# The Spatial-Temporal Variation Characteristics of Natural Vegetation Drought in the Yangtze River Source Region, China

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Area

^{2}(Figure 1). The elevation ranges from 6456 m in the West to 3512 mm in the East, with an average of 4779 m. The average annual precipitation is approximately 327.4 mm, which is concentrated from June to September. The average annual temperature is about −5.5–3.0 °C from northeast to southwest, with an average of 2.9 °C [27,29]. The drought index is 3.67 in the YRSR, which means the climate is very dry. The land cover in the YRSR consists primarily of grasslands (63.8%) and unused land (29.4%). Water area and forest land are less dominant land cover types, accounting for 6.5% and 0.3% of total area of YRSR. Due to the cold and dry climatic conditions, the eco-hydrology process of the whole region is sensitive to climate change.

#### 2.2. Datasets

#### 2.2.1. Hydro-Meteorological Data

#### 2.2.2. Land Use/Land Cover Data

#### 2.2.3. Soil Map and Soil Properties

#### 2.2.4. Digital Elevation Model (DEM) Data

#### 2.3. Methodology

#### 2.3.1. Drought Index and Drought Identification

#### Standardized Water Supply-Demand Index (SSDI)

_{i}) is defined as Equation (1)

_{i}and EWR

_{i}refer to green water flow and natural vegetation water requirement at each station or subregion for the ith month respectively. The GWF can be quantified by hydrological model. In this study, the ArcSWAT 2012 (https://swat.tamu.edu/software/arcswat) (Blackland Research & Extension Center, Temple, TX, USA) is used for model setup and parameterization and GWF estimation [32,33]. In the previous study, we already built a SWAT (Soil and Water Assessment Tool) model for YRSR and simulated the flows of green water, as shown in Yuan et al. [28]. Vegetation type, climate, and soil moisture can all determine the vegetation’s EWR, which was calculated by quota valuation mode in this research.

_{0}represents the potential evapotranspiration of vegetation (mm), which can be calculated by Penman–Monteith formula. Kc represents the plant water potential coefficient; Ks represents the soil moisture coefficient. The detailed mathematical procedure can be found in Zhao et al. [34].

^{k}) is calculated as Equation (3).

^{k}series:

^{k}; α, β, γ are the scale, shape, and origin parameters, respectively, which can be estimated by L-moment method [35].

_{0}= 2.515517, C

_{1}= 0.802853, C

_{2}= 0.010328, d

_{1}= 1.432788, d

_{2}= 0.189269, and d

_{3}= 0.001308. Table 1 describes the categorization of drought magnitude by SSDI.

#### Drought Event Identification Based on Theory of Runs

- 1.
- Drought duration (DD) is defined as the time between the initiation and termination of a drought event, which is expressed in months in this study.$$D{D}_{n}=T{t}_{n}-T{i}_{n}$$
_{n}refers to drought duration for the nth drought event. Ti_{n}and Tt_{n}are initiation time and termination time, respectively.

_{avg}refers average duration during a given period. DD

_{n}refers to drought duration for the nth drought event. ND is the number of drought events during a given period.

- 2.
- Drought severity (DS) is the sum of SSDIs during the drought duration.$$D{S}_{n}={\displaystyle \sum}_{i=1}^{D{D}_{n}}SSD{I}_{i}$$
_{n}refers to drought severity for the nth drought event.

_{avg}refers to average severity during a given period. DS

_{n}refers to drought severity for the nth drought event. ND is the number of drought events during a given period.

- 3.
- Drought peak (DP) is the maximum absolute value of SSDIs of a drought event.$$D{P}_{n}=\mathrm{max}\left(\left|SSD{I}_{T{i}_{n}}\right|,\left|SSD{I}_{T{i}_{n}+1}\right|,\cdots ,\left|SSD{I}_{T{t}_{n}-1}\right|,\left|SSD{I}_{T{t}_{n}}\right|\right)$$
_{n}refers to drought peak for the nth drought event. Ti_{n}and Tt_{n}are initiation time and termination time, respectively.

- 4.
- Drought coverage area (DA) is the region affected by the drought, which is calculated as follows:$$D{A}_{n}=\frac{A\left(n\right)}{A}\times 100\%$$
_{n}refers to the ratio of average drought affected area. A(i) is the area of region experiencing drought conditions. A is the area of the study region. In this research, the parameter A represents the area of grassland and forest ecosystem in the YRSR.

#### 2.3.2. Trend Analysis for Drought Characteristic

#### Linear Regression Analysis

_{slope}is the linear slope of the time series variable, which can be used to characterize the increase or decrease rate during a given study period; n is the number of years (here n = 15); X

_{i}is the drought parameter for the ith year (I = 1,2,…n).

#### Mann–Kendall Test

_{MK}, can be calculated by the following equation:

_{j}and X

_{k}are the annual values in the years j and k, respectively. The equation sgn(X

_{j}− X

_{k}) can be calculated as follows:

_{MK}follows a standard normal distribution, if |Z| > Z

_{1}

_{−α∕2}, where α denotes the significance level, then the trend is significant.

#### 2.3.3. Calculation of Bivariate Probability and Return Period via Copula Function

#### Selection of Marginal Distributions

_{m}is the empirical cumulative probability of the mth value. m represents mth smallest value in the dataset arranged in ascending order. n is the total number.

#### Selection of Copulas

_{XY}(x,y) is the bivariate probability distribution. F

_{X}(·) and F

_{Y}(·) are marginal distributions. X and Y are correlated variables.

_{emp}(u,v) is the empirical copula function. R

_{i}and S

_{i}are the ranks of the ith observed data. I(A) is the indicator function of event A which is presented as Equation (27).

#### Bivariate Probability and Return Period

_{D}

_{∩P}and P

_{D}

_{∪P}are bivariate probabilities for Case “∩” and Case “∪”, respectively. F

_{D}(·) and F

_{S}(·) are the marginal distributions for drought duration and severity, respectively. C(·) is the copula bivariate distribution for drought duration and severity.

_{D}

_{∩P}and T

_{D}

_{∪P}are bivariate probabilities for Case “∩” and Case “∪”, respectively. ζ =NY/ND, NY refers to the period of SSDI time series (years), and ND is the number of drought events in NY years [39].

## 3. Results and Discussion

#### 3.1. Time-Series Comparison of SSDI and SPEI with NDVI

_{NDVI}

_{, SSDI}) than does SPEI (r

_{NDVI}

_{, SPEI}). For example, the sub-basins with r

_{NDVI}

_{, SSDI}≥ 0.4 account for 63.4% of the total, while the sub-basins with r

_{NDVI}

_{, SPEI}≥ 0.4 account for only 25.6% (Figure 3). This indicates that the SSDI is superior to the SPEI for ecological drought assessment in the YRSR because it can capture the NDVI variation.

#### 3.2. Temporal and Spatial Variability of Drought Characteristics

#### 3.2.1. Temporal Variability of Droughts

#### 3.2.2. Spatial Pattern of Drought Characteristics

_{max}) recorded by SSDI was within the northern YRSR, with S

_{max}more than 25. Average drought count was significantly higher in Togton River Basin and Dam River Basin, where precipitation is less and temperature is lower.

#### 3.2.3. Effect of Time Scales on Drought Characteristics

#### 3.2.4. Sensitivity of Drought Characteristics to the Temperature

#### 3.3. Regional Bivariate Probability and Return Period

#### 3.3.1. Selection of the Marginal Distributions and Copulas

#### 3.3.2. Regional Bivariate Probability of Drought Events

_{D}

_{∩S}was 0.459, 0.434, 0.453, 0.484, 0.508 and the P

_{D}

_{∪S}was 0.590, 0.580, 0.577, 0.613, 0.645 in subregions I–V, respectively. For the drought event with DD > 3 and DS > 4.5(above severe grade), the P

_{D}

_{∩S}in the five subregions was 0.435, 0.411, 0.422, 0.461, 0.489 and P

_{D}

_{∪S}was 0.478, 0.465, 0.467, 0.504, 0.537. It could be found that the joint probabilities are different among the five subregions, with significantly larger P

_{D}

_{∩S}and P

_{D}

_{∪S}in Dam River Basin and Qumar River Basin, implying that the drought risk is higher in these regions.

#### 3.3.3. Bivariate Return Period of Drought Events

_{D}

_{∩S}= 11.5 year and T

_{D}

_{∪S}= 6.2 years for the YRSR. The two kinds of return period are compared, and the “∪” return periods are shorter than the “∩” return periods in all the sub-basins and the entire YRSR. Further, the univariate and bivariate drought return periods for different variation patterns were compared (Table 3). Apparently, the univariate return period is longer than “∪” return periods, while shorter than the “∩” return periods. With the DD, DP and DS increasing, both the “∪” and “∩” return periods increased. In addition, the difference between “∪” and “∩” return periods would also increase as the values of drought variables increase. Taking the entire YRSR as an example, the DD, DS and DP were about 11.1, 17.2 and 1.8, respectively, in a situation whereby the univariate return period was 50 years. For this particular event, the T

_{D}

_{∪S}, T

_{D}

_{∪S}and T

_{P}

_{∪S}were about 34.1, 28.9 and 29.6 years while the T

_{D}

_{∩S}, T

_{D}

_{∩S}and T

_{P}

_{∩S}were about 93.3, 186.6 and 161.5 years. The results are important for drought risk assessment and would be helpful in planning and management of water resources systems under severe or extreme drought scenarios.

#### 3.4. Spatial Distribution of Bivariate Probability and Return Period in the YRSR

_{D}

_{∪S}and P

_{D}

_{∩S}could be observed obviously. The bivariate probabilities of DD vs. DS increased from the north to the south, implying that the droughts in southern YRSR are relatively more severe and have longer duration. In the case of DD > 3.46 and DS > 5.37, the bivariate probabilities of P

_{D}

_{∪S}and P

_{D}

_{∩S}were more than 0.40 and more than 0.35 in the Dam River Basin. While in the Qumar River Basin, P

_{D}

_{∪S}and P

_{D}

_{∩S}were evaluated as 0.30–0.45 and 0.25–0.40, respectively. Comparing with P

_{D}

_{∪S}and P

_{D}

_{∩S}, the spatial difference of P

_{D}

_{∪P}, P

_{D}

_{∩P}, P

_{S}

_{∪P}, and P

_{S}

_{∩P}among YRSR is not obvious. P

_{D}

_{∪P}and P

_{S}

_{∪P}in nearly all of the sub-basins in YRSR were more than 0.45. The P

_{D}

_{∩P}and P

_{S}

_{∩P}in most parts of YRSR ranged from 0.30 to 0.33.

_{D}

_{∪S}and T

_{D}

_{∩S}remained in the variation range from 2.33–2.49 years and 2.67–2.85 years. While, those two kinds of return periods in Qumar River Basin were around 2.6 and 3.0 years, respectively. These results suggest that severe ecological drought events are more likely to occur in the Togton River Basin and Dam River Basin.

## 4. Conclusions

- The time-series of SSDI and Standardized Precipitation and Evapotranspiration Drought Index (SPEI) with Normalized Difference Vegetation Index (NDVI) were compared in this study. There exists a higher correlation between constructed SSDI and NDVI. This result indicated that the constructed SSDI was reliable and can reflect the comprehensive characteristics of the ecological drought information more easily and effectively.
- The YRSR had witnessed the most severe drought episodes in the periods of late-1970s, mid-1980s and mid-1990s, but the SSDI showed a wetting trend since the mid-2000s, mainly because of a warmer and wetter climate in the most recent 10 years. However, the climate change has different effects on the dry condition at seasonal scales. The drought affected areas in spring, summer and autumn have decreased since 2000 while this area in winter has increased. The drought duration and severity showed a spatial variation among different regions in the YRSR. Generally, droughts in the Southern YRSR were relatively more severe with longer drought duration, implying that the Southern YRSR was an area that had been facing challenging drought conditions. The average drought duration and severity in the YRSR would be less susceptible to changes in temperature when the increase temperature was above 1.0 °C. However, the characteristics would be more susceptible to temperature in the YRSR when the increase temperature were above 1.0 °C. The average drought duration and severity is shown to increase by 20.7% and 32.6% with a 1 °C increase in temperature for the hypothetical scenarios with ΔT > 1 °C.
- The return periods of five sub-basins and the entire YRSR for case ‘‘∩” were longer than those in case ‘‘∪” and their spatial trends are highly consistent. High return periods were found in Qumar River Basin. While, low return periods were found in most areas of Togton River Basin and Dam River Basin, implying that severe ecological drought events occurred more frequently.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Conflicts of Interest

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**Figure 2.**Drought event identification using the run theory for a given threshold level [9].

**Figure 3.**Drought event identification using the run theory for a given threshold level, SSDI = −1

^{*}: (

**a**) the correlation coefficient between SPEI and NDVI; (

**b**) the correlation coefficient between SSDI and NDVI; Note: sub-basins filled with grey mean there was no vegetation in these sub-basins; SSDI means standardized supply-demand water index.

**Figure 4.**Hovmoller-type diagrams for the temporal variability of the SSDI from 1 to 24-month scales at different subregions: (

**a**) Togton River Basin; (

**b**) Middle stream; (

**c**) Downstream; (

**d**) Dam River Basin; (

**e**) Qumar River Basin; (

**f**) YRSR.

**Figure 5.**The trend of SSDI values during 1960–2016: (

**a**) SSDI-12m of December; (

**b**) SSDI-3m of May; (

**c**) SSDI-3m of August; (

**d**) SSDI-3m of November; (

**e**) SSDI-3m of February. The crosshatch indicates that the trend is statistically significant at the 95% confidence level based on Mann–Kendall test.

**Figure 6.**Percentages of drought affected areas for (

**a**) year; (

**b**) spring; (

**c**) summer; (

**d**) autumn; (

**e**) winter.

**Figure 7.**Spatial distribution of drought duration (

**a**), severity (

**b**), peak (

**c**), maximum severity (

**d**), and drought count (

**e**) obtained on the basis of SSDI-6 values over YRSR during 1960–2016.

**Figure 10.**The box-whisker plots for drought characteristics: (

**a**) drought duration, (

**b**) drought severity, and (

**c**) drought peak. I–V represent Togton River Basin, Middle stream, Downstream, Dam River Basin, and Qumar River Basin, respectively.

**Figure 11.**Sensitivity on average (

**a**) drought duration (DD) and (

**b**) severity (DS) due to temperature change in the YRSR.

**Figure 12.**Comparison between empirical and theoretical CDFs of drought duration, severity, and peak in subregions I–V and entire YRSR. EXP, WBL, GP, GEV, and GAM are abbreviations for Exponential, Weibull, Generalized Pareto, Gamma, and Generalized Extreme Value distributions. The value of h is 1 if the test rejects the null hypothesis at the 5% significance level, or 0 otherwise. RMSE is the value of root-mean-square error. The dotted line indicates the 1:1 line.

**Figure 13.**Comparison between empirical and theoretical CDFs of bivariate distribution in subregions I–V and entire YRSR. The value of h is 1 if the test rejects the null hypothesis at the 5% significance level, or 0 otherwise. SED is the value of square Euclidean distance. The dotted line indicates the 1:1 line.

**Figure 14.**Bivariate probability of DD vs. DS, DD vs. DP and DS vs. DP: (a) “∪” bivariate probability; (b) “∩” bivariate probability.

**Figure 15.**Bivariate return periods of DD vs. DS, DD vs. DP and DS vs. DP: (a) “∪” return period; (b) “∩” return period. DD: Drought duration; DS: Drought severity; DP: Drought peak.

**Figure 16.**Spatial distribution of bivariate probabilities of DD vs. DS, DD vs. DP and DS vs. DP in Case ∪ and Case ∩ in the YRSR.

**Figure 17.**Spatial distribution of bivariate return periods of DD vs. DS, DD vs. DP and DS vs. DP in Case ∪ and Case ∩ in the YRSR.

Drought Grade | Range of SSDI Value |
---|---|

Near normal | 1.00 > SSDI > −1.00 |

Moderate drought | −1.00 ≥ SSDI > −1.50 |

Severe drought | −1.50 ≥ SSDI > −2.00 |

Extreme drought | −2.00 ≥ SSDI |

Subregion | DD vs. DS | DD vs. DP | DS vs. DP | |||
---|---|---|---|---|---|---|

Copula | Parameter (θ) | Copula | Parameter (θ) | Copula | Parameter (θ) | |

I | Frank | 33.094 | Frank | 8.192 | Frank | 10.202 |

II | Frank | 25.537 | Frank | 9.184 | Frank | 11.220 |

III | Frank | 31.090 | Frank | 7.205 | Frank | 8.897 |

IV | Frank | 32.708 | Frank | 9.804 | Frank | 11.906 |

V | Frank | 18.411 | Clayton | 2.042 | Clayton | 3.509 |

YRSR | Frank | 27.058 | Frank | 9.024 | Frank | 10.889 |

Region | T | DD | DS | DP | DD vs. DS Return Period | DD vs. DP Return Period | DS vs. DP Return Period | |||
---|---|---|---|---|---|---|---|---|---|---|

Case∪ | Case ∩ | Case∪ | Case ∩ | Case∪ | Case ∩ | |||||

Subregion I | 5 | 3.6 | 5.3 | 0.2 | 4.7 | 5.3 | 4.1 | 6.3 | 4.3 | 6.0 |

10 | 6.3 | 9.2 | 0.6 | 9.0 | 11.2 | 7.3 | 15.7 | 7.6 | 14.5 | |

20 | 9.0 | 13.2 | 1.0 | 16.5 | 25.4 | 12.9 | 44.1 | 13.4 | 39.2 | |

50 | 12.5 | 18.4 | 2.0 | 35.1 | 87.1 | 28.5 | 204.2 | 29.2 | 173.7 | |

100 | 15.2 | 22.3 | 3.1 | 62.3 | 253.9 | 53.7 | 719.7 | 54.6 | 598.3 | |

Subregion II | 5 | 3.2 | 4.9 | 0.2 | 4.7 | 5.4 | 4.2 | 6.1 | 4.3 | 5.9 |

10 | 5.7 | 8.7 | 0.5 | 8.8 | 11.5 | 7.5 | 14.9 | 7.8 | 13.9 | |

20 | 8.2 | 12.6 | 1.0 | 16.0 | 26.7 | 13.3 | 40.6 | 13.7 | 36.7 | |

50 | 11.5 | 17.6 | 1.9 | 33.8 | 96.1 | 29.0 | 182.6 | 29.7 | 158.2 | |

100 | 14.0 | 21.4 | 3.0 | 60.4 | 289.5 | 54.3 | 633.5 | 55.1 | 536.3 | |

Subregion III | 5 | 2.8 | 4.1 | 0.1 | 4.8 | 5.2 | 4.2 | 6.2 | 4.3 | 6.0 |

10 | 5.5 | 7.8 | 0.4 | 9.1 | 11.0 | 7.4 | 15.4 | 7.7 | 14.3 | |

20 | 8.1 | 11.6 | 0.7 | 16.9 | 24.5 | 13.1 | 42.6 | 13.6 | 38.1 | |

50 | 11.6 | 16.6 | 1.2 | 36.0 | 81.6 | 28.7 | 194.9 | 29.4 | 167.1 | |

100 | 14.2 | 20.4 | 1.7 | 63.7 | 232.0 | 54.0 | 682.7 | 54.8 | 571.7 | |

Subregion IV | 5 | 3.7 | 5.5 | 0.2 | 4.8 | 5.3 | 4.3 | 6.0 | 4.4 | 5.8 |

10 | 6.6 | 9.8 | 0.5 | 9.1 | 11.2 | 7.6 | 14.5 | 7.9 | 13.6 | |

20 | 9.5 | 14.0 | 0.8 | 16.6 | 25.1 | 13.4 | 39.2 | 13.9 | 35.7 | |

50 | 13.3 | 19.6 | 1.3 | 35.4 | 85.4 | 29.2 | 174.1 | 29.9 | 151.8 | |

100 | 16.1 | 23.9 | 1.8 | 62.7 | 246.9 | 54.5 | 599.6 | 55.4 | 511.0 | |

Subregion V | 5 | 3.1 | 4.8 | 0.1 | 4.8 | 5.3 | 4.3 | 5.9 | 4.5 | 5.6 |

10 | 6.2 | 9.5 | 0.6 | 9.1 | 11.1 | 7.7 | 14.2 | 8.2 | 12.8 | |

20 | 9.3 | 14.3 | 1.0 | 16.8 | 24.6 | 13.6 | 38.0 | 14.5 | 32.1 | |

50 | 13.3 | 20.5 | 1.7 | 35.9 | 82.2 | 29.4 | 166.1 | 31.0 | 129.6 | |

100 | 16.4 | 25.3 | 2.4 | 63.6 | 234.5 | 54.8 | 567.8 | 56.7 | 422.9 | |

YRSR | 5 | 3.1 | 4.8 | 0.2 | 4.7 | 5.3 | 4.2 | 6.1 | 4.3 | 5.9 |

10 | 5.5 | 8.5 | 0.6 | 8.9 | 11.4 | 7.5 | 15.0 | 7.8 | 14.0 | |

20 | 7.9 | 12.3 | 1.0 | 16.1 | 26.3 | 13.2 | 41.0 | 13.7 | 37.2 | |

50 | 11.1 | 17.2 | 1.8 | 34.1 | 93.3 | 28.9 | 185.0 | 29.6 | 161.5 | |

100 | 13.5 | 20.9 | 2.7 | 60.9 | 278.6 | 54.2 | 643.0 | 55.0 | 549.6 |

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## Share and Cite

**MDPI and ACS Style**

Yin, J.; Yuan, Z.; Li, T. The Spatial-Temporal Variation Characteristics of Natural Vegetation Drought in the Yangtze River Source Region, China. *Int. J. Environ. Res. Public Health* **2021**, *18*, 1613.
https://doi.org/10.3390/ijerph18041613

**AMA Style**

Yin J, Yuan Z, Li T. The Spatial-Temporal Variation Characteristics of Natural Vegetation Drought in the Yangtze River Source Region, China. *International Journal of Environmental Research and Public Health*. 2021; 18(4):1613.
https://doi.org/10.3390/ijerph18041613

**Chicago/Turabian Style**

Yin, Jun, Zhe Yuan, and Ting Li. 2021. "The Spatial-Temporal Variation Characteristics of Natural Vegetation Drought in the Yangtze River Source Region, China" *International Journal of Environmental Research and Public Health* 18, no. 4: 1613.
https://doi.org/10.3390/ijerph18041613