Comparison and evaluation of evapotranspiration estimations by different approaches in the Yellow River Basin

Terrestrial evapotranspiration (ET), referring to the amount of water vapor transferred from the land surface to the atmosphere, provides a critical energy-water-carbon nexus. Accurately estimating ET is of great significance for understanding the regional water cycle, water resource management, and climate change. However, it is a great challenge to accurately estimate regional-scale ET due to its spatial heterogeneity and the sparse distribution of ET gauge stations (Sun et al. 2011). As a result, different kinds of methods for estimating regional-scale ET have been developed, which can be classified into five categories: empirical statistical formulae (Wang et al. 2007), satellite remote sensing-based models land surface models, the meteorologically based complementary relationship models (Liu et al. 2019), and water balance-based methods (Palmroth et al. 2010). Based on the methods mentioned above, various ET products have been developed in the past decades, including global land surface ET products (GLASS ET) (Xie et al. 2022), which are mainly derived from satellite remote sensing-based models, and the Chinese surface ET product (CR ET) (Ma et al. 2019), which is obtained from the meteorologically based complementary relationship models. However, Zhang et al. (2019) disclosed that most ET products derived from five categories of regional-scale ET estimation methods failed to couple ET and GPP processes in the calculation of canopy stomatal resistance. Therefore, the effects of diverse environmental factors on stomatal conductance could not be fully considered, and consequently, a large uncertainty in ET estimation at plot, catchment and local scales could be generated. To enhance the accuracy of regional ET estimation, it is essential to couple ET and GPP products in the estimation process. Recent studies, including those by Liu et al. (2020), have demonstrated the advantages of utilizing NIRv as a more accurate descriptor of GPP. These findings emphasize the importance of incorporating NIRv-based GPP estimations into evapotranspiration models, which can lead to improved accuracy and a better understanding of the energy-water-carbon nexus. For instance, Zhou et al. (2022) estimated ET using the Penman–Monteith model, employing GPP values derived from NIRv as input. In contrast, Hu et al. (2013) estimated ET by combining the Shuttleworth–Wallace (SW) model with a light-use efficiency-based GPP model. It is worth noting that the SW model can inherently link GPP and ET through the canopy stomatal resistance. Therefore, accurately estimating canopy stomatal resistance within the SW model is essential for ET estimation, which can be achieved using GPP acquired from the light-use efficiency model or GPP derived from NIRv. However, it is important to highlight that GPP derived from NIRv has been infrequently employed in the SW model to date.

Either the two ET products mentioned above or the improved SW models inevitably have some uncertainties due to model structure deficiencies, input dataset errors, model parameter errors, and so on. Therefore, there is an urgent need to analyze their accuracy and uncertainty in ET estimation. The water balance method and the Three-Cornered Hat (TCH) method have been widely used to evaluate the accuracy and uncertainty of ET estimation. The water balance method is generally based on the assumption that the total water storage change (TWSC) is essential to estimate variability or trend of ET at regional scales, and the ET (ETWB) derived by it is often regarded as the basin average ET estimation. According to Zhang et al. (2022), the TWSC estimates from GRACE can accurately derive monthly ET from the water balance equation after the launch of the Gravity Recovery and Climate Experiment (GRACE) satellites and the GRACE Follow On (GRACE-FO) mission. The TCH method has usually been used to quantify the uncertainty of gridded datasets without prior knowledge (Scipal et al. 2008). The advantages of the TCH method are that it considers the correlated errors among various products, and does not require the products to be independent. The TCH method has been increasingly used to quantify uncertainties of precipitation, soil moisture, and total water storage at regional scales (Awange et al. 2016), but it is rarely applied for uncertainty analysis of ET estimation. Currently, several studies on the evaluation of ET products have been performed at regional scales (Bai & Liu 2018) but none of them have comprehensively assessed the improved SW model and ET products using different methods at different spatial and temporal scales. Furthermore, the accuracy and uncertainty of ET estimation obtained by integrating GPP values into the SW model, which are calculated by use of the light-use efficiency model and the NIRv, respectively, have also not been compared.

Since various ET products have different degrees of uncertainties, how to reduce the uncertainty of ET products and improve their accuracy is crucial to accurately estimate regional ET. Several studies revealed that the combination of multiple ET products by use of different fusion methods can reduce the uncertainty in ET estimation (Hobeichi et al. 2018). These ensemble methods include the Bayesian Three-Cornered Hat (BTCH), Bayesian Model Averaging, Weighting Approach, and others (Shao et al. 2022). Among these ensemble methods, the BTCH method is best choice for unmeasured basins because it can integrate ET products without any prior knowledge, while other methods must rely on the support of observations (He et al. 2020a, 2020b). To date, the majority of previous studies have focused solely on the verification of individual ET product or the comparison among existing ET products. However, few studies have attempted to reduce the uncertainty of ET estimation by integrating the improved ET model and ET products using fusion methods. The objectives of this study are to (1) improve the SW model by introducing the GPP processes derived by the satellite-based near-infrared reflectance (NIRv); (2) comprehensively evaluate the accuracy and uncertainty of ET estimations by the improved SW model (SW_GLASSGPP ET, SW_NIRvGPP ET) and ET products (GLASS ET, CR ET) at different spatial and temporal scales; (3) examine the applicability of the fused ET estimation (BTCH ET) with GLASS ET, CR ET, SW_GLASSGPP ET, and SW_NIRvGPP ET through the BTCH method.

In this study, two widely used ET products, meteorological and remote sensing data required for the improvement of the SW model, the GRACE-based TWSA and in-situ runoff data were collected. The detailed information on their time span, spatio-temporal resolution, and data source is described in Table 1. According to Table 1, the study period was chosen to be from 2003 to 2017, with a spatial resolution of 0.1° × 0.1°. In response to the data products with varying temporal and spatial resolutions, Python software was employed to average or sum the daily or 8-day resolution values into monthly values. The bilinear interpolation method was used to resample data products with higher spatial resolution to 0.1° × 0.1°.

According to previous studies on evaluation metrics and selection criteria of different ET products (Baik et al. 2018; Yin et al. 2020), under the consideration of the spatial and temporal resolution, access difficulty and model applicability, GLASS and CR ET products (abbreviated as GLASS ET and CR ET) (listed in Table 1) were chosen for comparison and fusion with the SW_GLASSGPP ET and SW_NIRvGPP ET.

The data required by the improved SW model for the ET estimation of the YRB includes meteorological, remote sensing data, and atmospheric CO₂ concentration data (listed in Table 1).

Meteorological data, including precipitation, air temperature, vapor pressure, shortwave downward radiation, longwave downward radiation, and wind speed, were collected from the China Meteorological Forcing Dataset (CMFD) (He et al. 2020a, 2020b), which were obtained by fusing GLDAS data, TRMM precipitation, GEWEX-XRB radiation data, and in-situ station data from 830 meteorological stations within China. Due to its continuity of time coverage and consistency of quality, CMFD has been widely used in previous China ET estimates.

Remote sensing data includes LCC, LAI, SMC, GLASS GPP, and NIRv GPP. The land cover classification (LCC) with a spatial resolution of 300 m × 300 m was collected from the EAS CCI-LC of the European Space Agency and used to generate the one with a spatial resolution of 0.1° × 0.1° for the YRB. Totally, seven land cover classifications were used in this study, i.e., evergreen needle-leaved forests (ENFs), deciduous needle-leaved forests (DNFs), evergreen broadleaf forests (EBFs), deciduous broadleaf forests (DBFs), shrubland, grassland, and cropland. The monthly soil moisture data with a spatial resolution of 0.05° × 0.05° was obtained from Mu et al. (2011) and utilized to generate the one with a spatial resolution of 0.1° × 0.1° for the YRB. The 8-day GLASS LAI product and the 8-day GLASS GPP product with a spatial resolution of 0.05° × 0.05° were acquired from the program of Global Land Surface Satellite (GLASS) product and used to derive the ones with a spatial resolution of 0.1° × 0.1° and a temporal resolution of 1 month for the YRB. The monthly NIRv GPP data with a spatial resolution of 0.1° × 0.1° for the YRB was acquired based on the one with a spatial resolution of 0.05° × 0.05° collected from Badgley et al. (2019).

Monthly atmospheric CO₂ concentration data was collected from NOAA, where globally averaged marine surface monthly mean data is available.

The data required for the evaluation of the improved SW model and ET products in this study include runoff, terrestrial water storage anomaly (TWSA) (listed in Table 1).

The monthly TWSA data for the YRB from 2003 to 2017 were downloaded from the GRACE/GRACE-FO Mascon grid data product (Tapley et al. 2019), and the missing data were filled by the linear interpolation method. The monthly runoff data from Huayuankou Gauge station during 2003–2017 were collected from the River Sediment Bulletin of China.

In this study, the improved SW model was applied to compute the monthly 0.1° × 0.1° grid-based ET for the period of 2003–2017 over the YRB. The r_sc is calculated by Formula (4), in which GPP obtained from GLASS GPP product and NIRv GPP product replaced P_n, and the determination of all other parameters referred to Shuttleworth & Wallace (1985). The computed ET was labeled as the SW_GLASSGPP ET and the SW_NIRvGPP ET, respectively.

At a basin scale, the water balance method based on precipitation, runoff, and the TWSC is usually regarded as the most accurate way for estimating ET (Bai et al. 2022). In this study, the monthly ET of the YRB above the Huayuankou Gauge station obtained by the water balance method was treated as its true ET, and used to verify the accuracy of GLASS ET, CR ET, SW_GLASSGPP ET, SW_NIRvGPP ET, and BTCH ET.

Finally, the R matrix can be obtained through iterative operation combined with Equation (11). The square root of the R diagonal values was considered to be the uncertainty of evaluated ET. The ratio of the uncertainty to the time series mean value is the relative uncertainty.

In this study, various ET products (GLASS ET, CR ET, SW_GLASSGPP ET, SW_NIRvGPP ET) were fused by use of the BTCH method to generate a new ET product (BTCH ET). The detailed information on the fusion process is described as follows:

The error variance of various ET estimations can be solved by the TCH method.

To comprehensively evaluate the performance of five ET estimations (GLASS ET, CR ET, SW_GLASSGPP ET, SW_NIRvGPP ET, and BTCH ET), four widely used metrics, including the coefficient of determination (R²), root mean squared error (RMSE), mean absolute error (MAE), and Nash–Sutcliffe efficiency coefficient (NSE), were selected (Zhang et al. 2019). These metrics provide a robust assessment of model performance, considering aspects such as correlation, error magnitude, and predictive efficiency. The evaluation results, including R², RMSE, MAE, and NSE values, are presented and discussed to elucidate the strengths and limitations of each ET estimation method.

From Figure 2, although the grid-based mean annual GLASS ET, CR ET, SW_GLASSGPP ET, and SW_NIRvGPP ET during 2003–2017 in the YRB all gradually decreased from the southeast to the northwest, they also presented different spatial distributions to some extent: the higher mean annual GLASS ET occurred in the central, south, and east regions with relatively lower values in the north and west regions; the annual mean CR ET was found to be higher in the southwest region and lower in the northern region, which may have led to underestimation of the actual ET values in the northern cropland areas; the higher mean annual SW_GLASSGPP ET and the SW_NIRvGPP ET both lay in the southeast region with lower one in the northwest region.

According to Figure 3, it can be seen that the areas in which annual GLASS ET, SW_GLASSGPP ET, and SW_NIRvGPP ET showed an increasing trend accounted for 77.86, 84.96, and 79.96% of the YRB total, respectively, while the area with the annual CR ET demonstrating a decreasing trend was 65.90% of the YRB total. In the western YRB, the annual GLASS ET presented a decreasing variation with years while the annual CR ET, SW_GLASSGPP ET, and SW_NIRvGPP ET displayed an increasing variation with years. In the central YRB, the annual GLASS ET, CR ET, SW_GLASSGPP ET, and SW_NIRvGPP ET all exhibited an increasing variation with years. In the southern YRB, the annual CR ET, SW_GLASSGPP ET, and SW_NIRvGPP ET all showed a decreasing variation with years with the annual GLASS ET having an increasing variation with years. Figure 4(a) illustrates that the annual areal mean values of GLASS ET were higher than those of CR ET, SW_GLASSGPP ET, and SW_NIRvGPP ET in each year. The annual areal mean GLASS ET, annual SW_GLASSGPP ET, and annual SW_NIRvGPP ET all showed an insignificant increasing trend with a linear fitting slope being 2.79, 2.08, and 1.82 mm/yr, respectively. However, the annual areal mean CR ET presented a slight decreasing trend with a slope of −1.62 mm/yr. The mean annual values of GLASS ET, CR ET, SW_GLASSGPP ET, and SW_NIRvGPP ET were 502.28, 408.46, 442.82, and 414.4 mm, respectively. As illustrated in Figure 4(b), the seasonal cyclical variations of the annual average GLASS ET, CR ET, SW_GLASSGPP ET, and SW_NIRvGPP ET have been investigated. It has been found that the highest evapotranspiration values occurred in July for all methods, with GLASS ET reaching 95.74 mm, CR ET at 81.76 mm, SW_GLASSGPP ET at 77.87 mm, and SW_NIRvGPP ET at 77.51. Conversely, the lowest evapotranspiration values were investigated in January or December, with GLASS ET at 6.23 mm, CR ET at 2.55 mm, SW_GLASSGPP ET at 3.40 mm, and SW_NIRvGPP ET at 3.43 mm. These results demonstrate that the seasonal patterns of ET in the study area exhibit consistency across various methods, displaying a general trend wherein ET values increase from January to July and subsequently decrease from July to December.

The analysis above indicated that there existed differences in ET estimations by GLASS ET, CR ET, SW_GLASSGPP ET, and SW_NIRvGPP ET.

According to Figure 5, although overestimations and underestimations by GLASS ET, CR ET, SW_GLASSGPP ET, and SW_NIRvGPP ET existed, their monthly areal values generally showed the similar variation patterns as the monthly ETWB did. This was also verified by the values of the R², RMSE, MAE, and NSE in Figure 6. The t-test proved that there existed a significant correlation between one of monthly areal GLASS ET, CR ET, SW_GLASSGPP ET, and SW_NIRvGPP ET and the monthly ETWB at a significant level of 0.01 (p < 0.01). The significant correlation and higher R², RMSE, MAE, and NSE values between one of monthly areal GLASS ET, CR ET, SW_GLASSGPP ET, and SW_NIRvGPP ET and the monthly ETWB implied that the monthly ET estimations by GLASS ET, CR ET, SW_GLASSGPP ET, and SW_NIRvGPP ET in the YRB achieved similar accuracy as monthly ETWB did. Figure 6 indicates that the SW_GLASSGPP ET and SW_NIRvGPP ET performed better with relatively higher R² and NSE values and lower RMSE and MAE values. In terms of the values of the R², RMSE, MAE, and NSE, the SW_GLASSGPP ET performed best, followed by SW_NIRvGPP ET, CR ET, and GLASS ET. This revealed that the improved SW model by introducing the GPP processes could enhance the accuracy of ET estimation.

According to Figure 7, the grid-based monthly average uncertainties of GLASS ET, CR ET, SW_GLASSGPP ET, and SW_NIRvGPP ET determined by the TCH method varied from 0.04 to 32.53 mm/month. The SW_NIRvGPP ET achieved the lowest areal mean uncertainty of 4.39 mm/month with a changing range of 0.04–10.63 mm/month. The GLASS ET owned the highest areal mean uncertainty of 11.61 mm/month with an uncertainty range between 1.42 and 32.53 mm/month. The areal mean uncertainty of SW_GLASSGPP ET and CR ET was 4.66 and 9.96 mm/month, respectively, with an uncertainty range of 0.2–11.58 and 4.42–27.55 mm/month, respectively. Figure 7 indicates that the grid-based average uncertainties of GLASS ET, CR ET, SW_GLASSGPP ET, and SW_NIRvGPP ET presented similar spatial variation patterns, with lower uncertainties in the west part of the YRB compared to the east part. However, GLASS ET, CR ET, SW_GLASSGPP ET, and SW_NIRvGPP ET also demonstrated different degrees of spatial distribution of uncertainty: GLASS ET exhibited higher uncertainty in the middle region with relatively lower uncertainty occurring in the east and south regions; the CR ET had lower uncertainty over middle and west areas with higher one in the southeast; the SW_GLASSGPP ET and the SW_NIRvGPP ET possessed very similar spatial distributions of uncertainties with higher uncertainty in the southeast region and lower one in the north and west regions. In general, the uncertainties of GLASS ET and CR ET in most grids were higher than those of SW_GLASSGPP ET and SW_NIRvGPP ET. When comparing the uncertainties of SW_GLASSGPP ET and SW_NIRvGPP ET, SW_NIRvGPP ET typically had lower uncertainties in most grids, particularly in the middle region. The analysis above also demonstrates that by incorporating GPP processes, the improved SW model can effectively reduce the average uncertainty of ET estimation.

As shown in Figure 8, the average uncertainties of GLASS ET, CR ET, SW_GLASSGPP ET, and SW_NIRvGPP ET varied across different land cover types. For different types of land covers, the average uncertainties of GLASS ET and CR ET were generally higher than those of SW_GLASSGPP ET and SW_NIRvGPP ET_. For any of DNF, ENF, EBF, DBF, grassland, and shrubland, GLASS ET demonstrated the highest average uncertainty, followed by CR ET, SW_GLASSGPP ET, and SW_NIRvGPP ET. However, for cropland, the rank changed, with CR ET having the highest average uncertainty, followed by GLASS ET, SW_NIRvGPP ET, and SW_GLASSGPP ET. This revealed that there existed differences in the spatial distribution of average uncertainties of GLASS ET, CR ET, SW_GLASSGPP ET, and SW_NIRvGPP ET.

In order to further evaluate the seasonal variations of ET uncertainty, the relative uncertainties in GLASS ET, CR ET, SW_GLASSGPP ET, and SW_NIRvGPP ET are displayed in Figure 9. Generally, higher relative uncertainties for all ET estimates were observed in the colder months (January, February, November, and December) compared to the warmer months (March to October). This can be attributed to the challenges associated with accurately estimating ET using various methods over snow and frozen soil processes during cold months. For the GLASS ET, the highest relative uncertainty was observed in December (38.57%), while the lowest was recorded in July (17.95%). The CR ET exhibited the highest relative uncertainty in January (22.88%) and the lowest in July (8.6%). Similarly, the highest relative uncertainty for the SW_GLASSGPP ET was found in January (17.78%) and the lowest in July (3.15%). Lastly, the highest relative uncertainty for the SW_NIRvGPP ET was observed in January (16.89%) and the lowest in June (3.03%). Overall, it is revealed that the relative uncertainties of these ET estimates vary seasonally, with generally higher uncertainties observed during the colder months. This highlights the importance of considering the effects of snow and frozen soil processes when interpreting the accuracy of different ET estimation methods.

From Figure 10, it can be found that the average weights of SW_NIRvGPP ET, SW_GLASSGPP ET, CR ET, and GLASS ET for all types of land cover were 35.84, 33.14, 15.79, and 15.23%. This indicated that the average weights of SW_NIRvGPP ET and SW_GLASSGPP ET were close and much higher than those of CR ET and GLASS ET. According to Figure 10, for any type of land cover, SW_NIRvGPP ET accounted for the biggest average weight, varying from 38.39 to 33.69%, and the average weight of SW_GLASSGPP ET is the second biggest with a range of 28.41 to 36.22%. For each type of land cover, the average weights of CR ET and GLASS ET significantly reduced compared with those of SW_NIRvGPP ET and SW_GLASSGPP ET. For cropland, EBF, grassland, ENF, DBF, DNF, and shrubland, the average weights of GLASS ET were 19.13, 14.18, 14.02, 13.58, 13.48, 13.11, and 12.62%, respectively, and these values for CR ET changed to 13.59, 22.64, 14.73, 18.23, 22.21, 17.33, and 12.77%, respectively.

The spatial distributions of grid-based mean annual BTCH ET and its changing trend from 2003 to 2017 are displayed in Figures 2 and 3. The variations of annual areal mean BTCH ET during 2003–2017 are demonstrated in Figure 4. From Figures 2 and 3, it can be found that the spatial distributions of the grid-based mean annual of BTCH ET and its changing trend were similar to those of the SW_NIRvGPP ET and SW_GLASSGPP ET. The areal mean annual BTCH ET was 436.7 mm with a range of 420.6–455.4 mm. Figure 4 illustrates that the annual areal mean BTCH ET showed an insignificant increasing trend with a slope of 1.53 mm/yr, and its fluctuation pattern was similar to that of SW_GLASSGPP ET.

The R², RMSE, MAE, and NSE between monthly areal mean BTCH ET and the monthly ETWB are illustrated in Figure 6. The figure indicates that the R², RMSE, MAE, and NSE of BTCH ET were 0.858, 11.69 mm/month, 15.08 mm/month, and 0.71, respectively. In terms of R², RMSE, MAE, and NSE, the SW_GLASSGPP ET performed best in ET estimation, followed by BTCH ET, SW_NIRvGPP ET, CR ET, and GLASS ET.

Water, energy, and vegetation factors are essential for accurate estimation of regional ET, and their lack could affect the accuracy of ET simulation (Xu et al. 2019). Table 2 presents the main input variables of the improved SW model and ET products, which highlights the differences in input data and processes employed by each method. It is important to note that the GLASS ET computation principle does not include precipitation or soil moisture as input variables. Mu et al. (2011) believed that ET value might be overestimated if the ET model uses vapor pressure deficit (VPD) instead of soil moisture or precipitation as its input. This is because VPD could be underestimated when the soil water content is low. Yin et al. (2020) found that the GLASS ET overestimated the annual areal mean ET value for the YRB. Our study also obtained similar results, with GLASS ET having higher annual areal mean values than CR ET, SW_GLASSGPP ET, and SW_NIRvGPP ET (see Figure 4). Furthermore, GLASS ET also showed the highest average uncertainty among all main land covers, except cropland (see Figure 8). Yao et al. (2014) concluded that the high uncertainty of GLASS ET might result from the coarse resolution of meteorological input data (1/2° × 2/3°). As to the CR ET, the vegetation-related information is not considered. Long et al. (2014) stated that the ET model without considering vegetation factors could not well capture the ET inter-annual variations. In our study, annual areal mean GLASS ET, SW_GLASSGPP ET, and SW_NIRvGPP ET all presented an increasing trend, whereas the annual areal mean value of CR ET showed a completely different changing trend with a slight decreasing tendency (see Figure 4). It could be inferred that CR ET product did not well depict the inter-annual variations. Meanwhile, the average uncertainty of CR ET exceeded that of GLASS ET only in cropland (see Figure 8). This might be due to CR ET product failing to take land cover information into account (Xu et al. 2018).

The improved SW model in our study performed better than the GLASS ET product and CR ET product in ET estimation in the YRB in terms of R², RMSE, MAE, and uncertainty. This has been verified by Zhang et al. (2019), who revealed that the ET model coupled with GPP value would greatly improve its ET simulation accuracy. Since the improved SW model incorporates all relevant water, energy, and vegetation factors, SW_GLASSGPP ET and SW_NIRvGPP ET produced by the improved SW model outperformed the GLASS ET and CR ET products (see Figures 6, 8, and 9). Liu et al. (2020) found that NIRv is a better descriptor of GPP compared to other indicators, such as solar-induced chlorophyll fluorescence (SIF) and MOD17A2 GPP product. Their study highlights the importance of NIRv in accurately estimating GPP, which in turn affects evapotranspiration estimation. In our study, the SW_NIRvGPP ET method performed better across all major land cover types except for croplands and exhibited the lowest relative uncertainty in comparison to SW_GLASSGPP ET for all months (see Figures 8 and 9). This supports Liu et al.'s (2020) findings, as the GPP values derived from NIRv are based on a simple calculation of the NIR radiance and NDVI, without the need for collecting additional environmental information such as temperature, precipitation, and VPD. This eliminates the potential for extra uncertainty in ET estimation that could arise from incorporating these meteorological variables. However, in cropland, the insensitivity of NIRv to non-vegetation targets induced by its saturation in areas with high leaf area indices (Wang et al. 2020) resulted in a higher uncertainty of SW_NIRvGPP ET.

Based on the aforementioned analysis, to reduce uncertainties in future research, efforts should be made to improve the spatial resolution of input data, incorporate missing key factors such as precipitation, soil moisture, and vegetation information, and improve the representation of vegetation processes in ET models. By addressing these sources of uncertainty, it is expected that more accurate and reliable methods for estimating ET can be developed.

Numerous studies have employed the water balance method to evaluate the accuracy of remotely sensed ET estimates. However, the precision of the water balance method in ET estimation necessitates further investigation. The accuracy of the water balance method is primarily influenced by the quality of the input data employed in Formula (5) and (6), including precipitation, runoff, and TWSC. Zhong et al. (2020) showed that the sparse rain gauge network in the YRB leads to the greatest uncertainty in the quality of precipitation data used for calculating ETWB using the water balance method. Moreover, the impacts of human activities and climate change on basin runoff data and storage changes inevitably introduce uncertainties. In this study, the precipitation data were obtained from the China Meteorological Forcing Dataset (CMFD), which combines GLDAS data, TRMM precipitation, GEWEX-XRB radiation data, and in-situ measurements from 830 Chinese meteorological stations. The CMFD dataset, characterized by its temporal continuity and consistent quality, has been substantiated as reliable through a multitude of studies (He et al. 2020a, 2020b). The runoff data are based on observed measurements, ensuring their accuracy. TWSA data are derived from the GRACE/GRACE-FO Mascon grid data product. Long et al. (2015) highlighted the unique advantages and high accuracy of GRACE satellite gravimetry data for calculating water storage changes in large-scale research basins (greater than 2 × 10⁵ km²). However, the limitations of GRACE/GRACE-FO satellite observation accuracy and resolution inevitably result in some uncertainties.

Considering these factors, Xu et al. (2019) proposed that the accuracy of the water balance method for estimating ET can be evaluated by analyzing the uncertainty of ET estimates obtained using the TCH method. Based on the water balance method estimates, the accuracies of SW_GLASSGPP ET and SW_NIRvGPP ET exceed those of CR ET and GLASS ET. At the monthly scale, the TCH method produces comparable results. These findings indicate that, considering the influence of various methodologies and input data quality, the accuracy of evapotranspiration calculations employing the water balance method is deemed acceptable.

In order to obtain an accurate ET estimation for the YRB, GLASS ET, CR ET, SW_GLASSGPP ET, and SW_NIRvGPP ET were fused using the BTCH method. This method has been shown to produce more accurate results than the common arithmetic average method, as demonstrated by Shao et al. (2022) and He et al. (2020a, 2020b). The arithmetic average method can be easily affected by poor products, particularly when the number of products is small.

In this study, the average weights of each ET product were calculated using the BTCH method based on their average uncertainties (refer to Formula (19)). These weights were then used to fuse the four ET products, resulting in the BTCH ET estimation. Although SW_GLASSGPP ET showed better performance than BTCH ET in terms of R², RMSE, MAE, and NSE, the lowest average uncertainty among all products was exhibited by BTCH ET, followed by SW_NIRvGPP ET, SW_GLASSGPP ET, CR ET, and GLASS ET.

Based on the analysis, it can be concluded that the BTCH ET estimation provides the best results for the YRB in terms of both accuracy and uncertainty.

In this study, the accuracy and uncertainty of ET estimations at different spatial and temporal scales, which were achieved by GLASS ET, CR ET, SW_GLASSGPP ET, SW_NIRvGPP ET, and BTCH ET, was comprehensively evaluated, and the applicability of the BTCH ET in the YRB was examined. The major findings can be summarized as follows:

• (1)

  There existed differences in ET estimations by GLASS ET, CR ET, SW_GLASSGPP ET, and SW_NIRvGPP ET in the YRB, which were reflected by different spatio-temporal changes of grid-based mean annual GLASS ET, CR ET, SW_GLASSGPP ET, and SW_NIRvGPP ET and different changing trends of the annual areal mean GLASS ET, SW_GLASSGPP ET, SW_NIRvGPP ET, and CR ET.

• (2)

  The monthly GLASS ET, CR ET, SW_GLASSGPP ET, and SW_NIRvGPP ET achieved the similar accuracy as monthly ETWB did in YRB in terms of R², RMSE, MAE, and NSE, with the SW_GLASSGPP ET and SW_NIRvGPP ET performing better than GLASS ET and CR ET.

• (3)

  The grid-based monthly average uncertainties of GLASS ET, CR ET, SW_GLASSGPP ET, and SW_NIRvGPP ET demonstrated different spatial variation patterns in the YRB, with the SW_GLASSGPP ET and SW_NIRvGPP ET having lower areal average uncertainty than GLASS ET and CR ET.

• (4)

  The BTCH ET achieved the second-best performance in ET estimation in terms of R², RMSE, MAE, and NSE, but it performed best in terms of the average uncertainty. Therefore, BTCH ET provided the best ET estimation for the YRB in terms of accuracy and uncertainty.

The outputs of this study provide a valuable reference for the ET estimation in river basins.

This work was supported by the Water Science Research Projects of the Inner Mongolia Autonomous Region, China (Grant No. NSK202201).

All relevant data are included in the paper or its Supplementary Information.

The authors declare there is no conflict.