Assessing hydraulic redistribution with the compensated average gradient heat-pulse method on rain-fed olive trees

Abstract

Aims

In this study on hydraulic redistribution (HR) in roots, we aimed to use the calibrated average-gradient (CAG) heat-pulse method, the novelty being the use of a much narrower averaging window for the signal analysis, in order to achieve a more linear calibration curve, allowing the HR quantification.

Methods

The study was conducted in 12 large roots of a rain-fed olive orchard, for 6 months without significant rain, when the predawn leaf water potential decreased to −2.4 MPa, and immediately following the first autumn rains.

Results

Detailed numerical modelling of the CAG method allowed verification of the response of the measurement system to a range of drivers, improving the linear range of the calibration response function, which has remained stable over the observations period. On average, reverse flow was observed during 30% of the summer nights and, in a conservative estimate, it increased to about 5% of total daily root flow before first autumn rain.

Conclusions

Reverse flow accounted on average for 2.6% of the total daily root flow, enabling upper roots to stay active during the very dry late-summer period. In qualitative terms, our results confirm the CAG method as a reliable tool to identify reverse flow and quantify HR when it occurs.

Annex 1

Application of the calibrated average gradient (CAG) heat-pulse method to measure sap flow in olive roots.

The calibrated average-gradient (CAG) heat-pulse method of Testi and Villalobos (2009) is a relatively new heat-pulse technique. The method consists of simply averaging the temperature difference signal (∆Ta) after the heat-pulse is applied, and then obtaining an empirical function V _C  = f (∆Ta) that is linear in the low-flow domain (10 cm/h < V _C  < 25 cm/h) where the sap flux density, V _C , is measurable with the traditional compensation heat-pulse method (CHPM). The strength of this method is that the calibrated function depends only on the sensor characteristics and the thermal properties of the wood, plus the curve also provides a self-calibration that can be used to resolve low and even reverse flows (Green and Romero 2012). Furthermore, it is possible to implement CAG without changing hardware used with the CHPM and with only minor changes to the software that analyses the temperature traces. In the experiments described in this paper, we have used conventional CHPM instrumentation (Tranzflo NZ Ltd., Palmerston North, New Zealand) combined with a regulated 10 V heat-pulse controller from MEZÃO (Oeiras, Portugal).

In practical terms, the conventional CHPM is first used to calculate a heat-pulse velocity as V_H = 900/tz. The results of a numerical model (Green et al. 2009) are then used to simulate the effects of probes and blockages (termed as ‘wounding’). Thereafter, a corrected heat-pulse velocity (V _C ) is determined assuming a wound width of 2.4 mm which is the size of the drill hole plus 0.8 mm. With the traditional CHPM measurement, our initial calculations of V_C are limited to values >1.9 cm/h because a cut-off time of 480 s has been applied to the duration of the temperature traces. Preliminary CHPM data from one of the roots (R11) is shown in Fig. 8. A flat line can be seen at the bottom of the V_C trace and this indicates those times (normally during the night) when the low flow rates cannot be resolved using CHPM.

Fig. 8

Diurnal pattern of heat-pulse velocity in a large root (Root 11) from an olive tree growing under rain-fed conditions, as measured by the compensation heat-pulse method (CHPM). Note the CHPM cannot resolve flows below 1.9 cm/h, since we are using a cut-off time of 480 s for the trace analysis

In our experiments, we have tested this combination approach (the CAG method) to resolve low flows (V_C < 1.9 cm/h). The analysis requires additional data processing to remove any signal noise from the V _C and ∆T traces. For that purpose, we have used a 9-point spline (Savitzky and Golay 1964) to filter the time series of sap flows measured every 15 min, essentially delivering a 2-h, time-centred, weighted average for both Vc and ∆T. The CAG method (Testi and Villalobos 2009) was used to obtain the measurement of ∆T, with a slight modification to the time-averaging window which was changed from 180 s to 60 s (Green et al. 2009; Green and Romero 2012) in order to extend the linear range of the ‘calibration’ relationship.

The average temperature gradient ∆T is larger at low flows and smaller at high flows so, for the purpose of visualization, the vertical temperature scale has been reversed (Fig. 9) to illustrate the correspondence between V_C (Fig. 8) and ∆T (Fig. 9). It is important to note that the ∆T signals have greater sensitivity in the low-flow regime (i.e. near the bottom of the ∆T trace) than V _C signals.

Fig. 9

Diurnal pattern of the average temperature gradient as calculated between 0 and 60 s following a 3-s heat-pulse applied to a large olive root (Root 11). The corresponding heat-pulse velocity is shown in Fig. 8

As stated earlier, the CHPM cannot resolve flows below ca. 1.9 cm/h. So, when we plot V _C against ∆T, and thereby derive the calibration curve for low flows, the response is flattened at the low end e.g. V _C  < 1.9 cm/h, and it also becomes slightly non-linear at the high end e.g. V _C  > 40–50 cm/h (Fig. 10). While there is likely to be a different response curve for each set of root measurements, perhaps due to different heat outputs and/or factors effecting heat transport and losses, there is a usually a very stable relationship that extends over many months, in the derived ‘calibration curves’ (Figs. 10 and 12). During the process of determining the calibration curves, smoothing filters were first applied to both the Vc and ∆T time series to minimise any scatter in the relationships. Thereafter, a regression analysis was applied to the linear part of the curve (where 5 < V _C  < 30 cm/h). The corresponding slope-factor is then applied to the original V_C data to extrapolate values of flows <5 cm/h. Otherwise, all flows where Vc > 5 cm/h are based on the original CHPM results. In this way, the CAG method always has a self-calibrating behaviour, and any sensor that has an output that is linear with temperature (such as a thermocouple) can be used with this method.

Fig. 10

The relationship between heat-pulse velocity (V _C , cm/h) and the average temperature gradient (∆T, ^oC) measured in a large olive root (Root-11). These data were obtained at 15 min intervals over a 4 d period (June 17–21, 2011). The upper circle separates the high flows (black markers, V _C  > 30 cm/h) from the low flows (white markers, 5 < V _C  < 30 cm/h). The lower circle (V _C  < 5 cm/h) represents the low-flow range that cannot be resolved by the compensation heat-pulse method (CHPM)

Figure 11 compares heat-pulse velocity measurements from the CHPM and the CAG method. Sometimes only the CAG approach can resolve low flows and provide evidence of reverse flow, a behaviour that is associated with redistribution of water (e.g. Jun 21–24). Other times, the diurnal flow regime can be resolved using CHPM alone (e.g. June 25–26) as was demonstrated for Root 5 during a prolonged period of elevated nocturnal flows associated with a recharge of plant water reserves.

Fig. 11

The diurnal pattern of heat-pulse velocity in a large root of an olive tree growing under rain-fed conditions, as measured by the calibrated average gradient method (CAG). The CAG method can resolve low flows down to zero and even indicates negative (reverse) flows on some nights. These data are for mid-summer (2011) when the olive trees are at the beginning of a period of moderate stress in terms of soil moisture levels and plant water status

Because the CAG method uses an internal calibration (V _C vs ∆T) to resolve these low flows, it would seem prudent to investigate how stable this relationship is over time. Figure 12 shows that the relationship of V _C vs ∆T is indeed very stable over a period of several months. While there is some degree of scatter at the low range of flows which could introduce errors such as false negative values, the stability of the calibration curve over such long period suggests there is likely to be very little additional wound response beyond the initial effects of probe implantation.

At this stage it can only be speculated as to what has caused the subtle changes to the calibration curve of Fig. 12. Here, we have identified small shifts in the CAG relationship for this root, and these are likely to be associated with a recent rainfall event (e.g. the black markers of Fig. 12). As this stage the CAG method seems to be quite sensitive to changes in wood water content, and it could be speculated that this shift in the measurement response might be due to a rehydration effect after such a prolonged period of drought. Numerical modelling has been carried out to address this response using the model of Green et al. (2003).

Fig. 12

The relationship between heat-pulse velocity (V _C ) and the average temperature gradient (∆T) measured in a large olive root (#11). The grey markers show data obtained at 15 min intervals over a 4 month period (June to September, 2011) of almost no rainfall and increasing soil moisture deficits. The black markers (for the period Nov 1–7, 2011) illustrate how the ‘calibration’ has changed following a 70 mm rainfall event. Note: data corresponding to V _C  < 5 cm/h have been removed from this plot

We have simulated the effect of two different wood moisture contents that would represent relatively dry sapwood under extreme water stress and relatively moist sap wood under little or no water stress. The simulations use basic physical and thermal properties of sapwood taken from literature (Table 3), to set the range of sapwood moisture contents. The question is “how might the calibration curve change if the wood water content increased from dry to moist conditions?” as might occur following a rainfall event. As Fig. 13 shows, if the sapwood moisture content were to change from dry to moist, then we are likely to see a widening of the temperature gradient at low flows that is associated with the increased heat capacity of the wetter wood. In practice, if we were applying the dry wood calibration to the wet wood scenario, then there could be a false negative flow of up to 20 cm/h. Thus, it is important to realise the effect of this rehydration on the measurement, and this raises questions about how to best apply the CAG method: questions such as “over what period should the data be averaged in order to apply the correct calibration procedure” from a plot of V _C vs T _G ”. In our work described here, we have recalculated a new V _C vs T _G curves for every day, using a 4-day backward-time filter with typical results shown in Fig. 10. In this case the linear part of the calibration curve is very stable.

Table 3 Volume fractions of wood (F _S , V/V) and water (F _L , V/V) in sapwood taken from the trunks of olive trees managed under different levels of water stress as determined from the pre-dawn leaf water potential (Ψ_pd, MPa)

Notwithstanding, the application of values from Table 1 (wood properties versus water potential in leaves) assumes in this case there is water potential equilibrium between shallow roots, deep roots and leaves at the end of a night and also that there is a correspondence between changes in Ψ_pd and changes in wood water content, which could be less true for isohydric (this case) than for anisohydric behaviour. 

Numerical modelling of the CAG method could be used to investigate the magnitude of any shift in calibration due to a rehydration of the root sap wood, and the results could be applied in a practical sense provided concomitant measurements of the wood water content were available in the roots during the measurement period. Such data were, however, not available. Instead, since it was not possible for us to measure changes in wood moisture content of selected roots during the experiments (F _L , L/L), we have adopted static values for these variables, as measured at the end of the experiment. Values of the volume fractions of wood and water, F _S and F _L (L/L), are important factors to convert from Vc to sap flux density, Js (cm/h), and we have used the working relationship of Js = (0.505 * F_S + F_L) Vc (Edwards and Warrick 1984).

Assuming F _L  = 0.42 as an average value, and using numerical modelling to quantify the effect on sap flow density, the results (top right panel of Fig. 13) show a reasonable ‘scatter’ or ‘shift’ in the calibration response function. Yet, such a magnitude of change might occur only over a whole summer and so, as a consequence, the shift (week to week) would never be as extreme as shown in the modelling results (cf. Figs. 12 and 13). Besides, the self-calibrating nature of the CAG method means these shifts are essentially accounted for by applying new calibrations every day, using the 4 day backward-time filtering approach. Furthermore, long term changes in the CAG calibration appear to be much less sensitive than is suggested by the extreme values used in this simulation of sapwood moisture effects (Fig. 12).

In addition, we have also simulated the effects of other practical factors, such as increasing wound width (W, mm), errors in probe location both upstream (X _U , mm) and downstream (X _D , mm) from the heater, and variations in heater power output (Q _P , W) to understand the system response of the CAG method. The results are shown in the bottom two panels of Fig. 13. Modelling confirms that a universal calibration curve, over the low-flow regime, should not be expected for every measurement of sap flow. Rather, the effects of changes in wound size, a misalignment and misplacement of sensors, and variation in the power output from the heaters each have an effect on the calibration curves, to differing degrees. Consequently, there is a practical need for regular updates on a daily or weekly basis, as has been done here.

Fig. 13

a to f (a top left, b top right). A sensitivity analysis of the CAG method to illustrate the effect of a change in (a) wood moisture content (F _L , m³ water per m³ dry wood) on the relationship between the corrected heat-pulse velocity (V_C, cm/h) and the average temperature gradient (∆T, ^oC); (b) wood moisture content on the relationship between the measured sap flux density (J_S, cm/h) and the average temperature gradient (∆T, ^oC); (c) ‘wound’ size (W, mm) on the relationship between measured sap flux density (J_S, cm/h) and the average temperature gradient (∆T, ^oC); (d) location of the downstream sensor (X_D, mm) and (e) location of the upstream sensor (X_U, mm); (f) heater output power (Q_P, W) on the relationship between the average temperature gradient (∆T) and the sap flux density (assuming the sapwood moisture content is F_L = 0.42 m³ m⁻³)