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

^{1}

^{2}

^{*}

## Abstract

**:**

_{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 m

^{3}per 1 km

^{2}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

_{a}= amount of initial abstraction (mm).

_{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].

_{a}< P) must be obeyed, else there will be no runoff (Q) occurring.

_{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.

_{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.

_{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}

_{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.

#### 2.2. Study Sites in Malaysia

#### 2.3. Decadal Analysis of Rainfall Runoff Models in Malaysia

_{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).

_{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.

_{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 (R

^{2}

_{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:

_{0.2}= (S

_{0.168})

^{0.851}

_{0.2}= the conventional curve number when λ = 0.2 and S

_{0.2}= the total abstraction amount (mm) when λ = 0.2.

_{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 (R

^{2}

_{adj}) for each correlation equation.

_{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).

_{L}

^{L}, else Q

_{L}= 0.

_{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.

_{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

^{2}

_{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

_{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).

_{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].

_{0.2}and S

_{L}in this study are tabulated in Table 3 and Table 4.

_{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 using Equation (9) and S correlation equations.

_{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 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}.

_{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 m

^{3}of runoff volume per 1 km

^{2}area if the design is based on the optimum CN

_{0.2}. The reason for assuming a 1 km

^{2}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 km

^{2}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 m

^{3}/km

^{2}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

## 4. Discussion

#### 4.1. Validity of I_{a} = 0.2S and the Newly Proposed Correlation of I_{a} = S^{L}

_{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].

_{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.

#### 4.2. Application of Newly Calibrated Runoff Predictive Models

_{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].

_{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 km

^{2}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.

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

_{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.

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

## 5. Conclusions

_{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 m
^{3}underestimation of the runoff volume per 1 km^{2}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.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Appendix A

_{a}= 0.2S and simplified Equation (1) to Equation (2), whereby P must be > 0.2S for runoff (Q) to occur.

_{a}and S in the form of I

_{a}= S

^{L}was substituted into Equation (1):

## Appendix B. Refer to Section 2.4, Equation (6) in [47] and Section 2, Equation (8) in [56]

_{a}= λS) as below [47,56]:

_{0.2}from P and Q values. Equation (7) is identical to Hawkins’ previous study [35,49]. By using Equation (7), S

_{0.2}can be calculated for each P–Q pair from all study sites and the correlation between S

_{0.2}and S

_{λ}can be established using SPSS. The correlation equation can then be integrated into the SCS-CN curve number model to determine CN

_{0.2}for each dataset.

## Appendix C

_{0.2}value derivation are summarized as below:

- The SCS stated that I
_{a}= λS, while the effective rainfall (P_{e}) = P − I_{a}, and therefore Equation (1) ($\mathrm{Q}=\frac{\mathrm{P}-{\mathrm{I}}_{\mathrm{a}}}{\mathrm{P}-{\mathrm{I}}_{\mathrm{a}}+\mathrm{S}}$) can be expressed as:

_{a}= S

^{L}instead of I

_{a}= λS

- 2.
- Given a P–Q dataset, the corresponding L
_{i}and S_{i}values to P_{i}and Q_{i}can be calculated through numerical analysis technique with Equation (6) or (A1). To date, there is no closed form for the general equation for S. Therefore, a numerical analysis technique will be used to solve for the corresponding S_{i}values. - 3.
- With bootstrap, a BCa procedure (selects 95–99% confidence interval level) to generate the confidence interval (CI) for derived L
_{i}and S_{i}datasets and check for its dataset normality in SPSS (or other statistical software):- (a)
- If the dataset is normally distributed, the optimum S and L values are found from the mean BCa CI to formulate a new runoff predictive model.
- (b)
- Otherwise, the S and L optimization process will refer to the median BCa CI (denote the optimum value of both parameters as L
_{optimum}and S_{optimum}).

- 4.
- To formulate the new SCS-CN rainfall runoff model, both L
_{optimum}and S_{optimum}values are substituted into Equation (1) with I_{a}= S^{L}. - 5.
- The corresponding S
_{i}values with the same P–Q dataset are computed, along with the L_{optimum}value with Equations (A1) or (6) through numerical analysis technique. - 6.
- Given (P
_{i}, Q_{i}) data pairs and λ = 0.2, S_{0.2i}values are computed with Equations (A3) or (7). - 7.
- S
_{0.2i}(from step 6) and S_{i}(from step 5) values are correlated to obtain a correlation equation between S_{0.2i}and S_{i}via SPSS for curve number (CN_{0.2}) value derivation. - 8.
- The S correlation equation from step 7 is substituted into the SCS curve number formula (${\mathrm{CN}}_{0.2}=\frac{\mathrm{25,400}}{{\mathrm{S}}_{0.2}+254}$) to derive the CN
_{0.2}value.

## Appendix D

**Table A1.**Comparison of the performance of the recalibrated model with the conventional model, based on the Nash–Sutcliffe index (E), the bias, and the Kling–Gupta efficiency index (KGE) for each decadal model in Peninsular Malaysia and East Malaysia, with the constraint I

_{a}< P applied to the conventional SCS-CN model.

Decadal Model | Power Regressed Model | Conventional SCS-CN Model | ||||
---|---|---|---|---|---|---|

E | Bias | KGE | E | Bias | KGE | |

70PM | 0.941 | 0 | 0.968 | 0.876 | 12.29 | 0.579 |

80PM | 0.906 | 0.497 | 0.947 | 0.506 | 24.85 | 0.346 |

90PM | 0.892 | 0 | 0.925 | 0.801 | 10.75 | 0.733 |

85EM | −0.387 | −1.910 | 0.307 | −0.108 | 9.49 | −0.401 |

90EM | 0.788 | 0 | 0.713 | 0.316 | 12.22 | 0.195 |

2KEM | 0.730 | 0 | 0.866 | 0.302 | 12.72 | 0.391 |

**Table A2.**The BCa confidence intervals of λ for each decadal model in Peninsular Malaysia and East Malaysia for the conventional SCS-CN model.

Decadal Model | Std. Dev. | 95% BCa CI for λ | 99% BCa CI for λ | ||||
---|---|---|---|---|---|---|---|

Lower | Upper | Variation | Lower | Upper | Variation | ||

70PM | 0.123 | 0.057 | 0.082 | 44.04% | 0.053 | 0.089 | 66.32% |

80PM | 0.088 | 0.014 | 0.018 | 27.48% | 0.014 | 0.020 | 40.91% |

90PM | 0.132 | 0.032 | 0.046 | 46.07% | 0.032 | 0.054 | 69.27% |

85EM | 0.259 | 0.028 | 0.072 | 158.77% | 0.025 | 0.080 | 218.59% |

90EM | 0.078 | 0.006 | 0.009 | 42.03% | 0.006 | 0.009 | 66.27% |

2KEM | 0.176 | 0.014 | 0.053 | 274.04% | 0.014 | 0.061 | 349.23% |

## Appendix E

_{0.2}= S

_{0.316}

^{0.896}

_{0.316}= S

_{0.2}

^{1.115}

_{0.2}as shown below. Equation (10) will be utilized to express S

_{0.2}in terms of CN

_{0.2}, and the resulting runoff model in terms of P and CN

_{0.2}will be expressed as follows. After further simplification of the equation, the simplified recalibrated runoff equation in terms of P and CN

_{0.2}for the 2KEM dataset model is presented as follows:

Peninsular Malaysia | |
---|---|

Decadal Datasets | Decadal Model Equations |

1970s (70PM) | ${\mathrm{Q}}_{0.168}=\frac{{\left[\mathrm{P}-{\left(2.947{\left(\frac{100}{{\mathrm{CN}}_{0.2}}-1\right)}^{0.195}\right)}^{}\right]}^{2}}{\left[\mathrm{P}-\left(2.947{\left(\frac{100}{{\mathrm{CN}}_{0.2}}-1\right)}^{0.195}\right)+\left(619.458{\left(\frac{100}{{\mathrm{CN}}_{0.2}}-1\right)}^{1.161}\right)\right]}$ |

1980s (80PM) | ${\mathrm{Q}}_{0.228}=\frac{{\left[\mathrm{P}-{\left(4.186{\left(\frac{100}{{\mathrm{CN}}_{0.2}}-1\right)}^{0.259}\right)}^{}\right]}^{2}}{\left[\mathrm{P}-\left(4.186{\left(\frac{100}{{\mathrm{CN}}_{0.2}}-1\right)}^{0.259}\right)+{\left(530.489{\left(\frac{100}{{\mathrm{CN}}_{0.2}}-1\right)}^{1.133}\right)}^{}\right]}$ |

1990s (90PM) | ${\mathrm{Q}}_{0.232}=\frac{{\left[\mathrm{P}-{\left(4.237{\left(\frac{100}{{\mathrm{CN}}_{0.2}}-1\right)}^{0.261}\right)}^{}\right]}^{2}}{\left[\mathrm{P}-\left(4.237{\left(\frac{100}{{\mathrm{CN}}_{0.2}}-1\right)}^{0.261}\right)+{\left(501.913{\left(\frac{100}{{\mathrm{CN}}_{0.2}}-1\right)}^{1.123}\right)}^{}\right]}$ |

East Malaysia | |

1985s (85EM) | ${\mathrm{Q}}_{0.332}=\frac{{\left[\mathrm{P}-{\left(7.959{\left(\frac{100}{{\mathrm{CN}}_{0.2}}-1\right)}^{0.375}\right)}^{}\right]}^{2}}{\left[\mathrm{P}-\left(7.959{\left(\frac{100}{{\mathrm{CN}}_{0.2}}-1\right)}^{0.375}\right)+{\left(518.869{\left(\frac{100}{{\mathrm{CN}}_{0.2}}-1\right)}^{1.129}\right)}^{}\right]}$ |

1990s (90EM) | ${\mathrm{Q}}_{0.274}=\frac{{\left[\mathrm{P}-{\left(5.505{\left(\frac{100}{{\mathrm{CN}}_{0.2}}-1\right)}^{0.308}\right)}^{}\right]}^{2}}{\left[\mathrm{P}-\left(5.505{\left(\frac{100}{{\mathrm{CN}}_{0.2}}-1\right)}^{0.308}\right)+{\left(507.502{\left(\frac{100}{{\mathrm{CN}}_{0.2}}-1\right)}^{1.125}\right)}^{}\right]}$ |

2000s (2KEM) | ${\mathrm{Q}}_{0.316}=\frac{{\left[\mathrm{P}-{\left(7.032{\left(\frac{100}{{\mathrm{CN}}_{0.2}}-1\right)}^{0.352}\right)}^{}\right]}^{2}}{\left[\mathrm{P}-\left(7.032{\left(\frac{100}{{\mathrm{CN}}_{0.2}}-1\right)}^{0.352}\right)+{\left(480.164{\left(\frac{100}{{\mathrm{CN}}_{0.2}}-1\right)}^{1.115}\right)}^{}\right]}$ |

## Appendix F

_{0.2}in the 2KEM dataset in East Malaysia is 73.76. With the highest recorded rainfall depth of 224 mm in the same decade, the estimated runoff can be calculated using Equation (10) for the S correlation and Equation (12) as 129.48 mm. As per Appendix E, the runoff equation for the 2KEM dataset model in terms of P and CN

_{0.2}has been recalibrated and is presented as follows:

_{0.2}= 73.76 and with a rainfall depth of 224 mm, the estimated runoff obtained is as follows:

_{0.2}value will result in a higher runoff amount; thus, to obtain the maximum runoff amount, the 99% BCa upper limit and the CN

_{0.2}will be selected to estimate the maximum runoff amount. As shown in Section 3.1 (Table 5), the 99% BCa lower and upper limit of CN

_{0.2}for the 2KEM model were 72.15 and 88.32 respectively.

_{0.2}= 88.32, the estimated runoff amount can also be obtained with a similar approach as shown above, resulting in a value of 179.58 mm. Comparing both the runoff amount estimated based on the collective representation (optimum CN

_{0.2}) and the 99% BCa upper limit of CN

_{0.2}, a runoff difference (Q

_{v}) of 50.10 mm is observed.

_{v}= 179.58–129.48 mm = 50.10 mm, thus

^{2}. Then, the calculation of the volume in the watershed can be shown as follows:

_{0.2}is 50,100 cubic meters, or 50.1 million liters. This shows that practitioners should consider not only the runoff estimate based on the optimum CN

_{0.2}value, but also the maximum estimated runoff, when designing flood control infrastructure, in order to reduce the risk of overflow due to inadequate capacity of flood control structures such as dams and flood walls.

## Appendix G

_{0.2}values.

_{a}) for both 70PM and 90EM can be determined by the following equations:

_{0.2}as follows for 70PM and 90EM (the derivation of the calibrated runoff model is summarized in Appendix E).

_{0.2}as follows:

_{0.2}(Equation (A7)) as follows:

_{v}) was calculated by Equations (A8) and (A9) as follows:

_{v}obtained from Equation (A8) and Equation (A9) were plotted against different CN

_{0.2}values, respectively. Figure A1 and Figure A2 show the runoff differences between the conventional SCS-CN rainfall runoff model (Equation (2)) and the calibrated model across different CN

_{0.2}values in both Peninsular Malaysia in the 1970s and East Malaysia in the 1990s.

_{v}) in Peninsular Malaysia was nearly 65 mm at a maximum rainfall amount (P) of 490 mm, while in East Malaysia, the highest runoff difference (Q

_{v}) was nearly 45 mm at a maximum rainfall amount (P) of 580 mm. This indicates a significant overprediction of the runoff depth if the calibrated model is not used.

**Figure A1.**The runoff difference between the conventional SCS-CN rainfall runoff model and the calibrated model across different CN

_{0.2}values in Peninsular Malaysia during the 1970s. Note: 490 mm is the highest recorded rainfall amount in Peninsular Malaysia.

**Figure A2.**The runoff difference between the conventional SCS-CN rainfall runoff model (Equation (2)) and the calibrated model across different CN

_{0.2}values in East Malaysia during the 1990s. Note: 580 mm is the highest recorded rainfall amount in East Malaysia.

^{3}/1 km

^{2}in the watershed area in Malaysia. This highlights the crucial need to revise and calibrate the rainfall runoff model using the power regression model of I

_{a}= S

^{L}. As illustrated in Figure A1 and Figure A2, without proper model calibration, a volume difference of nearly 65,000 m

^{3}or 45,000 m

^{3}in runoff could be overestimated in both Peninsular Malaysia and East Malaysia. This may lead to potential opportunity loss for flood prevention planning based on an overprediction of the conventional SCS-CN rainfall runoff model (Equation (2)).

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**Figure 1.**The original SCS data points from NEH-4 [15].

**Figure 3.**The decadal runoff trend for the interdecadal runoff difference between 70PM and 80PM, 80PM and 90PM, and 70PM and 90PM. The yellow box highlights the 99% BCa confidence interval of CN

_{0.2}for the Peninsular Malaysia dataset, in the range of 76–80.

**Figure 4.**The decadal runoff trend for the interdecadal runoff difference between 85EM and 90EM, 90EM and 2KEM, and 85EM and 2KEM. The yellow box highlights the 99% BCa confidence interval of CN

_{0.2}for the East Malaysia dataset, in the range of 80–86.

**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 | S_{L} (mm) | I_{a}/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 |

**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 | S_{L} (mm) | I_{a}/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 |

Decadal Model | Correlation Equation | R^{2}_{adj} | p-Value |
---|---|---|---|

70PM | S_{0.2} = S_{0.168}^{0.851} | 0.987 | <0.001 |

80PM | S_{0.2} = S_{0.228}^{0.881} | 0.998 | <0.001 |

90PM | S_{0.2} = S_{0.232}^{0.889} | 0.998 | <0.001 |

Decadal Model | Correlation Equation | R^{2}_{adj} | p-Value |
---|---|---|---|

85EM | S_{0.2} = S_{0.332}^{0.891} | 0.997 | <0.001 |

90EM | S_{0.2} = S_{0.274}^{0.887} | 0.998 | <0.001 |

2KEM | S_{0.2} = S_{0.316}^{0.896} | 0.998 | <0.001 |

**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 CN_{0.2} | ||||

Optimum S (mm) | Lower | Upper | Optimum CN_{0.2} | 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 |

**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 CN_{0.2} (mm) | Maximum Runoff Depth Estimated with Upper CN_{0.2} 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 |

**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, Q _{v, 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% |

**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, Q_{v, 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% |

Study Site | Dataset | Best Correlation Model | R^{2}_{adj} |
---|---|---|---|

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 |

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## Share and Cite

**MDPI and ACS Style**

Khor, J.F.; Lim, S.; Ling, L.
Evaluating the Effect of Deforestation on Decadal Runoffs in Malaysia Using the Revised Curve Number Rainfall Runoff Approach. *Water* **2023**, *15*, 1392.
https://doi.org/10.3390/w15071392

**AMA Style**

Khor JF, Lim S, Ling L.
Evaluating the Effect of Deforestation on Decadal Runoffs in Malaysia Using the Revised Curve Number Rainfall Runoff Approach. *Water*. 2023; 15(7):1392.
https://doi.org/10.3390/w15071392

**Chicago/Turabian Style**

Khor, Jen Feng, Steven Lim, and Lloyd Ling.
2023. "Evaluating the Effect of Deforestation on Decadal Runoffs in Malaysia Using the Revised Curve Number Rainfall Runoff Approach" *Water* 15, no. 7: 1392.
https://doi.org/10.3390/w15071392