Yanhui Liu · Fangjun Ding · Deyuan Shu ·Wenjun Zhao · Yingchun Chui · Yiju Hou · Peng Wu

Abstract Estimating stand transpiration of natural forests using traditional methods through up-scaling of sap fl ux density from sample trees based on stand sapwood area only is difficult because of the complexity of species, ages, and hierarchical structure of natural forests. To improve stand transpiration estimation, we developed an up-scaling method by considering the tree dominance effect based on the assumption that individual tree transpiration is affected by crown dominance and species, in addition to factors previously considered such as meteorological conditions, sapwood area,and soil moisture. In this study, the meteorological factors,soil moisture, and sap fl ux density of 15 sample trees of different species and dominance in a natural evergreen and deciduous broadleaved mixed forest were simultaneously monitored from March 2012 to February 2014 in the Karst mountain region in southwestern China. After establishing a single tree transpiration model which considers the effects of dominance and species, an up-scaling method was explored to estimate stand transpiration. The results show that the transpiration intensity increased exponentially with increasing tree dominance. The contribution to annual stand transpiration from a few dominant trees (5.4%of trees, 28.2% of basal area) was up to 65.0%. The corresponding contribution was 16.2% from sub-dominant trees(7.6% of trees, 16.2% of basal area) and 22.8% from middleand lower-layer trees (87.0% of trees, 55.6% of basal area).The variation of individual tree transpiration was mainly(97.9%) explained by tree dominance, but very weakly by tree species. The estimated annual stand transpiration was 300.2 mm when using the newly developed method which considers tree dominance, 52.5 mm (14.9%) lower than the estimation (352.7 mm) of traditional method which considers only the sapwood area effect, and 8.5 mm (2.7%) lower than the estimation (308.6 mm) which considers the effects of both species composition and sapwood area. The main tree characteristics affecting stand transpiration are tree size(sapwood area) and dominance. Consideration of tree dominance will signifi cantly improve stand transpiration estimation and provide a more solid basis for guiding integrated forest—water management at stand scale.

Keywords Karst broadleaved mixed forest · Forest canopy layer · Tree dominance · Sap fl ow · Tree transpiration · Forest water use

Introduction

Tree transpiration (TT) is an important physiological and hydrological process, and has an important infl uence on growth and the overall water balance of forestlands. However, it is difficult to accurately measure directly and therefore has always been a concern in forest ecological and hydrological studies. Many studies to estimate stand transpiration (ST) have been carried out based on thermal sensor technology used to determine sap fl ow (?ermák et al. 2004;Ma et al. 2005; Burgess and Dawson 2008). This created a greater awareness of the spatio-temporal variation of tree/stand transpiration and its relation with environmental factors. It was shown that TT is driven by multiple factors such as vegetation characteristics (species composition, age,diameter at breast height, height, sapwood area, leaf area,and canopy structure) (Delzon and Loustau 2005; Pfautsch et al. 2010; Tsuruta et al. 2015), meteorological factors(solar radiation, air/soil temperatures, wind speed, humidity, and potential evapotranspiration), soil properties (moisture, porosity, bulk density), and site conditions (location,elevation, slope aspect, slope gradient, and slope position)(Whitley et al. 2013; Chen et al. 2014; Huang et al. 2015).

At the level of a stand/sample plot, due to the relatively uniform meteorological, soil and site factors, it has been assumed that the sap fl ux density (the amount of sap fl ow per unit sapwood area and time) is identical among all individual trees within a stand. Therefore, the sapwood area or area of living tissues, diameter at breast height (DBH), or leaf area index (LAI) are often used as a scalar to carry out the up-scaling from measured sap fl ux density of sample trees to the ST (Vertessy et al. 1995). This method has been especially used for even-aged stands and plantations with a single canopy. However, it is difficult to accurately estimate the ST of multi-layered natural forests by this traditional method due to their complex structure of diverse tree species, size, and age (Dalsgaard et al. 2 011). The differences in morphology, anatomical structure, physiological ecology,and other characteristics of leaves of different species will result in differences in transpiration. Several studies of the infl uence of species composition on stand transpiration have been carried out. Dünisch and Morais ( 2002) reported that the transpiration of evergreen species was higher than that of partially-deciduous and deciduous species because the latter’s transpiration were decreased more signifi cantly during periods of low soil water potential and high saturation water vapor pressure defi cit. Chiu et al. ( 2016) estimated the ST of a broadleaved forest of multiple species in a warm temperate zone based on the measurement of sap fl ow of 12 species with a wide range in DBH (5.0—70.0 cm). There have also been studies about the age effect on the transpiration variation of pure stands with age, e.g., maximum ST was at 30 years for a eucalyptus plantation in Australia (Roberts et al. 2001). The transpiration ofRobinia pseudoacaciaL. in the loess hilly region of China was signifi cantly higher at 28 than at 12 years at both individual tree and stand level (Jiao 2016). In addition to the above factors, the relative position of the tree crown in the canopy, i.e. tree dominance, can also affect transpiration since it results in differences in crown size, leaf area, and micro-meteorological conditions such as decreased light, stable temperatures, higher humidities, and less leaf area in the lower canopy layer (Jung et al. 2 011).This will inevitably reduce the contribution to the total stand transpiration and increase the contribution from the upper canopy layer (Wullschleger et al. 2001). However, the effect of tree dominance on ST and its quantitative relations have not been studied, limiting accurate ST estimation of natural forests with their complex structure.

This study was conducted in a natural stand of complex species composition and hierarchical canopy structure in the Karst region of Maolan in southwestern China. The aim was to develop and test a new method to improve the estimation of stand transpiration of natural forests with complex canopy structure by considering the effect of stand structure such as species composition and tree dominance. If one monitored the sap fl ow of sample trees of all species and all dominance classes, or even of all trees, the workload would be too large to be practical. Therefore, an accurate, simple, economic,and highly efficient method is required for estimating stand transpiration.

Materials and methods

Study site

The site is located at the Guizhou Karst Forest Ecosystem Research Station (25.289°N, 107.948°E) within the experimental area of the Maolan National Nature Reserve in the south of Guizhou Province. This area has a subtropical monsoon humid climate with abundant rainfall but without severe cold winters or hot summers. The mean annual temperature is 18.3 °C, and mean temperature in January is 5.2 °C and 23.5 °C in July. The cumulative air temperature (≥ 10 °C) is 4598.6 °C. Mean annual precipitation is 1752.5 mm, mainly distributed from April to October. Average annual humidity is 83%. Annual total solar radiation is 63,289.80 kW m-2. The site is a typical Karst landform with [peak-cluster depression]. Elevation ranges from 430 to 1078.6 m. The soil is lime developed on carbonate rock.

The stand plot is located at the lower position of a westfacing slope with an elevation of 730 m. The forest type is evergreen and deciduous broadleaved mixed forest with a variety of tree species. The top canopy is dominated by species ofAcer wangchiiFang,Celtis sinensisPers., andDiospyros morrisianaHance. The middle canopy layer is occupied by the tree species ofCyclobalanopsis gracilis(Rehder et E. H. Wilson) W. C. Cheng et T. Hong,Euonymus dielsianusLoes. ex Diels,Castanopsis fargesiiFranch.,Carpinus pubescensBurkill, andPistacia chinensisBunge.The lower canopy consists mainly of tree species such asBrassaiopsis glomerulata var. longipedicellata,Pittosporum brevicalyx(Oliv.) Gagnep.,Cyclobalanopsis gracilis(Rehder et E. H. Wilson) W. C. Cheng et T. Hong,andPlanchonella obovata(R. Br.) Pierre as well as shrub species such asTarennoidea wallichii(Hook. f.) Tirveng. et C. Sastre andMiliusa sinensisFinet & Gagnep. The main herbaceous species areOphiopogon japonicus(Linn. f.)Ker-Gawl.,Strobilanthes cusia(Ness) W. Ktze. andNeottopteris antrophyoides(Christ) Ching. The plot is 0.09 ha with 34 tree species and 92 individual trees and a tree density of 1022 trees ha-1. Mean height and DBH of trees in the canopy is 9.5 m (3.4—25.0 m) and 12.3 cm (5.2—52.5 cm),respectively.

Fifteen samples of the main species of varying size were selected (Table 1). To quantitatively refl ect the vertical position of individual tree crowns in the forest canopy, tree dominance (Dc) , i.e., the relative height of the crown center in the canopy layer, was calculated using Eq. ( 1):

whereHandH cbare height (m) and crown bottom height of individual trees (m), respectively;H mandH cbmare height(m) and crown bottom height (m) of the highest tree in the plot, respectively.

Meteorological, soil moisture and leaf area index

Temperature (Ta, °C), relative humidity (RH, %), solar radiation (Rs, W m-2), and wind speed (U, m s-1) were continuously monitored by an automatic weather station(Campbell Scientifi c, Inc., Logan, UT) at a 25 m weather observation tower in the plot. Soil volumetric water content(θ, %) was monitored by moisture sensors installed at depths of 0—40 cm. Observation data were recorded every 10 min with a CR10X data logger (Campbell Scientifi c, Inc., Logan,UT). Vapor pressure defi cit (VPD, kPa) was calculated via an empirical formula established by Buschmann ( 1999). It is difficult to measure accurately individual tree LAI (leaf area index) due to crown overlapping. Mean stand LAI was measured once a month at 15 random sites with a plant canopy analyzer (CI-110, CID Bio-Science, Inc., Camas WA USA).

Sap fl ow calculation

From March 2012 to February 2014, sap fl ux density of the sample trees was continuously monitored with thermal diffusion sensors (Dynamax-1000, Dynamax Inc., Houston,TX, USA). Different sensors with lengths of TDP-10, TDP-30, and TDP-50 were used according to tree size. These sensors were installed on the north side of the sample tree trunk at breast height (1.3 m). The sensors were covered with aluminum foil to prevent the infl uence of solar radiation and rain and were composed of an upper and a lower probe. The upper probe was continuously heated while the lower probe was not. Based on the temperature difference between the two probes, the sap fl ux density (Js, g m-2s-1)was calculated using Eq. 2 (Granier 1 985). Only one to two sample trees, representing the canopy dominance of one tree species, were selected due to the limited number of sensors.

where ΔTis the temperature difference (°C) between heated and unheated probes; ΔT mis the temperature difference when the sap fl ow is zero. The sap fl ux (SF, g h-1) of an individual tree was calculated using Eq. ( 3):

Table 1 Basic characteristics of sample trees

whereA sis the sapwood area (cm2) of the tree stem at breast height and 0.36 a conversion factor considering the difference in time and area. To compare the transpiration among trees of different sizes after removing the crown area effect,Eq. ( 4) was used to determine the sap fl ow amount within a unit time and unit horizontal projected area of crown, i.e.,the TT intensity (Ec, g m-2h-1).

whereAcis the horizontal projected area (m2) of tree crown of sample trees.

Data analysis

The data were analyzed following: (1) test the dominance effect on tree transpiration (TT) and its relation using monthlyEcdata; (2) calculate daily TT and ST by considering the dominance (Dc) effect; (3) establish the daily stand transpiration model; and, (4) establish the comprehensive transpiration model refl ecting the coupled effects of the potential evapotranspiration (PET), relative extractable water (REW), and leaf area index (LAI).

Tree dominance effect on transpiration and response relations

The TT intensity (Ec)of all species in the stand is assumed to be affected by tree dominance (D c)and meteorological conditions, represented by the integrated parameter of potential evapotranspiration (PET, mm day-1), as shown in Eq. ( 5)because the effect of crown area has been partially ruled out. To minimize the interference of other factors (e.g., soil moisture and LAI), this assumption will be verifi ed using the monthly means ofEcof all sample trees in some months of the growing season with high and relatively stable soil moisture andLAI.The corresponding response relations and weather types will be further fi tted per month using collected data.

wheref(D c)is the dimensionless response function ofE cto tree dominance;εis the error term between the simulated and observedE c,and refl ects the effect of other factors(e.g., species and age) in addition toD c;e(e = ε/(PET×Ec)is defi ned as the infl uence coefficient of other factors; and 0.024 is a unit conversion factor considering the difference in time and area.

The calculation of PET was based on the FAO’s Penman－Monteith model (Eq. 6)

whereR nis the net radiation that reaches the ground (MJ m-2day-1);Gthe soil heat fl ux (MJ m-2day-1); Δ the slope of the saturated vapor pressure—temperature curve(kPa °C-1);γthe thermometer constant (kPa °C-1) ;Tthe daily mean temperature (°C);U2the wind speed (m·s-1);e sthe saturated vapor pressure (kPa); ande athe actual vapor pressure (kPa).

The model calculated stand transpiration

Summing the transpiration of all trees within plot by inputting the measuredD cvalue of each tree and the dailyPETinto the fi tted Eq. ( 5), the daily ST (E s,mm day-1) was calculated using Eq. ( 7).

whereD ciandA ciare the dominance and the horizontal projected area (m2) of the crown of theith tree in the plot; n,the number of trees in the plot;A standis the plot area (m2).

To assess the newly developed up-scaling method of stand transpiration estimation, Eq. ( 7), a traditional upscaling method which does not consider tree dominance but the weighted effect of projected area of tree crown, which partially refl ects the effect of species, see Eq. ( 8), was used to calculate daily ST. Due to the large number of species in the plot, some species were not sampled and their transpiration was assumed to equal the mean of the sample trees of the same genus. For the trees without the same genus of the sample trees, their transpiration was assumed to be the mean of sample trees of the same tree type (evergreen or deciduous).

whereE cj,A cjandn jare the TT intensity (g m-2h-1), the average horizontal projected area (m2) of tree canopy, and the number of thejth tree species. The 0.024 is a unit conversion factor considering the differences in time and area.

Stand transpiration was also estimated by another traditional up-scaling method, Eq. ( 9), which uses the mean transpiration intensity of all sample trees. The estimated ST will be compared with those from these two methods.

The optimum method was chosen based on the comparison of results from Eqs. ( 7), ( 8) and ( 9), and used to estimate the daily ST and to develop the daily ST model coupling the effects from environmental and stand structure factors.

Stand transpiration model considering main infl uencing factors

The ST (E s), calculated with Eq. (7 ), is affected by several factors, i.e., relative extractable water (REW) from the soil root zone, the LAI of the canopy, and meteorological factors (vapor pressure defi cit (VPD, kPa), solar radiation intensity (R s,W m-2), air temperature (T a,°C), etc.). To integrate and simplify the effects of the numerous meteorological factors onE s,dailyPETwas used.

After piloting the scatter diagrams forE s-PET,E s-REW,andE s-LAI, the ST variation trend with individual factors could be obtained using the upper boundary line (Schmidt et al. 2000). To do this, the x axes (PET,REWandLAI) were divided into numerous segments of equal length, the 1%maximum of observed data in each segment were excluded as abnormal values, and the maximum values in the remaining 99% were determined as the upper boundary data within each segment. According to the upper boundary lines, theEsresponse curves to individual factors off(PET),f(REW) andf(LAI)) were determined.

A comprehensive model refl ecting the coupled effects ofPET,REWandLAIon transpiration is described by Eq. ( 10).The fi tted parameter values in theE s-PET, E s-REWandE s-LAIrelations using upper boundary lines were used as the initial values to further fi t the parameters of this coupled model.

The REW was calculated with Eq. ( 11) (Chirino et al.2011).

whereθ,θ WP,andθ FCare the actual volumetric soil moisture(%), the volumetric soil moisture at wilting point (%) and at fi eld capacity (%) for soil layers 0—40 cm

The data were randomly divided into two groups, one used to fi t model parameters and the other to validate model accuracy. Model precision was assessed using the model efficiency indicator (E) calculated with Eq. ( 12).

whereE m,E e,andare to the measured, simulated and the means of TT (g m-2h-1) or ST (mm day-1), respectively.

Results

Differences in transpiration among species

Based on the averageE cof the sample trees in the summer of 2013, the transpiration intensity was compared among similar species (different genera but the same family; trees 1, 6 and 9;Fig. 1 a) and among sample trees of the same species (trees 7 and 8; Fig. 1 b) with various tree dominance. TheE camongst the sample trees of different species (trees 2, 6 and 13; Fig. 1 c)but with the same dominance was compared. The results show that theE cvalues of sample trees of the same family (trees 1, 6 and 9) are not close to each other, with t values of 26.58, 32.48 and 17.00 g m-2h-1, respectively. TheEcvalues of sample trees of the same species (trees 7 and 8) also differed greatly,with values of 15.76 and 41.58 g m-2h-1, respectively. TheE cof dominant sample trees was higher than trees of lower dominance, e.g., 163.5% higher for tree 8 (D c= 0.63) than tree 7 (D c= 0.40). However, there were no obvious differences inE cvalues in the range of 39.6—47.8 g m-2h-1among species with the same or similar dominance (D crange of 0.46—0.49).It appears that the difference in TT intensity among species at the same canopy layer is much smaller than that among the trees with different dominances but regardless of species. This indicates that theD ceffect onE cis much stronger than species.

Fig. 1 Comparison of the E c amongst dominance and species. a The E c of trees of different genera but the same family (trees 1, 6 and 9); b the E c of trees of the same species but with different dominance(trees 7 and 8); c: the E c of trees of different species but with the same or similar dominance(trees 2, 6 and 13)

Fig. 2 Exponential increase of a sap fl ux, b sap fl ux density( J s) and c E c with increasing dominance ( D c)

Relations between transpiration and dominance

To quantitatively describe the effect of dominance (D c)on tree transpiration with a minimum interference from other factors,data measured in mid-summer (August) were selected to plot a scatter diagram of monthly mean sapfl ux (SF) andD cof individual sample trees (Fig. 2 a), which showed an exponentially increase ofSFwith risingDc(R2= 0.989). However, becauseSFis also affected by the size of the sapwood area (A s), the relationship between sap fl ux density ofJsandD cwas further analyzed (Fig. 2 b), showing a largeDceffect on transpiration,i.e., theJsincreases with risingDc(R2= 0.683) after theA seffect is excluded. In addition, to exclude the effect of crown size (or leaf area) on TT, the relation between the transpiration intensity ofE cof individual trees and theirD cwas further analyzed (Fig. 2 c), showing a signifi cantD ceffect (R2= 0.979).Therefore, it may be concluded that tree dominance is a main factor affecting transpiration within the mixed natural forest.This effect can be quantifi ed. On sunny days in each season,the variation in dailyEcshows the same exponential increase with risingD c(Fig. 3).

Based on variations of TT withD c,Eq. ( 5) is expressed as:

The parameters ofkD1andkD2in Eq. ( 13) were fi tted using the monthly meanEcin August 2013 of all sample trees and theirD c.The results are shown in Table 2 with a R2of 0.921.The validation was performed using theE cdata of May, June and July 2013, with a R2of 0.944 (Fig. 4) and a model effi-ciency (E) of 0.934, indicating the high precision to predict tree transpiration with changingD c.

Tree transpiration relationships to months and weather types

As the fi tting with August data, the parameters of Eq. ( 13)were further fi tted with the data in each month and weather type (Table 3). During the fitting according to weather types, only data of sunny, cloudy, and rainy days in summer (June to August) were used; the effects of other factors such as air temperature and LAI were excluded. The parameter kD1showed a large variation among months and weather types (variation coefficient of 0.93) with higher values in warm months from May to September than in cool/cold months from December to April, and higher values on sunny days (0.006) and rainy days (0.005) than on cloudy days (0.002). The parameter kD2showed a small variation(variation coefficient of 0.10). Its May—September values were slightly lower than in other months, and higher on cloudy days (8.736) than on sunny days (7.159) and rainy days (7.331). From the fi tted parameters in Table 4, it is seen that the Dceffect on Ecis higher in the warmer months of May to September, and on warmer, sunny days than on cool/cold cloudy and rainy days.

Fig. 3 Exponential increase of E c with rising D c for typical sunny days in each season

Table 2 Estimated parameters of Eq. ( 13) using data of August 2013

Fig. 4 Comparison of monthly E c of sample trees measured in May,June and July of 2013 and their calculated values using Eq. ( 13)

Table 3 Parameters in Eq. ( 13) fi tted by month and summer weather

Infl uence of other factors on transpiration

The previous analysis shows thatD c(tree dominance) can explain theE cdifferences among individual trees. However,there is still a certain error (ε) which is determined by other factors such as species or microhabitat. The infl uence coeffi cients of other factors (e) in each season for sample trees are shown in Table 4. Theevalues are not close with each other among sample trees of the same species or the same genus. For example, theevalues differ signifi cantly between the two trees ofEuonymus dielsianusLoes. ex Diels (0.35,- 0.01) and two trees ofMachilus ichangensisReheder& E.H. Wilson (- 0.14, 0.36). Furthermore, theevalues did not show a large difference between the evergreen and deciduous species. Most sample trees (exceptCeltissinensisPers.) showed higherevalues in winter (- 0.33 to 0.99) than in other seasons (- 2.73 to 0.62), indicating the factors vary seasonally with LAI (leaf area index) also affecting theEc.The fi tting results of theEc—Dcmodel showed that theDc can explain 91.7—98.3% of the variation ofEc, while otherfactors only explain 1.7—8.3%. The infl uence of other factors is much lower than that ofDc.

Table 4 Errors ( e) caused by factors other than tree dominance to E c prediction

Applicability of individual tree transpiration relations

Using theE c-D crelational expression parameter values in each month (Table 3), and the time series ofPET(potential evapotranspiration) data, the daily transpiration of each sample tree was calculated and compared with measured values in 2013, as shown in Fig. 5 a, b and c with the examples of high, medium, and low dominance (trees 7, 2 and 15). The corresponding model efficiencies (E) were 0.874, 0.794 and 0.999, respectively. The transpiration relations can predict reasonably the daily transpiration of individual trees with any dominance.

Comparison of simulated stand transpiration of three methods

Daily ST (E sdc)was calculated after inputting the calculatedD cof each tree in the canopy into the new method 1 (Eq. ( 7)considering the effect of dominance and compared with the values (E ssp)using the traditional method (Eq. 8 , method 2).The results show that the traditional method over-estimates stand transpiration (ST) as it does not consider the effect of tree dominance but only the infl uence of species composition and area of sapwood. The calculated daily ST using the new method was also compared to values using Eq. ( 9) (method 3) which does not consider the infl uence of tree dominance and species, i.e., using the meanE cvalues of all sample trees and the stand sapwood area to calculate ST (Fig. 6 a).The variation trends of daily ST in 2012, estimated by all three methods, are identical. Nevertheless, the total transpiration values are much different, the lowest (300.2 mm) by method 1 is less than the method 2 value (308.6 mm) and signifi cantly less than the estimate (352.7 mm) by method 3.

TheE sin spring, summer, autumn, and winter, calculated using method 1 are listed in Table 5 and account for 22.5%,38.8%, 31.4% and 7.3%, respectively, of the annual total.Mean daily stand transpiration on sunny days was highest regardless of season. In summer and autumn, theE son cloudy days was higher than on rainy days but opposite in spring. In the summer with highPET, the difference in dailyE samong weather types was the largest;E son sunny days was 1.65 mm day-1, is 1.8 and 2.4 times of that of cloudy days (0.90 mm day-1) and rainy days (0.70 mm day-1),respectively.

Figure 6 b shows the number of trees in each dominance class and the corresponding annual transpiration calculated using theE c-D crelations. Only fi ve trees in the uppermost canopy (D c=0.8—1.0), with a tree number ratio of 5.4%and sapwood area ratio of 28.2% of the stand, contributed as high as 69.5% to the total ST. The number of trees and sapwood area were 34.8% and 38.9% in the middle canopy(D c=0.4—0.8), and 51.1% and 29.7% in the lower canopy(D c=0.2—0.4), but they contributed only 18.9% and 11.5%to annual ST. The eight trees in the lowest canopy layer(D c＜0.2) accounted for 8.7% of the total number of trees and 3.2% of the sapwood area and contributed only 0.5% of the total stand transpiration. Therefore, it may be concluded that tree dominance has a signifi cant effect on transpiration.

Fig. 5 Comparison between simulated and measured daily E c of individual trees of different dominance in 2013 ( a: upper tree, tree 7; b: middle tree, tree 2; c: lower tree, tree15)

Fig. 6 a Comparison of calculated ST from tree dominance relations ( E sdc) , tree species E c weighted average ( E ssp) ,and average E c of sample trees( E ssa) ; b ratios of number of trees and transpiration of different dominance classes to stand totals

Table 5 E s calculated with the relations considering tree dominance effect

Daily stand transpiration model coupling the effects of main infl uencing factors

Figure 7 a, b and c show the scatter plots between dailyE sandPET,REWandLAIin 2013, respectively. The upper boundary lines indicate the response pattern ofEsto the individualPET,REW,andLAIwhen the effects of other factors are minimum. TheE svaries withPETand follows an S-shaped curve, increasing with risingPETat fi rst near linearly, then gradually slowing and leveling offwhen thePETreaches a threshold of about 4.5 mm day-1. The variation ofE swith risingREWshows fi rst an increase and then a decrease after theREWreaches its optimal value of 0.723.The increase ofE swith risingLAIalso follows an S-shaped curve and theE sincreases become lesser when theLAIreaches a threshold of above 5.0.

Based on the upper boundary lines ofE sagainstPET,REWandLAI, the logistic function was used to express theE s-PETandE s-LAIresponse curves, and the Gauss function used to express theE s-REWresponse curve. SincePET,REW, andLAIaffect theE ssimultaneously, their individual response functions were multiplied together to form a comprehensive model of the daily standE s(E s-PRL model). The fi tted parameter values of the three single factor response curves through upper boundary line analysis (Fig. 7) were taken as the initial parameter values when the coupled model was fi tted using the non-linear regression method and some selected measured data. Fifty percent of the data in 2013 were randomly selected out for model verifi cation. The fi tting results are shown in Table 6, with R2as high as 0.961(Fig. 8) and a high model efficiency of 0.986, indicating a high model precision.

Fig. 7 The response of daily ST( E s) to the variation of a PET, b REW, and c LAI

Discussion

Factors infl uencing forest transpiration

The factors infl uencing forest transpiration may be divided into two types: environmental factors and biological factors. Environmental factors include weather factors (solar radiation, temperature, wind speed, vapour pressure defi cit,relative air humidity, and potential evapotranspiration) and soil water availability. Biological factors include the morphology, structure, and physiological characteristics of trees,such as the leaf area index, fi ne root quantity and distribution, area of sapwood, wood density, the number and size of wood tracheids, and leaf stomata behavior. The effects of these factors on transpiration differ among stands due to differences in stand structure, site conditions and other factors. Transpiration is an integrated effect of all these factors.

The differences in transpiration among individual trees is relatively small in even-aged stands and plantations with a single canopy due to similar niches and environment.However, the TT (single tree transpiration) can be greatly affected by the tree size or dominance in stands characterized by high density, intense competition and differentiation of trees, largely due to differences in light reception by the canopy. Previous studies have reported on the characteristics and quantitative relations of tree transpiration responses to environmental factors such as solar radiation, vapour pressure defi cits, soil moisture and the horizontal stand structure such as gaps and tree density (Dalsgaard et al. 2 011;Forrester 2015). However, few studies have investigated the effect of vertical stand structure (i.e., tree dominance).Nevertheless, as shown in this study, ignoring the effect of dominance will inevitably lead to an increased error of ST(stand transpiration) estimation, especially in summer and on sunny days when the transpiration potential is high.

Effect of tree dominance on transpiration

Several studies have shown that tree size has a considerable effect on sap fl ow and transpiration (Horna et al. 2011; Berry et al. 2017). Size is often expressed using DBH because of its easier measurement than height and its linear relation to the area of sapwood, crown area and height. In essence, relative tree height is a factor determining the vertical position of the crown in the canopy. Upper canopy trees obtain more solar radiation, and both ambient temperatures and vapour pressure defi cits are also higher (Otieno et al. 2014), thus have higher transpiration (Xiong et al. 2015). For example,in a Qinghai spruce forest (Wan et al. 2017) and a Xingan larch forest (Liu et al. 2016), transpiration of upper canopy trees was higher than that of the middle or lower canopy trees. The transpiration of dominant trees during sunny days was higher than that of subdominant trees (Strelcová et al. 2002). Therefore, tree dominance can refl ect changes in transpiration more realistically than the DBH and area of sapwood because the relation between height and DBH varies with environment, dominance (Strelcová et al. 2002),age (Trouvé et al. 2016), forest density, and species. Therefore, as long as height can be accurately determined and the relative tree height (dominance) calculated, this information should be used as to better refl ect transpiration differences among trees.

Besides factors of sunlight, air humidity, and temperature (Jung et al. 2011), tree dominance also strongly affects canopy leaf area index (Ellsworth and Reich 1993; Maguire and Bennett 1996), and root quantity and depth distribution(Ivanov et al. 2012). In this study,E cshowed an exponential increase with rising tree dominance as observed in similar studies, such as in a subtropical evergreen broadleaf forest on Dinghu Mountain (Otieno et al. 2014)and in tropical rain forests (Horna et al. 2011; Motzer et al. 2005). However,there have not been reports on the quantitative relationship between tree transpiration and tree dominance. Therefore,this study is a reference for similar future studies.

Effect of species on transpiration

How large are the differences in transpiration among tree species in a mixed forest, and how does this affectsestimation of stand transpiration through the up-scaling of sap fl ux density of sample trees? Some studies have shown species differences in leaf stomata behavior (Bond and Kavanagh 1999), leaf area index (Kaufmann 1985), the sapwood area ratio of the trunk (Zeppel et al. 2010), wood density and hydraulic characteristics (Gao et al. 2015), and therefore species should be one of the factors infl uencing stand transpiration. Kr?ber and Bruelheide ( 2014) found higher leaf stomata and xylem hydraulic conductivity of deciduous broadleaf tree species compared to evergreen species under similar age and environmental conditions.However, some studies have also reported little infl uence of species on sap fl ow response to environment (Link et al.2014), or no difference in hydraulic conductivity and stomata conductivity among species (Nabeshima and Hiura 2008). It has been suggested that hydraulic structure and wood density were more affected by tree age (Bucci et al.2004) and area of sapwood (Ewers et al. 2002).

Table 6 Fitted daily stand transpiration model coupling the effects of main infl uencing factors

Fig. 8 Comparison of observed and predicted E s in 2013 by coupled model ( E s- PRL)

The tree species differences in transpiration, when large enough to affect stand transpiration, may depend on stand structure since it can modify tree growth conditions, especially availability of light. Under similar light conditions,transpiration and stomata conductivity of lower canopy pine trees (12 m) were reported to be higher than that of taller trees (39 m) (Ryan et al. 2000). In study of both deciduous and evergreen species, species differences in transpiration might be larger in the dormant season than in the growing season due to larger differences in leaf area index caused by defoliation and leaf vitality. However, no differences in transpiration were found between deciduous and evergreen trees and among species in the growing season in this study,and the transpiration differences among individual trees depended on tree dominance. This study was conducted on just one plot and lacked duplicate sample trees for each species, and therefore it is difficult to analyze the effect of species in detail. However, it is clear that the infl uence of species on transpiration is far less than the effect of tree dominance, and the precision of stand transpiration estimates can be improved when considering the infl uence of dominance and species composition.

Stand transpiration up-scaling method considering multiple infl uencing factors

In traditional methods to estimate stand transpiration through up-scaling of sap fl ux of individual sample trees, conversion factors of DBH, area of sapwood and basal area are often used,with the underlying assumption that tree transpiration is not affected by species and tree dominance. This assumption and a corresponding up-scaling method can be applied without difficulty to even-aged and single-layered plantations because of the relatively uniform distribution and growth of trees due to similar meteorological and soil moisture conditions. However,the application will be problematic for mixed natural forests because of the multiple canopy layers caused by high density and diverse species and age, and the corresponding differences in micrometeorological and leaf area index conditions of individual trees. Therefore, tree transpiration is largely affected by dominance. Stand age or development stage is also an infl uencing factor. Some studies indicate that transpiration per unit leaf area from large/old trees is lower than from young trees (or saplings) under sufficient sunlight because of lower stomata conductivity and hydraulic conductivity of old trees (Barnard and Ryan 2003; Gao et al. 2015). It has been suggested that considering the dominance effect is necessary for estimating stand transpiration through the up-scaling of sap fl ux of sample trees (Dalsgaard et al. 2011).

When stand transpiration is estimated using traditional methods, it is difficult to represent the real average sap fl ux of a stand by the mean sap fl ux of sample trees. First, this is because of the low number of sample trees and secondly, the nonlinear response of sap fl ux to tree height or DBH as the exponential relation shown in this study and by Otieno et al.( 2014). The mean sap fl ow characteristics of a forest tend to be higher than those of average trees but close to those of dominant trees. Therefore, estimated stand transpiration using traditional methods may be higher or lower than the true value, depending on the dominance representativeness of sample trees. For example, in this study, the estimated annual stand transpiration (300.2 mm a -1 ) using the new method considering tree dominance is signifi cantly lower(14.9%) than the estimation (352.7 mm a-1) using the tradition method without considering tree dominance. Similarly,the estimated transpiration of aLarix principis-rupprechtii Mayr. plantation in semi-arid northwest China was 16—23%lower when considering tree dominance effect than without considering it (based on the mean sap fl ux of sample trees)(Li et al. 2015). Therefore, tree dominance was calculated according to the vertical location of the crown within the canopy, and its effect on transpiration was incorporated into the stand transpiration calculation for a more accurate estimation of the spatio-temporally varying transpiration of individual trees and stands.

The application potential of the model and suggestions for future studies

The model developed in this study for estimating the transpiration of individual trees and stands can be applied to both plantations with a simple stand structure and to natural stands or plantations with complex structures of species and vertical canopy layers. The quantitative relations between transpiration and tree dominance obtained can provide a scientifi c basis for guiding stand structure regulations for the integrated forest and water management.

However, the shortcomings are mainly due to the limitation of sample number. First of all, an insufficient number of trees were selected to monitor the transpiration of all tree species within each dominant class. Therefore, the species effect on transpiration was only preliminarily compared and considered to be lower than the effect of tree dominance and not accurately quantifi ed. This aspect should be strengthened in future studies. Secondly, the limited number of sample trees did not allow for the quantifi cation of transpiration variations along with dominance within the same species,and to establish a dominance-based transpiration model for each species. Further studies are required.

In addition to the limited number of sample trees, the possible effects on transpiration by diverse micro-environments(e.g., stone ditches and troughs, stone and soil surfaces),soil physical properties (thickness, porosity, moisture),and soil chemical conditions should be considered in future studies.These micro-habitat differences may lead to differences in tree development and corresponding water cycling and tree water use. In future studies, in addition to differences in the aboveground structure of trees, differences in underground structures (e.g., amount, quality, and spatio-temporal variation of fi ne roots) should also be considered. Finally, by increasing the number of plots to consider the effect of landscape factors (elevation, slope aspect, gradient, and position)on tree transpiration, may promote the up-scaling of sap fl ux from sample trees to the stand level but also to the slope,small watershed and even larger landscapes scales in the Karst region.

Conclusions

In this study, the transpiration of a natural forest of mixed species, age, and multi-layered canopy showed large differences among individual trees, mainly due to the effects of tree characteristics (e.g., dominance, species, and leaf area index), micrometeorological conditions and soil moisture. Under given conditions of weather and soil moisture at specifi c times, the differences in transpiration is mainly affected by the tree characteristics, showing an exponential increase in transpiration with increasing dominance, while not strongly affected by species. This can explain 97.3% of the transpiration variation of sample trees with different dominance. A small number of dominant trees are the main contributors to stand transpiration. This study has proposed a new up-scaling method for estimating stand transpiration from the sap fl ux of sample trees, and fi tted a new transpiration model coupling the effects of main infl uencing factors.This new model is characterized by the consideration of the effect of tree dominance. The annual stand transpiration estimated by this new model is 52.5 mm (14.9%) lower than the traditional method without considering tree dominance. This means that the new model can better estimate the daily transpiration of forests with complex structure compared to traditional methods by distinguishing the contribution of trees in different canopy layers. The effect of tree dominance must be considered when estimating stand transpiration through the up-scaling of sap fl ux of individual trees. The relationships of transpiration response to tree dominance and other factors and the daily stand transpiration model are useful guides to integrated forest—water management based on the precise transpiration prediction under changing conditions.