# Uncertainty in Rainfall Intensity Duration Frequency Curves of Peninsular Malaysia under Changing Climate Scenarios

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Study Area and Datasets

#### 2.1. Study Area

#### 2.2. Data and Sources

## 3. Methodology

#### 3.1. Procedure

- The GCM simulations for historical (1971–2010) and future (2006–2099) periods are interpolated to observed locations.
- MOS downscaling model is developed where quantile mapping (QM) is used to derive the bias correction factors by comparing GCM simulated rainfall with observed rainfall for the period (1971–2005).
- The bias correction factors derived from the historical period (1971–2005) are then applied on simulated GCM rainfall for different RCPs for the period 2006–2099.
- An artificial neural network (ANN) model is developed to disaggregate daily rainfall data to hourly rainfall data. The model is calibrated and validated with observe hourly rainfall data for the period 1971–2005.
- The ANN disaggregation model is used to generate hourly rainfall data from daily rainfall projected for the period 2006–2099.
- IDF curves are generated by fitting observed annual maximum of hourly rainfall data (1971–2005) with most suitable probability density function (PDF) and parameter estimation method.
- The disaggregated rainfall data are used to generate time series of annual maximum of hourly rainfall to develop IDF curves for climate change scenarios.
- The model correction factors (MCFs) are estimated for all the durations of rainfall by fitting the average of the ratios of the projected return periods to observed return periods in a polynomial equation.
- The MCFs are applied on the return periods of rainfall durations for future period to generate the IDF curves. The IDF curves are generated for all the 8 GCMs for both the RCP 4.5 and RCP 8.5, separately.
- Finally, the IDF curves are developed with uncertainty level, by estimating the 1st quartile, median and 3rd quartile of the return periods of different rainfall durations obtained from IDF curves generated for eight GCMs.

#### 3.2. Selection of Appropriate Probability Density Function and Paramter Estmation Method

#### 3.3. Rainfall Downscaling and Projections

- The GCM simulated rainfall is interpolated at each station using inverse an weighting distance method to generate GCM simulations at the observed location.
- The QM is used to compute the biases in GCMs by comparing 70% of the randomly-selected observed and GCM simulated daily rainfall for the period 1971–2005. The QM bias correction parameters are validated with the remaining 30% of observed and GCM simulated daily rainfall for the period 1971–2005.
- The derived QM parameters are used to correct the biases in the simulated daily rainfall of GCMs for both the RCP 4.5 and RCP 8.5 for the period 2006–2099.

^{2}), and Nash–Sutcliffe Coefficient of Efficiency (NSE),

_{sim,i}and x

_{obs,i}are the ith simulated and observed data, and n is the number of the observations.

#### 3.4. Disaggregation of Daily Rainfall and Generation of Projected IDF Curves

#### 3.5. Model Correction Factors

^{2}+ b x + c

_{1}, r

_{2}, r

_{3}, r

_{4}, r

_{5}, and r

_{6}respectively (see Table 6 in Section 4.5). The average of the ratios of all these six return periods (2, 5, 10, 25, 50 and 100 years) for 1 h duration rainfall will be, x

_{1}= (r

_{1}+ r

_{2}+ r

_{3}+ r

_{4}+ r

_{5}+ r

_{6})/6. In the same way, x

_{2}, x

_{3}, x

_{4}, x

_{5}, x

_{6}, and x

_{7}are computed for the durations 3, 6, 12, 24, 48, and 72 h respectively (see Table 6 (last line) and Table 7 in Section 4.5 the ratios for model BCC-CSM1.1). To calculate the MCFs (y

_{1}, y

_{2}, y

_{3}, y

_{4}, y

_{5}, y

_{6}, y

_{7}) for all these durations of rainfall projected by BCC.CSM1.1, the average of the ratios of the return periods obtained for all the durations are put into their polynomial equation (see Figure 8 and Equation (7) in Section 4.5). In this way MCFs are obtained separately for all durations (Table 9 in Section 4.5). Finally, the MCF developed for a GCM (BCC-CSM1.1) is multiplied with the observed (gauged) return periods (i.e., 2, 5, 10, 25, 50, and 100 years) for the same duration of rainfall. For example, the MCF of 1 h duration is multiplied with the observed 1 h duration rainfall for return periods, 2, 5, 10, 25, 50, and 100 years.

## 4. Results and Discussion

#### 4.1. Determination of Probability Density Function & Parameter Estimation Method

#### 4.2. The IDF Curves based on Historical Rainfall

#### 4.3. Climate Downscaling and Projections

^{2}, and NSE. The calibration and validation values of these indices for this station are presented in Table 5. It is found that all the GCMs performed well in term of all statistical indices used. The MAE values are in the range of 0.15–0.56 and the NRMSE value are in the range of 6.1–21.3. The PBIAS values are between 0.1 and 4.1. The values very near to zero indicate good performance of the models. The R

^{2}values are always found very near to 1, and NSE is above 0.9 in most of the cases. Similar types of results are also found in other stations for all models. The statistical indices values are very close to each other for different GCMs. Hence, it can be concluded that the QM-based MOS downscaling model has the capability of downscaling daily rainfall in the study area. The calibrated and validated MOS models are used for the projection of rainfall under RCP scenarios. Using the MOS downscaling model, rainfall is projected for the period of 2006–2099 for RCP 4.5 and RCP 8.5.

#### 4.4. Disaggregation of Rainfall

#### 4.5. Development of IDF Curves under Climate Change Scenarios

#### Model Correction Factor

^{2}+ 0.14 x + 1.47

#### 4.6. Development IDF Curves with Uncertainty

## 5. Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Location of the selected rain gauges on the map of peninsular Malaysia. The number in circle represents the station name and ID, as shown on the right side in figure.

**Figure 3.**Historical IDF curves developed using GEV-MLE for observed (gauged) rainfall data (1971–2005) at a station located in Kedah.

**Figure 5.**Comparison of observed hourly maximum rainfall and observed daily rainfall disaggregated to hourly maximum rainfall using ANN approach at station Kedah for (

**a**) BCC-CSM 1.1 for 1 h (

**b**) HadGEM2-ES for 3 h (

**c**) Nor-ESM-M for 12 h and (

**d**) CCSM4 for 72 h.

**Figure 6.**The IDF curves developed for station Kedah using GCMs simulated historical rainfall data (1971–2005).

**Figure 7.**The IDF curves developed for station Kedah using GCMs projected rainfall data (2006–2099).

**Figure 8.**Model Correction Factors (MCFs) for modelled rainfall intensities fitted into a polynomial equation for BCC-CSM1.1 for RCP 4.5 at Kedah.

**Figure 9.**Box plot showing the uncertainty in rainfall intensities for different rainfall durations and return periods (2, 5 and 10 years) at station Kedah under RCP 4.5 and RCP 8.5.

Centre(s) | Model | Resolution (Lat × Long) |
---|---|---|

Beijing Climate Center China | BCC-CSM1.1 | 2.8° × 2.8° |

Commonwealth Scientific and Industrial Research Organization/Queensland Climate Change Centre of Excellence Australia | CSIRO-Mk3.6.0 | 1.8° × 1.8° |

Institut Pierre Simon Laplace France | IPSL-CM5A-MR | 1.25° × 2.5° |

Atmosphere and Ocean Research Institute (The University of Tokyo), National Institute for Environmental Studies, and Japan Agency for Marine-Earth Science and Technology, Japan | MIROC-ESM | 2.8° × 2.8° |

Met Office Hadley Centre UK | HadGEM2-ES | 1.25° × 1.875° |

Meteorological Research Institute Japan | MRI-CGCM3 | 1.12° × 1.125° |

National Center for Atmospheric Research USA | CCSM4 | 0.94° ×1.25° |

Bjerknes Centre for Climate Research, Norwegian Meteorological Institute, Norway | NorESM1-M | 1.90° × 2.5° |

Functions | Equations | Parameters |
---|---|---|

GEV | $f\left(x\right)=\{\begin{array}{cc}\frac{1}{\sigma}exp(-{(1+kz)}^{-1/k}){(1+kz)}^{-1-1/k}& k\ne 0\\ \frac{1}{\sigma}\mathrm{exp}(-z-\mathrm{exp}(-z))& k=0\end{array}$ | where, $z=\frac{x-\mu}{\sigma}$ and k = shape parameter μ = location parameter σ = scale parameter |

Exponential | $f\left(x\right)=\{\begin{array}{cc}\lambda exp(-\lambda x)& x\ge 0\\ 0& x<0\end{array}$ | |

GP | $f\left(x\right)=\{\begin{array}{cc}\frac{1}{\sigma}{(1+kz)}^{-1-1/k}& k\ne 0\\ \frac{1}{\sigma}exp(-z)& k=0\end{array}$ | |

Gumbel | $f\left(x\right)=\frac{1}{\sigma}exp(-z-exp(-z))$ |

Estimators | Functions (PDFs) | Durations (Hour) | ||||||
---|---|---|---|---|---|---|---|---|

1 h | 3 h | 6 h | 12 h | 24 h | 48 h | 72 h | ||

MLE | GEV | 294.88 | 302.74 | 302.46 | 307.9 | 319.75 | 333.06 | 341.18 |

Gumbel | 295.05 | 302.81 | 302.77 | 308.17 | 319.79 | 333.12 | 341.2 | |

Exp | 331.19 | 348.82 | 352.79 | 355.99 | 362.27 | 372.3 | 379.05 | |

GP | 324.23 | 335.72 | 348.73 | 350.64 | 348.4 | 380.8 | 378.85 | |

GMLE | GEV | 296.32 | 303.97 | 302.84 | 308.29 | 320.88 | 335.53 | 342.74 |

Gumbel | 295.05 | 302.81 | 302.77 | 308.17 | 319.79 | 333.12 | 341.2 | |

Exp | 331.19 | 348.82 | 352.79 | 355.99 | 362.27 | 372.3 | 379.05 | |

GP | 445.27 | 493.66 | 505.88 | 504.24 | 498.67 | 504.61 | 504.26 | |

L-moments | GEV | 296.32 | 303.97 | 302.84 | 308.29 | 320.88 | 335.53 | 342.74 |

Gumbel | ∞ | ∞ | ∞ | ∞ | ∞ | ∞ | ∞ | |

Exp | ∞ | ∞ | ∞ | ∞ | ∞ | ∞ | ∞ | |

GP | 445.27 | 493.66 | 505.88 | 504.24 | 498.67 | 504.61 | 504.26 | |

Bayesian | GEV | 5395.3 | 6183.1 | 6027.8 | 6743.8 | 9059.1 | 12867 | 14697 |

Gumbel | ∞ | ∞ | ∞ | ∞ | ∞ | ∞ | ∞ | |

Exp | ∞ | ∞ | ∞ | ∞ | ∞ | ∞ | ∞ | |

GP | ∞ | ∞ | ∞ | ∞ | ∞ | ∞ | ∞ |

Station ID | State | 1 h | 3 h | 6 h | 12 h | 24 h | 72 h |
---|---|---|---|---|---|---|---|

1437116 | Johor Bahru | A | A | A | B | B | B |

5806066 | Kedah | A | A | A | A | A | A |

6103047 | Kedah | A | A | A | A | A | A |

2224038 | Melaka | A | A | A | A | B | B |

2725083 | Niger Sembilan | A | A | A | A | A | A |

3516022 | Selangor | A | A | A | A | A | A |

3411017 | Selangor | B | B | B | B | A | A |

3710006 | Selangor | A | A | A | A | A | A |

3519125 | Pahang | A | A | A | A | A | A |

3930012 | Pahang | A | A | A | A | A | A |

5302001 | Pinang | B | C | B | C | C | B |

4012143 | Perak | A | A | A | A | A | A |

4207048 | Perak | A | A | A | A | A | A |

5710061 | Perak | A | A | A | A | E | E |

4409091 | Perak | D | D | D | D | D | F |

6019004 | Kelantan | D | D | F | F | F | D |

4234109 | Terengganu | A | A | A | A | A | A |

5331048 | Terengganu | A | A | A | A | A | A |

3117070 | W. Persekutuan | A | A | D | D | D | A |

Station ID | Indices | Model | MAE | NRMSE % | PBIAS % | NSE | R^{2} |
---|---|---|---|---|---|---|---|

Kedah5806066 | Calibration | BCC-CSM1.1 | 0.31 | 12.1 | 1.1 | 0.95 | 0.91 |

CCSM4 | 0.27 | 12 | 0.6 | 0.97 | 0.93 | ||

CSIRO-Mk3.6.0 | 0.34 | 13.1 | 2.1 | 0.94 | 0.95 | ||

HadGEM2-ES | 0.36 | 14.6 | 0.3 | 0.94 | 0.93 | ||

IPSL-CM5A-MR | 0.33 | 12.1 | 3.1 | 0.92 | 0.92 | ||

MIROC-ESM | 0.21 | 8.8 | 0.2 | 0.91 | 0.96 | ||

MRI-CGCM3 | 0.34 | 12.9 | 1.3 | 0.94 | 0.95 | ||

NorESM1-M | 0.15 | 6.1 | 0.5 | 0.91 | 0.93 | ||

Validation | BCC-CSM1.1 | 0.45 | 20.6 | 2.1 | 0.93 | 0.92 | |

CCSM4 | 0.54 | 21.3 | 1.9 | 0.95 | 0.90 | ||

CSIRO-Mk3.6.0 | 0.56 | 21 | 0.1 | 0.96 | 0.91 | ||

HadGEM2-ES | 0.4 | 17.2 | 4.1 | 0.94 | 0.94 | ||

IPSL-CM5A-MR | 0.42 | 19 | 1.3 | 0.93 | 0.93 | ||

MIROC-ESM | 0.42 | 17.9 | 1.1 | 0.93 | 0.95 | ||

MRI-CGCM3 | 0.42 | 19.2 | 1 | 0.92 | 0.93 | ||

NorESM1-M | 0.45 | 17.8 | 1.9 | 0.94 | 0.93 |

Return Period (Years) | Duration (Hours) | ||||||
---|---|---|---|---|---|---|---|

1 h | 3 h | 6 h | 12 h | 24 h | 48 h | 72 h | |

2 | 0.91 | 0.90 | 1.09 | 1.48 | 1.61 | 1.63 | 1.55 |

5 | 1.01 | 1.05 | 1.29 | 1.62 | 1.65 | 1.56 | 1.46 |

10 | 1.19 | 1.45 | 1.48 | 1.70 | 1.68 | 1.55 | 1.42 |

25 | 1.62 | 1.59 | 1.78 | 1.78 | 1.72 | 1.54 | 1.39 |

50 | 2.15 | 1.97 | 2.07 | 1.83 | 1.75 | 1.55 | 1.37 |

100 | 2.95 | 2.56 | 2.41 | 1.88 | 1.78 | 1.56 | 1.37 |

Average of ratios of Return Period | 1.64 | 1.59 | 1.69 | 1.72 | 1.70 | 1.57 | 1.43 |

**Table 7.**Average of the ratios of modelled to observed rainfall intensities of return periods 2, 5, 10, 25, 50, and 100 years for various GCMs at Kedah for RCP 4.5.

Model | Duration (Hours) | ||||||
---|---|---|---|---|---|---|---|

1 h | 3 h | 6 h | 12 h | 24 h | 48 h | 72 h | |

BCC-CSM1.1 | 1.64 | 1.59 | 1.69 | 1.72 | 1.70 | 1.57 | 1.43 |

CCSM4 | 1.52 | 1.5 | 1.77 | 1.68 | 1.61 | 1.41 | 1.25 |

CSIRO-Mk3.6 | 2.17 | 1.98 | 2.09 | 1.96 | 1.85 | 1.61 | 1.44 |

HadGEM2-ES | 1.41 | 1.49 | 1.75 | 1.91 | 1.9 | 1.76 | 1.6 |

IPSL-CM5A-MR | 1.67 | 1.66 | 1.91 | 1.81 | 1.71 | 1.52 | 1.35 |

MIROC-ESM | 2.18 | 1.49 | 1.58 | 1.68 | 1.66 | 1.51 | 1.37 |

MRI-CGCM3 | 2.81 | 2.68 | 2.86 | 2.8 | 2.75 | 2.51 | 2.27 |

NorESM1-M | 1.92 | 1.7 | 2.13 | 2.24 | 2.17 | 1.93 | 1.73 |

Models | Polynomial Equations | |
---|---|---|

BCC-CSM1.1 | y = −0.02 x^{2} + 0.14 x + 1.47 | where, x is the average of the ratios of return periods and y is the Model correction factor (MCF) |

CCSM4 | y = −0.04 x^{2} + 0.25 x + 1.27 | |

CSIRO-Mk3.6 | y = −0.02 x^{2} + 0.04 x + 2.09 | |

HadGEM2-ES | y = −0.04 x^{2} + 0.38 x + 1.00 | |

IPSL-CM5A-MR | y = −0.04 x^{2} + 0.23 x + 1.44 | |

MIROC-ESM | y = 0.02 x^{2} − 0.21 x + 2.16 | |

MRI-CGCM3 | y = −0.03 x^{2} + 0.18 x + 2.59 | |

NorESM1-M | y = −0.04 x^{2} + 0.34 x + 1.47 |

Model | Duration (Hours) | ||||||
---|---|---|---|---|---|---|---|

1 h | 3 h | 6 h | 12 h | 24 h | 48 h | 72 h | |

BCC-CSM1.1 | 1.65 | 1.64 | 1.65 | 1.65 | 1.65 | 1.64 | 1.63 |

CCSM4 | 1.56 | 1.56 | 1.59 | 1.58 | 1.57 | 1.54 | 1.52 |

CSIRO-Mk3.6 | 2.08 | 2.09 | 2.09 | 2.09 | 2.10 | 2.10 | 2.11 |

HadGEM2-ES | 1.46 | 1.48 | 1.54 | 1.58 | 1.58 | 1.54 | 1.51 |

IPSL-CM5A-MR | 1.71 | 1.71 | 1.73 | 1.73 | 1.72 | 1.70 | 1.68 |

MIROC-ESM | 1.80 | 1.89 | 1.88 | 1.86 | 1.87 | 1.89 | 1.91 |

MRI-CGCM3 | 2.86 | 2.86 | 2.86 | 2.86 | 2.86 | 2.85 | 2.84 |

NorESM1-M | 1.98 | 1.93 | 2.01 | 2.03 | 2.02 | 1.98 | 1.94 |

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

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**MDPI and ACS Style**

Noor, M.; Ismail, T.; Chung, E.-S.; Shahid, S.; Sung, J.H.
Uncertainty in Rainfall Intensity Duration Frequency Curves of Peninsular Malaysia under Changing Climate Scenarios. *Water* **2018**, *10*, 1750.
https://doi.org/10.3390/w10121750

**AMA Style**

Noor M, Ismail T, Chung E-S, Shahid S, Sung JH.
Uncertainty in Rainfall Intensity Duration Frequency Curves of Peninsular Malaysia under Changing Climate Scenarios. *Water*. 2018; 10(12):1750.
https://doi.org/10.3390/w10121750

**Chicago/Turabian Style**

Noor, Muhammad, Tarmizi Ismail, Eun-Sung Chung, Shamsuddin Shahid, and Jang Hyun Sung.
2018. "Uncertainty in Rainfall Intensity Duration Frequency Curves of Peninsular Malaysia under Changing Climate Scenarios" *Water* 10, no. 12: 1750.
https://doi.org/10.3390/w10121750