3-1 Calibration experiment
3-1-1 Sample segments
The information of all twelve segment samples was shown in Table 1. The age of trees was 37 years old for tree No.1, 2 and 3; and was 35 years old for tree No. 4, 5 and 6. Diameter at breast height of all segments ranged from 15.5 to 19.8 cm, and tree height ranged from 26.5 to 19.3 m. Height of segments were not recorded for No.1, No.2 and No.3 segments, while it were recorded in another nine segments. The diameter of segment for the first three segments were smaller than other nine segments, it was about 12 cm.
For another nine segments, diameter of segment ranged from 12 to 15 cm. For 12 segments, sapwood depths in 7 segments were less than 2 cm. Sapwood depth in No. 3 was the smallest, and sapwood depths in three azimuths (east, south and west) were smaller than 1 cm. For those sapwood depth less than 2 cm, Clearwater formula (Eq. 3) was applied to avoid underestimating. However, if sapwood depth was less than 1 cm (No. 3 E, S, W; No. 5-1 S; No. 5-2 W; No. 5-3 S; No. 6-1 S), the sap flow density corrected by Clearwater formula will be extremely high, so this data would not be used in this study.
Response of sap flow density to pump pressure changes in segment No. 1 was shown in Fig. 8. When pump pressure changed, sap flow density changed obviously, but it took about 1 hour to reach a stable state. The thermal dissipation method underestimated the
corresponding real water uptake, while after applying corrected formula from Clearwater, the estimation of thermal dissipation probe was closer to real water uptake.
The photos of sapwood area after dye experiment for each segment and response of K (Eq. 2) to pump pressure changes in each segment were shown in Figure 9 and Figure 10. We can see that in most cases, the position of dyed area in the tree segments in 1 cm, 5cm and 10cm did not change a lot except for segment No. 1. So that we used the averaged sapwood depths from each azimuth, which was calculated from five points measurements.
One point was at azimuth, two points were 0.5 cm apart from azimuth and the other two points were 1.0 cm apart from azimuth. For the response of K to pump pressure changes in all segments (Fig. 10), it showed that there was azimuth variation in these 6 trees, but sap flow rates did not be highest in only one azimuth. From the dyed sapwood area in 1 cm, 5cm and 10cm, we could identify the azimuth with higher sap flow density, and it was mostly agree with that determining from the figure of response of K to pump pressure changes. We also could find that sapwood depth was not the reason that cause underestimated under the low sap flow rate condition. Because although sapwood depth was about 2 cm, the accuracy of the Granier sensor was low under the low sap flow rate condition.
3-1-2 Effect of sensor number
In calibration experiment, four sets of Granier sensors were used for each tree segment in order to improve the accuracy of real sap flow density estimation. To confirm potential errors due to the number of azimuthal direction, we calculated the ratio of sap flow density calculated by Granier and Clearwater formula (Fd_Granier_CW) and sap flow density calculated by real water uptake (Fd_actual) for the four combinations (1, 2, 3 and 4 sensors) (Fig. 11). The results showed that the estimations from just one set of sensor and from two sets of sensors might overestimate or underestimate real sap flow density significantly. While sensor number increased, the ratio of sap flow density calculated by Granier and Clearwater formula to real water uptake got closer to 1. That is to say, more sensor number could lead to more accurate estimation.
3-1-3 Effect of segment height
To understand whether different height of segments in the same tree may have similar results or not, tree No.4, 5 and 6 were cut into three segments for each tree. If different height of segment had dissimilar results, all sample segments should cut at sensor installed height. While if different height of segment had similar results, sample segments can be taken from anywhere under the first living branch height.
Therefore, sap flow densities measured by Granier probes (Fd_Granier) and calculated by water uptakes (Fd_actual) in tree No.4, 5 and 6 were compared (Fig. 12).
In figure 12, three segments of each tree in No.4, 5 and 6 showed similar trends. Height of segments has little impact on relationship between Fd_actual and Fd_Granier.
However, it was obvious that different trees had their own trend. So, the effect of different trees was larger than different height of segments. To sum up, different height of segments might have similar results, so all twelve sample segments in this study could have high representative in each whole sample tree.
3-1-4 Accuracy of thermal dissipation probe for Japanese cedar trees
Sap flow densities calculated by real water uptakes (Fd_actual) and measured by thermal dissipation probe (Fd_Granier) were compared in all sample segments (Fig. 13).
In Figure 13, the value of Fd_Granier was calculated only by Granier empirical formula without applying the corrected formula from Clearwater. So, thermal dissipation probes in most of sample segments were underestimated because the sapwood depths were shorter than 2 cm. Under this condition, Granier probes underestimated about 40% of the real water uptakes.
Fd_actual and measured by thermal dissipation probe with applying the corrected formula from Clearwater (Fd_Granier_CW) were compared in all sample segments (Fig.
14). With the corrected formula from Clearwater, Fd_Granier_CW in most of sample segments corresponded to Fd_actual accurately. Under this condition, Granier probes could estimate the real water uptakes accurately less than 10% error. This result implied that the original Granier formula may be suitable for Japanese cedar, and that sapwood depth significantly impacted on the accuracy of thermal dissipation method; hence, careful determination of sapwood depth was the key for the transpiration estimates.
On the other hand, in long term field sap flow density data, we found that the sap flow density of Japanese cedar trees in Taiwan ranged from 0 to 50 (cm3m-2s-1). Under the condition, Fd_Granier_CW may underestimate about 30% of Fd_actual (Fig. 15). This result suggested that the original Granier formula may not be suitable for Japanese cedar trees with the sap flow rate ranging from 0 to 50 (cm3m-2s-1) in central Taiwan.
3-1-5. Comparison with other calibration studies
Some studies showed that thermal dissipation original formula was not suitable for some tree species, and thermal dissipation methods in most cases were underestimated real sap flow rate though some cases were overestimated (Table 2). Previous studies that shown in Table 2 all used Granier 2 cm probe to conduct calibration experiment.
The accuracy of Granier estimation was low under low sap flow rate, while the accuracy of Granier estimation was relatively high when considerating both high and low
sap flow rate (Gutierrez & Santiago, 2006; Sun et al., 2012; Wiedemann et al., 2016), which was same with this study. Although the measurement errors was high when sap flow rate was high in some cases (Bush et al., 2010, Steppe et al., 2010; Sun et al., 2012).
After applying Clearwater formula (formula 3), the substantial improvement in accuracy of estimation could be found in Bush et al. (2010) and Paudel et al. (2013), which was the same with this study. However, some results showed that the application of Clearwater formula did not approve the accuracy (Sun et al., 2012).
In these previous studies, sample materials were derived from branches or stem segments, the range of sap flow rate may be affected by the origin of the materials. For branches, the data in low sap flow rate could be obtained, but for stem segments the data in low sap flow rate were rarely found (Table 2).
This study showed that the Fd_Granier_CW underestimated Fd_actual, probably due to xylem anatomy but not due to sapwood depth, pump pressure (see appendix 1), and azimuthal variations in Fd. Consequently, this study suggested that simple calibration experiment can approve the accuracy of Granier probe, and it is recommended to conduct calibration experiment for each species. The Granier probes and original formula were mostly suitable for softwood species, although it were not suitable for some softwood species (Table 2; Bush et al., 2010).
Fig. 8 Response of sap flow densities to pump pressure changes in segment No.1. The red line represents the period that recorded real water uptake through volumetric cylinder and also represents sap flow density which calculated from real water uptake.
Table 1 Information of all twelve Japanese cedar tree segments.
Segment DBH Diameter of
No. 1
No. 2
No. 3
No. 4-1
No. 4-2
No. 4-3
Fig. 9 Sapwood area for every 12 segment at 1 cm (a), 5cm (b) and 10 cm (c), and figures of sapwood area determined through GIMP (d).
No. 5-1
No. 5-2
No. 5-3
No. 6-1
No. 6-2
No. 6-3
No. 1
No. 2
No. 3
No. 4-1
No. 4-2
No. 4-3
No. 5-1
No. 5-2
No. 5-3
No. 6-1
No. 6-2
No. 6-3
Fig. 10 Response of K to pump pressure changes in each segment. Measured period represents the measured time of volumetric cylinder.
Fig. 11 The effect of sensor number to the accuracy of estimation from Granier sensor.
Fig. 12 Comparison of sap flow densities measured by Granier probes and calculated by real water uptakes in segment No. 4-1, 4-2, 4-3, 5-1, 5-2, 5-3, 6-1, 6-2, 6-3. Every dot is averaged from four azimuths in each segment, and the black solid line is one by one line.
Fig. 13 Comparison of sap flow densities calculated by real water uptakes and measured by Granier probes without applying corrected formula from Clearwater in all sample segments. Every dot is averaged from four azimuths in each segment, and the bar represents maximum and minimum value. The black solid line is one by one line.
Fig. 14 Comparison of sap flow densities calculated by real water uptakes and measured by Granier probes with applying corrected formula from Clearwater in all sample segments. Every dot is averaged from four azimuths in each segment, and bar represent maximum and minimum. Black solid line is one by one line.
Table 2 Comparisons of calibration experiment with other studies.
Fig. 15 Comparison of sap flow densities calculated by real water uptakes and measured by Granier probes with applying corrected formula from Clearwater in all sample segments (sap flow density ranged from 0 to 50 cm3m-2s-1). Every dot is averaged from four azimuths in each segment. Black solid line is one by one line.
Place Tree species Diameter of segment Range of sap flow rate Error Reference Taiwan Cryptomeria japonica 12.5-15 cm 2.3-148 (cm3m-2s-1) -0.04 this study Taiwan Cryptomeria japonica 12.5-15 cm 2.3-50 (cm3m-2s-1) -0.29 this study America Georgia Fagus grandifolia 15 & 21cm (DBH) 5-80 (cm3m-2s-1) -0.61 Steppe et al. (2010) America Georgia Liquidambar styraciflua 7.5±0.4 cm 0.05-1.0 (l h-1) -0.13 Sun et al. (2012) America Georgia Populus deltoides 7.5±0.4 cm 0-0.7 (l h-1) -0.32 Sun et al. (2012) America Georgia Quercus alba 7.5±0.4 cm 0-0.15 (l h-1) -0.20 Sun et al. (2012) America Georgia Ulmus americana 7.5±0.4 cm 0-0.6 (l h-1) -0.11 Sun et al. (2012) America Georgia Pinus echinata 7.5±0.4 cm 0-0.4 (l h-1) -0.13 Sun et al. (2012) America Georgia Pinus taeda 7.5±0.4 cm 0-1.4 (l h-1) 0.49 Sun et al. (2012)
Costa Rica Hyeronima alchorneoides 12-12.6 cm high -0.09 Gutiérrez and Santiago. (2006) Costa Rica Hyeronima alchorneoides 12-12.6 cm low -0.19 Gutiérrez and Santiago. (2006)
Costa Rica Ochroma lagopus 13-15 cm high -0.13 Gutiérrez and Santiago. (2006)
Costa Rica Ochroma lagopus 13-15 cm low -0.55 Gutiérrez and Santiago. (2006)
America utah Populus fremontii 5.08±0.15 15-1100 (cm3m-2s-1) 0.04 Bush et al. (2010) America utah Tilia cordata 4.83±0.15 15-255 (cm3m-2s-2) -0.01 Bush et al. (2010) Israel Bet-Dagan Malus domestica 4.06 cm 0-1026 (cm3m-2s-1) -0.05 Paudel et al. (2013) Israel Bet-Dagan Peltophorum dubium 3.98 cm 0-267 (cm3m-2s-1) -0.07 Paudel et al. (2013) Israel Bet-Dagan Prunus persica 3.98 cm 0-729 (cm3m-2s-1) -0.04 Paudel et al. (2013)
3-2 Estimation of long-term stand scale transpiration
3-2-1 Measurement of sapwood depth
The difference of sapwood depth between 2010 and 2016 of each tree was shown in Figure 16 (see appendix 2). In most cases, sapwood depth showed < 10 mm increases or
< 10 mm decreases (Fig. 16) with the average difference of -0.06 cm (appendix 2), so that we could assume that sapwood depth in this Japanese cedar plantation was not changed through these near 7 years period.
Results from calibration experiment showed that actual sapwood depth with Clearwater formula (formula 3) can substantially improve the accuracy of Granier probe, therefore dye injection experiment was conducted on 17 trees in the plot for field sap flow experiment in this study. Figure 17 showed relationship between sapwood depth determined by visual and by dye experiment (data see appendix 3). The intercept at the x-axis (Fig. 17) corresponded to the width of white zone in Japanese cedar which water content was lower than that in heartwood and there was no water movement in it; also, the dye solution did not go into white zone (Kumagai et al., 2005; Nakada et al., 1999;
Ohashi et al., 1985; Okada et al., 2012). Kumagai et al. (2005) showed that the width of white zone was about 1.0 cm for its study (i.e. about 0.6 cm in this study). So that we used the regression line to recalculate sapwood depth to get more accurate value which
named new sapwood depth in this study (Table 3). Average sapwood depth was 3.41 cm in original, while it was 2.81 cm after recalculated. Difference between them was 0.6 cm.
3-2-2 Effect of sapwood depth and radial variation on transpiration estimation
For field data, sapwood depth can affect stand transpiration estimation not only by radial variation (with Clearwater formula 3) but also by sapwood area estimation. In our study, because the sapwood depths were almost over than 2cm, we should consider the radial variation. Tseng (2011) compared sap flow density in 0-2cm and 2-4cm calculated without Clearwater formula in 6 sample trees, and concluded the sap flow density in 2-4cm was half of sap flow density in 0-2cm. Because at that time the actual sapwood depth was unknown, the Clearwater formula was not used. In this study, the actual new sapwood depth was obtained (Table 3), the sap flow density in 0-2cm and in 2-4cm with Clearwater correction was compared and new ratio (averaged of ratio for #5 and #7) of sap flow density between 0-2cm and 2-4cm was obtained (Fig. 19). The ratio of sap flow density calculated without Clearwater formula in 0-2 and 2-4 cm in #5 and #7 tree was about 50%
(Fig. 18) which was similar with that in Tseng (2011). New ratio calculated from the 2 trees shows that sap flow density in 2-4 cm was about 80% of that in 0-2cm (Fig. 19), which was 30% larger than that in Figure 18. Although 6 trees were examined for radial variation in Tseng (2011), the new sapwood depth in 4 trees of the 6 trees was too short
to apply Clearwater formula (i.e. < 3.2 cm). If we just consider new sapwood depth (Table 3), and do not consider tree growth, the data of sapwood area were shown in Table 4.
Compared with original one in Table 6, it showed the effect of new sapwood depth to sapwood area. The average sapwood area of all trees in original one (Table 6) was 368 cm2, while average sapwood area of all trees in Table 4 was 310 cm2. The new sapwood depth made averaged sapwood area become smaller (difference was 58 cm2).
If sapwood depth change, there were two things affected by it, one was 2-4 cm sap flow rate and the other was sapwood area. Result showed that the difference of annual stand transpiration between that “considered new sapwood depth” and the “original” one was 0.29 mm, which neared 0 (Fig. 20). The green dotted line with square (Fig. 20) showed that if just 2-4 cm sap flow rate (Fd2−4 in formula 9) changed from 0.5 to 0.8,
the yearly transpiration would become 122.28 mm which was 16 mm higher than that in
“original”. The blue dotted line with triangle (Fig. 20) showed that if just sapwood area
(As_stand in formula 6, ∑ni=1As_treei in formula 7, As2−4 and As0−2 in formula 9)
changed, the yearly transpiration was estimated as 96.04 mm, which was 10.07 mm lower than that in “original”. Therefore, although sap flow density in 2-4 cm became higher due
to Clearwater correction, the sapwood area became small, interaction of this two factors decreased the difference between the “considered new sapwood depth” and the “original”
one.
The Clearwater formula can substantially approve the accuracy of estimation because it just changed sap flow rate but not changed sapwood area. Here, one hypothesis have been proposed, that is, if sapwood depth lower than 2 cm, but we assumed it as 2 cm, the underestimation from inactive xylem could be compensated for the overestimation from sapwood area (Lu et al., 2004). Results in this study seemed to agree with this hypothesis. Despite the difference was small, this new sapwood depth was more accurate in theory, so it should be adopted in the following estimation of stand transpiration.
3-2-3 Changes in biometric parameters
The growth of DBH for each tree from 2010 to 2016 was shown in Figure 21. Table 5 showed DBH for each tree from 2010 to 2016 which was calculated from the DBH growth shown in appendix 4. Tree DBH growth ranged from around 0.5 mm to 4.5 mm per year, and DBH growth in tree # 3 and # 16 was relatively higher than other trees (Fig.
21). The average difference of DBH growth between 2010 and 2016 was 1.2 cm, and the highest was 2.3 cm for tree #3 and #16.
3-2-4 Effect of tree growth
Because of the long-term data (near 7 years), we would like to know the effect of tree growth on estimation of stand scale transpiration. Therefore, based on the calculated DBH in every year (Table 5), and sapwood depth obtained in 2010 (Table 3), sapwood area was derived from each tree in every year (Table 6). Table 6 showed that sapwood area changed from tree growth in near 7 years, the difference between original and data of 2016 ranged from 4 to 34 cm2, and averaged was 14 cm2. Taking transpiration in 2015 for example, the transpiration estimation from “original” one and “consider tree growth”
one were shown in Figure 22. Yearly stand transpiration estimation from original one was 106.11 mm, while stand transpiration estimation considered tree growth was 109.41 mm.
The difference between these two was only about 3.3 mm per year. It suggested that the effect of tree growth maybe could be neglected in this study, because the tree growth in this Japanese cedar plantation was small (averaged 14 cm2) in these 6 years in this site.
Therefore, for stand scale transpiration estimation from Sep 2010 to Mar 2017 in this study, tree growth was not considered.
Fig.16 Difference of sapwood depth between 2010 and 2016 for each tree in east and west sides and averaged sapwood depth.
Fig. 17 Regression of two kinds of sapwood depth. Sapdepth_visual represents sapwood depth that determined by visual; sapdepth_dye represents sapwood depth that determined by color from dye experiment.
Table 3 Original sapwood depth and new sapwood depth that calculated from the formula of regression line in Fig. 17.
Fig. 18 Comparison of sap flow density between 0-2 cm and 2-4 cm calculated without Clearwater formula in trees No. 5 and No. 7 in the period of 2010/08/10 to 2011/02/10.
Fig. 19 Comparison of sap flow density between 0-2 cm and 2-4 cm calculated with Clearwater formula in trees No. 5 and No. 7 in the period of 2010/08/10 to 2011/02/10.
Table 4 Sapwood area calculated by new sapwood depth (Table 3) and original DBH (obtained in 2010). “0-2 cm” means sapwood area at the ranged from 0-2 cm. “2-4 cm”
means total sapwood area at the ranged 2-4cm and over 4cm. “total” means total sapwood area for each tree.
Fig. 21 DBH growth for each tree from 2010 to 2016.
Fig. 20 Accumulation of monthly stand scale transpiration in 2015. Orange curve is the
“original” one; purple dotted line with circle is the one that “consider new sapwood depth”; while green dotted line with square is that consider new sapwood depth but just change 2-4 cm sap flow rate; blue dotted line with triangle is that consider new sapwood depth but just change sapwood area.
original 2010 2011 2012 2013 2014 2015 2016 Difference
Average 37.4 37.5 37.7 37.9 38.1 38.3 38.4 38.6 1.2 DBH (cm)
Tree No.
Table 5 DBH for each tree from 2010 to 2016. Difference represents difference between 2016 and original.
Table 6 Sapwood area calculated by DBH (Table 5) and sapwood depth obtained in 2010 (Table 3).
“0-2 cm” means sapwood area at the ranged from 0-2 cm. “2-4 cm” means total sapwood area at the ranged 2-4cm and over 4cm. “total” means total sapwood area for each tree.
0-2 cm 2-4 cm total 0-2 cm 2-4 cm total 0-2 cm 2-4 cm total 0-2 cm 2-4 cm total 0-2 cm 2-4 cm total 0-2 cm 2-4 cm total 0-2 cm 2-4 cm total 0-2 cm 2-4 cm total
NO. original 2010 2011 2012 2013 2014 difference:
2016-original
Fig. 22 Accumulation of monthly stand scale transpiration in 2015. Blue curve is the
“consider tree growth” one. While orange curve is the “original” one.
3-3 Application of indoor-calibration experiment results to field sap flow data
3-3 Application of indoor-calibration experiment results to field sap flow data