Identification of driving mechanisms of actual evapotranspiration in the Yiluo River Basin based on structural equation modeling

Abstract

Background

Actual evapotranspiration (ETa) is a crucial aspect of the hydrological cycle. It serves as a vital link between the soil–vegetation–atmosphere continuum. Quantifying the leading factors of regional ETa change and revealing the multi-factor compound driving mechanism of ETa evolution is necessary. Structural equation modeling (SEM) has been widely used to study the structural relationships between variables in large-scale areas. However, there is an urgent need for more in-depth exploration of these complex relationships at the grid scale. Therefore, the Yiluo River Basin, a representative area of soil and water conservation engineering demonstration in the Loess Plateau, was selected as the study area, and the SEM at the basin scale and grid-scale were constructed to carry out the research.

Results

The data indicate that ETa decreased at 1.97 mm per year at the watershed scale from 1982 to 2020. Climate change had the greatest impact on the change of ETa in the watershed, with a total impact coefficient of over 0.9. The direct impact of climate change on ETa increased by 0.571 from 1982–1992 to 1993–2020. The direct impact coefficients of vegetation cover and soil moisture decreased by 0.402 and 0.102, respectively, while the impact coefficient of the water body factors increased by 0.096. At the scale of individual grid cells, the ETa in the watershed was affected by changes in watershed climate, vegetation, and soil moisture, with contributions ranging from − 0.31 to 0.22, − 1.09 to − 0.08, and 0.61 to 0.90, respectively. Spatially, vegetation and soil moisture had a stronger impact on ETa in the upstream area, while climate change had a negative effect, and the downstream region had the opposite effect. Furthermore, the regulatory impact of large reservoirs mitigated the response of water surface evaporation to climate change in the upstream region.

Conclusions

The application of SEM at different spatial and temporal scales has effectively quantified the driving mechanisms behind actual evapotranspiration in the Yiluo River Basin, while visually representing the spatial distribution characteristics of various influencing factors on ETa. This research provides a theoretical foundation for studying slope water consumption processes and circulation mechanisms.

Background

Actual evapotranspiration (ETa) from watersheds is an important component of the hydrologic cycle, including vegetation evapotranspiration, canopy interception evaporation, soil evaporation, and water surface evaporation, which is affected by the complexity of climate, vegetation, soil, and water (Ling et al. 2022; Wang et al. 2023). China's vegetation cover has significantly increased due to large-scale ecological restoration and natural forest protection programs (Li et al. 2018). It has been shown that NDVI in the Loess Plateau increased at a rate of 0.0036/a over the past 31 years (Fan et al. 2023), and that vegetation restoration in the region is approaching the limits of sustainable water resources (Feng et al. 2016). However, warm humidification coexists with warm drying in this region, and climate change will directly affect evaporation from land and water surfaces and indirectly affect vegetation growth and soil moisture changes (Petra et al. 2019). In areas with sufficient rainfall, higher temperatures increase transpiration and vegetation evaporation. In areas with limited rainfall, vegetation requires more water, which can result in decreased soil moisture and evapotranspiration.

Meanwhile, in large catchment areas such as reservoirs, rivers, and lakes, water surface evaporation makes a significant contribution. To gain a deeper understanding of the ETa-driving mechanisms, it is crucial to quantitatively identify the dominant factors of ETa in the context of climate warming and vegetation greening. Additionally, revealing the spatial and temporal distribution characteristics of ETa drivers at the watershed and grid scales can help clarify the slope water consumption process and overall water-cycle mechanism.

Accurate calculation of ETa is crucial for quantitative studies of watershed driving mechanisms. Many researchers have made useful explorations and developed relatively mature estimation methods. The estimation of ETa involves various methods, including water balance estimation, remote sensing, and the use of potential evapotranspiration (PET). The water balance method indirectly infers ETa from the watershed by analyzing other water components (Xiong et al. 2023). Remote sensing estimation methods, such as the Surface Energy Balance Algorithm for Land (SEBAL) model, can distinguish between soil evaporation, vegetation transpiration, and interception components (Ma et al. 2023a, b; Mokhtari et al. 2023; Leonardo et al. 2021). However, limited by the time series length and the data's accuracy, it is better to calculate the ETa from the PET. Thornthwaite, Hargreaves (Chen et al. 2020), and Priestley-Taylor (Sumner and Jacobs 2005; Li et al. 2022) methods estimate PET through climatic factors.

The Penman–Monteith formula is a widely used and accurate method for calculating PET in current research. It integrates the physiological characteristics of the crop and aerodynamic parameters (Sur et al. 2023; Zerihun et al. 2023). Adjustment factors must be set based on the characteristics of the regional environment to calculate ETa by PET. These parameters are often empirical and based on local meteorological conditions or the relationship between precipitation and runoff. Choudhury (1999) and Yang et al. (2008) used the Budyko theory to establish a relationship based on the subsurface condition parameter n. This method is straightforward and yields satisfactory results. To quantify the drivers of watershed ETa, it is necessary to consider multiple factors such as climate change, vegetation cover, soil properties, and water conditions. Special attention should be paid to the compounding effect between these factors when attributing ETa (Zhang et al. 2015). Sensitivity Coefficient (Tabari and Talaee 2014), Generalized Additivity Model (Cao et al. 2023a, b), Causal Analysis method based on physical mechanism (Khan et al. 2021; Mishra et al. 2024) can effectively quantify the relationship between evapotranspiration and its influencing factors. However, further analysis is required to understand these driving factors' mutual feedback and synergies. Song et al. (2020) proposed the geographical detector model for identifying attribution in spatial dimensions. It determines the explanatory ability of a single factor on the spatial dissimilarity of the dependent variable. It identifies the strength, direction, and nature of the interaction between the two factors. Structural Equation Modeling (SEM) is better suited for identifying multi-factor compounding effects attributions than the geographical detector model, which can synthesize multiple observables and latent variables (Fan et al. 2016; Tarka 2018; Ma et al. 2023a, b). Yang et al. (2021) applied SEM to the attribution of ETa in the Haihe River Basin and explored the compound effects of vegetation growth and climate change on ETa. Ma et al. (2024) used SEM to investigate the effects of latitude, climate, and vegetation on spatial variations in ETa. The study provides an approach for identifying the attribution of ETa in watersheds. However, previous studies typically use the watershed as the basic unit for analyzing the water cycle process of the watershed as a whole. To more accurately identify the drivers of ETa, SEM should be applied to the grid scale. This approach can help reveal the driving mechanism of ETa from a spatial perspective.

The Yiluo River Basin is located in the lower middle reaches of the Yellow River. It is a typical demonstration area for soil and water conservation projects in the Loess Plateau region. The region has actively promoted the construction of ecological river corridors and the greening of mountainous areas, with remarkable results. In this study, the Yiluo River Basin was selected as the study area, and SEM was applied to quantitatively analyze the driving mechanisms of ETa at the watershed and grid scales, respectively. The steps to accomplish the study include: (1) calculate the ETa from the watershed using the Penman–Monteith formula and the Choudhury-Yang formula based on meteorological observations, and analyze its spatial and temporal trends; (2) Screen key drivers of ETa from the watershed using SEM; and (3) apply SEM to the watershed scale and grid-scale, respectively, to analyze the spatial and temporal distribution characteristics of the effects of each driving factor on ETa.

Data and methods

Overview of the study area

The Yiluo River Basin (109 °43′–113° 10′ E and 33° 39′–34° 54′ N) is located in Shaanxi and Henan provinces, China. It is named by the Luo River and its main tributary, the Yi River, with a total watershed area of 1.89 $\times {10}^{4}$ ${\text{km}}^{2}$. The river flows into the Yellow River from its source in the southwest (Cui et al. 2022). The watershed has an average elevation of 746 m. Mountains and hills dominate the southwest region, while the northeast region is relatively flat. The watershed exhibits a warm, temperate continental monsoon climate. The multi-year average temperature is 13.36 °C, with a precipitation of 676.8 mm, relative humidity of 65.05%, and ETa of 544.13 mm. After implementing soil and water conservation and ecological restoration measures, the vegetation in the watershed has significantly improved. Currently, the forest cover of the watershed is 45.3%. Additionally, the Basin contains two large reservoirs: Guxian Reservoir and Luhun Reservoir. Guxian Reservoir has been used since 1993, while Luhun Reservoir was constructed in 1965. However, due to safety concerns, it remained in a low-water operation until 2006, when it underwent comprehensive refurbishment and became fully operational (Fig. 1).

Fig. 1

Overview of the study area (The map shows the geographical location of the Yiluo River Basin, located on the Loess Plateau of the Yellow River Basin in China.)

Data source and collection

This paper utilizes meteorological station observation data from the China Meteorological Data Service Center from 1982 to 2020. The data includes daily measurements of temperature, precipitation, wind speed, sunshine duration, relative humidity, and evaporation from the evaporation pan. The National Tibetan Plateau Science Data Center provided temperature and precipitation data from 1901–2020 with a spatial resolution of 1 km. The GLDAS dataset provided PET, ETa, and soil moisture data from 1982 to 2020. The soil moisture data includes four layers: 0–10 cm, 10–40 cm, 40–100 cm, and 100–200 cm, with a spatial resolution of 0.25°. Monthly Normalized Differential Vegetation Index (NDVI) and Leaf Area Index (LAI) data from 1982 to 2020 with a spatial resolution of 1/12° are collected from GIMMS and NDVI data from 2001 to 2020 with a spatial resolution of 1 km is collected from MODIS satellites; The Chinese Academy of Sciences has published land use data from 1980 to 2020 with a spatial resolution of 1 km (Table 1).

Table 1 Data sources (including the source of the data used in the study, URL, and spatial and temporal resolution information)

The spatial resolution of this study was unified at 1 km. In implementing the structural equation model at the basin scale, this study adopts the method of regional statistics, and takes the whole Yiluo River Basin as the research area to count the surface mean or sum of different factors in the Basin. We use geographic information system (GIS) software to resample the grid scale study to ensure the correct modeling and calculation. Based on the 1 km grid, we unify the spatial resolution of different factor data and align the boundary, row number and column number to ensure that the R program can correctly correspond to the different elements of the grid unit.

Technical route

The Yiluo River Basin was used as the study area in this study. The ETa from the Basin was calculated using the Penman–Monteith and Choudhury-Yang formulas. Water surface evaporation was quantified using evaporation observations from an evaporation pan, and then the temporal and spatial trends of the ETa from the Basin were analyzed. The SEM was then used to attribute and identify the drivers of evapotranspiration's spatial and temporal evolution in the Yiluo River Basin from 1982 to 2020 at the watershed scale and grid-scale, respectively. The study divided the time scale into 1982–1992 and 1993–2020 to evaluate the effect of large reservoir operation on water surface evapotranspiration. These periods correspond to the time before and after the operation of large reservoirs, respectively. Meanwhile, the study distinguishes between two types of grids: land and water surface. SEM is constructed for each type to quantitatively analyze the spatial and temporal distribution characteristics of the ETa drivers (Fig. 2).

Fig. 2

Technical route (Firstly, the actual evapotranspiration of the Yiluo River Basin was calculated, and then the structural equation models of basin scale and grid-scale were constructed, respectively. The effects of meteorological factors, vegetation factors, soil moisture, water factors, and large reservoirs on actual evapotranspiration were analyzed.)

Methods

Calculation of actual evapotranspiration

The subsurface characteristic parameter n of the Yiluo River Basin was calculated inversely by taking the multi-year average values of precipitation, PET, and ETa from the GLDAS product according to the Choudhury-Yang formula (1) after calculating the potential evapotranspiration by the Penman–Monteith formula.

$${ET}_{a}=P\times n+\frac{\left(1-n\right)\cdot P}{PET}$$

(1)

where P is the multi-year average precipitation, and n is the parameter reflecting the characteristics of the subsurface of the Basin. The ETa in the Basin was calculated by combining the PET data from the meteorological observations with the subsurface condition parameter n. In this study, the data of potential evapotranspiration and actual evapotranspiration from the same data source (GLDAS) were used to derive the value of n through the formula. In the subsequent work, the calculation results of n were used to calculate the potential evapotranspiration combined with the data of the actual observation site. This ensures consistency of the calculation results with the observatory observations and improves the accuracy of the regional calculation while also considering the spatial distribution characteristics of the subsurface conditions. In addition, surface evaporation uses evapotranspiration observations from the evaporation pan.

Structural equation model based on partial least squares (PLS-SEM)

Structural Equation Modeling (SEM) is a statistical method based on the covariance matrix of variables to analyze the relationship between variables, which is suitable for analyzing the path relationship between complex variables. However, the traditional structural equation model has high requirements for the data used. The data must follow the normal distribution and the observed variables should not be highly correlated. Therefore, this study used the SEM based on partial least squares (PLS-SEM).

The PLS-SEM method differs from the traditional SEM method, which focuses on estimating of path coefficients and the explanatory power of potential variables. It does not assume that the data obey the normal distribution, and aims to extract the principal components of latent variables, by compressing the original variables to construct latent variables, rather than directly estimating the relationship between latent variables, thereby reducing the direct dependence between variables and reducing the sensitivity to collinearity.

This study used R (a statistical analysis software) to simulate PLS-SEM. The construction steps of the model are the same as those of the traditional SEM, and the potential variables, observation variables and influence paths are determined according to the physical mechanism. After determining the model path matrix, we input the data corresponding to the variables, and call the 'plspm' package in R for simulation calculation.

Because PLS-SEM does not require the data to conform to the normal distribution, the fitting index GFI\RMSEA\NFI\CFI based on the assumption of data normality is not suitable for evaluating PLS-SEM. A GOODNESS-OF-FIT(GOF) is provided in the R language package to reference whether the model fits well. In this study, it is considered that GOF reaches 0.5, which is a good fitting level.

In addition to GOF, the model's results include the degree of explanation of direct and indirect effects between factors. The degree of explanation refers to the model's ability to explain a potential variable's variance. The direct influence refers to the direct path coefficient from one potential variable to another. Indirect influence refers to the path coefficient from one potential variable to another through the mediating role of other potential variables.

Model construction

We used the composition of ETa in the Yiluo River Basin as a categorization criterion to identify the drivers, construct the observed and latent variables in the structural equation modeling separately, and plan the impact pathways. In this study, precipitation (PRE), temperature (TEM), relative humidity (HUM), wind speed (WIN) and sunshine duration (SSD) were selected as climatic factors; Normalized Difference Vegetation Index (NDVI) and Leaf Area Index (LAI) were selected as vegetation factors; Four layers of soil moisture at different depths (0–10 cm, 10–40 cm, 40–100 cm, 100–200 cm) were selected; Water surface area and reservoir storage volume were selected as water body factors. To evaluate the effects of large reservoirs in the Yiluo River Basin, a reservoir capacity factor was added to the post-1993 structural equation modeling analysis.

In planning pathways between potential variables, climatic factors, as the main drivers of environmental change, directly impact vegetation, soil moisture, water, and evapotranspiration. Vegetation cover not only directly affects evapotranspiration, but also acts directly on soil moisture changes. Also, soil moisture and water surface evaporation contribute directly to watershed ETa (Fig. 3).

Fig. 3

Conceptual model of watershed-scale ETa-driven SEM (The dashed box indicates that the storage coefficient is taken into account in the model for 1993–2020. The ellipse represents the latent variable, the rectangle represents the observed variable, and the path and the arrow represent the influence and direction between the factors.)

Structural equation modeling was used to analyze the spatial distribution of evapotranspiration drivers in the Yiluo River Basin at the grid cell scale, aiming for comprehensive characterization. Due to the independence of the water surface, the water surface grid needs to be extracted using multi-year land use data. Meteorological, vegetation, and soil factors are considered in the terrestrial grid cells (Fig. 4a), and the effect of climatic factors on water surface evaporation is considered in the water surface grid cells (Fig. 4b). Additionally, to analyze the impact of large reservoirs on the climate change response mechanism of water surface evapotranspiration, the water surface grid was divided into two periods, with 1993 as the reference year.

Fig. 4

Conceptual modeling of structural equation models at the spatial grid scale (The ellipse represents the latent variable, the rectangle represents the observed variable, and the path and the arrow represent the influence and direction between the factors.)

Results

Spatial and temporal evolution of actual evapotranspiration in the Yiluo River Basin

From 1982 to 2020, the annual average ETa in the Yiluo River Basin was 544.13 mm, decreasing at 1.97 mm/a. The lowest point was in 2012, which experienced a decrease and then an increase in trend (Fig. 5a). Intra-annual variation reaches a maximum in July and a minimum in December or January (Fig. 5b). The annual variation ranges from 51.45 mm to 110.86 mm. The average ETa decline rate at the watershed surface was 0.013 mm/a spatially. The Basin exhibited a spatial distribution characterized by a slower decline rate in the southwestern mountainous areas and a faster decline rate in the northeastern plains (Fig. 5c).

Fig. 5

Trends in the spatial and temporal evolution of ETa in the Yiluo River Basin (a is the inter-annual variation of ETa, b is the intra-annual variation of ETa, and c is the spatial distribution of the trend in ETa)

Drivers of actual evapotranspiration at the watershed scale

The simulation results for 1982–1992 (Fig. 6) and 1993–2020 (Fig. 7) have a goodness-of-fit greater than 0.5 when using the watershed scale as the study unit. This indicates a moderate level of simulation. Between 1982 and 1992, the model accounted for 0.91, 0.84, and 0.75 of ETa, vegetation factors, and soil moisture, respectively, and a lower percentage for water body factors. The results indicate that vegetation changes directly impacted ETa during this period, with a direct impact coefficient of 0.833. In contrast, climate change, water body factors, and soil moisture had smaller direct impacts on ETa, with impact coefficients of − 0.023, − 0.006, and − 0.185, respectively. Climate change significantly impacts vegetation, as evidenced by a path coefficient of 0.914. It significantly negatively affects soil moisture, with a path coefficient of − 1.146. The path coefficient for the effects of vegetation factors on soil moisture was 0.312. Climate change was the dominant factors in the change of ETa during this period, with a degree of influence of 0.902, primarily through indirect effects. The total effect of vegetation factors on ETa was 0.775, a contribution second only to climate change (Table 2).

Fig. 6

Simulation results of basin scale Structural Equation Model from 1982 to 1992 (The paths with a significance level of 0.05 are indicated by solid lines, while dashed lines indicate non-significant paths. Red numeric markers denote positive impacts, while negative impacts are denoted by blue numeric markers.)

Fig. 7

Simulation results of basin scale Structural Equation Model from 1993 to 2020 (The paths with a significance level of 0.05 are indicated by solid lines, while dashed lines indicate non-significant paths. Red numeric markers denote positive impacts, while negative impacts are denoted by blue numeric markers.)

Table 2 Effects of evapotranspiration driving factors from 1982 to 1992

From 1993 to 2020, the degree of explanation for the water body factors increased with the addition of the reservoir capacity factors. However, the degree of explanation for ETa, vegetation factors, and soil moisture decreased to 0.876, 0.835, and 0.534, respectively. Compared with 1982–1992, the direct effect of climate change on ETa increased to 0.549, which is a significant enhancement; at the same time, its effect on vegetation factors and soil moisture decreased. The effect of vegetation factors on soil moisture shifted from positive to negative, as the effect of vegetation factors and soil moisture on ETa decreased by 0.502 and 0.406, respectively. In contrast, the degree of effect of water body factors on ETa increased by 0.096. The total impact of climate change on ETa remained at about 0.9, but the dominant mode shifted from an indirect to a direct impact. Additionally, the total impact of vegetation factors on ETa declined by 0.436 compared to 1982–1992 (Table 3).

Table 3 Effects of evapotranspiration driving factors from 1993 to 2020

Characterization of the spatial distribution driven by actual evapotranspiration at the grid scale

SEM was applied separately for land and water surfaces at the grid cell scale. In simulating the terrestrial grid cells, the goodness of fit for the model was greater than 0.58, with a mean of 0.66 and a standard deviation of 0.01 (Fig. 8a). The explanations provided by the model for ETa were concentrated between 0.77 and 0.88, with an average of 0.84. This suggests that the main factor contributing to the variation of ETa in the Yiluo River Basin is the compounding effect of natural drivers (Fig. 8b). The interpretation of ETa shows a decreasing trend in spatial distribution from upstream to downstream. Higher interpretations are observed in the southwest, while lower interpretations are observed in the northeastern plains (Fig. 8c).

Fig. 8

Goodness-of-fit of spatial structure equations and interpretation of ETa for terrestrial grids (a is the histogram of the distribution of goodness-of-fit, b is the histogram of the distribution of the explained degree of ETa, and c is the spatial distribution of the explained degree of ETa.)

The data distribution of the impact of climate change on ETa shows a bimodal shape, and its spatial distribution decreases from upstream to downstream. Climate change has promoted the change of ETa (Fig. 9a and d). The effects of climate change on vegetation and soil moisture show similar trends in numerical distribution. In general, the impact of climate factors on vegetation (Fig. 9b and e) is greater than that on soil moisture (Fig. 9c and f).

Fig. 9

Climate change impacts on ETa, vegetation and soil moisture (plots a, b, and c are histograms of the distribution of climate change impacts on ETa, vegetation and soil moisture, respectively, and d, e and f are spatial distribution maps.)

The influence of vegetation factors on ETa was concentrated between 0.11 and 0.65, which indicates that vegetation factors play a positive role in the change of ETa in the Yiluo River Basin (Fig. 10a). The spatial distribution of ETa in the upper and middle reaches of the Basin was highly affected by vegetation changes, while the lower reaches were relatively less affected (Fig. 10b). The effect of soil moisture on ETa was concentrated between − 0.26 and 0.06 (Fig. 10c). In the upper reaches of the Basin, the influence of soil moisture on evapotranspiration was mainly positive, and the influence of soil moisture on evapotranspiration in the lower reaches was mainly negative (Fig. 10d).

Fig. 10

The impact of vegetation (a, b) and soils (c, d) on actual evapotranspiration (a and c are distribution histograms and b and d are spatial distribution maps, respectively)

From 1982 to 1992, the coefficient of influence of climate change on water surface evaporation in the simulation of the water surface grid ranged from 0.83–0.90. The water surface evaporation was affected by natural climate change conditions, which increased from upstream to downstream accompanied by the increase in water volume (Fig. 11). The impact coefficients of climate change on water surface evaporation decreased from 1993 to 2020, ranging from 0.69 to 0.82 (Fig. 11).

Fig. 11

The impacts of climate change on water surface evaporation in the water surface grids (a is the spatial distribution of impact coefficients from 1982–1992, b is the spatial distribution of impact coefficients from 1993–2020, and c is a scatter plot showing the latitude and longitude data. The red dotted line represents the latitude and longitude of the Guxian Reservoir location, the green dotted line represents the latitude and longitude of the Luhun Reservoir location, and the blue dotted line represents the latitude and longitude of the confluence of the Yi River and the Luo River.)

Regarding spatial distribution, the areas upstream of Luhun Reservoir and near the confluence of the Yi and Luo Rivers are more rapidly impacted by climate change (Fig. 11). The upstream distribution of the reservoir remains constant, increasing from upstream to downstream. However, from the reservoir section to the downstream of the Basin, the degree of water surface evaporation affected by climate change shows a decreasing distribution.

Discussion

Impact of climate change on evapotranspiration

The study showed that evapotranspiration in the Yiluo River Basin decreased throughout the Basin from 1982 to 2020, consistent with findings by Li et al. (2018) and Ling et al. (2022). Climate change is a significant factor in the changes observed in actual evapotranspiration from watersheds. The primary influences are generally considered to be increasing temperatures and decreasing precipitation (Snyder et al. 2010). Meanwhile, researchers have widely emphasized climatic factors such as solar radiation, relative humidity, and wind speed (Zheng et al. 2022). The monsoon climate of the middle reaches of the Yellow River is characterized by distinct features resulting from the influence of the Asian summer winds and large-scale circulation (Ren et al. 2023). The analysis revealed that the climate change pattern in the Yiluo River Basin from 1982 to 2020 was characterized by both warm-drying and warm-wetting conditions. The temperature has been increasing at a rate of 0.03 °C/a, precipitation has been increasing in 69.8% of the area, but the mean annual ETa has been decreasing at a rate 1.97 mm/a. Additionally, the relative humidity decreased by 1.30% per year, the wind speed increased by 0.09 m/s per year, and the number of sunshine hours decreased at 3.42 h/a.

By comparing the results of the two phases, 1982–1992 and 1993–2020, it is evident that climatic factors always dominate the actual ETa in the watershed, with a total effect of over 0.9. The direct effect of climate change on ETa is significantly stronger in the second phase than in the first phase. However, the dominant factors that affect evapotranspiration response to climate change vary across different climatic regions (Tabari and Talaee 2014). Zhang et al. (2010) demonstrated that net radiation (r = 0.55) was the most sensitive meteorological variable for ET, followed by relative humidity (r = − 0.49). Liu et al. (2016) showed that vegetation's influence on ET in the humid zone is diminished. The study of Li et al. (2022) further indicated that in the dry zone, relative humidity and precipitation are the main influencing factors, while temperature, net radiation and wind speed play a dominant role in the humid zone. This study constructed an SEM with climatic factors as latent variables, integrating temperature, precipitation, relative humidity, wind speed, and sunshine duration. The simulation results indicated that temperature, precipitation, and relative humidity are the primary influencing factors in the Yiluo River Basin, with regression path coefficients greater than 0.8 among the climatic factors. Sunshine duration and wind speed are secondary factors, with the negative regression path coefficient of wind speed.

During the period 1982–1992, climate change affected ETa directly and indirectly through vegetation and soil, with the degree of indirect effect amounting to 0.925. Spatially, the impact of climate change on ETa shows a distribution pattern that is high in the upper reaches and low in the lower reaches. The reason is that in the Yiluo River Basin, vegetation changes positively impact ETa changes, and soil moisture changes have obvious spatial differences in regional ETa changes. Due to the high vegetation coverage in the upper reaches of the Basin, meteorological factors mainly indirectly affect ETa through vegetation. This indirect effect is weakened in the lower reaches.

Impact of vegetation changes on evapotranspiration

Vegetation change can significantly impact regional ETa and is susceptible to climate change (Yang et al. 2010; Lian et al. 2022). According to Wang et al. (2021a, b), vegetation greening is the primary cause of changes in evapotranspiration in the Yellow River Basin. Yang et al. (2021) also showed that the direct effect of vegetation change on ETa is more significant than climate change in the Yiluo River Basin. The study results indicate that vegetation varies on ETa depending on the period. The largest direct effect of vegetation on ETa was observed during 1982–1992, which was 0.81 greater than the effect of climate change. However, the direct effect of vegetation on ETa decreased during 1993–2020 compared to 1982–1992. This could result from the intensification of climate change, leading to stronger direct impacts on ETa.

Meanwhile, implementing soil and water conservation measures, such as returning farmland to forests and grasses to farmland, resulted in an overall increase in vegetation cover in the Yiluo River Basin from 1982 to 2020. However, Wang et al. (2021a, b) found that an increase in NDVI leads to a decrease in evapotranspiration in dry climatic regions, which may have mitigated the effect of vegetation on ETa. Over the past 40 years, NDVI and LAI in the Yiluo River Basin have increased at 0.001/a and 0.007/a, respectively. This is in contrast to the downward trend observed in ETa. The study utilized a similar methodology to investigate the correlation between precipitation and vegetation potential evapotranspiration ratios in the Yiluo River Basin. The results indicated that most of the Basin exhibited arid characteristics, which aligns with the spatial simulation outcomes of the SEM.

In addition, changes in soil moisture can be influenced by changes in vegetation cover (Bernard and Nader 1991). This study found that changes in vegetation contributed to an increase in soil moisture from 1982 to 1992. However, the path coefficient changed from positive to negative from 1993 to 2020. The data indicated that the recent increase in vegetation cover has contributed, to some extent, to the decrease in soil moisture in the area. Meanwhile, the spatial distribution trends of the effects of vegetation factors on soil moisture were similar to those of the rates of change of NDVI and LAI. This suggests that their effects on soil moisture are more pronounced in areas with faster growth of vegetation cover.

Impact of large reservoirs on evapotranspiration

This study compares and analyzes the impacts of large reservoirs on watershed ETa by dividing it into two periods. The time when the Guxian Reservoir was put into operation serves as the node. Simulations using SEM at the watershed scale revealed that while the reservoir capacity volume and water area have relatively small effects on ETa, they are still important factors that cannot be ignored. In addition, by comparing the simulation results of the two time periods, it is found that the contribution of the water body factors is increasing significantly.

The study also found that the large reservoirs have a moderating effect on regional climate change. The simulation results indicated an overall decrease in water surface evaporation in the Yiluo River Basin due to climate change from 1993–2020 compared to 1982–1992. However, the spatial distribution of the driving factors of climate change on water surface evaporation has changed significantly in this context. Unlike before the reservoir operation, water surface evaporation from the reservoir cross-section to the downstream of the watershed gradually weakens due to the degree of influence of climate change.

In an attribution study that analyzed the impact of large reservoirs on ETa, we drew quantitative conclusions by comparing the attribution results for the periods before and after reservoir operation. However, we also identified some SEM limitations when applied to spatial grid cells. When attributing, it is important to consider both the surface area of large reservoirs and water levels. However, the constructed model must be adjusted when transforming the grid cell type from terrestrial to water or vice versa. Additionally, the model simulation requires a certain sample size of data as input, which limits its flexibility in adapting to dynamic changes in the grid cell type. Furthermore, the requirement for precise data constrains the study's further development.

Conclusion

The study quantified the driving mechanisms of ETa at the watershed and grid-scale in the Yiluo River Basin using SEM. The drivers' compound effects and distribution characteristics in the spatio-temporal dimension are analyzed. The following conclusions were made:

(1) From 1982 to 2020, the annual average ETa in the Yiluo River Basin was 544.13 mm, decreased with a trend of 1.97 mm/a, with an intra-annual distribution that peaked in July and was lowest in December or January each year. The whole Basin shows a spatial distribution pattern with a small decline rate in the southwestern mountains and a large decline rate in the northeastern plains.

(2) Climate change is the dominant factors influencing the ETa changes in the Basin, with a total influence of more than 0.9, followed by the influence of vegetation changes. Compared with 1982–1992, in 1993–2020, the influence of climate change on ETa in the watershed changed from indirect to direct, with the direct influence increasing by 0.572; in addition, the direct influence of water body factors on ETa increased by 0.096, and the direct influences of vegetation changes and soil moisture on ETa weakened by 0.502 and 0.406, respectively.

(3) The ETa in the Yiluo River Basin is influenced by vegetation and soil moisture, particularly in the upstream area. Additionally, the impact of climate change on ETa differs between the upstream and downstream areas. In the upper reaches of the Basin with higher vegetation coverage, ETa is more strongly affected.

(4) Large reservoirs have significantly altered the spatial distribution of the driving force of climate change on water surface evaporation in the water surface grid. Under natural conditions, the impact of climate change on water surface evaporation gradually increases from upstream to downstream. However, after the operation of large reservoirs, the response of water surface evaporation to climate change gradually diminishes from the reservoir cross-section to the downstream of the watershed.