## 1 Introduction
Concurrent high-spatial- and -temporal-resolution ET products need to properly depict spatial and temporal ET variation in catchments, and the minimum requirement for this is daily ET datasets with 1 km spatial resolution, as these are then conducive to field-scale water management. The Heihe River Basin is a pivotal water resource in China for maintaining the existence and socioeconomic development of the so called \"oasis\" in the Hexi Corridor, an area that has a dry climate, scarce precipitation, and depleted groundwater [13; 14]. The major demands on water in the Heihe River Basin are due to plant transpiration and soil evaporation. In recent years, poorly regulated irrigation has led to serious deterioration of the water resources in the Heihe River Basin [14]. Concomitant with this has been a marked reduction in the available water supply for agriculture due to drought. Hence, there is a pressing need for daily ET products at the field and watershed scales to help local governments to develop reasonable irrigation and water conservation measures. A number of simulation experiments on ET have been carried out in the Heihe River Basin. [PERSON] et al. [15] conducted field observations of ET from grasslands in the upstream of the Heihe River, and they evaluated the FAO-Penman-Monteith (FAO-PM), Priestley-Taylor (PT), and Hargreaves-Samani (HS) models based on their observations, noting that the PT model yielded the highest accuracy in estimating daily ET. [PERSON] et al. [16] evaluated the adaptability of Penman-Monteith (PM), ASCE-Penman-Monteith (ASCE-PM), and Priestley-Taylor (PT) models for grassland in the upstream of the Heihe River by using observations, and the results showed that the PM model was the most effective for estimating ET in grassland. Due to the higher surface heterogeneity and the climatic conditions in the Heihe River Basin, this model is more demanding. TSEB (two-source energy balance) is a more physical-based model using satellite-based thermal infrared (TIR) to obtain surface ET data, while the TSEB-SM (two-source energy balance-soil moisture) model is an enhanced version of TSEB that incorporates a surface soil water stress index into its coupled evaporation and transpiration algorithm. Specifically, the TSEB-SM model initially computes the surface soil water stress index to capture both soil dryness and plant transpiration. Subsequently, this index is considered alongside other factors, such as surface temperature and vegetation type, to more accurately estimate the soil evaporation and plant transpiration rates. The TSEB-SM model can effectively handle study areas across a wide range of soil moisture conditions, from fully saturated to extremely arid soils, thereby providing improved accuracy in estimating both soil evaporation and plant transpiration. The aims of this study were to (1) simulate the daily surface ET in the Heihe River Basin from 2000 to 2020 based on the TSEB-SM model, (2) evaluate the accuracy of the simulation results directly with ground-based observations and indirectly with the TCH (three-cornered hat) method in combination with daily PML-V2 ET and SEBAL (Surface Energy Balance Algorithm for Land) ET data, and (3) characterize the spatial and temporal patterns of surface ET in the Heihe River Basin from 2000 to 2020.