Estimation model of single tree transpiration based upon heat pulse velocity and micrometeorological data

Transcription

1 Exchange Processes at the Land Surface for a Range of Space and Time Scales (Proceedings of the Yokohama Symposium, July 1993). IAHS Publ. no.212, Estimation model of single tree transpiration based upon heat pulse velocity and micrometeorological data M. HASHINO & H. YOSHIDA Department of Civil Engineering, Faculty of Engineering, The University of Tokushima, Tokushima, 770, Japan Abstract An estimating methodology of single tree transpiration is proposed. This consists of transpiration submodel based on heat pulse velocity and soil water uptake submodel by roots. Model parameters are identified by means of heat pulse velocity and micrometeorological data. This method applies to observed data at single tree (Cryptomeria japonica) in the Shirakawadani experimental basin in Tokushima prefecture, Japan. INTRODUCTION The heat pulse technique is a simple method for measuring tree transpiration in forest hydrology, so that many researchers have tried to estimate tree transpiration of various kind of vegetation. In order to estimate transpiration of a tree, heat pulse velocity (HPV) is usually converted directly into sap flux in previous methods because sap flux results in transpiration at the canopy. Those methods require, however, many preparations and several steps of conversion; e.g. measuring sapwood area, the wounded width by implantation of sensors and HPV at several points even in a tree, correcting the observed HPV by a numerical method (Swanson & Whitfield, 1981), converting the corrected HPV into sap flux by means of measured sapwood area. Essentially, cutting trees method must need to verify the agreement between the estimated sap flux and the measured water uptake at the cutting section. The methodology which combines the heat pulse technique and the energy balance method (e.g. Hatton & Vertessy, 1990) seems to be of use. However, the energy balance method needs detail profiles of micrometeorological data instead of cutting trees in order to verify the estimation of sap flux. It is, in general, difficult to get those data in actual basins. Then, in an engineering point of view, authors propose a new methodology based upon both of HPV and micrometeorological data at the canopy in order to estimate single tree transpiration without cutting these trees and the many measurements and conversions. The proposed transpiration model relates HPV directly with transpiration rate given by correcting Penman's potential évapotranspiration at the canopy, and needs HPV, air temperature, humidity, wind speed and radiation. Soil moisture is also necessary to take account of the reduction of water uptake by roots. Once model parameters are identified, it is possible to estimate transpiration only with micrometeorological data and soil moisture.

2 138 M. Hashino & H. Yoshida MODELLING POINTS Models of the Soil-Plant-Atmosphere Continuum (SPAC) must incorporate the interaction processes among soil, vegetation and atmosphere. In our modelling, the "transpiration submodel" (Hashino & Yoshida, 1991) and the "soil water uptake submodel" represent the water movement between vegetation and atmosphere and between soil and vegetation, respectively. It is the modelling point of "transpiration submodel" to formulate the relationship between transpiration at the canopy and HPV at the stem. In general, it is difficult to measure directly the actual transpiration from a tree. Measurements obtained from outdoor experiments in the campus of The University of Tokushima (Hashino & Yoshisa, 1991) suggest that (a) the diurnal pattern of HPV is similar to that of transpiration and (b) daily potential évapotranspiration calculated by the Penman equation E P (Penman, 1948) is approximately proportional to the observed daily transpiration Er, that is, E T =<^E P as shown in Fig. 1. However, in the case which we estimate hourly transpiration, the transpiration coefficient 4> is not a universal constant during a day and the diurnal pattern of HPV is not different from that of Ep, because the Penman equation does not take account of plant physiology. Then, <j> is supposed to be dependent on the water condition of a tree, thus <j> is defined as an exponential function of the water deficit of a tree. We are able to modify Ep in order to determine <j> and obtain Ep by making use of the similarity of the diurnal pattern between HPV and transpiration. E P can be easily calculated by means of temperature, humidity, wind speed and radiation observed at one point nearby the canopy. Therefore our modelling does not require cutting trees, measuring sapwood area and other calibrations. 0) 8.0 es * 6.0 S >> _o co «1 4.0 s a g H Penman's potential évapotranspiration (mm/day) Fig. 1 Relationship between daily transpiration and Penman's potential évapotranspiration. The soil water uptake submodel is based upon the phenomenon that the decrease of soil moisture causes the reduction of soil water uptake by roots (Kramer, 1969). It is the modelling point to formulate the relationship between water uptake by roots and soil water potential measured by tensiometers, so that transpiration process can take account of the soil water condition and, thus, the resultant reduction of transpiration. The proposed model enables us to estimate hourly transpiration with the observation of HPV, micrometeorological data and soil moisture potential.

3 TRANSPIRATION SUBMODEL The water balance equation is given by Estimation model of single tree transpiration 139 =E,-E T (1) dr where S is water in a tree (mm), Eg is water uptake rate by roots (mm h" 1 ), and Ej is transpiration rate (mm h 1 ). Swanson & Whitfield (1981) pointed out that the observed HPV is not proportional to sap velocity, so that authors supposed that Eg which is closely related with sap velocity is not proportional to HPV V h, i.e. V h =KE s p. In the daytime, it is supposed that S reduces below S c which is the water of a tree at predawn and a tree is under the stressed water condition. Then, water stress of a tree S T is defined as follows: S T = S C -S (2) Equation (1) is transformed into Equation (3) as to S T ^= 7.- v (3) dt Since the reduction of water potential in a tree due to transpiration causes water uptake by roots, it is supposed that (a) water uptake rate Eg is dependent on water stress S T, (b) the water unbalance of a tree Ej-Eg, that is, ds T /dt is closely related to the water condition in a tree, (c) because the rapid increase or decrease of transpiration rate and water uptake rate just after the drawn or the sunset has impacts upon the water condition, the derivative of E,.-E s has to be incorporated. Based upon these three assumptions, the water movement equation in a tree is given as follows: d(...-..) S T = -a( r - v ) - P-A^_^Z +yes (4) dt where a,15 and y are constants. Substituting Equation (3) for Equation (4) gives the fundamental equation: d 2 S r ds T P L + a-l + S T = ye s (5) dt 2 dt It is valid that the transpiration coefficient 4> defined as the ratio of transpiration rate and Penman's potential évapotranspiration rate, because the increase of water stress S T causes closing stomata and the consequent reduction of transpiration. The relationship between 4> and S T is given by cj)(s r ) =(t> m exp(-u,.) < 6 > where <j> m is 4> at S T =0 and f is a recession coefficient.

4 140 M. Hashino & H. Yoshida Equation (5) is the second linear differential equation as to S T, thus the solution depends on the discriminant D=a 2-4B. There are three cases of the solution. However, as described in later section, all identified parameters show that the discriminant D is negative, so that in this paper, the subject is focused on the case that D is negative. In this case, the difference equation estimating Ej i+1, S Ti+, and 4> i+1 are derived as E v.i = [^i^p^a.b^-a^e^-e^-la^l / [1+1,4 Y S TM = A^+A^E^ + lie^+e^xl-aj *m = i, ex PK%,) (7) (8) (9) where A = ex P(-^A0 i sin(o)af), A 0 = cxp(-tiaf) -sin(cj)a?)+cos(coaf) a) CO A? = exp(- ia?) sin ( co Ar ) + cos ( co At ), A, = u 2 + co- 0) a vla 2-4f3 H =, co = 2(3 2f3 Equations (7) and (8) have only an unknown variable E si+1 which is given by the numerical solution of the equations. Transpiration rate Ej i+1 is given by the product of the transpiration coefficient 4> and Penmans's potential évapotranspiration E Pi+1 as shown in Equation (10). E rj = *, (10) Table 1 Identified parameters from June to October in a IS y K P ^SMAX Month June July August September October 4> m J"

5 SOIL WATER UPTAKE SUBMODEL Estimation model of single tree transpiration 141 Outdoor experiments performed in the campus of The University of Tokushima (Hashino & Yoshida, 1991) show that (a) when soil moisture potential is below a certain critical value, the transpiration coefficient linearly reduces (e.g. Feddes et al., 1978 etc.) and (b) even on fine days when soil is moist, HPV is approximately constant in the midday as shown in Fig. 3. The relationship between soil moisture potential ^f and water uptake rate E s is assumed as follows: (vp c <W) E s m I xy h -\y\ VL-VC E SMAX ( V<^;) (11) 0 ( < 0 ) where "* is soil moisture potential (cm H 2 0), E s ('5 r ) is water uptake rate at arbitrary ^ (mm h" 1 ), E SMAX is the upper limit value of E s ( 1 i r ) under the optimal soil moisture condition (mm h" 1 ), ^c is ^ where E s starts to reduce and ^L is ^ where E s =0. PARAMETER IDENTIFICATION Model parameters are a, fi, 7, K, p, <j> m, f, ~ty c, ^L and E SMAX. Parameters except for 4> m and f determine the basic structure of the model, however, 4> m and f may be affected by the plant physiological activities. Then parameters except for 4> m and f are supposed to be unique and <j> m and f are supposed to vary respectively during the observation period. Since authors consider that the data which we can measure in the basin as to the transpiration process is HPV, minimizing the square sum of estimating error F defined as equation (10) by the nonlinear least squares method (Kotani, 1979) give optimal parameters. F = E(^ h,esti? (12) where V hobsi is the observed HPV, V hcsti is estimated HPV from the relation: V h,e S ti = KE SMt i p, and N is the number of data. F for a combination of parameters is calculated by the following procedure. Step 1: Set i=l. Step 2: Calculate the transpiration coefficient ^ from S T (ti) by Equation (9). Step 3: Calculate transpiration rate at t=t; Erft) by Equation (11) as the product of the Penman's potential évapotranspiration E P (ti) and the transpiration coefficient <j>- t. Step 4: Calculate the estimated water uptake rate E s (t;) from transpiration rate E T (t i ) by Equations (7) and (8). Step 5: Calculate water uptake rate E s ("^i) which takes account of the soil

6 142 M. Hashino & H. Yoshida moisture condition and the upper limit value of water uptake rate by Equation (10). Step 6: If E s (tj) is less than E s (^i) then it is judged that water uptake is reduced and go to Step 7. Otherwise, it is judged that water uptake is reduced and go to Step 8. Step 7: Recalculate transpiration rate E^tj) by Equation (11) based upon Es(tj). Set i=i+l and return to Step 2. Step 8: Substitute E s (tj) for E s ( j). Step 9: Recalculate Ejft) by Equation (11) based on the substituted Es(tj) at Step 8. Step 10: Set i=i+l and return to Step 2. The reducing process of water uptake rate is incorporated in Step 6, so that transpiration rate may be estimated by taking account of the actual water uptake rate affected by the dry soil moisture condition and the upper limit value of water uptake rate. Once model parameters are identified, transpiration is easily calculated only by means of micrometeorological data and soil moisture potential without HPV. This is the merit of the proposed model. APPLICATION AND DISCUSSION The Shirakawadani experimental basin is located about 100 km west of Tokushima City, Western Japan (latitude 33 52'N, longitude 'E). On the north-faced slope, HPV was measured at a breast height of a 30 year old Cryptomeria japonica with the altitude of 750 m. Air temperature, humidity, wind speed and net radiation were observed nearby the canopy. Table 1 shows model parameters identified as to only fine days for June to October in Because instruments did not work for some days, parameters were not always obtained as to all fine days. The discriminant D of Equation (5) is negative. Parameters <j> m and f vary during the observation period. Parameters c and ^L which prescribe the reduction of water uptake due to the decrease of soil moisture were not identified. Fig. 2 shows diurnal patterns of the observed and estimated HPV, the transpiration coefficient <j> and soil moisture potential from June 18 to 22 in The estimated HPV agrees with the observation. Soil moisture potential is greater than -200 cm H 2 0 which is supposed to be slightly under the field capacity. The transpiration coefficient which represents the ratio of Penman's potential évapotranspiration E P and the actual transpiration Ep shows the same diurnal patterns as HPV or soil moisture potential, and varies in the same extent during the observation period. The diurnal patterns from July 8 to 12 are illustrated in Fig. 3. Even in this case, the estimated HPV agrees with the observation. Soil moisture potential varies periodically in the observation period. However, the transpiration coefficient varies more narrowly than Fig. 2 and the minimum value is also less than Fig. 2. Soil moisture potential varies in the same level, nevertheless, transpiration coefficient has different value in each case. Therefore, it is supposed that soil moisture is not so dominant in the reduction of water uptake by roots, and parameters ^c and ^L were not identified in the period. The daily relative error is less than about several percents

7 Estimation model of single tree transpiration Jul.8 Jul.9 Jul.10 Julll Jul.12 Fig. 2 Diurnal patterns of HPV, transpiration coefficient and soil moisture potential from June 18 to 22 in 1992 (solid line: observed HPV, symbol: estimated HPV). Fig. 3 Diurnal patterns of HPV, transpiration coefficient and soil moisture potential from July 8 to 12 in 1992 (solid line: observed HPV, symbol: estimated HPV). in each day, so that in the practical point of view, the proposed model could estimate HPV and transpiration rate. The HPV estimated by making use of the unique parameters except for <j> m and f agree with the observation, so that the basic structure of the proposed model have been established. However, model parameters <j> m and f do not vary consistently during the observation period. Because observed data may have some errors and those parameters are supposed to be affected by the plant physiological activities; e.g. the opening of stomata etc.. The point of issue, however, must be examined in detail by the accumulation of the observed data. The proposed model is available only for the estimation of the single tree transpiration. Thus, it is necessary to take account of the spatial variability of HPV and other data in order to estimate the basin scale transpiration. CONCLUSION A methodology estimating single tree transpiration has proposed. Model parameters

8 144 M. Hashino & H. Yoshida were identified by means of HPV and Penman's potential evaporation calculated with micrometeorological data without cutting trees. The estimated HPV agreed with the observation, so that authors consider that the basic concept of authors' methodology has been established and the proposed model could be applied to the estimation of the single tree transpiration. Parameters concerned with the reduction of water uptake under the dry soil condition was not identified. The upper limit of water uptake rate was not apparently confirmed. Furthermore, model parameters 4> m and f vary in each month, so that these points at issue have to be verified by the accumulation of data in future. Acknowledgement This paper is supported by a grant of Ninon Seimei Zaidan (Prof. K. Muraoka, Osaka Univ.). Authors are grateful to Dr. Tatemasa Hirata in the National Institute for Environmental Studies for his valuable comments on the tensiometers. REFERENCES Feddes, R.A., Kowalik, P.J. & Zaradny, H. (1978) Simulation of field water use and crop yield. Centre for Agricultural Publishing and Documentation, Wageningen, The Netherlands. Hashino, M. & Yoshida, H. (1991) Transpiration model associated with sap flow and meteorological data. lahspubl. no. 204, Hatton, T.J. & Vertessy, R.A. (1990) Transpiration of plantation Pinus radiata estimated by the heat pulse method and the Bowen ratio. Hydrol. Processes 4, Kotani, T. (1979) Minimization of nonlinear multi-variable function. Osaka Univ. Computer Center News 32, Kramer, P.J. (1969) Plant and soil water relationships - A modern synthesis. McGraw-Hill, New York. Morikawa, Y. (1974) Sap flow in Chamaecyparis obtusa in relation to water economy of woody plants (in Japanese with English abstract). For. Bull. Tokyo Univ. 66, Olbrich, B.W. (1991) The verification of the heat pulse velocity technique for estimating sap flow in Eucalyptus grandis. Can. J. For. Res. 21, Penman, H.L. (1948). Natural evaporation from open water, bare soil and grass. Proc. Roy. Soc. London A 193, Swanson, R.H. & Whitfield, D.W. (1981) A numerical analysis of heat pulse velocity theory and practice. J. Exp. Bot. 32,