, Neelam, Poonch, Kanshi, and Naran, make up the Mangla watershed. In the catchment area, precipitation and snowmelt generated runoff, representing the reservoir's intake. The water stored in various basins, such as the Neelam, Poonch, Kanshi, Jhelum, and Naran basin, will flow to the river Jhelum as runoff at the Mangla catchment.

Dataset
There are twelve rain gauge stations in the boundary of the Mangla reser shown in Figure 7. Nine stations are in Pakistan while the remaining are in India. contains information about these stations and Figure 7 depicts their location. The gauge stations allow us to mimic the runoff generated and dropping into the Jhelum at the Mangla. The four rain gauge stations are in the Indian territory and cover a region for the contribution of runoff from the Mangla basin above the Jhelum Rive on daily rainfall for 29 years from January 1978 to Dec 2007 from nine stations loc Pakistan is obtained in the Pakistan Metrological Department. The daily rainfall four stations outside of Pakistan are obtained from [46]. The rainfall data of these t stations are averaged arithmetically to calculate the point of rainfall over the Bas corresponding discharge is the inflow to the Mangla reservoir used in this study.

Dataset
There are twelve rain gauge stations in the boundary of the Mangla reservoir, as shown in Figure 7. Nine stations are in Pakistan while the remaining are in India. Table 1 contains information about these stations and Figure 7 depicts their location. These rain gauge stations allow us to mimic the runoff generated and dropping into the Jhelum River at the Mangla. The four rain gauge stations are in the Indian territory and cover a broad region for the contribution of runoff from the Mangla basin above the Jhelum River. Data on daily rainfall for 29 years from January 1978 to Dec 2007 from nine stations located in Pakistan is obtained in the Pakistan Metrological Department. The daily rainfall data of four stations outside of Pakistan are obtained from [46]. The rainfall data of these thirteen stations are averaged arithmetically to calculate the point of rainfall over the Basin. The corresponding discharge is the inflow to the Mangla reservoir used in this study.

Performance Evaluation
While dealing with some hydrological processes, determining the model's goodness depends upon various statistical parameters, such as rainfall-runoff modeling. The current study employs four statistical evaluation metrics to determine the model's goodness. The basic formulas of these four statistical parameters are: AIC = mln(RMSE) + 2n (7) For an efficient correlation between expected and observed values, R 2 is between 0 and 1. The model will be considered the most efficient when the correlation coefficient value approaches 1 or is equal to 1. The range of model efficiency RMSE values is between 0 and 1. The better the model, the lower the RMSE number, while the worse the model or data, the higher the RMSE value. Most hydrological studies provide NSE values as percentages [24,47]. In Equation (7), where m is the number of input-output training patterns, n is the number of parameters to be detected and RMSE is the root-mean-square error between the network output and target. The RMSE statistics are predicted to improve when more parameters are introduced to a model, whereas the AIC statistics punish the model for having more parameters and, as a result, tend to produce more parsimonious models [48].

Results
The current work aims to simulate the rainfall-runoff process using several methodologies, such as SDTs, TB, and DTFs, and then compare the findings of these models with MLP. This rainfall-runoff modeling uses several rainfall combinations to obtain statistically significant results. The input data employed in this study are the lagging rainfall data, whereas the desired output is the observed inflow into the Mangla reservoir. To forecast current runoff Q(t), the eleven input combinations of lagged precipitation are given in Table 2. Selecting a suitable collection of inputs is essential for accurate data-driven rainfall and runoff forecasting. We employed Akaike's information criterion (AIC) for the analysis inputs combination and the AIC values of selected input combinations shown in Table 2.
This study uses daily rainfall-runoff data spanning 29 years, beginning in January 1978 and ending in December 2007. The remaining data is utilized for validation and testing, while the first fifteen years of data, beginning in January 1978 and ending in December 1993, are used for training purposes. Lagged rainfall was used as the input data for the rainfallrunoff models, while present discharge served as the model's desired output. Prediction models were constructed utilizing the four applied approaches of SDTs, DTFs, TB, and MLP. The models' statistical evaluation is presented in Tables 3-10. During the training and testing of the models, it was observed that the error rate was acceptable and improved from the training to the test process with different input combinations. The error rate was improved as an acceptable value when input combinations were changed from a 1-day lag to a 10-day lag. Overall, the percent of improvement for DTFs in terms of R 2 was 57%; for RMSE, it was found to be a 17% improvement.

Input Combinations AIC
P(t) 4.5432 P(t), P(t-1) 4.2015 P(t), P(t-1), P(t-2) 4.1534 P(t), P(t-1), P(t-2), P(t-3) 3.9812 P(t), P(t-1), P(t-2), P(t-3), P(t-4) 3.9678 P(t), P(t-1), P(t-2), P(t-3), P(t-4), P(t-5) 3.9561 P(t), P(t-1), P(t-2), P(t-3), P(t-4), P(t-5), P(t-6) 3.8911 P(t), P(t-1), P(t-2), P(t-3), P(t-4), P(t-5), P(t-6), P(t-7) 3.6582 P(t), P(t-1), P(t-2), P(t-3), P(t-4), P(t-5), P(t-6), P(t-7), P(t-8) 3.5121 P(t), P(t-1), P(t-2), P(t-3), P(t-4), P(t-5), P(t-6), P(t-7), P(t-8), P(t-9) 3.3140 P(t), P(t-1), P(t-2), P(t-3), P(t-4), P(t-5), P(t-6), P(t-7), P(t-8), P(t-9), P(t-10) 3.1480    Table 3 demonstrates that the performance parameters of TB and MLP are nearly identical. SDT's performance is underrated in comparison to the other three approaches. The bold results from Tables 3-10 shows the best overall outputs of models applied in rainfall runoff prediction. In a manner analogous to Table 3, the performance of the DTFs is superior to that of the other three applied models, while the performance of the TB and MLP is comparable.  Table 4 indicate that MLP is less efficient for analyzing runoff when a combination of the three is used.  Table 7 indicate that the DTF is a more effective solution than SDT, TB, and MLP. The training and testing stages produce R 2 and NSE values for the DTF in the range of 0.89 and 0.83, while the RMSE and MSE values produce 13,000 and 9000 cumecs, respectively. In the SDT, 0.25 is specified for R 2 , and the exact value is specified for NSE. RMSE and MAE are between 25,000 and 19,000 cumecs. R 2 is found to be 0.26 using the TB technique, and NSE is 0.27. The final RMSE and MAE values fall somewhere in a range that goes from 24,000 to 17,000 cumecs. The exact value of 0.17 is shown for MLP's R 2 and NSE. In contrast, RMSE and MAE range from 20,000 and 25,000 cumecs, respectively. Table 8 shows that R 2 and NSE for DTFs are between 0.90 and 0.80. RMSE and MAE are 12,000 and 9000 cumecs. SDTs and TB have a 0.25 square correlation and NSE. RMSE and MAE are 250,000 and 180,000 cumecs. 0.20 is MLP's R 2 and NSE. RMSE and MAE range from 25,000 to 19,000 cumecs. MLP is underestimated compared to DTFs, TB, and SDTs. MLP has a lower potential than other techniques. Table 9 reveals that the R 2 and NSE values for DTFs are in the region of 0.9 to 0.8, giving it an advantage over TB, SDTs, and MLP. It is evidenced by the fact that DTFs come out on top. The results for RMSE and MAE range between 10,000 and 8000 cumecs. R 2 and NSE have 0.25 and 0.27 for SDTs, whereas RMSE and MAE have 25,000 and 17,000 cumecs, respectively. TB has an R 2 value of 0.35 and an NSE value of 0.30. Its RMSE value is 24,000 cumecs and its MAE value is 16,000 cumecs. The minimum likelihood proportionate has the lowest value of any statistical parameter. These are the results for R 2 , NSE, RMSE, and MAE: 0.20, 0.18, 26,000, and 18,000 cumecs, respectively. The DTFs models were the most accurate based on the R 2 , and NSE values lie between 0.9 and 0.8, as shown in Table 10. The RMSE and the MAE come in at 10,000 cumecs and 7000 cumecs, respectively. R 2 values of 0.30 and NSE values of 0.27 are comparable for SDTs and TB, whereas RMSE values of 24,000 cumecs and MAE values of 17,000 cumecs are reported for each. The MLP model has a value of 0.19 for R 2 and a comparable amount for NSE. However, the RMSE value is 25,000 cumecs and the MAE value is 19,000 cumecs. Figure 8a,b depicts the performance parameters R 2 , NSE, MAE, and RMSE for each input combination for the best DTFs model to examine the effect of the previously mentioned input combinations. Figure 8a demonstrates the variation in R 2 across input combinations. Figure 8a shows an increase in R 2 values from input combination 1 with a single P(t) precipitation value to input combination 4, which has P(t), P(t-1), P(t-2), and P(t-3) precipitation data, followed by a constant value. Figure 8b shows a similar pattern for NSE fluctuations. Similarly, Figure 8a,b illustrates the fluctuation of RMSE and MAE, respectively, with selected input combination changes. (c) depicts the overall RMSE and MAE values. Figure 8a,b demonstrates a significant reduction in error values from input combinations up to the input combination, which is consistent with the R 2 and NSE values (4). According to the findings, it is possible to assert that the precipitation P(t), P(t-1), P(t-2), and P(t-3) contain complete data about the watershed's hydrological signature and that there is no vital information hidden in the lag precipitation data. This assertion can be supported by stating that the lag precipitation data do not contain any relevant information.
RMSE value is 24,000 cumecs and its MAE value is 16,000 cumecs. The minimum likeli-hood proportionate has the lowest value of any statistical parameter. These are the results for R 2 , NSE, RMSE, and MAE: 0.20, 0.18, 26,000, and 18,000 cumecs, respectively. The DTFs models were the most accurate based on the R 2 , and NSE values lie between 0.9 and 0.8, as shown in Table 10. The RMSE and the MAE come in at 10,000 cumecs and 7000 cumecs, respectively. R 2 values of 0.30 and NSE values of 0.27 are comparable for SDTs and TB, whereas RMSE values of 24,000 cumecs and MAE values of 17,000 cumecs are reported for each. The MLP model has a value of 0.19 for R 2 and a comparable amount for NSE. However, the RMSE value is 25,000 cumecs and the MAE value is 19,000 cumecs. Figure 8a, b depicts the performance parameters R 2 , NSE, MAE, and RMSE for each input combination for the best DTFs model to examine the effect of the previously mentioned input combinations. The flow duration curves (FDC) in Figure 9 were developed to test the efficacy of developed models in projecting low, medium, and high flows. Figure 9a-d are FDCs generated with various combinations of precipitation and lag precipitation series, such as 1-day precipitation, lag-3-day precipitation, lag-5-day precipitation, lag-8-day precipitation, and lag-10-day precipitation, respectively. The flows on these FDCs can be classed as low, medium, or high. If the flow range with exceedance probability is between 0 and 10, the flow is classified as high. If it is from 11 to 89, the flow is classified as medium, which further separates into two classes: low-medium if the flow ranges from 11 to 49, and high-medium if the flow runs between 50 and 89. The discharge is below the 50th percentile when it exceeds 89 [15]. It can be shown from Figure 9a that DTFs and MLP both underestimate the observed discharge for all three high, medium, and low flows. Figure 9b illustrates that MLP and DTFs tie for high and high medium flow with observed discharge. Figure 9c represents DTFs and MLP, which are comparable for high and medium flow. MLP underestimates the observed discharge in the region of low flow and low, medium flow. Figure 9d shows that DTFs capture the high, medium, and low flow with observed discharge better than MLP, and the last Figure 9e directs the best relationship with observed discharge for DTFs, including high, medium, and low flow. medium if the flow runs between 50 and 89. The discharge is below the 50th percentile when it exceeds 89 [15]. . It can be shown from Figure 9a that DTFs and MLP both underestimate the observed discharge for all three high, medium, and low flows. Figure 9b illustrates that MLP and DTFs tie for high and high medium flow with observed discharge. Figure 9c represents DTFs and MLP, which are comparable for high and medium flow. MLP underestimates the observed discharge in the region of low flow and low, medium flow. Figure 9d shows that DTFs capture the high, medium, and low flow with observed discharge better than MLP, and the last Figure 9e directs the best relationship with observed discharge for DTFs, including high, medium, and low flow.

Discussion
The DTF was the best technique in the training and testing applied soft compu techniques, such as MLP, SDTs, DTFs, and TB. The average values of R 2 and NSE dis ered during the training and testing of models were found to be more than other t

Discussion
The DTF was the best technique in the training and testing applied soft computing techniques, such as MLP, SDTs, DTFs, and TB. The average values of R 2 and NSE discovered during the training and testing of models were found to be more than other techniques, as shown in Tables 5-10. The percent of improvement in terms of R 2 and RMSE in the outputs of DTFs up to the maximum value of 57% and 17%, respectively, compared to other techniques. Many researchers quoted that results from DTFs are generally equal to 1 and many others [22,49,50]. R 2 is one of the most significant model evaluation criteria that many hydrologists and researchers have found and utilized for predicting and forecasting the behavior of various hydrological cycle components [30]. The RMSE findings of all the different input combinations demonstrated that the DTFs have a higher ability to predict rainfall and runoff than SDTs and TB while the models are being trained and tested. The reduced value of the root-mean-square error (RMSE) demonstrates that the model is accurate [51]. DTFs and SDTs were previously used for streamflow forecasting and showed good potential [22]. In Figure 8a,b, TB and SDTs demonstrated the most effective results of 1.00 in training modeling techniques at all stations, according to the NSE results for both train and test cases of soft computing techniques. SDTs, TB, and MLP showed less efficient results. The higher NSE value shows the models' efficiency [52]. Figure 8a,b shows that the DTF has better runoff prediction than SDT and TB, according to RMSE values. DTF is a more effective MLP than the conventional one [22]. A smaller value of the RMSE indicates the model's fitness [53]. So, the DTFs are the most effective technique for rainfall and runoff prediction for the Mangla watershed, according to NSE results previously mentioned by [54]. Figure 9 shows that hydrographs of the low, medium, and high streams were made using soft computing techniques such as SDTs, DTFs, and MLP to analyze their capability. These techniques were used to create the hydrographs. DTFs have good potential for predicting runoff. For the evaluation of catchment features, the lower and upper regions of the FDCs are essential parts. The low flow component of the FDC indicates how well the catchment can support itself during hot and dry weather. The catchment is likely to have the flood regime indicated by the high flow portion [7,15].
In contrast to the considerably smoother curves towards the upper portion, which are due to floods caused by snowmelt, steep curves show floods mostly driven by rain in small catchments. The flat curves in the low flow region represent flows resulting from either natural or artificial streamflow [15]. SDTs, DTFs, TB, and MLP were tested in the observed hydrographs with high, medium, and low flows. Numerous investigations from the past have shown that the FDCs' demonstrations of exceedance probability versus the simulated and observed flows that represent the specified discharges were surpassed during the designated period [55,56]. When the flow is between or equal to 1 and 10 percent of the time, it is deemed to be high. The flow rate is deemed high when it falls within 1 to 10 percent of the period.
Similarly, flows are considered medium flows from the 11th to the 89th percentile and low flows from the 90th to the 100th percentile. The flow from the 11th to the 49th percentile is considered a high-medium flow, while the flow from the 50th to the 89th percentile is considered a low-medium flow [56]. Compared to other FDCs of SDTs, TB, and MLP, DTFs are a better method for medium-high and high percentile flows and correlate with the observed flow duration curve. The FDCs of TB bond with observed flow FDCs superior to others for low and medium-low percentile flows. The FDCs of all Mangla watershed stations observed and predicted by various soft computing approaches revealed that DTFs outperformed. DTFs are better than other techniques in forecasting medium-high and high discharges, while TB is better at estimating low and medium-low discharges over the long term. SDTs can predict high-flow runoffs.

Conclusions
This study evaluates the performance of SDTs, DTFs, TB, and MLP for rainfall-runoff analysis. The analysis and observations show that DTFs are superior to all other data-driven approaches, including SDTs, TB, and MLP. In contrast, based on the outcomes of performance evaluation criteria, DTFs are assessed as the most successful advanced soft computing approach among other applied approaches. In addition, SDTs and TB have fared better in yearly streamflow forecasts. However, the SDTs were deemed the most effective approach for the Mangla catchment. The accuracy between observed and forecast runoff in the current catchment was evaluated using FDCs. The results of FDCs revealed that the DTFs was a superior method for medium-high and high-percentile flows and had stronger correlations with the FDC of observed flow than other methods. MLP is frequently compared to DTFs because both methods model data with nonlinear connections between variables and manage interactions. However, neural networks have certain disadvantages in comparison to DTFs. The MLP model is not easily comprehensible. When examining DTFs, TB, and SDTs, it is straightforward to observe that an initial variable splits the data into two categories, and subsequently, further variables separate the following child groups. This information is quite helpful for the researcher attempting to comprehend the data's nature.
Soft computing approaches have limitations that focus on data and strive to extract variables and relations from raw data, yielding more accurate answers without using analytical laws and equations. Many issues remain; in some cases, physical principles are not fulfilled. It can be utilized in the forecasting of numerous different hydrological processes, including evapotranspiration, rainfall-runoff, and sediment transport. This study further investigates that DTFs have a higher potential for rainfall-runoff analysis.  Data Availability Statement: Data used to support the study's findings can be obtained from the corresponding author upon request.
Acknowledgments: All the authors thank King Mongkut's University of Technology Thonburi, Bangkok, Thailand and Bahauddin Zakariya University, Multan, Pakistan, for their support and technical help.

Conflicts of Interest:
The authors declare no conflict of interest.