Based on observed precipitation and runoff data, monthly actual evapotranspiration (ETa) was calculated by the hydrological budget balance method in the Nu River Basin (NRB) and Lancang River Basin (LCRB). The performance of three developed complementary relationship methods, the nonlinear advection-aridity (nonlinear AA) method, generalized complementary relationship method (B2015), and sigmoid generalized complementary function (H2018), on simulating (ETa) were evaluated. The evaluation results showed that three methods were able to accurately simulate monthly (ETa) series. The NSE between the monthly (ETa) simulated by the nonlinear AA, B2015, and H2018 methods and the water-balance-derived (ETa) were 0.89, 0.83, and 0.91, respectively. The R-square were 0.90, 0.84, and 0.93, respectively. Overall, the H2018 method showed the best performance. The parameter α had a negative correlation with regional aridity index. Annual (ETa) and precipitation showed significant increasing trends during 1956–2018 in the basins at all temporal scales (dry and wet seasons and annual series). Runoff also exhibited an increasing trend in each sub-basin, except for the downstream region of the LCRB. The increasing magnitudes of wet reason precipitation and runoff in the mid-stream region was the highest, with the value of 73.7 mm/10a and 44.9 mm/10a, respectively. The (ETa) increased dramatically in the downstream region, the magnitude reached 25.9 mm/10a. Precipitation was the main factor leasing to (ETa) change. The increasing magnitude of (ETa) accounted for 42.4% of the precipitation increment. Research on the influence mechanism between meteorological factors and (ETa) showed that the contribution rate of air temperature to (ETa) was the highest, reaching 23.5%, which showed a significant positive correlation. The second was wind speed, whose contribution rate was − 10.2% on average, and even reached − 14.1% in the upstream region of the NRB. The correlation coefficient between (ETa) and wind speed was highest in mid-stream region of the NRB, which was greater than 0.80. The contribution rates of increasing humidity to (ETa) were − 12.5% and − 9.2% in the NRB and LCRB, respectively. (ETa) was negatively correlated with humidity. The negative correlation was especially strong in the mid-stream region, with coefficients were greater than − 0.65. The sunshine hours had the least effect on (ETa), and the contribution rates were − 6.5% and − 4.1%, respectively.