Soil moisture is a key parameter for the circulation of water and energy exchange between surface and the atmosphere, playing an important role in hydrology, agriculture, and meteorology. Traditional methods for monitoring soil moisture suffer from spatial discontinuity, time-consuming processes, and high costs. Remote sensing technology enables the non-destructive and efficient retrieval of land information, allowing rapid soil moisture monitoring to schedule crop irrigation and evaluate the irrigation efficiency. Satellite data with different resolutions provide different observation scales. Evaluating the accuracy of estimating soil moisture based on open and free satellite data, as well as exploring the comprehensiveness and adaptability of different satellites for soil moisture temporal and spatial observations, are important research contents of current soil moisture monitoring. The study utilized three types of satellite data, namely GF-1, Landsat-8, and GF-4, with respective temporal and spatial resolutions of 16 m (every 4 days), 30 m (every 16 days), and 50 m (daily). The gray relational analysis (GRA) was employed to identify vegetation indices that selected sensitivity to soil moisture at varying depths (3 cm, 10 cm, and 20 cm). Then, this study employed random forest (RF), Extra Tree (ETr), and linear regression (LR) algorithms to estimate soil moisture at different depths with optical satellite data sources. The results showed that the accuracy of soil moisture estimation was different at different growth stages. The model accuracy exhibited an upward trend during the middle and late growth stages, coinciding with higher vegetation coverage; however, it demonstrated a decline in accuracy during the early and late growth stages due to either the absence or limited presence of vegetation. Among the three satellite images, the vegetation indices derived from GF-1 exhibited were more sensitive to vegetation characteristics and demonstrated superior soil moisture estimation accuracy (with R² ranging 0.129–0.928, RMSE ranging 0.017–0.078), followed by Landsat-8 (with R² ranging 0.117–0.862, RMSE ranging 0.017–0.088). The soil moisture estimation accuracy of GF-4 was the worst (with R² ranging 0.070–0.921, RMSE ranging 0.020–0.140). Thus, GF-1 is suitable for vegetated areas. In addition, the ETr model outperformed the other models in both accuracy and stability (ETr model: R² ranging from 0.117 to 0.928, RMSE ranging from 0.021 to 0.091; RF model: R² ranging from 0.225 to 0.926, RMSE ranging from 0.019 to 0.085; LR model: R² ranging from 0.048 to 0.733, RMSE ranging from 0.030 to 0.144). Utilizing GF-1 is recommended to construct the ETr model for assessing soil moisture variations in the farming land of northern China. Therefore, in cases where there are limited ground sample data, it is advisable to utilize high-spatiotemporal-resolution remote sensing data, along with machine learning algorithms such as ETr and RF, which are suitable for small samples, for soil moisture estimation.

Reference evapotranspiration (ET₀) is an essential component in hydrological and ecological processes. The Penman–Monteith (PM) model of Food and Agriculture Organization of the United Nations (FAO) model requires a number of meteorological parameters; it is urgent to develop high-precision and computationally efficient ET₀ models with fewer parameter inputs. This study proposed the genetic algorithm (GA) to optimize extreme learning machine (ELM), and evaluated the performances of ELM, GA-ELM, and empirical models for estimating daily ET₀ in Southwest China. Daily meteorological data including maximum temperature (T_max), minimum temperature (T_min), wind speed (u₂), relative humidity (RH), net radiation (R_n), and global solar radiation (R_s) during 1992–2016 from meteorological stations were used for model training and testing. The results from the FAO-56 Penman–Monteith formula were used as a control group. The results showed that GA-ELM models (with R² ranging 0.71–0.99, RMSE ranging 0.036–0.77 mm·d⁻¹) outperformed the standalone ELM models (with R² ranging 0.716–0.99, RMSE ranging 0.08–0.77 mm·d⁻¹) during training and testing, both of which were superior to empirical models (with R² ranging 0.36–0.91, RMSE ranging 0.69–2.64 mm·d⁻¹). ET₀ prediction accuracy varies with different input combination models. The machine learning models using T_max, T_min, u₂, RH, and R_n/R_s (GA-ELM5/GA-ELM4 and ELM5/ELM4) obtained the best ET₀ estimates, with R² ranging 0.98–0.99, RMSE ranging 0.03–0.21 mm·d⁻¹, followed by models with T_max, T_min, and R_n/R_s (GA-ELM3/GA-ELM2 and ELM3/ELM2) as inputs. The machine learning models involved with R_n outperformed those with R_s when the quantity of input parameters was the same. Overall, GA-ELM5 (T_max, T_min, u₂, RH and R_n as inputs) outperformed the other models during training and testing, and was thus recommended for daily ET₀ estimation. With the estimation accuracy, computational costs, and availability of input parameters accounted, GA-ELM2 (T_max, T_min, and R_s as inputs) was determined to be the most effective model for estimating daily ET₀ with limited meteorological data in Southwest China.