1. Introduction
To increase the various ecosystem services supplied by forests, such as erosion control, timber production, carbon sequestration, and water regulation, afforestation has been encouraged worldwide, including in dryland regions. However, afforestation has increased the consumption of water, which is inherently scarce in the vast dryland regions [
1,
2,
3,
4,
5]. The water used by forests in some sites and in some periods can even exceed annual precipitation [
3,
6]. Many studies have confirmed soil moisture decrease and even dried soil layers [
6] and remarkable water yield reduction due to large-scale afforestation in the watersheds on the Loess Plateau in Northwest China [
7,
8,
9,
10,
11,
12]. Thus, increasing attention has been given to forest water consumption [
13] and balanced forest-water management.
Quantifying plant transpiration (T) variation is important for not only the estimation of a water budget but also the elucidation of the role of T in an energy budget, the effects of hydrological flows on vegetation production, and ecosystem responses to climate change [
14,
15,
16,
17]. Tree T, which utilizes a large proportion of forest evapotranspiration [
3], is a key factor affecting the stability and services of forests, and the regional water balance, or even water supply security [
13,
18,
19,
20]. Therefore, it is very necessary to fully understand and accurately predict T dynamics [
17,
21,
22], especially in vast dryland regions with variable climates and severe water shortages. To simplify the study of forest T variation, the numerous influencing parameters can be grouped into three factors: the weather-related evaporative driver, the soil moisture-related extractable soil water, and the vegetation-related canopy T capacity. Establishing a daily T model that can couple all three factors and be applied easily is the basic requirement for forest T predictions under changing environmental and canopy conditions. However, this kind of study is still very rare, although there have been many studies on the effects of individual factors.
Forest T is firstly determined and usually limited by the atmospheric potential evapotranspiration (PET), which is an integrated effect of many weather parameters, such as temperature, radiation, and vapor pressure deficit (VPD) [
23,
24]. PET could explain over 60% of the T variation in a black locust (
Robinia pseudoacacia) plantation on the Loess Plateau of China [
25]. The study showed a mean ratio of 58% (range 50–64%) of daily T to daily PET [
26]. Many PET–T relation studies of various tree species in different regions [
26,
27,
28,
29] have been conducted usually using a logistic, linear, or quadratic equation to describe the T response to PET but without considering other influencing factors.
Quantifying the relationship between T and relative extractable soil water content (REW) has been an interesting topic in forest hydrology. The use of REW, rather than the absolute soil moisture, allows a direct comparison among the studies with different soil physical properties. Some of these studies were conducted on forests for a number of tree species in various counties [
26,
27,
28,
30,
31,
32,
33,
34]. These studies showed a common T variation trend with rising soil moisture, which initially increases quickly and almost linearly but thereafter gradually stops increasing and approaches a maximum when the REW reaches a threshold usually in the range of 0.2–0.5. Nonlinear (asymptotic) models, such as quadratic, logistic, logarithmic, negative exponent, and piecewise equations, are often used to depict the T response to rising REW.
Soil moisture is the key factor limiting tree growth and forest T in dryland regions. Li et al. [
35] found that the reduction in forest T by REW accounted for 16% of the total potential T in a growing season for the same larch plantation as that in this study in a semiarid climate. However, this result was based on a simplified T–REW relation, leaving out the effect of evaporative demand. In fact, evaporative demand most often controls the T variation in the field, and the phenomenon that T is limited by soil moisture appears only during periods of a high soil water deficit [
36,
37]. For example, Ungar et al. observed that soil moisture acted as the primary driver for forest T only when the soil moisture was below 0.15 cm
3·cm
−3 [
28]. The forest T and its response to REW were often controlled or affected by varying weather conditions [
38]. A study in a
Cyclobalanopsis glauca forest in South China showed that the T responses to soil moisture were more intense under conditions of higher VPD [
39]. To obtain an ideal T–REW relation, some studies have been conducted with seedlings in chambers under artificially manipulated weather conditions [
25] or in a field where the data on cloudy, overcast, and rainy days or days with extremely large or small VPD are excluded [
32]. It is possible that such an analysis is unable to properly represent the actual T behavior in the field.
In addition to PET and REW, forest canopy leaf area index (LAI) is also a key factor affecting T, as has been confirmed by many studies, such as those of Vertessy et al., Zimmermann et al., and Forrester et al. [
40,
41,
42]. Based on a review of studies on 20 forests and 12 tree species under different climate types, Granier et al. derived a generic response of canopy conductance to a rising LAI within the range of 0–11 [
43]. The T first increases with rising LAI but at a declining rate, and then, T stops increasing when the LAI exceeds a threshold. However, the T response to LAI is expressed differently, often as a linear, power, or single asymptote equation or piecewise equations. Even some individual studies have concluded that T is not correlated with LAI [
41]. The main reason to explain the diverse T–LAI relations could possibly be the difference in the LAI range among the above studies, such as 2.9–4.8 [
40], 1–11 [
43], 0.6–1.6 [
41], and 1–6 [
42]. Only the LAI varies within a big enough range (e.g., >6), the whole T response to LAI including the LAI threshold, from that T stops increasing with LAI, can be observed.
Forest T is codetermined by weather conditions, soil moisture, and vegetation characteristics, but direct studies on the simultaneous response of T to these factors are rare. The vast majority of the existing studies are focused on the response of forest canopy conductance to environmental factors. A multiplication approach has often been used to couple the effects of individual factors (e.g., PET, REW, and LAI) [
44,
45]. Granier et al. used such an approach to describe the T response to multiple meteorological factors (radiation, VPD, and temperature), soil moisture, and LAI, based on the measured data of forests of 21 broadleaved or coniferous tree species under different climates (temperate, mountain, tropical, and boreal) [
43]. A similar study was conducted on the forest canopy conductance of oak (
Quercus robur) in the Netherlands [
46,
47], and maritime pine (
Pinus pinaster Ait.) in the Landes de Gascogne Forest of southwestern France [
23,
48]. However, such studies on forest T are still rare.
In this study, the daily T variation in a semiarid larch plantation was continuously measured in the growing season of 2010–2014. Due to the power supply failure, some T data were seriously missed; especially due to the instrument fault of a plant canopy analyzer (LAI-2000 type, LI-COR, Lincoln, Nebraska, USA), the LAI could not be measured in 2011 and 2013. Therefore, only the data from the dry year of 2010, normal year of 2012, and wet year of 2014 were used. The aims of this paper were to (1) establish a simple but solid model for predicting the daily T of forests under field conditions, and (2) clarify the importance of LAI, REW, and PET to the T variation at the study site. This study will promote a better understanding of the daily T response to varying environmental and canopy conditions and supply a basis for the integrated forest-water management.
2. Materials and Methods
2.1. Site Description
This study was performed in the small watershed of Diediegou, located in the semiarid northern part (106°4′55″ E–106°9′15″ E, 35°54′12″ N–35°58′33″ N) of the Liupan Mountains, in the midwestern part of the Loess Plateau in Northwest China (
Figure 1). The elevation range is 1973–2615 m a.s.l. The climate is semiarid continental monsoon, with a mean annual air temperature of 6–7 °C, a frost-free period of 130 days, and a mean annual precipitation of 425 mm that mainly occurs from June to September.
This small watershed lies in the transition zone between the loess hilly area and the lithosol mountain area. The main soil type is gray cinnamon soil (partly corresponding to the Calciustoll, Argiustoll and Haplumbrept in the USA soil classification system). The native vegetation in this watershed is meadow and broadleaved deciduous forests, which had been completely destroyed in recent history [
49]. Afforestation has been encouraged since the 1980s, mainly to stop severe soil erosion and produce timber. The dominant forest is now pure plantations of
Larix principis-rupprechtii, which distribute only on the shady (north-facing) or semi-shady (northwest- and northeast-facing) slopes in this semiarid study region [
50].
2.2. Plot Setup
This study was carried out in a permanent larch plantation plot with an area of 30 × 30 m
2 at the foot of a shady slope at the lower reach of the small watershed. This plot has an elevation of 2055 m a.s.l., a slope gradient of 11°, and a soil thickness of >2 m and with granular sandy loam. Since the establishment of this plantation in 1986 through afforestation, no thinning has been implemented due to a strict logging ban policy. This is a young and even-aged plantation with one canopy layer and less tree size differentiation. From 2010 to 2014, the plot was characterized by a significant (
p < 0.01) increase of canopy density from 0.80 to 0.85, mean tree height from 9.41 to 10.65 m, mean diameter at breast height (DBH) from 10.13 to 11.02 cm, total sapwood area from 8480 to 9910 cm
2, and maximum LAI (LAI
max) from 4.92 to 5.63 in midsummer (
Table 1).
2.3. LAI and Sapwood Area Measurement
The canopy LAI was measured every 10 days during the study period from May to October with a plant canopy analyzer (LAI-2000 type, LI-COR, Lincoln, NE, USA) at 12 fixed sites in the plot.
After the measurement of DBH (cm), the sapwood area (
As, cm
2) of each tree was calculated by Equation (1) [
51] and then summed as the plot estimation:
2.4. Weather Parameter Measurements
A weather station (Weatherhawk, Logan, Utah, USA) was placed in an open area 100 m away from the plot to automatically monitor the precipitation (P, mm), air temperature (T
a, °C), relative air humidity (RH, %), solar radiation (R
s, w·m
−2), and wind speed (U, m·s
−1) to calculate the PET (mm·day
−1) with the Food and Agriculture Organization (FAO) Penman-Monteith Equation [
52] every 5 min.
2.5. Soil Moisture Measurements
The soil water potential (ψ, MPa) for the layers of 0–10, 10–20, 20–40, and 40–60 cm were monitored with equilibrium tensiometers (EQ15; Ecomatik, Dachau, Germany) at a representative site in terms of canopy density and site conditions but at least 1 m away from tree trunks to avoid the influence of stem flow. Data were collected every 5 min by a logger (DL6; Delta-T Devices, Cambridge, UK), converted into volumetric soil moisture (θ, vol.%) with a series of equations relating ψ and θ determined at the same site [
53], and then calculated into the relative extractable soil water content (REW) [
54] with Equation (2). The reason for converting ψ to θ and REW, not directly using them, is to make the study results applicable for sites with different soil hydrological properties:
where
θact is the actual volumetric soil moisture in the main root zone of the 0–60 cm soil layer [
55];
θWP is the
θ of the wilting point (ψ = −1.5 MPa) with a value of 18.5%; and
θFC is the θ of the field capacity (ψ = −0.01 MPa) with a value of 45.3% [
36].
2.6. Sap Flow Measurements and T Calculations
The characteristics of tree height, DBH, clean bole length, and canopy diameter of all individual trees in the plot were measured in the early stage of the growing season of every year. Based on these measurements, 4–5 sample trees (
Table 2) with straight trunks and healthy crowns were selected for sap flow measurements. There was no significant difference (
p > 0.05) in the features of sample trees among different years.
The sap flow density was measured using thermal diffusion probes (SF-L; Ecomatik, Dachau, Germany). Each set of probes consisting of four 20-mm-long sensors (S-1, a heated sensor powered by a constant current in 12 v voltage; S-0, S-2, and S-3 as reference sensors) was mounted at the breast height of the north side of the trunk after the outer bark was peeled off and then covered with aluminum foil to avoid physical damage and thermal influences from solar radiation. Data were recorded by a data logger (DL2; Delta-T Devices, Cambridge, UK) every 5 min.
The temperature difference between sensors was calculated using Equation (3). The Baseline 3.0 Software (Dr. Yavor Parashkevov, University of Duke, Durham, North Carolina, USA) was used to determine the
. Then, the temperature data were transferred to sap flow density (
, ml·cm
−2·min
−1) using Equation (4) [
56]:
where
is the difference in instantaneous temperature (°C) between the heated sensor and reference sensors;
is the value of
when the sap flow is nil;
,
, and
are the temperature differences between S-1 and S-0, S-1 and S-2, and S-1 and S-3, respectively.
The daily T (T, mm·day
−1) of the forest plot was calculated using Equation (5):
where
(ml·cm
−2·min
−1) is the average of
of the sample trees; S (m
2) is the projected area of the plot; and ∑
As (cm
2) is the cumulative sapwood area of all trees within the plot.
The field measurements started on the 12, 2, and 8 of May in 2010, 2012, and 2014, respectively, but ended on the 30 September in all years. The data were partly or totally missed randomly due to equipment or power supply failure for 17, 52, and 36 days in 2010, 2012, and 2014, respectively, and were excluded from the later analysis.
The SF-L sensor is a product after improving the Granier sensor (SF-G) by subtracting the separately measured natural vertical background temperature gradient within sapwood (expressed as ()/2 in Equation (3)) from the temperature difference between the two needles (expressed as in Equation (3)) of the Granier sensor. Therefore, the SF-L sensor becomes significantly more accurate and the important reference point of zero sap flow (ΔTmax) remains stable over long periods. The exact determination of the point of zero sap flow requires additional continuous monitoring of an electronic dendrometer. Therefore, the SF-L sensor is not suitable for small trees with DBH < 8 cm. This led to a fact that the mean height and DBH of sample trees were more or less higher than the plot average. However, this should not be critical because the calculation procedure was the same among all years, the contribution of small trees to the daily T of the whole plot was mostly reflected by their sapwood area (see Equation (5)), and the mean sapwood area ratio of the small trees to the whole plot was just 12% within the study period. Therefore, we assumed that the systematic error in T estimation caused by the sample tree size higher than plot average has no effect on our analysis.
2.7. Derivation of the Daily T Model
The stomatal conductance control contains two aspects: plant physiological and hydraulic characteristics [
57]. Physiological control is mainly concerned with stomatal response to photosynthetic drive and VPD under the water-sufficient condition [
58]; while the hydraulic characteristics are mainly in the process of root water uptake—catheter transport—water loss from stomatal. Serious water stress can lead to xylem cavitation and embolism. Then, the hydraulic transmission structure of soil—root—xylem is destroyed, and the water conductivity will decline rapidly [
59]. Based on above, we assume that no synergistic interactions exist among the influencing variables. The basic form of the daily T model in this study is a multiplication coupling the T response equations to PET, REW and LAI, as shown in Equation (6):
where
Tmax is the maximum T (mm·day
−1) when PET, REW, and LAI show no limit to T at the same time; ƒ(
i) is the equation describing the T response to factor
i (PET, REW, or LAI).
The daily T variation is simultaneously influenced by many factors in the field; thus, it is difficult to derive the individual factor effect using raw field data. To see how T responded to each factor and following what function type, the disturbance from other factors not assessed was excluded through the fitting of the upper boundary line [
60] based on the selected data points, which were above the values of the mean plus one standard deviation in each segment of the factor. The needles of larch trees gradually lost their vitality in October due to the decreasing temperature, but they remained at the crown and were still measured as LAI. Therefore, only the data from May to September were used in the analysis below.
A boundary line analysis (Ram Oren’s H
2O Ecology Group from Duke University) was performed to determine the function type of
f(
i), and then, the software SAS 9.4 (SAS Institute Inc., Cary, NC, USA) was used to fit the parameters in Equation (6), with field-measured data of 2010 and 2012. Then, the model was validated with field-measured data of 2014. The model fit quality was assessed using both the absolute error (A) (Equation (7)) and relative error (B) (Equation (8)):
where
MTi is the field-measured T (mm·day
−1);
CTi is the T (mm·day
−1) calculated by the model developed in this study; and n is the number of valid measurements.
Additionally, the model fit quality was assessed by the non-dimensional efficiency criterion of Nash and Sutcliffe (E), as shown in Equation (9) [
61]:
where
MTm is the mean of all measured T during the whole study period.
E varies from minus infinity to 1, and the latter corresponds to a perfect fit.
2.8. Uncertainy and Sensitivity Analysis
The modelling approach contains the potential uncertainty source from PET, REW, and LAI. The quantification of the effect of these uncertainties on the T calculation requires the knowledge of the aforementioned model variables and of their statistical variability and correlation structure. In this study, the uncertainties were evaluated by computing a defined relative sensitivity (
RS) [
62], as shown in Equation (10):
where
CP is the relative change of a given variable (PET, REW, LAI),
AS is the corresponding relative change of output (T),
Ps and
Pb are the postperturbed and original values of a given variable, respectively;
Cb is the measured T, and
Cs is the computed T using Equation (6) by inputting the given variable values with perturbation (i.e., PET increased or decreased by 10%) and the original values of other variables (i.e., REW, LAI). The perturbation magnitude (
CP) was ±10% with respect to the original data.
2.9. Assessment of the Individual Factor Effects on Daily T
Based on the measured data of PET, REW, and LAI, missing daily T due to the failure of power supply or other reasons was calculated using Equation (6) to form a complete data set of daily T during the entire growing season. Then, the monthly T and total T of the growing season were calculated by summing daily T. The common reference to assess an individual factor effect on T (at the daily, monthly, and growing season scales) in year i (here the dry year 2010 and normal year 2012) is the corresponding T values (Tj) observed in year j (here the wet year 2014) under the reference conditions of PETj, REWj, and LAIj. The T in 2014 was least restricted by PET, REW, and LAI, since the REW and LAI in 2014 were the largest and the mean PET (3.04 mm·day−1) was slightly lower than its maximum (3.06 mm·day−1). The T limitation by only one factor can be calculated by inputting the actual measured value of this factor into Equation (6), while other factors remain at their reference conditions. For example, the T limitation by only PET (T(PETi)) is calculated by inputting the actual PETi and the reference values of other factors (REWj and LAIj) into Equation (6). Then, the difference between T(PETi) and Tj, i.e., ∆T(PETi), is viewed as the effect of only PET on T. The same process was used to calculate ∆T(REWi) and ∆T(LAIi). A positive or negative value represents a promotion or limitation effect. The relative effect on T was assessed by the ratios of ΔT(PETi)/Tj, ΔT(REWi)/Tj, and ΔT(LAIi)/Tj.
5. Conclusions
The complex influences of many environmental and vegetation factors on forest T can be simplified into three aspects, i.e., PET, REW, and LAI. PET reflects the atmospheric evapotranspiration driver mainly determined by meteorological factors; REW reflects the soil water supply capacity mainly determined by soil moisture and soil physical properties; LAI reflects the forest capacity of water consumption mainly determined by the leaves amount. The T response to rising PET follows a binomial equation, describing the T increase with a declining rate until the PET threshold of 5.4 mm·day−1; the T response to both REW and LAI follows a saturated exponential equation, describing the rapid T increase until the threshold of REW (0.4) and LAI (4). These T response equations to individual factors were coupled to form a mechanism-based and multiplicative model of the daily T of the studied larch plantation. Both the calibration and validation of this model showed a satisfactory accuracy. Therefore, it can predict the T response to changing environmental and canopy conditions, and separate the contribution of individual factors or their combinations to the T in different time scales.
Using this T model and taking the baseline of the wet year of 2014 with the highest T, the contribution of individual factors to the T change was assessed in the monthly and annual (growing season) scales. For the total T in the growing season of the dry year of 2010, all individual factors had a limitation effect, with the order of PET > LAI > REW; while it showed a limitation effect of LAI and REW and a weak promotion effect of PET in the normal year of 2012, with the limitation order of LAI > REW > PET. It seems that the limitation effect of all three factors is bigger in the drier year than in the wetter year. However, the effect of individual factors on the monthly T varied among observation months and years. In the dry year of 2010, the main limiting factors to T changed from PET and LAI in the first half growing season to REW in the later growing season. In the normal year of 2012, the PET effect on T changed from limitation in May and July to promotion in June, August, and September, and the effect amplitude decreased as the month went on; the REW effect of T limitation was low and stable; while the LAI effect on T was always limitation and its amplitude increased. All these led to an integrated result that the limitation to monthly T was mainly contributed by canopy LAI.