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Water content measurement in tree wood using a continuous linear heating technique
International Journal of Thermal Sciences 88 (2015) 164e169
Contents lists available at ScienceDirect
International Journal of Thermal Sciences journal homepage: www.elsevier.com/locate/ijts
Water content measurement in tree wood using a continuous linear heating technique k b, N. Nadezhdina b M. Trcala a, *, J. Cerm a a b
Department of Wood Science, Dendrology and Geobiocenology, Mendel University in Brno, Brno, Czech Republic Department of Forest Botany, Dendrology and Geobiocenology, Mendel University in Brno, Brno, Czech Republic
a r t i c l e i n f o
a b s t r a c t
Article history: Received 1 May 2014 Received in revised form 6 September 2014 Accepted 29 September 2014 Available online
This paper deals with the analytical and experimental analysis of heat transfer in the xylem of trees and the determination of stem water content (WC). The aim of this paper was to derive and verify a new approach to WC calculation from measured temperature differences around a continuously heated needle. The configuration of heater and thermocouples of the heat field deformation (HFD) method for sap flow measurements was taken for this purpose. The suggested formula is derived from the heat conduction equation with a continuous linear source of heating. The ability of the HFD method to nondestructively determine the radial distribution of the local conditions of sap flow measurements under zero flow (referred to as K-value) was used to derive the radial distribution of WC. Examples of the application of our method on several contrasting species with different plant hydraulic architecture are given where calculated WC along stem xylem radius was compared with its direct gravimetrical measurements or with relative determination of wetness of cross-sectional stem discs using a modified differential translucence method. The proposed method enables water content measurements during continuous linear heating and is important for information about WC and sap flow together per day or season when there is possible to extrapolate the temperature difference for zero flow condition. © 2014 Elsevier Masson SAS. All rights reserved.
Keywords: Heat field deformation method Heat transfer equation Thermal conductivity Water content
1. Introduction Internally stored water in tree stems contributes to daily transpiration even in well-watered trees, indicating that stored water plays an important role not only during periods of drought, but whenever water transport occurs within the tree [28]. Water stored within the woody tissues of trees has been viewed as a reservoir from which water can be withdrawn to buffer the evaporative demands of a transpiring plant canopy [19,25,27,7]. Attempts to better visualize the spatial distribution of water in woody tissues have led to the promising use of gamma-ray attenuation [8], nuclear magnetic resonance [4], and computer tomography [18], and to the application of methods such as stem capacitance [9,10], electrical resistance [1,2], and time-domain reflectometry [5,10] for the study of relative changes in stem water content [27]. However, absolute values of water content are still
* Corresponding author. E-mail addresses: [email protected] (M. Trcala), [email protected] k), [email protected] (N. Nadezhdina). (J. Cerm a http://dx.doi.org/10.1016/j.ijthermalsci.2014.09.018 1290-0729/© 2014 Elsevier Masson SAS. All rights reserved.
a “hot topic” in tree water relations research after almost 20 years have passed since Holbrook [9] pointed out that attention must be directed toward improved methods for in situ monitoring of stem water content in order to better quantify the contribution of stem water storage to the whole-plant water balance. WC is also an important parameter for sap flow methodology. All thermodynamics methods based on application of heat pulses require determination of WC in sapwood for sap flux density calculations from measured heat pulse velocity. Schenk et al. [20] strongly underlined the importance of seasonal changes of active conducting sapwood area and wood water content on sap flow estimation. When a tree is drying, its sapwood area may become narrower [6,21] and this may negatively influence the results of flow up-scaling according to the sapwood area unless its real changes are taken into account. Usually sapwood area and WC are determined destructively by an increment borer just before or after sap flow measurements. In most of the cases, the WC is determined only once and without taking into account the spatial and seasonal variability of sapwood parameters. Active water-conducting area [21] and its changes over time [3] are well determined in real time by multi-point sap flow
M. Trcala et al. / International Journal of Thermal Sciences 88 (2015) 164e169
measurements using the HFD method. The effect of possible changes in WC on sap flow measurements using the HFD method is objectively corrected by changes of the K-value in each point of measurements along stem xylem radius. The K-value represents the temperature differences around a linear heater under zero flow. Hence, the K-value reflects a condition of zero flow without the need to provide destructive treatment as it is required for many sap flow methods. All the above mentioned including the consideration of real anisotropy of sapwood has been first considered in the HFD using a side probesLater this HFD configuration was used by Vandegehuchte and Steppe [26] for a method referred to as Sapflowþ which was reported to enable regular updates of water content values for more accurate calculation of sap flux densities without application of destructive gravimetrical measurements of WC. Until now thermodynamic approaches were used for in-situ water content measurement based on heat pulses [11,26]. However, there were no examples of practical use of WC monitoring by Sapflowþ pez-Bernal et al. [11] underlined that the presented in Ref. [26]. Lo ability of the volumetric specific heatecompensated heat pulse (VSHeCHP) methodology to provide actual values of WC is uncertain at the present stage of understanding. Thermodynamic approaches to water content measurement need more research. This work introduces a new approach to measurement of water content in sapwood using continuous linear heating. Whenever sap flow radial profiles were measured by the HFD method, the K-value for each measuring point along the needle was also evaluated as it is the input parameter in formula for sap flow calculation. It was assumed that the K-value can be used for the calculation of water content under zero flow conditions based on continuous sap flow measurements using the HFD method. As the K-value is an important attribute for sap flow calculation in the HFD methodology and should be determined for each measuring point along the xylem radius, the possibility to determine the radial variability of WC is presented. By application of more multi-point sensors around the tree stem for long-term measurements, spatial and seasonal WC monitoring has become also possible. To demonstrate this, in addition to the main aim of WC calculation, we investigated spatial (radial and circumferential) and seasonal variability of WC in tree stems of several species with different wood anatomy. 2. Material and methods 2.1. Theoretical analysis 2.1.1. Analytical solution of thermal conductivity According to the generally known partial differential equation (Eqn. (1)) describing the temperature field solely for heat conduction (not for convection because we can assume the sap flow is zero), the analytical analysis of continuous linear heating can be performed. The zero sap flow condition is recorded during HFD measurement and can be determined although the current sap flow is not zero (it is the advantage of the HFD method).
rc
vT V$lVT ¼ q; vt
lT
165
v2 T v2 T lL 2 ¼ q; 2 vx vy
(2)
where lT and lL are the thermal conductivities of wood in the tangential and axial directions respectively. The analytical solution of the equation (Eqn. (2)) for a continuous line-source of heat H (W m1) along the length of heated needle is based on Green's function theory [17] and is the following:
dT ¼ T dx1 ; dy1 T dx2 ; dy2
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u ulL dx2 þ lT dy2 H 2 2 pffiffiffiffiffiffiffiffiffi lnt ¼ 2p lL lT lL dx21 þ lT dy21 (3)
where T(x, y) is temperature (K) at point [x, y] (origin [0, 0] of coordinate system is in place of heating), and H is heat power per unit length along the line (W m1). After modifications we can use the derived analytical equation (Eqn. (3)) in this way:
H dx pffiffiffiffiffiffiffiffiffi ln ðdTabove Þ0 ¼ ðTabove Tside Þ0 ¼ dy 2p lL lT
sffiffiffiffiffi! lL ; lT
where dx is horizontal distance of side thermocouples from heater (m) and dy is vertical distance of above thermocouples from heater (m). Note: (dTabove)0 ¼ (Tabove Tside)0 ¼ (Tside Tbelow)0 ¼ (dTbelow)0 ¼ K is the temperature difference under zero sap flow condition that is recorded (extrapolated) during HFD measurement (see Introduction and Fig. 1). Both thermal conductivities lT and lL are functions of water content WC and it is proved that lL ¼ klT, where often and also here we assume k ¼ 2 [13] and thus we can use the following formula for calculating lT:
pffiffiffi kdx pffiffiffi ln : lT ¼ dy 2pðdTabove Þ0 k H
(5)
You can see the dependence of thermal conductivity on the temperature difference in an additional figure (Fig. 7). Therefore the calculated thermal conductivity lT can be used to derive the water content WC through the physical quantity called moisture M in wood (lT / M / WC), using the following relations: 2.1.2. Derivation of water content from thermal conductivity Some important physical quantities describing material properties of wood are described below. Moisture M (mass definition) [23] and water content (volume definition) WC are defined as [22]:
(1)
where T is temperature (K), l is matrix of thermal conductivity coefficients of fresh sapwood (W m1 K1), r is density of fresh sapwood (kg m3), c is specific heat of fresh sapwood (J kg1 K1), q is heat power (W m3), t is time and V denotes the vector differential operator V ¼ (v/vx,v/vy,v/vz). Because we assume the steady state condition (the derivative of a temperature with respect to time is equal to zero) and only 2D heat transfer in plane xy, thus the equation (Eqn. (1)) is simplified into equation (Eqn. (2)):
(4)
Fig. 1. Scheme of sensor (HFD configuration).
166
M. Trcala et al. / International Journal of Thermal Sciences 88 (2015) 164e169
Fig. 2. Radial profile of calculated and measured water content for Dracaena draco. Fig. 4. Radial profile of calculated water content for Olea europaea.
M¼
mwater Vwater ; WC ¼ m0 Vwood
(6)
where mwater is weight of water, m0 is weight of dry wood, Vwater is volume of water and Vwood is volume of wet wood. The wood porosity is defined and can be calculated from density and moisture as follows.
P M ¼
Vp
¼1
where P(M) is wood porosity (Eqn. (7)), a ¼ 0.4 for M < 0.4 and a ¼ 0.55 for M > 0.4 (for sapwood is almost always M > 0.4 and thus we use a ¼ 0.55). From the Eqn. (8) we can express the moisture M (Eqn. (9)) and subsequently the water content WC (Eqn. (10)):
rk 1000 þM rs 1000
Vwood r ¼ 1 k ð0:653 þ MÞ; 1000
(7)
where Vp is volume of pores in volume of wet wood Vwood with moisture M, rk ¼ m0/Vwood is convection wood density, rs is density of wood substance (rs ¼ 1531.4 kg m3) [24,29]. Now we can introduce the equation for thermal conductivity (Eqn. (8)) that is necessary to calculate moisture M (Eqn. (9)) and water content WC (Eqn. (10)) in the wood of trees. The determination of the thermal conductivity is based on models derived by MacLean [13]:
rk ð0:217 þ aMÞ þ 0:024P M ; lT M ¼ 1000
(8)
Fig. 3. Calculated water content in comparison with gravimetrically determined water content of a Dracaena draco tree.
Fig. 5. Radial profiles of calculated water content for spruce trees. Indication of trees corresponds to that applied in [3].
M. Trcala et al. / International Journal of Thermal Sciences 88 (2015) 164e169
167
Fig. 6. K-value determination from recorded temperature differences for the outermost xylem layers (4 mm below cambium) of two spruce trees A (left) and D (right). Sap flow was monitored for a duration of 2 months [3]. Indication of temperature differences corresponds to those applied in the HFD methodology [16].
r 1 0:024 0:217 M ¼ 1000 lT 0:024 þ k rs 1000
(9)
ðrk ða 0:024ÞÞ; WC ¼
rk M: rwater
(10)
2.2. Experimental analysis 2.2.1. Experimental verification For verification of the presented theoretical approach we used our earlier data gained when sap flow measurements and gravimetrical estimation of stem water content were conducted either in the same plant (in the case of dragon tree) or in different trees of the same species (olive trees). In the case of spruce trees, direct gravimetrical measurements of WC in sapwood were not conducted; however, all sample trees were harvested at the end of measurements and stem discs were taken from them with the aim to evaluate the extent of sapwood by the modified differential translucence method (MDT) [21]. MDT is a destructive method based on visual evaluation of sapwood after felling the trees, assuming that translucent areas in the stem cross-section are functional and wetter than non-translucent areas where the water transport has ceased [21].
Fig. 7. Dependence of the thermal conductivity lT on the temperature difference dTbelow.
2.2.2. Plant material and climatic conditions Sap flow in a Dracaena draco plant (DBH equal to 40.8 cm, height around 8 m) was measured in February 1999 in Los Naranjeros (Tenerife, Canary Islands). The climate type is Mediterranean, with a mean annual temperature of 12.6 C and an annual precipitation of 460e930 mm. The samples from the stem of this plant were taken by an increment borer for gravimetrical estimation of the stem water content. Thus, this dragon tree can be used for direct verification of our approach to evaluation of WC using K-values. Sap flow in two olive trees (Olea europea L., cv Coratina) with different DBH (15 and 40 cm) but similar sapwood depth (4 cm) were measured in an olive orchard located near Andria, southern Italy (41120 N, 16100 E, 175 m a.s.l.). Mean annual rainfall is 530 mm, distributed from September to April. Yearly means of temperatures are 11 and 21 C, respectively. More details about sap flow measurements in olive from this orchard are described in Nadezhdina et al. [15]. Average WC calculated for these trees was compared against direct gravimetrical measurements of WC in an olive tree conducted earlier [6]. A study of long-term (around 2 months) sap flow dynamics and its radial profiles in several spruce trees (Picea abies) was performed in summer 2011 in the experimental site Hoxmark (59 400 N, 10 430 E), SE Norway, where a Norway spruce forest about 50 years old had marks of spruce dieback in some trees. Several pairs of symptomatic and non-symptomatic trees were selected to study reasons of this tree dieback. Besides sap flow measurements also stem discs were taken after measurements. These discs were analysed using the modified differential translucence method (MDT) to determine the extent of the functional sapwood. Results of this study are described in details in Refs. [21,3]. In this paper we analysed the same data from the point of view of differences in stem water content in healthy (non-symptomatic) and damaged (symptomatic) trees. We used the same pairs of trees whose discs are shown in Ref. [3]. They are marked as A & a and D & d, where big letters are used to mark non-symptomatic trees and the small letters mark symptomatic trees. Additionally, we checked the stability of initial WC (IWC) for two non-symptomatic trees A and D during a longer period similar to the duration of sap flow measurements in these trees. For another two pairs analysed in the paper [3] we looked on symptomatic trees b and c as they had significant circumferential differences in sap flow radial profiles. Our aim was to check spatial variability of WC in the same trees as well. 2.2.3. Sap flow measurements Sap flow in all sample trees was measured by the heat field deformation (HFD) method [12,16]. Multi-point HFD sensors were used, allowing measurements of sap flow in different xylem layers
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M. Trcala et al. / International Journal of Thermal Sciences 88 (2015) 164e169
across the conductive sapwood. Sensors consist of a linear heater and two pairs of differential thermocouples (symmetrical and asymmetrical) that measure the temperature differences in axial (dTsym) and tangential (dTasym) directions around the linear heater as raw data. Each needle of the multi-point sensor contained six thermocouples; distance between them within each needle varied (10 mm for dragon tree and olive and 12 mm for spruce trees). The temperature data were recorded by data loggers (Unilog, Environmental Measuring Systems Inc., Czech Republic). The heating system was powered by car batteries. In this study we only analysed the K-value spatial distribution and we calculated the WC based on the K-value in order to characterize the spatial variability of WC corresponding to conditions of zero flow in sample trees. It consisted of the linear heater (a resistance wire) inserted in the stainless hypodermic needle 1.5 mm in outer diameter (inner 1.0 mm) situated in the sapwood and four thermocouples copperconstantan, with measuring points 5 mm from needle tip in similar needles and situated at the distance of 15 in axial direction (up and down the heater) and 5 mm in tangential one (right and left side of the heater) (see Fig. 1). The heater tip was inserted 15 mm deeper than the depth of sensing needles. Total resistance of the heater wire was 60.5 U (204.8 U m1) and applied direct current voltage of 4.24 (low heating) or 5.83 (high). this gives the power (U2/R) ¼ 0.297 or 0.652 W, respectively [12,16]. 3. Results and discussion 3.1. Gravimetrical verification The suggested new procedure (Eqns. (4)e(10)) for the calculation of water content was experimentally verified for a D. draco tree (R ¼ 200.8 mm) with a high water content. The verification consisted of a comparison of the water content calculated from temperature differences measured during the continuous linear heating with the water content measured gravimetrically (Fig. 2). Fig. 3 shows that the equations (Eqns. (4)e(10)) provide relatively reliable results (R2 ¼ 0.765) even in extreme conditions (high water content in a tree with low density). For another example a tree with contrasting wood anatomy was chosen e an olive tree with high wood density. WC calculated from the K-value in the olive was twice as low as that in the D. draco tree. The radial profile of the calculated water content (Fig. 4) fits well with that measured gravimetrically for olive published earlier (see Fig. 2 in Ref. [6]). 3.2. Modified differential translucence method verification Fig. 5 shows radial profiles of calculated water content for spruce trees. Sap flow radial profiles substantially differed for the southern (S) and northern (N) sides of non-symptomatic tree A especially in the outer xylem layers [3], which was later displayed by their partial dysfunction (see disc for tree A in the same paper). Correspondently, we found that WC in the southern tree side was substantially higher than in the northern side and differences were larger for the outer xylem layers. Sap flow profiles in the symptomatic tree a was rather closer to that recorded in the northern side of tree A and could be also explained by the dysfunction of the outer sapwood xylem around tree a [3]. WC for tree a was also rather similar to that recorded for the northern side of tree A (Fig 5 e upper panel). Sapwood depth was larger in c compared with b where it was very short. We have confirmed this fact by the calculation of WC, which was higher for c. Moreover, tree b had a large region of decay inside the heartwood. Decay was very close to functional sapwood from the northern side. We calculated the increase in WC for inner xylem in tree b from this northern side - and the results correspond
to the above-mentioned experimental observations. We observed (MDT method) an area of drier wood between the functional sapwood and the decay from the southern side of tree b, which corresponds to our calculation in which WC was lower in the inner xylem from the southern tree side (Fig 5 e middle panel). Sapwood depth was greater in tree D compare to d which is visible from sap flow radial profiles and stem discs [3]. The same is visible from our formula results in which the WC values were lower for d and almost stable for the inner stem xylem layers corresponding to the lowest value in tree D (Fig 5 e lower panel). 3.3. Water content decrease Sap flows in two non-symptomatic spruce trees A and D were monitored during the whole summer with an indication of unchanged sap flow density throughout the whole period in tree A, and with significantly decreasing sap flow density in tree D [3]. In agreement with the sap flow we also found that the K-value in tree D increased during this period, from 1.8 to 2.6 C in contrast to the stable K-value (K ¼ 1.9 C) in tree A (Fig. 6). It indicates that WC in tree D gradually decreased (from 52.58% to 30.56% according to above mentioned method, Eqns. (4)e(10). This WC decrease was observed in all xylem layers of this tree. As it is known in the HFD method, the K-value includes information about the basic wood properties and heat conductances in both, axial and tangential directions [14,16]. The K-value depends on the sensor geometry (the distances of the thermocouples from the heater) and the surrounding conditions including the level of power supply. If the surrounding conditions are maintained stable, it is possible to monitor internal changes (mainly wood water content). This may open the opportunity to investigate and control the biological health of trees as it is shown on examples of trees A and D (Fig. 6). 4. Conclusion The formula for water content calculation was derived from the steady-state two-dimensional partial differential equation describing heat conduction in wood under zero sap flow conditions using the HFD configuration The formula was tested on several tree species under different conditions. The results show the applicability of the approach for measuring water content during continuous linear heating (e.g. during sap flow measurement by the HFD method). Our new approach for the non-destructive determination of WC can be also useful for other sap flow methods dependent on the knowledge of WC. The approach is important for synchronous information about WC and sap flow radial profiles. It can provide information about the health state: although there are species where WC is typically higher in heartwood compared to sapwood the usual trend is that there is less water in heartwood. If not e we should proceed with caution e there could be decay inside. Acknowledgements The work was supported by OP Education for Competitiveness (European Social Fund and the state budget of the Czech Republic) CZ.1.07/2.3.00/30.0017 Postdocs in Biological Sciences at MENDELU. References [1] R. Borchert, Water storage in soil in tree stems determines phenology and distribution of tropical dry forest trees, Ecology 75 (1994a) 1437e1449. [2] R. Borchert, Water status and development of tropical trees of during seasonal drought, Trees 8 (1994b) 115e125.
M. Trcala et al. / International Journal of Thermal Sciences 88 (2015) 164e169 k, S. Rosner, N. Nadezhdina, Sap flow [3] I. Børja, J. Svĕtlík, V. Nadezhdin, J. Cerm a dynamics as a diagnostic tool in Norway spruce, Acta Hortic. 991 (2013) 31e36. [4] G.F. Byrne, J.J. Landsberg, M.L. Benson, The relationship of above-ground dry matter accumulation by Pinus radiata to intercepted solar radiation and soil water status, Agric. For. Meteorol. 37 (1986) 63e73. [5] J. Constantz, F. Murphy, Monitoring moisture storage in trees using timedomain reflectometry, J. Hydrol. 119 (1990) 31e42. [6] J. Cerm ak, N. Nadezhdina, Sapwood as the scaling parameter - defining according to xylem water content or radial pattern of sap flow? Ann. For. Sci. 55 (1998) 509e521. [7] J. Cermak, J. Kucera, W.L. Bauerle, N. Phillips, T.M. Hinckley, Tree water storage and its diurnal dynamics related to sap flow and changes in stem volume in old-growth Douglas-fir trees, Tree Physiol. 27 (2007) 181e198. [8] W.R.N. Edwards, P.G. Jarvis, A method for measuring radial differences in water-content of intact tree stems by attenuation of gamma-radiation, Plant Cell Environ. 6 (1983) 255e260. [9] N.M. Holbrook, Stem water storage, in: B.L. Gartner (Ed.), Plant Stems: Physiology and Functional Morphology, Academic Press, San Diego, 1995, pp. 151e174. [10] N.M. Holbrook, M.J. Burns, T.R. Sinclair, Frequency and time-domain dielectric measurements of stem water content in the arborescentp alm, Sabalp almetto, J. Exp. Bot. 43 (1992) 111e119. pez-Bernal, L. Testi, F.J. Villalobos, Using the compensated heat pulse [11] A. Lo method to monitor trends in stem water content in standing trees, Tree Physiol. 32 (2012) 1420e1429. k, V. Nadezhdin, Heat field deformation method for sap [12] N. Nadezhdina, J. Cerm a k, N. Nadezhdina (Eds.), Proceedings of the 4th flow measurements, in: J. Cerm a International Workshop on Measuring Sap Flow in Intact Plants, Publishing House of Mendel University, Brno, Czech Republic, 1998, pp. 72e92. [13] J.D. MacLean, Thermal conductivity of wood, Heat Pipe Air Cond. 13 (1941) 380e391. k, J. Gaspa rek, V. Nadezhdin, A. Prax, Vertical and [14] N. Nadezhdina, J. Cerm a horizontal water redistribution within Norway spruce (Picea abies) roots in the Moravian Upland, Tree Physiol. 26 (2006) 1277e1288. [15] N. Nadezhdina, V. Nadezhdin, M.I. Ferreira, A. Pitacco, Natural variability of sap flow in trunks and branches of mature olive trees, Tree Physiol. 27 (2007) 105e113.
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[16] N. Nadezhdina, M. Vandegehuchte, K. Steppe, Sap flux density measurements based on the heat field deformation method, Trees 26 (2012) 1439e1448. [17] A.D. Polyanin, Handbook of Linear Partial Differential Equations for Engineers and Scientists, Chapman & Hall/CRC Press, Boca RatoneLondon, 2002, ISBN 1584882999. s, Water in stems of sessile oak [18] A. Raschi, R. Tognetti, H.W. Ridder, C. Bere (Quercus petraea) assessed by computer tomography with concurrent measurements of sap velocity and ultrasound emission, Plant Cell Environ. 18 (1995) 545e554. [19] E.R.C. Reynolds, Transpiration as related to internal water content, Nature London 208 (1965) 1002. [20] H.J. Schenk, S. Espino, A.N. Mendez, A.J. McElrone, Limitations in the hydraulic pathway: effects of xylem embolisms on sap velocity and flow, Acta Hortic. 991 (2013) 323e332. tlík, I. Bu˛ rja, S. Rosner, J. Cerm k, V. Nadezhdin, N. Nadezhdina, Differ[21] J. Sve a ential translucence method as a supplement to sap flow measurement in Norway spruce with symptoms of top dieback, Acta Hortic. 991 (2013) 285e292. k, Nonlinear finite element analysis of thermal inertia in [22] M. Trcala, J. Cerm a heat-balance sap flow measurement, Int. J. Therm. Sci. 76 (2014) 200e207. [23] M. Trcala, A 3D transient nonlinear modeling of coupled heat, mass and deformation fields in anisotropic material, Int. J. Heat Mass Transfer 55 (2012) 4588e4596. [24] J.F. Siau, Wood. Influence of Moisture on Physical Properties, Virginia Polytechnic Institute and State University, NY, 1995. [25] N.C. Turner, P.E. Waggoner, Effects of changing stomatal width in a red pine forest on soil water content, leaf water potential, bole diameter and growth, Plant Physiol. Lanc. 43 (1968) 973. [26] M.W. Vandegehuchte, K. Steppe, Sapflowþ: a four needle heat pulse sap flow sensor enabling nonempirical sap flux density and water content measurements, New Phytol. 196 (2012) 306e317. [27] S.D. Wullschleger, P.J. Hanson, D.E. Todd, Measuring stem water content in four deciduous hardwood with a time domain reflectometry, Tree Physiol. 16 (1996) 809e815. €sler, Link between diurnal stem radius changes and [28] R. Zweifel, H. Item, R. Ha tree water relations, Tree Physiol. 21 (2001) 869e877. [29] Ch Skaar, WoodeWater Relations, Springer-Verlag, Berlin, New York, Tokio, 1988.
Contents lists available at ScienceDirect
International Journal of Thermal Sciences journal homepage: www.elsevier.com/locate/ijts
Water content measurement in tree wood using a continuous linear heating technique k b, N. Nadezhdina b M. Trcala a, *, J. Cerm a a b
Department of Wood Science, Dendrology and Geobiocenology, Mendel University in Brno, Brno, Czech Republic Department of Forest Botany, Dendrology and Geobiocenology, Mendel University in Brno, Brno, Czech Republic
a r t i c l e i n f o
a b s t r a c t
Article history: Received 1 May 2014 Received in revised form 6 September 2014 Accepted 29 September 2014 Available online
This paper deals with the analytical and experimental analysis of heat transfer in the xylem of trees and the determination of stem water content (WC). The aim of this paper was to derive and verify a new approach to WC calculation from measured temperature differences around a continuously heated needle. The configuration of heater and thermocouples of the heat field deformation (HFD) method for sap flow measurements was taken for this purpose. The suggested formula is derived from the heat conduction equation with a continuous linear source of heating. The ability of the HFD method to nondestructively determine the radial distribution of the local conditions of sap flow measurements under zero flow (referred to as K-value) was used to derive the radial distribution of WC. Examples of the application of our method on several contrasting species with different plant hydraulic architecture are given where calculated WC along stem xylem radius was compared with its direct gravimetrical measurements or with relative determination of wetness of cross-sectional stem discs using a modified differential translucence method. The proposed method enables water content measurements during continuous linear heating and is important for information about WC and sap flow together per day or season when there is possible to extrapolate the temperature difference for zero flow condition. © 2014 Elsevier Masson SAS. All rights reserved.
Keywords: Heat field deformation method Heat transfer equation Thermal conductivity Water content
1. Introduction Internally stored water in tree stems contributes to daily transpiration even in well-watered trees, indicating that stored water plays an important role not only during periods of drought, but whenever water transport occurs within the tree [28]. Water stored within the woody tissues of trees has been viewed as a reservoir from which water can be withdrawn to buffer the evaporative demands of a transpiring plant canopy [19,25,27,7]. Attempts to better visualize the spatial distribution of water in woody tissues have led to the promising use of gamma-ray attenuation [8], nuclear magnetic resonance [4], and computer tomography [18], and to the application of methods such as stem capacitance [9,10], electrical resistance [1,2], and time-domain reflectometry [5,10] for the study of relative changes in stem water content [27]. However, absolute values of water content are still
* Corresponding author. E-mail addresses: [email protected] (M. Trcala), [email protected] k), [email protected] (N. Nadezhdina). (J. Cerm a http://dx.doi.org/10.1016/j.ijthermalsci.2014.09.018 1290-0729/© 2014 Elsevier Masson SAS. All rights reserved.
a “hot topic” in tree water relations research after almost 20 years have passed since Holbrook [9] pointed out that attention must be directed toward improved methods for in situ monitoring of stem water content in order to better quantify the contribution of stem water storage to the whole-plant water balance. WC is also an important parameter for sap flow methodology. All thermodynamics methods based on application of heat pulses require determination of WC in sapwood for sap flux density calculations from measured heat pulse velocity. Schenk et al. [20] strongly underlined the importance of seasonal changes of active conducting sapwood area and wood water content on sap flow estimation. When a tree is drying, its sapwood area may become narrower [6,21] and this may negatively influence the results of flow up-scaling according to the sapwood area unless its real changes are taken into account. Usually sapwood area and WC are determined destructively by an increment borer just before or after sap flow measurements. In most of the cases, the WC is determined only once and without taking into account the spatial and seasonal variability of sapwood parameters. Active water-conducting area [21] and its changes over time [3] are well determined in real time by multi-point sap flow
M. Trcala et al. / International Journal of Thermal Sciences 88 (2015) 164e169
measurements using the HFD method. The effect of possible changes in WC on sap flow measurements using the HFD method is objectively corrected by changes of the K-value in each point of measurements along stem xylem radius. The K-value represents the temperature differences around a linear heater under zero flow. Hence, the K-value reflects a condition of zero flow without the need to provide destructive treatment as it is required for many sap flow methods. All the above mentioned including the consideration of real anisotropy of sapwood has been first considered in the HFD using a side probesLater this HFD configuration was used by Vandegehuchte and Steppe [26] for a method referred to as Sapflowþ which was reported to enable regular updates of water content values for more accurate calculation of sap flux densities without application of destructive gravimetrical measurements of WC. Until now thermodynamic approaches were used for in-situ water content measurement based on heat pulses [11,26]. However, there were no examples of practical use of WC monitoring by Sapflowþ pez-Bernal et al. [11] underlined that the presented in Ref. [26]. Lo ability of the volumetric specific heatecompensated heat pulse (VSHeCHP) methodology to provide actual values of WC is uncertain at the present stage of understanding. Thermodynamic approaches to water content measurement need more research. This work introduces a new approach to measurement of water content in sapwood using continuous linear heating. Whenever sap flow radial profiles were measured by the HFD method, the K-value for each measuring point along the needle was also evaluated as it is the input parameter in formula for sap flow calculation. It was assumed that the K-value can be used for the calculation of water content under zero flow conditions based on continuous sap flow measurements using the HFD method. As the K-value is an important attribute for sap flow calculation in the HFD methodology and should be determined for each measuring point along the xylem radius, the possibility to determine the radial variability of WC is presented. By application of more multi-point sensors around the tree stem for long-term measurements, spatial and seasonal WC monitoring has become also possible. To demonstrate this, in addition to the main aim of WC calculation, we investigated spatial (radial and circumferential) and seasonal variability of WC in tree stems of several species with different wood anatomy. 2. Material and methods 2.1. Theoretical analysis 2.1.1. Analytical solution of thermal conductivity According to the generally known partial differential equation (Eqn. (1)) describing the temperature field solely for heat conduction (not for convection because we can assume the sap flow is zero), the analytical analysis of continuous linear heating can be performed. The zero sap flow condition is recorded during HFD measurement and can be determined although the current sap flow is not zero (it is the advantage of the HFD method).
rc
vT V$lVT ¼ q; vt
lT
165
v2 T v2 T lL 2 ¼ q; 2 vx vy
(2)
where lT and lL are the thermal conductivities of wood in the tangential and axial directions respectively. The analytical solution of the equation (Eqn. (2)) for a continuous line-source of heat H (W m1) along the length of heated needle is based on Green's function theory [17] and is the following:
dT ¼ T dx1 ; dy1 T dx2 ; dy2
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u ulL dx2 þ lT dy2 H 2 2 pffiffiffiffiffiffiffiffiffi lnt ¼ 2p lL lT lL dx21 þ lT dy21 (3)
where T(x, y) is temperature (K) at point [x, y] (origin [0, 0] of coordinate system is in place of heating), and H is heat power per unit length along the line (W m1). After modifications we can use the derived analytical equation (Eqn. (3)) in this way:
H dx pffiffiffiffiffiffiffiffiffi ln ðdTabove Þ0 ¼ ðTabove Tside Þ0 ¼ dy 2p lL lT
sffiffiffiffiffi! lL ; lT
where dx is horizontal distance of side thermocouples from heater (m) and dy is vertical distance of above thermocouples from heater (m). Note: (dTabove)0 ¼ (Tabove Tside)0 ¼ (Tside Tbelow)0 ¼ (dTbelow)0 ¼ K is the temperature difference under zero sap flow condition that is recorded (extrapolated) during HFD measurement (see Introduction and Fig. 1). Both thermal conductivities lT and lL are functions of water content WC and it is proved that lL ¼ klT, where often and also here we assume k ¼ 2 [13] and thus we can use the following formula for calculating lT:
pffiffiffi kdx pffiffiffi ln : lT ¼ dy 2pðdTabove Þ0 k H
(5)
You can see the dependence of thermal conductivity on the temperature difference in an additional figure (Fig. 7). Therefore the calculated thermal conductivity lT can be used to derive the water content WC through the physical quantity called moisture M in wood (lT / M / WC), using the following relations: 2.1.2. Derivation of water content from thermal conductivity Some important physical quantities describing material properties of wood are described below. Moisture M (mass definition) [23] and water content (volume definition) WC are defined as [22]:
(1)
where T is temperature (K), l is matrix of thermal conductivity coefficients of fresh sapwood (W m1 K1), r is density of fresh sapwood (kg m3), c is specific heat of fresh sapwood (J kg1 K1), q is heat power (W m3), t is time and V denotes the vector differential operator V ¼ (v/vx,v/vy,v/vz). Because we assume the steady state condition (the derivative of a temperature with respect to time is equal to zero) and only 2D heat transfer in plane xy, thus the equation (Eqn. (1)) is simplified into equation (Eqn. (2)):
(4)
Fig. 1. Scheme of sensor (HFD configuration).
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Fig. 2. Radial profile of calculated and measured water content for Dracaena draco. Fig. 4. Radial profile of calculated water content for Olea europaea.
M¼
mwater Vwater ; WC ¼ m0 Vwood
(6)
where mwater is weight of water, m0 is weight of dry wood, Vwater is volume of water and Vwood is volume of wet wood. The wood porosity is defined and can be calculated from density and moisture as follows.
P M ¼
Vp
¼1
where P(M) is wood porosity (Eqn. (7)), a ¼ 0.4 for M < 0.4 and a ¼ 0.55 for M > 0.4 (for sapwood is almost always M > 0.4 and thus we use a ¼ 0.55). From the Eqn. (8) we can express the moisture M (Eqn. (9)) and subsequently the water content WC (Eqn. (10)):
rk 1000 þM rs 1000
Vwood r ¼ 1 k ð0:653 þ MÞ; 1000
(7)
where Vp is volume of pores in volume of wet wood Vwood with moisture M, rk ¼ m0/Vwood is convection wood density, rs is density of wood substance (rs ¼ 1531.4 kg m3) [24,29]. Now we can introduce the equation for thermal conductivity (Eqn. (8)) that is necessary to calculate moisture M (Eqn. (9)) and water content WC (Eqn. (10)) in the wood of trees. The determination of the thermal conductivity is based on models derived by MacLean [13]:
rk ð0:217 þ aMÞ þ 0:024P M ; lT M ¼ 1000
(8)
Fig. 3. Calculated water content in comparison with gravimetrically determined water content of a Dracaena draco tree.
Fig. 5. Radial profiles of calculated water content for spruce trees. Indication of trees corresponds to that applied in [3].
M. Trcala et al. / International Journal of Thermal Sciences 88 (2015) 164e169
167
Fig. 6. K-value determination from recorded temperature differences for the outermost xylem layers (4 mm below cambium) of two spruce trees A (left) and D (right). Sap flow was monitored for a duration of 2 months [3]. Indication of temperature differences corresponds to those applied in the HFD methodology [16].
r 1 0:024 0:217 M ¼ 1000 lT 0:024 þ k rs 1000
(9)
ðrk ða 0:024ÞÞ; WC ¼
rk M: rwater
(10)
2.2. Experimental analysis 2.2.1. Experimental verification For verification of the presented theoretical approach we used our earlier data gained when sap flow measurements and gravimetrical estimation of stem water content were conducted either in the same plant (in the case of dragon tree) or in different trees of the same species (olive trees). In the case of spruce trees, direct gravimetrical measurements of WC in sapwood were not conducted; however, all sample trees were harvested at the end of measurements and stem discs were taken from them with the aim to evaluate the extent of sapwood by the modified differential translucence method (MDT) [21]. MDT is a destructive method based on visual evaluation of sapwood after felling the trees, assuming that translucent areas in the stem cross-section are functional and wetter than non-translucent areas where the water transport has ceased [21].
Fig. 7. Dependence of the thermal conductivity lT on the temperature difference dTbelow.
2.2.2. Plant material and climatic conditions Sap flow in a Dracaena draco plant (DBH equal to 40.8 cm, height around 8 m) was measured in February 1999 in Los Naranjeros (Tenerife, Canary Islands). The climate type is Mediterranean, with a mean annual temperature of 12.6 C and an annual precipitation of 460e930 mm. The samples from the stem of this plant were taken by an increment borer for gravimetrical estimation of the stem water content. Thus, this dragon tree can be used for direct verification of our approach to evaluation of WC using K-values. Sap flow in two olive trees (Olea europea L., cv Coratina) with different DBH (15 and 40 cm) but similar sapwood depth (4 cm) were measured in an olive orchard located near Andria, southern Italy (41120 N, 16100 E, 175 m a.s.l.). Mean annual rainfall is 530 mm, distributed from September to April. Yearly means of temperatures are 11 and 21 C, respectively. More details about sap flow measurements in olive from this orchard are described in Nadezhdina et al. [15]. Average WC calculated for these trees was compared against direct gravimetrical measurements of WC in an olive tree conducted earlier [6]. A study of long-term (around 2 months) sap flow dynamics and its radial profiles in several spruce trees (Picea abies) was performed in summer 2011 in the experimental site Hoxmark (59 400 N, 10 430 E), SE Norway, where a Norway spruce forest about 50 years old had marks of spruce dieback in some trees. Several pairs of symptomatic and non-symptomatic trees were selected to study reasons of this tree dieback. Besides sap flow measurements also stem discs were taken after measurements. These discs were analysed using the modified differential translucence method (MDT) to determine the extent of the functional sapwood. Results of this study are described in details in Refs. [21,3]. In this paper we analysed the same data from the point of view of differences in stem water content in healthy (non-symptomatic) and damaged (symptomatic) trees. We used the same pairs of trees whose discs are shown in Ref. [3]. They are marked as A & a and D & d, where big letters are used to mark non-symptomatic trees and the small letters mark symptomatic trees. Additionally, we checked the stability of initial WC (IWC) for two non-symptomatic trees A and D during a longer period similar to the duration of sap flow measurements in these trees. For another two pairs analysed in the paper [3] we looked on symptomatic trees b and c as they had significant circumferential differences in sap flow radial profiles. Our aim was to check spatial variability of WC in the same trees as well. 2.2.3. Sap flow measurements Sap flow in all sample trees was measured by the heat field deformation (HFD) method [12,16]. Multi-point HFD sensors were used, allowing measurements of sap flow in different xylem layers
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across the conductive sapwood. Sensors consist of a linear heater and two pairs of differential thermocouples (symmetrical and asymmetrical) that measure the temperature differences in axial (dTsym) and tangential (dTasym) directions around the linear heater as raw data. Each needle of the multi-point sensor contained six thermocouples; distance between them within each needle varied (10 mm for dragon tree and olive and 12 mm for spruce trees). The temperature data were recorded by data loggers (Unilog, Environmental Measuring Systems Inc., Czech Republic). The heating system was powered by car batteries. In this study we only analysed the K-value spatial distribution and we calculated the WC based on the K-value in order to characterize the spatial variability of WC corresponding to conditions of zero flow in sample trees. It consisted of the linear heater (a resistance wire) inserted in the stainless hypodermic needle 1.5 mm in outer diameter (inner 1.0 mm) situated in the sapwood and four thermocouples copperconstantan, with measuring points 5 mm from needle tip in similar needles and situated at the distance of 15 in axial direction (up and down the heater) and 5 mm in tangential one (right and left side of the heater) (see Fig. 1). The heater tip was inserted 15 mm deeper than the depth of sensing needles. Total resistance of the heater wire was 60.5 U (204.8 U m1) and applied direct current voltage of 4.24 (low heating) or 5.83 (high). this gives the power (U2/R) ¼ 0.297 or 0.652 W, respectively [12,16]. 3. Results and discussion 3.1. Gravimetrical verification The suggested new procedure (Eqns. (4)e(10)) for the calculation of water content was experimentally verified for a D. draco tree (R ¼ 200.8 mm) with a high water content. The verification consisted of a comparison of the water content calculated from temperature differences measured during the continuous linear heating with the water content measured gravimetrically (Fig. 2). Fig. 3 shows that the equations (Eqns. (4)e(10)) provide relatively reliable results (R2 ¼ 0.765) even in extreme conditions (high water content in a tree with low density). For another example a tree with contrasting wood anatomy was chosen e an olive tree with high wood density. WC calculated from the K-value in the olive was twice as low as that in the D. draco tree. The radial profile of the calculated water content (Fig. 4) fits well with that measured gravimetrically for olive published earlier (see Fig. 2 in Ref. [6]). 3.2. Modified differential translucence method verification Fig. 5 shows radial profiles of calculated water content for spruce trees. Sap flow radial profiles substantially differed for the southern (S) and northern (N) sides of non-symptomatic tree A especially in the outer xylem layers [3], which was later displayed by their partial dysfunction (see disc for tree A in the same paper). Correspondently, we found that WC in the southern tree side was substantially higher than in the northern side and differences were larger for the outer xylem layers. Sap flow profiles in the symptomatic tree a was rather closer to that recorded in the northern side of tree A and could be also explained by the dysfunction of the outer sapwood xylem around tree a [3]. WC for tree a was also rather similar to that recorded for the northern side of tree A (Fig 5 e upper panel). Sapwood depth was larger in c compared with b where it was very short. We have confirmed this fact by the calculation of WC, which was higher for c. Moreover, tree b had a large region of decay inside the heartwood. Decay was very close to functional sapwood from the northern side. We calculated the increase in WC for inner xylem in tree b from this northern side - and the results correspond
to the above-mentioned experimental observations. We observed (MDT method) an area of drier wood between the functional sapwood and the decay from the southern side of tree b, which corresponds to our calculation in which WC was lower in the inner xylem from the southern tree side (Fig 5 e middle panel). Sapwood depth was greater in tree D compare to d which is visible from sap flow radial profiles and stem discs [3]. The same is visible from our formula results in which the WC values were lower for d and almost stable for the inner stem xylem layers corresponding to the lowest value in tree D (Fig 5 e lower panel). 3.3. Water content decrease Sap flows in two non-symptomatic spruce trees A and D were monitored during the whole summer with an indication of unchanged sap flow density throughout the whole period in tree A, and with significantly decreasing sap flow density in tree D [3]. In agreement with the sap flow we also found that the K-value in tree D increased during this period, from 1.8 to 2.6 C in contrast to the stable K-value (K ¼ 1.9 C) in tree A (Fig. 6). It indicates that WC in tree D gradually decreased (from 52.58% to 30.56% according to above mentioned method, Eqns. (4)e(10). This WC decrease was observed in all xylem layers of this tree. As it is known in the HFD method, the K-value includes information about the basic wood properties and heat conductances in both, axial and tangential directions [14,16]. The K-value depends on the sensor geometry (the distances of the thermocouples from the heater) and the surrounding conditions including the level of power supply. If the surrounding conditions are maintained stable, it is possible to monitor internal changes (mainly wood water content). This may open the opportunity to investigate and control the biological health of trees as it is shown on examples of trees A and D (Fig. 6). 4. Conclusion The formula for water content calculation was derived from the steady-state two-dimensional partial differential equation describing heat conduction in wood under zero sap flow conditions using the HFD configuration The formula was tested on several tree species under different conditions. The results show the applicability of the approach for measuring water content during continuous linear heating (e.g. during sap flow measurement by the HFD method). Our new approach for the non-destructive determination of WC can be also useful for other sap flow methods dependent on the knowledge of WC. The approach is important for synchronous information about WC and sap flow radial profiles. It can provide information about the health state: although there are species where WC is typically higher in heartwood compared to sapwood the usual trend is that there is less water in heartwood. If not e we should proceed with caution e there could be decay inside. Acknowledgements The work was supported by OP Education for Competitiveness (European Social Fund and the state budget of the Czech Republic) CZ.1.07/2.3.00/30.0017 Postdocs in Biological Sciences at MENDELU. References [1] R. Borchert, Water storage in soil in tree stems determines phenology and distribution of tropical dry forest trees, Ecology 75 (1994a) 1437e1449. [2] R. Borchert, Water status and development of tropical trees of during seasonal drought, Trees 8 (1994b) 115e125.
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