# Assessing Agricultural Drought in the Anthropocene: A Modified Palmer Drought Severity Index

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Description of the Study Area

^{2}[22], accounting for approximately 3.4% of the total national area. The Haihe River Basin faces the Bohai Sea to the east and the Loess Plateau to the west, and it adjoins the Yellow River in the south and the Yanshan Mountains in the north, according to the northwest Inner Mongolian Plateau. The mountains and plateaus in the north and west of the basin take up around 60% of the whole area, and have temperate grassland plants and warm temperate deciduous broad-leaved forest [40]. The eastern and southeastern areas mainly comprise the North China Plain, which has a long history of agricultural reclamation and is one of the major grain production areas in China. The double cropping system of winter wheat–summer maize is predominant in the plain area [41,42] and the single cropping system of spring maize is distributed mainly in northern parts of Hebei and Shanxi Provinces.

## 3. Data and Methodology

#### 3.1. Data Sources

#### 3.2. Methodology

_{i}, PL

_{i}, PR

_{i}, and PRO

_{i}are the potential evapotranspiration, recharge, loss and runoff in week i, respectively; and ET

_{i}, L

_{i}, R

_{i}, and RO

_{i}are the actual evapotranspiration, recharge, loss and runoff in week i, respectively. The bar over a term indicates an average value.

_{s,i}and PL

_{u,i}are the potential water loss from the surface and underlying layers in week i (mm), respectively. PE

_{i}is the potential evapotranspiration in week i (mm), which was calculated by the Penman–Monteith method; AWC is the combined available moisture capacity (mm); and S

_{s,i}and S

_{u,i}represent the initial available moisture stored in the surface and underlying layers in week i (mm), respectively.

_{i}and ET

_{i}are the potential evapotranspiration and actual evapotranspiration in week i respectively (mm), I

_{i}is the irrigation amount in week i (mm), P is the precipitation in week i (mm).

_{s,i}and S

_{u,i}represent the initial available moisture stored in the surface and underlying layers in week i respectively (mm); I

_{i}is the irrigation amount in week i (mm); and the L

_{s,i}and L

_{u,i}represent the water loss from the surface and underlying layers in week i, respectively (mm).

_{i}is the potential recharge in week i (mm), and RO

_{i}is the runoff in week i (mm).

_{j}is the irrigation amount in week j (mm); Thd represents the auto-irrigation threshold in the specified growth stage; SW

_{j}is the initial soil moisture content in week j (mm); FC respects the field capacity (mm); D

_{j}is the soil water deficit in week j (mm); I

_{quota}is the irrigation quota in the specified growth stage (mm); m is the annual frequency of irrigation; and W is the annual irrigation quantity per unit area (mm). The irrigation amount varies in different periods of crop growth. In this study, the irrigation quota is based upon irrigation scheduling in the Haihe River Basin, as shown in Table 1.

_{i}is the soil water deficit in week i (mm); AWC is the combined available moisture capacity (mm); and S

_{s,i}and S

_{u,i}represent the initial available moisture stored in the surface and underlying layers in week i (mm), respectively.

_{j}= 0), otherwise, go to the next step.

_{j}= 0, otherwise, go to the next step.

_{j}= 0.

_{j}) is higher than the irrigation quota in the specified growth stage (for example, for the jointing stage for spring maize showed in Table 1, I

_{quota}= 75 mm), I

_{j}= I

_{quota}, otherwise, I

_{j}= D

_{j}.

_{i}is the PDSI value for the ith week and X

_{i−}

_{1}is previous week’s PDSI value.

## 4. Results and Discussion

#### 4.1. Soil Moisture Analyses

#### 4.2. Frequency Analyses

#### 4.3. Time Series Analyses

#### 4.4. Spatial Analyses

## 5. Conclusions

- (1)
- Comparing the farmland soil moisture in Luancheng station, the correlation coefficients between the results simulated by the modified model and the observed values from 2007 to 2012 were 0.73, 0.76, 0.85, 0.51, 0.76 and 0.84, respectively; which had increased by 32.7%, 24.6%, 16.4%, 15.9%, 40.7% and 37.7%, respectively, compared with the performance of the original method. It turned out that the simulation results were ideal and provided a more objective response to the farmland moisture-changing process.
- (2)
- The statistical analyses indicated that the frequencies of mild dry and wet reported by the PDSI were 21% and 14% for Luancheng, and 17% and 13% for Daxing, respectively, which did not fit with the belief that the frequency of mild dry should be approximately equal to mild wet. Contrarily, the IrrPDSI reported a nearly normal distribution, and mild dry and wet occurred with a close frequency (12% for Luancheng and 10% for Daxing, respectively). Moreover, the results showed that 39 of the 47 stations in the study area based on IrrPDSI had nearly normal distributed values, whereas only half of the stations examined based on the PDSI did.
- (3)
- The time series plot of the two PDSIs showed that the IrrPDSI reported a normal or mild wet category in Luancheng station and incipient or mild dry in Daxing station during July and December 2002, respectively; whereas the PDSI reported more negative results than the IrrPDSI. The report of agricultural disasters confirmed that the results reported by the IrrPDSI were more consistent with the real conditions.
- (4)
- The spatial analyses showed that the results reported by IrrPDSI matched historical records better than the PDSI during the irrigated season, which showed that irrigation can usually effectively relieve drought conditions. There were insignificant differences between the distributions of dry–wet based on the two indices during the non-irrigated season as a result of infrequent irrigation.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 4.**The average annual weighting factor related to average moisture demand, average moisture supply and the average absolute moisture anomaly.

**Figure 5.**Time series plot of weekly soil moisture from the water balance models and observations in Luancheng in the years (

**a**) 2007; (

**b**) 2008; (

**c**) 2009; (

**d**) 2010; (

**e**) 2011; (

**f**) 2012. The correlation coefficient (r) is also shown.

**Figure 6.**Plots showing the frequency of the two weekly PDSI values (

**a**) over the entire range of PDSI values and (

**b**) over the major PDSI categories for Luancheng.

**Figure 7.**Plots showing the frequency of the two weekly PDSI values (

**a**) over the entire range of PDSI values and (

**b**) over the major PDSI categories for Daxing.

**Figure 9.**Spatial distribution of dry and wet based on the PDSI in the Haihe River Basin for (

**a**) 21 April; (

**b**) 21 May; (

**c**) 14 July; and (

**d**) 14 August 2011; and (

**e**) 21 April; (

**f**) 21 May; (

**g**) 7 July; and (

**h**) 7 August 2012.

**Figure 10.**Spatial distribution of dry and wet based on the IrrPDSI in the Haihe River Basin for (

**a**) 21 April; (

**b**) 21 May; (

**c**) 14 July; and (

**d**) 14 August 2011; and (

**e**) 21 April; (

**f**) 21 May; (

**g**) 7 July; and (

**h**) 7 August 2012.

Region | Crop Type | Growth Stage for Irrigation | Irrigation | Auto-Irrigation Threshold ^{d} | |
---|---|---|---|---|---|

Frequency | Amount (mm) | ||||

Western Hebei, Beijing, Tianjing and south Shanxi ^{a} | Winter wheat | Sowing (1–10 Octobor) | 1 | 58 | 0.6 |

Tillering (20 November–10 December) | 1 | 80 | 0.5 | ||

Jointing (10 March–14 April) | 1 | 65 | 0.55 | ||

Heading (10–30 April) | 1 | 68 | 0.55 | ||

Filling (1–30 May) | 2 | 75 | 0.55 | ||

67 | 0.55 | ||||

Summer maize | Jointing (1–30 July) | 1 | 64 | 0.55 | |

Filling (20 August–20 September) | 1 | 64 | 0.6 | ||

Northern Shandong, northern Henan and eastern Hebei ^{b} | Winter wheat | Sowing (15–30 Octobor) | 1 | 63 | 0.6 |

Tillering (20 November–10 December) | 1 | 70 | 0.5 | ||

Jointing (10 March–14 April) | 1 | 65 | 0.55 | ||

Heading (10–30 April) | 1 | 70 | 0.55 | ||

Filling (1–30 May) | 2 | 67 | 0.55 | ||

65 | 0.55 | ||||

Summer maize | Jointing (1–20 July) | 1 | 61 | 0.55 | |

Filling (1–30 August) | 1 | 71 | 0.6 | ||

Northern Shanxi and northern Hebei ^{c} | Spring maize | Jointing (10 June–10 July) | 1 | 75 | 0.55 |

Tasseling (20–30 July) | 1 | 75 | 0.6 | ||

Filling (1–30 August) | 1 | 75 | 0.6 |

PDSI Value | Class |
---|---|

≥4.00 | Extreme wet |

3.00 to 3.99 | Severe wet |

2.00 to 2.99 | Moderate wet |

1.00 to 1.99 | Mild wet |

0.50 to 0.99 | Incipient wet |

0.49 to −0.49 | Normal |

−0.50 to −0.99 | Incipient drought |

−1.00 to −1.99 | Mild drought |

−2.00 to −2.99 | Moderate drought |

−3.00 to −3.99 | Severe drought |

≤−4.00 | Extreme drought |

PDSI | IrrPDSI |
---|---|

$\begin{array}{l}L=\{\begin{array}{ll}0\hfill & P\ge PE\hfill \\ {L}_{s}+{L}_{u}\hfill & P<PE\hfill \end{array}\\ Where\text{\hspace{0.17em}\hspace{0.17em}}{L}_{s}=PE-P\text{\hspace{0.17em}}or\text{\hspace{0.17em}}{S}_{s}\hfill \\ \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}{L}_{u}=(PE-P-{L}_{s})\cdot {S}_{u}/AWC\hfill \end{array}$ | $\begin{array}{l}L=\{\begin{array}{ll}0\hfill & P+I\ge PE\hfill \\ {L}_{s}+{L}_{u}\hfill & P+I<PE\hfill \end{array}\\ Where\text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}{L}_{s}=PE-P-I\text{\hspace{0.17em}}or\text{\hspace{0.17em}}{S}_{s}\\ \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}{L}_{u}=(PE-P-I-{L}_{s})\cdot {S}_{u}/AWC\end{array}$ |

$R=\{\begin{array}{ll}0\hfill & \hfill P\le PE\hfill \\ R-PE\hfill & \hfill 0<P-PE<PR\hfill \\ PR\hfill & \hfill P-PE\ge PR\hfill \end{array}$ | $R=\{\begin{array}{ll}0\hfill & \hfill P+I\le PE\hfill \\ R+I-PE\hfill & \hfill 0<P+I-PE<PR\hfill \\ PR\hfill & \hfill P+I-PE\ge PR\hfill \end{array}$ |

$RO=P-ET-PR\text{\hspace{0.17em}}$ | $RO=P+I-ET-PR$ |

$ET=\{\begin{array}{ll}PE\hfill & PE\le P\text{\hspace{0.17em}}\hfill \\ P+L\hfill & PE>P\hfill \end{array}$ | $ET=\{\begin{array}{ll}PE\hfill & PE\le P+I\hfill \\ P+L\hfill & PE>P+I\hfill \end{array}$ |

- | ${I}_{j}=\{\begin{array}{ll}0\hfill & Thd\le S{W}_{j}/FC\hfill \\ Min\left({D}_{j},\text{\hspace{0.17em}}{I}_{quota}\right)\hfill & Thd>S{W}_{j}/FC\hfill \end{array}$ |

$\begin{array}{l}d=P-\stackrel{\u2322}{P}\\ \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}=P-(\alpha \cdot PE+\gamma \cdot PRO+\beta \cdot PR-\delta \cdot PL)\end{array}$ | $\begin{array}{l}d=P+I-\stackrel{\u2322}{Q}\\ \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}=P+I-(\alpha \cdot PE+\gamma \cdot PRO+\beta \cdot PR-\delta \cdot PL)\end{array}$ |

${K}^{\prime}=1.5{\mathrm{log}}_{10}\left[\left(\frac{\overline{PE}+\overline{R}+\overline{RO}}{\overline{P}+\overline{L}}+2.8\right)/\overline{D}\right]+0.5$ | ${K}^{\prime}=1.42\mathrm{ln}\text{\hspace{0.17em}}\left(\frac{\overline{PE}+\overline{R}+\overline{RO}}{\overline{Q}+\overline{L}}/\overline{D}\right)+4.68$ |

$K=\frac{17.67}{{\displaystyle {\sum}_{j=1}^{N}\overline{D}{K}^{\prime}}}{K}^{\prime}$ | $K=\frac{610.35}{{\displaystyle {\sum}_{j=1}^{N}\overline{D}{K}^{\prime}}}{K}^{\prime}$ |

$Z=K\cdot d$ | $Z=K\cdot d$ |

${X}_{i}=0.897{X}_{i-1}+{Z}_{i}/3$ | ${X}_{i}=0.785{X}_{i-1}+{Z}_{i}/45.491$ |

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## Share and Cite

**MDPI and ACS Style**

Yang, M.; Xiao, W.; Zhao, Y.; Li, X.; Lu, F.; Lu, C.; Chen, Y.
Assessing Agricultural Drought in the Anthropocene: A Modified Palmer Drought Severity Index. *Water* **2017**, *9*, 725.
https://doi.org/10.3390/w9100725

**AMA Style**

Yang M, Xiao W, Zhao Y, Li X, Lu F, Lu C, Chen Y.
Assessing Agricultural Drought in the Anthropocene: A Modified Palmer Drought Severity Index. *Water*. 2017; 9(10):725.
https://doi.org/10.3390/w9100725

**Chicago/Turabian Style**

Yang, Mingzhi, Weihua Xiao, Yong Zhao, Xudong Li, Fan Lu, Chuiyu Lu, and Yan Chen.
2017. "Assessing Agricultural Drought in the Anthropocene: A Modified Palmer Drought Severity Index" *Water* 9, no. 10: 725.
https://doi.org/10.3390/w9100725