The experiments were conducted in P. tabulaeformis plantations from May 1 to September 30, 2014 in the Anjiapo catchment, Dingxi County (35°35′N, 104°39′E) of Gansu Province in western Chinese Loess Plateau. The annual mean precipitation (period: 1990–2013) in the study area is 420 mm with great seasonal variations. Over 60% of the precipitation falls between July and September, and over 50% occurs in the form of storm. The average monthly air temperature ranges from −7.4 °C to 27.5 °C, with a mean annual temperature of 6.3 °C. The average annual pan evaporation is 1510 mm. The soil belongs to Chernozem according to the IUSS Working Group WRB (2006). The soil was developed from loess parent material, forming a relatively thick profile (Wang et al., 2010). Vegetation restoration had been widely implemented in the area where P. tabulaeformis trees were planted in 1986. The land uses in the study area included croplands, grasslands, artificial shrublands, and woodlands.

P. tabulaeformis plantations were installed about 40 years ago to reforest abandoned farmlands. The understory was few grasses, and the contribution of water use by understory vegetation and bare soil surface was not calculated in this study. An experimental plot of 20 m×20 m was set in a plantation located at the southeast-facing slope with a declination of 26°. Up to 64 P. tabulaeformis were planted in the plot during 2009 when this study was carried out. The tree density and basal area were 1600 trees ha⁻¹ and 25.6 m² ha⁻¹, respectively. The tree canopy height (H) and diameter at breast height (DBH, 1.3 m above the ground) were recorded for all trees >1 cm in DBH in the plot. The average tree H and DBH in the plot were 9.4 m and 10.5 cm, respectively. The distribution of trees DBH in the plot is presented in Table 1. The leaf area index (LAI) in the plot was measured once a month through the study period with a plant canopy analyzer (LAI-2000, Li-Cor, Lincoln, NE, USA). The averaged LAI from April to October was 2.96.

We installed a meteorological tower approximately 100 m from the study site. The recorded meteorological variables were wind speed, air temperature, relative humidity, net and photosynthetically active radiation, rainfall, and atmospheric pressure. These parameters were measured using an AG1000 automatic weather station (Onset Computer Corporation, Pocasset, MA, USA). Rainfall was measured with a tipping-bucket rain gauge (model TE525, metric; Texas Electronics, Dallas, TX).

Volumetric soil moisture was measured by using probes (Em 50, Decagon Devices, Pullman, WA, USA) installed at five depths below the soil surface (10, 20, 30, and 40 cm) in the P. tabulaeformis woodlands. The monitoring sites were located in the upper, middle, and lower portions of the selected study plot, with one sensor per soil depth and slope position. Soil water content was measured every 2 days by means of oven drying to validate the soil moisture data provided by the probes during the study period.

We used the data from the weather station to estimate evapotranspiration with the Penman–Monteith equation, which had been strongly recommended for estimating evapotranspiration:

Sap flow density (F_d) of the P. tabulaeformis trees was measured with Granier-type sensors (Granier, 1987) from May to September 2014. Sapwood thickness was measured with a tree core drill. The sapwood thickness of P. tabulaeformis trees in the study site ranged from 0.5 cm to 1.0 cm (mean±SD=0.73±0.10, n=27). Thus, 10 mm-long sensors were used in this study. Each sensor consisted of two cylindrical probes, a continuously heated upper probe, and an unheated lower probe. Both probes were 10 mm in length and 2 mm in diameter, covered by an aluminum tube to homogenize temperature along their length. When installing the probes, two pieces of bark of 2 cm×2 cm approximately 15 cm vertically apart on the north side of the sampled trees at breast height were peeled until the cambium was exposed. Two holes 10 mm in depth and 2 mm in diameter were drilled radially at the center of the exposed cambium with a portable drill. The probes were then inserted into the two holes of each sample tree. The upper heated probe included a heater that was continuously supplied with 0.15 W (James et al., 2002) constant power. The lower unheated probe served as a temperature reference. Both probes contained a copper–constantan thermocouple in the middle. These thermocouples were joined at the constantan side. The copper leads were connected to a data logger (CR1000, Campbell Scientific) with a multiplexer (AM16/32, Campbell Scientific) programmed to measure the temperature difference between the two probes directly. Temperature differences between the two probes were scanned every 30 s, and 30 min averages were recorded. After installation, the exposed cambium and the probe were covered with silicone gel to prevent water from contacting the probe. The portion of the stem equipped with the probes was covered with an aluminum mantle and then wrapped with several layers of aluminum foil. The purpose of this procedure is to prevent solar radiation from heating the area being measured and to avoid the effect of natural temperature gradients in the stem. The edges of each aluminum mantle were also sealed with silicone gel to prevent water entry. The temperature difference between the two probes was affected by the sap flow close to the upper heated probe. The mean sap flow density (F_d, m³ m⁻² min⁻¹) along the length of the heated probe was calculated on the basis of the temperature difference between the two probes using the empirical equation of Granier (1987):

Stand transpiration (E_c) was extrapolated from the sap flow measurements of individual trees using the following equation (Granier et al., 1996):

Precipitation (P) is the only source of water (i.e., input) in the Anjiapo catchment. The change in soil water content (ΔSW) is controlled by (1) canopy interception (I), (2) soil evaporation (E), (3) plant transpiration (T), (4) runoff (R), and (5) drainage at the bottom layer of the soil profile (D). Data of E and I were from our previous study (Jian et al., 2015). D is nil in the study area according to in situ observations. R was ignored. The soil water balance in the root zone (1 m) is given as follows:

Stepwise multiple regression analyses were performed to determine the relationships between daily changes in stand transpiration and environmental factors (soil water content, photosynthetically active radiation, vapor pressure deficit, and potential evapotranspiration). All statistical analyses were conducted using the SPSS software package version 18.0 (IBM, USA). The regression equations were performed in SigmaPlot version 11.0 (Systat Software, Chicago, Illinois, USA). For all tests, we used a significance level of P < 0.05.

Soil water content from 0 cm to 10 cm was the highest and fluctuated significantly with increasing rainfall, with 46.5% of the variation coefficient for P. tabulaeformis. Rainfall affected the soil water content at 10 cm depth more frequently than the other three soil depths. The soil water content and variation coefficient in deep soil layers were relatively low (Fig. 1). The soil water content at 10 cm depth responded to rain events if the cumulative rainfall over a 3–5 day period exceeded 10–12 mm. Single rain events of less than 10 mm slightly affected the soil water content at 20, 30 or 40 cm depth (Fig. 1). Soil water content generally increased during the rainy season (nearly 70% of annual precipitation occurs during May to September in this region).

A regression equation between A_s and DBH ranging from 3.3 cm to 24.4 cm was derived from the measurements of 30 sampled trees, covering the range of tree DBH in the whole plot. The A_s of P. tabulaeformis trees was reliably described as a power function of DBH (A_s=0.541 DBH^1.403, R²=0.924, P<0.001). The cumulative sapwood area of each DBH class (A_si) and the ratio of A_si to the A_st are shown in Table 1.

The sap flow density in P. tabulaeformis exhibited distinct diurnal variation throughout the growing season. Three diurnal variation examples of sap flow density in P. tabulaeformis in sunny, cloudy, and rainy days are shown in Fig. 2. Sap flow density was low and relatively steady at night and before dawn under the three weather conditions. During sunny days, the sap flow density gradually increased after 06:30 h, reached the peak value of 0.184 cm⁻³ cm⁻² cm⁻¹ after 13:00 h, gradually decreased after 14:30 h, sharply decreased after 18:00 h, and then stabilized after 20:30 h. Meanwhile, the sap flow density during cloudy and rainy days increased approximately 1 h later than that during sunny days. In addition, the variation of sap flow density was not significant. During sunny days, Q and D exhibited the same trend as the daily course of sap flow density. This phenomenon is clearly shown by the coincident high and low values in Fig. 2A. Up to 1–2 h time lag existed between the sap flow and D. Moreover, no significant time lag was observed with Q. Determinant coefficients (R²) of sap flow with Q and D under the three weather conditions are presented in Table 2.

The experimental period was hot, relatively rainy, and humid (Figs. 3B and C). The stand transpiration (E_c) of P. tabulaeformis during the study period showed a mean value of 1.91 mm day⁻¹, ranging from 0.78 mm day⁻¹ to 2.93 mm day⁻¹. The mean daily transpiration rates in May, June, July, August, and September were 1.84±0.21, 1.63±0.29, 2.19±0.19, 2.06±0.23, and 1.27±0.25 mm day⁻¹, respectively. Cumulative transpiration was 291.4 mm, equivalent to 89.1% of the total rainfall during this period.

In most cases, increased stand transpiration (E_c) coincided with the increased values of daily photosynthetically active radiation (Q_o) and mean daily vapor pressure deficit (D_Z) normalized by daylight hours (Fig. 3). For instance, E_c values were 2.21 and 2.45 mm day⁻¹ on May 11th and June 17th, respectively. On September 6th and 8th, when water demand was low because of cloudy day, E_c values were 1.39 and 0.79 mm day⁻¹, respectively. On days when rain occurred, E_c was greatly reduced (Fig. 3). On September 16th, when sudden rainfall occurred with associated humid and cloudy weather conditions, E_c was 0.89 mm day⁻¹. Similarly, the succession of rainy days on September 1st and 15th suppressed E_c. However, on some rainy days followed by sunshine, such as June 30th, July 29th, and August 24th, E_c was relatively high. Daily E_c patterns of P. tabulaeformis showed relatively low values under sunny weather conditions from May 24th to June 8th, although Q_o remained high (Fig. 3).

Determinant coefficients (R²) of daily vapor pressure deficit (D_Z), daily photosynthetically active radiation (Q_o), air temperature (T_a), soil water content (SW), and potential evapotranspiration (ET₀) with stand transpiration (E_c) in each month are presented in Table 3. During the experimental period, daily changes in transpiration correlated with Q_o (R²=0.305–0.802), D_Z (R²=0.311–0.824), Ta (R²=0.465–0.672), SW (R²=0.306–0.802), and ET₀ (R²=0.206–0.403).

The multiple linear regression equations of E_c with SW, D_Z, Q_o, T_a, and ET₀ are shown in Table 4. SW only significantly affected E_c in May. E_c was the result of D_Z and Q_o in June, July, and September. In August, E_c mainly depended on D_Z, Q_o, and T_a.

Total transpiration sharply increased with D_Z at low levels (D_Z < 0.9 kPa) but leveled off at increased D_Z values (Fig. 4a). Despite considerable data scattering, increases in Q_o up to values of 0–500 W m⁻² induced a reasonably linear increase in transpiration, after which transpiration leveled off for increased values of Q_o (Fig. 4b).

The daily soil water content in the P. tabulaeformis plots from May to September 2013 was calculated using the water balance equation. The results are presented in Table 5. The net soil water storage (ΔSW) was negative in each month throughout the experimental period.

Throughout the growing season, the sap flow density of P. tabulaeformis varied regularly, especially during sunny days (Fig. 2). Giorio & Giorio (2003) also reported that the variation in sap flow for olive tree during sunny days was greater than that during cloudy days. Yue et al. (2008) pointed out that the sap flow of Larix principi-rupprechtii, an important principal species for afforestation in North–West China, changes regularly from day to night in later growing season in both typical sunny and cloudy days. However, the sap flow rate during sunny days was greater than that during cloudy days. We found that P. tabulaeformis trees at night presented remained sap flow values different than zero, which cannot be night transpiration. The most probable process is because the trunk, as an important source of water storage and capacitance, replenishes water (Goldstein et al., 1998). Yaseef et al. (2009) reported that Juglans mandshurica demonstrates several peaks of sap flow rate. In specific, the sap flow still occurs at night, but the sap flow rate at this period is much lower than that during day time and is constant. Ma et al. (2001) also indicated that the sap flow rate of Betula platyphylla at night is 11.47%–39.93% of that during the whole day and that the variation in sap flow rate is greater during sunny days than during cloudy days. Moran et al. (2009) reported that the seasonal variation of the hourly sap flow rate of two eucalyptus plantations is similar between the two sites. However, their values were relatively higher during the wet season than during the dry season. Moreover, the variation of the sap flow rate was large during the dry season. In this experiment, the diurnal and seasonal variations of E _c in P. tabulaeformis under different weather conditions were in agreement with previous studies. In addition, the results (Fig. 2) indicated that the sap flow density in P. tabulaeformis exhibited no significant “noon depression” phenomenon. At noon, the stomata of P. tabulaeformis are not completely closed; thus, tree transpiration continues during this time of the day. Alternatively, sap flow measured in the trunk shows liquid water movement within this organ, with a time lag compared with the vapor phase at the stomatal level. Independent measurements of leaf transpiration and stomatal conductance at noon can allow us to elucidate this phenomenon.

The daily transpiration of P. tabulaeformis ranged from 0.78 mm to 2.93 mm in 2014, with a mean value of 1.91 mm day⁻¹. These values were lower or similar than those reported for some coniferous forests of cold climates (Alsheimer et al., 1998; Bosch et al., 2014). In this regard, Alsheimer et al. (1998) found that canopy transpiration varies from 1.4 mm day⁻¹ to 2.8 mm day⁻¹ for 140-year-old Norway spruce (Picea abies) stands in the Lehstenbach catchment, Germany. Lagergren & Lindroth (2002) reported that transpiration ranges from 0.95 mm day⁻¹ to 2.65 mm day⁻¹ in the wet, cool season in Norway spruce stands in a boreal forest in central Sweden. Differences between forests in canopy transpiration are expected because of the significant influences of tree physiology (Lagergren & Lindroth, 2002), stand density (Alsheimer et al., 1998), the stand age (Alsheimer et al., 1998), and soil moisture availability.

The sap flow rate in tree species is related to meteorological factors. Chazdon (2008) indicated that D _Z and Q_o considerably affect the stand transpiration of apple trees (Malus domestica) and that the sap flow rate increases with D_Z and Q_o during sunny days. An experimental result in the southern Ningxia hilly area of northern China showed that Q_o, T_a, and relative humidity are the three significant environmental factors determining the daily transpiration of Larix principi-rupprechtii (Moran et al., 2009). In another study, the average daily stand transpiration of two eucalyptus (Eucalyptus urophylla) plantations is significantly related to available SW and daily D_Z (Chen et al., 2008). In the present experiment, the trunk sap flow rate in P. tabulaeformis was influenced by D_Z and Q_o. However, the magnitude of the influence of these two environmental factors on the sap flow rate varied in each month. Similarly, another study in north–east China showed that T_a, relative humidity, and Q_o are the major three factors affecting the sap flow rate of B. platyphylla during sunny days, but the role of the three factors varies at the different growth stages (Chazdon et al., 2008).

The imbalance between water supply and demand was particularly acute under the poor growing conditions of May in the study area (Table 5). The soil surface is often considered as an important source of water for plant transpiration (Rodrίguez–Caballero et al., 2012). Considering the low rainfall of 16.4 mm in May (Table 5), SW was expected to be a key factor limiting stand transpiration in this month. For this reason, we can conclude that different environmental factors drive stand transpiration at different time periods. SW was more important than Q_o and D_Z in influencing stand transpiration in May.

The P. tabulaeformis trees in the study site can still meet their water demand even though transpiration is frequently restricted by the soil water availability in the upper soil profile as shown by the influence of SW in May. The transpiration rates remained high despite the high temperature and intense radiation on representative clear days for P. tabulaeformis (Fig. 3). This condition was due to the deep and developed rooting systems. Our previous studies in the same area reported that the roots of P. tabulaeformis show a distribution pattern that can reach 2.8 m in depth (Jian et al., 2014). However, the majority of absorbing roots were concentrated in the upper 1.0 m of the soil.