Alisson Macendo Amaral·Frederico Antonio Loureiro Soares·Lucas Melo Vellame·Marconi Batista Teixeira

Abstract The tropical arboreal species Brazilian mahogany (Swietenia macrophylla) is very important economically and ecologically,for which understanding ecophysiological variables such as sap flow will improve understanding of the species and its cultivation.This paper aims to measure uncertainties (U) involved in the application of the heat ratio method for determining sap flow in Brazilian mahogany using sets of heating probes and thermometers installed on plants of 18 months of age,cultivated in Yellow Latosol,under a weighing lysimeter and located in a protected environment.The uncertainty in sap flow was calculated as the combination of uncertainty in the thermal diffusivity (U k),conductive section (U Sc) and corrected sap velocity (U Vc).U k had greater weight in determining the flow of sap in Brazilian mahogany,when compared to U Sc and U Vc .The thermal diffusivity during the cycle,or period evaluated,must be adjusted to improve the accuracy of the heat ratio method because the sap flow overestimated transpiration by 15.0%.When soil water was optimal In addition,the vapor pressure deficit linearly and indirectly influenced the SF with a difference of 14.6%.

Keywords Heat pulse·Diffusivity·Reliability·Transpiration·Vapor pressure deficit

Introduction

Brazilian mahogany (Swietenia macrophyllaKing;Meliaceae) is a perennial,deciduous,tropical tree species native to Brazil,widely distributed in Central and South America and western India,Malaysia and southern China (Leão 2011;Mi et al.2019).It has numerous applications in furniture,joinery,compound fertilizer and heavy metal remediation and as an antimicrobial,anti-inflammatory,antioxidant agent (Mukaromah et al.2017).In addition,it is widely exploited in Brazil in management of forests and recovery of degraded areas,restoration of ecosystems and in the protection of slopes due to its rapid apical growth and homogeneity (Teixeira et al.2013;Da Rocha et al.2016;Mukaromah et al.2017;Correia et al.2018).

The sustainable management of ecosystems and,consequently of water resources,depends on the evaluation of water use by plants,their physiological responses,and factors that govern such mechanisms,and the principal process for understanding water use is transpiration (De Paula et al.2013;Shen et al.2015).Sap flow is an ecophysiological variable widely used as an approximation of transpiration,making it a valuable tool for understanding the complex,interrelated processes that underlie physiological functions that directly depend on the water content in the plant (Forster 2017;Larekeng et al.2019).The ability to modulate sap flow allows trees to change their water status by removing water from storage sites such as sapwood,cell walls,inactive vessels,mesophyll,cambial tissues,phloem and parenchyma(González-Rodríguez et al.2017).

The method proposed by Burgess et al.(2001) uses heat transport to determine the flow of sap in the plant and is widely cited in the literature (Green and Romero 2012;Forster 2014,2019;Fuchs et al.2017);therefore,the reliability that method is of very importance to estimate how significant are the uncertainties in the sap flow associated with transpiration (Green and Romero 2012;Looker et al.2016;Peters et al.2018;Flo et al.2019) and should be quantified.

The reliability of a measurement must be expressed in terms of the uncertainties involved,whether in the measurement system or determination method (Amaral et al.2018)and,few reports have included the uncertainties involved in the determination methods of sap flow using a heat pulse(e.g.,Hernandez-Santana et al.2015;Fuchs et al.2017;Flo et al.2019;Forster 2019).

In view of these concerns,here we sought to contribute to the knowledge about the uncertainties involved in the application of the heat ratio method proposed by (Burgess et al.2001) in determining the flow of sap in Brazilian mahogany when soil water potential is optimal.

Materials and methods

Experimental area,instrumentation and experimental conditions

The study was conducted in a protected environment located in an experimental area belonging to the Federal University of Recôncavo of Bahia (UFRB) close to the Nucleus for Water Engineering in the Soil (NEAS) in the city of Cruz das Almas,BA (39°06′W;12°48′S).Eighteenmonth-old Brazilian mahogany seedlings were grown in 3 weighing lysimeters,with 1 additional plant grown in a tank under representative experimental conditions.The plants had an average diameter and height equal to 5.98 and 384 cm,respectively.The lysimeters were composed of a 0.5 m3tanks placed on weighing platforms by load cells (model AL90901T,1000 × 0.1 kg;Alfa Instruments,São Paulo,Brazil).At the base of the tanks,drainage systems were installed that consisted of layers of 0.1 m of gravel no.1,0.01 m of washed sand,and a shade-type screen between the filter elements.A Yellow Latosol with a clayey texture was used within the weighing lysimeters.

Self-compensating drippers using microtube bypass line extenders and pressurized by a horizontal axis hydraulic pump provided irrigation.Irrigations were provided daily based on the crop’s water demand and the soil water balance.Water replenishment via irrigation was carried out until the mass of the lysimeters was raised to a value corresponding to the maximum holding capacity soil,that is,the optimal water potential in the soil of −10 kPa.The soil surface was covered with plastic canvas so that mass variations in the lysimeter were due to transpiration and water replacement processes in the soil.These variations were converted into soil water potential by reverse modeling.

The total mass of the lysimeter set (tank,drainage system,and dry soil) was determined before the first irrigation.The soil water content (Ө) in the lysimeter was calculated as the difference between the dry and wet mass of the soil,extracted from the variations in mass in the lysimeter.

To convertӨvalues to soil water potential,we used inverse modeling to estimate soil hydraulic parameters,i.e.,water retention curve and saturated hydraulic conductivity.In applying inverse modeling,we saturated the soil of one weighing lysimeter without a plant that was filled with the same soil used in the lysimeters for cultivation.After saturation with closed drains,the soil began to dry as a result of only evaporation for 26 days.We measured variations in water content in the soil (Ө) using four timedomain-reflectometry (TDR) probes placed in the soil the weighing lysimeter at depths of 0.10,0.20,0.30,and 0.40 m.We calculated the evaporation variations from the mass variations recorded in the weighing lysimeter.We measuredӨand evaporation at 1-h intervals.

Hourly evaporation data were input into HYDRUS-1D software,version 4.17 (Simunek et al.2013) to determine soil hydraulic parameters:saturated water content(Өs),content of residual water (Өr),empirical adjustment parameters (nandλ) and saturated hydraulic conductivity(Ks).With the parameters,average values of water pressure in the soil were estimated daily based on values ofӨobtained by the mass variations in the lysimeters.The resulting hydraulic parameters and statistical indicators are shown in Table 1.

Table 1 Hydraulic parameters of Yellow Latosol inside the lysimeter

Sap flow by heat pulse

To measure sap flow (SF),we used heat pulses through the heat ratio method (HRM) proposed by (Marshal 1958) and modified by Burgess et al.(2001).For this purpose,we constructed probes 20 mm long with a diameter of 1.2 mm and used a hypodermic needle for pharmaceutical use.In each plant,we inserted a set of two probes to measure the sap’s temperature (thermocouple) and one heater to generate the heat pulse.

For the probes,we constructed type T thermocouples(copper/constantan) with wires that were 0.13 mm in diameter (Omega Engineering,Norwalk,CT,USA) and placed them in the middle portion of the inside of the needle and then applied epoxy resin for insulation.For the heating probe,a constantan wire was wound around the outside of the needle so that its length allowed a resistance of 60 Ω.The thermocouple probes were placed at an equal distance of 0.6 cm from the heater and wrapped in lamination paper in the form of a“skirt”to reduce the effects from natural temperature gradients (NTG) on the measurements.

All the instruments were connected to a datalogger model CR1000 (Campbell Scientific,Logan,UT,USA),which was previously programmed to energize the heaters with 12 V,thereby generating a power dissipation of 2.4 W when heated.We adopted a pulse time of 10 s at 10 min intervals between the pulses.The temperature variations measured by the thermocouple probes in a measurement time of 80 s after heat pulse application were stored in the datalogger every 10 min.We performed preliminary tests on a representative plant of Brazilian mahogany under ideal soil water conditions to adjust the pulse times,the interval between pulses,and the time to measure the temperature rise in the upper and lower probes after the application of the pulses.The collected data were used to calculate the temperature increments and to program datalogger.This program was then used on all plants grown in the weighing lysimeters (data not disclosed).

The variables required to determine the sap flow,which are the calculated sap velocityVh,corrected spacing of the lower probe relative to the heater (x2),corrected velocityVc,sap velocityVs,thermal diffusivityk,conductivity of fresh woodKgwand of dry woodKw,porosityFv,and the heat capacity of the woodcwere calculated as recommended by Burgess et al.(2001).We created conditions of zero flow by sectioning the stem above and below the set of probes after the evaluation period,and we used ln (v1/v2) to correctx2(Vandegehuchte and Steppe 2013;Forster 2014).

To determine basic density of wood (ρb) and water content of the sapwood (mc),we removed disks that were 2 cm thick from the stem above the position of the probes,weighed them on an analytical balance with a reading error of 0.01 g,and dried them at 75 °C in a kiln with forced air ventilation for 72 h (Silva et al.2018).The ratio of the sample’s dry mass to its volume (as determined by Archimedes principle) is represented byρb,andmccorresponds to the ratio of the difference between the sample’s wet mass and dry mass to its dry mass.Finally,we determine the sap flow from the product of the sap velocity and the area of the conduction section,which we determine using images of the conduction sections of the plants using the Image Pro Plus software (Media Cybernetics,Rockville,MD,USA).

We quantified mahogany transpiration through the mass variations in the lysimeter.To do so,we covered the lysimeters with plastic tarpaulin to prevent mass variations arising from the evaporation process.

Comparison of heat pulse speed (V h) for different measurement durations

Marshal’s (1958) heat pulse method modified by Burgess et al.(2001) recommends that the measurement of temperature increments in thermocouple probes assumes a linearity between 60 and 100 s after the application of the heat pulse.Considering that the speed of the heat pulse (Vh) depends on these increments,on the diffusivity and on the corrected position of the probe below the heater,the Kruskal–Wallis statistical test was applied to determine any significant differences betweenVhmeasured at 60,80 and 100 s after applying the pulse for two consecutive days.

Determination of uncertainty in the heat ratio method

The variables with greater influence on the measurement of sap flow in the heat ratio method are thermal diffusivity (k),the conductive section of the sap (Sc) and the corrected sap velocity (Vc);therefore,the uncertainty in the sap flow is the combination of the uncertainties of these variables.Equation (1) is appropriate for calculating the combined variance of correlated variables (Inmetro 2008;Amaral et al.2018;Chen et al.2018) and was used to derive the uncertainty equations of the variables that influence the calculation of sap flow by heat ratio.

whereG=f(x1,x2,x3,…,x n);σ2=variance,andρ(x i,x j)=c orrelatio n coefficient between the input quantitiesx iandx j.

The weight (i.e.,sensitivity) that each input variable has on the output variable was determined by the sensitivity coefficient (S) expressed by Eq.(2),and the degree of correlation between the input variables was determined using Pearson’s correlation coefficient (r),since the input variables are quantitative (Eq.3) (Inmetro 2008).

whereSis sensitivity coefficient;ΔYis variation in the output variable;Yois initial value of the output variable;ΔXis variation in the input variable;andXois initial value of the input variable.

wherer=linear correlation coefficient,x iandy i=input variables to be correlated,and=averages of the set of values of the input variables to be correlated.

Uncertainty in thermal diffusivity (U k)

By the method of Burgess et al.(2001),the variables that change the measurement ofkare thermal conductivity(Kgw),heat capacity (c) and wood density (ρ).In this case,where the uncertainties are independent,the uncertainty inkis expressed by the combined uncertainty ofKgw,candρaccording to Eq.(4).

whereUkis uncertainty in thermal diffusivity,UKgwis uncertainty in thermal conductivity,Ucis uncertainty in heating capacity,andUρis uncertainty in wood density.

Uncertainty in thermal conductivity (U Kgw)

The thermal conductivity uncertainty () consists of the propagated uncertainty of the measurands dry mass (md),fresh mass (mf),volume (v) and sapwood water content(mc) that contribute toUKgw independently (md,mf,v,mc)and dependently toρ(md,mc);ρ(mf,mc).Therefore,UKgwcan be quantified by Eq.(5).The variances considered were 0.288% (mdandmf) and 2.887% (v) corresponding to the uncertainties of the scale and beaker,respectively calculated as 0.5d/√3 wheredis the smallest unit measured with the equipment,andmcis 35% as described by Silva et al.(2018).

whereUKgwis uncertainty in thermal conductivity,Smdis dry mass sensitivity coefficient,Umdis dry mass uncertainty,Smfis fresh mass sensitivity coefficient,Umfis fresh mass uncertainty,Svis volume sensitivity coefficient;Uvis volume uncertainty,Smcis sapwood water content sensitivity coefficient,andUmcis sapwood water content uncertainty.

Uncertainty in heat capacity (U c)

In determining the heat capacity (c),the input variables are the dry (md) and fresh (mf) mass of the wood and the heat capacities of the wood (cw) and sap (cs).Considering the influence independent ofmd,mf,cwandcsand dependent and correlated withcwandcs,the uncertainty in the heat capacity (Uc) can be expressed by Eq.(6).In this case,the variances considered were 0.288% (mdandmf) as described inUKgw;0.956% (cw) and 22.73% (cs) according to the heat capacities determined by Becker and Edwards (1999) for thermal amplitude of 0 to 50 °C in stems of trees.

whereUcis uncertainty in heat capacity,Smdis dry mass sensitivity coefficient,Umdis dry mass uncertainty,Smfis fresh mass sensitivity coefficient,Umfis fresh mass uncertainty,Scwis sensitivity coefficient of the heat capacity of the wood,Ucwis uncertainty in heat capacity of the wood,Scsis sensitivity coefficient of the heat capacity of the sap,andUcsis uncertainty in heat capacity of the sap.

Uncertainty in basic wood density (U ρ)

Knowing that in determining the basic density of the wood the uncertainties of the measurands fresh mass (mf) and volume (v) contribute only independently,one can express the uncertainty of the basic density of the wood (Uρ) by Eq.(7).The variances used were 0.288% (mf) and 2.887% (v) (see determination ofUKgw).

whereUρ is uncertainty in basic wood density,Smfis fresh mass sensitivity coefficient,Umfis fresh mass uncertainty,Svis volume sensitivity coefficient,Uvis volume uncertainty.

Uncertainty in sap flow (U SF)

It is convenient to consider that the uncertainty in the sap flow(USF) is the combination between the uncertainty in the thermal diffusivity (Uk) propagated and the uncertainties in the conductive section (Usc) and corrected sap velocity (UVc) (Eq.8).

whereUSFis uncertainty in sap flow,Ukis uncertainty in the thermal diffusivity,UScis uncertainty in the conductive section,andUVcis uncertainty in corrected sap speed.

Uncertainty in the conductive section (U sc)

The contribution of the conductive section uncertainty to sap flow depends only on the conductive section area (A) in isolation and can be calculated by Eq.(9).The variance used was 0.385%,which corresponds to a growth in diameter of 0.0116 cm day−1in irrigated African mahogany,estimated by the growth curves in a study proposed by Alves Júnior et al.(2016).

whereUscis uncertainty in the conductive section,andUAis uncertainty in conductive section area.

Uncertainty in corrected sap speed (U Vc)

The uncertainty in the corrected sap speed (Uvc) is influenced by the uncertainty of coefficientβused in the positional correction of the lower probe (x2) and depends on the spacing between the probes and the wound diameter.SoonUVccan be calculated by Eq.(10).The variation used in the calculation ofUvcwas 3.05 × 10−10%,which corresponds to the variation in the deviations between the measured and simulated values of the sap velocity (Vh),consideringβequivalent to 1.7023 (R2=0,9993) for a probe spacing of 0.6 and 0.17 cm of wound diameter.

whereUvcis uncertainty in the corrected sap velocity,Sβis sensitivity coefficient of β coefficient,andUβis uncertainty of β coefficient.

Association between sap flow,transpiration and vapor pressure deficit

The sap flow calculated by the heat ratio method and the transpiration determined by the weighing lysimeter were associated by means of linear regression under optimal conditions of soil water potential of −10 kPa (theoretical potential of the field capacity) to verify the relationship between these physiological variables.The sap flow and the transpiration of mahogany were related on a daily scale due to the high sensitivity in the measurement of the lysimeters on an hourly scale.

Sap flow was also associated with vapor pressure deficit by regression and on an hourly scale because this variable is directly associated with air temperature,relative humidity,wind speed and leaf water potential.The interaction of these temporal factors directly influences perspiration and,consequently,sap flow.

Results and discussion

The temperature increments measured by the upper (v1) and lower (v2) probes after successive pulses at a time of high atmospheric demand (14:00) are shown in Fig.1.The increments inv1were greater than inv2because the upward flow conditions (SF ＞ 0) provide heat transport by conduction and convection in the upper probe and only by conduction in the lower probe.Under these conditions,the maximum temperature variation was 2.8 °C.

Fig.1 Temperature variation in thermocouple probes v1 (upper) and v2 (lower) after successive pulses lasting 600 s (10 min)

In addition,in the initial moments after applying the heat pulse,the temperature increases were abrupt and then decreases gradually until they stabilized (600 s).

Although we used a pulse time and interval between pulses similar to that used by Fuchs et al.(2017),they adjusted the dissipated power to 2.5 W (25 J) in five tree species with diffuse-porous sapwood so that the temperature rise in the probes varied between 0.7 at 1.5 °C to avoid additional damage to the tissue near the probes.Bayona-Rodrigues and Romero (2016) adjusted the heater power to 3.5 W (35 J) forElaeis guineensisJacq.,Forster (2019)used 4.0–4.9 W (40–49 J) for the heater power forTecoma capensis(Thunb.) Lindl.,and Green and Romero (2012)used a dissipated power of 5.0 W (50 J) forVitex lucens;no tissue damage was reported.In the present study,we did not observe any injury inSwietenia macrophyllaKing due to the generated potency by the heater (2.4 W).

Several groups that used the method proposed by Burgess et al.(2001) configured the heating system to operate with different pulse durations and intervals,e.g.,Eller et al.(2018),3.0 s and 30.0 min;Morton et al.(2016),2.0–4.0 s and 15.0 min;Salomón et al.(2017),10.0 s and 15.0 min;and Wang et al.(2018),5.0 s and 30.0 min.Thus,the duration,interval and power of the pulses must be adjusted for each species,so that the data collected are appropriate for the study.

The velocity of the heat pulses (Vh) during part of two consecutive days for durations of 60,80,and 100 s are shown in Fig.2.The curves were similar,especially at night,when sap flow is considered negligible (SF approaches zero) due to low convective transport and reduced vapor pressure deficit (VPD).According to the Kruskal–Wallis multiple comparison test,there were no significant differences betweenVhin the measurement times mentioned above (P=0.710).

Fig.2 Heat pulse velocity during part of two consecutive days in the measurement durations of 60,80 and 100 s

For Burgess et al.(2001) the linearity inVhafter 60 s of pulses is the result of insignificant increments in the v1/v2probe ratios,and according to Fuchs et al.(2017) and Wang et al.(2018),it is also possible to use the average of 40 measurements between the 60 and 100 s after pulses due to this linearity.

Under the conditions of the present study,Vhcould be calculated for any time (60,80 or 100 s) with an average time of 80 s after the heat pulse recommended for measuring the increments necessary for the sap flow calculations for Brazilian mahogany.

Table 2 summarizes the sensitivity coefficients (weights)of the variables that influence the quantification of thermal diffusivity (k) and,consequently,the sap flow (SF).It was found that the variables with the greatest uncertainties in the determination ofkare,in order,the thermal conductivity of fresh wood (Kgw;12.8%),the heat capacity (c;6.16%) and the basic wood density (ρb;5.72%).Thermal diffusivity is an important variable in the calculations of the velocity of the heat pulse,and the uncertainties in its calculation usually arise from the variation in the moisture content of the sapwood and the density of the wood (Forster 2019),corroborating the results shown.It is observed thatKgwinfluences with the greatest uncertainty in the measure of k because this variable expresses an ease with which heat moves through the plant stem by convection and conduction.In addition,Kgwandρbwere more sensitive to variation inmf,whilecwas more sensitive than the other components to variation inms;that is,water content was more expressive inKgwandρbbecause of variables related to water status of the plant,whilecis proportional to the dry mass of the stem.Vergeynst et al.(2014) found that theρb andkofPlatanus occidentalisL.increase with increasing water content,whilecis more strongly influenced when water content is low,similar to what we found here.

Table 2 Coefficients of sensitivity and uncertainties of variables that influence thermal diffusivity and sap flow in Swietenia macrophylla determined using the Burgess et al.(2001) heat ratio method

Minor influences of the uncertainties of the conductive section (Sc) and of the corrected sap velocity (Vc) for sap flow were found because the variances used in the calculation were small (see determination ofU scandU Vc).

It is possible to verify that the uncertainty ink(15.31%)corresponds almost totally to the uncertainty in the SF(15.32%),since the most expressive variables in their determinations,due to the propagated uncertainties,were themfandmsof conductive section where the probe set was installed.Thermal diffusivity is a crucial variable to determine the density of sap flow,because thermal diffusivity is directly and linearly proportional to sap flow;that is,any error inkwill cause an equal error in the sap flow density and,therefore,in the sap flow calculated when using the heat ratio method (Vandegehuchte et al.2012).

Figure 3 shows the linear relationship between transpiration and the sap flow of Brazilian mahogany under ideal soil water conditions.The variation of 15% between these physiological processes is close to the uncertainty of the sap flow (15.32%) with greater weight attributed to the thermal diffusivity (15.31%) (Table 2).

In the present study,thermal diffusivity was determined under zero flow conditions and extended to the entire evaluation period,which may have contributed part of the above observed difference in the results,since the water status of the plant directly influences the heat dissipation generated by the pulses and consequently the sap flow and transpiration.It is probable that corrections in thermal diffusivity minimize the observed differences,however,the methodology of these corrections was not possible in this study due to experimental conditions.Thus,more studies are needed.

According to Eliades et al.(2018),it is common in the literature on the use of the heat ratio method to use a singlekas initially proposed by Marshal (1958) of 2.5 × 10−3cm2s−1as in the study of Zhao et al.(2017);can be determined in conditions of zero flow with stem section,as in this study or in the study of Forster (2017) or when there is no biophysical driving force (low vapor pressure deficit) (Yu et al.2018).However,kcan vary significantly from the standard value and throughout the measurement period;therefore,errors in its calculation can lead to errors inVh calculations and,subsequently,to an over-or underestimation of transpiration when correlated with the sap flow (Forster 2017).

In accordance with Burgess et al.(2001),an initial value ofkin the calculation of sap flow does not transmit considerable errors in transpiration estimates;however,Looker et al.(2016) refute that this statement is only valid under conditions of low water content in the sapwood.Otherwise,the flow of sap may be underestimated or overestimated by 10.0%.Therefore,variations inmcandρbcan considerably influence sap flow and transpiration.

An approach by Vandegehuchte and Steppe (2012) suggests a methodology for correcting thermal diffusivity to reduce variations of up to 10.0% in the sap flow due to the use of the method of Burgess et al.(2001),as the original method does not consider changes in the relative water content in the sapwood.However,it is seen that,to consider the variation of the water content over an evaluated period,destructive samples must be taken to adjust the diffusivity,which may compromise the stem structure of the plants and change the properties related to sap flow and transpiration.Thus,for Steppe et al.(2015),in cases where it is difficult,if not impossible,to carry out species-specific calibrations,the lack of this method calibration should not lead to the rejection of a manuscript,as long as the resulting error is not very different from those reported in the literature.

The methods for determining sap flow are still theoretically correct and produce realkvalues,even though the analytical equation from which these methods are derived does not consider the diffuse movement of water in the sapwood(Vandegehuchte and Steppe 2012).Thus,the difference observed between sap flow and trasnpiration is attributed to the use of the heat ratio method and the boundary conditions of this study and can be minimized by adjusting the thermal diffusivity in smaller time scales such as days to decrease the uncertainties in the determination of sap flow,since in the heat pulse methods,they are less susceptible to the lack of specific calibrations and to natural thermal gradients (Vandegehuchte and Steppe 2013;Fuchs et al.2017).

Figure 4 showed sap flow of Brazilian mahogany and vapor pressure deficit (VPD) over time and how they are related using a regression analysis.A linear relationship with good adjustment between the VPD and the sap flow(R2=0.85) was shown with a difference of approximately 14.6% between the parameters,similar to that observed in Fig.3 and in the uncertainty of the sap flow (Table 2).For this result,the atmospheric demand imposed by DPV influenced the flow of sap in an indirect way through transpiration of the plant.

Fig.3 Relationship between transpiration and sap flow in Brazilian mahogany for soil water potentials close to −10 kPa.T transpiration,SF sap flow

The VPD,the gradient between the vapor pressure of dry atmosphere and the humid interior of the leaves,is considered the driving force of transpiration rates and one of the main influencing factors (Rodrigues et al.2011;Tonello and Teixeira Filho 2011;Sinclair 2017).Previous studies show a strong temporal correlation between sap velocity and VPD with variations throughout the day and night with rapid responses without observable delay (Chambers et al.2017).These results corroborate those shown because the sap flow followed the course of the vapor pressure deficit without any noticeable time delay (Fig.4).

Fig.4 Sap flow of Brazilian mahogany and vapor pressure deficit(DPV) over time

In addition,lower DPVs are associated with negative sap flow values that normally occur at night (Fig.5).This is possible because the mahogany was in ideal water conditions in the soil (approximately −10 kPa),therefore,without the effect of water stress.The linear relationship found in this study disagrees with Doronila and Forster (2013) who state that a linear relationship between sap flow and DPV indicates stomata open and water is lost through the leaves at night,while a quadratic relationship demonstrates stomatal modulation throughout the day.

Fig.5 Relationship between vapor pressure deficit and sap flow in Brazilian mahogany for soil water potentials close to −10 kPa

Thus,under ideal conditions of water in the soil,the vapor pressure deficit commanded the sap flow with a difference similar to that found between flow and transpiration processes.

Conclusion

The uncertainty in thermal diffusivity has greater weight in the uncertainty of sap flow in Brazilian mahogany.The flow of sap overestimated the transpiration of Brazilian mahogany by 15.0% in optimal conditions of soil water potential,the difference of which is attributed to the uncertainty of the heat ratio method.Further studies are needed to adjust the thermal diffusivity of Brazilian mahogany during the cycle or period evaluated.The vapor pressure deficit influenced the flow of sap indirectly through transpiration,with a variation of approximately 14.6% between processes.

AcknowledgementsThe authors acknowledge the Nucleus for Water Engineering in the Soil and the Instrumentation and Embedded Technology Laboratory at the Federal University of Reconcavo Bahia;and the professor Alisson Jadavi Pereira da Silva for contributions.