# A Proposal to Evaluate Drought Characteristics Using Multiple Climate Models for Multiple Timescales

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methodology

#### 2.1. Description of the Case Study Area: Vu Gia-Thu Bon Basin

^{2}. The VG-TB basin is surrounded by two main provincial administrative territories Quang Nam and Da Nang. The basin is characterized by a steep topography and the altitude ranging from 0 m at the coast to 2567 m in elevation above sea level (m.a.s.l) in the west (Figure 1).

#### 2.2. Data

#### 2.2.1. Observational Data

#### 2.2.2. Gridded Data

#### 2.3. Methods

#### 2.3.1. Delta Change Factor

#### 2.3.2. Unequal Weights

_{i}and O

_{i}represent simulated and observed monthly data, respectively. The method of unequal weights is briefly expressed with the following steps with an assumption of N climate simulations:

- (1)
- Calculation of the statistical indices on the basic of the historical observations and climate simulations from regional climate models forced by the reanalysis data of the European Centre for Medium-Range Weather Forecasts during 1989–2008. Each climate simulation receives a rank from 1 to N depending on the levels of perfect score for each statistical index, starting with the best as 1 and the worst is N. As an example, if the RMSE index of the ith climate model has the best score (the perfect score of RMSE is zero), the received rank is 1. Then, an ensemble rank order (r) as an integer number is calculated from the average of the ranks they span for each climate simulation.
- (2)
- Calculation of rank sum for each climate simulation by N-r + 1 with N is the number of climate simulations.
- (3)
- Establishing a reciprocal matrix between sets of models a
_{ij}= 1/a_{ji}with i,j ranging from 1 corresponding to the best climate simulation which has the largest rank sum to N and a_{ij}= 1 as i = j. a_{ij}is determined by the difference of rank sum between sets of models plus 1. - (4)
- Estimation of weights matrix w
_{ij}= a_{ij}/${\sum}_{1}^{\mathrm{N}}{\mathrm{a}}_{\mathrm{ij}}$ (i,j = 1, N) - (5)
- Estimation of each weight for each climate simulation w
_{i}= ${\sum}_{\mathrm{j}=1}^{\mathrm{N}}{\mathrm{w}}_{\mathrm{ji}}$ (i = 1, N) with ${\sum}_{\mathrm{i}=1}^{\mathrm{N}}{\mathrm{w}}_{\mathrm{i}}=1$.

#### 2.3.3. Standardized Precipitation Index (SPI)

#### 2.3.4. Non-Parametric Mann–Kendall Test

_{j}and x

_{k}are the data values in time series j and k respectively, and

_{o}) assumes that there is no trend in meteorological droughts over time; the alternative hypothesis (H

_{1}) assumes that there is an upward or downward trend over time. The mathematical equations for calculating Var(S) and standardized test statistics Z are presented in previous studies [25,26,47,51,52]. An upward, downward, or no trend will be assessed at α significance level of 0.05. The computed probability is greater than the specific significance level α (H

_{o}is rejected); the increasing trend responds to a positive value of Z and a negative value of Z indicates a decreasing trend. There is no trend if the computed probability is less than the level of significance (H

_{o}is accepted). At the α significance level of 0.05, the null hypothesis of no trend is rejected if |Z

_{MK}| > 1.96.

#### 2.3.5. The Sen’s Slope Estimator

_{j}and x

_{k}, x

_{j}and x

_{k}are the data values at time j and k (j > k) respectively, j is time after time k. The Sen’s is computed by the median slope as:

## 3. Results and Discussions

#### 3.1. Calculation of Weights for Each Climate Model

#### 3.2. Calculation of SPI

#### 3.3. Projection Trends in SPI

## 4. Conclusions

## Supplementary Materials

## Funding

## Conflicts of Interest

## References

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**Figure 2.**The probability transformation from fitted gamma distribution to the standard normal distribution.

**Figure 3.**Scatter plot ofthe precipitation simulations with equal and unequal weights minus observations over the whole VG-TB during 1989–2008 (mm/month).

**Figure 4.**Standardized precipitation index (SPI)for multiple timescales under RCP4.5 scenario (2021–2050) for Danang station.

Historical (1986–2005) | RCP4.5 (2021–2050) | RCP8.5 (2021–2050) | Spatial Resolution | Temporal Resolution | |
---|---|---|---|---|---|

RegCM4 forced by MPI-ESM-MR (REG/MPI) | 1 | 1 | 1 | 20 km | Monthly |

RegCM4 forced by IPSL-CM5A-LR (REG /IPSL) | 1 | 1 | 1 | 20 km | Monthly |

RegCM4 forced by ICHEC-EC-EARTH (REG/ICHEC) | 1 | 1 | 1 | 20 km | Monthly |

RegCM4 forced by HadGEM2-AO (REG/HadGEM) | 1 | 1 | 1 | 20 km | Monthly |

SNU-MM5 forced by HadGEM2-AO (SNU/HadGEM) | 1 | 1 | 1 | 20 km | Monthly |

RSM forced by HadGEM2-AO (RSM/HadGEM) | 1 | 1 | 1 | 20 km | Monthly |

ln(Nash) | RMSE | Nash | |
---|---|---|---|

REG/ICHEC | 0.935 | 170.67 | 0.523 |

REG/IPSL | 0.941 | 157.44 | 0.594 |

REG/MPI | 0.937 | 171.90 | 0.516 |

REG/HadGEM | 0.891 | 256.72 | −0.079 |

SNU/HadGEM | 0.913 | 252.75 | −0.046 |

RSM/HadGEM | 0.880 | 278.93 | −0.274 |

ln(Nash) | RMSE | Nash | Average | Ensemble Rank | Rank Sum | |
---|---|---|---|---|---|---|

REG/ICHEC | 3 | 2 | 2 | 2.3 | 2 | 5 |

REG/IPSL | 1 | 1 | 1 | 1.0 | 1 | 6 |

REG/MPI | 2 | 3 | 3 | 2.7 | 3 | 4 |

REG/HadGEM | 5 | 5 | 4 | 4.7 | 5 | 2 |

SNU/HadGEM | 4 | 4 | 5 | 4.3 | 4 | 3 |

RSM/HadGEM | 6 | 6 | 6 | 6.0 | 6 | 1 |

REG/IPSL | REG/ICHEC | REG/MPI | SNU/HadGEM | REG/HadGEM | RSM/HadGEM | Total | |
---|---|---|---|---|---|---|---|

REG/IPSL | 1 | 2 | 3 | 4 | 5 | 6 | 21 |

REG/ICHEC | 1/2 | 1 | 2 | 3 | 4 | 5 | 15.5 |

REG/MPI | 1/3 | 1/2 | 1 | 2 | 3 | 4 | 10.83 |

SNU/HadGEM | 1/4 | 1/3 | 1/2 | 1 | 2 | 3 | 7.08 |

REG/HadGEM | 1/5 | 1/4 | 1/3 | 1/2 | 1 | 2 | 4.28 |

RSM/HadGEM | 1/6 | 1/5 | 1/4 | 1/3 | 1/2 | 1 | 2.45 |

Total | 61.15 |

**Table 5.**Percentages of drought and wet events under considered multiple timescales under RCP4.5 scenario over basin during 2021–2050 (%).

Classification | Min | 25% | Median | 75% | Max | |
---|---|---|---|---|---|---|

SPI-1 | Moderatelywet | 1.4 | 1.5 | 2.1 | 2.2 | 2.8 |

Moderately dry | 1.4 | 1.7 | 2.1 | 2.2 | 3.1 | |

SPI-3 | Moderatelywet | 0.8 | 1.2 | 1.4 | 1.9 | 2.2 |

Moderately dry | 1.1 | 2.6 | 3.1 | 3.4 | 3.9 | |

SPI-6 | Moderately wet | 0.6 | 1.1 | 1.3 | 1.9 | 2.5 |

Moderately dry | 1.4 | 3.7 | 3.8 | 4.2 | 5.1 | |

SPI-9 | Moderately wet | 0.3 | 0.3 | 1.3 | 2.4 | 3.4 |

Moderately dry | 1.7 | 3.3 | 4.0 | 4.5 | 6.0 | |

SPI-12 | Moderately wet | 0.0 | 0.3 | 0.7 | 1.8 | 3.7 |

Moderately dry | 0.9 | 3.2 | 3.7 | 4.4 | 6.3 | |

SPI-24 | Moderately wet | 0.3 | 1.8 | 2.4 | 3.5 | 5.9 |

Moderately dry | 0.0 | 0.4 | 4.2 | 5.5 | 6.5 |

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**MDPI and ACS Style**

Tien Thanh, N.
A Proposal to Evaluate Drought Characteristics Using Multiple Climate Models for Multiple Timescales. *Climate* **2018**, *6*, 79.
https://doi.org/10.3390/cli6040079

**AMA Style**

Tien Thanh N.
A Proposal to Evaluate Drought Characteristics Using Multiple Climate Models for Multiple Timescales. *Climate*. 2018; 6(4):79.
https://doi.org/10.3390/cli6040079

**Chicago/Turabian Style**

Tien Thanh, Nguyen.
2018. "A Proposal to Evaluate Drought Characteristics Using Multiple Climate Models for Multiple Timescales" *Climate* 6, no. 4: 79.
https://doi.org/10.3390/cli6040079