# Development of a Temperature-Based Model Using Machine Learning Algorithms for the Projection of Evapotranspiration of Peninsular Malaysia

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## Abstract

**:**

## 1. Introduction

## 2. Study Area

^{2}(50,424 square mile). The area’s topography comprises undulating lands with high mountains in the central region. Forests cover a major part of the peninsula, particularly the central region. The Melaka straits bind the peninsula in the West and the South China sea in the east. Peninsular Malaysia consists of several islands with varying areas. The Penang and Langkawi islands in the northwest are the most notable among the islands. The position of peninsular Malaysia in Southeast Asia and its topography are presented in Figure 1.

## 3. Data

## 4. Methodology

- Gene expression programming (GEP) was used to generate a temperature-based empirical equation for the estimation of ET for peninsular Malaysia
- The accuracy of the newly developed empirical model was assessed by comparing its performance with the existing temperature-based empirical methods
- GCMs were used to downscale and project temperatures at the study locations.
- The newly developed GEP ET model was used to project the ET of Peninsular Malaysia from the GCM projected temperature

#### 4.1. Gene Expression Programming (GEP)

- Selection of fitness function or a set of fitness functions. The Nash–Sutcliff Efficiency (NSE) was considered for the fitness function.
- Selection of a set of terminals and a set of functions. The inputs were selected according to their influence on ET.
- Creation of chromosomes from the selected terminals and functions.
- Setting the chromosomal architecture.
- Selection of the linking function.
- Selection of genetic operators.

#### 4.2. Temperature-Based ET Methods

#### 4.3. Temperature Downscaling and Projections

## 5. Results & Discussion

#### 5.1. Development of Temperature-Based ET Equations Using GEP

#### 5.2. Performance Evaluation of GEP ET Equations

#### 5.3. Projection of ET

_{min}and T

_{max}at the Alor Setar station are given in Figure 6 as an example.

## 6. Discussion

## 7. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**(

**a**) Location of peninsular Malaysia on the map of Southeast Asia; (

**b**) Geographical position of peninsular Malaysia. The topography and location of the meteorological stations are also provided.

**Figure 2.**Variability in monthly average (

**a**) daily maximum, mean, and minimum temperatures; (

**b**) evapotranspiration in the study area from 1975 to 2014.

**Figure 3.**The procedure used to generate ET empirical equations using gene expression programming (GEP).

**Figure 4.**Density scatter plots showing the relative performance of the GEP (

**a**) ET model compared to (

**b**) FAO Blaney-Criddle, (

**c**) Linacre, (

**d**) Kharrufa, (

**e**) Hargreaves and Samani, (

**f**) Trajkovic, and (

**g**) Ravazzani ET models.

**Figure 5.**Box plot of (

**a**) normalized root mean square error (%), (

**b**) percentage bias, (

**c**) modified index of agreement, and (

**d**) Kling-Gupta efficiency in estimating ET by different empirical models. The vertical red line in the plot indicates the ideal line.

**Figure 6.**Projection of annual daily average of (

**A**) minimum and (

**B**) maximum temperature in Alor Setar stations for RCP2.6, RCP4.5, RCP6.0 and RCP8.5.

**Figure 7.**Projected changes (%) in the annual average of daily ET for three future periods: (

**a**) 2010–2039; (

**b**) 2040–2069; and (

**c**) 2070–2099 compared to the historical period (1975–2005) for four RCPs at different locations of peninsular Malaysia.

**Figure 8.**Projections of the annual average of daily ET at Alor Setar station for (

**a**) RCP2.6; (

**b**) RCP4.5; (

**c**) RCP6.0; and (

**d**) RCP8.5 for the period 2010–2099.

Model Developing Institute | Model Name | Resolution (Lon × Lat) |
---|---|---|

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

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

Met Office Hadley Centre, UK | HadGEM2-ES | 1.87° × 1.25° |

Atmosphere and Ocean Research Institute, The University of Tokyo, Japan | MIROC-ESM | 2.8° × 2.8° |

Bjerknes Centre for Climate Research, Norwegian Meteorological Institute, Norway | NorESM1-M | 2.5° × 1.9° |

Geophysical Fluid Dynamics Laboratory, USA | GFDL-CM3 | 2.5° × 2.0° |

Commonwealth Scientific and Industrial Research Organization, Australia | CSIRO-Mk3.6.0 | 1.86° × 1.87° |

Institut Pierre Simon Laplace, France | IPSL-CM5A-MR | 1.26° × 2.5° |

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

No | Model | Input Parameter | Equation |
---|---|---|---|

1 | FAO Blaney-Criddle [53] | T_{mean} | $\mathrm{p}\left(0.46{\mathrm{T}}_{\mathrm{mean}}+8.13\right)$ |

2 | Linacre [54] | T_{mean} | $\frac{\frac{700\left({\mathrm{T}}_{\mathrm{mean}}\pm 0.006\mathrm{z}\right)}{100-\mathrm{L}}+15\left({\mathrm{T}}_{\mathrm{mean}}-{\mathrm{T}}_{\mathrm{d}}\right)}{80-{\mathrm{T}}_{\mathrm{mean}}}$ |

3 | Kharrufa [55] | T_{mean} | $0.34{\mathrm{pT}}_{\mathrm{mean}}{}^{1.30}$ |

4 | Hargreaves and Samani [56] | T_{mean}, T_{min}, T_{max}, R_{a} | $\left(0.0023\frac{{\mathrm{R}}_{\mathrm{a}}}{2.45}\right){\mathrm{TD}}^{0.5}\left({\mathrm{T}}_{\mathrm{mean}}+17.8\right)$ |

5 | Trajkovic [57] | T_{mean}, T_{min}, T_{max}, R_{a} | $\left(0.0023{\mathrm{R}}_{\mathrm{a}}\right){\mathrm{TD}}^{0.424}\left({\mathrm{T}}_{\mathrm{mean}}+17.8\right)$ |

6 | Ravazzani [58] | T_{mean}, T_{min}, T_{max}, R_{a} | $\left(0.817+0.00022\mathrm{z}\right)\left(0.0023{\mathrm{R}}_{\mathrm{a}}\right)\left({\mathrm{TD}}^{0.5}\right)\left({\mathrm{T}}_{\mathrm{mean}}+17.8\right)$ |

_{mean}is the average temperature (°C); R

_{a}is the extraterrestrial radiation (MJ/m

^{2}/day).

Station Name | Model |
---|---|

Alor Setar | [(0.708527 + T_{max} + (T_{max}/−0.570404)) × ((T_{max} + T_{min}) × (0.708527/T_{max}))] + [0.271 × T_{min}−4.310577] + [T_{max}−((39.983448 + T_{min})/(6.337066 + T_{min}))] |

Bayan Lepas | [−2.659455/(T_{min} + ((T_{min} + T_{max}) × (−2.659455/T_{max})))] − [9.144561] + [((T_{max} + 2.659455) × T_{max})/(T_{min} + 1.002563 + 2 × T_{max})] |

Ipoh | [−9.89798−T_{min}] + [(2 × T_{max}−T_{min} + 2.245544)/8.36405] + [T_{min} + 7.706391] |

Kota Bharu | ((T_{max}/4.688568) − (4.688568/T_{min}) − 4.688568) + (−1.946625/((T_{min}×−1.946625) + T _{max} + 5.589417)) + (T_{max}/(T_{min} − ((T_{min} + T_{max})/(T_{min}^2)))) |

Kuala Terenggannu | (T_{max}/5.405304) + ((2 × T_{max} + 2 × T_{min})/((T_{max}^0.13211) + (T_{max} × 5.950409)))+((T _{min} + T_{max})/(12.843872 − T_{max})) |

Kuantan | (((T_{min} × −1.63205) + (T_{min}/−1.63205))/((T_{min} × T_{max})/(T_{min} − 1.63205))) +(((−4.044677/(T _{min}/T_{max})) + 1.682221 − T_{max})/−4.044677) − 4.384247 |

Melaka | ((−8.459076 + T_{max})/T_{max}) + ((T_{max} − T_{min})/((2 × T_{max})/(0.269501 + T_{max}))) +(−8.391388/(T _{min} − 18.419738)) |

Muadzam Shah | [((T_{min} − T_{max})/(7.168945 − T_{max}))/((7.168945/T_{max}) − 7.411835)] + [((−6.097015/T_{min}) − (4.724793 + T_{min}))/((T_{max} × 4.724793) + (−6.097015/T_{max}))] + [((T_{min} − T_{max})/(−9.070129 − T_{max}))/(1.893555/T_{min})] |

Senai | [(−5.88443 − T_{min} + T_{max})/(−3.50461 + 2T_{min})] + [−10.39233/(T_{min} − 14.90024)] + [2T_{max}^{2}/T_{min}^{2}] |

Subang | [−4.079162/T_{min}] + [(6.476776 − T_{min})/(T_{max}/(T_{min} − T_{max}))] +[−14.214936/(−12.751648 + T _{min})] |

Station Name | NSE | MAE | RMSE | md |
---|---|---|---|---|

Alor Setar | 0.98 | 4.7 | 7.9 | 1.0 |

Senai | 0.94 | 5.4 | 7.6 | 0.9 |

Bayan Lepas | 0.92 | 6.6 | 8.9 | 0.9 |

Ipoh | 0.81 | 7.3 | 9.3 | 0.7 |

Muadzam Shah | 0.79 | 6.9 | 8.9 | 0.8 |

Subang | 0.76 | 6.1 | 7.6 | 0.7 |

Kuantan | 0.99 | 3.3 | 4.8 | 1.0 |

Melaka | 0.94 | 6.1 | 9.3 | 0.9 |

Kota Bharu | 0.87 | 10.1 | 12.1 | 0.8 |

Kuala Terenggannu | 0.95 | 5.8 | 10.3 | 0.9 |

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**MDPI and ACS Style**

Muhammad, M.K.I.; Shahid, S.; Hamed, M.M.; Harun, S.; Ismail, T.; Wang, X.
Development of a Temperature-Based Model Using Machine Learning Algorithms for the Projection of Evapotranspiration of Peninsular Malaysia. *Water* **2022**, *14*, 2858.
https://doi.org/10.3390/w14182858

**AMA Style**

Muhammad MKI, Shahid S, Hamed MM, Harun S, Ismail T, Wang X.
Development of a Temperature-Based Model Using Machine Learning Algorithms for the Projection of Evapotranspiration of Peninsular Malaysia. *Water*. 2022; 14(18):2858.
https://doi.org/10.3390/w14182858

**Chicago/Turabian Style**

Muhammad, Mohd Khairul Idlan, Shamsuddin Shahid, Mohammed Magdy Hamed, Sobri Harun, Tarmizi Ismail, and Xiaojun Wang.
2022. "Development of a Temperature-Based Model Using Machine Learning Algorithms for the Projection of Evapotranspiration of Peninsular Malaysia" *Water* 14, no. 18: 2858.
https://doi.org/10.3390/w14182858