# Evaluation of Long-Term Trends of Rainfall in Perak, Malaysia

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

^{2}exposed to flooding, which consequently affects approximately 4.82 million people with an estimated economic loss of USD 299 million [13,14]. Flooding in Malaysia is primarily caused by intense and frequent monsoons and convective rains [15]. Flooding in Pahang, Perak, and Kelantan between 20 December 2014, and 1 January 2015, has raised many uncertainties regarding future flooding risk. The predominant cause of this calamity, according to the Dartmouth Flood Observatory, was monsoon rainfall, which affected more than 215,000 people [16]. Therefore, owing to the stochastic and uncertain nature of rainfall, information about its spatial and temporal variability is essential for early flood warning and future planning.

^{2}and a population of 2.46 million. The past few decades have seen an increasing trend of flooding in the state [15]. Despite huge investments in flood management, the recurring nature of floods poses a serious threat to the state’s economy and the lives of its citizens. Some studies have concluded that increased rainfall trends on a spatiotemporal basis may contribute to frequent flooding [26].

## 2. Study Area and Data Source

#### 2.1. Description of the Study Area

^{2}, which makes it the second-largest state in Peninsular Malaysia. Geographically, it is situated between the 100°0′ E to 102°0′ E latitude and 3°30′ N to 6°0′ N longitude (Figure 1). Agriculture is the major land use of the state that covers 41% area of the state followed by forest (28%), and urban lands encompass 22% area, respectively [27].

#### 2.2. Data Acquisition and Preliminary Analysis

## 3. Methodology

#### 3.1. Rainfall Indices

#### 3.2. Precipitation Concentration Index (PCI)

_{i}represents the monthly rainfall for the ith month, the minimum theoretical value of PCI is 8.3, demonstrating the uniform distribution of rainfall among all months [31]. However, the values of PCI larger than 16.7 indicate the irregular precipitation distribution and the values greater than 20 represent the strong irregular precipitation distribution.

#### 3.3. Autocorrelation Analysis

_{i}is the ith observation, $\stackrel{\_}{X}$ is the mean and n is the sample size. After testing the presence of${r}_{1}$, the null hypothesis was tested on 0.05 significance using a two-tailed test by Equation (3).

#### 3.4. Trend Free Pre-Whitening Analysis

- (1)
- Estimation of the Theil–Sen slope (TSS) of the time series.
- (2)
- De-trend the time series by implementing Equation (4):$${X}_{t}^{\u2019}={X}_{t}-TSS\left(t\right)$$
_{t}is the values of the time series at time t, and TSS(t) is the Theil–Sen slope. - (3)
- Test the ${r}_{1}$ again for the detrended time series; if the value of the ${r}_{1}$ does not reflect a serial correlation, then the MK test can be applied to the original time series data set. Contrary to this, if the ${r}_{1}$ shows the correlation, pre-whiten the de-trended series using Equation (5):$${Y}_{t}^{\u2019}={X}_{t}^{\u2019}-\left({r}_{1}{X}_{t-1}\right)$$
- (4)
- The monotonic trend is then added back to the pre-whitened time series as mentioned in Equation (6):$${Y}_{t}^{\u201d}={Y}_{t}^{\u2019}+TSS\left(t\right)$$

#### 3.5. Trend Analysis

_{o}) and alternative hypotheses (H

_{1}). H

_{o}describes the no trend in time series, whereas the H

_{1}depicts the monotonic trend in the data. The test statistics S of MK can be calculated as described by Equation 7 [37,38]:

_{j}and x

_{k}are the consecutive data values, and sgn(θ) is the sign function which can be calculated as:

#### 3.6. Abrupt Change Analysis

_{k}for a time series x

_{i}where (1 ≤ i ≤ n), using Equation (11):

_{k}represents the rank series; x

_{i}, x

_{j}are the data values at the time i and j, respectively; r

_{i}, on the other hand, is the rank statistics for data pairs (x

_{i}, x

_{j}) and n shows the length of the data series.

_{k}is distributed as a normal distribution. Therefore, the expected value of rank statistics and variance can be calculated as:

_{k}represents a progressive or standardized variable that has zero mean value with unit standard deviation. Therefore, its value varies around zero and the values above zero indicate positive trends in the dataset and vice versa.

_{k}values can be estimated in a backward manner with the time series starting from the end of the series. Once the progressive and retrograde series have been computed, the plot of UF

_{k}and UB

_{k}can provide the abrupt change in the time series. Abrupt changes can be defined as the change in the climatic data other than the normal variations. If the trends are significant, the abrupt change can be attributed to the graphical representation when both curves intersect each other. Furthermore, it can also provide the location of the year when the trend started. However, if the trends are not statistically significant, the curves will intersect each other up to the end of the time series [39].

#### 3.7. Spatial Analysis

_{j}and x

_{k}represent the data values at time j and k and (j > k). The median of the N pairs of Q

_{i}is the Sen’s estimator and can be determined by Equation (17):

## 4. Results

#### 4.1. Temporal Trends in Rainfall Series

#### 4.2. Sudden Changes in Rainfall Series

_{k}curve of the RX1Day indicated a relatively constant trend from 1980 to 1999 when it crossed the retrograded or UB

_{k}curve indicating the trend. While a steadily decreasing trend was observed after 1999 up to 2007 when it crossed the critical limit indicating the significant decreasing trend. The UF

_{k}curve of RX5Day initially portrayed the increasing trend while intersecting the UB

_{k}curve in 1984, representing the start of a trend with some fluctuations up to 2001. It then started to decrease from 2001 and crossed the critical line, which confirmed the decreasing trends in the RX5Day index after 2006. For R95p, the UF

_{k}showed the increasing trend from 1985 to 1990 but started to decrease gradually after 1990. It intersected the critical value in 1995 the decreasing trends were more obvious in the year of 2008. The extreme indices of R99p and PRCPTOT illustrated somewhat the same trend during the period of 35 years with decreasing trend at the start of the 21st century and became significant in 2007.

_{k}curves showed the increasing trends for the late 80′s but then started to decrease after 1994–2014. The R10mm did not portray any significant trend as the progressive and retrograded curves cross each other inside the upper and lower limit. It has been mentioned by [43] that if both curves cross each other inside the critical limit, then there is no significant change in the time series. The R20mm also depicted the same trends as R99p, i.e., increasing in the late 1980s and then decreasing trend up to 2014. The results of SMK for CDD, as shown in Figure 3a, indicate the increasing trends of dry spells during the study period with a start from 1989, and the change was significant in 2006. In contrast, the analysis of wet spells has shown declining trends over the state.

_{k}curve of SWM showed the increasing trends from 1980 to 1989, but then it started to decline. The curve crossed the critical value in 2006 and then decreased significantly. For monthly time series, it is evident that a significant increasing trend occurred during the 80s; however, at the end of the twentieth century, the trends started to decrease since 2005. The same phenomenon was observed for annual rainfall as well, which showed the increasing trend in 1986 and then followed the constant pattern. Later, it depicted the decreasing trend in 2007–2008. As for the analysis of all these indices, the abrupt change point was detected at the intersection of UF

_{k}and UB

_{k}curves. It can be observed that almost all the change points have a similar starting time. The change was started in the late 90s over the Perak, and then it started to decrease. With the start of the twenty-first century, the decrease was more obvious in all rainfall indices.

#### 4.3. Variations in the Concentration of Annual Rainfall

#### 4.4. Spatial Distribution of Annual Rainfall

## 5. Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Characteristics of study area and distribution of mean annual rainfall over Perak, Malaysia.

**Figure 2.**(

**a**) Autocorrelation Function (ACF) analysis of rainfall indices. The red-dotted lines depict the 0.05 significance level and the x-axis shows the lag in the time series. (

**b**) Autocorrelation Function (ACF) analysis of rainfall. The red dotted lines depict the 0.05 significance level, and the x-axis shows the lag in the time series.

**Figure 3.**(

**a**) Results of sequential Mann–Kendall test on rainfall indices. (

**b**) Results of sequential Mann–Kendall test on rainfall indices.

**Figure 5.**Spatial distribution of long-term (1980–2014) seasonal, monthly, and annual rainfall rates over Perak, Malaysia. The sub-figures (

**a**–

**d**) represents the NEM, IM 1, SWM, and IM2 respectively. The rate of change in seasonal rainfalls are as per the definition given in Table 3, while the sub-figures (

**e**,

**f**) have the units in mm/month and mm/year, respectively.

**Table 1.**Description of automatic rainfall stations with geographic coordinates in Perak, Malaysia (1980–2014).

Station ID | Location | Longitude | Latitude | Avg. Annual Rainfall |
---|---|---|---|---|

(mm) | ||||

5710061 | Dispensari Keroh | 101.00 | 5.71 | 1881 |

5411066 | Kuala Kenderong | 101.15 | 5.42 | 1961 |

5210069 | Stesen Pem. Hutan Lawin | 101.06 | 5.30 | 1606 |

5207001 | Kolam Air JKR Selama | 100.70 | 5.22 | 2632 |

5005003 | Jln. Mtg. Buloh Bgn Serai | 100.55 | 5.01 | 1682 |

4811075 | Rancangan Belia Perlop | 101.18 | 4.89 | 1728 |

4807016 | Bukit Larut Taiping | 100.79 | 4.86 | 3566 |

4511111 | Politeknik Ungku Umar | 101.13 | 4.59 | 2178 |

4409091 | Rumah Pam Kubang Haji | 100.90 | 4.46 | 1730 |

4311001 | Pejabat Daerah Kampar | 101.16 | 4.31 | 3131 |

4207048 | JPS Setiawan | 100.70 | 4.22 | 1501 |

4010001 | JPS Teluk Intan | 101.04 | 4.02 | 2133 |

**Table 2.**Preliminary analysis of monthly, seasonal, and annual rainfall over Perak, Malaysia (1980–2014).

Months | Min. | Max. | SD. | Avg. | Coeff. of Var. | Share |
---|---|---|---|---|---|---|

(mm) | (mm) | (mm) | (mm) | (%) | (%) | |

Jan | 38.10 | 204.43 | 42.30 | 115.94 | 36 | 5.38 |

Feb | 23.41 | 242.36 | 56.40 | 125.04 | 45 | 5.80 |

Mar | 21.89 | 353.50 | 69.54 | 180.24 | 39 | 8.36 |

Apr | 71.66 | 355.62 | 67.82 | 217.45 | 31 | 10.08 |

May | 52.69 | 302.74 | 59.74 | 189.40 | 32 | 8.78 |

Jun | 50.50 | 191.32 | 39.05 | 124.92 | 31 | 5.79 |

Jul | 60.63 | 256.34 | 56.04 | 142.51 | 39 | 6.61 |

Aug | 6.48 | 265.75 | 64.32 | 161.35 | 40 | 7.48 |

Sep | 77.66 | 363.70 | 66.48 | 207.09 | 32 | 9.60 |

Oct | 126.92 | 426.38 | 75.87 | 248.96 | 30 | 11.55 |

Nov | 111.53 | 469.57 | 66.74 | 262.38 | 25 | 12.17 |

Dec | 56.26 | 354.67 | 63.04 | 181.13 | 35 | 8.40 |

Annual | 1352.93 | 2735.49 | 337.05 | 2156.41 | 16 | 100.00 |

NEM | 23.41 | 469.57 | 81.86 | 171.12 | 48 | 22.74 |

IM 1 | 21.89 | 355.62 | 70.72 | 198.84 | 36 | 26.42 |

SWM | 6.48 | 302.74 | 60.01 | 154.55 | 39 | 20.54 |

IM 2 | 77.66 | 426.38 | 73.88 | 228.03 | 32 | 30.30 |

Indices | Description | Units |
---|---|---|

RX1Day | Monthly maximum 1-day rainfall | mm |

RX5Day | Monthly maximum consecutive 5-day rainfall | mm |

R95p | Annual total rainfall when RR > 95p | mm |

R99p | Annual total rainfall when RR > 99p | mm |

PRCPTOT | Annual total rainfall in wet days | mm |

R10mm | Annual count of days when Rainfall ≥ 10 mm | days |

R20mm | Annual count of days when Rainfall ≥ 20 mm | days |

CDD | Maximum length of dry spell, maximum number of consecutive days with RR < 1 mm | days |

CWD | Maximum length of wet spell, maximum number of consecutive days with RR ≥ 1 mm | days |

SDII | Simple precipitation intensity index | mm/day |

NEM | Northeast Monsoon occurs from November to February | mm |

IM 1 | Inter-monsoon 1 occurs from March to April | mm |

SWM | Southwest Monsoon occurs from May to August | mm |

IM 2 | Inter-monsoon 2 occurs from September to October | mm |

Monthly | Monthly Rainfall | mm |

Annual | Annual Rainfall | mm |

Indices | SW Test | p-Value |
---|---|---|

RX1Day | 0.99 | 0.90 |

RX5Day | 0.97 | 0.54 |

R95p | 0.97 | 0.45 |

R99p | 0.95 | 0.16 |

PRCPTOT | 0.94 | 0.07 |

R10mm | 0.93 | 0.03 |

R20mm | 0.96 | 0.17 |

CDD | 0.92 | 0.07 |

CWD | 0.87 | 0.06 |

SDII | 0.97 | 0.51 |

NEM | 0.96 | 0.57 |

IM 1 | 0.99 | 0.63 |

SWM | 0.99 | 0.31 |

IM 2 | 0.98 | 0.39 |

Monthly | 0.98 | 0.10 |

Annual | 0.94 | 0.07 |

Indices | Z | p-Value | Sen’s Slope (mm) |
---|---|---|---|

RX1Day | −1.80 | 0.0713 | −0.3067 |

RX5Day | 0.00 | 0.9773 | 0.0172 |

R95p | −0.70 | 0.4955 | −2.3000 |

R99p | −0.60 | 0.5403 | −0.6947 |

PRCPTOT | −0.40 | 0.6701 | −1.9933 |

R10mm | 0.10 | 0.8982 | 0.0312 |

R20mm | −0.20 | 0.8754 | 0.0000 |

CDD | 1.80 | 0.0759 | 0.1000 |

CWD | −0.60 | 0.5218 | −0.0909 |

SDII | −0.40 | 0.6902 | −0.0071 |

NEM | 1.10 | 0.2695 | 0.2038 |

IM 1 | 0.10 | 0.9515 | 0.0246 |

SWM | −2.20 | 0.0299 | −0.2942 |

IM 2 | −0.80 | 0.4410 | −0.3196 |

Monthly | −0.70 | 0.4661 | −0.0235 |

Annual | −0.40 | 0.6701 | −1.8293 |

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**MDPI and ACS Style**

Hanif, M.F.; Mustafa, M.R.U.; Liaqat, M.U.; Hashim, A.M.; Yusof, K.W.
Evaluation of Long-Term Trends of Rainfall in Perak, Malaysia. *Climate* **2022**, *10*, 44.
https://doi.org/10.3390/cli10030044

**AMA Style**

Hanif MF, Mustafa MRU, Liaqat MU, Hashim AM, Yusof KW.
Evaluation of Long-Term Trends of Rainfall in Perak, Malaysia. *Climate*. 2022; 10(3):44.
https://doi.org/10.3390/cli10030044

**Chicago/Turabian Style**

Hanif, Muhammad Faisal, Muhammad Raza Ul Mustafa, Muhammad Usman Liaqat, Ahmad Mustafa Hashim, and Khamaruzaman Wan Yusof.
2022. "Evaluation of Long-Term Trends of Rainfall in Perak, Malaysia" *Climate* 10, no. 3: 44.
https://doi.org/10.3390/cli10030044