Sensitivity of transpiration to influencing factors at varying drought levels in Schima superba

Introduction: Uneven rainfall distribution alters tree water use patterns, ultimately influencing plantation establishment.

Methods: Based on monthly rainfall, six drought levels were classified. Whole-tree sap flux and meteorological variables were monitored across these levels from 2010 to 2013 in a pure Schima superba plantation in South China. The relationships between daily transpiration (T_t) and the influencing factors were modeled using the Support vector regression (SVR) method. Shapley additive explanations (SHAP) values were employed to characterize the sensitivity and contributions of four environmental variables to T_t.

Results: The results indicate that monthly rainfall (RF_t) significantly influences the sensitivity of these four environmental variables to T_t when RF_t exceeds 300 mm (Level 6). Furthermore, when RF_t is 300 mm or less (Levels 1–5), the sensitivity of these factors and their total contributions to T_t are independent of tree size.

Discussion: Our findings indicate that the decoupling between T_t and environmental factors may be a significant characteristic of ongoing water stress during high rainfall months. Additionally, these findings enhance the predictive capability of machine learning models in assessing tree water use.

Introduction

Global climate change has led to an increase in the number of extreme weather events in recent years (Zia et al., 2021; Brunet et al., 2024). Since the year 2000, southern China has experienced several severe droughts, particularly during four significant events in 2001, 2006–2007, 2009–2010 and 2020–2021, which have been identified as extreme “Water crisis” (Zhang et al., 2018). The uneven distribution of rainfall is a major factor contributing to drought in this region, which seriously affects the ecological establishment of plantations. Specifically, the intensity and frequency of rainfall profoundly influence the physiological behavior and ecological environment of trees. Even during prolonged mild to moderate drought, trees become particularly vulnerable to carbon starvation and biological invasion, potentially leading to chronic mortality (McDowell et al., 2008; da Silva et al., 2013; Anderegg et al., 2013; Chen et al., 2018; Kono et al., 2019).

Transpiration plays a crucial role in the physiological functioning of trees and serves as the primary mechanism for water use. Its dynamics are influenced by various internal and external factors. Meteorological conditions primarily govern instantaneous changes in transpiration, while soil factors determine its overall level (Wullschleger et al., 1998; Jiao et al., 2019). However, these influences may differ among trees of various sizes and ontogenetic stages (Andrade et al., 1998; Meinzer et al., 2001; Meinzer, 2003). Long-term synchronous monitoring of whole-tree sap flow and environmental factors significantly enhance our understanding of the relationship between these internal and external factors influencing tree water use, ultimately improving prediction efficiency. However, few studies have focused on the performance of tree transpiration responses to meteorological factors under varying drought conditions.

Environmental factors are critical in driving water movement within plants. Photosynthetically active radiation ( $PA{R}_t$ ) influences the opening and closing of stomata by affecting the amount of CO₂ absorbed during photosynthesis and heating the leaf surface, which subsequently impacts transpiration rates (Kume, 2017; Li et al., 2021). The air vapor pressure deficit ( $VP{D}_t$ ) significantly alters the water vapor pressure difference between the leaves and the surrounding air, directly affecting the transport of water vapor from the internal leaf to the external atmosphere (Fricke, 2017). Similarly, wind speed ( $W{S}_t$ ) affects the boundary layer resistance of plant leaves, as well as the dynamics of stomatal opening and closing and overall leaf temperature (Monteith and Mike, 1990; Holwerda et al., 2012; Carvalho et al., 2015). Furthermore, soil moisture content ( $S{M}_t$ ) impacts the ability of plant roots to absorb and transport water. A thorough understanding of these causal relationships provides a theoretical basis for predicting transpiration models based on environmental factors (Jarvis, 1976). The close relationships between sap flow, transpiration calculated based on sap flow and environmental factors have been demonstrated using double-variable analysis and multiple linear regression in different climate zones and forest types (e.g., Juhász et al., 2013; Shen et al., 2015; Wang et al., 2017; Han et al., 2019; Chen et al., 2022). However, multiple linear regression requires strict null assumptions, including linearity, independence and normality, while double-variable analysis did not adequately quantify the contributions of eigenvalues. In contrast, machine learning (ML) methods does not impose these stringent requirements. They not only demonstrate higher prediction accuracy and stability in drought sensitivity analysis but also effectively uncover and capture the relationships between input variables and forecast outcomes. Furthermore, they elucidates interactions among input variables through interpretive tools such as the SHAP algorithm and more sophisticated models. This comprehensive approach enhances our understanding of which factors are most sensitive to drought prediction (Zhang et al., 2024; Uexkull et al., 2016; Saha et al., 2023). Although ANNs are gaining increasingly popularity in predicting tree transpiration due to their flexible requirements (e.g., Liu et al., 2009; Whitley et al., 2009; Xu et al., 2017; Tu et al., 2019), there are currently no studies on Support vector Regression (SVR) in this context. The study emphasizes exploring the application of ML methods for analyzing tree transpiration sensitivity to drought. The objectives of this paper are to (1) determine the sensitivity of meteorological factors to the transpiration of three tree sizes across six levels of drought, as well as their total contributions to transpiration using SVR, and (2) examine how these responses vary with different drought levels and tree sizes.

Materials and methods

Field site and plant materials

The experiments were conducted at the South China Botanical Garden station of the Chinese Academy of Sciences in Guangzhou, Guangdong, China (113°21′E 23°10’N, 40 m altitude). This area experiences a subtropical monsoon climate, characterized by a wet season (April to September) and a dry season (November to January), with an annual average temperature of 21.8°C. The region receives an averages annual precipitation in 1710.5 mm, with over 80% occurring during the wet season. A pure Schima superba forest was established in the mid-1980s at a density of 1,046 plants per hectare. We sampled 15 30-year-old individuals as test objects and divided them into three size classes based on the method of Mei et al. (2010a) (Table 1).

Table 1

Table 1. Characteristics of tree samples.

Sap flux density and transpiration measurement

Granier’s thermal dissipation probe (TDP) (Granier, 1985) was used to measure xylem sap flux density ( $F_t$ , g·m⁻²·s⁻¹). These probes were 2 mm in diameter and 20 mm in length, consisting of a copper-constantan thermojunction. They were radially inserted into the sapwood of the stem samples at approximately 0.15 m apart vertically at breast height. The sensors were placed on the northern side and covered with aluminum foil to protect them from sunlight, while the top of the probes was sealed with waterproof silicone. The heated upper probe was supplied with a constant power of 0.2 W, while the unheated lower probe served as a reference. The temperature difference between the two probes were averaged every 30 s, and data were collected at 10-min intervals using a Delta-T logger. These records were then used to calculate $F_t$ using the empirical equation proposed by Granier (1987). Due to the substantial variation in sap flux at depths greater than 40 mm in the sapwood of Schima Superba (approximately 45% of the flux occurs at depths of 0-40 mm) (Mei et al., 2010b), the mean flux was calculated by adding the sap flux at these two depths, weighted by their respective areas. The weights were determined based on the ratio of sapwood area within the two depths to the total sapwood area. Whole-tree transpiration ( $T_t$ , g) was calculated every 10 min by

$\begin{array}{ll}{T}_t=\sum \left(F_{0-40}\times A_{0-40}+F_{40}\times A_{40}\right)\times \mathrm{t}& (1)\end{array}$

where, $F_{0-40}$ and $F_{40}$ represent the sap flux density in the outer xylem (0–40 mm) and inner xylem (>40 mm), respectively, while $A_{0-40}$ and $A_{40}$ are the sapwood areas corresponding to these densities, as calculated by Zhao et al. (2018). The time interval, t, is 600 s, with data averaged and recorded every 10 min by the logger.

Environmental measurements

Five environmental variables were monitored approximately 2 m above the forest upper canopy. Wind speed ( $W{S}_t$ , m·s⁻¹) was monitored using an AN4 Anemometer (Delta-T Devices Ltd., Cambridge, UK). Air temperature ( $Ta$ , °C) and relative humidity ( $RH$ , %) were monitored using a RHT2V-418 sensor (Delta-T Devices Ltd., Cambridge, UK). The air vapor pressure deficit ( $VP{D}_t$ , kPa) was calculated using the difference in vapor pressure between saturated and ambient air, combining the effects of air temperature and relative humidity. Photosynthetically active radiation ( $PA{R}_t$ , W·m⁻²) was monitored with a Li-Cor quantum sensor (LI-190SA, LI-COR, USA). Soil moisture content ( $S{M}_t$ , m⁻³·m⁻³) was assessed using three frequency domain sensors (SM200, Delta-T Devices, UK) at a depth of 30–40 cm. Monthly rainfall ( $R{F}_t$ , mm) data were obtained from the Guangzhou Statistics Bureau¹. All variables were recorded using the same logger as the sap flux measurements.

SVR

Support vector regression (SVR) is a significant extension of Support vector machine (SVM) specifically designed to address regression problems. It works by identifying a hyperplane defined by the equation $\mathrm{f}\left(\mathrm{x}\right)={\omega }^T\mathrm{x}+\mathrm{b}$ (representing the predicted value in the linear case) that creates a margin of $\left[\mathrm{f}\left(\mathrm{x}\right)-\epsilon ,\mathrm{f}\left(\mathrm{x}\right)+\epsilon \right]$ . The goal is to position this hyperplane so that most training samples fall within the margin, satisfying the condition |y − f(x)| ≤ ɛ, while keeping the complexity of the model as low as possible. This process can be formulated as an optimization problem:

min $\begin{array}{ll}\frac{1}{2}\parallel \omega {\parallel }^2+C{\displaystyle \sum }_{i=1}^m\left({\xi }_i+{\xi }_i^{\ast }\right)& (2)\end{array}$

subject to $\{\begin{array}{c}\hfill y_i-{\omega }^T{x}_i-b\le \epsilon +{\xi }_i\hfill \\ \hfill {\omega }^T{x}_i+b-y_i\le \epsilon +{\xi }_i^{\ast }\hfill \\ \hfill {\xi }_i,{\xi }_i^{\ast }\ge 0,i=1,\dots ,m\text{.}\hfill \end{array}$

where $\omega$ denotes the weight vector, C > 0 is the regularization parameter that balances the model’s fit accuracy and generalization ability (with C = 0.08 here). $\epsilon$ is the tolerance for prediction error (with $\epsilon$ =0.01 here). These two parameters can be determined using GridSearchCV from Scikit-learn. b is the bias, $x_i$ is the $i$ -th observation of the input vector (x ϵ R^d), and ${\xi }_i$ and ${\xi }_i^{\ast }$ are slack variables for guarding against outliers.

To transform the constrained optimization problem (Equation 2) into an unconstrained optimization one, Lagrange multipliers are introduced to formulate the Lagrangian function:

$\begin{array}{l}L\left(\omega ,{\xi }^{\ast },\xi ,\lambda ,{\lambda }^{\ast },\alpha ,{\alpha }^{\ast }\right)=\frac{1}{2}\parallel \omega {\parallel }^2+C{\displaystyle \sum }_{i=1}^m\left({\xi }_i+{\xi }_i^{\ast }\right)\\ +{\displaystyle \sum }_{i=1}^m{\alpha }_i\left(-y_i+{\omega }^T{x}_i+b-\epsilon -{\xi }_i\right)\\ +{\displaystyle \sum }_{i=1}^m{\alpha }_i^{\ast }\left(y_i-{\omega }^T{x}_i-b-\epsilon -{\xi }_i^{\ast }\right)-{\displaystyle \sum }_{i=1}^m{\lambda }_i{\xi }_i+{\lambda }_i^{\ast }{\xi }_i^{\ast }\end{array}\text{ (3)}$

Where ${\alpha }_i$ , ${\alpha }_i^{\ast }$ , ${\lambda }_i$ and ${\lambda }_i^{\ast }$ are Lagrange multipliers; the first two correspond to inequality constraints, while the last two are associated with the non-negative constraints.

The minimum of Equation 3 can be determined based on the Karush-Kuhn-Tucker (KKT) conditions, yielding the dual optimization form in Equation 4 by taking the partial derivatives with respect to $\omega$ , b, ${\xi }_i$ and ${\xi }_i^{\ast }$ (Vapnik, 1995; Smola and Schölkopf, 2004):

$\begin{array}{l}max-\frac{1}{2}{\displaystyle \sum }_{i,j=1}^m\left({\alpha }_i-{\alpha }_i^{\ast }\right)\left({\alpha }_j-{\alpha }_j^{\ast }\right)x_i{x}_j-\epsilon {\displaystyle \sum }_{i=1}^m\left({\alpha }_i+{\alpha }_i^{\ast }\right)\\ +{\displaystyle \sum }_{i=1}^m{y}_i\left({\alpha }_i-{\alpha }_i^{\ast }\right)\end{array}\text{ (4)}$

subject to $\{\begin{array}{c}\hfill {\displaystyle \sum }_{i=1}^m\left({\alpha }_i^{\ast }-{\alpha }_i\right)=0\hfill \\ \hfill 0\le {\alpha }_i,{\alpha }_i^{\ast }\le C\hfill \end{array}$

thus, $\omega$ is equal to ${\displaystyle \sum }_{i=1}^m\left({\alpha }_i^{\ast }-{\alpha }_i\right)x_i$ , and the function approximation can be rewritten as follows:

$\begin{array}{ll}\mathrm{f}\left(\mathrm{x}\right)={\displaystyle \sum }_{i=1}^m\left({\alpha }_i^{\ast }-{\alpha }_i\right)\mathrm{x}+\mathrm{b}& (5)\end{array}$

Equation 5 represents the linear case (Kernel = ‘Linear’). For the nonlinear case, SVR can map the input data to a higher-dimensional kernel space using kernel functions such as Gaussian, Polynomial and Sigmoid kernels.

Data and analyses

According to the Chinese meteorological industry standard ‘Rainfall Process Classification’ (QX/T 489–2019), six levels of rainfall intensity were defined based on monthly rainfall to explore the sensitivity of environmental factors to sap flux in three classes of S. superba under drought stress (Table 2). Accordingly, six datasets were selected from the years 2010–2013, each comprising 10-min interval sap flux data and the corresponding environmental data when $PA{R}_t$ was at least 5 w·m⁻². Of these datasets, 80% were used for training, while the remaining 20% were used for testing. Daily transpiration ( $T_t$ ), calculated using Equation 1 for each class, was modeled as an output series using SVR with Scikit-learn in Python 3.12, with environmental variables served as input series. All series were standardized, denoised, and made stationary using the z-score method, Haar transformation, and differencing before modeling. Their stationarity and white noise characteristics were assessed using the Augmented Dickey-Fuller test and the Portmanteau test. During the testing phase, the Nash-Sutcliffe Efficiency coefficient (NSE) and Root Mean Square Error based on the observations’ standard deviation (RSR) were used to evaluate the effectiveness of the SVM models considering their advantages (Moriasi et al., 2007). The Root Mean Square Error (RMSE) was utilized to determine the optimum kernel function.

$\begin{array}{ll}\mathrm{N}\mathrm{S}\mathrm{E}=1-\frac{{{\displaystyle \sum }}_{i=1}^n{\left(P_i-O_i\right)}^2}{{{\displaystyle \sum }}_{i=1}^n{\left(O_i-{\overline{O}}_i\right)}^2}& (6)\end{array}$

$\begin{array}{ll}\mathrm{R}\mathrm{S}\mathrm{R}=\sqrt{\frac{{{\displaystyle \sum }}_{i=1}^n{\left(P_i-O_i\right)}^2}{{{\displaystyle \sum }}_{i=1}^n{\left(O_i-{\overline{O}}_i\right)}^2}}& (7)\end{array}$

$\begin{array}{ll}\mathrm{RMSE}=\sqrt{\frac{{{\displaystyle \sum }}_{i=1}^n{\left(O_i-{\overline{O}}_i\right)}^2}{n}}& (8)\end{array}$

Table 2

Table 2. Characteristics of six levels and data choosing.

Where $P_i$ is the predicted value, $O_i$ is the actual value, and ${\overline{O}}_i$ is the average of the actual value; n is the total number of datasets. The prediction accuracy of the models was evaluated as follows: I. very good (0.75 < NSE ≤ 1 and 0 ≤ RSR ≤ 0.5); II. good (0.65 < NSE ≤ 0.75 and 0.5 < RSR ≤ 0.6); III. Satisfactory (0.5 < NSE ≤ 0.65 and 0.6 < RSR ≤ 0.7); IV. unsatisfactory (NSE ≤ 0.5 and 0.7 < RSR).

Shapley additive explanations (SHAP) was first utilized to explain the results of the SVR models for $T_t$ . Unlike traditional correlation and determination coefficients, SHAP values can highlight the direction of each feature’s contribution and quantify their impacts on the final prediction, regardless of whether they are present in the test instances (Mastropietro et al., 2023). In this context, the sensitivity of environmental factors to $T_t$ is quantified by the mean value of |SHAP|. A higher mean value indicates greater sensitivity of those factors to $T_t$ , and vice versa. The accumulation of SHAP values reflects the total contributions of these factors to $T_t$ .

Results

Daily transpiration, sap flux and environmental factors variation

At all six levels, the coefficient of variation (CV.) of $T_t$ and $F_t$ exhibited consistent variation (Figure 1a), while their means did not align (Figure 1b). The $T_t$ of Class 1 was the highest, followed by Class 2 and 3. In contrast, $F_t$ did not consistently follow the class order, with the exception of Level 2, where Class 2 showed the highest value. This suggests that larger trees use more water in terms of transpiration. Notably, both $T_t$ and $F_t$ reached their highest values at Level 5, which may be attributed to their relative stability, indicated by lower CV value (Figure 1b).

Figure 1

Figure 1. Changes in the original series of sap flux (Ft), daily transpiration (Tt) and their Coefficient of Variation (CV) across Levels 1 to 6. (a) mean values of Ft and CV for both Ft and Tt. (b) mean value of Tt.

Only the mean of $S{M}_t$ varied consistently across the levels, indicating that monthly rainfall significantly affects $S{M}_t$ . Compared to Level 1, $S{M}_t$ showed a modest increase of 4% at Level 2, while it increased the most—by 52%—at Level 6 (Figure 2a). Additionally, $S{M}_t$ exhibited the smallest variability among the factors (Figure 2b). For other environmental variables, the highest mean values of $PA{R}_t$ , $VP{D}_t$ and $W{S}_t$ were observed at Level 5, Level 4 and Level 1, respectively, while the lowest values were found at Level 2 for $PA{R}_t$ , Level 2 for $VP{D}_t$ and Level 4 for $W{S}_t$ (Figures 2a,b). Overall, $W{S}_t$ exhibited the largest variability across Levels 1–4 (Figure 2b).

Figure 2

Figure 2. Changes in the original series of environmental factors and their Coefficient of Variation (CV) across Levels 1 to 6. (a) mean values of soil moisture (SMt) and photosynthetically active radiation (PARt). (b) mean values of wind speed (WSt), air vapor pressure deficit (VPDt), and the CV for SMt, VPDt and PARt.

Model establishing and calibration

For rigor, the time series of all participating models used for training were stationary and no-white noise (Table 3). The first-order difference of $S{M}_t$ (denoted as D. $S{M}_t$ ) for Level 2, 5 and 6 was stationary (p < 0.05), while D. $S{M}_t$ for Level 2 exhibited white noise characteristics (p > 0.05). The series for the others levels were stationary and non-white noise at the current order (p < 0.05).

Table 3

Table 3. Augmented Dickey-Fuller test for unit root and Portmanteau test for white noise.

Eighteen SVR models with linear kernels, based on Equation 8 and corresponding to six levels, were developed, with the predictions shown in Figure 3. Fifteen models across all three classes at Levels 1–5 were successfully constructed and performed very well based on Equations 6 and 7, with NSE values ranging from 0.77 ~ 0.98 and RSR values from 0.16 ~ 0.48. However, only three models corresponding to the three classes at level 6 performed poorly, with NSE values ranging from −0.41 to −0.17 and RSR values from 1.08 to 1.19.

Figure 3

Figure 3. SVR testing results for daily transpiration in Classes1 to 3 across Levels 1 to 6. (a) Level 1. (b) Level 2. (c) Level 3. (d) Level 4. (e) Level 5. (f) Level 6.

Sensitivity of transpiration to environmental factors

From Figure 3f, the very poor performance of the SVM models at Level 6 indicated that the four environmental factors are insensitive to daily transpiration ( $T_t$ ). As a result, the total contribution of all factors to $T_t$ at Level 6 could not be predicted. At Levels 1–5, where high-accuracy prediction models were established, $PA{R}_t$ was found to be the most sensitive factor to $T_t$ , followed by $VP{D}_t$ and $W{S}_t$ , with $S{M}_t$ exhibiting the least sensitivity (Figures 4d–f–8d–f). However, the sensitivity of the three classes did not differ significantly across Levels 1–5 (p > 0.05, Table 4), suggesting that the observed sensitivity is not related to tree size. Interestingly, the total contributions of $PA{R}_t$ and $VP{D}_t$ to $T_t$ does not align with this order, except at levels 4 and 5 (Figures 4a–c–8a–c). The Mann–Whitney U test indicated that the contributions of all factors to $T_t$ among the three classes did not differ significantly between Levels 1–5 (p > 0.05, Table 5). Similar results were observed within levels, except for $W{S}_t$ at level 5 and $S{M}_t$ at level 1. Additionally, the directions of contribution were consistent across the same levels. However, the effect of $S{M}_t$ to $T_t$ for three classes at Levels 2 and 5 could not be predicted, as D. $S{M}_t$ was considered white noise.

Figure 4

Figure 4. SHAP values of environmental factors affecting transpiration in Classes 1 to 3 at Level 1. (a-c) SHAP values for Class 1 to 3. (d-f) mean |SHAP values| for Class 1 to 3.

Figure 5

Figure 5. SHAP values of environmental factors affecting transpiration in Classes 1 to 3 at Level 2. (a-c) SHAP values for Class 1 to 3. (d-f) mean |SHAP values| for Class 1 to 3.

Figure 6

Figure 6. SHAP values of environmental factors affecting transpiration in Classes 1 to 3 at Level 3. (a-c) SHAP values for Class 1 to 3. (d-f) mean |SHAP values| for Class 1 to 3.

Figure 7

Figure 7. SHAP values of environmental factors affecting transpiration in Classes 1 to 3 at Level 4. (a-c) SHAP values for Class 1 to 3. (d-f) mean |SHAP values| for Class 1 to 3.

Figure 8

Figure 8. SHAP values of environmental factors affecting transpiration in Classes1 to 3 at Level 5. (a-c) SHAP values for Class 1 to 3. (d-f) mean |SHAP values| for Class 1 to 3.

Table 4

Table 4. Mann–Whitney U test results for the mean |SHAP| values of all factors across three classes at Level 1–5.

Table 5

Table 5. Mann–Whitney U test for the accumulated SHAP values of all factors across three classes at Level 1–5.

Interaction of environmental factors

External environmental factors not only affect the transpiration of trees individually but also regulate transpiration through complex interactions. For example, high $PA{R}_t$ , and high $VP{D}_t$ generally increase transpiration. However, under conditions of low $S{M}_t$ or increased $W{S}_t$ , trees may respond to these factors by closing their stomata, thereby limiting transpiration. The synergistic or antagonistic interactions among these factors depend on specific environmental conditions, plant species, and forest types. From Supplementary Figures 1, 4, 6, it is evident that $S{M}_t$ (at Levels 1, 3 and 4), $W{S}_t$ and $VP{D}_t$ (at Levels 1–5) did not significantly impact the influence of $PA{R}_t$ to $T_t$ across the three tree classes at Levels 1, 3 and 4, as they transitioned without trends with $PA{R}_t$ . This indicates that there is no interaction between $S{M}_t$ and $PA{R}_t$ , $W{S}_t$ and $PA{R}_t$ , or $VP{D}_t$ and $PA{R}_t$ concerning $T_t$ . In contrast, $S{M}_t$ negatively influenced the effects of $VP{D}_t$ and the reduction of $W{S}_t$ to the predicted $T_t$ (Supplementary Figures 2, 3) across all classes at Levels 1, 3 and 4, except for class 1 at Level 1 (Supplementary Figures 2a1, 3a1). Similarly, $W{S}_t$ also negatively impacted the influence of $VP{D}_t$ to $T_t$ across all classes at Levels 1–5 (Supplementary Figure 5), except for Class 3 at Level 5 (Supplementary Figure 5e3).

Discussion

Several key factors, including $R{F}_t$ , $Ta$ , $RH$ , $PA{R}_t$ , $VP{D}_t$ , $W{S}_t$ and $S{M}_t$ , have been identified as major determinants of tree transpiration (e.g., Juhász et al., 2013; Shen et al., 2015; Wang et al., 2017; Wei et al., 2017; Xu and Yu, 2020; Chen et al., 2022). However, Ta, RH, and $VP{D}_t$ , which is derived from the first two, are often considered simultaneously in regression models, potentially leading to collinearity issues (e.g., Yu et al., 2009; Liu et al., 2017; Wei et al., 2017; Han et al., 2019). While some studies employ principle component analysis (PCA) to address collinearity, eliminating multicollinear factors can enhance the efficiency of deep learning (DL) models (O'Brien et al., 2004; Juice et al., 2016; Xu and Yu, 2020; Li et al., 2022). Fan et al. (2020) compared the three ML models and one DL model in estimating daily maize transpiration, finding that deep neural networks (DNN) outperformed the others, with support vector machines (SVM) being the next best. In contrast, this study utilized an SVM that accounts for autocorrelation to analyze the sensitivity of the whole-tree transpiration of S. superba is to environmental factors, particularly because DNNs performed poorly. Variables included were $PA{R}_t$ , $VP{D}_t$ , $W{S}_t$ and $S{M}_t$ , while Ta and RH were excluded. Additionally, monthly precipitation was considered a limiting factor for measuring drought.

Overall, $PA{R}_t$ and $VP{D}_t$ exhibited the highest sensitivity to $T_t$ when $R{F}_t$ ≤300 mm (Levels 1–5), during which the SVR models were well-developed. Numerous studies have been conducted across different climate zones and ecosystems. Based on traditional regression analysis, the influence of $VP{D}_t$ on $F_t$ and transpiration is often greater than that of $PA{R}_t$ in tropical climate zones (e.g., Oguntunde and Oguntuase, 2007; Köhler et al., 2010; Huang et al., 2021). Conversely, in temperate climates, the impact of $PA{R}_t$ tends to be greater than that of $VP{D}_t$ (e.g., Huang et al., 2010; Yue et al., 2008; Zheng and Wang, 2015; Shen et al., 2015; Wei et al., 2017; Thomsen et al., 2020). Although this research was conducted in a subtropical climate zone, $T_t$ was found to be more responsive to $PA{R}_t$ than to $VP{D}_t$ , aligning with the findings of Wang et al. (2017). However, $VP{D}_t$ exhibited the opposite trend, except at Level 3, indicating that depressed trees are unable to tolerate water deficits in their leaves. This may be attributed to their relatively unstable CO₂ assimilation and low biomass allocation due to shallow roots (Sabir et al., 2020; Zafar et al., 2019). The effects of $W{S}_t$ on $F_t$ and transpiration were inconsistent due to substantial temporal variation (e.g., Tang et al., 2006; Chen et al., 2019; Chen et al., 2022), although significant effects were noted (e.g., Oguntunde and Oguntuase, 2007; Huang et al., 2010; Huang et al., 2015). There are primarily two different responses of transpiration to increases in $W{S}_t$ , as noted by Laplace et al. (2013): linear responses (e.g., Juhász et al., 2013; Wang et al., 2017) and saturated responses (e.g., Li et al., 2022; Chen et al., 2024). Moreover, $W{S}_t$ tends to affect the daytime $F_t$ more than nighttime $F_t$ (Han et al., 2019). In our study, $W{S}_t$ was the third most sensitive factor affecting daytime $T_t$ of S. superba, exhibiting linear decreases. Additionally, it influences other factors. Komatsu et al. (2006) found that the promotion of $VP{D}_t$ to $F_t$ depends on $W{S}_t$ <0.7 m·s⁻¹. We observed that $W{S}_t$ negatively influenced the overall promotion of $VP{D}_t$ to $T_t$ (Supplementary Figure 5). However, tree size did not significantly influence the responses of $T_t$ to $PA{R}_t$ , $VP{D}_t$ and $W{S}_t$ (Table 4), despite the theoretical expectation that larger trees would have a greater impact due to their increased surface area in contact with the atmosphere. The discrepancy may be attributed to variations in the actual contact area, which could depend on other factors such as the vertical distribution of leaf area and transient differences caused by fluctuations in wind speed, rather than just plant height and leaf size. Similar to $W{S}_t$ , most studies suggest that $S{M}_t$ significantly affects $S{F}_t$ and transpiration, except for those by Tang et al. (2006), Shen et al. (2015), and Ma et al. (2017). Our results supports the views although it showed the least sensitive to $T_t$ , which aligns with Huang et al. (2021). The finding that $S{M}_t$ has a greater negative effect on $T_t$ in Class 1 compared to the positive effects observed in Class 2 and 3 at the same level (level 4) is inconsistent with the observation that larger trees with deeper roots are less sensitive to depletion in $S{M}_t$ (Dawson, 1996). This inconsistency may arise because trees benefit from more effective roots in the upper moist soil layer (Wei et al., 2017; Ochoa and Abdallah, 2023). Additionally, $S{M}_t$ influenced the promotion of $VP{D}_t$ and the demotion of $W{S}_t$ in relation to $T_t$ (Supplementary Figures 3, 5). However, it has no effect on the increase of $PA{R}_t$ to $T_t$ , nor do $W{S}_t$ , $VP{D}_t$ (Supplementary Figures 1, 4, 6), even during Level 1 of the worst drought. In other words, $PA{R}_t$ affected $T_t$ independently, while the others did not. Across different levels (1–5), the total contributions of all four factors to $T_t$ also do not vary with tree size (Table 5). One possible cause could be that the drought was not severe enough, as our study site is located in a humid region of China. In contrast, a decoupling occurs between $T_t$ and environmental factors when $R{F}_t$ exceeds 300 mm. This decoupling may lead to an abnormal transpiration rate, resulting in the formation and accumulation of bubbles in the xylem ducts, which affects water transport and can cause cavitation in the xylem. Consequently, even during high rainfall months, if a tree has previously experienced drought stress, its transpiration rate may remain abnormal, leading to continued water stress. Additionally, some studies indicate that this abnormality is significantly related to the obstruction of stomatal behavior caused by rainfall (Smith and McClean, 1989; Meinzer et al., 1995; Meinzer et al., 1997; Lu et al., 2016). Therefore, it is essential to pay closer attention to the impact of immediate rainfall on transpiration and its relationship with environmental factors. Given the low sensitivity of ${\mathrm{S}\mathrm{M}}_t$ on $T_t$ in S. superba, we recommend mitigating the transpiration rate imbalance caused by rainfall thresholds by incorporating other shallow-rooted tree species.

Conclusion

This study demonstrates the application of Machine Learning (ML) in assessing tree water use concerning drought sensitivity analysis, revealing the threshold effect of monthly rainfall on the coupling of environmental factors in relation to transpiration. Five SVR models, which accounted for autocorrelation in daily transpiration of S. superba at five drought levels, revealed that daily transpiration is sensitive to all four environmental factors when $R{F}_t$ ≤300 mm, in the following order: $PA{R}_t$ > $VP{D}_t$ > $W{S}_t$ > $S{M}_t$ . The mean total contributions to $T_t$ were ranked as follows: $VP{D}_t$ > $PA{R}_t$ > $W{S}_t$ > $S{M}_t$ . Additionally, this sensitivity and total contributions did not vary with tree size. However, when $R{F}_t$ >300 mm, daily transpiration becomes insensitive to all environmental factors.

Data availability statement

The data analyzed in this study is subject to the following licenses/restrictions: The data that support the findings of this study are available on request from the corresponding author. Requests to access these datasets should be directed to Xiaowei Zhao, eHd6ZXZlckAxNjMuY29t.

Author contributions

XZ: Conceptualization, Formal analysis, Funding acquisition, Investigation, Methodology, Writing – original draft, Writing – review & editing. LZ: Data curation, Investigation, Project administration, Resources, Supervision, Writing – review & editing.

Funding

The author(s) declare that financial support was received for the research and/or publication of this article. This study was financially supported by the scientific Research Foundation for Ph.D, Shangluo University (23SKY010).

Conflict of interest

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Generative AI statement

The authors declare that no Gen AI was used in the creation of this manuscript.

Publisher’s note

All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.

Supplementary material

The Supplementary material for this article can be found online at: https://www.frontiersin.org/articles/10.3389/ffgc.2025.1572414/full#supplementary-material

Footnotes

1. ^http://tjj.gz.gov.cn/

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