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Environmental controls on sap flow in black locust forest in Loess Plateau, China

Black locust accounts for over 90% of artificial forests in China’s Loess Plateau region. However, water use of black locust is an uphill challenge for this semi-arid region. To accurately quantify tree water use and to explain the related hydrological processes, it is important to collect reliable data for application in the estimation of sap flow and its response to environmental factors. This study measured sap flow in black locust in the 2015 and 2016 growth seasons using the thermal dissipation probes technique and laboratory-calibrated Granier’s equation. The study showed that the laboratory calibrated coefficient α was much larger than the original value presented by Granier, while the coefficient β was similar to the original one. The average daily transpiration was 2.1 mm day−1 for 2015 and 1.6 mm day−1 for 2016. Net solar radiation (Rn) was the key meteorological factor controlling sap flow, followed by vapor pressure deficit (VPD) and then temperature (T). VPD had a threshold control on sap flow at threshold values of 1.9 kPa for 2015 and 1.6 kPa for 2016. The effects of diurnal hysteresis of Rn, VPD and T on sap flow were evident, indicating that black locust water use was conservative.


Results and Discussions
Laboratory calibration. Sap flux in cut stems of black locust was measured directly and the results plotted in Fig. 1. Figure 1A shows the relationship between measured SFD by gravimetric measurements and that calculated based on Granier's original calibration. The ratio of the mean between the measured and calculated SFD was ~13, which was large and indicated larger errors in the direct application of Granier's calibration to calculate SFD of black locust tree.
SFD can be underestimated if part of the sensor probes is in contact with inactive xylem, which underestimation could exceed 80% if the percent inactive xylem is more than 50% 44 . In this study, average sapwood depth was 1.00 ± 0.20 cm. This was shorter than the probe length, indicating that on the average, 40-60% of the probe was in Figure 1. Relationship between measured and calculated SFD using Granier's calibration equation with and without correction for partial probe contact with non-hydraulic active xylem (A); measured SFD versus flux density index K (B); calculated SFD using Graner's original calibration versus our lab-calibrated equation (C); and the relationship between measured and calculated SFD using our lab-calibrated equation (D). The solid lines are the goodness-of-fit regressions with a null interception. The results are from laboratory calibration experiments with cut stems. contact with inactive xylem ( Table 1). The Clearwater's 44 correction method for inactive xylem was then used to correct the values along with the uncorrected ones plotted in Fig. 1A. The resulting ratio between the measured and calculated SFD after correction was 4.77, still large and indicative of underestimation of SFD with Granier's original calibration even after Clearwater's correction. Results similar to the one obtained in this study have been reported for Quercus gambelii Nutt. 26 , Elaeagnus angustifolia L, Gleditsia triacanthos L. and Sophora japonica L. 17 and Quercus prinus willd. and Quercus velutina Lam. 45 .
In order to determine the relationship between SFD and flux index K for black locust, measured SFD with K regression was used. The resulting relationship was a power function (similar to Granier's original equation) and was significant (p < 0.0001) for α coefficient of 0.051 (Eq. 1) and β coefficient of 1.18 (Fig. 1B). The new coefficients obtained represented the departures from the Granier's original calibration where α and β were 0.0119 g cm −2 s −1 and 1.231, respectively 8 . Differences between our lab-calibrated coefficients and those from the original calibration were obvious after plotting SFD against K (Fig. 1C). Actually, the original calibration could result in ~80% reduction in SFD compared with SFD from lab-calibration with Clearwater's 44 correction. Also the reduction ratio was larger than values reported for other tree species 19,20,27,46,47 , but smaller than the values reported by de Oliveira Reis et al. 48 , Taneda and Sperry 26 and Bush et al. 17 (Table 1).
Compared with the original coefficients of Granier 8 , our lab-calibrated coefficients for the original calibration equation significantly improved gravimetric measurement prediction. The discrepancy between TDP and gravimetric measurement reduced from 80% underestimation via the original coefficients to 3.5% underestimation via our new coefficients (with Clearwater's correction, Fig. 1A and D). This suggested that the application of our lab-calibrated coefficients with Clearwater's correction almost completely avoided the notorious SFD underestimation in other experiments (Fig. 1).
Several studies on calibration results of TDP sensors compare SFD calculated by TDP technique with that derived from gravimetric measurement, such as cut tree/stem experiments. Although good agreements have been reported for some diffuse-porous tree species using the original calibration, the issues of large underestimations have remained for most ring-porous species 17,26 , and the range of underestimation is also large with values within 6-90% 47 ( Table 1). The possible reasons for the divergence between published calibration results for TDP sensors include physiological (e.g., tree species), technical (e.g., sensor designs) and other methodological factors (e.g., calibration experimental setup) 18,20,47 . Physiologically, the heterogeneity of vessel density and its distribution in various tree species (ring-porous and diffuse-porous) may induce heterogeneous flux density within the stem (e.g., steep radial SFD gradients or azimuth variations), which may not be fully covered when only few sensor probes are used in calibration experiments and therefore introduce biases or errors in calculated results. Technically, different type of sensors (e.g., custom-made or modified Granier's type) that partially deviate from the original design (e.g., shape and size) are used. With even the difference in geometry or heating power, Granier's original calibration equation is usually applied to estimate SFD without testing the suitability of the original calibration to the altered ones. This eventually induces biases or errors in the final results.
Methodologically, different calibration setups have been used to generate water flows through stem segments, including sub-atmospheric pressure method and positive pressure method 47 . The application of the positive pressure method could affect thermal conductivity and temperature differences (ΔT) between two sensor probes through evaporation cooling of water that possibly leaks from the vicinity of the sensor probes 47 to introduce potential errors in the calibration results. Sub-atmospheric pressure could also introduce potential biases by inducing small amounts of air around sensor surfaces, affecting thermal conductivity between sensors and stem xylem. Furthermore, embolism of xylem vessels in the surrounding wound during installation period cannot be completely avoided, deceasing thermal conductivity. This could reduce SFD around sensor probes to also introduce possible biases in the calibration results. Even though quantity analysis of the biases or errors was not attempted in our study, we still confirmed that the derived parameters of α and β in this study can provide a useful reference for the calculation of SFD using thermal dissipation method for black locust trees in the Loess Plateau region. Moreover, a further validation of the new coefficients (e.g., for black locust pots with gravimetric measurements) could be done to further increase reliability.
Black locust field water use. Water use of black locust trees during the measurement period was estimated by the combination use of SFD (calculated with our lab-calibrated coefficients), sapwood area (As) and DBH relationship and stand density of trees. In this study, the relationship between As and DBH was significant (R 2 = 0.92, p < 0.0001, Fig. 2), with coefficients of 0.4024 for β 1 and 1.90 for β 2 (Eq. 5). The sapwood area per hectare was 5.3 m 2 ha −1 in 2015 and 5.1 m 2 ha −1 in 2016. Total water use during the measurement period in 2015 was 316 mm, with the maximum in July (28% over the total) and average of 2.1 mm day −1 . Total water use in 2016 was 298 mm, with the maximum also in July (25%) and average of 1.6 mm day −1 .
Only few studies have been conducted on seasonal water use of black locust trees in China's Loess plateau region, which results disagreed with the results in this study ( Table 2). Wang et al. 36 noted total seasonal (April-October) water use of 74 mm for 30-year-old black locust stands. Chen et al. 37 38,39 found for 12 and 28-year-old stands values in the range of 21-54 mm (0.14 mm day −1 and 0.39 mm day −1 respectively for the two stands) in the May-September period of 2014. The large discrepancy between our result and those of other studies was likely due to the use of the original calibration in those studies. Other possible reasons for the discrepancy could include physiological (e.g., vessel density and distribution), topographic factors (e.g., slope and slope direction) and meteorological conditions (e.g., Rn, VPD and etc., Table 2). Water use estimates similar to the one in this study have been reported for other tree species in this study area, including reports for Ziziphus jujube 41 Table 2).
Black locust transpiration factors. The controls of environmental factors on sap flux density (SFD) vary with time [49][50][51][52][53] . In order to determine annual variability of environmental controls on SFD, the relationship between SFD and four key environmental factors -net solar radiation (Rn), vapor pressure deficit (VPD), temperature (T) and soil moisture content (SWC) -was determined based on hourly data taken in 2015 and 2016 ( Fig. 3). At hourly time-step, SFD was linearly related with Rn (R 2 = 0.66 for 2015 and 0.75 for 2016) and parabolically with VPD (R 2 = 0.49 for 2015 and 0.53 for 2016) and T (R 2 = 0.28 for 2015 and 0.32 for 2016), but had no clear relationship with SWC. The parabolic relationship between SFD and VPD was a convex function fit, while that between SFD and T was a concave function fit. The regression equations, regression curves and determination coefficients (R 2 ) for the two years (2015 and 2016) are shown in Fig. 3. The relationship between SFD and the four environmental factors varied significantly, expect for SWC where the correlation between SFD and Rn was more significant than that between VPD and T. This indicated that among the four key environmental factors, Rn had the predominant control on sap flow in the study area.
Threshold controls for VPD on SFD have been determined in a number of studies 20,[53][54][55][56][57] . In this study, threshold controls for VPD on SFD are obvious ( Fig. 3B1 and B2). As indicated by the arrows in the figures, SFD leveled off just below the threshold value, after increasing almost linearly with increasing VPD. The threshold value varied with time, environmental conditions and tree species 20,55,58-60 . Here, VPD threshold values were different for 2015 (~1.9 kPa) and 2016 (~1.6 kPa).
Several studies have reported an observed closely relationship between SWC and SFD for a variety of tree species 25,61-63 . However, no close relations were detected in this study ( Fig. 3D1 and D2), which agreed well with the findings of Holscher et al. 64 , Horna et al. 63 and Jiao et al. 38 . The SWC values with insignificant variations during our experimental periods accounted for the weak relations between SWC and SFD. In this study, however, only one soil profile was selected for soil moisture content measurement. This failed to take into account heterogeneity of SWC, although large spatial variations in soil properties and SWC within forest land were expected. This may preclude the general understanding of the correlation between SFD and SWC, requiring more detailed studies in this direction.

References
Plant species Wood classification TDP sensor Applied pressure method α (g cm −2 s −1 ) β The average diurnal courses of hourly mean SFD was also related to Rn, VPD and T for the measurement periods in both 2015 and 2016 (Fig. 4). The mean values were used in this study to minimize uncertainty. For the two years, the diurnal patterns of SFD and diurnal time lags between SFD and Rn, VPD and T were similar. During the experimental periods, the diurnal course of VPD almost matched those of T ( Fig. 4A1 and A2). In the morning, SFD increased sharply after sunrise and lagged behind Rn by a factor of 1 hour. However, the increases in VPD and T markedly lagged behind that in Rn by a factor of about 2 hours. Although the diurnal curves were similar for the four variables, the time of the day for peak values were different. While the peak time for Rn lagged behind that for SFD by a factor of about 1 hour for the two years, the peak of Rn was quite narrower than that of SFD. VPD and T peaks occurred almost at the same time, but lagged behind that of SFD by a factor of about 4 hours. SFD decreased to a relatively low level after sunset and then leveled off, but lagged behind Rn by a factor of 2 hours. Conversely, VPD and T continued to decrease through the night until after sunrise the next day.
Many studies have reported the effects of diurnal hysteresis on sap flux due to environmental factors 20,24,53,55,60,65 . To further explain this effect, the effects of time lag due to the three environmental factors (Rn, VPD and T) on SFD were plotted in Fig. 5. The hysteresis effects were quite evident in 2015 and 2016 experimental periods. The average relationship between 1-hourly SFD and Rn induced an anti-clockwise hysteresis loop, indicating that the variation in SFD in a day lagged behind that in Rn ( Fig. 5A1 and A2). For VPD and T, the relationship with SFD was a clockwise hysteresis loop, indicating that the variation in VPD and T in a day lagged behind that in SFD (Fig. 5B1,B2 and C1-C2). These findings were similar to those reported by O'Grady et al. 66 , Chen et al. 51 , Zheng and Wang 67 , Mei et al. 53 and Niu et al. 20 . In this study, it seemed that at diurnal scale, black locust had the maximum rate of SFD when VPD, Rn and T were not particularly high. On the other hand, favorable environmental conditions for transpiration (i.e., higher Rn, VPD and T) prevented further increase in SFD. Therefore, the diurnal hysteresis between SFD and environmental factors was a self-protection mechanism that enabled black locust to avoid overlaps of peak SFD and peak environmental factors (Rn, VPD and T) and therefore preventing excessive water extraction from the trunk. This prevented xylem vessel embolism and caused the collapse of hydrological conductive system of the xylem 51,65 . It is also a conservative water use strategy of black locust in response to environmental drivers.

Conclusions
Species-specific coefficients for the Granier's original calibration equation were derived for black locust tree in the laboratory, which differed significantly from the original coefficients, with the coefficient α much larger than the original one and the coefficient β somehow similar. In the study, our new coefficients with clearwater's correction almost accounted for the underestimation and also allowed for more precise estimation for black locust SFD by using the TDP technique. During the period of the experiment, average daily transpiration was 2.1 mm day −1 and 1.6 mm day −1 in 2015 and 2016, respectively. Analysis showed that the control of environmental factors on black locust tree transpiration and then on SFD was similar for the two experimental years, with net solar radiation (Rn) as the key environmental factor, followed by vapor pressure deficit (VPD) and then temperature (T). While soil moisture content (SWC) had no significant relationship with SFD, VPD had a threshold control on black locust tree water use. The threshold values were different for the two years, with ~1.9 kPa for 2015 and ~1.6 kPa for 2016.
The effects of diurnal hysteresis of environmental factors -namely Rn (anti-clockwise rotation), VPD (clockwise rotation) and T (clockwise rotation) -on sap flow were evident in the experiment. The variations in VPD and T lagged behind that in SFD, while the variation in SFD lagged behind that in Rn at diurnal scale. Furthermore, the hysteresis between SFD and environmental factors (Rn, VPD and T) were a self-protection    mechanism used by black locust to avoid overlapping peak SFD and environmental factors (Rn, VPD and T). This prevented excessive water extraction and xylem vessel embolism, which caused the collapse of conductive system.

Materials and Methods
Study site. The study was conducted in Yeheshan Provincial Nature Forest Reserve (34°31.76′N, 107°54.67′E and at altitude of 1090 m), which is located in Fufeng County, Shaanxi province and south of the Loess Plateau in China (Fig. 6). It is a warm semi-humid temperate region with continental monsoon climate. The mean air temperature, average annual precipitation and the related standard deviations for 1958-2016 are 12.7 ± 0.64 °C and 580 ± 139 mm, respectively. Precipitation, which mainly occurs in the months of May through October, has large inter-annual variations. The over 50 m depth of loess soil is predominantly silt loam, with mean particle-size distribution of 5.8% sand, 73.4% silt and 20.9% clay. Black locust is the dominant tree species at the site and has an average height of 10 m and density of 2450 trees/ha 2 . The tree forest was established in the early 2000s on former farmlands set aside in 1999 for the implementation of the "Grain-for-Green" project. Grass such as Stipa bungeana, Artemisia sacrorum and Artemisia scoparia naturally grow under the forest canopy. Black locust starts to sprout in mid-April and begins to senesce in October. Leaf area index (LAI, i.e. leaf area per unit ground area) hits peak values in late June. The understory LAI hits maximum values in early June.  This was done by first fitting a Blu-Tack (Bostik Ltd, Leicester, UK) around the interface between the probes and the tree. Then a 10 cm × 30 cm foam strip coil was fitted around and between sensor wires. Finally, a sheet of 50 cm wide aluminum reflective foam insulator was wrapped above the probes and around the tree, which was secured at the top with duct tape. The protection was left open at the bottom to allow air flow around the area of the probes and prevent water from collecting under the insulation. Sensors were checked monthly and changed when broken. Data were recorded every 10 min using the CR1000 data logger (CR1000, Campbell Scientific Inc., Logan, Utah, USA). The Granier equation 8 is given as follows:

Meteorological measurements.
where − − Fd (g cm s ) 2 1 is sap flux density (SFD); α and β are empirical constants with suggested values of 0.0119 and 1.231, respectively: and K is a dimensionless variable defined as:  where ΔT max is the temperature difference obtained under zero flow conditions; and ΔT is the temperature difference between two probes.
In the case where a portion of the probe is inserted into a non-conducting sapwood, ΔT is bias corrected as: where ΔTbc is the bias-corrected ΔT; and a and b are the proportions of the probe in active sapwood and inactive sapwood (b = 1 − a), respectively 44 .

Sap flux calibration.
A total of 12 stem segments (each 3 m in length and 6-10 cm in diameter) were harvested with a saw in the field and taken to the laboratory after protection with wet towels covered on the two cut ends and sealed with plastic bags. The stem segments were re-cut under water and the ends trimmed with a sharp blade. The dimensional characteristics of the stem segments used for calibration are shown in Table 3. The calibration experiment was set up as described by Herbst et al. 46 ; Paudel et al. 19 and Niu et al. 20 . A 5 cm strip of the tree bark was removed from near the top end of the stem and held upright using a ring stand, hose clamps and rubber gaskets with plastic tubing connected to a reservoir of filtered 20 mm KCl solution. Two additional sensors were installed on the opposite sides of the stem following the procedure described above with the heated probe below (downstream) and the reference probe above (upstream). Water flowing through the stem was collected at the bottom end using an Erlenmeyer flask and weighted on an electronic balance (0.1 g). The flow rate was measured by the balance over a series of pressures (0.005-0.04 MPa), which was achieved by varying the height of the reservoir 20,44 . Following each change in pressure, the pressure was held for a minimum of 30 min for the flow measurement to stabilize. The maximum temperature difference between the probes of each sensor was recorded under zero flow condition about 2-3 hours after the application of pressure ended. Following each flow measurement, 0.5% Safranin O solution was added to the reservoir and passed through the stem segments to measure the conducting sapwood area and sapwood depth between the two probes. In most cases, the dye was pulled through the stems for about 60 min after it was clearly visible in the bottom end reservoir (Erlenmeyer flask). This procedure allowed the conversion of the volume of flow to mean sap flow density (SFD, Fd, g m −2 s −1 ). Stem segments were then sectioned with a saw at the level of each heated probe and the cross-section area of the stained sapwood estimated with an Epson Perfection V700 Photo scanner (Seiko Epson Corporation, Nagano, Japan) and ImageJ (version 1.44p) image analysis software.

Stand-scale transpiration estimation.
To calculate stand-scale transpiration, field measurements of where F d av , is the average SFD; i is the measured tress, i = 1, 2, …n; and A c i , is the sapwood area of tree i. In general, transpiration rates of trees are calculated as SFD times sapwood area. For each tree within the plot (10 × 10 m), sapwood area was estimated from DBH as follows: where DBH is the diameter at breast height of a black locust tree within the plot; and β 1 and β 2 are the fitted parameters.
Stem # Diameter (cm) Length (cm) Sapwood depth (cm) Sapwood area (cm 2 )  Table 3. Characteristics of stem segments collected for calibration analysis. Standard error (SE) is ±1 of the standard error of the mean.
In this study, total sapwood area per unit ground area was calculated by establishing five 10 m × 10 m (100 m 2 ) plots within the stand and measuring DBH for every black locust tree in each plot. The stand-scale black locust transpiration was calculated as follows [69][70][71] : where ETt is the forest transpiration; A c is sapwood area of the stand; A G is the stand area; and A A c G is the total sapwood area per unit ground area.