# Propagation from Meteorological to Hydrological Drought and Its Influencing Factors in the Huaihe River Basin

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## Abstract

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## 1. Introduction

## 2. Study Area and Data

#### 2.1. Study Area

#### 2.2. Data

## 3. Methodology

#### 3.1. Drought Characterizing

#### 3.1.1. Drought Indices

#### 3.1.2. Drought Identification

- (1)
- Initial identification. Set threshold τ = −1 to capture drought events;
- (2)
- Pooling adjacent droughts. Interval time criteria (t
_{c}) was selected to pool mutually dependent droughts. If the interval time t between two adjacent droughts is less than the predefined t_{c}and the drought index between two droughts is less than 0, then two adjacent droughts can be pooled to form a new drought event. Repeat the procedure until the interval time between all the droughts is greater than t_{c}. Then, t_{c}is predefined as 10 days for both meteorological and hydrological drought identification; - (3)
- Excluding minor droughts. Minor droughts with a short duration have little impact on hydrological conditions but large impacts on drought characterization. If the duration of a drought event is less than the predefined minimum duration D
_{min}, then the event is excluded. The D_{min}is predefined as 10 and 30 days for meteorological and hydrological drought identification, respectively.

#### 3.1.3. Estimation of Drought Characteristics

- Drought duration (D) is the period from the onset time to end time of a drought event;
- Drought severity (S) is the sum of SPI/SRI values during a drought;

- Drought development speed (DS) is the change rate of the drought index from the onset time (t
_{o}) to the peak time (t_{p}) during the drought development stage and recovery speed (RS) [29] is the change rate of the drought index from the peak time (t_{p}) to the end time (t_{e}) at the drought recovery stage. To reduce the fluctuation of daily series without significantly changing the onset and end time of drought events, the 5-day moving average process is first employed to the daily SPI/SRI series (Figure 3). Then, DS and RS are calculated as follows:$$\mathrm{DS}=\frac{D{V}_{DP}}{{t}_{\mathrm{p}}-{t}_{\mathrm{o}}}$$$$\mathrm{RS}=\frac{D{V}_{RP}}{{t}_{\mathrm{e}}-{t}_{\mathrm{p}}}$$_{DP}and DV_{RP}are the deficit volumes of rainfall/streamflow in terms of the 5-day moving average drought index in the development and recovery period, respectively. Additionally, t_{o}, t_{p}, and t_{e}are the onset, peak, and end time of a drought event. For a pooled drought event, DS (RS) refers to the development (recovery) speed of the first (last) drought.

#### 3.2. Propagation Relationship Analysis

#### 3.2.1. Matching Meteorological and Hydrological Drought Events

_{o}and M

_{e}are the onset and end time of a meteorological drought event, respectively; H

_{o}is the onset time of a hydrological drought event. D

_{M}and D

_{H}are the duration of meteorological and hydrological drought events, respectively. Since the number of drought events decreases with the increase of timescale [12,30], the number of drought events at longer timescales would be limited for statistical analysis. Therefore, meteorological and hydrological drought events both at 30-day scale are utilized to ensure that the sufficient number of meteorological and hydrological drought events are matched for further statistical analysis.

#### 3.2.2. Quantification of Propagation Relationship

_{H|M}), the propagation time (T

_{P}), and the propagation ratio of drought characteristics (R

_{P}) of matched meteorological and hydrological drought events. The Type-2 and Type-3 propagation are quantified by their occurrence probability (P

_{M|NH}and P

_{H|NM}, respectively).

- Occurrence probability of Type-1 propagation (P
_{H|M}) is defined as the probability that a hydrological drought (referred to as H) is triggered when a meteorological drought (referred to as M) occurs. Conditional probability is widely used in studies of probabilistic drought prediction [31,32] and probabilistic links between matched meteorological and hydrological drought characteristics [23,24]. Here, we apply the bivariate conditional probability based on the copula function to estimate P_{H|M}. Assuming that X and Y are random variables with marginal distributions $u={F}_{X}\left(x\right)$ and $v={F}_{Y}\left(y\right)$, the bivariate conditional probability $P\left(Y\le y|X\le x\right)$ is given by:$$P\left(Y\le y|X\le x\right)=\frac{P\left(X\le x,Y\le y\right)}{P\left(X\le x\right)}=\frac{C\left(u,v\right)}{u}$$

_{H|M}reflects the sensitivity of hydrological to meteorological drought, and the higher probability indicates that meteorological drought is more likely to propagate to hydrological drought.

- Occurrence probability of Type-2 propagation (P
_{M|NH}) is defined to describe the situation that a meteorological drought (M) occurs but no hydrological drought occurs (referred to as NH). P_{M|NH}equals the bivariate conditional probability $P\left(X\le x|Y\ge x\right)$, given by:$$P\left(X\le x|Y\ge y\right)=\frac{P\left(X\le x,Y\ge y\right)}{P\left(Y\ge y\right)}$$_{M|NH}is calculated as the ratio of the number of meteorological drought events triggering hydrological drought events to the total number of meteorological drought events in the record period, given by:$${P}_{M|NH}=1-\frac{{n}_{l}}{{n}_{m}}$$_{m}is the total number of meteorological drought events. - Occurrence probability of Type-3 (P
_{H|NM}) is defined to quantify the situation that a hydrological drought event occurs without a proceeding meteorological drought event (referred to as NM). P_{H|NM}equals the bivariate conditional probability of $P\left(Y\le y|X\ge x\right)$, given by:$$P\left(Y\le y|X\ge x\right)=\frac{P\left(X\ge x,Y\le y\right)}{P\left(X\ge x\right)}$$

_{H|NM}is calculated as:

_{h}is the total number of hydrological drought events.

- Propagation time (T
_{P}) is the time difference between the onset of matched meteorological and hydrological drought events.$${T}_{P}={H}_{o}-{M}_{o}$$_{o}and H_{o}are the onset time of matched meteorological and hydrological drought events. For the many-to-one situation, M_{o}refers to the onset time of the first meteorological drought event. - Propagation ratio of drought characteristics (R
_{P}) is the ratio of matched meteorological to hydrological drought event characteristics, given by:$${R}_{P}=\frac{1}{n}{\displaystyle \sum}_{i=1}^{n}\frac{{C}_{M,i}}{{C}_{H,i}}$$_{M,i}and C_{H,i}are the characteristics (duration, severity, and development/recovery speed) of matched meteorological and hydrological drought events, respectively; n is the number of hydrological drought events triggered by meteorological drought events. The drought characteristics considered here include the duration, severity, and development/recovery speed, and consequently we have R_{P}_{-D}, R_{P}_{-S}, R_{P}_{-DS}, and R_{P}_{-RS}to represent the propagation ratio of duration, severity, development speed, and recovery speed, respectively. For the many-to-one situation, when calculating R_{P}_{-D}or R_{P}_{-S}, the C_{M,i}should be the sum of duration or severity of all meteorological drought events that triggers the ith hydrological drought event; when calculating R_{P}_{-DS}(R_{P}_{-RS}), the C_{M,i}should be the development (recovery) speed of the first (last) meteorological drought event that triggers the ith hydrological drought event.

#### 3.3. Influence of Climate, Catchment Properties, and Human Activities on Drought Propagation

#### 3.3.1. Selected Influencing Factors

#### 3.3.2. Analyze the Influence with the Correlation Analysis

## 4. Results

#### 4.1. Characteristics of Meteorological and Hydrological Drought Events

_{H}(DS of hydrological drought) ranges from 0.06 to 1.58 and the RS

_{H}(RS of hydrological drought) varies from 0.05 to 1.50 among all catchments. The DS

_{M}(DS of meteorological drought) ranges from 0.05 to 1.68 and the RS

_{M}(RS of meteorological drought) varies from 0.05 to 1.60 among all catchments. DPL and CTG have higher DS

_{H}than other catchments and BT has the lowest RS

_{H}. For catchments with high DS, the drought develops fast to its peak, implying a stronger need for early drought monitoring and quicker response to alleviate hydrological drought than those catchments with low DS. For catchments with low RS, drought recovers slowly to normal conditions, which needs more human interventions such as water imports by water transfer to reduce drought impacts.

#### 4.2. Propagation Features from Meteorological to Hydrological Droughts

_{H|M}) that a hydrological drought is triggered when a meteorological drought occurs is investigated based on copula functions. Before using the Copula function to build the joint distribution, the correlation between the SPI and SRI series is tested with Spearman correlation. The Spearman correlation coefficient indicates a relatively strong nonlinear relationship between SPI and SRI series except for LH, BT, and ZM catchment (Figure 7). Among Gaussian, t, Clayton, and Gumbel copula, the Gumbel copula has the least AIC, indicating that it fits the joint distribution of SPI and SRI the best. Based on the best-fit Copula function, P

_{H|M}is calculated and shown in Figure 7. P

_{H|M}varies from 0.25 to 0.48 among all catchments. P

_{H|M}is relatively low indicating that less than half of the meteorological drought can trigger a hydrological drought. P

_{H|M}is the highest in TJH and the lowest in LH, BT, and ZM (0.25, 0.27, and 0.28, respectively). LH, BT, and ZM also have the weakest correlation between the SPI and SRI series. TJH is located in a mountainous area, with higher rainfall and less percentage of crop land, while LH, ZM, and BT are located in a plain terrain, with less rainfall but more intense human activities. The differences between distinct catchments indicate the comprehensive effect of climate and catchment properties on the drought propagation relationship. It should be noted that the catchment with higher occurrence probability of Type-1 propagation is not equal to the catchment with a more severe hydrological drought. For example, the average drought severity of TJH at 30-day scale (−87.20) is much lower than that of LH (−101.75), which is the lowest P

_{H|M}among all catchments (Figure 4).

_{M|NH}) varies from 0.63 to 0.77 in all catchments (Figure 8). The occurrence probability of Type-3 (P

_{H|NM}) is shown in Figure 8. P

_{H|NM}varies from 0.31 to 0.58, which means that 31–58% of hydrological drought events occurs without proceeding to meteorological drought events, i.e., hydrological drought events occur without obvious precipitation deficits. P

_{H|NM}in LH, ZM, and BT is the highest, while the lowest P

_{H|NM}is in TJH, which is opposite to the occurrence probability of Type-1 propagation (P

_{H|M}). Due to the plain terrain associated with catchment storage and intense human activities in LH, ZM, and BT, meteorological and hydrological droughts show a weak synchronization in these catchments, which may increase the occurrence of Type-3 propagation. Figure 8 also shows that the propagation ratio of duration (R

_{P-D}) and severity (R

_{P-S}) are all lower than 1 indicating that duration lengthens and severity amplifies in drought propagation. The variation of severity (accumulated anomaly) in our studies differs from that in Liu et al. [4]. This is due to the fact that we investigate the propagation phenomenon just in temporal view, and drought propagation in higher dimensions (space-time dimensions) may exhibit different features. It can be observed that the propagation ratio of development/recovery speed (R

_{P}

_{-DS}and R

_{P}

_{-RS}in Figure 8) is greater than 1, which means that drought development and recovery speed reduces in propagation from meteorological to hydrological drought. Except for the common discussed propagation features concluded in [2,3], the reduction of speed can also be regarded as an important feature of drought propagation, which can provide valuable information about the internal process of diverse drought types.

_{P}) from meteorological to hydrological drought is shown in Figure 9. The T

_{P}ranges from 1 to 47 days in study catchments. It is obvious that there is a lag of onset time from meteorological to hydrological drought. ZT and TJH with a smaller area, mountainous terrain, and near-natural conditions have relatively short T

_{P}of 1–21 days. A shorter T

_{P}indicates that there will be less time to take measures to resist hydrological drought once the meteorological drought occurs. The maximum T

_{P}is 47 days in ZM. BT and LH also have a relatively high propagation time longer than 40 days. It is also observed that the catchments with low occurrence probability of Type-1 propagation (P

_{H|M}) and high occurrence probability of Type-3 (P

_{H|NM}), such as LH, BT, and ZM, have a long T

_{P}compared with Figure 7.

#### 4.3. Impacts of Climate and Catchment Properties on Drought Propagation

_{P}) and occurrence probability of Type-1 propagation (P

_{H|M}). The BFI and TI show a positive relationship with T

_{P}with a Pearson coefficient of 0.65 and 0.64. The catchment storage related to soil buffering and aquifer recharge-discharge processes can modulate climate variability signals propagating along a terrestrial hydrological system, determining that the time of streamflow responds to precipitation anomalies [35]. P

_{H|M}is negatively related to BFI and TI with a coefficient of −0.75 and ‒0.63. Catchments with high BFI or TI usually have high resistance to meteorological drought and decrease the probability of triggering hydrological drought. DS and RS characterizing the hydrological internal process show a significantly negative relationship with BFI and TI (r < −0.6) and a weak relationship with climate factors.

#### 4.4. Impacts of Reservoir on Hydrological Drought and Drought Propagation

^{3}storage capacity but there is no reservoir in TJH. In this way, the impact of reservoir on hydrological drought and drought propagation is isolated and the difference of hydrological drought characteristics can be attributed to reservoir regulation.

_{P}) and occurrence probability of Type-1 propagation (P

_{H|M}) in two catchments is very close. However, there is a considerable increase in occurrence probability of Type-3 (P

_{H|NM}) of XIN compared with TJH, which means that the percentage of a hydrological drought occurring without the occurrence of a proceeding meteorological drought event in XIN is lower than that in TJH. This indicates the role of the reservoir in increasing the occurrence of Type-3 propagation.

## 5. Discussion

#### 5.1. How to Quantify Propagation Time from Meteorological to Hydrological Drought?

#### 5.2. Which One Performs Better in Representing the Effect of Catchment Properties on Drought Propagation, Base Flow Index or Topographic Index?

#### 5.3. How Does Irrigation Affect Hydrological Drought?

## 6. Conclusions

- (1)
- The occurrence probability of Type-1 propagation varies from 0.25 to 0.48 among all catchments. The propagation time ranges from 1 to 47 days in study catchments. Catchments with low occurrence probability of Type-1 propagation is found in LH, BT, and ZM, which also have a longer propagation time. Features of Type-1 propagation include the lengthening of duration, amplification of severity, lag of onset time, and reduction of speed.
- (2)
- Climate factors have a significant effect on hydrological drought duration, while the topographic index (TI) from TOPMODEL representing catchment properties significantly correlates with hydrological drought severity. The base flow index (BFI) and TI indicating catchment storage show the strongest relationship with propagation time, probability, and development/recovery speed. Partial correlation analyses show that the impact of crop land on hydrological drought is far less than that of TI, indicating that the impact of irrigation on hydrological drought is less than that of catchment properties.
- (3)
- Reservoir operation has a significant effect on alleviating the duration and severity of extreme hydrological drought. However, it also increases the occurrence of Type-3 propagation due to the impoundment of reservoir upstream at the end of flood season. The off-set of two sides of effect on hydrological drought may be the reason that the average hydrological drought characteristics of paired-catchment is very close.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Location of the catchments and hydrological stations (

**a**) and land cover types in the Huaihe River Basin in 2010 (

**b**).

**Figure 2.**Pooling and excluding procedure in drought identification. (Note: t

_{c}and D

_{min}are the predefined criteria to pool adjacent droughts and exclude minor droughts, respectively).

**Figure 3.**A conceptualization of drought development and recovery in terms of SPI and SRI. (Note: DV

_{DP}and DV

_{RP}are the deficit volumes of rainfall/streamflow in terms of the 5-day moving average drought index in the development and recovery period, respectively. Additionally, t

_{o}, t

_{p}, and t

_{e}are the onset, peak, and end time of a drought event).

**Figure 4.**Drought duration and severity at 30-, 90-, 180-, and 365-day scale in HRB: (

**a**) Meteorological drought duration (M-D); (

**b**) meteorological drought severity (M-S); (

**c**) hydrological drought duration (H-D); (

**d**) hydrological drought severity (H-S).

**Figure 5.**Drought speed at 30-day scale in HRB: (

**a**) Meteorological drought development speed (M-DS); (

**b**) meteorological drought recovery speed (M-RS); (

**c**) hydrological drought development speed (H-DS); (

**d**) hydrological drought recovery speed (H-RS).

**Figure 6.**Examples of drought propagation: (

**a**) The one-to-one situation of Type-1 at 30-day scale in HB catchment; (

**b**) the many-to-one situation of Type-1 at 30-day scale in HB catchment; (

**c**) Type-2 at a 30-day scale in HB catchment; (

**d**) Type-3 at 30-day scale in XIN catchment.

**Figure 7.**Occurrence probability of Type-1 propagation and Spearman coefficient of SPI and SRI in HRB (30-day scale).

**Figure 8.**Occurrence probability of Type-2 (P

_{M|NH}) and Type-3 (P

_{H|NM}), ratio of duration (R

_{P}

_{-D}), ratio of severity (R

_{P}

_{-S}), ratio of development speed (R

_{P}

_{-DS}), and recovery speed (R

_{P}

_{-RS}) in HRB.

**Figure 10.**Pearson correlation coefficient between catchment properties, hydrological drought characteristics, and propagation features. (Note: the grid without a number or filling represents the significance level of correlation coefficient, which is less than 0.05).

**Figure 11.**Meteorological and hydrological drought processes in paired-catchment during 1999–2001: (

**a**) Benchmark catchment (TJH); (

**b**) hydrological drought severity of two catchments; (

**c**) reservoir-regulated catchment (XIN).

**Figure 12.**Propagation time calculated by (

**a**) Pearson correlation coefficient; (

**b**) peak/onset time difference; (

**c**) Wavelet analysis for DPL; (

**d**) Wavelet analysis for LH. (Note: all above are calculated based on SPI and SRI at 30-day scale).

Catchments | Longitude (°) | Latitude (°) | Area (km^{2}) | Annual Precipitation (mm) |
---|---|---|---|---|

Dapoling (DPL) | 113.75 | 32.42 | 1640 | 997 |

Changtaiguan (CTG) | 114.07 | 32.32 | 3090 | 1005 |

Xixian (XX) | 114.73 | 32.33 | 10,230 | 1020 |

Huaibin (HB) | 115.42 | 32.43 | 15,780 | 1034 |

Tanjiahe (TJH) | 113.88 | 31.90 | 173 | 1232 |

Zhuganpu (ZGP) | 114.65 | 32.17 | 1639 | 1128 |

Xinxian (XIN) | 114.87 | 31.62 | 274 | 1319 |

Huangchuan (HC) | 115.05 | 32.13 | 2050 | 1202 |

Ruzhou (RZ) | 112.85 | 34.15 | 2912 | 628 |

Xiagushan (XGS) | 112.72 | 33.87 | 359 | 802 |

Zhongtang (ZT) | 112.57 | 33.75 | 467 | 928 |

Luohe (LH) | 114.03 | 33.58 | 12,150 | 767 |

Gaocheng (GC) | 113.13 | 34.40 | 631 | 670 |

Zhongmou (ZM) | 114.03 | 34.73 | 2132 | 634 |

Bantai (BT) | 115.07 | 32.72 | 11,104 | 972 |

Jiangjiaji (JJJ) | 115.73 | 32.30 | 5631 | 1246 |

Index Name | Abbreviation | Details | Units |
---|---|---|---|

Average annual precipitation | P | Average annual precipitation is calculated using Thiessen polygon based on station observational data. | mm |

Seasonality index | SI | The index represents the degree of variability in monthly precipitation within a year [11]. | |

Drainage area | Area | The total drainage area of catchment. | Km^{2} |

Drainage density | Dense | The total length of all the streams and rivers in a drainage basin divided by the total area of catchment. | Km/Km^{2} |

Base flow index | BFI | The ratio of base flow and total runoff. Base flow was separated from the total streamflow using the digital filter method [34]. | - |

Topographic index | TI | ln (α/tanβ) from TOPMODEL [33], α is the cumulative upslope area draining through the per contour length to a pixel and tanβ is the local slope angle of the cell. | - |

NDVI | NDVI | NDVI quantifies vegetation by measuring the difference between near-infrared (which vegetation strongly reflects) and red light. | - |

Ratio of reservoir capacity | Res | The ratio of the reservoir storage capacity to the annual average runoff of the catchment, reflecting the impact of reservoir on runoff (only the large- and medium-sized reservoir are considered). | % |

Ratio of crop land | Crop | The ratio of catchment covered by crop land derived from GlobeLand30 to catchment area, reflecting the proportion of agricultural irrigation consumption in total runoff. | % |

**Table 3.**Partial correlation coefficient between drought characteristics and significant influencing factors.

Area | P | TI | BFI | |
---|---|---|---|---|

HD | −0.431 | −0.684 (*) | −0.140 | 0.225 |

HS | 0.460 | 0.722 (*) | 0.156 | 0.410 |

P_{H|M} | −0.198 | 0.502 | 0.037 | −0.395 |

T_{P} | 0.205 | 0.117 | 0.028 | 0.307 |

Catchment | Area (km^{2}) | Precipitation (mm) | ET (mm) | BFI | TI | Land Cover | |
---|---|---|---|---|---|---|---|

Crop Land | Forests | ||||||

TJH (no reservoir) | 173 | 1232 | 64.2 | 0.140 | 7.811 | 17.80% | 82.10% |

XIN (reservoir) | 274 | 1319 | 64.0 | 0.165 | 7.538 | 13.80% | 81.60% |

Catchment | HD (Day) | HS | T_{P} (Day) | P_{H|M} | P_{H|NM} | ||
---|---|---|---|---|---|---|---|

Average | Maximum | Average | Maximum | ||||

TJH (no reservoir) | 64.6 | 169 | −121 | −277 | 10.7 | 0.48 | 0.31 |

XIN (reservoir) | 62.5 | 163 | −108 | −255 | 11.0 | 0.45 | 0.46 |

Difference (%) | −3.3 | −3.6 | −10.7 | −7.9 | 2.8 | 6.3 | 48.4 |

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## Share and Cite

**MDPI and ACS Style**

Wang, J.; Wang, W.; Cheng, H.; Wang, H.; Zhu, Y. Propagation from Meteorological to Hydrological Drought and Its Influencing Factors in the Huaihe River Basin. *Water* **2021**, *13*, 1985.
https://doi.org/10.3390/w13141985

**AMA Style**

Wang J, Wang W, Cheng H, Wang H, Zhu Y. Propagation from Meteorological to Hydrological Drought and Its Influencing Factors in the Huaihe River Basin. *Water*. 2021; 13(14):1985.
https://doi.org/10.3390/w13141985

**Chicago/Turabian Style**

Wang, Jingshu, Wen Wang, Hui Cheng, Hongjie Wang, and Ye Zhu. 2021. "Propagation from Meteorological to Hydrological Drought and Its Influencing Factors in the Huaihe River Basin" *Water* 13, no. 14: 1985.
https://doi.org/10.3390/w13141985