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Sap flow of several olive trees estimated with the heat-pulse technique by continuous monitoring of a single gauge
Environmental and Experimental Botany 49 (2003) 9 /20 www.elsevier.com/locate/envexpbot
Sap flow of several olive trees estimated with the heat-pulse technique by continuous monitoring of a single gauge Pasquale Giorio a,, Giovanni Giorio b a
Istituto per lo Studio dei Problemi Agronomici dell’Irrigazione nel Mezzogiorno, Consiglio Nazionale delle Ricerche, Via cupa Patacca, 85, 80056 Ercolano (Naples), Italy b Metapontum-Agrobios, S.S. Jonica 106 Km 448, 2, 75010 Metaponto (Matera), Italy Received 7 March 2002; received in revised form 21 May 2002; accepted 21 May 2002
Abstract The use of the compensation heat-pulse velocity (CHPV) technique to estimate sap flow in olive trees as a means of irrigation scheduling can be a difficult task because of the naturally heterogeneity of hydraulic functioning of sapwood area in this species. As a result, the monitoring of an unreasonably large number of both trees and CHPV gauges per tree is needed for accurate estimation of orchard transpiration. The approach used in this paper restricts the monitoring of a large number of both trees and gauges to a very short time (a day) and allows the long term estimation of transpiration of several olive trees by the continuous monitoring of a sole CHPV gauge installed in a single tree. In an experimental olive orchard in southern Italy, we monitored six CHPV gauges in three well irrigated trees (treatment T100) and six CHPV gauges in three rain-fed trees (treatment T0) at half hour intervals for 60 days during summer 1999. For each i th gauge at each day, we linearly regressed the sap flow (Qi , l h1) against the mean sap flow of the all other n/1 gauges of the same treatment (Qmi ). The regression parameters were used to obtain an estimation of Qmi (EQmi ) throughout the trial using the data of any single i th gauge. In order to test the prediction power of the model of i th gauge, the estimated mean sap flow (EQmi ) values were regressed day by day against the actually measured Qmi . The same procedure was also applied at the time scale of a day, that is to the daily cumulative value of Qi and Qmi . In all cases, we obtained high statistical significance of the models applied to data as confirmed by the high adjusted R2 estimates. Our analyses show the feasibility of estimating the transpiration rate of many trees by monitoring sap flow in a single tree by the use of a sole CHPV gauge. The results of this work indicate that CHPV can be a useful and powerful method for irrigation scheduling for olive and other tree species. # 2002 Elsevier Science B.V. All rights reserved. Keywords: Irrigation scheduling; Olea europaea ; Sap flow; Transpiration; Water use
1. Introduction
Corresponding author. Tel.: /39-081-5746606; fax: /39081-7718045 E-mail address: [email protected] (P. Giorio).
Water deficit is becoming a serious problem in the Mediterranean basin where 70% of fresh water is used for irrigation with an efficiency of 50%. For sound irrigation of olive orchards it would be
S0098-8472/02/$ - see front matter # 2002 Elsevier Science B.V. All rights reserved. PII: S 0 0 9 8 - 8 4 7 2 ( 0 2 ) 0 0 0 4 4 - 8
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desirable to have a technique for irrigation scheduling based on the plant’s actual need for water (Ferna´ndez et al., 2001). Tree transpiration can be determined as sap (water) flow estimated by heat-pulse (Huber and Schmidt, 1937; Cohen et al., 1981), heat-balance (Steinberg et al., 1990; Sakuratani, 1981) or (empirical) thermal dissipation (Granier, 1985, 1987) techniques. Compared with forestry, measurement of sap flow on tree crops by means of the heat-pulse technique has been less frequent and restricted to few species. Green and Clothier (1988) measured sap flow in apple and kiwifruit after developing a compensation heat-pulse velocity (CHPV) system. In olive, the same CHPV system has been used in Spain on either roots to study hydraulic behaviour (Moreno et al., 1996) or trunks to estimate whole-tree water consumption (Ferna´ndez et al., 1997) and its relationships with physiological and environmental variables (for a review: Ferna´ndez and Moreno, 1999). Irrigation scheduling has been the subject of many studies which have explored the use of several methods (Jensen, 1981). The saving of water and energy, the improved crop productivity and alleviation of pollution hazards stimulate the adoption of irrigation scheduling as a practice supported by non-subsidized private enterprises (Leib et al., 2002). Estimation of sap flow by the CHPV technique as a means of irrigation scheduling of olive orchards has recently been discussed by Ferna´ndez et al. (2001). These authors reported great variability between CHPV gauges inserted in the same trunk at different azimuth positions, with max/min difference nearly equal to the average sap flow. They concluded that in olive orchards, estimation of the total water consumption of representative trees by means of the CHPV technique needs the (continuous) monitoring of 2 /4 gauges per trunk because of the azimuthally heterogeneity of sapwood hydraulic functioning in this species. We also observed high variability in sap flow in olive trees in relation to azimuth position. As a consequence, the only way to increase the accuracy of sap flow estimation is to monitor a few trees with at least two or, if possible, four gauges per trunk (Ferna´ndez et al., 2001). The necessity of
monitoring a certain number of trees derives from another drawback in using the CHPV technique in olive as the gauges need to be inserted into the ‘smooth and straight’ part of the trunk (Ferna´ndez et al., 2001) which is not such a simple task in this species. When water use of representative trees is known, scaling up to the orchard level can be done by some scalars (Wullschleger et al., 1998) which will not be discussed in this paper. Irrigation scheduling of orchards based on sap flow can be technically difficult because it requires complex and expensive instrumentation for the adequate monitoring of a sufficient number of trees. For this reason, we here adopt an approach to estimate the average sap flow of many olive trees by using the CHPV technique that overcomes the problems underlined above. The idea stems from the observation that, although a single CHPV gauge may not be accurate to estimate transpiration of an olive tree, during a long term trial it still maintains a high resolution of response to the physiological and environmental factors affecting sap (water) flow, such as radiation, vapor pressure deficit and stomatal conductance. Indeed, we observed a remarkable constancy in the relationship between the outputs of any pair of CHPV gauges installed either both in the same trunk or in the trunks of different trees, provided the trees are subjected to relatively similar soil and atmospheric conditions. Our work is ultimately based on the same assumption highlighted by Smith and Allen (1996) for the constancy existing in the relationships between the single members of a plant community. On this basis, and being supported by the visual inspection of sap flow dynamic of several gauges, we expected a strong positive correlation to be observed between the sap flow measured by a gauge ith (Qi , l h1) and the mean sap flow of the canopy measured as the average of a set of different n/1 gauges (Qmi ). Therefore, it should be possible to estimate the parameters of this linear relation by means of regression analysis and use them to obtain an estimate of the mean sap flow (EQmi ) of many trees during other days from the Qi values measured with just a single gauge. Our expectation was that (real time) long term monitoring of the average sap flow of many trees in an olive orchard would be achieved by the
P. Giorio, G. Giorio / Environmental and Experimental Botany 49 (2003) 9 /20
continuous monitoring of a single gauge whereas the whole set of gauges on representative trees needs to be monitored only during a very short time. In this study, to test our hypothesis we analysed the data of an experiment which was primarily carried out to study the physiological and environmental control of olive tree transpiration measured in terms of sap flow (Giorio and d’Andria, 2002).
2. Material and methods 2.1. Experimental site and olive trees The experiment was carried out in 1999 at the CNR-ISPAIM experimental farm located near Benevento, in the Campania region in southern Italy (148 43? E, 418 6? N; 250 m above sea level). The soil has a volumetric soil water content (uv, m3 m 3) of 35.6% measured at soil matrix potential of /0.03 MPa and 21.2% at /1.5 MPa. The olive trees (Olea europaea L., cv Kalamata) were selected in a 7-year-old orchard planted in 1992 with trees spaced at 3/6 m2. The rain-fed treatment (T0) was compared with the daily dripirrigated treatment (T100) that, allowing for useful rains, received 100% of crop evapotranspiration (ETc). ETc was estimated by correcting class A pan evaporation by empirical coefficients (Doorenbos and Pruitt, 1977). More details can be found in Giorio et al. (1999). 2.2. Sap flow by compensation heat-pulse technique Sap (water) flow was estimated by the CHPV technique (Huber and Schmidt, 1937; Marshall, 1958; Swanson and Whitfield, 1981) with the system developed by Green and Clothier (1988) as calibrated for the olive tree by Ferna´ndez et al. (1997, 2001). In brief, each heat-pulse gauge consists of a linear heater and two temperature probes, one installed at 15 mm down-stream and the other at 5 mm up-stream of the heater. Each temperature probe has four (copper /constantan) thermocouple junctions spaced along the radius of the cross section. Both the heater and the temperature probes were 1.8 mm thick. After the heat-
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pulse has been released, its ‘ideal’ velocity (Vh, mm s1) can be calculated by measuring the ‘crossing’ time (tz, s) needed for the up- and down-pair of thermocouples to reach an equal temperature during the heating, according to the equation: Vh /(Xd/Xu)/(2 tz), where Xd and Xu are the relative distances (X , mm) of the downstream- and the upstream-sensor, respectively, from the heater which is used to release the heat-pulse. Every half hour, after 1 s heat pulsing, tz of all four pairs of thermocouples was monitored to calculate heatpulse (ideal) velocity along the radial profile. Ideal velocity was then corrected by empirical coefficients as given by Green and Clothier (1988) for 2.0 mm wound width, to allow for the non-ideal water transport in the plant tissue and the intrusive nature of the gauges. Such coefficients were found to be correct for this species in calibration experiments carried out by Ferna´ndez et al. (2001) using the same system. From the radial profile of corrected heat-pulse velocity (Vc, mm h 1), sap flux density is estimated and then integrated over all the cross section to obtain sap flow (Q , l h1) (see Green and Clothier, 1988; Green, 1997; Ferna´ndez et al., 2001, for details). The CHPV stations of the two treatments were powered by 12 V batteries and controlled by two data-loggers (Campbell Sci. Co., Logan, UT, model CR 23X). The gauges, the associated electronics and the software used to run the system and calculate sap flow were made by the group of Green and Clothier at the Environment and Risk Management Group of the HortResearch Institute (Palmerston North, New Zealand). We will use sap flow nomenclature as similar as possible to what was suggested by Edwards et al. (1996). We used data of sap flow monitored at half hour intervals for 60 days from July 10th (day of year, DOY, 191) on three trees in T0 and three trees in T100. Two CHPV units were intrusively installed at night into each trunk (North and South side) at about 0.4 m above ground for both T0 trees (gauges named A to F) and T100 trees (gauges named G to N). Therefore, a total of 12 CHPV gauges were monitored. In each treatment, we were forced to select three nearby trees along a row in order to connect the six gauges to the datalogger. Trees of the two treatments strongly
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differed in size because irrigation had started in 1994. The basal area below the cambium was 4,490 (9/400) mm2 in treatment T0 and 11,210 (9/2,200) mm2 in treatment T100. In this paper, we use the time of day (TOD) expressed in fractions of 24, ranging from 0 to 1 (e.g. 0.5 for noon time). We also combine DOY and TOD to obtain the day time at a specific day of year (DOY ×/TOD).
2.3. Statistical analysis Estimation of the regression parameters was made using the measurements of all six gauges for each irrigation treatment. For each single i gauge, the linear regression model was: Qmijk aik bik Qijk eijk ;
(1)
where the response variable Qmijk is the mean of sap flow at the time jth of the day k th across the n/1 gauges; the independent variable Qijk is the sap flow of gauge ith at the time jth of the day k th; aik and bik are the linear regression parameters for the gauge ith at the day k th; eijk is the random error term. Estimates of model parameters, aˆik and bˆik ; derived by the least-squares method and the adjusted R2, the coefficient of determination, which explains the portion of the variation of Qmijk that is explained by variation in Qijk in the model, were used as a measure of the goodness of fit of the regression model to the sample observations. Notably, since the regression model contains a single independent variable, the R2 is equivalent to the square of the correlation between Qijk and Qmijk . The t or the F statistics were used for testing the null hypotheses on the estimates of the model parameters. Finally, in order to verify the presence of a first order autocorrelation between the errors, the Durbin /Watson test was also performed for each model. First of all, for each day we performed a calibration step to obtain the estimates of the parameters of the linear regression (the intercept aˆik and the slope bˆik ) between the measured sap flow of each ith gauge (Qijk ) and the measured mean of all other (n/1) gauges of the same treatment (Qmijk ), according to model (1).
For this calibration procedure, carried out at each single DOY, we used day time data from 06:00 to 18:00 h (that is TOD 0.25 /0.75) to avoid unreasonable increases in the error caused by low sap flow values (e.g. those observed at night) which are too near to the background noise (see Fig. 1 as a typical time course observed). For each gauge, the linear regression parameter estimates, aˆik and bˆik ; of calibration obtained at any single day were used to obtain for all days of the trial and without any restriction on day time, the estimated or predicted mean sap flow of all other n/1 gauges (EQmijk ) from the measured sap flow of the gauge i th (Qijk ) at the time jth of the day k th, as follows: EQmijk aˆik bˆik Qijk :
(2)
In order to test the prediction power of the
Fig. 1. Typical time course of sap flow (Qijk , l h 1) of the gauge i th at time j th of DOY k th for the three trees of: (a) treatment T0, gauges A to F; and (b) treatment T100, gauges G to N. Data refer to DOY 191 of 1999 with TOD expressed in fraction of 24 h (e.g. 191.50 represents noon time on 191 DOY).
P. Giorio, G. Giorio / Environmental and Experimental Botany 49 (2003) 9 /20
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model of ith gauge, the estimated mean sap flow (EQmijk ) values obtained by the above equation were regressed day by day against the actual measured Qmijk of the other n/1 gauges using the following model: Qmijk a ik b ik EQmijk e ijk ;
(3)
or ˆik bˆik Qijk )e Qmijk a ik b ik (a ijk :
(3:1)
Although the calibration parameters were estimated for each gauge at any DOY during the trial, in order to simplify the verification we arbitrarily restricted the analysis to DOYs 191, the first day, 222, in the right middle, and 247, at the end of the experiment. Farmers should be interested in estimating water consumption at the time scale of the day and the aim of this paper was to show that measuring the whole set of gauges is only necessary for a very short time (say a single day). We therefore applied the regression performed at half hour intervals in a single day to estimate the mean value of the daily cumulated sap flow of all other n/1 gauges (EQmi×k ) from the daily cumulated sap flow of a single gauge of each DOY (Qi×k ). Importantly, EQmi×k was estimated for all DOY, thereby performing the verification not only frontward, such as when using the calibration parameters obtained for DOY 191 but even backward as in the case of the other two DOY (222 and 247). All statistical analyses were performed using specific procedures of the STAT module of the SAS System for Windows, Release 8.01 TS (SAS Institute Inc., 1991a,b).
3. Results 3.1. Estimation at (half) hour intervals 3.1.1. Calibration procedure Typical relationships between the sap flow of gauge i (Qijk ) and the mean sap flow of all other (n/1) gauges of the same treatment (Qmijk ) for the three arbitrary selected days during the trial,
Fig. 2. Relationship between sap flow (Qijk , l h 1) of the gauge i th at time j th of DOY k th and the mean of sap flow across the other n/1 gauges (Qmijk , l h 1), for DOY 191, 222 and 247 for both treatment T0 (gauges A to F) and T100 (gauges G to N). Data refer to day time from 06:00 to 18:00 h (that is TOD, from 0.25 to 0.75) and are used to estimate the regression parameters for calibration (see full text for details).
DOY 191, 222 and 247, for all gauges of both treatments T100 and T0 (Fig. 2) showed a good correlation as expected from our hypothesis. The estimates of the parameters of the linear regressions (/aˆik ; bˆik ) between Qijk and Qmijk performed using data at day time (06:00 to 18:00 h) for each day from DOY 191 to 247 for treatment T100 and from DOY 191 to 250 for treatment T0 are reported in Fig. 3. The estimates of bik (/bˆik ) were for all the models statistically different from 0 (data not shown) and remained fairly constant for all gauges during most of the period for both treatment T0 (Fig. 3a) and T100 (Fig. 3d). Conversely, the estimates of the intercept parameter,
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Fig. 1. This parameter at the same time showed a good constancy as demonstrated by the low variation coefficient, though it was 12.08% in gauge B and 17.64% in gauge G. For all gauges of both T0 and T100, the overall mean of the adjusted R2 estimates ranged between 0.91 and 0.98, with the exception for gauge B in T100 (0.79). The associated variation coefficient was 14.47% for the same gauge but it was quite low in all other gauges. Finally, estimates of Durbin/Watson statistics were fairly close to 2 for almost all the models tested, indicating absence of auto-correlated errors (data not shown). These data indicate the closeness of the relationship between Qijk and Qmijk and hence the goodness of fit of the model to the observed data. 3.1.2. Verification procedure
Fig. 3. Linear regression parameter estimates (slope, bˆik ; intercept, aˆik and adjusted R2) of the calibration procedure for the relationship between Qijk and actual measured Qmijk shown in relation to DOY of both treatment T0 (gauges A to F) and T100 (gauges G to N). Missing data in the first part of the trial were due to technical problems.
aˆijk (Fig. 3b and e) were not statistically different from 0 (data not shown), with greater variability observed in T100 compared with T0. The latter result may be the effect of the higher sap flow recorded in the well irrigated treatment, due first of all to the different plant size. The adjusted R2 estimates were extremely high for all models and remained constant during the trial for all gauges in T100 (Fig. 3f), while slightly lower values were observed for most of T0 gauges (Fig. 3c). The overall mean and the variation coefficient of the linear regression parameter estimates reported in Fig. 3 are shown in Table 1. The mean of the distribution of slope estimates reflected the variability among gauges and treatments observed in
3.1.2.1. Verification procedure using calibration at DOY 191. The parameter estimates of linear regression between Qijk and Qmijk (Fig. 3) for data measured on DOY 191, named aˆi191 ; bˆi191 ; were used to obtain the estimates of Qmijk , named EQm191 ijk ; from Qijk measured throughout the trial, as follows: EQm191 ˆi191 bˆi191 Qijk : ijk a
(4)
Following this step, in order to verify the prediction power of the model, we derived the estimates of parameters of the model (3): Qmijk aik bik EQm191 ijk ; ijk e
(5)
or Qmijk aik bik (aˆi191 bˆi191 Qijk )eijk :
(5:1)
; bˆik ) and The regression parameter estimates (/aˆik 2 the adjusted R estimates for the above model for each day throughout the trial (that is the verification procedure) for both T0 and T100 are reported in Fig. 4. The slope parameter estimates were always statistically significant (data not shown) and fairly close to 1 in almost all the gauges in both T0 (Fig. 4a) and T100 (Fig. 4d). Similarly, the intercept estimates (Fig. 4b and e) were not significantly different from 0 (data not shown). The adjusted R2 estimates were extremely high and
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Table 1 Mean and variation coefficient of the distribution of bˆik (slope), aˆik (intercept) and adjusted R2 of calibration procedure showed in Fig. 3 of both treatment T0 (gauges A to F) and T100 (gauges G to N) T0
A
B
C
1.31 9.62
1.15 12.08
0.60 11.44
1.17 7.63
0.98 7.14
0.95 7.05
/0.02 /210.84
0.09 60.80
0.05 48.64
0.06 68.81
/0.04 /108.48
0.06 63.22
0.96 2.06
0.79 14.47
0.97 1.12
0.92 7.06
0.94 4.21
0.91 4.87
Mean slope %cv Mean intercept %cv Mean adjusted R2 %cv T100 Mean slope %cv Mean intercept %cv Mean adjusted R2 %cv
G
H
I
D
E
L
F
M
N
1.26 17.64
1.05 7.33
1.76 8.21
0.63 5.13
0.70 7.94
1.14 6.16
0.09 164.51
0.28 34.62
0.12 77.64
/0.06 /94.51
/0.09 /88.69
/0.04 /267.25
0.98 1.11
0.95 3.29
0.97 2.58
0.98 1.21
0.98 0.84
0.97 2.35
constant in the T100 treatment (Fig. 4f), whereas they were slightly more variable in treatment T0 (Fig. 4c) which, however, showed values higher than 0.8 throughout the trial with the exception of gauge B. The data reported in Fig. 4 are summarized in Table 2. The mean of the distribution of the slope estimates for gauges in treatment T100 ranged between 0.91 and 1.07, with the exception of gauge M which showed a value of 1.14. The variation coefficient for the slope was high in gauge G (17.24%) but fairly low in all other gauges (4.74/ 7.99%). The means of the distribution of the adjusted R2 estimates of all T100 gauges were extremely high (between 0.96 and 0.99), with a variation coefficient in the range 0.65 /2.81%. For the treatment T0, the overall mean of the slope estimates for gauge C was 1.23 whereas in all the other gauges it ranged between 0.95 and 1.13, with the variation coefficient ranging from 6.23 to 12.39%. The mean of the adjusted R2 estimates during the trial was 0.83 for gauge B with a variation coefficient of 11.52%, whereas in all other T0 gauges it ranged between 0.93 and 0.98, with the variation coefficient ranging from 1.55 to 6.89%.
As expected, other than from the analyses carried out on a daily basis, evidence of predictability of mean sap flow from the single ith gauge value also results from the relationship between Qmijk and EQm191 ijk for the whole data-set, that is by using the calibration parameters obtained on DOY 191 for the data of all DOY. The R2 was as low as 0.85 for gauge B (T0) but ranged between 0.91 and 0.98 in all other gauges (data not shown). For treatment T100, the verification procedure was also carried out by using the calibration parameters obtained for both 222 and 247 DOY. We present here only the summarized results (Table 3) as they were similar to what was obtained for the calibration at DOY 191. The overall mean of the slope estimates for the linear regression between EQmkijk and the actual Qmijk were all close to unity, with the exception of gauge G which showed a value of 0.71 for the calibration at DOY 247. The adjusted R2 estimates ranged between 0.96 and 0.99 for calibration at both 222 and 247 DOY (Table 3). The radial pattern of sap velocity can potentially affect the prediction power of our model if it changes after the calibration procedure has been carried out. Vc decreased both toward the centre of
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estimate the mean for all other n/1 gauges of the same treatment (EQmi×k ). The relationship between the (measured) Qmi×k and its estimation, EQmi×k , is reported in Fig. 6 for all gauges of treatment T100 throughout the trial (from DOY 191 to 247). This verification procedure used the slope estimates for the calibration carried out on DOY 191 (Fig. 3). Again, the adjusted R2 were higher than 0.97 in all gauges with the slopes fairly close to unity (Table 4), indicating the very good fit of model to data and the possibility of predicting the daily average sap flow of many trees by using the daily sap flow from a single gauge.
4. Discussion
Fig. 4. Linear regression parameter estimates (slope, b; ik intercept, aik and adjusted R2) of the verification procedure 191 for the relationship between EQmijk (estimated with the calibration procedure carried out using data of 191 DOY) and actual measured Qmijk shown in relation to DOY of both treatment T0 (gauges A to F) and T100 (gauges G to N). Missing data in the first part of the trial were due to technical problems.
the trunk and in the proximity of the cambium in both treatments (Fig. 5). However, the general trend of radial patterns remained essentially unchanged, though with decreasing Vc during the trial due to the reduced potential evapotranspiration. 3.2. Estimation at day time scale In order to simplify data processing by using a time scale of more practical interest, the slope estimate of the calibration model (1) obtained during a selected day, bˆik ; can be multiplied by the daily cumulative Qijk of each DOY (Qi×k ) to
A very straightforward way to determine transpiration of a stand is by measuring sap flow in each tree of a representative plot but it is logistically unfeasible because of the large number of trees and associated instrumentation to manage. Smith and Allen (1996) showed that in monoculture crops or forest plantations with closed canopy, a significant variation of transpiration among the plants should not be expected. In these cases, plant density is a sufficient parameter to scale up the transpiration of a number of individual plants to the canopy level. This is because in such plant communities, the members are of similar size and they are subjected to the same environmental conditions. Allen and Grime (1995) reported high values for the cross-correlations between sap flow measured in stems of savannah shrubs which allowed scaling up by the use of the basal cross-sectional area or, potentially, the stem leaf area. In our experiment, we think that the significant variation in sap flow among the gauges for the same treatment can be ascribed to the heterogeneity in hydraulic functioning of sapwood area of Olive. Nevertheless, gauges maintained the strong correlation needed to estimate the average sap flow (Figs. 1 /3). In both treatments, though with the exception of one T0 gauge which showed a value of 0.79, the mean of the distribution of the adjusted R2 estimates between sap flow of any single gauge and the mean across the other gauges was higher than 0.90
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Table 2 (slope), aik (intercept) and adjusted R2 of verification procedure shown in Fig. Mean and variation coefficient of the distribution of bik 4, obtained using calibration parameters at DOY 191 of both treatment T0 (gauges A to F) and T100 (gauges G to N) T0
A
B
Mean slope %cv Mean intercept %cv
Mean slope %cv Mean intercept %cv
D
E
F
0.95 8.54
0.96 12.39
1.23 10.72
1.16 8.30
1.00 6.23
1.13 6.51
0.01 231.59
/0.04 /190.48
/0.05 /47.92
/0.09 /53.50
/0.02 /156.59
/0.11 /31.70
0.97 1.55
0.83 11.52
0.98 3.65
0.93 6.89
0.96 2.04
0.94 3.38
Mean adjusted R2 %cv T100
C
G
H
I
L
M
N
1.00 17.24
0.91 6.54
0.91 7.99
1.07 4.74
1.14 7.53
1.03 5.70
0.01 1392.76
/0.03 /296.75
0.07 124.11
/0.07 /76.16
/0.05 /148.30
/0.07 /135.23
0.99 1.04
0.98 0.65
0.98 2.04
0.98 0.92
0.96 2.81
0.97 1.96
Mean adjusted R2 %cv
Kc as reported by FAO papers no. 24 and 56 (Doorenbos and Pruitt, 1977; Allen et al., 1998). It is assumed that Kc changes with time and that this change can only be ascribed to either the changed size of the measured crop (i.e. to the plant growth) or to a different response to the environment, compared with the reference (steady) crop. When
(Table 1), indicating that such behaviour discussed by Smith and Allen (1996) is shown by the trees of olive orchards. Ultimately, this is the direct consequence of what is already widely accepted on transpiration. In fact, it is known that potential (evapo)transpiration of any crop is related to that of a (steady) reference crop by means of the factor
Table 3 (slope), aik (intercept) and adjusted R2 of verification procedure obtained using Mean and variation coefficient of the distribution of bik calibration parameters at (top ) 222 DOY and (bottom ) 247 DOY of treatment T100 (gauges G to N) G DOY 222 regression Mean slope %cv
H
I
L
M
N
1.12 17.25
1.01 6.54
0.98 7.99
0.93 4.74
0.99 7.53
0.99 5.71
/0.08 /194.54
0.09 98.73
/0.06 /154.08
0.06 79.99
/0.04 /173.01
0.02 551.01
0.98 0.92
0.96 2.81
0.97 1.96
0.99 1.04
0.98 0.65
0.98 2.04
DOY 247 regression Mean slope %cv
0.71 17.25
0.97 6.54
1.15 7.99
1.07 4.74
1.06 7.53
1.16 5.71
Mean intercept %cv
0.24 45.22
0.13 67.38
0.00 3641.26
/0.01 /323.51
/0.09 /77.74
/0.27 /38.25
0.98 0.92
0.96 2.81
0.97 1.96
0.99 1.04
0.98 0.64
0.98 2.04
Mean intercept %cv Mean adjusted R2 %cv
Mean adjusted R2 %cv
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Fig. 6. Relationship between estimated daily-cumulated sap flow (EQmi×k , l d 1) and the actual measured Qmi×k , for each DOY during the trial for all gauges (G to N) of treatment T100.
Fig. 5. Corrected heat-pulse velocity (Vc, mm h 1) in relation to radial depth below the cambium calculated at noon time for DOY 193, 222 and 247 for both treatment T0 (gauges A to F) and T100 (gauges G to N). DOY 193 was preferred to DOY 191 because the latter was a cloudy day.
we compare plants of the same crop, although they are growing, they maintain the same relative size for a relatively long time if they grow slowly, as for olive trees, and are obviously subjected to the same environmental conditions. We should, therefore, not expect significant variations during time in the relationships between the transpiration of the single trees. In most cases reported in the literature, several individual members (plants or stems) are monitored over a range of a scalar, such as the basal area, observed in the canopy. Once the relationship between sap flow and the scalar is established, it is then possible to scale the transpiration of the sampled individuals up to the canopy level. As
reviewed by Wullschleger et al. (1998), these scalars include crown area projection, leaf, basal and sapwood area (Hatton et al., 1995; Teskey and Sheriff, 1996; Dunn and Connor, 1993). It was shown by Hatton et al. (1995) that the most difficult step in the estimation of a poplar stand regarded the accuracy of the measurement of water use of individual trees whereas the scalingup process did not represent the main source of error (Wullschleger et al., 1998). For modern intensive and irrigated olive orchards with adequate management, it should be easy to perform such scaling up, because the plant size should not differ considerably among trees, with the main difficulties in scaling up being overcome by accurate estimation of sap flow in representative trees. Our analyses (Fig. 4, Tables 2 and 3) indicate that a simple model can predict the mean sap flow of many trees in an olive orchard at least over 2 months of the irrigation season, from the actual (continuous) monitoring of a single gauge, provided it has been calibrated against the whole set of gauges for a limited period of time such as a single day. This applies not only at the time scale of a hour but of a day as well (Fig. 6, Table 4) which is of great interest for irrigation scheduling of olive orchards based on the actual water use of trees. In fact, the estimated transpiration in both treatment T100 (QT100×k , mm per day) and T0
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19
Table 4 Regression analysis results (slope, intercept, with standard error, adjusted R2 and F statistic) between the estimated daily-cumulated sap flow EQmi×k and the actual measured Qmi×k , shown in Fig. 6 Probe
Adjusted R2
Intercept estimate
Standard error
Prob./F a
Slope estimate
Standard error
Prob./F b
G H I L M N
0.977 0.979 0.977 0.988 0.989 0.995
3.25 0.30 /1.01 /2.13 0.88 1.24
0.225 0.255 0.299 0.189 0.156 0.115
0.0001 0.2374 0.0001 0.0001 0.0001 0.0001
0.880 1.065 1.033 1.193 1.036 0.981
0.014 0.016 0.016 0.013 0.011 0.007
0.0001 0.0001 0.0457 0.0001 0.0018 0.0104
Prob./F is the probability of getting a greater F statistic than that observed if the null hypothesis is true. a The null hypothesis is H0: intercept/0. b The null hypothesis is H0: slope/1.
(QT0×k , mm per day) showed a good correlation with reference evapotranspiration (ETo, mm per day) (QT100×k /0.24 ETo/0.04, r2 /0.89; QT0×k /0.09 ETo/0.05, r2 /0.86) (Giorio et al., unpublished data). The radial patterns of sap velocity in our case (Fig. 5) were more complex than those found by Ferna´ndez et al. (2001). The high prediction power of the model indicates that our approach is robust and that it could be applied under a wide range of conditions provided they are imposed to all trees. In our experiment we found no evidence against the continuous use of CHPV gauges for several months in olive trees because of reduced sensitivity due to injury effects caused by the intrusive nature of the probes. A result which agrees what stated by Ferna´ndez et al. (2001) who used the same CHPV system in Olive. In this paper we did not study any procedure for scaling up but we aimed to simplify the monitoring of several CHPV gauges in representative trees. Because of the naturally heterogeneity in hydraulic functioning of sapwood area in olive and the difficulties in installing several gauges in a single tree, the only way to obtain accurate estimation of tree transpiration is to intensify the sampling of both gauges and trees. We think that our approach could be used to reduce to the minimum the management of the complex CHPV instrumentation designed for scheduling irrigation in olive orchards on the basis of actual tree water use.
5. Conclusions This study indicates that the CHPV technique can be used to estimate the sap flow of an olive orchard in real time, by continuous measurement of sap flow in a single gauge (Qijk ). This stems from the possibility of estimating the mean sap flow of many gauges (Qmijk ) from Qijk , having performed a linear regression (calibration) against all other gauges in a single day of measurement. The estimation can be done at the time scale of both hour and day using the same calibration parameters. This approach can drastically reduce the complexity of the instrumentation required during the irrigation season. We think it may be suitable for irrigation scheduling if the orchard is characterised by uniform plant size and environmental conditions, as in this situation we expect that scaling up water use to the orchard level may be simply performed on the basis of plant density or average basal trunk area. To check the extensibility of the approach, similar analyses should be carried out in the case of traditional olive orchards with great differences between trees. However, grouping the orchard trees in relation to their size and other factors may solve the potential problem. What obviously remains is the problem of assessing the minimum number of gauges and representative trees needed for accurate estimation of actual orchard transpiration. As our approach restricts the procedure to a single day of measure-
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ments, it calls for a large number of gauges during calibration in order to improve such accuracy.
Acknowledgements The research was supported by the EU-Structural Funds project, agreement C-94-3580, the Coordinated CNR-project ‘Agenzia 2000’ No. CNRC003DE7 and the Chamber of Commerce of Benevento (Italy).
References Allen, R.G., Pereira, L.S., Raes, D., Smith, M., 1998. Crop evapotranspiration, guidelines for computing crop water requirements. FAO Irrigation and Drainage, Paper no. 56, Food and Agriculture Organisation of the United Nations, Rome. Allen, S.J., Grime, V.L., 1995. Measurements of transpiration from savannah shrubs using sap flow gauges. Agric. Forest Meteorol. 75, 23 /41. Cohen, Y., Fuchs, M., Green, G.C., 1981. Improvement of the heat-pulse method for determining sap flow in trees. Plant Cell Environ. 4, 391 /397. Doorenbos, J., Pruitt, W.O., 1977. Guidelines for predicting crop water requirements. FAO Irrigation and Drainage, Paper no. 24, Food and Agriculture Organisation of the United Nations, Rome. Dunn, G.M., Connor, D.J., 1993. Analysis of sap flow in mountain ash (Eucalyptus regnans ) forests of different ages. Tree Physiol. 13, 321 /336. Edwards, W.R.N., Becker, P., Cermak, J., 1996. A unified nomenclature for sap flow measurements. Tree Physiol. 17, 65 /67. Ferna´ndez, J.E., Moreno, F., 1999. Water use by the olive tree. J. Crop Prod. 2, 101 /162. Ferna´ndez, J.E., Palomo, M.J., Diaz-Espejo, A., Clothier, B.E., Green, S.R., Giron, I.F., Moreno, F., 2001. Heat-pulse measurements of sap flow in olives for automating irrigation: tests, root flow and diagnostics of water stress. Agric. Water Manage. 51, 99 /123. Ferna´ndez, J.E., Palomo, M.J., Diaz-Espejo, A., Giron, I.F., 1997. Calibrating the compensation heat-pulse technique for measuring sap flow in olive. Acta Hort. 474, 455 /458. Giorio, P., d’Andria, R., 2002. Sap flow estimated by compensation heat pulse velocity method in olive trees under two irrigation regimes in southern Italy. Acta Hort. (in press). Giorio, P., Sorrentino, G., d’Andria, R., 1999. Stomatal behaviour, leaf water status and photosynthetic response
in field-grown olive trees under water deficit. Environ. Exp. Bot. 42, 95 /104. Granier, A., 1985. Une nouvelle me´thode pour la mesure du flux de se`ve brute dans le tronc des arbres. Ann. Sci. Forest. 42, 193 /200. Granier, A., 1987. Evaluation of transpiration in a Douglas-fir stand by means of sap flow measurements. Tree Physiol. 3, 309 /319. Green, S.R., 1997. Measurements of sap flow by the heat-pulse method. An Instruction Manual for the HPV System. HortResearch Institute, Palmerston North (New Zealand), p. 41. Green, S.R., Clothier, B.E., 1988. Water use of kiwifruit vines and apple trees by heat-pulse technique. J. Exp. Bot. 39, 115 /123. Hatton, T.J., Moore, S.J., Reece, P.H., 1995. Estimating stand transpiration in a Eucalyptus populnea woodland with the heat pulse method: measurement errors and sampling strategies. Tree Physiol. 15, 219 /227. Huber, B., Schmidt, E., 1937. Eine Kompensationmethode zur thermoelektrischen Messung langsamer Saftstro¨me. Ber. Deutsch. Bot. Ges. 55, 514 /529. Jensen, M.E., 1981. Summary and challenges. In: Irrigation Scheduling For Water and Energy Conservation in the 80’s, ASAE Special Publication 23 /81, pp. 225 /231. Leib, B.G., Hattendorf, M., Elliott, T., Matthews, G., 2002. Adoption and adaptation of scientific irrigation scheduling: trends from Washington, USA as of 1998. Agric. Water Manage. 55, 105 /120. Marshall, D.C., 1958. Measurement of sap flow in conifers by heat transport. Plant Physiol. 33, 385 /396. Moreno, F., Ferna´ndez, J.E., Clothier, B.E., Green, S.R., 1996. Transpiration and root water uptake by olive trees. Plant Soil 184, 85 /96. SAS Institute Inc., 1991. SAS† System for Regression, 2nd ed. SAS Institute Inc., Cary, NC, p. 210. SAS Institute Inc., 1991. SAS/STAT† user’s guide, version 6, 4th ed., vols. 1 /2. SAS Institute Inc., Cary, NC. Sakuratani, T., 1981. A heat balance method for measuring water flux in the stem of intact plants. J. Agric. Meteorol. 37, 9 /17. Smith, D.M., Allen, S.J., 1996. Measurement of sap flow in plant stems. J. Exp. Bot. 47, 1833 /1844. Steinberg, S.L., van Bavel, C.H.M., McFarland, M.J., 1990. Improved sap flow gauge for woody and herbaceous plants. Agron J. 82, 851 /854. Swanson, R.H., Whitfield, D.W.A., 1981. A numerical analysis of heat-pulse velocity theory and practice. J. Exp. Bot. 32, 221 /239. Teskey, R.O., Sheriff, D.W., 1996. Water use by Pinus radiata trees in a plantation. Tree Physiol. 16, 273 /279. Wullschleger, S.D., Meinzer, F.C., Vertessy, R.A., 1998. A review of whole-plant water studies in trees. Tree Physiol. 18, 499 /512.
Sap flow of several olive trees estimated with the heat-pulse technique by continuous monitoring of a single gauge Pasquale Giorio a,, Giovanni Giorio b a
Istituto per lo Studio dei Problemi Agronomici dell’Irrigazione nel Mezzogiorno, Consiglio Nazionale delle Ricerche, Via cupa Patacca, 85, 80056 Ercolano (Naples), Italy b Metapontum-Agrobios, S.S. Jonica 106 Km 448, 2, 75010 Metaponto (Matera), Italy Received 7 March 2002; received in revised form 21 May 2002; accepted 21 May 2002
Abstract The use of the compensation heat-pulse velocity (CHPV) technique to estimate sap flow in olive trees as a means of irrigation scheduling can be a difficult task because of the naturally heterogeneity of hydraulic functioning of sapwood area in this species. As a result, the monitoring of an unreasonably large number of both trees and CHPV gauges per tree is needed for accurate estimation of orchard transpiration. The approach used in this paper restricts the monitoring of a large number of both trees and gauges to a very short time (a day) and allows the long term estimation of transpiration of several olive trees by the continuous monitoring of a sole CHPV gauge installed in a single tree. In an experimental olive orchard in southern Italy, we monitored six CHPV gauges in three well irrigated trees (treatment T100) and six CHPV gauges in three rain-fed trees (treatment T0) at half hour intervals for 60 days during summer 1999. For each i th gauge at each day, we linearly regressed the sap flow (Qi , l h1) against the mean sap flow of the all other n/1 gauges of the same treatment (Qmi ). The regression parameters were used to obtain an estimation of Qmi (EQmi ) throughout the trial using the data of any single i th gauge. In order to test the prediction power of the model of i th gauge, the estimated mean sap flow (EQmi ) values were regressed day by day against the actually measured Qmi . The same procedure was also applied at the time scale of a day, that is to the daily cumulative value of Qi and Qmi . In all cases, we obtained high statistical significance of the models applied to data as confirmed by the high adjusted R2 estimates. Our analyses show the feasibility of estimating the transpiration rate of many trees by monitoring sap flow in a single tree by the use of a sole CHPV gauge. The results of this work indicate that CHPV can be a useful and powerful method for irrigation scheduling for olive and other tree species. # 2002 Elsevier Science B.V. All rights reserved. Keywords: Irrigation scheduling; Olea europaea ; Sap flow; Transpiration; Water use
1. Introduction
Corresponding author. Tel.: /39-081-5746606; fax: /39081-7718045 E-mail address: [email protected] (P. Giorio).
Water deficit is becoming a serious problem in the Mediterranean basin where 70% of fresh water is used for irrigation with an efficiency of 50%. For sound irrigation of olive orchards it would be
S0098-8472/02/$ - see front matter # 2002 Elsevier Science B.V. All rights reserved. PII: S 0 0 9 8 - 8 4 7 2 ( 0 2 ) 0 0 0 4 4 - 8
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desirable to have a technique for irrigation scheduling based on the plant’s actual need for water (Ferna´ndez et al., 2001). Tree transpiration can be determined as sap (water) flow estimated by heat-pulse (Huber and Schmidt, 1937; Cohen et al., 1981), heat-balance (Steinberg et al., 1990; Sakuratani, 1981) or (empirical) thermal dissipation (Granier, 1985, 1987) techniques. Compared with forestry, measurement of sap flow on tree crops by means of the heat-pulse technique has been less frequent and restricted to few species. Green and Clothier (1988) measured sap flow in apple and kiwifruit after developing a compensation heat-pulse velocity (CHPV) system. In olive, the same CHPV system has been used in Spain on either roots to study hydraulic behaviour (Moreno et al., 1996) or trunks to estimate whole-tree water consumption (Ferna´ndez et al., 1997) and its relationships with physiological and environmental variables (for a review: Ferna´ndez and Moreno, 1999). Irrigation scheduling has been the subject of many studies which have explored the use of several methods (Jensen, 1981). The saving of water and energy, the improved crop productivity and alleviation of pollution hazards stimulate the adoption of irrigation scheduling as a practice supported by non-subsidized private enterprises (Leib et al., 2002). Estimation of sap flow by the CHPV technique as a means of irrigation scheduling of olive orchards has recently been discussed by Ferna´ndez et al. (2001). These authors reported great variability between CHPV gauges inserted in the same trunk at different azimuth positions, with max/min difference nearly equal to the average sap flow. They concluded that in olive orchards, estimation of the total water consumption of representative trees by means of the CHPV technique needs the (continuous) monitoring of 2 /4 gauges per trunk because of the azimuthally heterogeneity of sapwood hydraulic functioning in this species. We also observed high variability in sap flow in olive trees in relation to azimuth position. As a consequence, the only way to increase the accuracy of sap flow estimation is to monitor a few trees with at least two or, if possible, four gauges per trunk (Ferna´ndez et al., 2001). The necessity of
monitoring a certain number of trees derives from another drawback in using the CHPV technique in olive as the gauges need to be inserted into the ‘smooth and straight’ part of the trunk (Ferna´ndez et al., 2001) which is not such a simple task in this species. When water use of representative trees is known, scaling up to the orchard level can be done by some scalars (Wullschleger et al., 1998) which will not be discussed in this paper. Irrigation scheduling of orchards based on sap flow can be technically difficult because it requires complex and expensive instrumentation for the adequate monitoring of a sufficient number of trees. For this reason, we here adopt an approach to estimate the average sap flow of many olive trees by using the CHPV technique that overcomes the problems underlined above. The idea stems from the observation that, although a single CHPV gauge may not be accurate to estimate transpiration of an olive tree, during a long term trial it still maintains a high resolution of response to the physiological and environmental factors affecting sap (water) flow, such as radiation, vapor pressure deficit and stomatal conductance. Indeed, we observed a remarkable constancy in the relationship between the outputs of any pair of CHPV gauges installed either both in the same trunk or in the trunks of different trees, provided the trees are subjected to relatively similar soil and atmospheric conditions. Our work is ultimately based on the same assumption highlighted by Smith and Allen (1996) for the constancy existing in the relationships between the single members of a plant community. On this basis, and being supported by the visual inspection of sap flow dynamic of several gauges, we expected a strong positive correlation to be observed between the sap flow measured by a gauge ith (Qi , l h1) and the mean sap flow of the canopy measured as the average of a set of different n/1 gauges (Qmi ). Therefore, it should be possible to estimate the parameters of this linear relation by means of regression analysis and use them to obtain an estimate of the mean sap flow (EQmi ) of many trees during other days from the Qi values measured with just a single gauge. Our expectation was that (real time) long term monitoring of the average sap flow of many trees in an olive orchard would be achieved by the
P. Giorio, G. Giorio / Environmental and Experimental Botany 49 (2003) 9 /20
continuous monitoring of a single gauge whereas the whole set of gauges on representative trees needs to be monitored only during a very short time. In this study, to test our hypothesis we analysed the data of an experiment which was primarily carried out to study the physiological and environmental control of olive tree transpiration measured in terms of sap flow (Giorio and d’Andria, 2002).
2. Material and methods 2.1. Experimental site and olive trees The experiment was carried out in 1999 at the CNR-ISPAIM experimental farm located near Benevento, in the Campania region in southern Italy (148 43? E, 418 6? N; 250 m above sea level). The soil has a volumetric soil water content (uv, m3 m 3) of 35.6% measured at soil matrix potential of /0.03 MPa and 21.2% at /1.5 MPa. The olive trees (Olea europaea L., cv Kalamata) were selected in a 7-year-old orchard planted in 1992 with trees spaced at 3/6 m2. The rain-fed treatment (T0) was compared with the daily dripirrigated treatment (T100) that, allowing for useful rains, received 100% of crop evapotranspiration (ETc). ETc was estimated by correcting class A pan evaporation by empirical coefficients (Doorenbos and Pruitt, 1977). More details can be found in Giorio et al. (1999). 2.2. Sap flow by compensation heat-pulse technique Sap (water) flow was estimated by the CHPV technique (Huber and Schmidt, 1937; Marshall, 1958; Swanson and Whitfield, 1981) with the system developed by Green and Clothier (1988) as calibrated for the olive tree by Ferna´ndez et al. (1997, 2001). In brief, each heat-pulse gauge consists of a linear heater and two temperature probes, one installed at 15 mm down-stream and the other at 5 mm up-stream of the heater. Each temperature probe has four (copper /constantan) thermocouple junctions spaced along the radius of the cross section. Both the heater and the temperature probes were 1.8 mm thick. After the heat-
11
pulse has been released, its ‘ideal’ velocity (Vh, mm s1) can be calculated by measuring the ‘crossing’ time (tz, s) needed for the up- and down-pair of thermocouples to reach an equal temperature during the heating, according to the equation: Vh /(Xd/Xu)/(2 tz), where Xd and Xu are the relative distances (X , mm) of the downstream- and the upstream-sensor, respectively, from the heater which is used to release the heat-pulse. Every half hour, after 1 s heat pulsing, tz of all four pairs of thermocouples was monitored to calculate heatpulse (ideal) velocity along the radial profile. Ideal velocity was then corrected by empirical coefficients as given by Green and Clothier (1988) for 2.0 mm wound width, to allow for the non-ideal water transport in the plant tissue and the intrusive nature of the gauges. Such coefficients were found to be correct for this species in calibration experiments carried out by Ferna´ndez et al. (2001) using the same system. From the radial profile of corrected heat-pulse velocity (Vc, mm h 1), sap flux density is estimated and then integrated over all the cross section to obtain sap flow (Q , l h1) (see Green and Clothier, 1988; Green, 1997; Ferna´ndez et al., 2001, for details). The CHPV stations of the two treatments were powered by 12 V batteries and controlled by two data-loggers (Campbell Sci. Co., Logan, UT, model CR 23X). The gauges, the associated electronics and the software used to run the system and calculate sap flow were made by the group of Green and Clothier at the Environment and Risk Management Group of the HortResearch Institute (Palmerston North, New Zealand). We will use sap flow nomenclature as similar as possible to what was suggested by Edwards et al. (1996). We used data of sap flow monitored at half hour intervals for 60 days from July 10th (day of year, DOY, 191) on three trees in T0 and three trees in T100. Two CHPV units were intrusively installed at night into each trunk (North and South side) at about 0.4 m above ground for both T0 trees (gauges named A to F) and T100 trees (gauges named G to N). Therefore, a total of 12 CHPV gauges were monitored. In each treatment, we were forced to select three nearby trees along a row in order to connect the six gauges to the datalogger. Trees of the two treatments strongly
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differed in size because irrigation had started in 1994. The basal area below the cambium was 4,490 (9/400) mm2 in treatment T0 and 11,210 (9/2,200) mm2 in treatment T100. In this paper, we use the time of day (TOD) expressed in fractions of 24, ranging from 0 to 1 (e.g. 0.5 for noon time). We also combine DOY and TOD to obtain the day time at a specific day of year (DOY ×/TOD).
2.3. Statistical analysis Estimation of the regression parameters was made using the measurements of all six gauges for each irrigation treatment. For each single i gauge, the linear regression model was: Qmijk aik bik Qijk eijk ;
(1)
where the response variable Qmijk is the mean of sap flow at the time jth of the day k th across the n/1 gauges; the independent variable Qijk is the sap flow of gauge ith at the time jth of the day k th; aik and bik are the linear regression parameters for the gauge ith at the day k th; eijk is the random error term. Estimates of model parameters, aˆik and bˆik ; derived by the least-squares method and the adjusted R2, the coefficient of determination, which explains the portion of the variation of Qmijk that is explained by variation in Qijk in the model, were used as a measure of the goodness of fit of the regression model to the sample observations. Notably, since the regression model contains a single independent variable, the R2 is equivalent to the square of the correlation between Qijk and Qmijk . The t or the F statistics were used for testing the null hypotheses on the estimates of the model parameters. Finally, in order to verify the presence of a first order autocorrelation between the errors, the Durbin /Watson test was also performed for each model. First of all, for each day we performed a calibration step to obtain the estimates of the parameters of the linear regression (the intercept aˆik and the slope bˆik ) between the measured sap flow of each ith gauge (Qijk ) and the measured mean of all other (n/1) gauges of the same treatment (Qmijk ), according to model (1).
For this calibration procedure, carried out at each single DOY, we used day time data from 06:00 to 18:00 h (that is TOD 0.25 /0.75) to avoid unreasonable increases in the error caused by low sap flow values (e.g. those observed at night) which are too near to the background noise (see Fig. 1 as a typical time course observed). For each gauge, the linear regression parameter estimates, aˆik and bˆik ; of calibration obtained at any single day were used to obtain for all days of the trial and without any restriction on day time, the estimated or predicted mean sap flow of all other n/1 gauges (EQmijk ) from the measured sap flow of the gauge i th (Qijk ) at the time jth of the day k th, as follows: EQmijk aˆik bˆik Qijk :
(2)
In order to test the prediction power of the
Fig. 1. Typical time course of sap flow (Qijk , l h 1) of the gauge i th at time j th of DOY k th for the three trees of: (a) treatment T0, gauges A to F; and (b) treatment T100, gauges G to N. Data refer to DOY 191 of 1999 with TOD expressed in fraction of 24 h (e.g. 191.50 represents noon time on 191 DOY).
P. Giorio, G. Giorio / Environmental and Experimental Botany 49 (2003) 9 /20
13
model of ith gauge, the estimated mean sap flow (EQmijk ) values obtained by the above equation were regressed day by day against the actual measured Qmijk of the other n/1 gauges using the following model: Qmijk a ik b ik EQmijk e ijk ;
(3)
or ˆik bˆik Qijk )e Qmijk a ik b ik (a ijk :
(3:1)
Although the calibration parameters were estimated for each gauge at any DOY during the trial, in order to simplify the verification we arbitrarily restricted the analysis to DOYs 191, the first day, 222, in the right middle, and 247, at the end of the experiment. Farmers should be interested in estimating water consumption at the time scale of the day and the aim of this paper was to show that measuring the whole set of gauges is only necessary for a very short time (say a single day). We therefore applied the regression performed at half hour intervals in a single day to estimate the mean value of the daily cumulated sap flow of all other n/1 gauges (EQmi×k ) from the daily cumulated sap flow of a single gauge of each DOY (Qi×k ). Importantly, EQmi×k was estimated for all DOY, thereby performing the verification not only frontward, such as when using the calibration parameters obtained for DOY 191 but even backward as in the case of the other two DOY (222 and 247). All statistical analyses were performed using specific procedures of the STAT module of the SAS System for Windows, Release 8.01 TS (SAS Institute Inc., 1991a,b).
3. Results 3.1. Estimation at (half) hour intervals 3.1.1. Calibration procedure Typical relationships between the sap flow of gauge i (Qijk ) and the mean sap flow of all other (n/1) gauges of the same treatment (Qmijk ) for the three arbitrary selected days during the trial,
Fig. 2. Relationship between sap flow (Qijk , l h 1) of the gauge i th at time j th of DOY k th and the mean of sap flow across the other n/1 gauges (Qmijk , l h 1), for DOY 191, 222 and 247 for both treatment T0 (gauges A to F) and T100 (gauges G to N). Data refer to day time from 06:00 to 18:00 h (that is TOD, from 0.25 to 0.75) and are used to estimate the regression parameters for calibration (see full text for details).
DOY 191, 222 and 247, for all gauges of both treatments T100 and T0 (Fig. 2) showed a good correlation as expected from our hypothesis. The estimates of the parameters of the linear regressions (/aˆik ; bˆik ) between Qijk and Qmijk performed using data at day time (06:00 to 18:00 h) for each day from DOY 191 to 247 for treatment T100 and from DOY 191 to 250 for treatment T0 are reported in Fig. 3. The estimates of bik (/bˆik ) were for all the models statistically different from 0 (data not shown) and remained fairly constant for all gauges during most of the period for both treatment T0 (Fig. 3a) and T100 (Fig. 3d). Conversely, the estimates of the intercept parameter,
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Fig. 1. This parameter at the same time showed a good constancy as demonstrated by the low variation coefficient, though it was 12.08% in gauge B and 17.64% in gauge G. For all gauges of both T0 and T100, the overall mean of the adjusted R2 estimates ranged between 0.91 and 0.98, with the exception for gauge B in T100 (0.79). The associated variation coefficient was 14.47% for the same gauge but it was quite low in all other gauges. Finally, estimates of Durbin/Watson statistics were fairly close to 2 for almost all the models tested, indicating absence of auto-correlated errors (data not shown). These data indicate the closeness of the relationship between Qijk and Qmijk and hence the goodness of fit of the model to the observed data. 3.1.2. Verification procedure
Fig. 3. Linear regression parameter estimates (slope, bˆik ; intercept, aˆik and adjusted R2) of the calibration procedure for the relationship between Qijk and actual measured Qmijk shown in relation to DOY of both treatment T0 (gauges A to F) and T100 (gauges G to N). Missing data in the first part of the trial were due to technical problems.
aˆijk (Fig. 3b and e) were not statistically different from 0 (data not shown), with greater variability observed in T100 compared with T0. The latter result may be the effect of the higher sap flow recorded in the well irrigated treatment, due first of all to the different plant size. The adjusted R2 estimates were extremely high for all models and remained constant during the trial for all gauges in T100 (Fig. 3f), while slightly lower values were observed for most of T0 gauges (Fig. 3c). The overall mean and the variation coefficient of the linear regression parameter estimates reported in Fig. 3 are shown in Table 1. The mean of the distribution of slope estimates reflected the variability among gauges and treatments observed in
3.1.2.1. Verification procedure using calibration at DOY 191. The parameter estimates of linear regression between Qijk and Qmijk (Fig. 3) for data measured on DOY 191, named aˆi191 ; bˆi191 ; were used to obtain the estimates of Qmijk , named EQm191 ijk ; from Qijk measured throughout the trial, as follows: EQm191 ˆi191 bˆi191 Qijk : ijk a
(4)
Following this step, in order to verify the prediction power of the model, we derived the estimates of parameters of the model (3): Qmijk aik bik EQm191 ijk ; ijk e
(5)
or Qmijk aik bik (aˆi191 bˆi191 Qijk )eijk :
(5:1)
; bˆik ) and The regression parameter estimates (/aˆik 2 the adjusted R estimates for the above model for each day throughout the trial (that is the verification procedure) for both T0 and T100 are reported in Fig. 4. The slope parameter estimates were always statistically significant (data not shown) and fairly close to 1 in almost all the gauges in both T0 (Fig. 4a) and T100 (Fig. 4d). Similarly, the intercept estimates (Fig. 4b and e) were not significantly different from 0 (data not shown). The adjusted R2 estimates were extremely high and
P. Giorio, G. Giorio / Environmental and Experimental Botany 49 (2003) 9 /20
15
Table 1 Mean and variation coefficient of the distribution of bˆik (slope), aˆik (intercept) and adjusted R2 of calibration procedure showed in Fig. 3 of both treatment T0 (gauges A to F) and T100 (gauges G to N) T0
A
B
C
1.31 9.62
1.15 12.08
0.60 11.44
1.17 7.63
0.98 7.14
0.95 7.05
/0.02 /210.84
0.09 60.80
0.05 48.64
0.06 68.81
/0.04 /108.48
0.06 63.22
0.96 2.06
0.79 14.47
0.97 1.12
0.92 7.06
0.94 4.21
0.91 4.87
Mean slope %cv Mean intercept %cv Mean adjusted R2 %cv T100 Mean slope %cv Mean intercept %cv Mean adjusted R2 %cv
G
H
I
D
E
L
F
M
N
1.26 17.64
1.05 7.33
1.76 8.21
0.63 5.13
0.70 7.94
1.14 6.16
0.09 164.51
0.28 34.62
0.12 77.64
/0.06 /94.51
/0.09 /88.69
/0.04 /267.25
0.98 1.11
0.95 3.29
0.97 2.58
0.98 1.21
0.98 0.84
0.97 2.35
constant in the T100 treatment (Fig. 4f), whereas they were slightly more variable in treatment T0 (Fig. 4c) which, however, showed values higher than 0.8 throughout the trial with the exception of gauge B. The data reported in Fig. 4 are summarized in Table 2. The mean of the distribution of the slope estimates for gauges in treatment T100 ranged between 0.91 and 1.07, with the exception of gauge M which showed a value of 1.14. The variation coefficient for the slope was high in gauge G (17.24%) but fairly low in all other gauges (4.74/ 7.99%). The means of the distribution of the adjusted R2 estimates of all T100 gauges were extremely high (between 0.96 and 0.99), with a variation coefficient in the range 0.65 /2.81%. For the treatment T0, the overall mean of the slope estimates for gauge C was 1.23 whereas in all the other gauges it ranged between 0.95 and 1.13, with the variation coefficient ranging from 6.23 to 12.39%. The mean of the adjusted R2 estimates during the trial was 0.83 for gauge B with a variation coefficient of 11.52%, whereas in all other T0 gauges it ranged between 0.93 and 0.98, with the variation coefficient ranging from 1.55 to 6.89%.
As expected, other than from the analyses carried out on a daily basis, evidence of predictability of mean sap flow from the single ith gauge value also results from the relationship between Qmijk and EQm191 ijk for the whole data-set, that is by using the calibration parameters obtained on DOY 191 for the data of all DOY. The R2 was as low as 0.85 for gauge B (T0) but ranged between 0.91 and 0.98 in all other gauges (data not shown). For treatment T100, the verification procedure was also carried out by using the calibration parameters obtained for both 222 and 247 DOY. We present here only the summarized results (Table 3) as they were similar to what was obtained for the calibration at DOY 191. The overall mean of the slope estimates for the linear regression between EQmkijk and the actual Qmijk were all close to unity, with the exception of gauge G which showed a value of 0.71 for the calibration at DOY 247. The adjusted R2 estimates ranged between 0.96 and 0.99 for calibration at both 222 and 247 DOY (Table 3). The radial pattern of sap velocity can potentially affect the prediction power of our model if it changes after the calibration procedure has been carried out. Vc decreased both toward the centre of
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P. Giorio, G. Giorio / Environmental and Experimental Botany 49 (2003) 9 /20
estimate the mean for all other n/1 gauges of the same treatment (EQmi×k ). The relationship between the (measured) Qmi×k and its estimation, EQmi×k , is reported in Fig. 6 for all gauges of treatment T100 throughout the trial (from DOY 191 to 247). This verification procedure used the slope estimates for the calibration carried out on DOY 191 (Fig. 3). Again, the adjusted R2 were higher than 0.97 in all gauges with the slopes fairly close to unity (Table 4), indicating the very good fit of model to data and the possibility of predicting the daily average sap flow of many trees by using the daily sap flow from a single gauge.
4. Discussion
Fig. 4. Linear regression parameter estimates (slope, b; ik intercept, aik and adjusted R2) of the verification procedure 191 for the relationship between EQmijk (estimated with the calibration procedure carried out using data of 191 DOY) and actual measured Qmijk shown in relation to DOY of both treatment T0 (gauges A to F) and T100 (gauges G to N). Missing data in the first part of the trial were due to technical problems.
the trunk and in the proximity of the cambium in both treatments (Fig. 5). However, the general trend of radial patterns remained essentially unchanged, though with decreasing Vc during the trial due to the reduced potential evapotranspiration. 3.2. Estimation at day time scale In order to simplify data processing by using a time scale of more practical interest, the slope estimate of the calibration model (1) obtained during a selected day, bˆik ; can be multiplied by the daily cumulative Qijk of each DOY (Qi×k ) to
A very straightforward way to determine transpiration of a stand is by measuring sap flow in each tree of a representative plot but it is logistically unfeasible because of the large number of trees and associated instrumentation to manage. Smith and Allen (1996) showed that in monoculture crops or forest plantations with closed canopy, a significant variation of transpiration among the plants should not be expected. In these cases, plant density is a sufficient parameter to scale up the transpiration of a number of individual plants to the canopy level. This is because in such plant communities, the members are of similar size and they are subjected to the same environmental conditions. Allen and Grime (1995) reported high values for the cross-correlations between sap flow measured in stems of savannah shrubs which allowed scaling up by the use of the basal cross-sectional area or, potentially, the stem leaf area. In our experiment, we think that the significant variation in sap flow among the gauges for the same treatment can be ascribed to the heterogeneity in hydraulic functioning of sapwood area of Olive. Nevertheless, gauges maintained the strong correlation needed to estimate the average sap flow (Figs. 1 /3). In both treatments, though with the exception of one T0 gauge which showed a value of 0.79, the mean of the distribution of the adjusted R2 estimates between sap flow of any single gauge and the mean across the other gauges was higher than 0.90
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17
Table 2 (slope), aik (intercept) and adjusted R2 of verification procedure shown in Fig. Mean and variation coefficient of the distribution of bik 4, obtained using calibration parameters at DOY 191 of both treatment T0 (gauges A to F) and T100 (gauges G to N) T0
A
B
Mean slope %cv Mean intercept %cv
Mean slope %cv Mean intercept %cv
D
E
F
0.95 8.54
0.96 12.39
1.23 10.72
1.16 8.30
1.00 6.23
1.13 6.51
0.01 231.59
/0.04 /190.48
/0.05 /47.92
/0.09 /53.50
/0.02 /156.59
/0.11 /31.70
0.97 1.55
0.83 11.52
0.98 3.65
0.93 6.89
0.96 2.04
0.94 3.38
Mean adjusted R2 %cv T100
C
G
H
I
L
M
N
1.00 17.24
0.91 6.54
0.91 7.99
1.07 4.74
1.14 7.53
1.03 5.70
0.01 1392.76
/0.03 /296.75
0.07 124.11
/0.07 /76.16
/0.05 /148.30
/0.07 /135.23
0.99 1.04
0.98 0.65
0.98 2.04
0.98 0.92
0.96 2.81
0.97 1.96
Mean adjusted R2 %cv
Kc as reported by FAO papers no. 24 and 56 (Doorenbos and Pruitt, 1977; Allen et al., 1998). It is assumed that Kc changes with time and that this change can only be ascribed to either the changed size of the measured crop (i.e. to the plant growth) or to a different response to the environment, compared with the reference (steady) crop. When
(Table 1), indicating that such behaviour discussed by Smith and Allen (1996) is shown by the trees of olive orchards. Ultimately, this is the direct consequence of what is already widely accepted on transpiration. In fact, it is known that potential (evapo)transpiration of any crop is related to that of a (steady) reference crop by means of the factor
Table 3 (slope), aik (intercept) and adjusted R2 of verification procedure obtained using Mean and variation coefficient of the distribution of bik calibration parameters at (top ) 222 DOY and (bottom ) 247 DOY of treatment T100 (gauges G to N) G DOY 222 regression Mean slope %cv
H
I
L
M
N
1.12 17.25
1.01 6.54
0.98 7.99
0.93 4.74
0.99 7.53
0.99 5.71
/0.08 /194.54
0.09 98.73
/0.06 /154.08
0.06 79.99
/0.04 /173.01
0.02 551.01
0.98 0.92
0.96 2.81
0.97 1.96
0.99 1.04
0.98 0.65
0.98 2.04
DOY 247 regression Mean slope %cv
0.71 17.25
0.97 6.54
1.15 7.99
1.07 4.74
1.06 7.53
1.16 5.71
Mean intercept %cv
0.24 45.22
0.13 67.38
0.00 3641.26
/0.01 /323.51
/0.09 /77.74
/0.27 /38.25
0.98 0.92
0.96 2.81
0.97 1.96
0.99 1.04
0.98 0.64
0.98 2.04
Mean intercept %cv Mean adjusted R2 %cv
Mean adjusted R2 %cv
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P. Giorio, G. Giorio / Environmental and Experimental Botany 49 (2003) 9 /20
Fig. 6. Relationship between estimated daily-cumulated sap flow (EQmi×k , l d 1) and the actual measured Qmi×k , for each DOY during the trial for all gauges (G to N) of treatment T100.
Fig. 5. Corrected heat-pulse velocity (Vc, mm h 1) in relation to radial depth below the cambium calculated at noon time for DOY 193, 222 and 247 for both treatment T0 (gauges A to F) and T100 (gauges G to N). DOY 193 was preferred to DOY 191 because the latter was a cloudy day.
we compare plants of the same crop, although they are growing, they maintain the same relative size for a relatively long time if they grow slowly, as for olive trees, and are obviously subjected to the same environmental conditions. We should, therefore, not expect significant variations during time in the relationships between the transpiration of the single trees. In most cases reported in the literature, several individual members (plants or stems) are monitored over a range of a scalar, such as the basal area, observed in the canopy. Once the relationship between sap flow and the scalar is established, it is then possible to scale the transpiration of the sampled individuals up to the canopy level. As
reviewed by Wullschleger et al. (1998), these scalars include crown area projection, leaf, basal and sapwood area (Hatton et al., 1995; Teskey and Sheriff, 1996; Dunn and Connor, 1993). It was shown by Hatton et al. (1995) that the most difficult step in the estimation of a poplar stand regarded the accuracy of the measurement of water use of individual trees whereas the scalingup process did not represent the main source of error (Wullschleger et al., 1998). For modern intensive and irrigated olive orchards with adequate management, it should be easy to perform such scaling up, because the plant size should not differ considerably among trees, with the main difficulties in scaling up being overcome by accurate estimation of sap flow in representative trees. Our analyses (Fig. 4, Tables 2 and 3) indicate that a simple model can predict the mean sap flow of many trees in an olive orchard at least over 2 months of the irrigation season, from the actual (continuous) monitoring of a single gauge, provided it has been calibrated against the whole set of gauges for a limited period of time such as a single day. This applies not only at the time scale of a hour but of a day as well (Fig. 6, Table 4) which is of great interest for irrigation scheduling of olive orchards based on the actual water use of trees. In fact, the estimated transpiration in both treatment T100 (QT100×k , mm per day) and T0
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19
Table 4 Regression analysis results (slope, intercept, with standard error, adjusted R2 and F statistic) between the estimated daily-cumulated sap flow EQmi×k and the actual measured Qmi×k , shown in Fig. 6 Probe
Adjusted R2
Intercept estimate
Standard error
Prob./F a
Slope estimate
Standard error
Prob./F b
G H I L M N
0.977 0.979 0.977 0.988 0.989 0.995
3.25 0.30 /1.01 /2.13 0.88 1.24
0.225 0.255 0.299 0.189 0.156 0.115
0.0001 0.2374 0.0001 0.0001 0.0001 0.0001
0.880 1.065 1.033 1.193 1.036 0.981
0.014 0.016 0.016 0.013 0.011 0.007
0.0001 0.0001 0.0457 0.0001 0.0018 0.0104
Prob./F is the probability of getting a greater F statistic than that observed if the null hypothesis is true. a The null hypothesis is H0: intercept/0. b The null hypothesis is H0: slope/1.
(QT0×k , mm per day) showed a good correlation with reference evapotranspiration (ETo, mm per day) (QT100×k /0.24 ETo/0.04, r2 /0.89; QT0×k /0.09 ETo/0.05, r2 /0.86) (Giorio et al., unpublished data). The radial patterns of sap velocity in our case (Fig. 5) were more complex than those found by Ferna´ndez et al. (2001). The high prediction power of the model indicates that our approach is robust and that it could be applied under a wide range of conditions provided they are imposed to all trees. In our experiment we found no evidence against the continuous use of CHPV gauges for several months in olive trees because of reduced sensitivity due to injury effects caused by the intrusive nature of the probes. A result which agrees what stated by Ferna´ndez et al. (2001) who used the same CHPV system in Olive. In this paper we did not study any procedure for scaling up but we aimed to simplify the monitoring of several CHPV gauges in representative trees. Because of the naturally heterogeneity in hydraulic functioning of sapwood area in olive and the difficulties in installing several gauges in a single tree, the only way to obtain accurate estimation of tree transpiration is to intensify the sampling of both gauges and trees. We think that our approach could be used to reduce to the minimum the management of the complex CHPV instrumentation designed for scheduling irrigation in olive orchards on the basis of actual tree water use.
5. Conclusions This study indicates that the CHPV technique can be used to estimate the sap flow of an olive orchard in real time, by continuous measurement of sap flow in a single gauge (Qijk ). This stems from the possibility of estimating the mean sap flow of many gauges (Qmijk ) from Qijk , having performed a linear regression (calibration) against all other gauges in a single day of measurement. The estimation can be done at the time scale of both hour and day using the same calibration parameters. This approach can drastically reduce the complexity of the instrumentation required during the irrigation season. We think it may be suitable for irrigation scheduling if the orchard is characterised by uniform plant size and environmental conditions, as in this situation we expect that scaling up water use to the orchard level may be simply performed on the basis of plant density or average basal trunk area. To check the extensibility of the approach, similar analyses should be carried out in the case of traditional olive orchards with great differences between trees. However, grouping the orchard trees in relation to their size and other factors may solve the potential problem. What obviously remains is the problem of assessing the minimum number of gauges and representative trees needed for accurate estimation of actual orchard transpiration. As our approach restricts the procedure to a single day of measure-
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ments, it calls for a large number of gauges during calibration in order to improve such accuracy.
Acknowledgements The research was supported by the EU-Structural Funds project, agreement C-94-3580, the Coordinated CNR-project ‘Agenzia 2000’ No. CNRC003DE7 and the Chamber of Commerce of Benevento (Italy).
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