# Analysis for Spatio-Temporal Variation Characteristics of Droughts in Different Climatic Regions of the Mongolian Plateau Based on SPEI

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Description of Study Area

^{2}(Figure 1a).

#### 2.2. Data Sources

#### 2.3. Methodology

#### 2.3.1. Standardized Precipitation-Evapotranspiration Index (SPEI)

- (1)
- Calculate the potential evapotranspiration PET by the Penman–Monteith model:$$PE{T}_{i}=\frac{0.408\Delta \left({R}_{n}-G\right)+\gamma \frac{900}{T+273}{U}_{2}\left({e}_{a}-{e}_{d}\right)}{\Delta +\gamma \left(1+0.34{U}_{2}\right)}$$
- (2)
- Calculate the water balance:$${D}_{i}={P}_{i}-{\left(PET\right)}_{i}$$$${D}_{n}^{k}={\displaystyle \sum}_{i=0}^{k-1}\left[\frac{2\left(i+1\right)}{k\left(k+1\right)}\left({P}_{n-1}\right)-PE{T}_{n-1}\right],n\ge k$$
- (3)
- The water balance is normalized into a log-logistic probability distribution to calculate the SPEI index series as follows:$$f\left(x\right)=\frac{\beta}{\alpha}{\left(\frac{x-\gamma}{\alpha}\right)}^{\beta -1}{\left[1+{\left(\frac{x-\gamma}{\alpha}\right)}^{\beta}\right]}^{-2}$$$$\beta =\frac{2{\omega}_{1}-{\omega}_{0}}{6{\omega}_{1}-{\omega}_{0}-6{\omega}_{2}},\alpha =\frac{\left({\omega}_{0}-2{\omega}_{1}\right)\beta}{\mathsf{\Gamma}\left(1+1/\beta \right)\mathsf{\Gamma}\left(1-1/\beta \right)},\gamma ={\omega}_{0}-\alpha \mathsf{\Gamma}\left(1+1/\beta \right)\mathsf{\Gamma}\left(1-1/\beta \right)$$$\mathsf{\Gamma}\left(\beta \right)$ is a Gamma function about $\beta $. Thereby, the cumulative function of probability density of ${D}_{i}$ is obtained.$$F\left(x\right)={\left[1+{\left(\frac{\alpha}{x-y}\right)}^{\beta}\right]}^{-1}$$
- (4)
- With F(x), the SPEI can easily be obtained as the standardized values of F(x).$$SPEI=\omega -\frac{{C}_{0}+{C}_{1}\omega +{C}_{2}{\omega}^{2}}{1+{d}_{1}\omega +{d}_{2}{\omega}^{2}+{d}_{3}{\omega}^{3}}$$

#### 2.3.2. Trend Analyzed Method

- (1)
- Mann–Kendall (MK) test

_{1}, x

_{2}, …, x

_{n}, n is the length of the time series and the MK method defines the statistic S as follows [34] (Equations (8)–(10)):

_{j}and X

_{k}are the corresponding measured values of j and k year, and k > j.

_{1}− a/2, i.e., at the alpha confidence level, there is a significant up or down trend in the time-series data. |Z| ≥ 1.96 indicate that they passed the significance test with 95% confidence.

- (2)
- Sen’s Slope detection method

- (3)
- The Sen’s slope detection method can reduce or avoid the influence of data missing and abnormality on the statistical results [30,31,32]. The Sen slope formula is as follows (Equations (11) and (12)):$${S}_{ij}=M\left[\frac{{X}_{j}-{X}_{i}}{j-i}\right]$$
_{i}and X_{j}are the sequence values at the i-th and j-th, respectively, 1 < i < j < n, and n is the sequence length. The Sen’s slope is the median value of slope, determined by the parity of the total number of S_{ij}determined by the sequence length n, where k is an integer related to the length of the sequence, N = n(n − 1)$$S=\{\begin{array}{cc}{S}_{k+1},& N=2k+1\\ \frac{{S}_{k}+{S}_{k+1}}{2},& N=2k\end{array}$$

#### 2.3.3. Sequential Mann–Kendall Abrupt Detection Method

_{i}(m

_{1}, m

_{2}, ..., m

_{n}) is constructed by X

_{1}, X

_{2}, ..., X

_{n}, and m

_{i}is X

_{i}> X

_{j}(1 ≤ j ≤ i). Cumulative variable d

_{k}is defined as follows:

_{k}mean and variance are defined as follows:

_{i}is a statistic sequence calculated by time series X

_{1}, X

_{2}, ..., X

_{n}. Arrange the time series Xi in reverse order, repeat the above calculation process and make

_{i}and UB

_{i}) have intersection points, which are within the significance level interval, the intersection points indicate a significant abrupt change.

#### 2.3.4. Empirical orthogonal function (EOF)

_{1}≥ λ

_{2}≥ … ≥ λ

_{m}, and the corresponding eigenvectors are v

_{1}≥ v

_{2}≥ … ≥ v

_{n}, which form a matrix V = (v

_{1}, v

_{2}, …, v

_{m}), where V is a space function and each array represents a typical spatial field and is only related to space.

## 3. Results

#### 3.1. Identify Drought Period Within Different Climatic Regions of the Mongolian Plateau

#### 3.2. Temporal Variability of Droughts

#### 3.2.1. M–K Abrupt Change Analysis Based on SPEI-12 and Slope Analysis Before and After Abrupt Change

#### 3.2.2. Seasonal Variability

_{Feb}) to demonstrate drought magnitude in winter. In the same way, SPEI-3

_{May}, SPEI-3

_{Aug}, and SPEI-3

_{Nov}are used to represent drought magnitude in spring, summer, and fall, respectively. We therefore computed the Sen’s slope based on all four seasons’ SPEI-3 for all climate stations, which demonstrates the seasonal drought trend across the MP, shown in Table 3.

#### 3.3. Spatial Variability of Droughts

#### 3.3.1. Annual Drought Trend Detected by SPEI Analysis

#### 3.3.2. Seasonal Trend of SPEI in Different Climatic Regions

_{Feb}) to demonstrate drought magnitude in winter. In the same way, SPEI-3

_{May}, SPEI-3

_{Aug}, and SPEI-3

_{Nov}were used to represent drought magnitude in spring, summer, and fall, respectively. Similar to Section 3.3.1, we therefore computed the Sen’s slope based on all four seasons’ SPEI-3 for all climate stations, which demonstrates the seasonal drought trend across the MP, shown in Figure 5.

_{Aug}for 133 stations across all three climate regions.

#### 3.3.3. Spatial Distribution of the Drought Frequency Categorized by Relative Severity

#### 3.4. Spatial Distribution Characteristics of Droughts (Decomposition and Expansion of EOF)

## 4. Discussion

#### 4.1. Aridification Trend of the Mongolian Plateau under the Background of Climate Change

#### 4.2. Drought Variations in Different Climatic Regions at the Seasonal Scale and Their Impacts

## 5. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**(

**a**) Geographic location of the Mongolian plateau (MP); (

**b**) locations of weather stations and typical climatic regions in the MP; (

**c**) 90 m Digital Elevation Model of the MP.

**Figure 2.**Dynamic characteristics of SPEI-3 in Region I (

**a**); SPEI-3 in Region II (

**b**); SPEI-3 in Region III (

**c**); SPEI-3 in the MP (

**d**); SPEI-12 in Region I (

**e**); SPEI-12 in Region II (

**f**); SPEI-12 in Region III (

**g**); SPEI-12 in the MP (

**h**) from 1980 to 2015.

**Figure 5.**Spatial patterns of trends per 10a for Spring (

**a**); Summer (

**b**); Autumn (

**c**); and Winter (

**d**) in the Mongolian Plateau during 1980–2015.

**Figure 6.**Frequencies of Annual Mild Droughts (

**a**), Moderate Droughts (

**b**), Severe Droughts (

**c**) and Extreme Droughts (

**d**) during 1980–2015 (at different severity grades).

**Figure 7.**PC1 and PC2 Time Series Variations for Analysis of SPEI-12 Principal Components based on Annual Drought Variations in Different Climatic Regions in the Mongolian Plateau from 1980 to 2015.

**Figure 8.**Spatial Distribution of (

**a**) EOF1 and (

**b**) EOF2 for Annual Drought Variations in Different Climatic Regions in the Mongolian Plateau from 1980 to 2015.

**Figure 9.**Line Chart for Mean Precipitations in Fall at Stations with Mitigated Droughts in 1980–2015.

**Figure 10.**Line Chart for Mean Precipitations (Snowfalls) in Winter,1980–2015 (the average precipitations in 1980–1999 and 1999–2015 were 1.99 mm and 2.6 mm, respectively).

Grade | Type | SPEI Value |

0 | Normal | more than −0.5 |

1 | Mild drought | (−1.00, −0.5] |

2 | Moderate drought | (−1.50, −1.00] |

3 | Severe drought | (−2.00, −1.50] |

4 | Extreme drought | less than −2.00 |

**Table 2.**Sen’s slope of SPEI-12 in all three climatic regions and their average values before and after year 1998.

Periods | Areas | Slope | 1980–1998 Average SPEI-12 | 1999–2015 Average SPEI-12 |
---|---|---|---|---|

Year | I | −0.0243 * | 0.3711 | −0.4083 |

II | −0.0241 * | 0.3499 | −0.3838 | |

III | −0.0307 * | 0.4330 | −0.4768 | |

MP | −0.0234 * | 0.3685 | −0.4070 |

Zone | Season | Slope | 1980–1998 Average SPEI-3 | 1999–2015 Average SPEI-3 |
---|---|---|---|---|

Ⅰ | Spring | –0.0011 | 0.0094 | 0.0019 |

Summer | –0.0231 * | 0.3594 | –0.3939 | |

Autumn | –0.0235 * | 0.2887 | –0.3050 | |

Winter | 0.0241 * | –0.1872 | 0.2389 | |

Ⅱ | Spring | –0.0157 | 0.1377 | –0.1352 |

Summer | –0.0232 * | 0.3671 | –0.3999 | |

Autumn | –0.0055 | 0.0846 | –0.0668 | |

Winter | 0.0090 | –0.0690 | 0.1094 | |

Ⅲ | Spring | –0.0247 * | 0.2134 | –0.2253 |

Summer | –0.0257 * | 0.4043 | –0.4387 | |

Autumn | –0.0177 | 0.1257 | –0.1279 | |

Winter | –0.0016 | 0.0202 | 0.0198 | |

MP | Spring | –0.0138 | 0.1086 | –0.1076 |

Summer | –0.0236 * | 0.3684 | –0.4051 | |

Autumn | –0.0139 | 0.1559 | –0.1529 | |

Winter | 0.0098 | –0.0911 | 0.1294 |

Mode-1 | Mode-2 | Mode-3 | Mode-4 | Mode-5 | Mode-6 | Mode-7 | Cumulated Explained Variance | |
---|---|---|---|---|---|---|---|---|

Ⅰ | 43.79% | 10.12% | 7.75% | 5.76% | 3.33% | 3.09% | 2.65% | 76.48% |

Ⅱ | 39.22% | 15.94% | 5.39% | 5.10% | 3.60% | 3.28% | 2.75% | 75.28% |

Ⅲ | 50.59% | 11.27% | 6.82% | 4.51% | 3.33% | 3.19% | 2.42% | 82.14% |

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## Share and Cite

**MDPI and ACS Style**

Jin, L.; Zhang, J.; Wang, R.; Zhang, M.; Bao, Y.; Guo, E.; Wang, Y.
Analysis for Spatio-Temporal Variation Characteristics of Droughts in Different Climatic Regions of the Mongolian Plateau Based on SPEI. *Sustainability* **2019**, *11*, 5767.
https://doi.org/10.3390/su11205767

**AMA Style**

Jin L, Zhang J, Wang R, Zhang M, Bao Y, Guo E, Wang Y.
Analysis for Spatio-Temporal Variation Characteristics of Droughts in Different Climatic Regions of the Mongolian Plateau Based on SPEI. *Sustainability*. 2019; 11(20):5767.
https://doi.org/10.3390/su11205767

**Chicago/Turabian Style**

Jin, Laiquan, Jiquan Zhang, Ruoyu Wang, Minghua Zhang, Yuhai Bao, Enliang Guo, and Yongfang Wang.
2019. "Analysis for Spatio-Temporal Variation Characteristics of Droughts in Different Climatic Regions of the Mongolian Plateau Based on SPEI" *Sustainability* 11, no. 20: 5767.
https://doi.org/10.3390/su11205767