3.1 Correlation analysis
To analyze the primary meteorological factors influencing rainfall and pan evaporation, regression analysis was conducted between the multi-year average rainfall and evaporation in the YHH basin and the multi-year average values of various meteorological elements. The results are presented in the following figures, with the red lines representing the regression curves, the dark red areas indicating the 95% confidence bands, and the light red areas representing the 95% prediction bands.
As shown in Fig. 10, rainfall in the YHH basin is positively correlated with relative humidity and negatively correlated with temperature, wind speed, and solar radiation. The correlation with wind speed is relatively weaker among these factors.
As illustrated in Fig. 11, solar radiation exerts the most significant influence on evaporation in the YHH basin, followed by relative humidity and air temperature, while the impact of wind speed on evaporation is relatively minor. This conclusion forges a significant foundation for a more profound comprehension of the climatic traits and evaporation mechanisms within the basin. It also furnishes beneficial references that can aid in the research and decision-making endeavors across related domains.
To further delve into the effects of meteorological factors on rainfall and pan evaporation across different basins and to provide more informed support for local policies, a Pearson correlation analysis was conducted on each meteorological element in each basin.
Table 1
Correlation analysis between rainfall and meteorological elements in each basin
Drainage basin | Temperature(℃) | Wind speed(m/s) | Relative humidity(%) | Solar radiation(MJ/m²) |
---|
Yellow River basin | − .147 | − .640** | .892** | − .616** |
Huai River basin | − .592** | − .477** | .824** | − .648** |
Haihe basin | − .087 | − .375* | .344* | − .278 |
**. The significant level of correlation coefficient is 0.01 |
*. The significant level of correlation coefficient is 0.05 |
Table 1 reveals that rainfall in each basin is positively correlated with relative humidity and negatively correlated with air temperature, wind speed, and solar radiation. Specifically, rainfall in the Yellow River basin and the Huai River basin is highly positively correlated with relative humidity, involving Pearson correlation coefficients of 0.892 and 0.824, respectively, both passing the 0.01 significance test. In the Yellow River basin, there is a weak correlation between rainfall and air temperature, evidenced by a Pearson correlation coefficient of -0.147. In contrast, the correlation with wind speed and solar radiation is more pronounced, with Pearson correlation coefficients of -0.640 and − 0.616, respectively, both passing the 0.01 significance test. In the Huai River basin, rainfall is negatively correlated with air temperature, wind speed, and solar radiation. The correlation coefficients are − 0.592, -0.477, and − 0.648, respectively, all passing the 0.01 significance test. In the Haihe River basin, rainfall does not exhibit significant correlations with air temperature, wind speed, relative humidity, or solar radiation. The weakest of these non-significant correlations is with air temperature, characterized by a Pearson correlation coefficient of -0.087.
Table 2
Correlation analysis between pan evaporation and meteorological elements in each basin
Drainage basin | Temperature(℃) | Wind speed(m/s) | Relative humidity(%) | Solar radiation(MJ/m²) |
---|
Yellow River basin | .714** | .333** | − .856** | .887** |
Huai River basin | .646** | .166 | − .861** | .894** |
Haihe basin | .766** | .212 | − .857** | .909** |
**. The significant level of correlation coefficient is 0.01 |
*. The significant level of correlation coefficient is 0.05 |
Table 2 indicates that pan evaporation in each basin is negatively correlated with relative humidity and positively correlated with air temperature, wind speed, and solar radiation. The correlation between pan evaporation and relative humidity, as well as solar radiation, is significant in all basins, all passing the 0.01 significance test. Among these, solar radiation exhibits the strongest correlation with pan evaporation in all basins. The Pearson correlation coefficients between pan evaporation and solar radiation in the YHH basin are 0.887, 0.894, and 0.909, respectively, all passing the 0.01 significance test. In the basins, the relationship between relative humidity and pan evaporation is notably strong and inverse, ranking as the second most significant correlation. The Pearson correlation coefficients are − 0.856, -0.861, and − 0.857, respectively. The correlation between pan evaporation and wind speed is the weakest in all basins, involving Pearson correlation coefficients of 0.333, 0.166, and 0.212, respectively.
The correlation analysis reveals that among the meteorological factors influencing rainfall and pan evaporation across the basins, relative humidity and solar radiation exhibit the strongest correlations with both variables. This finding aligns with previous analyses.
3.2 Center of gravity transfer model
The ArcGIS spatial interpolation method can yield the distribution patterns of the multi-year average values of meteorological elements in a region. However, this method only reflects the distribution of meteorological elements within the basin, failing to analyze the spatiotemporal evolution patterns of these elements. Moreover, the precision of the element distribution obtained through interpolation is relatively low. Therefore, the center of gravity migration model was hereby introduced to analyze the distribution and multi-year migration characteristics of elements within the basin by calculating the positions of the centers of gravity for each element from 1950 to 2023, as well as the distances and directions of gravity migration between each decade. The multi-year migration coordinates of the centers of gravity are presented in Table 3, where x and y correspond to the decimal degree coordinate system within ArcGIS.
Table 3
Annual mean barycentric migration coordinates of meteorological elements in the Huang-Huai-hai basin
Year | Rainfall | Evaporation | Temperature | Wind speed | Relative humidity | Solar radiation |
---|
x | y | x | y | x | y | x | y | x | y | x | y |
---|
1950 | 115.92 | 38.75 | 112.31 | 36.01 | 115.89 | 38.36 | 115.95 | 38.71 | 115.83 | 38.66 | 115.77 | 38.69 |
1960 | 115.74 | 38.58 | 112.26 | 36.00 | 115.90 | 38.39 | 115.95 | 38.70 | 115.79 | 38.67 | 115.79 | 38.72 |
1970 | 115.82 | 38.80 | 112.23 | 36.06 | 115.87 | 38.33 | 115.94 | 38.69 | 115.82 | 38.69 | 115.78 | 38.68 |
1980 | 115.75 | 38.63 | 112.41 | 36.07 | 115.89 | 38.35 | 115.94 | 38.71 | 115.81 | 38.69 | 115.78 | 38.68 |
1990 | 115.96 | 38.73 | 112.41 | 36.09 | 115.91 | 38.42 | 115.94 | 38.69 | 115.79 | 38.63 | 115.78 | 38.70 |
2000 | 115.62 | 38.48 | 112.52 | 35.97 | 115.90 | 38.40 | 115.94 | 38.72 | 115.77 | 38.64 | 115.80 | 38.71 |
2010 | 115.85 | 38.75 | 112.40 | 35.98 | 115.85 | 38.37 | 115.91 | 38.71 | 115.82 | 38.69 | 115.77 | 38.70 |
2023 | 115.08 | 38.28 | 112.38 | 35.81 | 115.86 | 38.36 | 115.94 | 38.71 | 115.75 | 38.61 | 115.76 | 38.70 |
To grasp a more detailed understanding of the specific distances involved in gravity migration during each time period, the Vincenty formula was employed for calculation. Introduced by Vincenty in 1975, the Vincenty formula is a geodetic method designed to calculate distances between two points on the Earth's ellipsoidal surface. It effectively translates latitude, longitude, and distance into a solution for the geodetic problem [17]. The specific formula is as follows.
\({d_f}=R\sqrt {{{({\theta _A} - {\theta _B})}^2}+\cos \left[ {\frac{{{\theta _A}+{\theta _B}}}{2}} \right]\Delta {\lambda ^2}}\)
where, \({d_f}\)represents the planar distance between two locations; \({\theta _A}\)and\({\theta _B}\)are the latitudes of the two locations, measured in radians; \(\Delta \lambda\)is the difference in longitude between the two locations, also measured in radians; and R denotes the average radius of the Earth. The calculation results are presented in Table 4.
Table 4
Annual mean center of gravity migration distance and direction of various meteorological elements in the Huang-Huai-hai basin (distance unit: km)
Year | Rainfall | Evaporation | Temperature | Wind speed | Relative humidity | Solar radiation |
---|
Distance | Direction | Distance | Direction | Distance | Direction | Distance | Direction | Distance | Direction | Distance | Direction |
---|
1950–1960 | 24.53 | southwest | 4.63 | southwest | 3.45 | northeast | 1.11 | southwest | 3.65 | northwest | 3.76 | northeast |
1960–1970 | 25.43 | northeast | 7.20 | northwest | 7.17 | southwest | 1.41 | southwest | 3.42 | northeast | 4.53 | southwest |
1970–1980 | 19.85 | southwest | 16.22 | northeast | 2.83 | northeast | 2.22 | northwest | 0.87 | southwest | 0.00 | southwest |
1980–1990 | 21.35 | northeast | 2.22 | northwest | 7.98 | northeast | 2.22 | southwest | 6.89 | southwest | 2.22 | northwest |
1990–2000 | 40.57 | southwest | 16.61 | southeast | 2.29 | southwest | 3.34 | northwest | 2.06 | northwest | 2.06 | northeast |
2000–2010 | 36.06 | northeast | 10.86 | northwest | 5.49 | southwest | 2.83 | southwest | 7.05 | northeast | 2.83 | southwest |
2010–2023 | 84.97 | southwest | 18.99 | southwest | 1.41 | southeast | 2.60 | southeast | 10.77 | southwest | 0.87 | southwest |
The path of the forward migration of the centers of gravity for meteorological elements in the YHH basin from 1950 to 2023 is depicted in Fig. 12.
Figure 12 reveals that the migration paths of the multi-year average centers of gravity for meteorological elements from 1950 to 2023 display distinct patterns the spatial distribution of long-term average rainfall and pan evaporation in the basin. These patterns highlight the intricate complexities of regional climate change. The migration span of the rainfall center of gravity is notably pronounced, tracing an eastward then westward migration path that spans across an 8-degree change in longitude. From the latitudinal perspective, it initially moves southward, then northward, and finally back southward, with the final latitudinal shift not exceeding the initial study position. The overall migration trend of the rainfall center of gravity exhibits a “southeast-northwest-southeast” pattern. During the period spanning from 2010 to 2023, the migration span of the rainfall center of gravity reaches its maximum of 84.97 km, possibly attributed to the pronounced influence of monsoons on the Huang-Huai-Hai region during this period [18]. Changes in monsoon strength and direction significantly affect rainfall distribution and intensity, resulting in substantial shifts in the rainfall center of gravity.
The migration trajectory of the evaporation center of gravity shares some similarities with that of the rainfall center of gravity, presenting a similar “southeast-northwest-southeast” pattern. This phenomenon is speculated to be related to the interaction between rainfall and evaporation, as changes in rainfall quantity will directly affect the surface moisture content, subsequently influencing the evaporation process. In contrast, the temporal migration patterns of the centroids of meteorological elements exhibit distinct regional characteristics. The migration trajectories of temperature and solar radiation generally follow a “northeast-southwest-northeast” path, a trend that aligns with findings from related research. This pattern is speculated to be related to the geographical location and climatic characteristics of the Huang-Huai-Hai region [19]. Situated within the East Asian monsoon zone, the Huang-Huai-Hai basin experiences a distribution of temperature and solar radiation that is significantly influenced by monsoonal circulation patterns. Possibly due to the atmospheric circulation and water vapor transport in the region, the migration trajectories of wind speed and relative humidity, on the other hand, exhibit a “southwest-northeast-southwest” pattern.
Notably, the centers of gravity for rainfall, evaporation, wind speed, and relative humidity show consistent migration directions in longitude, while the migration directions for temperature and solar radiation are also consistent. This may be related to the interactions and correlations among these elements. For instance, temperature and solar radiation are important factors affecting evaporation, and their changes will directly influence the amount of evaporation, thereby affecting the distribution and intensity of rainfall. Changes in wind speed and relative humidity are also crucial factors influencing rainfall and evaporation [20].