# Drought Analysis in the Yellow River Basin Based on a Short-Scalar Palmer Drought Severity Index

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## Abstract

**:**

## 1. Introduction

## 2. Study Area and Data

#### 2.1. Study Area

^{2}. From northwest to southeast, the elevation presents a gradually decreased pattern and ranges between 1 and 6199 m above the sea level. The Tibet Plateau, Loess Plateau and Huang-Huai-Hai Plain are three primary geomorphic types of this basin [28]. Climatically, the mean annual temperature varies between 4 and 14 °C. Precipitation is unevenly distributed over YRB which divides the whole basin into four climate zones from northwest to southeast, i.e., arid, semi-arid, semi-humid and humid zones. In addition, precipitation and temperature have significant seasonality, where summer is generally rainy and hot while winter is cold and dry.

#### 2.2. Data

## 3. Methods

#### 3.1. VIC Model Simulation

#### 3.2. Modified scPDSI

_{2}which could correct the high frequency of extreme events and realize automatic calibration of the index behaviors at any locations (Figure 2). Focusing on the hydrologic accounting module (improvement 1) and standardization process (improvement 2), further modifications on scPDSI were conducted in following sections to address the shortcomings of moisture estimation and time scale. Implementation of the method was based on the source code (compiling in Visual C) of scPDSI, which was downloaded from the National Agricultural Decision Support System (NADSS, available online at http://nadss.unl.edu/).

#### 3.2.1. Coupling VIC Model for Hydrologic Accounting

_{i}and ${\stackrel{~}{\mathrm{P}}}_{i}$ represent the water supply and demand for the ith (i = 1, 2, …, 12) month in a calendar year. α, β, γ, and δ are weighting coefficients defined in the following manner:

_{0}represents the moisture storage of all soil layers at the beginning of a specific month; Similarly, S

_{s}, S

_{m}, and S

_{b}denote the moisture storage for surface, middle and bottom soil layers, respectively. All above variables are in unit of mm.

#### 3.2.2. Time Scale Modification

_{1}with a new Palmer variant, namely the Z index generated. Then Wells et al. [27] employed ten Z values accumulated at 3, 6, 9, 12, 18, 24, 30, 36, 42, and 48 months, respectively, to represent the extremely dry condition (the top-right panel of Figure 2). A recent literature by Liu et al. [26] found that different selections of cumulative Z values will influence the time scale of the index in a significant way. To make scPDSI capable for detecting droughts of short time scales, in this study, a new sample of cumulative Z values, accumulated at 1–9 months are used instead (the bottom-right panel of Figure 2). These 9 points are further fitted by a linear regression equation:

_{t}represents the current PDSI value. C is the value of calibration index (e.g., 4, 3, …, 4). Palmer assumed that the change between any two values of X

_{t}is constant for a given severity of drought. Based on this hypothesis, equations for computing duration factors p and q can be obtained through a complicated formula derivation process (see Wells et al. [27] for detail):

_{i}of ith month is expressed as the weighted sum of the precedent PDSI value X

_{i}

_{−1}and the current moisture anomaly Z

_{i}:

_{2}, and a backtracking process (the solid arrows in Figure 2).

#### 3.3. Standardized Drought Indices

## 4. Results and Discussion

#### 4.1. Model Performance

#### 4.2. Time Scale and Frequency Analysis

#### 4.3. Drought Trend and Its Influencing Factors

#### 4.4. Performances in Drought Monitoring

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Locations of national meteorological stations, soil moisture observation sites and hydrological stations over YRB.

**Figure 2.**Flowchart of modified scPDSI’s procedure. The dashed arrows direct the computation process of PDSI, and the solid arrows denote the modifications in scPDSI. Improvement steps 1 and 2 show our improvements to the hydrologic accounting and standardization process, respectively.

**Figure 3.**Daily calibration (1961–1990) and validation (1991–2012) results for five hydrological stations situated at the (

**a**) upper, (

**b**–

**e**) middle and downstream parts of YRB.

**Figure 4.**Spatial distribution of correlation coefficients between VIC simulated (average values of top two soil layers) and observed monthly soil moisture during 1991–2008.

**Figure 5.**(

**a**) Average autocorrelation coefficients of VIC-scPDSI9, SPI3, SPEI3 and scPDSI over YRB. The blue dashed line is the boundary (corresponding to the 0.05 significance level) of the presence of serial autocorrelation. (

**b**) The boxplots of lagged months when the drought index series are not correlated.

**Figure 6.**Time series of (

**a**) SPI, (

**b**) SPEI, (

**c**) scPDSI, and (

**d**) VIC-scPDSI9 values averaged over the whole YRB. The shadows denote the 25th–75th percentile range of index values over YRB.

**Figure 7.**(

**a**) Frequency distributions of scPDSI and VIC-scPDSI9 values. The grey and blue shadows denote the 75th–90th percentile range of frequency values over YRB. (

**b**) The boxplots of scPDSI and VIC-scPDSI9 values of 1500 grids at extremely and severe dry levels.

**Figure 8.**Spatial distribution of MK test statistics for annual and seasonal index values of VIC-scPDSI9 (left column), SPI3 (middle column), and SPEI3 (right column), respectively. The absolute values of MK statistics of 2.576, 1.96 and 1.645 correspond to the 1, 5 and 10% significance levels, respectively.

**Figure 9.**The boxplots of correlation coefficients between VIC-scPDSI9, SPI3, SPEI3 against five hydrological variables.

**Figure 11.**Time series of drought area at mildly to extremely dry levels by VIC-scPDSI9. The small rectangle panels show the spatial distribution of accumulated drought severity for six typical drought events.

**Figure 12.**Spatial evolution of the 2000 drought indicated by (

**a**–

**d**) VIC-scPDSI9, (

**e**–

**h**) ESACCI anomaly, and (

**i**–

**k**) NDVI anomaly.

Hydrological Station | Abbreviation | Longitude (°E) | Latitude (°N) | Digital Elevation Model (m) | Drainage Area (10^{4} km^{2}) | Areal Average Precipitation (mm/year) |
---|---|---|---|---|---|---|

Tangnaihai | TNH | 100°09′ | 35°30′ | 2960 | 12.2 | 520.8 |

Lanzhou | LZ | 103°49′ | 36°04′ | 1774 | 10.07 | 480.7 |

Toudaoguai | TDG | 111°04′ | 40°16′ | 1000 | 14.53 | 390.9 |

Wubao | WB | 110°43′ | 37°27′ | 960 | 6.56 | 394.5 |

Longmen | LM | 110°35′ | 35°40′ | 393 | 6.24 | 402.2 |

Hejin | HJ | 110°48′ | 35°34′ | 553 | 12.21 | 485.7 |

Xianyang | XY | 108°42′ | 34°19′ | 406 | 10.07 | 555.1 |

Huaxian | HX | 109°46′ | 34°35′ | 481 | 14.53 | 544.3 |

Sanmenxia | SMX | 111°22′ | 34°49′ | 614 | 4.75 | 398.2 |

Huayuankou | HYK | 113°39′ | 34°55′ | 106 | 4.18 | 440.2 |

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## Share and Cite

**MDPI and ACS Style**

Zhu, Y.; Liu, Y.; Ma, X.; Ren, L.; Singh, V.P.
Drought Analysis in the Yellow River Basin Based on a Short-Scalar Palmer Drought Severity Index. *Water* **2018**, *10*, 1526.
https://doi.org/10.3390/w10111526

**AMA Style**

Zhu Y, Liu Y, Ma X, Ren L, Singh VP.
Drought Analysis in the Yellow River Basin Based on a Short-Scalar Palmer Drought Severity Index. *Water*. 2018; 10(11):1526.
https://doi.org/10.3390/w10111526

**Chicago/Turabian Style**

Zhu, Ye, Yi Liu, Xieyao Ma, Liliang Ren, and Vijay P. Singh.
2018. "Drought Analysis in the Yellow River Basin Based on a Short-Scalar Palmer Drought Severity Index" *Water* 10, no. 11: 1526.
https://doi.org/10.3390/w10111526