# Identification of Seasonal Sub-Regions of the Drought in the North China Plain

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Area and Data Source

#### 2.2. Standardized Precipitation Evapotranspiration Index

^{−2}/d), when the calculated time step is less than 10 days, it can be ignored; R

_{n}stands for net radiation (MJm

^{−2}/d); γ for hygroscope constant (kPa/°C); T is the daily average temperature (°C); u

_{2}is the wind speed at 2 m above the ground (m/s); Δ is the slope between saturated vapor pressure and temperature curve under a given temperature (kPa/°C); e

_{s}is the saturated vapor pressure (kPa), and e

_{a}is the actual vapor pressure in the air (kPa). R

_{n}can be calculated by solar radiation (R

_{s}) [40]. In Equation (2), n is sunshine hours (h), N is the maximum possible duration of sunshine or daylight (h), R

_{a}is extraterrestrial radiation (MJm

^{−2}/d); a

_{s}and b

_{s}stand for empirical coefficients of recommended values 0.25 and 0.5 respectively [42].

_{i}= P − PET. According to the procedure of Vicente-Serrano (2010), the three-parameter log-logistic probability distribution is used to simulate the rate of water equilibrium accumulation [34] but the probabilistic weighted moment of the original data sequence used in its calculation formula is replaced by unbiased estimation in this study [38]. The probability density function (Equation (3)) and probability distribution function (Equation (4)) of a three-parameter log-logistic are expressed as:

_{i}values in the range (γ< D

_{i}< ∞). Parameters of the log-logistic distribution can be obtained following the L-moment procedure [43]. When L-moments are calculated, the parameters can be obtained following Singh et al. [44]:

_{s}is the probability weighted moments of order s, which can be estimated by unbiased estimation [34,45,46]:

_{i}value, P = 1 − F(x). If P > 0.5, then P is replaced by 1 − P and the sign of the resultant SPEI is reversed. The constants are C

_{0}= 2.515517, C

_{1}= 0.802853, C

_{2}= 0.010328, d

_{1}= 1.432788, d

_{2}= 0.189269, and d

_{3}= 0.001308 [34]. The value range of SPEI is [−3~3]. Positive and negative values indicate wetness and drought, respectively. Kolmogorov–Smirnov test was performed on the fitting model between the difference between precipitation and PET and the expected value of the log-logical distribution. The data was proved to come from the same distribution, which indicates that the statistical assumptions will be proved to be valid in the North China Plain. The monitoring effect of this drought index was verified by using historical documents and reference materials [47].

#### 2.3. Empirical Orthogonal Function Analysis

_{ij}is the jth observation value at the ith meteorological station. And X

_{m×n}can be seen as a linear combination of k spatial feature vectors and corresponding time weight series:

## 3. Results

#### 3.1. Seasonal rEOFs

#### 3.1.1. Spring (March/April/May)

#### 3.1.2. Summer (June/July/August)

#### 3.1.3. Fall (September/October/November)

#### 3.1.4. Winter (December/January/February)

#### 3.2. Seasonal Trends

#### 3.3. Correlation of Variation in Subregions

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Study area of the North China Plain region with red dots that illustrate meteorological station.

**Figure 2.**Sub-regions recognized in the North China Plain for spring drought variability (

**a**) and the standardized rotated principal component (rPC) time series for sub-regions in spring (

**b**). Each sub-region in (

**a**) has a number that corresponds to its rPC time series in (

**b**), respectively. Sub-region boundaries are thick black lines. The color bar on (

**a**) represents the correlation coefficient between the time series of rPC and the original drought data set of each meteorological station (interpolation using inverse distance weighted method). The color bar on the right represents the magnitude and sign of each rPC time series from 1960 to 2017. Negative and positive rPC values indicate dry and wet conditions, respectively. Time series of rPC are 9-year running average filtered.

**Figure 3.**Sub-regions recognized in the North China Plain for summer drought variability (

**a**) and the standardized rotated principal component (rPC) time series for sub-regions in summer (

**b**). Each sub-region in (

**a**) has a number that corresponds to its rPC time series in (

**b**), respectively.

**Figure 4.**Sub-regions recognized in the North China Plain for fall drought variability (

**a**) and the standardized rotated principal component (rPC) time series for sub-regions in fall (

**b**). Each sub-region in (

**a**) has a number that corresponds to its rPC time series in (

**b**), respectively.

**Figure 5.**Sub-regions recognized in the North China Plain for winter drought variability (

**a**) and the standardized rotated principal component (rPC) time series for sub-regions in winter (

**b**). Each sub-region in (

**a**) has a number that corresponds to its rPC time series in (

**b**), respectively.

**Figure 6.**Sub-regions show significant trends in seasonal analysis. The symbol (

**a**–

**d**) stands for sub-region 5 of spring, sub-region 4 of summer, sub-region 6 of fall, and sub-region 7 of winter, respectively. Uf is a sequence of statistics calculated in chronological sequence. Ub is a sequence of statistics calculated in reverse chronological sequence. If the value of Uf or Ub is greater than 0, it indicates an upward trend while is shows a downward trend when the value is less than 0. When they pass a critical line, it indicates a significant upward or downward trend.

**Figure 7.**Trends for Standardized Precipitation Evapotranspiration Index (SPEI) between 1960 and 2017 for (

**a)**(spring), (

**b**) (summer), (

**c**) (fall), and (

**d**) (winter). Only sub-regions with statistically significant trends using the modified Mann–Kendall test (significance level 0.05) are indicated in the sub-region code. The trend is interpolated by inverse distance weighting.

**Figure 8.**The correlation coefficients between sub-region rPC time series. The symbol (

**a**–

**d**) stands for spring, summer, fall, and winter, respectively.

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**MDPI and ACS Style**

Cui, Y.; Zhang, B.; Huang, H.; Wang, X.; Zeng, J.; Jiao, W.; Yao, R.
Identification of Seasonal Sub-Regions of the Drought in the North China Plain. *Water* **2020**, *12*, 3447.
https://doi.org/10.3390/w12123447

**AMA Style**

Cui Y, Zhang B, Huang H, Wang X, Zeng J, Jiao W, Yao R.
Identification of Seasonal Sub-Regions of the Drought in the North China Plain. *Water*. 2020; 12(12):3447.
https://doi.org/10.3390/w12123447

**Chicago/Turabian Style**

Cui, Yanqiang, Bo Zhang, Hao Huang, Xiaodan Wang, Jianjun Zeng, Wenhui Jiao, and Rongpeng Yao.
2020. "Identification of Seasonal Sub-Regions of the Drought in the North China Plain" *Water* 12, no. 12: 3447.
https://doi.org/10.3390/w12123447