*3.4. Spatial Evolution Characteristics of ET0*

The EOF analysis of *ET*<sup>0</sup> was conducted under four future emission scenarios in the YRB for 2022–2100, and the results were tested for modal significance using the North test, which are presented in Table 2 and Figures 10 and 11. As presented in Table 2, the first three modes of *ET*<sup>0</sup> in SSP126 passed the North test with a cumulative variance contribution of 88.68%; the first two modes of *ET*<sup>0</sup> in SSP245 passed the North test with a cumulative variance contribution of 90.18%; the first two modes of *ET*<sup>0</sup> in SSP370 passed the North test with a cumulative variance contribution of 94.32%; and the first mode of *ET*<sup>0</sup> in SSP585 passed the North test with a cumulative variance contribution of 93.55%.

**Figure 9.** Wavelet analysis of *ET*<sup>0</sup> in the Yellow River Basin under four future emission scenarios (SSP126, SSP245, SSP370, and SSP585), including wavelet coefficient contour plots of the real part (**a**,**c**,**e**,**g**) and wavelet variance plots (**b**,**d**,**f**,**h**).


**Table 2.** Main modes and contributions of *ET*<sup>0</sup> under future climate scenarios in EOF analysis.

**Figure 10.** Main modal eigenvectors of the EOF of the *ET*<sup>0</sup> spatial field in the Yellow River Basin for 2022–2100 under scenarios SSP126 (**a**–**c**), SSP245 (**d**,**e**), SSP370 (**f**,**g**), and SSP585 (**h**), where SSP126/245/370/585–EOFi (contribution/%) in each figure represents the i-th modal eigenvector (EOFi) of *ET*<sup>0</sup> under scenarios SSP126/245/370/585, with the contribution of each mode in parentheses. The red dashed lines in (**b**,**c**,**e**,**g**) are the positive and negative dividing lines of the eigenvectors.

Under the SSP126 scenario, the first EOF modal eigenvector (EOF1) of *ET*<sup>0</sup> in the YRB was positive, reflecting a spatially consistent trend of *ET*<sup>0</sup> across the region, and exhibited an increasing trend from the northwest to the southeast, indicating a more pronounced increase in *ET*<sup>0</sup> in the lower YRB (Figure 10a). EOF2 and EOF3, which explained 20.56% of the variations, reflected the secondary spatial characteristics of *ET*<sup>0</sup> with opposite trends from northwest to southeast and from north to south (Figure 10b,c). Combined with the temporal coefficients (Figure 11a), PC1 and PC2 exhibited roughly the same trend, with an increasing trend from 2022 to 2100, particularly after the 2150s when PC1 and PC2 remained positive, indicating that *ET*<sup>0</sup> remained high throughout this period. PC3 fluctuated at a value of approximately 0, reflecting no significant trend in *ET*0. Under SSP245 and SSP370, the EOF1 eigenvectors of *ET*<sup>0</sup> in the basin were all positive, exhibiting spatial trends of larger values in the upper and middle reaches and smaller values in the lower reaches, as well as larger values in the central and western parts and smaller values in the northern and eastern parts (Figure 10d,f). All the EOF2 eigenvectors exhibited a secondary spatial trend of positive in the northwest and negative in the rest of the basin, with a relatively larger increase in *ET*<sup>0</sup> near the source area in the upper part of the basin and a relatively larger decrease in *ET*<sup>0</sup> in the south. Combined with the temporal coefficients (Figure 11b,c), PC1 and PC2 exhibited an increasing trend from 2022 to 2100 under the SSP245 and SSP370 scenarios, and PC1 increased more than PC2, particularly after the 2060s, when PC1 and PC2 always maintained positive values, indicating that *ET*<sup>0</sup> remained high during this period. The distribution of EOF1 eigenvectors for *ET*<sup>0</sup> in the basin under the SSP585

scenario was similar to that of EOF1 under the SSP245 scenario (Figure 10h), with an increasing trend in the time coefficient PC1 (Figure 11d), indicating an increasing trend in *ET*<sup>0</sup> in the basin and a significant increase in *ET*<sup>0</sup> after the 2060s.

**Figure 11.** Principal component time coefficients (PC1–PC3) and their polynomial fits for the EOF analysis of future *ET*<sup>0</sup> in the Yellow River Basin under four emission scenarios ((**a**) SSP126, (**b**) SSP245, (**c**) SSP370, and (**d**) SSP585).

As observed from the spatial variations in annual *ET*<sup>0</sup> in the YRB in the near-, mid-, and long-term future relative to historical periods in the 21st century (Figure 12), the nearannual *ET*<sup>0</sup> growth was generally low on an annual scale, and the rate of *ET*<sup>0</sup> change was even negative in parts of Tai'an, Shandong Province, located in the lower reaches of the YRB, at −6.09% under the SSP370 scenario. In the mid- and long-term future scenarios, the *ET*<sup>0</sup> rate of change gradually increased in the whole basin, and the areas with high *ET*<sup>0</sup> variations were primarily concentrated in the YRB source area and a small part of the northern basin. In the lower reaches, the *ET*<sup>0</sup> change rate was low, and the variations were spatially distributed as high in the west and low in the east. As the radiative forcing increased, the increase in *ET*<sup>0</sup> became more significant, ranging from −3.08 to 50.78% under SSP126, from −1.32 to 68.88% under SSP245, from −6.09 to 89.30% under SSP370, and from −1.27 to 112.91% under SSP585. A maximum variation of 112.91% was observed in the western part of the YRB in the long-term future (2081–2100) under the SSP585 scenario.

**Figure 12.** Spatial variations in the near (2022–2040; **a**,**d**,**g**,**j**), mid- (2041–2060; **b**,**e**,**h**,**k**), and long (2081–2100; **c**,**f**,**i**,**l**) term future annual *ET*<sup>0</sup> of the Yellow River Basin relative to the historical period (1901–2014) under four SSP scenarios (SSP126, SSP245, SSP370, and SSP585).

#### **4. Discussion**
