Evaluating the Effect of Deforestation on Decadal Runoffs in Malaysia Using the Revised Curve Number Rainfall Runoff Approach

Abstract

This study presents a revised and calibrated Soil Conservation Service (SCS) curve number (CN) rainfall runoff model for predicting runoff in Malaysia using a new power correlation I_a = S^L, where L represents the initial abstraction coefficient ratio. The traditional SCS-CN model with the proposed relation I_a = 0.2S is found to be unreliable, and the revised model exhibits improved accuracy. The study emphasizes the need to design flood control infrastructure based on the maximum estimated runoff amount to avoid underestimation of the runoff volume. If the flood control infrastructure is designed based on the optimum CN_0.2 values, it could lead to an underestimation of the runoff volume of 50,100 m³ per 1 km² catchment area in Malaysia. The forest areas reduced by 25% in Peninsular Malaysia from the 1970s to the 1990s and 9% in East Malaysia from the 1980s to the 2010s, which was accompanied by an increase in decadal runoff difference, with the most significant rises of 108% in Peninsular Malaysia from the 1970s to the 1990s and 32% in East Malaysia from the 1980s to the 2010s. This study recommends taking land use changes into account during flood prevention planning to effectively address flood issues. Overall, the findings of this study have significant implications for flood prevention and land use management in Malaysia. The revised model presents a viable alternative to the conventional SCS-CN model, with a focus on estimating the maximum runoff amount and accounting for land use alterations in flood prevention planning. This approach has the potential to enhance flood management in the region.

1. Introduction

Water is crucial for supporting life and economic development, but it is a scarce resource. Freshwater accounts for only 2.5% of the water on Earth, which is suitable for basic human needs such as drinking, cooking, and bathing. The scarcity of water is a result of the disparity between its supply and demand. Research on effective water resource management is essential, and it is also a practical subject. However, water-related disasters such as floods and droughts can result in the loss of life and property, making it difficult to manage water resources effectively [1].

The analysis of extreme hydrometeorological events is crucial in characterizing and comprehending the meteorological conditions that cause severe rainstorms and subsequent devastating floods. The situation becomes worse when these extreme events overlap. Compound extremes pose significant challenges and dangers to communities, especially when they involve hydrometeorological events such as floods, surges, droughts, and heatwaves that can be deadly. To better mitigate and adapt to these compound hydrometeorological extremes, it is necessary to have a better understanding of these events and their potential occurrence. The detection of trends in hydroclimatic variables such as temperature, precipitation, and streamflow plays a significant role in understanding the variations and changes in the climate. It is essential to comprehend the connections between the trends in climate fluctuations and extreme hydrometeorological events in order to plan for water and agricultural management and anticipate the dangers associated with these events [2,3,4,5].

Flooding is a destructive occurrence that happens when water overflows onto land and rises above its typical level, usually due to excessive rainfall that cannot be absorbed by the soil, which results in runoff. When the volume of runoff surpasses the capacity of available flood control infrastructure, water overflows and causes flooding. These events can have severe consequences for individuals and countries alike, as they threaten lives, especially of those living in low-lying areas, and result in significant financial losses from infrastructure damage and recovery efforts. To mitigate these impacts, it is crucial to understand the relationship between rainfall and runoff, which will improve the accuracy of runoff estimates and help the government better plan for flood management. For example, by having precise and reliable rainfall runoff models, governments can ensure the construction of adequate flood control systems, such as retention ponds and drainage systems, which will help reduce the risk of future floods [6,7].

Over the past few decades, a significant amount of research activities have been focused on the analysis and modelling of rainfall runoff, leading to the development of various types of models. The main objective is to predict the occurrence of floods in advance and prevent the associated losses. Hydrologic analysis and design rely heavily on the central aspect of rainfall runoff modelling, which depicts the interconnected surface and subsurface processes within a watershed. The importance of rainfall runoff modelling extends beyond hydrology and water resource management, as it aids in planning for watershed water resources, managing reservoirs, and preparing for drought and potential flood hazard events. Additionally, it provides insights into catchment yields and responses, water availability, and changes over time, making it a fundamental issue in watershed hydrology modelling and research [8,9,10,11].

Given the non-linear nature of the process, accurate simulations of the rainfall runoff process are crucial in hydrology and water resources management, and are highly dependent on the inputs to the simulation model. Despite the complexity associated with the transformation of rainfall into runoff, runoff analysis is crucial in predicting natural disasters such as floods and droughts. Furthermore, it plays a crucial role in the design and operation of water resource projects such as barrages, dams, and water supply schemes, and is necessary for water resources planning, development, and flood mitigation efforts [8,9,10,11].

The curve number (CN) model (Equation (1)) was created in 1954 by the United States Department of Agriculture (USDA) and Soil Conservation Services (SCS) to study rainfall and runoff using limited data from less than 200 catchments in the USA.

$$\mathrm{Q}=\frac{{\left(\mathrm{P}-{\mathrm{I}}_{\mathrm{a}}\right)}^2}{\mathrm{P}-{\mathrm{I}}_{\mathrm{a}}+\mathrm{S}}$$

(1)

where P = rainfall depth (mm), Q = runoff depth (mm), S = catchment maximum potential water retention (mm), and I_a = amount of initial abstraction (mm).

The SCS proposed the initial abstraction coefficient ratio (λ) relationship, I_a = λS, but the equation was weakly supported by data available at the time. To simplify calculations, the SCS set a constant value of 0.2 for λ in the equation (Figure 1), which became the conventional SCS-CN rainfall runoff prediction model (Equation (2)) [12,13,14,15].

$$\mathrm{Q}=\frac{{\left(\mathrm{P}-0.2\mathrm{S}\right)}^2 }{\mathrm{P}+0.8\mathrm{S}}$$

(2)

where the restriction of P > 0.2S (or I_a < P) must be obeyed, else there will be no runoff (Q) occurring.

The widely used CN runoff model was not specifically designed for many applications, yet is cited in hydrological manuals and incorporated into software. The accuracy and reliability of the model are important for related software and handbooks [16,17,18,19,20,21]. Researchers from various countries have challenged the use of a fixed value of 0.2 for the initial abstraction coefficient ratio (λ) in the equation I_a = λS, suggesting different ranges for λ that vary by region [22,23,24]. Using a fixed value of 0.2 can lead to inaccurate predictions of runoff amounts. Over 60 years, studies have aimed to find the optimal λ value to improve the model’s accuracy and reliability, but none have re-evaluated the relationship between I_a and S. The conventional model uses a linear correlation of I_a = 0.2S, which, if different, could change the entire model and require re-evaluation and re-derivation.

Urban flooding is a growing issue, causing loss of life, economic losses, and extensive destruction. Floods are the most frequent natural disaster globally, with climate change increasing rainfall frequency and intensity. Urbanization and construction activities lead to increased impervious surfaces, limiting natural infiltration and evapotranspiration and converting rainfall into runoff. These factors, along with human resource demands on water quality and quantity, have led to harmful ecological and economic impacts on catchment water resources. Climate change, human activities, and land use changes impact the amount of surface water flow, known as runoff depth, with urbanization having a negative impact, and land conversion to grass or forest having a positive impact. Changes in vegetation and forest area can also significantly impact the runoff regime [25,26,27,28,29,30,31,32,33].

Based on previous studies, the linear correlation model of I_a = 0.2S proposed by the SCS was not statistically significant using the original data from 1954. Instead, the best linear models found were I_a = 0.112S [34] and I_a = 0.111S [35]. Thus, it is crucial to reassess the recalibration of the SCS-CN rainfall runoff model before using it, given the discreditation of the linear correlation of I_a = 0.2S.

In this paper, the SCS-CN rainfall runoff model was revised and calibrated using the power correlation I_a = S^L, which has previously been explored by the authors in a separate study [12], to predict runoff in Peninsular Malaysia and East Malaysia. The results of this study demonstrate the potential for the newly calibrated power regressed model to be used to model decadal rainfall runoff conditions in Malaysia. Additionally, the study established a correlation between deforestation and urbanization on runoff increment in both Peninsular Malaysia and East Malaysia.

2. Materials and Methods

2.1. New Power Correlation of I_a = S^L

To date, no research has been conducted to calibrate the SCS-CN model using a nonlinear correlation between I_a and S. Therefore, this study re-evaluates the runoff prediction ability of the conventional SCS-CN rainfall runoff model (Equation (2)) against the newly derived SCS model using a power correlation equation (I_a = S^L) to simplify the fundamental SCS model (Equation (1)) and calibrate it using local rainfall runoff datasets with statistical methods. The newly formulated runoff predictive model will only have two fitting parameters, namely S and L, to maintain its parsimonious form as SCS fundamental Equation (1). The proposed parameter L is also a dimensionless parameter similar to SCS’s λ.

The previous SCS conventional rainfall runoff model, Equation (2), was simplified with I_a = 0.2S. However, past studies found Equation (2) to be insignificant at the α = 0.01 level, making it necessary to re-derive the model to improve the accuracy of its runoff predictions [34,35].

2.2. Study Sites in Malaysia

This study utilized data collected by the Department of Irrigation and Drainage (DID), a Malaysian federal agency. DID’s Hydrological Procedure no. 11 (DID-HP 11) gathered 474 pairs of rainfall runoff data from watersheds across Malaysia from 1964 to 2016, while DID’s Hydrological Procedure no. 27 (DID-HP 27) collected 227 pairs of rainfall runoff data from 1970 to 2000 [36,37]. The study combined both datasets, resulting in a total of 701 rainfall runoff datasets (rainfall range: 7–575 mm) collected from 1964 to 2016 for analysis. Thus far, this study has utilized the most extensive and up-to-date compilation of rainfall runoff data provided by the Malaysian federal agency, which encompasses a wide range of rainfall amounts. Figure 2 shows the catchment areas in Malaysia.

2.3. Decadal Analysis of Rainfall Runoff Models in Malaysia

In this study, decadal rainfall runoff analyses were conducted. The analysis covered Peninsular Malaysia and East Malaysia. For Peninsular Malaysia, data from 1970 to 2000 were divided into three decadal models: 1970s (70PM), 1980s (80PM), and 1990s (90PM). For East Malaysia, data from 1985 to 2016 were divided into three decadal models: 1985–1989 (85EM), 1990–1999 (90EM), and 2000–2016 (2KEM). After dividing the data into decade models, a decadal analysis was conducted to compare and analyze the trends in runoff conditions in Malaysia during each decade with the help of inferential statistics.

This study used statistical analysis to determine the optimal values of S and L for each decadal group. The bootstrapping method with the bias corrected and accelerated (BCa) procedure was conducted with 2000 random sampling (with replacement) at alpha = 0.01 through International Business Machine Corporation’s (IBM)’s Statistical Packages for Social Sciences (SPSS, version 21.0) statistical software to determine the total abstraction value (S), dimensionless initial abstraction ratio coefficient (L), and generated respective 99% confidence intervals (CI) for S and L. These results were then utilized to formulate a new SCS-CN rainfall runoff model and for the calculation of the CN value. The normality of the datasets was tested using the Kolmogorov–Smirnov and Shapiro–Wilk tests to determine whether the mean or median confidence intervals should be chosen for optimizing S and L for each dataset [38]. The Shapiro–Wilk test was given priority as it was more significant for sample sizes less than 2000, and all datasets in this study had a sample size of less than 2000. If the Shapiro–Wilk and Kolmogorov–Smirnov tests had a p-value of less than 0.05, it indicated that the datasets were not normally distributed, and the median CI was used for variable optimization, and vice versa [38].

The data distribution free bootstrap BCa technique was used in this study due to its robustness for analyzing rainfall runoff data [39,40,41]. Furthermore, the analytical module for bootstrap BCa is readily available in the IBM SPSS statistical software, making it a convenient choice for conducting the analysis needed in this study. The BCa method has the benefit of correcting biases and being able to produce the confidence interval of a particular variable at a selected significance level, which is very useful for further statistical analysis [39,40,41,42].

The calibration of the SCS runoff model was aimed to have zero bias in its overall prediction results by using a supervised numerical algorithm to find the best values of L and S that fulfilled the zero bias optimization constraint, within the 99% confidence interval of the bootstrap BCa. If zero bias optimization could not be achieved within the confidence interval, the optimization was set to maximize the Nash–Sutcliffe index (E). The accuracy and performance of the models were evaluated for each dataset based on the Nash–Sutcliffe index (E).

This study employs the Nash–Sutcliffe index (E), bias, and the Kling–Gupta efficiency (KGE) index to assess the predictive performance of the models. Equations (3)–(5) were used to calculate the E, bias, and KGE, respectively [12,43,44,45,46].

$$\mathrm{E}=1-\frac{{\sum }_{\mathrm{i}=1}^{\mathrm{n}}{\left({\mathrm{Q}}_{\mathrm{predicted}}-{\mathrm{Q}}_{\mathrm{observed}}\right)}^2}{{\sum }_{\mathrm{i}=1}^{\mathrm{n}}{\left({\mathrm{Q}}_{\mathrm{predicted}}-{\mathrm{Q}}_{\mathrm{mean}}\right)}^2}$$

(3)

$$\mathrm{BIAS}=\frac{{\sum }_{\mathrm{i}=1}^{\mathrm{n}}{\left({\mathrm{Q}}_{\mathrm{predicted}}-{\mathrm{Q}}_{\mathrm{observed}}\right)}^{ }}{\mathrm{n}}$$

(4)

$$\mathrm{KGE}=1-\sqrt{{\left(\mathrm{r}-1\right)}^2+{\left(\frac{{\mathsf{\sigma }}_{\mathrm{sim}}}{{\mathsf{\sigma }}_{\mathrm{obs}}}-1\right)}^2+{\left(\frac{{\mathsf{\mu }}_{\mathrm{sim}}}{{\mathsf{\mu }}_{\mathrm{obs}}}-1\right)}^2}$$

(5)

where ${\mathsf{\sigma }}_{\mathrm{sim}}$ = the modelling results’ standard deviation, ${\mathsf{\sigma }}_{\mathrm{obs}}$ = the observed dataset’s standard deviation, ${\mathsf{\mu }}_{\mathrm{sim}}$ = average of modelling results, ${\mathsf{\mu }}_{\mathrm{obs}}$ = average of observed dataset, and r = correlation between modelling results and observed dataset.

In earlier research, the general formula for S was derived from Equation (1), which allowed for the computation of S through a closed form equation based on the P and Q data pairs [23,24,47,48]. To date, the power model I_a = S^L substitution into Equation (1) in this study did not produce any closed form equation for S. Therefore, a numerical analysis technique is the only way to determine the value of S. The simplified formula for S is given in Equation (6) (the steps to derive and simplify the general formula for S based on the power regression model are outlined in Appendix A).

$${(2{\mathrm{S}}^{\mathrm{L}}+\mathrm{Q}-2\mathrm{P})}^2=4\mathrm{SQ}+{\mathrm{Q}}^2$$

(6)

The numerical analysis technique was used to find the optimum values of L and S (denoted as S_L), according to the P and Q data pairs in this study by applying Equation (6). On the other hand, the S_0.2 values for each data pair were also calculated using the general equation for S (Appendix B and shown in Equation (7)) [22,23,24,34,35,47,48,49] for curve number calculation.

$${\mathrm{S}}_{0.2}=5\left(\mathrm{P}+2\mathrm{Q}-\sqrt{4{\mathrm{Q}}^2+5\mathrm{PQ} }\right)$$

(7)

The S_L and S_0.2 values were calculated separately according to the P and Q data pairs using Equations (6) and (7). The SPSS regression module was utilized to find the best correlation between S_L and S_0.2 datasets and determine the best correlation equation for the study site. This was done to examine the relationship between S_L and S_0.2 and convert S_L back to its equivalent S_0.2 value to obtain the conventional SCS curve number (CN_0.2), which is commonly used by SCS practitioners. This correlation technique was introduced in [48]. The objective was to find the strongest correlation between S_L and S_0.2, with the highest adjusted R-squared value (R²_adj), using SPSS statistical software [48,50,51] (the process is summarized in Appendix C). For example, the best correlation equation from SPSS between S_L and S_0.2 for the 1970s dataset in Peninsular Malaysia (modeled as 70PM) was identified in SPSS as:

S_0.2 = (S_0.168) ^0.851

(8)

As introduced by the SCS, the equation to calculate the SCS curve number value is

$${\mathrm{CN}}_{0.2}=\frac{\mathrm{25,400}}{254+{\mathrm{S}}_{0.2}}$$

(9)

where CN_0.2 = the conventional curve number when λ = 0.2 and S_0.2 = the total abstraction amount (mm) when λ = 0.2.

Equation (9) can also be expressed as Equation (10).

$${\mathrm{S}}_{0.2}=254\left(\frac{100}{{\mathrm{CN}}_{0.2}}-1\right)$$

(10)

By substituting the best correlation equation (Equation (8)) back into the SCS curve number (Equation (9)), the conventional curve number for the 70PM can then be calculated with Equation (11).

$${\mathrm{CN}}_{0.2}=\frac{\mathrm{25,400}}{254+\left({\left({\mathrm{S}}_{0.234}\right)}^{0.88}\right)}$$

(11)

The relationship between S_L and S_0.2 is crucial in evaluating the effectiveness of the rainfall runoff model established using the power regression model (Equation (11)). The correlation equation linking S_L and S_0.2 is essential in converting S_L back to its equivalent S_0.2 value so that the conventional SCS curve number (CN_0.2) can be calculated with Equation (9) for use by SCS practitioners again [47,48,51]. The suitability of the correlation equation for the datasets was determined by calculating the adjusted coefficients of determination (R²_adj) for each correlation equation.

The trend in runoff over the decades in Peninsular Malaysia and East Malaysia was analyzed to determine the changes in runoff amounts over time in both regions. The runoff predictions made by the newly calibrated model based on the power regression equation (I_a = S^L) were determined for each decade. To find the runoff predictions for the newly calibrated model, the general equation for runoff (Q) was derived by incorporating I_a = S^L into Equation (1), resulting in Equation (12).

$${\mathrm{Q}}_{\mathrm{L}}=\frac{{\left[\mathrm{P}-{\mathrm{S}}_{\mathrm{L}}^{ \mathrm{L}}\right]}^2}{\left[\mathrm{P}-{\mathrm{S}}_{\mathrm{L}}^{ \mathrm{L}}+{\mathrm{S}}_{\mathrm{L}}^{ }\right]}$$

(12)

where P > S_L^L, else Q_L = 0.

The correlation equation between S_L and S_0.2 that was determined using SPSS was substituted into the runoff equation (Equation (12)) to determine the Q_L values for each study site. Since the best correlation equation for each site may not be the same, each site had its own specific equations to represent its runoff equation, expressed in terms of CN_0.2 values, after substituting the S correlation equations and Equation (10) back into the general runoff equation (Equation (1)). The derivation of the general runoff model for the power regressed model is summarized in Appendix E.

The interdecadal runoff differences were determined once the runoff estimates were obtained for each decadal group. For example, the interdecadal runoff difference in Peninsular Malaysia between the 1970 and 1980 was obtained by subtracting the runoff amount from the decadal models of the 1970s (named as 70PM) from that of the 1980s (80PM). A positive interdecadal runoff indicates that the runoff increased from the 1970s to the 1980s, while a negative difference indicates a decrease. The interdecadal runoff difference between the 1970s and 1980s, 1980s and 1990s (model named 90PM), and 1970s and 1990s were identified for Peninsular Malaysia, while the interdecadal runoff between 1985 (named as 85EM) and 1990s (90EM), 1990s (90EM) and 2000s (2KEM), and 85EM and 2KEM were identified for East Malaysia.

The Sen’s slope was also calculated for each interdecadal runoff difference model to understand the trend in the runoff changes. The Sen’s slope represents the median of all slopes in the interdecadal runoff difference model and can help estimate the percentage change in runoff estimates based on any rainfall depth and within the selected CN_0.2 range. By calculating the Sen’s slope for each decadal model, practitioners can compare changes in runoff magnitude among the models and observe whether the trend in runoff changes throughout the decades shows an uptrend or downtrend.

2.4. Analysis of the Impact of Deforestation on the Rainfall Runoff Conditions in Malaysia

In the past, studies have shown the impact of deforestation and afforestation on runoff trends. To understand the effect of forest area in Malaysia on the runoff amount from rainfall events, the forest area data in both Peninsular Malaysia and East Malaysia were collected. The analysis aimed to understand the relationship between changes in forest area and changes in runoff through the decades in both regions.

For Peninsular Malaysia, forest area data from 1970 to 2000 were used in a comparison with available runoff data within the same time frame. For East Malaysia, forest area data from 1985 to 2016 was included to examine the relationship between changes in forest area and changes in runoff.

The best fit model between the annual runoff and annual forest area was identified to show the relationship between the two and the impact of changes in forest area reduction on the runoff amount. The adjusted coefficient of determination (R²_adj) was used to assess the fitness of the best fit model to the data [50].

3. Results

3.1. Decadal Analysis of Runoff Trends in Peninsular Malaysia and East Malaysia

This paper combines datasets from DID-HP 11 and DID-HP 27 to create three decadal models: the 70PM, 80PM, and 90PM for Peninsular Malaysia. In East Malaysia, the combined datasets from DID-HP 11 and DID-HP 27 also created three decadal models: the 85EM, 90EM, and 2KEM.

S and L were calculated from the data pairs of P and Q in each decadal model, and the BCa 99% CI was used to generate confidence intervals for both parameters. The optimal values for S and L were then identified from these intervals.

Table 1. The optimum S (S_L), L, I_a to S ratio, Nash–Sutcliffe index, bias, and KGE index for each decadal dataset in Peninsular Malaysia.

Decadal Model	L	SL (mm)	Ia/S	E	BIAS	KGE
70PM	0.168	187.81	0.013	0.941	0	0.968
80PM	0.228	183.31	0.018	0.906	0.497	0.947
90PM	0.232	175.30	0.019	0.892	0	0.925

and

Table 2. The optimum S (S_L), L, I_a to S ratio, Nash–Sutcliffe index, bias, and KGE index for each decadal dataset in East Malaysia.

Decadal Model	L	SL (mm)	Ia/S	E	BIAS	KGE
85EM	0.332	152.23	0.035	−0.387	−1.910	0.307
90EM	0.274	121.11	0.031	0.788	0	0.713
2KEM	0.316	152.40	0.032	0.730	0	0.866

show the results of the statistical analysis for all decadal datasets in Peninsular Malaysia and East Malaysia, respectively. The I_a to S ratio, Nash–Sutcliffe index (E), bias, and Kling–Gupta efficiency index (KGE) were also calculated based on the optimal S and L values (Appendix C explains the method for formulating the model).

In Peninsular Malaysia, the Nash–Sutcliffe index ranges from [0.892, 0.941] and the Kling–Gupta efficiency (KGE) index ranges from [0.925, 0.968], indicating that the new power regressed model provides accurate runoff estimates. The bias is also relatively low, ranging from [0, 0.497]. In East Malaysia, the 85EM decadal group shows a negative value for the Nash–Sutcliffe index; however, a KGE of 0.307 implies that the model performs better than its benchmarked mean value [36]. For the other decadal groups in East Malaysia, the Nash–Sutcliffe index ranges from [0.730, 0.788] and the KGE ranges from [0.713, 0.866], indicating that the new power regression model provides accurate estimates with a bias of 0. Both the Peninsular Malaysia and East Malaysia decadal datasets calculated I_a to S ratios (Table 1 and Table 2) that are in line with previous studies, which support the claim that the I_a to S ratio should be around 0.05 (5%) or less [16,18,23,24,34,35,47,49,51,52].

With the calculated optimum values of S and L for each decadal dataset, the corresponding runoff equation can be determined, as shown in Appendix E. The best correlation equations for S_0.2 and S_L in this study are tabulated in

Table 3. The S correlation equation for each decadal group in Peninsular Malaysia.

Decadal Model	Correlation Equation	R2adj	p-Value
70PM	S0.2 = S0.1680.851	0.987	<0.001
80PM	S0.2 = S0.2280.881	0.998	<0.001
90PM	S0.2 = S0.2320.889	0.998	<0.001

and

Table 4. The S correlation equation for each decadal group in East Malaysia.

Decadal Model	Correlation Equation	R2adj	p-Value
85EM	S0.2 = S0.3320.891	0.997	<0.001
90EM	S0.2 = S0.2740.887	0.998	<0.001
2KEM	S0.2 = S0.3160.896	0.998	<0.001

.

The results in Table 3 show that the S correlation equations for Peninsular Malaysia have high adjusted R-squared values, ranging from 0.987 to 0.998, and Table 4 shows that the S correlation equations for East Malaysia also have high adjusted R-squared values, ranging from 0.997 to 0.998. This indicates that the S correlation equations fit the dataset well, with a p-value of less than 0.001. With the S correlation equations for each decadal dataset, the runoff prediction models can be identified and the interdecadal runoff difference model can be obtained accordingly, as described in Section 2.3.

The study employed the Sen’s slope to determine the trend in runoff across different decades in Malaysia, encompassing all recorded rainfall events in DID HP 11 and 27 with rainfall depths ranging from 7 mm to 575 mm. As the interdecadal runoff differences were found to be non-normally distributed, the study deemed the Sen’s slope appropriate for analysis. Furthermore, the distributions of slopes for all interdecadal models in Peninsular Malaysia and East Malaysia were also non-normally distributed, leading to the use of the median values as the representative value for all scenarios.

The results show that the collective Sen’s slope for each interdecadal model in Peninsular Malaysia is 0.032 (with a confidence interval of [0.022, 0.043]) for the 70PM to 80PM model, 0.013 (with a confidence interval of [0.010, 0.020]) for the 80PM to 90PM model, and 0.045 (with a confidence interval of [0.032, 0.062]) for the 70PM to 90PM model; all models are significant with p < 0.01. For East Malaysia, the collective Sen’s slope for each interdecadal model is 0.007 (with a confidence interval of [−0.003, 0.063]) for the 85EM to 90EM model, 0.010 (with a confidence interval of [0.003, 0.014]) for the 90EM to 2KEM model, and 0.018 (with a confidence interval of [0.009, 0.021]) for the 85 to 2KEM model; all models are also significant with p < 0.01.

According to Figure 3, the highest overall Sen’s slope runoff difference (%) in Peninsular Malaysia is between the 70PM and 90PM interdecadal runoff model, followed by the 70PM–80PM model, and the lowest is the 80PM–90PM model. As shown in Figure 4, the highest overall Sen’s slope runoff difference (%) in East Malaysia is between the 85EM and 2KEM interdecadal runoff model, followed by the 90EM–2KEM model, and the lowest is the 85EM–90EM model.

The Sen’s slope is used to estimate the percentage increase in runoff relative to the rainfall depth. For instance, the Sen’s slope runoff difference (%) between the 70PM and 90PM model in Peninsular Malaysia is 0.045, which means that the expected increase in runoff with 100 mm of rainfall is 4.5 mm (4.5% of the rainfall depth).

The optimum S value and BCa 99% CI for each decadal model in Peninsular and East Malaysia were determined using the S correlation equations and Equation (9). This enabled the calculation of the optimum CN_0.2 and its BCa 99% CI. For example, the optimum S value for the 70PM decadal model in Peninsular Malaysia is 187.81 mm, with a corresponding S_0.2 of 86.09 mm. Using Equation (9), the calculated CN_0.2 is 74.68. The optimum value and 99% BCa CI for CN_0.2 are shown in

Table 5. The optimum S, optimum CN_0.2, and its corresponding BCa 99% CI for both Peninsular Malaysia and East Malaysia.

Peninsular Malaysia
Decadal Model		BCa 99% CI for S (mm)			BCa 99% CI for CN0.2
	Optimum S (mm)	Lower	Upper	Optimum CN0.2	Lower	Upper
70PM	187.81	137.59	194.85	74.69	74.09	79.36
80PM	183.31	137.60	183.31	72.04	72.04	76.83
90PM	175.30	120.37	191.21	71.99	70.41	78.22
East Malaysia
85EM	152.23	50.89	152.23	74.26	74.26	88.45
90EM	121.11	63.55	127.29	78.29	77.53	86.47
2KEM	152.40	50.49	166.95	73.76	72.15	88.32

using Equation (9) and S correlation equations.

The maximum runoff amount is a critical reference for engineers, as floods occur when the runoff exceeds the capacity of flood control infrastructure. By using Equations (10) and (12) and the S correlation equation, the maximum runoff amount can be estimated within the 99% BCa CI of CN_0.2 for the maximum rainfall depth (details of the calculation can be found in Appendix E). The results of the runoff estimation obtained from the optimum CN_0.2, the maximum runoff amount estimated from the upper limit of the BCa 99% CI of CN_0.2, and the difference between both estimated results are tabulated in

Table 6. The highest recorded rainfall depth, the runoff estimation obtained from the optimum CN_0.2, the maximum runoff amount estimated based on the BCa 99% CI of CN_0.2, and the runoff difference between both estimated results through each decade for both Peninsular Malaysia and East Malaysia.

	Peninsular Malaysia
Decadal Model (Appendix E)	Highest Rainfall Depth Recorded (mm)	Estimated Runoff Depth based on the Optimum CN0.2 (mm)	Maximum Runoff Depth Estimated with Upper CN0.2 Limit (mm)	Estimated Runoff Depth Difference (mm)
70PM	485	353.46	380.50	27.04
80PM	420	290.27	314.15	23.88
90PM	306	192.29	217.31	25.02
	East Malaysia
85EM	175	88.13	131.33	43.20
90EM	575	472.20	515.16	42.96
2KEM	224	129.48	179.58	50.10

for both Peninsular Malaysia and East Malaysia to show the runoff depth difference based on the highest rainfall depth recorded for each decade between the optimum CN_0.2 and the upper limit CN_0.2.

The results shown in Table 6 highlight the importance of building flood control infrastructure based on the maximum estimated runoff amount. The differences between the runoff estimates based on the optimum CN_0.2 values and the upper limit of the BCa 99% CI for CN_0.2 demonstrate the potential consequences of not designing the flood prevention infrastructure based on the maximum estimate. For example, in the 2KEM decadal model, the calculated runoff difference was 50.10 mm, which translates to an underestimation of 50,100 m³ of runoff volume per 1 km² area if the design is based on the optimum CN_0.2. The reason for assuming a 1 km² watershed area is to facilitate the visualization of the consequences of incorrect estimations that may be referred to by practitioners or engineers. This is equivalent to nearly 20 Olympic-sized swimming pools volume difference for 1 km² watershed (the calculation of runoff volume is detailed in Appendix F). If the flood control infrastructure is designed based only on the reference of optimum CN_0.2, it may not have enough capacity to handle the runoff volume difference of 50,100 m³/km² watershed area in the case of a maximum runoff event, leading to possible flooding. The results in Table 6 serve as a warning to practitioners that the design of flood prevention infrastructure should not solely rely on the optimum CN_0.2 runoff estimation, but also take into consideration the maximum estimated runoff amount to reduce the risk of flooding.

3.2. Impact of Human Activities on Runoff Amount in Malaysia

The results of both the Kolmogorov–Smirnov and Shapiro–Wilk tests indicate that the runoff data for both Peninsular Malaysia and East Malaysia are not normally distributed (p < 0.01), so the median runoff for each year will represent the overall annual runoff. Over the decades, the forested areas in both Peninsular Malaysia and East Malaysia have decreased. The changes in forested areas and the runoff difference under maximum rainfall conditions over the decades in both regions are presented in

Table 7. The decadal changes in the amount and the corresponding percentage of forest area and runoff difference in Peninsular Malaysia.

Interdecadal Period	Forest Area		Model Runoff Difference, Qv, observed
	(‘000 Ha)	(%)	(mm)	(%)
1970s–1980s	−1736.47	−21.69%	5.71	42.26%
1980s–1990s	−381.18	−6.00%	8.91	46.36%
1970s–1990s	−2032.94	−25.39%	14.62	108.22%

and

Table 8. The decadal changes in the amount and the corresponding percentage of forest area and runoff difference in East Malaysia.

Interdecadal Model	Forest Area		Runoff Difference, Qv, observed
	(‘000 Ha)	%	(mm)	(%)
1987s–1990s	−771	−5.71%	0.25	1.75%
1991s–2000s	−1057	−7.89%	4.35	29.90%
1987s–2010s	−1167	−9.24%	4.60	32.17%

.

Table 7 and Table 8 present the decreasing trend in forest areas in Malaysia over the decades, with the most significant declines of 25% in Peninsular Malaysia from the 1970s to the 1990s and 9% in East Malaysia from the 1980s to the 2010s. This reduction in forest area is accompanied by an increase in the decadal runoff difference, with the most significant rises of 108% in Peninsular Malaysia from the 1970s to the 1990s and 32% in East Malaysia from the 1980s to the 2010s. To examine the connection between changes in forest area and changes in runoff amount, the best correlation models between forest area and runoff amount for both regions were identified, along with the adjusted coefficient of determination (adjusted R-squared) for each model, and are shown in

Table 9. The best correlation models for each dataset and the corresponding adjusted R-squared.

Study Site	Dataset	Best Correlation Model	R2adj
Peninsular Malaysia	Runoff and FA	$\mathrm{Q}={ \mathrm{e}}^{\left(\frac{19629.67}{\mathrm{FA}}\right)}$	0.947
East Malaysia	Runoff and FA	$\mathrm{Q}={ \mathrm{e}}^{\left(\frac{38499.45}{\mathrm{FA}}\right)}$	0.949

Note: Q is the runoff amount (mm) and FA is the forest area (‘000 Ha).

.

The best correlation model that links the forest area and runoff for both Peninsular Malaysia and East Malaysia demonstrates a significant negative correlation between the two. A high adjusted R-squared in the range of [0.947, 0.949] and a p-value of less than 0.001 indicate a strong correlation between the forest area reduction and the increase in runoff. This observation aligns with prior studies, which suggest that deforestation or reduction in forest area results in an increase in runoff [28,29,30,33].

4. Discussion

4.1. Validity of I_a = 0.2S and the Newly Proposed Correlation of I_a = S^L

Previous research has shown that the linear correlation (I_a = 0.2S) proposed by the SCS in 1954 to simplify its rainfall runoff model, which is widely used as the conventional SCS runoff prediction (Equation (2)), lacks statistical verification even within its own datasets [23,34]. This has led to numerous reports of inaccuracies and inconsistencies in the model’s runoff predictions by studies worldwide [17,18,24,34,38,49,51,52,53,54,55].

The SCS proposed a linear correlation of I_a = 0.2S in 1954 to simplify Equation (1) [13,14,15], but two studies have shown it to be statistically insignificant even to the original SCS dataset. These studies found that the best correlation should be I_a = 0.111S or I_a = 0.112S, instead of I_a = 0.2S [34,35]. Unlike previous studies, which calibrated the SCS-CN runoff predictive model based on I_a = λS, this study assessed the use of a non-linear correlation between I_a and S in the form of I_a = S^L to simplify Equation (1) and revise the SCS-CN rainfall runoff model to improve its runoff estimates.

The use of Equation (2) in education raises serious concerns. It could lead students to adopt a simplified and flawed approach for runoff prediction, which would have a wide impact on related fields such as water resource management, environmental science, and civil engineering. As Equation (2) was found to be statistically insignificant even to its original dataset, this can mislead students into following a faulty rainfall runoff model. Additionally, continued use of Equation (2) in educational resources such as textbooks, software, government agency handbooks, and training perpetuates the use of an unreliable runoff prediction method. Updating and enhancing the SCS-CN model for educational purposes is crucial to ensure that students and professionals have accurate and effective tools for runoff prediction. Only with the corrected rainfall runoff model can the reliability and accuracy of the model, along with the related software, be improved and applied in industry in the future.

4.2. Application of Newly Calibrated Runoff Predictive Models

This study uses the largest collected rainfall runoff dataset from watersheds in Malaysia under the DID-HP 11 and DID-HP 27 programs for analysis. The results showed that the power regression model was better at predicting runoff compared to the conventional SCS-CN rainfall runoff (Equation (2)), where the accuracy and the consistency of the model had been improved significantly. The comparison of the model performance is summarized in Appendix D. The ratios of I_a to S were found to be mostly 5% or lower and far from the SCS’s proposed value of 0.2 (20%) [17,18,24,34,38,49,51,52,53,54,55]. This shows that the calibrated and revised models are able to produce outcomes that are in line with the published results from past research. In addition, the newly revised model has been tested with multiple datasets across different catchments in Malaysia, China, and Greece and has demonstrated enhanced runoff estimation accuracy to formulate the CN runoff model with the power correlation of I_a = S^L [12].

This study also highlights the importance of designing flood control infrastructure based on the maximum estimated runoff amount. The runoff estimates based on the upper limit of the BCa 99% CI for CN_0.2 were significantly higher than the estimates based on the optimum CN_0.2 values. Not designing flood prevention infrastructure based on the maximum estimate could result in an underestimation of the runoff volume of approximately 20 Olympic-sized swimming pools per 1 km² area (Table 6). This revised CN model has the potential to improve water resource management by providing more accurate runoff predictions for different soil and hydrological conditions. This can aid in making better informed decisions about water availability and flood hazards, as accurate quantification of runoff is crucial for managing water resources, particularly for predicting floods.

The revised CN model allows for a more precise calculation of runoff from a specific region considering various soil and hydrological conditions. This information is critical for effective water resource management, as it predicts water availability and helps assess flood risks, reducing harm to infrastructure, lives, and finances caused by floods. It is crucial for professionals in the field to be familiar with the improved SCS rainfall runoff model and consider using it in their work. This revised model has the ability to give more accurate and reliable predictions of runoff, which can greatly enhance water resource management and flood prediction outcomes. With the enhanced rainfall runoff model, potential flood issues can be coped with in a much more efficient way, helping practitioners reduce financial loss caused by flood damage and poor flood prevention planning.

4.3. Decadal Runoff Trend Analaysis in Both Peninsular Malaysia and East Malaysia

The increasing trend in runoff in both Peninsular Malaysia and East Malaysian watersheds over the decades is a matter of concern for flood mitigation. The amount of runoff, which is a measure of the flow of water, is an important factor in the prediction of flood hazards. By using the BCa 99% CI for CN_0.2 calculation in both regions, it is possible to determine the maximum runoff across the decades, which indicates that the maximum runoff amount has increased over time. This trend highlights the need to be proactive in mitigating the risk of flooding. It is important for engineers and hydrologists in Malaysia to take note of this trend and plan flood control infrastructure accordingly. Proper planning and management of flood control infrastructure can help to mitigate the impact of floods and reduce the risk of damage to people, property, and the environment.

This study examined the link between deforestation and runoff. A correlation between decreasing forest area and increasing runoff amounts in Peninsular Malaysia and East Malaysia over the decades was established (Table 7, Table 8 and Table 9). This demonstrates that deforestation has contributed to the increase in runoff. These results align with previous research indicating that deforestation can lead to higher runoff. Therefore, it is crucial for federal agencies to implement effective forest management strategies, such as afforestation or reforestation, to mitigate runoff and potential flood problems.

It is crucial to understand the impact of deforestation on runoff, as this can have significant implications for water resource management and flood mitigation. By implementing proper forest management strategies, the negative effects of deforestation can be mitigated, which can help to reduce the risk of flooding and improve water resource management. This highlights the importance of considering the relationship between deforestation and runoff in order to make informed decisions about the management of forested areas.

4.4. Exploring the Application of Machine Learning for Rainfall Runoff Prediction

In the last few decades, machine learning has become increasingly popular in hydrology research. Several machine learning techniques, including long short-term memory (LSTM), adaptive neuro-fuzzy inference systems (ANFIS), multilayer perceptron (MLP), wavelet neural networks (WNN), ensemble prediction systems (EPS), support vector machines (SVM), support vector regression (SVR), and artificial neural networks (ANN), have been introduced by researchers to enhance the precision and effectiveness of predictive models. Hybrid machine learning approaches, such as ANFIS and WNN, have also been found to offer improved accuracy and performance for long-term and short-term rainfall runoff models [44]. Furthermore, machine learning can be applied to resolve the issue of a lack of time series data for flow hydrographs due to the absence of gauged stations by using flood modelling methods, such as the reverse flood routing model, HEC-RAS, and GIS flood maps. The new rainfall runoff model proposed in this study may also benefit from being combined with machine learning techniques [19,20,21].

5. Conclusions

This study employed a new correlation (I_a = S^L) to calibrate the SCS rainfall runoff prediction framework (Equation (1)) using inferential statistics. It assessed the accuracy of the newly calibrated model, analyzed the decadal runoff trends in Malaysia, and studied the effect of deforestation on the runoff trends. The main findings are:

• This study demonstrated the unreliability of the SCS’s proposed relation of I_a = 0.2S, indicating a need to update the SCS runoff prediction model. The new power correlation of I_a = S^L shows improved accuracy in runoff prediction. The results align with previous global studies, indicating an I_a to S ratio of around 5% or less, which is significantly different from the traditional value of 0.2 (20%) proposed by the SCS. On average, the power regression model exhibits a 138% higher predictive accuracy than the conventional SCS-CN model, as measured by the KGE index.
• This study emphasizes designing flood control infrastructure based on the maximum estimated runoff amount. Not using this estimate could result in a 50,100 m³ underestimation of the runoff volume per 1 km² watershed area in Malaysia, as indicated by the difference between the optimum CN_0.2 values and the upper limit of the BCa 99% CI for CN_0.2.
• This study found a strong correlation between decreasing forest area and increasing runoff difference in Malaysia over time. Peninsular Malaysia saw a 25% reduction in forest area from the 1970s to the 1990s, and East Malaysia experienced a 9% reduction from the 1980s to the 2010s. This was accompanied by an increase in decadal runoff difference, with the most significant increases of 108% in Peninsular Malaysia from the 1970s to the 1990s and 32% in East Malaysia from the 1980s to the 2010s.
• The proposed methodology requires a minimum dataset of 25 data pairs for accurate inferential results and relies on the bootstrap BCa method for optimizing key variables and formulating a new runoff predictive model. Therefore, using statistical software with this method is essential. Future studies may consider incorporating machine learning methods to further enhance the model’s performance.