The intra-annual intrinsic water use efficiency dynamics based on an improved model

The carbon isotope fractionation value (Δ) has been widely used to infer the intrinsic water use efficiency (iWUE) of C3 plants. Currently, the most commonly used iWUE method (expressed as iWUEtra) in tree-rings assumes that the mesophyll conductance in plants is infinite. However, many observation-based studies have pointed out that such an assumption leads to overestimating the impact of carbon dioxide (CO2) on iWUE in plants. In this study, a constant gs/gm ratio (0.79) is introduced for calculating iWUE (expressed as iWUEmes). We apply this iWUEmes model to our newly developed intra-annual (10 samples per ring) Δ13C chronologies of Cryptomeria fortunei tree for 1965–2017 at Gu Mountain Area and our annual Δ13C chronology of Pinus massoniana tree for 1865–2014 at Niumulin Natural Reserve in southeast China. Using dendrochronology techniques, our analysis shows that the current iWUEtra model overestimates the iWUE values by approximately a factor of two and that the iWUE value of trees inferred from iWUEmes modeling decreases significantly in summer-autumn time, which likely indicates that alternative factors play a role in limiting the degree of iWUE improvement under the drought-stressed forest in southeast China.


Introduction
Stable isotopes in tree-rings could provide palaeoclimate reconstructions with perfect annual resolution and statistically defined confidence limits to study a variety of natural phenomena or events (Farquhar et al. 1989;McCarroll and Laoder 2004;Huang et al. 2007;Silva Lucas and Anand 2013;Liu et al. 2014;Smith et al. 2016). For example, as a proxy, the stable carbon isotope ratios in tree-rings are often used to reconstruct past climate and environmental changes (Farquhar et al. 1989;Ehleringer and Cerling 1995;Franks et al. 2013) and to study the physiological and ecological changes of trees caused by past climate regime (Tei et al. 2014).
Intrinsic water use efficiency (iWUE) in plants is a physiological efficiency that represents the ratio of net assimilation (A) and stomatal conductance to water vapor (g w ). It reflects the relationship between plant water consumption and dry matter production, therefore is a comprehensive physiological and ecological index for evaluating the suitability of plant growth (McCarroll and Laoder 2004;Matthias et al. 2004). The increase in atmospheric CO 2 levels (C a ) can theoretically increase the intercellular CO 2 concentration of plant leaves (C i ), and therefore, can promote the photosynthesis of plants, resulting in a "fertilization effect" (Huang et al. 2007). In addition, this increase in C a also causes a decrease in stomatal conductance (Prentice and Harrison 2009;Silva Lucas and Anand 2013). Consiquently, iWUE shows an increasing trend with the increase of C a , which can alleviate drought to a certain extent and is beneficial to the growth of plants in arid and semi-arid areas (Leavitt 1993;Dawson et al. 2002;Andrea et al. 2014;Liu et al. 2014;Fu et al. 2016).
The current iWUE model proposed by Farquhar et al. (1989) is shown in Eq. 7 below which has been widely used to infer iWUE based on the δ 13 C values in climate archives, such as pasture (Köhler et al. 2012), tree-rings (Franks et al. 2013;Der Sleen et al. 2015), or animal tissue (Barbosa et al. 2010). Compared with the instantaneous iWUE measured by gas exchange, the biomass-based Δ provides a time-integrated iWUE and enables time series analysis from days to thousands of years (Matthias et al. 2004;Soh et al. 2019;Adams et al. 2020).
However, some researchers consider that the traditional model's biased prediction of iWUE limits its application to qualitative assessment (Seibt et al. 2008;Ma et al. 2020;Gong et al. 2022). The main limitation of using the traditional iWUE model (iWUE tra ) is the simplification of the mesophyll conductance (g m , the diffusion conductance of CO 2 from the intercellular space to the carboxylation site). This assumption leads to significant overestimation of WUE ) and errors in the rate of WUE gain with time (Gong et al. 2022), as g m is not conservatively high (Seibt et al. 2008;Flexas et al. 2010). In other words, it may not be appropriate to apply an infinite or species-specific constant g m in the iWUE model. In general, the wide application of the 12 C/ 13 C isotope fractionation method in calculating the iWUE usually ignores the influence of the mesophyll conductance, either because of technical reasons (difficult to measure mesophyll conductance), or because its impact is assumed to be relatively small (assuming infinite g m exists in iWUE tra ) (Ulli et al. 2008;Franks et al. 2013;Stangl et al. 2019). Ma et al. (2020) showed that the overestimation effect of the iWUE tra model was more pronounced at lower Δ, i.e., it is not a systematic bias. Based on an integrated analysis of published data worldwide, g s /g m was relatively stable between long-term drought stress treatments and plant functional groups, with an average value of 0.79 (g s , the stomatal conductance to CO 2 ). For mechanistic studies or quantitative predictions that require high accuracy, it is recommended to use species-specific g s /g m into the iWUE mes model for iWUE estimation. While in the absence of species-specific g s /g m information, it is recommended to use the empirical coefficient g s /g m = 0.79 for calculation. The iWUE mes model can more accurately predict the iWUE in plants and can be widely used in research fields such as plant physiology, paleoclimate reconstruction, and crop breeding screening.
In southeast subtropical China, the Western Pacific Subtropical High (WPSH) causes high temperatures and low rainfall during the summer-autumn time (Li et al. 2013). Li et al. (2017) suggested that the contribution of iWUE to the tree growth in southeast China is not significant in most periods. The promotion of the increased iWUE on tree growth in southeast China determined by Li et al. (2019) does not compensate for the growth limitation caused by drought. The above results were all based on analyses of the whole rings and the iWUE tra modellings have shown similar conclusions that the iWUE increased significantly with increasing C a while the growth was not stimulated in trees in southeast China (Li et al. , 2019. This shows that C a is probably not the only factor that affects the iWUE of trees in different regions. Yet, the cause and influencing factors of the iWUE changes during the growing season are still unknown. Here, we hypothesize that, because of higher climate variability and more stable C a , the intra-annual scale can better reflect how the iWUE changes and what affects it. To test this, ten higher-resolution intra-annual tree-ring δ 13 C chronologies from 1965 to 2017 at Gu Mountain Area (GM), combined with our tree-ring δ 13 C data from Niumulin Natural Reserve (NML) that has previously been published , were established. This study aims to (1) calculate the iWUE of trees at GM using the higher-resolution iWUE mes model that includes the g m effect; (2) show the characteristics of iWUE on the intra-annual (representing the drastic changes of climate variables from winter to summer) and annual scales (representing the longer inter-annual change of C a ) with two different models; and (3) further disentangle the relationship between C a , climate, and iWUE under droughtstressed conditions.

Sampling site and climate data
Our study sites were at Gu Mountain Area (GM, 25°20′-26°05′ N, 119°22′-119°25′ E, about 8 km away from the downtown area of Fuzhou City) and Niumulin Natural Reserve (NML, 25°23′-25°25′ N, 117°55′-117°57′ E)   (Fig. 1). GM is located in the transition zone from the south subtropical zone to the mid-subtropical zone. It is warm and humid with abundant rainfall throughout the year (Zhang et al. 2009). According to the nearest Fuzhou meteorological observation data from 1953 to 2019, the average annual precipitation is 1366 mm, and the average annual temperature is 19.9 ℃. Pinus massoniana and Cryptomeria fortunei are constructive species within the well-protected forests. In July of 2018, a total of 186 tree cores were collected from a sample of 87 living Cryptomeria fortunei trees with a mean age of 75 years at GM. In April of 2014, a total of 83 tree cores were collected from a sample of 41 living Pinus massoniana trees with a mean age of 154 years at NML. These were collected using 5-mm diameter increment borers to extract 2-3 cores from each tree at a height of 1.3 m. The tree-ring samples at both sites were free from environmental pollution (Chen et al. 2021). The climate data of GM and NML sampling sites are obtained from the nearby Fuzhou meteorological station and Yong'an meteorological station, respectively.
In order to obtain more real-time data on C i during the growing season for trees, we downloaded the monthly global C a observation data from the Mauna Loa Observatory in Hawaii (gml.noaa.gov/ccgg/trends/) (19°45′32.4″ N, 155°27′22.8″ W), USA, for the period 1958-2017. Furthermore, we calculated meteorological variables and C a corresponding to 10 intra-annual periods based on the length of the tree growing season (April-October) at GM.
Then, we calculated the vapor pressure deficit (VPD, kPa) at the GM, which is obtained from the temperature and humidity corresponding to each intra-annual time by the following equation (Campbell and Norman 1977): where RH is the relative humidity of the air, T is the air temperature; the constants a, b, and c are 0.611 kPa, 17.502, and 240.97 ℃, respectively.

Separation of high-resolution intra-annual tree-rings
Cores were air dried and hand-sanded with sand paper up to 1200 grit. Visual crossmatching and skeleton plots were used to assign a calendar date to each ring (Stokes and Smiley 1968). In order to retain as much climate information in tree-rings as possible, our paper mainly used a spline function with an average length of two thirds of the steps for the sampled rings to remove the tree growth trend. We applied the Friedman method for several rings with unsatisfactory fitting effect. Moreover, in order to avoid the influence of extreme values on the average tree-ring chronology caused by phenomena such as growth release caused by the sudden weakening of competition among trees, we employed the ARSTAN program to select the biweight averaging method to calculate the tree-ring chronology, for this method assigns less weight to extreme values that deviate from the average growth condition of tree-rings (Cook 1985) (Fig. S1).
Using the results from the COFECHA and the moving correlation coefficient between a single sample core and the master sequence, we selected a total of 6 Cryptomeria fortunei tree cores with higher correlation coefficients, longer sequences, relatively wide annual rings, no obvious differences in growth, and with the fewer missing rings. These were used to carry out high-resolution experiments of stable carbon isotopes in tree-rings. In this study, the average ring width of Cryptomeria fortunei tree we used is 5 mm. In order to obtain more accurate and high-resolution intra-annual sub-samples, we measured the width of each annual ring of each tree core in advance and divided it into 10 sub-samples equally. We then cut off each sub-ring using a dissecting scalpel according to the calculated width value.

Chemical treatment and stable isotope measurement
With a slight improvement on the method proposed by Liu et al. (2007), we followed the standard method (Leavitt 2008) to mix each intra-annual sub-sample and to extract α-cellulose from the wood. We used custom-made hourglass tubes to realize the full reaction of the chemistry reagent, thereby speeding up the further steps and saving experimental time. The more details for the improved extraction processes are described briefly in the supplementary document.
We packed 0.08-0.12 mg of α-cellulose in tin capsules for stable isotope measurement using the Flash Elemental Analyzer coupled with a Thermo Scientific MAT 253 (Thermo Electron Corporation, Bremen, Germany). Each sample was repeatedly measured two to four times. The charcoal black (standard sample, δ 13 C = − 22.43‰) was used to calibrate the values of δ 13 C gained from tree-ring α-cellulose. For convenience, the rate of stable carbon isotope ( 13 C/ 12 C) was defined in delta (δ) according to the Vienna Pee Dee Belemnite (VPDB) standard (Leavitt 2008), in parts per thousand (‰): where R sample and R standard represent the 13 C/ 12 C ratios of tree-ring α-cellulose sample and VPDB standard, respectively. We performed 3 replicate measurements for each sample and calculated a low standard deviation of 0.15‰ for the measurements with the STDEV function in Excel.
Isotopic discrimination between atmospheric CO 2 carbon and plant carbon (Δ; see Farquhar and Richards 1984) in C3 plants is a result of the preferential use of 12 C over 13 C during photosynthesis, and it is defined as follows: where Δ 13 C is the stable carbon isotope discrimination, where δ 13 C a and δ 13 C p refer to the δ 13 C values of ambient air and plant cellulose, respectively. δ 13 C a represents a constant value of − 6.4‰ before 1850 C. E. (Smith et al. 2016), and the δ 13 C a value after 1850 C. E. is calculated based on the bubbles in ice core and monitoring data (McCarroll and Loader 2004;Liu et al. 2014; Belmecheri and Lavergne 2020).

Stable carbon isotopic analysis
The field tree growth monitoring research conducted at the GM study site shows that the cambium cells of Cryptomeria fortunei begin to expand around April, and the entire lignification process ends around November . Combined with dendrometer data, we determined that the entire growing season of Cryptomeria fortunei in the study site is approximately from April 6th to November 5th each year, of which June 15th is the dividing line between earlywood and latewood. To find this, we used the method developed by Berkelhammer and Stott (2009), combined with the observed growth dates of the earlywood and latewood of the Cryptomeria fortunei. We then used the following equation to assign dates to the 10 sub-samples in each ring and recorded the dates of these samples' stable carbon isotope values (Table 1): where s i is the date of the start of growing season, which is taken as April 6 and remains unchanged; e s is the length of the earlywood growing season (70 days for earlywood; 203 days for latewood); n s is the sample number; and n t is the total number of sub-samples in each ring. The "intra-annual variation" below refers to the variation for 10 sub-samples corresponding to 10 intra-annual periods based on the length of the tree growing season (April-October).

Traditional intrinsic water use efficiency model (iWUE tra )
We assumed that the values of C a and δ 13 C a at the sampling site are equal to the C a and its carbon isotope, respectively, as previous studies have revealed (Li et al. , 2019. The discrimination of atmospheric CO 2 by plants (the fractionation of carbon isotopes (Δ 13 C)) is an important indicator of the intrinsic water use efficiency of plants. After conversion, the following formula is obtained (Farquhar et al. 1989): where A is the net photosynthetic rate of the plant; g w is the stomatal conductance to water vapor; C a and C i are the intercellular and in the atmospheric CO 2 concentrations, respectively; and the value of C i /C a in the formula can be calculated using Eq. 6 (Farquhar et al. 1989): where a (4.4‰) represents the isotope discrimination of atmospheric CO 2 entering in the intercellular space and b (27‰) represents the isotope discrimination value due to the carboxylation (Farquhar et al. 1989). Therefore, based on the linear formula between Δ 13 C and C a , the traditional model of iWUE is obtained (Ehleringer and Cerling 1995): where the subscript "tra" represents the traditional simple intrinsic water use efficiency model.

Improved intrinsic water use efficiency model (iWUE mes )
Here, we used an improved model of iWUE that includes the effect of g m (denoted as iWUE mes ) .
where the subscript "mes" indicates that this expression accounts for mesophyll conductance effects; C a is the CO 2 mole fraction in the atmosphere; a m (1.8‰) is the fractionation associated with CO 2 dissolution and diffusion in the mesophyll; Г* is the CO 2 compensation point in the absence of mitochondrial respiration; b' (29‰) and f′ (11‰) represent the fractionations due to carboxylation and photorespiration, respectively; a s (4.4‰) is the 12 C/ 13 C fractionations during CO 2 diffusion through the stomata; the errors in g m estimates can be corrected by using a constant g s /g m ratio (0.79) based on measurements of a wide range of plant species from different functional groups (including grasses and herbaceous legumes), in moist and dry conditions .
According to the iWUE model, the C i value (Tei et al. 2014) in the leaves can be inferred using Eq. 9: Moreover, in order to obtain the seasonal variations of the two iWUE time series, we calculated the ratios between iWUE tra and iWUE mes for the corresponding periods.

Tree-ring width chronology and climate-growth relationship at GM
The annual tree-ring width variability of Cryptomeria fortunei at the GM site mainly showed three stages: a downward trend of width from 1965 to 1985, an upward trend with the highest width level between 1986 and 2001, and another downward trend from 2001 to 2017. In general, the tree-ring width across the whole period from 1965 to 2017 showed a "W-shaped" trend (Fig. S1).
The standard chronology of tree-ring width (STD) at the GM site showed the most significant negative correlation with temperature and sunshine hours in the previous July, the current June, and the current June to September, respectively. Meanwhile, the STD at the GM site showed the most significant positive correlation with relative humidity in the current June, July, October, and the current June to September (Fig. 2).

Tree-ring Δ 13 C chronology and Δ 13 C-climate relationship at GM
For the study period of 1965-2017, we observed that the intra-annual average values of both tree-ring δ 13 C and Δ 13 C have clear seasonal patterns (Fig. 3 and Fig. S2). Overall, the intra-annual tree-ring δ 13 C values decreased from April 18-April 29 to October 01-November 05 (− 0.051), reaching the maximum during October 01-November 05 (Fig. S2). In addition, the intra-annual tree-ring Δ 13 C is relatively stable (− 0.24‰), reaching the minimum during April 06-April 17 and the maximum during April 18-April 29.
The correlation analyses between the 10 tree-ring Δ 13 C chronologies and the corresponding climate data at GM from 1965 to 2017 showed that except Apr 30-May 10, May 23-Jun 01, and Jun 02-Jun 14, the tree-ring Δ 13 C chronologies in other intra-annual times during 53 years are related to climate data in varying degrees (Fig. 4). Tree-ring Δ 13 C chronology was positively correlated with sunshine hours during the beginning of the growing season for Apr 06-Apr 17 (r = 0.277, p < 0.05). The tree-ring Δ 13 C chronology in each intra-annual time during the early-wood growing season was significantly negatively correlated with vapor pressure deficit, with the strongest appearing in Apr 18-Apr 29 (r = − 0.348, p < 0.05). The tree-ring Δ 13 C chronologies were significantly negatively correlated with temperature for Jun 15-Jul 20 (r = − 0.286, p < 0.05) and Jul 21-Aug 25 Fig. 3 (a)The ratio of tree-ring stable carbon isotope of Cryptomeria fortunei and the ratio of atmospheric stable carbon isotope from 1965 to 2017 at GM and (b) the discrimination of tree-ring stable carbon isotope from 1965 to 2017 Fig. 4 The Pearson correlations between the annual tree-ring Δ 13 C chronologies and the corresponding climatic variables for 10 intra-annual sub-samples from 1965 to 2017 at GM (r = − 0.271, p < 0.05). The tree-ring Δ 13 C chronology was significantly positively correlated with sunshine hours for Aug 26-Sep 30 (r = 0.343, p < 0.05). For Oct 01-Nov 05, tree-ring Δ 13 C chronology was not only significantly negatively correlated with temperature (r = − 0.341, p < 0.05), but also significantly positively correlated with relative humidity (r = 0.345, p < 0.05).
We found that the intra-annual tree-ring Δ 13 C at the GM site from 1965 to 2017 was positively correlated with relative air humidity from April 18 to September 30 (P > 0.05) and significantly correlated with the humidity for October 01-November 05 (r = 0.351, p < 0.001). The intra-annual tree-ring Δ 13 C was significantly positively correlated with sunshine hours for April 06-April 17 and August 26-September 30. A significant negative correlation between the intra-annual tree-ring Δ 13 C and the temperature was observed during the summer time (i.e., June 15-July 20, July 21-August 25, and October 01-November 05) (Fig. 5).

Fig. 5
The Pearson correlation between the intra-annual tree-ring Δ 13 C and the climatic variables from 1965 to 2017 at GM. The black (red) horizontal dash lines represent the 95% (99%) confidence level At the GM site, the ratios of iWUE tra to iWUE mes were 1.88, 1.89, 1.90, 1.91, 1.92, 1.93, 1.96, 1.96, 1.94, and 1.91 during the 10 periods studied on the intra-annual scale, which gradually increased from April 06-April 17 to July 21-August 25 (4.6%) and peaked during July 21-August 25. At the NML study site, the average ratio of iWUE tra to iWUE mes was 2.05 on the inter-annual scale, which decreased from 2.08 in 1965 to 1.99 in 2014.

The relationship between iWUE chronologies and climate
Taken as a whole, the relative importance of each climate variables to the intra-annual iWUE mes and iWUE tra values for the period of 1965-2017 is assessed on the basis of stepwise regression results with relaimpo package in R program (Fig. 8). Referring to R 2 and to the number of retained series (with p < 0.1), the climate factor that contributes the most to the iWUE in trees regardless of the model is relative humidity, followed by sunshine hours and temperature. Meanwhile, the least contributing climate factor is precipitation. Specifically, during April 06-April 17, the difference in the contribution of temperature, precipitation, and sunshine hours to the iWUE calculated using the two iWUE models was the greatest. Intra-annual iWUEs (iWUE mes and iWUE tra ) and VPD (a), atmospheric CO 2 concentration (C a ) and intercellular CO 2 concentrations (C i ) inferred from iWUE tra and iWUE mes (b) and climate variables (c) at GM study site for the period of 1965-2017

Summer drought stress and tree growth
The correlation analysis revealed a drought stress during summer on tree growth at GM (Fig. 2). The stressed growth patterns caused by such summer drought have also been revealed in nearby regions of eastern Fujian province. For example, Li et al. (2017) and Li et al. (2019) revealed that the growth of Pinus massoniana was mainly controlled by the July-September precipitation in the eastern region of the Fujian province. Chen et al. (2016) also demonstrated that the July-August precipitation is the major limiting factor for the tree-ring growth of Pinus taiwanensis on Daiyun Mountain of the Quanzhou area, southeast of the Fujian province. The presence of the summer drought stress is because the peak temperature in July-August was accompanied by relatively low precipitation during this period. The high temperature, strong light, low precipitation, and thus low relative humidity in the summer months may lead to stomatal closure and an increase in evaporation from the soil. This increased evaporation causes a decrease in water supply for tree growth. In such conditions, a relatively low precipitation and, thus, a low relative humidity can be limiting factors for tree growth.
This study did not find any significant positive response to winter temperatures as observed in other studies in southeastern China (Duan et al. 2013). At the sampling site used by Chen et al. (2016), the growth of trees is limited due to the low temperature in winter due to the high altitude. This situation does not exist in GM sampling site. These summer drought stressed growth patterns found in humid subtropical China are different from the drought stressed pattern in arid western China, where a significant and negative response to summer temperature was often the case (Chen et al. 2021), as the warminginduced evapotranspiration in the arid region can be more stressful for vegetation growth than that in the humid region with relatively abundant precipitation (Fang et al. 2015).

Effects of sunshine and relative humidity on tree-ring Δ 13 C
On the annual scale , the positive correlation between tree-ring Δ 13 C and sunshine hours in the early growing season at GM indicates that the length of sunshine around the beginning of the growing season promotes the photosynthesis of Cryptomeria fortunei leaves, which is consistent with the conclusions of previous studies (Zhang et al. 2012;Lei et al. 2009;Li et al. 2014) (Fig. 4). At the late growing season, Δ 13 C is negatively correlated with temperature and positively correlated with precipitation and humidity. The higher temperature intensifies the drought, and the CO 2 consumption capacity of photosynthesis is greater than that of atmospheric CO 2 supplement. Therefore, the discrimination ability of plants to 13 C is weakened and Δ 13 C value decreases (Liu et al. 2007;McCarroll and Loader 2004) (Fig. 4).
In GM, Cryptomeria fortunei tree-ring Δ 13 C had significant negative correlations with temperature during the second half of the year (from June 15 to November 05), and it had a significant positive correlation with sunshine hours from August 26 to September 30 (Fig. 5). From early June, photosynthesis started to increase because of the relatively high amount of sunshine hours and the sufficient precipitation accumulated in the previous period (Silva Lucas and Anand 2013). Under such conditions with enhanced photosynthesis, intensified consumption of the C i can be associated with reduced discrimination of the carbon isotope (Eq. 5) (Allison and Francey 1999;Berkelhammer and Stott 2009). Meanwhile, the relatively high precipitation and relative humidity could increase the stomatal conductance and thus increase the supply of C i with more CO 2 , which could promote carbon isotope discrimination (Eq. 5). The high temperature associated enhancement of the evapotranspiration could reduce the stomatal conductance and thus the C i , leading to reduced carbon isotope discrimination (Eq. 5). For such hot and humid climatic conditions in the GM study site, the temperature may be sufficient for photosynthesis, while the relative humidity can be insufficient because of the WPSH (West Pacific Subtropical High) (Li et al. 2013). For example, previous studies in Fujian Province, including Fang Guangyan (25°53′ N, 119°11′ E) and Niu Mulin (25°26′ N, 117°56′ E), have also found that the tree-ring Δ 13 C was mainly controlled by the low relative humidity and the high amount of sunshine hours from July to September Xu et al. 2018).

The iWUE mes and iWUE tra at the study sites
On the annual scale, there were significant trends of increasing iWUE tra and iWUE mes for both Cryptomeria fortunei (the slope for iWUE mes being: 0.04, p < 0.001; the slope for iWUE tra being: 0.08, p < 0. 001, and Pinus massoniana (the slope for iWUE mes being: 0.12, p < 0.001; the slope for iWUE tra being: 0.23, p < 0.001, 1865-2014) at both sites in this study. This is consistent with the variability of global C a during the past 100 years, with increasing from 300 to 380 μmol mol −1 (McCarroll and Loader 2004). The results are in agreement with a recent study which showed that iWUE of trees generally increased during the 20th century, although the rate of iWUE gain overtime might have been overestimated (Gong et al. 2022). Such rising C a is affecting the photosynthetic properties of trees in several ways (Körner 2003). For instance, in controlled experiments, CO 2 assimilation was generally stimulated and stomatal conductance was reduced by increased CO 2 (Picon et al. 2010), suggesting that plants are able to increase their intrinsic wateruse efficiency as CO 2 levels rise (Bert et al. 1997;Ceulemans et al. 2007). However, it is obvious that the increasing trends of iWUE mes have slowed down significantly in the past 10 years, which is not available with iWUE tra model.
On the intra-annual scale, the difference between iWUE tra chronology and iWUE mes chronology is more apparent during the summer-autumn time (July 21-September 30) (Fig. 7a). Analyzing the intra-annual time segment can provide higher resolution and higher rates of change for climate variables (20.2% for annual temperature variability during 1965-2017; 46.1% for intra-annual temperature variability during 1965-2017), therefore reproducing more accurate climate variables in the environment where the trees grew at that time (Li et al. 2011). The sharp decline in C a from July to September (i.e., summerautumn) in our study sites was attributed to the vigorous photosynthesis of plants (the C a can be fixed quickly) (Liu et al. 2008) and the active atmospheric convection (the nearsurface CO 2 can be quickly transported to the upper air) .
Theoretically, under the drought limitation in summer and autumn (Figs. 2 and 7c), the stomata of Cryptomeria fortunei trees would close (Gan et al. 2017;Guo et al. 2018;Zheng et al. 2021), resulting in the decrease of C i , and finally leading to the increase of iWUE (Tei et al. 2014) (Eq. 5). However, this was not the case in our study, as we observed an opposite trend for the iWUE mes value during July 21-September 30 (Fig. 7a). There are several possible reasons for this difference. Firstly, C a dropped drastically, especially during July 21 to August 25, which will fundamentally change the C of trees. The second reason is the increased maximum temperature (sunshine) and VPD from July 21 to August 25 in GM. Some previous studies have reported a positive correlation between iWUE and high temperature (Seibt et al. 2008;Battipaglia et al. 2014), in contrast to which, our species responded negatively to the maximum temperature (Fig. 7c). The iWUE mes in our studied species negatively reacted to high VPD (Fig. 7a), which are in line with the results of an experimental study conducted by Grossnickle et al. (2005). The strong negative correlations of iWUE mes with temperature and VPD during both pre-monsoon and monsoon likely imply that higher temperature leads to photosynthetic limitation and higher evapotranspiration, leading to lower iWUE in Cryptomeria fortunei trees (Seibt et al. 2008;Urban, et al. 2017a, b).

Conclusions
Based on the high-resolution δ 13 C of Cryptomeria fortunei tree-rings at the GM study site, our analysis shows that the iWUE mes model (Eq. 8) can be used to reasonably estimate the intrinsic water use efficiency of trees. Our study suggests that both of the iWUEs calculated from the two models (iWUE tra and iWUE mes ) show a significant increasing trend, while the trend differs on inter-annual and intra-annual scales. On the inter-annual scale, iWUE is overestimated by approximately a factor of two, though this overestimation has decreased in the past 10 years. On the intra-annual scale, iWUE is overestimated by a factor of two on average, and the degree of overestimation has decreased slightly during July 21 through August 25. The most distinct difference in iWUEs calculated using the two models (iWUE tra and iWUE mes ) appears in the summer-autumn time, when the iWUE mes model indicates that the iWUE of trees has decreased significantly rather than increased. As our study shows, the iWUE mes model can more effectively estimate iWUE without these levels of overestimation.