Temporal and spatial distributions of precipitation on the Huang-Huai-Hai Plain during 1960 – 2019, China

The Huang-Huai-Hai Plain is an important commercial grain production base in China. Understanding the temporal and spatial variations in precipitation can help prevent drought and ﬂ ood disasters and ensure food security. Based on the precipitation data for the Huang-Huai-Hai Plain from 1960 to 2019, this study analysed the spatiotemporal distribution of total precipitation at different time scales using the Mann – Kendall test, the wavelet analysis, the empirical orthogonal function (EOF), and the centre-of-gravity model. The results were as follows: (1) The winter precipitation showed a signi ﬁ cant upward trend on the Huang-Huai-Hai Plain, while other seasonal trends were not signi ﬁ cant. (2) The precipitation on the Huang-Huai-Hai Plain shows a zonal decreasing distribution from southeast to northwest. (3) The application of the EOF method revealed the temporal and spatial distribution characteristics of the precipitation ﬁ eld. The cumulative variance contribution rate of the ﬁ rst two eigenvectors reached 51.5%, revealing two typical distribution ﬁ elds, namely a ‘ global pattern ’ and a ‘ north-south pattern ’ . The ‘ global pattern ’ is the decisive mode, indicating that precipitation on the Huang-Huai-Hai Plain is affected by large-scale weather systems. (4) The annual precipitation barycentres on the Huang-Huai-Hai Plain were located in Jining city and Taian city, Shandong Province, and the spatial distribution pattern was north-south. The annual precipitation barycentres tended to move southwest, but the trend was not obvious. The annual precipitation barycentre is expected to continue to shift to the north in 2020.


GRAPHICAL ABSTRACT INTRODUCTION
In recent years, the global climate has been abnormal, and the surface temperature has continued to increase.
Droughts, heavy rains, and floods have occurred frequently and have been widely distributed and severe (Costa & Soares ). Precipitation is an important indicator to describe the climate characteristics of a specific area. The temporal and spatial distributions of precipitation directly affect the regional hydrological situation and the temporal and spatial distributions of water resources (Aziz & Burn ). In the research on the impact of climate change on China's water cycle and water resources, many studies have been carried out in the past 20 years and some new insights have been obtained. For example, the study found that the national average annual precipitation in the past half-century has exhibited obvious decadal and multi-decadal fluctuations (Liu et al. a, b; Ren et al. ).
Although the overall trend of precipitation in China is not obvious, the spatial difference is significant. Precipitation

).
As to the reasons for the long-term trend of precipitation in some regions, some studies believe that it may be related to global warming (Li & Luo ). The Huang-Huai-Hai Plain is located in eastern China. The plain has a warm temperate monsoon climate with co-occurring rain and heat, and it is a vital commodity grain base in China.
Affected by climate change, precipitation on the Huang-Huai-Hai Plain showed a decreasing trend and the degree of temporal and spatial variability increased. This has further aggravated the tight water shortage situation (Rong & Luo ), seriously threatening the area's agricultural production and the safety of residents' domestic water (Zhang et al. ). Therefore, understanding the characteristics of the temporal and spatial changes in precipitation is of great significance to the assessment and management of water resources, flood control and drought relief, and agricultural arrangements on the Huang-Huai-Hai Plain (Worku et al. ). () analysed the temporal and spatial characteristics of extreme precipitation on the Huang-Huai-Hai Plain. However, there are few studies on the temporal and spatial variation characteristics of total precipitation on the Huang-Huai-Hai Plain. The precipitation barycentre can reveal the overall distribution characteristics of regional precipitation.
Its dynamic trajectory reflects the dispersion, transfer, and dominant distribution of precipitation, which is helpful when analysing the differences in and balance of regional precipitation (Luo et al. ). However, current research on the distribution and shifts in precipitation barycentres on the Huang-Huai-Hai Plain is relatively lacking.
Based on monthly precipitation data on the Huang-Huai-Hai Plain over the past 60 years, this paper analysed the temporal and spatial characteristics of total precipitation in the study area and revealed the migration of the precipitation barycentre in the past 60 years using the M-K test, wavelet analysis, the empirical orthogonal function (EOF), and the centre-of-gravity model. This study is expected to provide references for the sustainable use of water resources, agricultural production, and disaster prevention on the Huang-Huai-Hai Plain.

Study region
The Huang-Huai-Hai Plain is located between 32-40 N and 112-121 E, with a plain area of 3.1 × 10 5 km 2 (27% of the total plain area in China), and it includes most or part of

Mann-Kendall test
where if Z is greater than 0, the sample data shows an increasing trend, and if Z is less than 0, the sample data shows a decreasing trend. At jZj values greater than or equal to 1.28, 1.64, and 2.32, the sample data has passed the significance test with a reliability of 90, 95, and 99%, respectively. Huai-Hai Plain. Its mother wavelet is ψ(t) ¼ e ict e Àt 2 =2 , the processed data represent the anomaly value, and the wavelet variance is calculated according to the obtained wavelet coefficients. The specific calculation formula is as follows: where Var(a) and W f (a,b) are the wavelet variance and wavelet coefficient, respectively.

Empirical orthogonal function
EOF is a method used to analyse matrix data structure features and extract main data features. It can reflect the spatial distribution characteristics of precipitation fields to a certain extent (Sarkar & Kafatos ). Before analysis, the selected data are usually processed into the anomalous form to obtain X m×n , where m is the number of stations and n is the number of years. We decompose the matrix X m×n , that is,

Centre-of-gravity model
The centre-of-gravity model is a concept originally from physics, and it refers to the point through which the resultant force of gravity of the fulcrum of an object in any orientation passes. The concept of the centre of gravity is extended to an area, that is, the regional centre of gravity. The regional centre of gravity, also known as the spatial average, is the extent of the average of a certain geographic element or development element in a two-dimensional space. It refers to the moment when a certain geographic or development element reaches a balance on the spatial plane within a certain period. The regional centre of gravity not only helps in analysing the development process, status, and trend of regional elements but also reflects the spatial fluidity and aggregation of regional elements. The regional centre of gravity is generally calculated by the centre-of-gravity model. or interannual precipitation barycentre of the area is calculated as follows: where X and Y are the longitude and latitude coordinates, respectively, of the centre of gravity of the monthly or interannual precipitation; X i and Y i are the longitude and latitude coordinates, respectively, of the ith weather station; P i is the monthly or interannual precipitation of the ith weather station; and n is the total number of meteorological stations in the area.

Temporal variation characteristics of precipitation
Precipitation trend analysis   periodic changes at the scales of 10-14a and 17-23a, both of which experienced 2.5 alternating cycles of high and low rainfall. The first main period was 23a. The autumn precipitation anomaly sequence exhibited noticeable periodic changes at the two scales of 14-18a and 16-21a. It has experienced 3 and 2 alternating cycles of high and low rainfall, respectively. The first main period was 12a. The winter precipitation anomaly sequence had noticeable periodic changes at the two scales of 12-16a and 14-26a, both of which included 1.5 alternating cycles of high and low rainfall. The first main period was 21a. The annual precipitation anomaly sequence on the Huang-Huai-Hai Plain had two-scale change cycles of 8-14a and 21-26a, both of which had 1.5 alternating cycles of high and low rainfall.
The first main period was 10a.

Spatial distribution characteristics of precipitation
Spatial distribution of precipitation and its variability  Hai Plain. The spatial distribution map of mode 1 and mode 2 of the Huang-Huai-Hai Plain is shown in Figure 5.
The variance contribution rate of the first eigenvector is 33.1%, which is much higher than the contribution rate of the second mode. Thus, it can reflect the main characteristics of spatial precipitation changes on the Huang-Huai-Hai Plain and is a decisive mode. Figure 5   Niño event has officially formed in 2020 (weak intensity).
Affected by this El Niño event, in the summer of 2020, the intensity of the subtropical high in the western Pacific will be relatively strong, and the precipitation in China will generally be distributed in a spatial pattern of 'more in the north and south and less in the middle'. Higher precipitation occurs in summer, and floods are stronger than droughts. It is expected that the precipitation barycentre in 2020 will continue to shift to the north.

CONCLUSIONS
(1) The annual precipitation on the Huang-Huai-Hai Plain exhibited obvious interannual and interdecadal changes.
The precipitation showed an upward trend in spring and winter and a downward trend in summer and autumn.
The precipitation in winter exhibited a significant upward trend. Annual and seasonal precipitation on the Huang-Huai-Hai Plain had obvious periodic characteristics of multiyear changes. In the research time period, most of them experienced 1.5 or 2.5 alternating cycles of high and low rainfall. In terms of primary cycles, the first main periods of the precipitation sequence in spring, summer, autumn, and winter were 9a, 23a, 12a, and 21a, respectively. The first main period of the annual precipitation series was 10a.
(2) The annual precipitation on the Huang-Huai-Hai Plain was unevenly distributed. The precipitation showed a zonally decreasing distribution from the southeast to northwest. The climate tendency rate of the Huang-Huai-Hai Plain was distributed in the interval of À32 to 24 mm/10a. The largest increase in precipitation occurred in Fuyang city and Bengbu city in Anhui Province. The largest decrease in precipitation occurred in Tangshan city and Qinhuangdao city in Hebei Province.
The application of the EOF method revealed the temporal and spatial distribution characteristics of the precipitation field. There were two main types of spatial distributions of annual precipitation on the Huang-Huai-Hai Plain: a 'global pattern' and a 'north-south pattern'.
The 'global pattern' is a decisive mode.
(3) The interannual precipitation barycentres on the Huang-Huai-Hai Plain were distributed in Jining city and Taian city, Shandong Province. The spatial distribution pattern of the precipitation barycentres was in the south-north direction as a whole, with a small degree of dispersion and obvious directionality. In the past 60 years, the longitudes and latitudes of the interannual precipitation barycentres showed a nonsignificant decrease. Therefore, the precipitation barycentres generally moved to the southwest, but the trend was not obvious. It is expected that the precipitation barycentre in 2020 will continue to shift to the north.