Precipitation is widely considered as a crucial index toward the apprehension of global climate change. Hence, it becomes imperative to explore spatiotemporal patterns and the interlinked factors of precipitation in the basin. In the study, the spatial and temporal variability of precipitation and the individual or integrated effects of various atmospheric teleconnections on precipitation variations are explored in the Yellow River Basin. The total precipitation showed a slightly declining tendency during 1950–2019 and the dependence relationship of precipitation gradient on latitude and longitude is different in various seasons and elevations. The spatiotemporal variability of precipitation is more sensitive to the latitude gradient. For each 1-degree increase in longitude and latitude, the average annual precipitation increases/decreases by 10.73 and 57.24 mm, respectively. Moreover, the precipitation spatiotemporal patterns could be interpreted by four empirical orthogonal functions (EOFs) modes about 71.9% of precipitation variations. The strength of the linkages between various circulation factors and precipitation varied at different time scales. The integrated effects of multiple factors should be taken into consideration in explaining precipitation variability at all time scales. It is expected that the study can be helpful for understanding the internal mechanism of the hydrological cycle in the YRB.

  • Long-term spatiotemporal variability of precipitation was explored in the Yellow River Basin.

  • Teleconnection between precipitation and circulation indices was detected.

  • New insights into coupled effects of multiple atmospheric teleconnections on precipitation.

Graphical Abstract

Graphical Abstract
Graphical Abstract

Precipitation is an irreplaceable link in the local or global hydrological cycle process. Its variability regulates the plant reproduction and growth, the amount of river runoff, and phenology as well as the ecosystem stability in the arid and semi-arid region of the Yellow River Basin (YRB) (Wang et al. 2017; Xue et al. 2017). Moreover, part of the terrestrial freshwater mainly comes from precipitation, which is a limited and scarce resource of the region. It is not only owing to its unpredictable and unstable availability but also its severe scarcity in the YRB (Liu et al. 2019a). The precipitation variations have shown significant temporal and spatial variability at the basin due to the complexity of climate patterns and terrain of the basin (Gao & Wang 2017). Meanwhile, human-induced greenhouse gas emissions combined with climate changes have contributed to global warming, which is further intensified by the redistribution of global precipitation resources in space and time (Liu et al. 2019a). Consequently, the trends and variations of precipitation need to be continuously explored and studied, especially the precipitation spatiotemporal patterns and underlying causes.

Precipitation is a typical climate variable that varies over time and space, which would be more suitable for analyzing precipitation variability by linking temporal and spatial changes. Moreover, with the rapidly changing environment, the precipitation series have a significant nonstationary behavior because of the effects of multifarious driving factors (Guan et al. 2019). Hence, substantial studies have been made in exploring the spatiotemporal and trend changes of precipitation in various parts of the world (Qin & Xie 2016; Wu et al. 2016; Yang et al. 2020; Mathew et al. 2021). Zhang et al. (2014) pointed out that the precipitation was gradually decreasing and the rainstorm events were unevenly distributed in the YRB. The change in precipitation also attracts more attention in the southern Mongolian plateau, including the duration and frequency of the precipitation (Wang et al. 2021b). Moreover, Gherardi & Sala (2019) found that extreme precipitation events tended to increase over the global arid regions at different temporal scales. The extreme precipitation events also exhibited an increased tendency in spatial coverage and frequency in the the Yangtze River Basin since 1970 (Li et al. 2021). Global climate change has brought varying degrees of impact on precipitation in various regions. Consequently, the study of spatiotemporal patterns and trend variability of precipitation is imperative in the Yellow River Basin (YRB).

The spatiotemporal variability of precipitation is strongly correlated with global atmospheric teleconnections (Nalley et al. 2019; Wang et al. 2020). There was an intimate association between the precipitation dipole pattern and the summer North Atlantic Oscillation (NAO) in the Tibetan Plateau. However, the relationship had been weakened because of the regional variation of atmospheric circulation, which is caused by the asymmetrical wave propagation around Eurasia since the late 1990s (Liu et al. 2021). Mohammadi et al. (2020) investigated the temporal and spatial teleconnections among Peruvian precipitation and other oceanic oscillations. And they pointed out the El Niño/Southern Oscillation (ENSO) is the major climate control factor for extremely dry or wet conditions in Peru. Xu et al. (2015) mentioned the change in Pacific Decadal Oscillation (PDO) phase might affect the precipitation variation of southern China because of the atmospheric circulation characteristics over Eurasia. Besides, substantial research has indicated that the Arctic Oscillation (AO) was a major synoptic factor influencing the change of precipitation in the middle to high latitudes of the Northern Hemisphere (Givati & Rosenfeld 2013; Wang et al. 2020). Recently, the comprehensive effects of various atmospheric circulation elements on spatial consistency and time variation of precipitation have been a research hotspot (Jiang et al. 2013; Nalley et al. 2019; Li et al. 2021). For instance, the ENSO combined with PDO has a dominant integrated effect on the winter regional extreme rainfall at large scales on time in the Yangtze River Basin (Li et al. 2021). Nalley et al. (2019) emphasized that the collective influence of multiple teleconnection factors should be considered when explaining the precipitation variability. Additionally, the YRB has a large range of longitude and latitude, and therefore, the characteristics of the climate system and its causes are very complex (Liu et al. 2019b; Wang et al. 2022). The precipitation variability over time and space of the YRB is not only affected by internal dynamical causes and thermal conditions, but also by the external forcing factors such as the thermal forcing of the Tibetan Plateau and various atmospheric circulations (Liu et al. 2008, 2021; Zhang et al. 2014; Xu et al. 2015).

Nevertheless, there are fewer studies on long-term precipitation trend variations and spatiotemporal consistency in the YRB. And then, the individual or coupled effects of various teleconnection factors on the precipitation are especially far less known. The individual or coupled effects of various teleconnection factors on precipitation are especially far less known. And then, the bivariate wavelet coherence (WTC) provided us with effective methods to reveal the interactions of two nonlinear hydrometeorological time series at different time–frequency domains (Wang et al. 2021a). However, the WTC method would lose its usefulness when more than three variables are involved in the study. Hence, the novel approach of multiple wavelet coherence (MWC) is proposed based on the WTC method (Hu & Si 2016). Moreover, Hu & Si (2016) also compared the MWC with multivariate empirical mode decomposition and multiple spectral coherence methods and they pointed out that the MWC method had a significant advantage in revealing the scale independence relationships of multiple variables.

Thus, the main objectives of this study are as follows: (1) to assess the long-term spatiotemporal trends and distribution variations of precipitation in the YRB; (2) to evaluate the precipitation gradient against the elevation, longitude, and latitude; (3) to analyze the dominant spatiotemporal modes of annual precipitation; and (4) to explore the individual or comprehensive impacts of diversified atmospheric circulation factors (ENSO, NAO, PDO, and AO) on the precipitation variability in the YRB.

Study area

The YRB covers 795,000 km2, which is from 95°53′E to 119°05′E and from 32°10′N to 41°50′N. It stretches across four geomorphological units from west to east: the Tibetan Plateau, Inner Mongolia Plateau, Loess Plateau, and North China Plain (Jiang et al. 2020; Figure 1). The Yellow River is one of the largest water systems, and it spans nine provinces or is autonomous. The population around the basin is 420 million, accounting for 30.3% of the national population. The gross domestic product (GDP) of the basin was 8 trillion yuan, accounting for about 14% of the national total (Xie et al. 2019). Most areas of the YRB are in the arid or semi-arid climatic zones, and the topography, rainfall, and vegetation are diverse in different regions. Affected by the complex monsoon circulations and atmospheric circulations, the climate pattern is significantly different in the whole basin. The gradient of temperature in the east-west direction is obviously larger than that in the south-north direction.
Figure 1

Overview of the location and elevation of the YRB and the gauging weather stations.

Figure 1

Overview of the location and elevation of the YRB and the gauging weather stations.

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Meteorological observation data

The database of precipitation covering every month from 1950 to 2019 is used to explore and analyze the spatial and temporal variations of precipitation in the YRB. The precipitation data of 82 national gauging stations are obtained from the National Meteorological Center of China (http://data.cma.cn/), and the distribution of the weather stations can be seen in Figure 1. It is an official and authoritative meteorological unit, and the data are of high enough quality after being reviewed by many parties. Besides, the missing precipitation data are extended based on the interpolation method in the study. The annual and monthly total precipitation of the YRB are aggregated from all stations by the Thiessen polygon method (Ye et al. 2020).

Climate data

Global climate changes have significant indirect impacts on precipitation variations. In this study, four dominant circulation pattern indices are used to discuss and analyze the potential mechanism of spatial and temporal pattern changes of precipitation in the YRB, including the AO, the NAO, the PDO, and the ENSO. The empirical orthogonal function (EOF) method is employed to explore the winter sea level pressure (SLP). It found there is a zonal symmetric structure because of the leading mode of SLP variations poleward of 20N° in the Northern Hemisphere. This global scale circulation mode is regarded as the AO and the corresponding principal component (PC) time series is named the Arctic Oscillation Index (AOI) (Thompson & Wallace 1998). Similarly, the index of NAO is used to express the divergence of zonal mean monthly normalized SLP anomalies between low-pressure centers in Southwest Iceland and high-pressure centers in Gibraltar (Jones et al. 1997). The index of PDO can describe the major interdecadal changes in the large-scale climate in the Pacific Ocean. It is the outcome of the EOF analysis on the monthly mean sea surface temperature (SST) anomaly north of 20N° in the North Pacific Ocean (Mantua et al. 1997). The ENSO is the most crucial interannual ocean–atmosphere interaction mode in the equatorial Pacific, and it has an irreplaceable position in the change of global climate (Trenberth 1997). The monthly index of Niño3.4, AO, and NAO, PDO come from the NOAA Physical Sciences Laboratory (https://www.psl.noaa.gov/).

Stepwise multiple regression

The stepwise multiple regression (SMR) model is employed to explore the dependence relationships of precipitation gradient (PG) on the geographical location and elevation of the basin. The SMR model determined whether the independent variables should be retained that were gradually introduced to the model by the F-test. Hence, the variables retained in the model are not only important but also have no severe multicollinearity. The calculation formula of the SMR model is as follows:
formula
(1)
where P represents the mean annual precipitation (mm) of the basin. Lat and Lon represent the latitude and longitude, respectively. The ki (i = 1, 2, 3) is the partial regression coefficient (precipitation gradient). The k0 and are the constant and the error term, respectively.
Then, the R2 is utilized to determine the performance of the SMR model, which is calculated as:
formula
(2)
where yi and are the measured value and the observed mean value, respectively. is the fit value of the SMR model, and n represents the number of stations. Generally, the acceptable level of the model is R2 > 0.5.

Empirical orthogonal function

The EOF analysis method is employed to reveal the spatial and temporal modes of precipitation over the YRB. This approach has been widely applied since Lorenz (1956) introduced it to meteorological or climatic studies (Lorenz 1956). The EOF analysis mainly consists of three components: eigenvectors (EOFs reflecting the spatial patterns of variables), principal components (PCs reflecting the variations of corresponding spatial mode with time), and eigenvalues. Thus, the EOF method was a spatiotemporal decomposition tool, which can be defined as:
formula
(3)
where EOF is an m × m orthogonal matrix, and PC is an m × n matrix of principal components. The m and n are the numbers of meteorological stations and the length of observation times, respectively.
The original matrix is processed in the anomaly form to achieve a data matrix X, then the covariance matrix Z is constructed:
formula
(4)
where XT is the transposed matrix of X. Then the eigenvectors V and the eigenvalues of the square matrix Z are calculated according to the following formula:
formula
(5)
where E is an m × m diagonal array:
formula
(6)

Generally, the eigenvalues are listed in the order . Each of them matches a column of the eigenvector called the EOF.

Then the spatial pattern EOF is projected to the original data matrix to define the PCs using the relation:
formula
(7)
where each row of the PC corresponds to the time coefficients of each eigenvector. Besides, the variance contribution rate of the kth EOF is obtained by the following formula:
formula
(8)

Evidently, the larger the eigenvalue , the greater contribution of the corresponding EOF to the total variance. Moreover, the North criterion is employed to test the significance level (95%) of the EOF patterns in this study (North et al. 1982), only the modes that pass the significance test are the signals with physical significance and can accurately reflect the variations of the original meteorological element field.

Bivariate wavelet coherence and multiple wavelet coherence

The bivariate WTC is a useful method to investigate the correlation in time–frequency domains of two nonlinear data sequences. Assuming the X and Y are two different data sequences, the WTC can be described as (Torrence & Compo 1998):
formula
(9)
The value of is between 0 and 1; the higher the value the stronger the consistency of the two time series. The and are the wavelet transforms of X and Y, is the cross-wavelet spectrum of X and Y. The S is the smoothing operator, and its relationship with others is shown as:
formula
(10)
The Sscale stands for the smoothing with scale, and Stime is for the time. The smoothing operator selected comes from Torrence & Webster (1999) in this paper, and is mainly used to study Morlet wavelet. The MWC also depends on the cross- and auto-wavelet power spectra among the independent variable (X (X = X1, X2, … Xn)) and dependent variable (Yt), which is the same as the WTC method. The cross- and auto-wavelet power spectra of an independent variable X can be described as (Koopmans 1974):
formula
(11)
where is the cross-wavelet power spectra (when ij) or the auto-wavelet power spectra (i = j). The cross-wavelet power spectra can be expressed by independent variable X and dependent variable Y, as:
formula
(12)
where represents the cross-wavelet power spectra between Xi and Y at scale s and location . Then, the MWC between dependent variable Y and independent variable X can be defined as (Hu & Si 2016):
formula
(13)
where is the complex conjugate of .

The Monte Carlo method is selected to examine the significance level (95%) of WTC and MWC in this study (Hu & Si 2016). The percentage area of significant agreement (PASC) could be calculated from the percentage of average wavelet coherence (AWC) or MWC values, which is passing the 95% significance test at all time scales (Hu & Si 2016; Nalley et al. 2019). The WTC/MWC and PASC are effective methods to assess the scale dependence between precipitation and large-scale circulation factors.

Interannual variations in precipitation

In this study, the precipitation trend is detected through linear regression, which is represented by the slope of the line. The annual mean precipitation appears as continuous fluctuation characteristics in the YRB during the entire study time (Figure 2(a)). The maximum and minimum values of annual mean precipitation appeared in 1964 and 1965, with 670.8 and 348.5 mm, respectively. Besides, the multi-year average of precipitation is 491.5 mm/a, with a declining rate of about 0.88 mm/10a (p > 0.1). The results also support the previous studies based on gauge-observed data from the Yellow River, which indicate that the annual total precipitation is decreasing. Moreover, there is not a uniform distribution of annual precipitation in the YRB. After analysis, December is the lowest month for annual average monthly precipitation. And the multi-year average monthly precipitation is almost concentrated in July, August, and September, accounting for 56.9% of the annual precipitation (Figure 2(b)). Notably, the average precipitation in July is as high as 109.2 mm, accounting for approximately 22.3% of the total precipitation per year in the YRB. The hydrometeorological variables are affected by complex ocean–atmosphere interactions. The YRB includes Chinese central and northern regions, and the moisture content depends closely on the precipitation in the region. Precipitation in this region is concentrated in summer and is mainly caused by the East Asian Summer Monsoon (EASM) from the western Pacific. Figure 2(c) and 2(d) shows the spatial mean precipitation and trends per year of the YRB, respectively. The YRB has a great difference in altitude from west to east with many mountains and diverse landforms, which leads to the spatial difference of precipitation in the basin largely. Specifically, the precipitation increases with the decrease in latitude, and there is also an uptrend from the west to the east. The downstream of the basin has the largest precipitation in the whole region, with an average annual precipitation of about 1,000 mm. The minimum precipitation in the basin covers the inner flow region of the middle reaches of the basin (104°–110°E, 36°–41°N), and the annual average precipitation was about 200–300 mm. Moreover, the spatial trend variation of precipitation is significantly different from the radial or zonal direction in the YRB (Figure 2(d)). The annual precipitation near the headstream increases with each passing year, and its average growth rate exceeds 1 mm/a. On the contrary, there is also an obvious declining trend of the mean annual precipitation in the lower middle reaches and lower reaches. And the precipitation trend has almost no fluctuation per year from Tangnaihai to Wubu (Figure 2(d)).
Figure 2

Variations in the (a) annual mean trends of precipitation in the YRB, (b) annual distribution of precipitation, (c) annual spatial mean variations of precipitation, and (d) annual spatial trends on the YRB from 1950 to 2019.

Figure 2

Variations in the (a) annual mean trends of precipitation in the YRB, (b) annual distribution of precipitation, (c) annual spatial mean variations of precipitation, and (d) annual spatial trends on the YRB from 1950 to 2019.

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Precipitation gradient characteristics variations

As mentioned above, the precipitation showed significant gradient variation characteristics along with elevation, longitude and latitude (Figure 2(c)). First, we investigated the linear relations of average annual precipitation (1950–2019) from the 82 gauging stations against elevation and geospatial position (longitude and latitude) in the YRB (Figure 3). Evidently, the precipitation gradient along with an elevation of the basin displayed two contrasting patterns. One group, consisting of 55 gauging stations, lies mainly in the middle and lower of the YRB with an elevation of less than 1,800 m (Figure 3(a)). The mean annual precipitation exhibited a significant decreasing tendency with the elevation (−27 mm/100 m, R2 of 0.35, p < 0.01). While another group, consisting of 27 gauging stations and mainly lying upstream of the YRB, keeps an obvious uptrend of the average precipitation with elevation per year (9 mm/100 m, R2 of 0.21, p < 0.01).
Figure 3

Relationships between the mean annual precipitation from 82 gauging stations against the elevation (a), longitude (b), and latitude (c) for 1950–2019 in the YRB.

Figure 3

Relationships between the mean annual precipitation from 82 gauging stations against the elevation (a), longitude (b), and latitude (c) for 1950–2019 in the YRB.

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The location, including longitude and latitude, is also a significant driving factor affecting annual precipitation. Thus, the relationships between latitude and longitude and annual precipitation in the YRB were further investigated in this study (Figure 3(b) and 3(c)). Evidently, the annual precipitation gradient along with the longitude has increased in the YRB (10.73 mm/°E, R2 = 0.075). The areas with high longitude in the YRB, close to the Western Pacific Ocean, are easily exposed to more water transported from the sea, so the precipitation in these areas is more compared with other regions.

Besides, the annual precipitation gradient along with the latitude exhibited a significant decreasing trend (57.24 mm/°N, R2 = 0.44, p < 0.01), which indicates that annual precipitation is more easily affected by latitude in the basin. In addition, the East Asian monsoon also has a non-negligible impact on the precipitation in the YRB, especially in the region with low latitudes. This leads to spatial differentiation of precipitation in the YRB, and the south has more rainfall than the north.

We further explored the dependence relationships of monthly precipitation gradient (PG) against the elevation and geographical location of the basin by the SMR model. According to the relevance between elevation and precipitation (Figure 3(a)), the data were divided into two parts with 1,800 m as the boundary, and the gauging stations are located in the upper and middle-lower reaches of the YRB, respectively. Figure 4 shows the coefficient of determination R2 of the SMR model and the monthly precipitation gradient against elevation, longitude, and latitude. The coefficient of determination R2 of the monthly SMR model of different groups was all higher than 0.6 (Figure 4(a)), which indicates that the dependence relationships of monthly precipitation on elevation, longitude, and latitude are relatively stable throughout the whole year. In the first group (an elevation lower than 1,800 m), the monthly precipitation gradient showed a negative correlation with elevation in all months. The precipitation gradient (absolute value) in summer (June, July, and August) was the largest, with an average value of about 0.353 mm/100 m (Figure 4(b)). The vertical gradient of monthly precipitation in the relatively high altitude area is low in spring (Figure 4(b)), while the zonal gradient of precipitation is relatively large, indicating that the dependence relationship between spring precipitation gradient and latitude was stronger in the relatively high elevation. Moreover, in the relatively low elevation region of the basin, the monthly radial precipitation gradient in summer is larger than that of the zonal gradient of monthly precipitation. The monthly radial and zonal monthly precipitation gradients of precipitation were 0.979 mm/°E and 0.563 mm/°N in summer in the relatively low elevation region of the basin, respectively.
Figure 4

Relationships of monthly precipitation gradient (PG) against elevation, longitude, and latitude. (a) The coefficient of determination R2 of the stepwise multiple regression model, (b) the precipitation gradient against elevation, (c) the precipitation gradient against longitude, and (d) the precipitation gradient against latitude. H1 and H2 represent the first group and second group, respectively.

Figure 4

Relationships of monthly precipitation gradient (PG) against elevation, longitude, and latitude. (a) The coefficient of determination R2 of the stepwise multiple regression model, (b) the precipitation gradient against elevation, (c) the precipitation gradient against longitude, and (d) the precipitation gradient against latitude. H1 and H2 represent the first group and second group, respectively.

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Dominant spatiotemporal modes of annual precipitation in the YRB

In this study, the main spatiotemporal modes of annual average precipitation are analyzed and studied by the EOF method in the YRB. The interpretation of the first four EOF models can fully explain the 71.9% variability of the average precipitation from 1950 to 2019. The first eigenvector (EOF1) represented the most important dominant distribution pattern of annual average precipitation with the highest variance contribution rate of 41.4%. And the values of the first eigenvector (EOF1) appeared to be a consistently positive feature (Figure 5(a)) in the YRB. Moreover, EOF1 values keep an obvious increasing trend from upstream to downstream and from northern to southern, further indicating that the southern precipitation is higher than the north and the precipitation in the upstream region is higher than the lower of Yellow River. The results further confirmed the long-term spatiotemporal distribution pattern change of mean annual precipitation (Figure 2(c)). Additionally, Figure 6(a) appears the temporal variations of the PC of EOF1, the positive phase of PC1 is characterized by the wet mode with more precipitation, whereas the negative phase is characterized by a dry pattern with relatively less precipitation in the YRB. The amplitude of PC1 has a slight downward trend, which is caused by the gradual decline of the total precipitation between 1950 and 2019. Moreover, the PCs of EOF1 appeared to have changed and were dominated by interannual variability during the entire study period. In the 1950s and mid-1960s, the PC1 has large positive fluctuations but has small negative amplitudes thereafter (Figure 6(a)). This implies that there is a transition of EOF1 from the active to stationary phase of the dominant pattern about the mean annual precipitation in the YRB.
Figure 5

The four leading modes of changes in mean annual precipitation of EOF analysis in the YRB, (a) EOF1 with the variance contribution of 41.4%, (b) EOF2 with the variance contribution of 14.3%, (c) EOF3 with the variance contributions of 10.6%, and (d) EOF4 with the variance contributions of 5.6%.

Figure 5

The four leading modes of changes in mean annual precipitation of EOF analysis in the YRB, (a) EOF1 with the variance contribution of 41.4%, (b) EOF2 with the variance contribution of 14.3%, (c) EOF3 with the variance contributions of 10.6%, and (d) EOF4 with the variance contributions of 5.6%.

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Figure 6

(a–d) The temporal variations of the principle component (PC) of EOF analysis.

Figure 6

(a–d) The temporal variations of the principle component (PC) of EOF analysis.

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The second dominant mode (EOF2; Figure 5(b)) showed the remarkable decreasing trends variability of average precipitation per year in the YRB. And the EOF2 and PC2 (Figure 6(b)) could explain approximately 14.3% of annual average precipitation variations. For PC2, its variation in the basin was significant and implied a significantly decreased trend during the entire research period. Moreover, from the EOF2, the average precipitation is decreasing in the lower of Tongguan, and the same conclusion could be obtained through the spatial variation of precipitation in the YRB (Figure 2(d)). The precipitation variances explained by EOF3 and PC3 account for 10.6% (Figures 5(c) and 6(c)), which is slightly lower than the percent variances explained by EOF2. The spatial pattern of precipitation reflected by EOF3 is significantly different from that of EOF1 and EOF2, while EOF3 mainly represents the distribution pattern of seasonal precipitation in the basin. The low center of EOF3 is located near Tongguan, which implies the decreasing trend of precipitation in spring or autumn in this area (Figure 5(a) and 5(c)). Besides, an opposite signal could be seen outside the region near Tongguan, and the precipitation in spring or autumn in this region showed an increasing trend during 1950–2019. PC3 presented a slightly increasing trend, which indicated an increasing wet pattern of precipitation in spring or autumn in the basin. And the EOF4 and PC4 modes (Figures 5(d) and 6(d)) explained about 5.6% of the precipitation variability. The EOF4 shows that there was a more humid phase than others throughout the study and the mean annual precipitation showed a remarkable rising tendency in the headstream of the Yellow River. The temporal mode of PC4 (Figure 6(d)) also showed a significant upward trend, and it showed that the annual average precipitation was relatively high basin headwater area of the basin from 1950 to 2019. The spatial pattern is also confirmed by the annual precipitation spatial trend analysis (Figure 2(d)).

Effect of the individual factor on the precipitation variations

As global warming intensifies, the variations in precipitation become more complex and abnormal (Iqbal et al. 2018). As one of the most important hydrological cycle components, precipitation is a highly nonlinear and nonstationary index that reflects the change of water resources, especially in the arid and semi-arid regions of the YRB. The precipitation is easily affected by multiple driving factors, and there are complex interactions among different driving factors (Xue et al. 2017). Therefore, the WTC and MWC methods are adopted to assess the independent or coupled effects on the precipitation in the YRB. The scale dependence and phase relationships were revealed among monthly precipitation and circulation factors (AO, NAO, PDO, and ENSO) in 1950–2019 (Figure 7). The results showed that the annual and interannual (3–5a) influences of AO were the most dominant during 1950–1995 (Figure 7(a)), and the average coherence of WTC and PASC were 0.324 and 4.65%, respectively (Table 1). Thompson & Wallace (2000) indicated that the AO can control and change the track and intensity of the westerly wind, and then the moisture transported by the wind has a significant effect on the precipitation of the YRB. Moreover, the negative AO was characterized by a southward shift of the polar front jet (PFJ) and southward advection of an arctic cold wave, which causes high precipitation in the Northern Hemisphere with the middle latitude (Matsuo & Heki 2012). The WTC and PASC between the average annual precipitation and NAO are 0.319 and 7.77%, respectively. According to Figure 7(b), there exists an intermittent coherence at the annual period between NAO and mean annual precipitation. The scattered interannual and interdecadal high coherence were also observed for NAO and the mean annual precipitation in the YRB (Figure 7(b)). The phase change of NAO is usually accompanied by variations of the westerly wave, jet stream, water vapor transport, and storm track in the middle and high latitudes, and could also cause interdecadal variations of precipitation in the Northern Hemisphere (Wang et al. 2017). Furthermore, increasing studies show that the NAO mainly affects the precipitation change in the YRB by modulating the intensity of the Westerlies and changing the distribution of water vapor flux (Gao & Wang 2017; Liu et al. 2019a).
Table 1

The WTC/MWC and PASC between annual total precipitation and individual or combinations of two, three, and four circulation factors

FactorsWTC/MWCPASC (%)
WTC AO 0.324 4.65 
NAO 0.319 7.77 
PDO 0.387 7.40 
ENSO 0.354 7.59 
AO–NAO 0.626 10.35 
AO–PDO 0.612 8.83 
MWC-2 AO–ENSO 0.587 6.35 
NAO–PDO 0.589 8.63 
NAO–ENSO 0.580 7.28 
PDO–ENSO 0.609 6.23 
AO–NAO–PDO 0.783 12.34 
MWC-3 AO–NAO–ENSO 0.762 11.38 
AO–PDO–ENSO 0.763 8.33 
NAO–PDO–ENSO 0.750 8.24 
MWC-4 AO–NAO–PDO–ENSO 0.877 12.88 
FactorsWTC/MWCPASC (%)
WTC AO 0.324 4.65 
NAO 0.319 7.77 
PDO 0.387 7.40 
ENSO 0.354 7.59 
AO–NAO 0.626 10.35 
AO–PDO 0.612 8.83 
MWC-2 AO–ENSO 0.587 6.35 
NAO–PDO 0.589 8.63 
NAO–ENSO 0.580 7.28 
PDO–ENSO 0.609 6.23 
AO–NAO–PDO 0.783 12.34 
MWC-3 AO–NAO–ENSO 0.762 11.38 
AO–PDO–ENSO 0.763 8.33 
NAO–PDO–ENSO 0.750 8.24 
MWC-4 AO–NAO–PDO–ENSO 0.877 12.88 
Figure 7

(a–d) WTC between annual total precipitation and different circulation factors in the YRB. The arrow direction represents the phase relations between precipitation and various influencing factors, and the negative and positive phases are pointing to the left and right, respectively.

Figure 7

(a–d) WTC between annual total precipitation and different circulation factors in the YRB. The arrow direction represents the phase relations between precipitation and various influencing factors, and the negative and positive phases are pointing to the left and right, respectively.

Close modal

We found that the annual average precipitation is easily affected by PDO in the YRB, the WTC and PASC are 0.387 and 7.40%, respectively. The EASM is itself influenced by the PDO, that is the weakened ocean–land thermal contrast occurred when the phase shifts from a negative to a positive PDO in north China (Qian & Zhou 2014). Therefore, the PDO indirectly regulates the precipitation variability through the EASM over the monsoon region of the YRB (Liu et al. 2019a). And the ENSO also has a remarkable effect on the change of precipitation in the basin, the WTC and PASC between ENSO and precipitation are 0.354 and 7.59%, respectively. The interannual periodic difference is not obvious between ENSO and the annual average precipitation from 1960 to 1990. In fact, many previous studies had been verified that ENSO had an important influence on climate change in Asia (Ouyang et al. 2014; Wang et al. 2021a). The warm ENSO, called El Nino, usually causes a notable reduction in precipitation in the middle and lower Yellow River (Ouyang et al. 2014). And the influences of them on precipitation were different from month to month and unevenly spatially distributed over the basin (Ouyang et al. 2014). The reason for more precipitation is most likely that the east of the basin is close to the ocean and affected by the East Asian monsoon (Zhou et al. 2012).

Coupled effects of multiple atmospheric teleconnections on the precipitation variability

There is much evidence to indicate that precipitation is influenced in a complex manner by multiple driving forces simultaneously (Ouyang et al. 2014). And the coupled effects of multiple factors on the precipitation change are analyzed by the MWC method. Table 1 is the MWC and PASC (%) from the average annual precipitation and various coupled factors. Moreover, an additional explanatory factor should be considered to have a statistical significance only when the PASC was increased by at least 5% (Hu & Si 2016). Obviously, the WTC/MWC has a positive relationship with the change in the number of explanatory factors, while PASC has no prominent change relationship. The mode of AO–NAO could explain the precipitation variations best in all the two-factor combinations, the MWC and PASC are 0.626 and 10.35%, respectively.

Furthermore, there was an intermittent high coherence between the precipitation and AO–NAO at the annual scale during the entire study time (Figure 8(a)). The pattern of AO–NAO–PDO could explain the precipitation variations in all the three-factor combinations better; the corresponding values of MWC and PASC are 0.783 and 12.34%, respectively. Especially, the significant coherence area between precipitation and the pattern of AO–NAO–PDO is similar to that of AO–NAO. Furthermore, the value of PASC did not increase significantly when increasing the number of the explanatory factor, the PASC value of the four-factor combination of AO–NAO–PDO–SST was only 12.88%. The phenomenon could be explained as follows: (i) the increase of the PASC threshold for statistical significance with an additional factor (Ng & Chan 2012; Wang et al. 2021a) and (ii) the variances that are explained by the new factor might have been explained by the other factors (Hu & Si 2016). The MWC analysis indicates that only one atmospheric circulation factor considered is insufficient to explain the precipitation variability at all time scales. Additionally, unlike most past research that individually analyzed the relationships between precipitation and various atmospheric circulation factors, the results of the current study emphasized that we should further consider the integrated effects of multiple atmospheric circulation factors. Moreover, land use change will be affected by climate change in both direct and indirect ways, and local deforestation and urbanization will, to some extent, also feed back into the climate system. Large-scale urbanization processes would also affect regional and global hydrological cycles by altering land surface temperatures and vegetation coverage (Swann et al. 2012; IPCC 2021). In terms of its effect on atmospheric circulation, the difference in the thermal gradient between deforested areas and adjacent areas would affect the horizontal surface winds and thus alter the rainfall zones (Swann et al. 2012). The influence of human activities on the regional and global climate exhibited a complex positive and negative feedback balance mechanism, which resulted in strong spatial and temporal differences and uncertainty of precipitation variations in the YRB (Wang et al. 2021a). In the future, more effort will be exerted to explore the direct or indirect effect of human activities (deforestation and urbanization) on regional and global climate change based on the observed and high-resolution reanalysis data through the earth system models.
Figure 8

(a–k) MWC between precipitation and different atmospheric circulation factors.

Figure 8

(a–k) MWC between precipitation and different atmospheric circulation factors.

Close modal

In the study, the long-term spatiotemporal variations of precipitation are explored in the YRB based on the observation data. The precipitation gradient against the elevation, longitude, and latitude was evaluated using the SMR model. Besides, we explored the dominant spatiotemporal modes of annual precipitation by the EOF method. Furthermore, the WTC and MWC methods were selected to explore the individual or integrated effects of various atmospheric circulation factors (ENSO, NAO, PDO, and AO) on the precipitation variability in the YRB. The summary is as follows:

  • (1)

    Diagnosis of the long-term tendency of precipitation reveals that the multi-year average of precipitation presents a slightly declined trend of about 0.88 mm/10a, while the precipitation in the upstream area showed a significant increasing trend. The dependence relationships of monthly precipitation gradient against elevation, longitude, and latitude by the SMR model indicated that the precipitation was more sensitive to longitude.

  • (2)

    Due to about 71.9% of the total variance, four dominant patterns of annual precipitation could sufficiently reflect the spatiotemporal patterns of precipitation in the YRB. EOF1 represented the dominant precipitation distribution, which is highly consistent and homogeneous owing to the values of EOF1 showing a consistently positive feature. EOF2 elucidated that the precipitation downstream of the Tongguan showed a significant decreasing tendency, which was demonstrated by the spatial trend analysis of the precipitation. Moreover, the EOF3 and EOF4 showed the seasonal and regional spatiotemporal modes of precipitation in the YRB, respectively.

  • (3)

    The wavelet coherence analysis indicated that the linkages between precipitation and individual circulation factor varied at different time scales. The MWC showed that the precipitation variations were controlled by multiple influencing factors simultaneously. The MWC and PASC (%) between precipitation and the combination of AO–NAO–PDO are 0.783 and 12.34%. Hence, it is vital to consider the comprehensive effects of multiple influencing factors when interpreting precipitation variations.

This study was funded by the National Natural Science Foundation of China-Shandong Joint Fund (U2006227, U1906234).

All relevant data are available from an online repository or repositories. (http://data.cma.cn/).

The authors declare there is no conflict.

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