## Abstract

The Haihe River basin is the main grain production base and the highland of economic strategic development in China. Based on daily meteorological data during 1960–2020, the characteristics of drought evolution in the Haihe River basin were analyzed by the standardized precipitation evapotranspiration index (SPEI). Pearson correlation method and cross-wavelet analysis were used to explore the correlation between the SPEI and climate factors (global warming, sunspots, and atmospheric circulation indices). Global warming has led to a trend of increasing drought in the basin, and there is an obvious zonality in the change of the trend, with the strongest impact on the central region of the basin (112°E–120°E, 38°N–41°N). The SPEI was negatively correlated with the number of sunspots. The more sunspots there were, the more severe the drought in the basin. The drought was most susceptible to the El Niño-Southern Oscillation (ENSO) and the Atlantic Multidecadal Oscillation (AMO), followed by the Arctic Oscillation (AO) and the Pacific Decadal Oscillation (PDO). The North Atlantic Oscillation (NAO), the Pacific North America index (PNA), and the Western Pacific index (WP) were the least associated with the drought in the basin.

## HIGHLIGHTS

The drought trend and the relationship between drought and climatic factors were analyzed.

The drought trend is obviously aggravated in the Haihe River basin.

Drought caused by global warming has an obvious zonal trend.

The more sunspots there were, the more severe the drought.

The drought is mainly affected by the ENSO and AMO.

### Graphical Abstract

## INTRODUCTION

Drought, as an extreme climate event with high frequency, long duration, and wide impact, has seriously affected global economic and social development (Hui *et al.* 2021; Ling *et al.* 2022). A growing number of countries around the world are potentially at risk of drought (Sahana *et al.* 2021). The global economic losses caused by drought account for 42% of total natural disasters every year (Han *et al.* 2021). The research shows that from 1950 to 2008, the global average annual growth rate of drought-stricken areas is about 1.74% (Potop *et al.* 2012; Spinoni *et al.* 2014). Since the mid-1950s, much of North Africa, Alaska, Canada, and Eurasia have experienced widespread droughts (Dai *et al.* 2004; Dai 2011). According to the Intergovernmental Panel on Climate Change (IPCC) Fifth Assessment Report, the average global surface temperature has increased by around 0.85 °C in the past 130 years, and the rising temperature has led to an increasing trend in global drought (Hijioka *et al.* 2014).

The area affected by drought is approximately 20.50 × 10^{4} km^{2} in China, resulting in food loss of 16.26 × 10^{10} kg (Han *et al.* 2021), which is enough to feed 60 million people a year. With the proposal of national strategies such as the Bohai economic circle and Beijing–Tianjin–Hebei integration, higher standards are proposed to ensure water safety in the basin. Since the 1960s, droughts have been experienced frequently in the basin due to climate change and anthropogenic factors. Drought affects an average of roughly 16% of the planted area each year, severely constraining socio-economic development and threatening national food security (Yue *et al.* 2015). To resist or mitigate the negative effects of drought on human beings, it is important and urgent to analyze the evolutionary trends of drought and its causes.

Drought research in the Haihe River basin mainly focuses on the applicability evaluation of drought indicators, drought characteristics analysis, and drought influencing factors analysis. For example, Han *et al.* (2016) compared the applicability of three drought indices (percentage of precipitation departure, precipitation *Z* index, and Palmer drought index) in the basin. Liu *et al.* (2014) and Wang *et al.* (2016) explored the characteristics of drought in the basin by the standardized precipitation index (SPI) and comprehensive meteorological drought index (CI), respectively, and both found a trend of severe drought. Wang *et al.* (2020) analyzed the temporal and spatial evolution characteristics and 500 hPa isopotential height anomaly in the basin. However, the current analysis of the causes of drought is mainly focused on correlation analysis of drought with a (single) climatic factor in the basin. Few studies have combined multiple climatic causes to analyze drought in the basin. Collecting a number of academic articles it can be found that global mean temperature, sunspots, and atmospheric circulation indices are closely related to the occurrence of drought. In terms of frequency and intensity of drought, there is a potential correlation between global mean temperature increase and regional drought (Hijioka *et al.* 2014). Under the impact of global warming, agricultural production has declined in most regions, leading to a food shortage for a growing population (Abrar Faiz *et al.* 2020). Changes in the number of sunspots can cause fluctuations in global received energy, affecting sea surface temperature by changing atmospheric circulation and affecting local climate by changing air-sea coupling (Padmanabhan & Rao 1990). In addition, there is also a certain correlation between regional drought and atmospheric circulation. Some atmospheric circulation indices have potential relationships with climate patterns in northern China (including the Haihe River basin). The characteristics of the Arctic Oscillation (AO) and North Atlantic Oscillation (NAO) in the Northern Hemisphere winter and their impacts on climate change are important indicators for evaluating climate system models (Linderholm *et al.* 2011; Li *et al.* 2021). The Atlantic Multidecadal Oscillation (AMO) is one of the most important interdecadal signals in the world, which can reflect the extreme high-temperature events in North China (Oate-Valdivieso *et al.* 2020). Pacific Decadal Oscillation (PDO) is a strong trigger for climate change and is one of the major factors causing large 10-year climate changes worldwide (Mantua *et al.* 1997). The El Niño-Southern Oscillation (ENSO) reflects the anomalous warming of seawater in the equatorial eastern Pacific. As a first-order external force, it increases the possibility of drought in North China by changing the tropical and subtropical circulation anomalies and influencing the middle and high latitudes through remote correlation (Wang *et al.* 2014). Several studies revealed that climate variables such as ENSO and PDO could aggravate the characteristics, duration, and intensity of droughts (Martins *et al.* 2018; Nieves *et al.* 2022). In recent years, studies have repeatedly confirmed that the Pacific North America index (PNA) and Western Pacific index (WP) are remotely correlated with the extreme climate in North China (Gao & Wang 2017; Yang *et al.* 2019; Wang *et al.* 2021). The analysis of the correlation between the above factors and drought evolution is more significant, which is helpful to reveal the causes of drought evolution in the Haihe River basin more accurately.

In the study, the standardized precipitation evapotranspiration index (SPEI) was applied as a drought indicator to analyze the evolutionary characteristics of drought by Mann–Kendall trend and mutation test based on the measured daily meteorological data (1960–2020). The Pearson correlation method and cross-wavelet analysis were used to analyze the relationship between drought and global warming, sunspots, and atmospheric circulation indices (NAO, AO, PDO, ENSO, PNA, WP, and AMO) in the Haihe River basin. It helps to identify the main climatic factors of drought evolution in the basin. These studies provide theoretical and technical support for drought monitoring and early warning, ecological environment construction, agricultural disaster prevention and mitigation, and rational allocation of water resources.

## REGION AND DATA

### Research area

*et al.*2013; Zhang

*et al.*2017). In this paper, 38 meteorological stations in the basin and two meteorological stations adjacent to the basin were selected (Figure 1).

### Data sources

The daily meteorological data come from China Meteorological Data Service Centre (http://data.cma.cn/), including daily precipitation, maximum temperature, minimum temperature, average temperature, relative humidity, atmospheric pressure, and sunshine hours.

In this paper, we selected the global mean temperature from 1960 to 2020 as an indicator to study the relationship between drought and global warming. Global mean temperature data are from NASA's Goddard Institute of Space Research (GISS) (http://data.giss.nasa.gov/gistemp/). The sunspot data come from World Data Center for the production, preservation and dissemination of the international sunspot number (http://sidc.oma.be/silso/dayssnplot).

The Southern Oscillation Index (SOI) and the mean sea surface temperature (Niño 3.4) were analyzed as important indices for characterizing ENSO. To analyze the main atmospheric circulation indices controlling drought in the Haihe River basin, we selected eight atmospheric circulation indices datasets from the NOAA Climate Prediction Center (https://psl.noaa.gov/data/climateindices/list/), including NAO, AO, PDO, SOI, Niño 3.4, PNA, WP, and AMO.

## METHODS

### Standardized precipitation evapotranspiration index

SPEI was proposed by Vicente-Serrano *et al.* (2010) on the basis of SPI in 2010, and the degree of deviation from the average state of precipitation and potential evapotranspiration difference was used to characterize the dry and wet state of a region. The calculation of potential evapotranspiration in the SPEI includes the Thornthwaite formula (Pereira & Pruitt 2004), Hargreaves formula (Wang *et al.* 2015) and Penman–Monteith formula (Tong *et al.* 2018). The key to SPEI calculation is potential evapotranspiration. Compared with the first two formulas, the potential evapotranspiration based on Penman–Monteith formula is more consistent with the measured data in arid and humid areas (Chen & Sun 2015). Therefore, we use the Penman–Monteith formula to calculate the potential evapotranspiration.

- (1)Calculate the potential evapotranspiration ().where is the slope of the vapor pressure curve (kPa/°C);
*R*is the net radiation at the land surface (MJ/(m_{n}^{2}·d));*G*_{0}is the soil heat flux density; is the psychrometric constant (6.77 Pa/°C);*T*is the mean daily air temperature (°C); is the average daily wind speed at a 2-m height (m/s);*e*is the saturation vapor pressure (kPa); and_{s}*e*is the actual vapor pressure (kPa)._{a} - (2)
- (3)
- (4)
- (5)

The climate category can be classified based on the SPEI: when SPEI ∈ (0.5, +∞), the climate category is ‘wet’, and the greater the SPEI is, the more obvious the wet degree; when SPEI ∈ (−0.5, 0.5), the climate category is ‘normal’; when SPEI ∈ (−∞, −0.5), the climate category is ‘drought’, and the smaller the SPEI is, the more serious the drought.

SPEI has multi-timescale characteristics, SPEI-1 (1-month timescale) reflects monthly wet and dry levels, SPEI-3 (3-month timescale) reflects seasonal wet and dry levels, SPEI-6 (6-month timescale) reflects 6-month scale wet and dry levels, and SPEI-12 (12-month timescale) reflects annual wet and dry levels. In this paper, SPEI-1 and SPEI-12, the drought rules of these two scales have a great impact on agricultural development and ecological environment construction (Shamshirband *et al.* 2020). Therefore, the drought indicators of these two scales are selected for research.

### Mann–Kendall trend and mutation test

#### Mann–Kendall trend test

*i*and

*j*years of the time series;

*n*is the length of the time series; is the number of data points in the

*i*group. When the value of the trend measure index is positive, it means that the time series shows an upward trend. When the value of the trend measure index is negative, it means that the time series shows a downward trend. When the normalized statistic is , it means that the time series passes the significance test, otherwise it fails the significance test.

#### Mann–Kendall mutation test

*et al.*2021). Therefore, it has excellent detection and analysis effect and is often used in temperature and precipitation series change detection.where is the sum of all the numbers of the value corresponding to time

*i*greater than that corresponding to time

*j*;

*n*is the length of time series; and are the data corresponding to the

*i*and

*j*years of time series.

By analyzing the calculated statistical series and , the trend change of the sample series can be obtained. If the value of is greater than 0, the sample series shows an upward trend; otherwise, it shows a downward trend; and when the curve or curve exceeds the critical threshold of significance level, the trend of upward or downward trend of the sample data is very significant. By analyzing the statistical series, the time point at the beginning of the mutation can be determined and the time domain of the mutation can be pointed out. If there is an intersection point between curve and curve , and the intersection point is between the critical level of significance, it indicates that the intersection point of the two curves is the time point at which the mutation may start.

### Pearson correlation method

*et al.*2014). It is an accurate statistical method to measure the linear relationship between two variables, which is applied to time series with normal distribution. Both climate factors and characterizing drought (SPEI) are normally distributed time series, so this method is suitable for the study of climate factors and characterizing drought (SPEI) (Maraun & Kurths 2004). In this paper, we used the Pearson correlation method to analyze the relationship between drought and climate factors. Assuming that the two variables are

*X*as the index characterizing drought (SPEI) and

*Y*as the relevant parameter of climate factors (global mean temperature, sunspots and atmospheric circulation indices), the Pearson correlation coefficient () between the two variables (

*X, Y*) can be calculated by the following equation:where and denote the mean values of

*X*and

*Y*, respectively.

### Cross-wavelet analysis

*et al.*2009; Duan

*et al.*2014). The phase angle of the cross-wavelet reflects the hysteresis characteristics of two time series in different time domains, and the correlation of two time series in the time–frequency domain can be analyzed according to the positive and negative phase angles (Grinsted

*et al.*2004; Dong

*et al.*2013). Assuming that the two time series are and , where

*X*is the index characterizing drought (SPEI) and

*Y*the relevant parameter of climate factors (global mean temperature, sunspots and atmospheric circulation indices), and the continuous wavelet transform is and , respectively, the cross-wavelet spectrum is defined as:where is a complex conjugate of . The cross-wavelet energy spectrum is the absolute value of , that is .

The cross-wavelet energy spectrum was generated by MATLAB software. The cross-wavelet energy spectrum reveals the contribution of the two signal sequences to the overall variance in each harmonic component, thus allowing the frequency structure of the two signals correlated significantly to be examined. We used cross-wavelet energy spectrum to analyze the associations between drought and the climate factors. In the cross-wavelet energy spectrum, the thin black solid line is the influence cone of the wavelet boundary effect, the thick black solid line indicates that the correlation coefficient passes the red noise test with a confidence level of 95%, indicating the two time series are significantly correlated. In the analysis, ‘ → ’ indicates that the drought and climate factors have the same phase change, that is the drought and climate factors are positive correlation. ‘ ← ’ indicates that the drought and climate factors have the opposite phase change, that is the drought and climate factors are negative correlation. ‘ ↑ ’ means that the phase change of the climate factor is 90° ahead of the drought phase, that is, the phase change of the climate factor is 1/4 cycles ahead of the drought phase. Also, ‘ ↓ ’ means that the phase change of the climate factor is 90° behind the drought phase, that is, the phase change of the climate factor is 1/4 cycles behind the drought phase (Jevrejeva *et al.* 2003).

## DROUGHT EVOLUTION CHARACTERISTICS

### Temporal characteristics of drought

*Z*

_{SPEI-12}was −2.07, which passed the significance test of 0.05 (Figure 2(a)). The SPEI-12 in the basin showed regular positive and negative alternations from 1960 to 1980, indicating that drought and wet years alternated. In 1980–1985, SPEI-12 was mainly negative, and in 1985–1990, SPEI-12 was mainly positive. During this period, climate change was abnormal. From 1997 onwards, the SPEI-12 declined rapidly and remained close to negative during the period 1997–2003, showing a significant difference from the previous 30-year trend. The Mann–Kendall statistics continued to decrease, and the mutation occurred in approximately 1992 (Figure 2(b)). The period 1980–1990 was the transitional period of climate change in the basin, and the drought degree increased significantly after this period, which is in agreement with the results of Li

*et al.*(2015).

### Spatial characteristics of drought

*et al.*2017). Local governments should strengthen the construction of drought water sources, build cross-regional water transfer projects, strengthen regional water resources allocation and scheduling, and enhance regional drought emergency water supply capacity.

## CLIMATIC FACTORS ANALYSIS

### Correlation analysis with global warming

*et al.*2014), which has a stronger impact on the central region of the Haihe River basin.

In fact, any parameter significantly related to global mean temperature may be the reason for drought change. For example, without considering other factors, the temperature basically decreases from low latitudes to high latitudes, so the isothermal line is generally parallel to the latitude line, and the latitude has a certain influence on regional drought. Aerosol has a strong correlation with global mean temperature. The change in aerosols may affect drought by changing atmospheric radiation (Cox *et al.* 2008). Therefore, the correlation between global mean temperature and drought in the basin is not a single linear correlation, but there is a complex relationship.

### Correlation analysis with sunspots

### Correlation analysis with atmospheric circulation indices

#### Correlation between SPEI and atmospheric circulation indices

Correlation . | Month . | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

1 . | 2 . | 3 . | 4 . | 5 . | 6 . | 7 . | 8 . | 9 . | 10 . | 11 . | 12 . | |

Positive | SOI | SOI | SOI | SOI | SOI | WP | WP | WP | SOI | NAO | SOI | SOI |

Negative | WP | WP | AMO | AMO | AMO | AMO | AMO | AMO | Niño 3.4 | Niño 3.4 | Niño 3.4 | Niño 3.4 |

Correlation . | Month . | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

1 . | 2 . | 3 . | 4 . | 5 . | 6 . | 7 . | 8 . | 9 . | 10 . | 11 . | 12 . | |

Positive | SOI | SOI | SOI | SOI | SOI | WP | WP | WP | SOI | NAO | SOI | SOI |

Negative | WP | WP | AMO | AMO | AMO | AMO | AMO | AMO | Niño 3.4 | Niño 3.4 | Niño 3.4 | Niño 3.4 |

#### Cross-wavelet analysis between SPEI and atmospheric circulation indices

The cross-wavelet energy spectrum of the SPEI-12 and PDO has a resonance period of 16–48 months from 1968 to 1978 and a positive phase resonance period of 96–128 months from 1994 to 2009, passing the 0.05 significance level. The cross-wavelet energy spectrum of the SPEI-12 and AO showed a resonance period of 17–60 months from 1962 to 2015. The cross-wavelet energy spectrum of the SPEI-12 and AMO has a resonance period of 26–48 months between 1964 and 1974 and a resonance period of 66–128 months from 1970 to 2013. The former is obvious at the 0.05 significance level, while the latter is not obvious at the 0.05 significance level. In the cross-wavelet energy spectrum of the SPEI-12 and Niño3.4, the significant period for continuity of time series data tested at the 0.05 significance level for standard red noise is the strongest, and the dominant resonance period of 9–64 months is shown throughout the study area. The positive correlation is greater before 1985, and the negative correlation is greater after 1985.

In summary, the atmospheric circulation indices that have the greatest impact on drought in the basin are Niño 3.4 and SOI; the effects of AO and NAO on drought are similar, and they have significant effects on temperature and precipitation in the Northern Hemisphere (Wang *et al.* 2021). Niño 3.4 is a positive number or SOI is a negative number, corresponding to the ENSO event, which is continuously circulated over a period of 2–7 years. Niño 3.4 is the only index that has a continuous resonance period during the study period and has the strongest correlation throughout the study period. However, through cross-wavelet analysis, it is found that the results are slightly different from those of the Pearson correlation method. In particular, in the Pearson correlation method (Figure 8(a)), there is a negative correlation between SPEI-12 and AMO, but this law cannot be clearly captured in cross-wavelet analysis (Figure 9). On the one hand, the Pearson correlation method uses monthly scale data for analysis, while cross-wavelet uses annual scale for analysis, so there will be errors with different scales (Band *et al.* 2022). On the other hand, the Pearson correlation method is linear, and cross-wavelet analysis is nonlinear. Nonlinearity is an interaction that is more complex than linearity. It is no longer a simple direct change of linear increase or decrease with a certain variable but may create a situation involving uncertain changes in direction, leading to different increases or decreases.

## CONCLUSION

In this study, the SPEI of 40 meteorological stations during 1960–2020 was used to analyze the drought evolution characteristics and climate factors in the Haihe River basin. The Mann–Kendall trend and mutation test were used to analyze the drought evolution characteristics by SPEI. The Pearson correlation method and cross-wavelet analysis were used to study the correlation between the SPEI and atmospheric circulation indices. The major discoveries are as follows:

The trend of drought variation during 1960–2020 is dominated by a significant increase in the Haihe River basin. In terms of time, drought and wet years alternated between 1960 and 1990, with abrupt changes near 1992 and increased drought in the following 20 years; spatially, almost all of the basin showed a trend of growth in the degree of drought, and the central plain (near Tianjin) showed the most significant increasing drought trend. This increasing trend in drought implies a risk of increased drought in the basin in the future.

Global warming has led to an increased drought trends in the Haihe River basin, and there is an obvious zonality in the change of the trend, with the strongest impact on the central region of the basin (112°E–120° E, 38°N–41° N). The SPEI was negatively correlated with the number of sunspots in the basin. The more sunspots there were, the more severe the drought.

In the past 61 years, the drought was most susceptible to ENSO (SOI and Niño 3.4) and AMO, followed by AO and PDO. NAO, PNA and WP were least associated with the drought in the basin. The SOI and WP have a positive correlation with the SPEI in most months, and the AMO and Niño 3.4 have a negative correlation with the SPEI in most months.

In this paper, the Pearson correlation method and cross-wavelet analysis are not organically combined when studying the correlation between climate factors and drought. Also, this paper did not investigate the complex interrelationships between global warming, sunspots, and atmospheric circulation indices. In future studies, the interconnections among them will be further explored in depth.

## FUNDING

This work was supported by the National Key R&D Program of China (No. 2021YFC3200204) and the National Natural Science Foundation of China (No. 52079125).

## AUTHOR CONTRIBUTIONS

M.L. contributed to investigation, conceptualization, methodology, writing-original draft, funding acquisition, and formal analysis; X.G. contributed to methodology, software, validation, formal analysis, and writing-original draft. Y.Z. contributed to visualization, investigation, software, validation. L.Y. contributed to conceptualization, resources, supervision, writing-review and editing. Q.X. contributed to data reduction and data analysis.

## DATA AVAILABILITY STATEMENT

Data cannot be made publicly available; readers should contact the corresponding author for details.

## CONFLICT OF INTEREST

The authors declare there is no conflict.