Spatiotemporal variations of multi-scale drought in Shandong Province from 1961 to 2017

Drought has caused serious damage to the water resource system and agricultural production in Shandong Province, China. This study calculated the standardized precipitation evapotranspiration index (SPEI) based on the monthly precipitation and average temperature data of 25 meteorological stations in Shandong Province from 1961 to 2017. The trend analysis method and ArcGIS software were utilized to analyze the multi-scale (SPEI-1, SPEI-3, and SPEI-12) spatiotemporal changes of drought. The results revealed that (1) The intensity of drought showed an increasing trend in Shandong Province from 1961 to 2017; (2) The main periods of the drought on the seasonal scale (spring, summer, autumn, and winter) and annual scale were 8 years, 4 years, 15 years, 4 years, and 4 years, respectively; (3) Of the four seasons, the frequency of drought in autumn and winter were the highest. At the annual scale, the high-frequency drought areas were mainly concentrated in the southern mountainous regions; (4) In terms of the spatial change trend of drought, Shandong Province as a whole displayed a trend of becoming wet in the central and southwest regions and dry in the eastern region; and (5) Droughts were discovered to be simultaneously in ﬂ uenced by multiple atmospheric circulation indices in Shandong Province.


GRAPHICAL ABSTRACT INTRODUCTION
Global climate change has become one of the most complex challenges facing mankind in the 21st century and is seriously impacting both the regional ecological environment and the sustainable development of human society (Schär et al. ). Of these effects, the warming of the climate has increased the surface evapotranspiration and precipitation in a strongly regional way (Bongaarts ), resulting in significant increases in the frequency and intensity of extreme climate events such as high temperatures, floods, and droughts (You et al. ; Li et al., ).
Among the many types of extreme climate crises, drought, as the most common natural disaster, displays the characteristics of high frequency, long duration, wide range of impact, and so on (Aghakouchak et al. ). Droughts affect more people than any other hazard, they are one of the main natural hazards regarding their economic and environmental impacts, with negative effects on industrial production, citizens' lives, ecological environment, extension of forests or vegetation activity (Hayes et al. ; Cook et al. ; Hao et al. ). Droughts also lead to a shortage of water resource, impact agricultural production, affect the safety of domestic water for residents, and even cause great harm to the ecological environment (Chen et al. ). As a large agricultural country, China's agriculture is the foundation of its national economy, and drought is the main restricting factor affecting its agricultural economy (Zhang & Diao ). Therefore, timely and accurate research on the spatial and temporal distribution characteristics of regional drought will help us to clearly understand the mechanisms of drought evolution and implement drought prevention and mitigation measures both scientifically and effectively. The potential evapotranspiration over the same period is also taken into account in order to reflect regional droughts more comprehensively. Yu et al. ()

Data source and quality control
The meteorological data in this study came from the   researchers should conduct quality control again in order to eliminate erroneous or suspicious data. This study conducted data quality control and site selection according to the following principles: (1) The data at a given station should not be <57 years; (2) If a station has >5% temperature and precipitation data missing or data missing for >3 consecutive months, the data will not be utilized. When a small amount of data is lacking from a single station, the interpolation of precipitation and temperature from two or more nearby stations is used to fill the gap, so as to obtain the complete data sequence; (3) Rainfall, snowfall, and sleet are the default precipitation types. Ultimately, the monthly precipitation and average temperature data from 25 meteorological stations were selected from 1961 to 2017 for analysis. According to the international seasonal division principle, March-May was defined as spring, June-August as summer, September-November as autumn, and December-February of the next year as winter.
The basic spatial data of Shandong Province used in this study came from the 30 m × 30 m digital elevation model data downloaded from the Geospatial Data Cloud website (http://www.gscloud.cn/).

Large-scale atmospheric circulation
The large-scale ocean atmospheric circulation indices selected for use in this study included the Arctic Oscillation (AO) gov/psd/enso/mei/index.html).

Standardized precipitation evaporation index
In this study, the SPEI was used to examine droughts in Shandong Province. This index was proposed by Vicente- The SPEI is mainly constructed from the difference between precipitation and evapotranspiration. The calculation process is as follows.
First, potential evapotranspiration (PET) is calculated where A represents a constant, H refers to the annual heat index, and T i represents the 30-day average temperature.
The constants H and A are calculated as follows: A ¼ 6:75 Ã 10 À7 H 3 À 7:71 Ã 10 À5 H 2 þ 1:792 Ã 10 À2 H þ 0:49: Second, the differences between monthly precipitation and evapotranspiration are calculated as where D i represents the difference between precipitation and evapotranspiration, and P i and PET i refer to monthly precipitation and evapotranspiration, respectively.
Third, the D i data are sequentially normalized. D i is fitted using a log-logistic probability distribution F(x), which is defined as follows: where α, β, and γ are obtained by linear fitting, via the following calculations: where Γ is the factorial function, and ω 0 , ω 1 , ω 2 are the weighted moments of D i , which are calculated as follows: where N is the number of months in the study.
Finally, the cumulative probability density is standardized: When the probability density P 0.5: If P > 0.5, the value of P can be represented by 1 -P: Drought frequency The formula for calculating the drought frequency P is as follows: where n is the number of droughts in the data series, and m is the number of data series.

Trend analysis
The linear trend analysis in this study utilized two methods: linear trend estimation and the Mann-Kendall trend test.
Linear trend estimation was used to analyze the inter- The linear tendency estimation formula is as follows: where Y is the SPEI value, t is the time, a is the linear trend term, and a × 10 is the change of the SPEI value every 10a,

Analysis of drought periodicity in Shandong Province
In order to study the characteristics of drought periodicity at multiple time scales in Shandong Province, the SPEI-3 and SPEI-12 were examined using Morlet wavelet analysis.  dong Province was the lowest, 25.86% (Figure 8(b)). The drought frequency in summer (25.5%-36.5%) was slightly higher than that in spring, with droughts mainly occurring in northern and southeastern Shandong Province, and the lowest value 25.5% occurring on the southwest and central regions (Figure 8(c)). The frequency of drought was highest in the autumn, ranged from 28% to 40.5%, and the high-frequency areas were mainly concentrated in eastern Shandong (Figure 8(d)). The frequency of drought in winter was slightly lower than that in autumn and was mainly concentrated in eastern Shandong, which reached 40.35%, while other regions consistently ranged from 25% to 33% (Figure 8(e)). At the annual scale, regional differences were relatively large at drought occurrence frequency and unevenly distributed in Shandong Province, and the frequency of drought occurrence was relatively high in the central, south and northwest of Shandong Province, all more than 35%, and the lowest value 26% occurring on the southwest of Shandong Province ( Figure 8(f)).
Spatial distribution characteristics of different drought types at different time scales drought on the southwest region was the lowest, approximately 1-5% (Figure 9(b1)-9(b4)). In summer, the highfrequency area of slight drought was mainly concentrated in the central part of the province, while moderate drought was the opposite, and there was almost no extreme drought in the northern part of Shandong Province (Figure 9(c1)-9(c4)). In autumn, the frequency of slight drought ranged from 8% to 23%, which was the highest of the four seasons, the frequency of moderate and severe drought on the southwest and south region was the highest, 19% and 10.5% respectively (Figure 9(d1)-9(d4)). In winter, the frequency of slight drought ranged from 6% to 23%, which exhibited a high-low-high distribution pattern from northwest to southeast, the frequency of moderate drought varied between 7 and 23%, which was the highest of the four seasons (Figure 9(e1)-9(e4)). At the annual scale, the     The results of this paper can provide reference for local government departments to prevent drought and manage water resources.