Measuring sap flow with the heat balance approach using constant and variable heat inputs

AGRICULTURAL AND FOREST METEOROLOGY ELSEVIER

Agricultural and Forest Meteorology 85 (1997) 239-250

Measuring sap flow with the heat balance approach using constant and variable heat inputs J.F. Kjelgaard ~'*, C.O. Stockle a, R.A. Black b, G.S. Campbell c a Biological Systems Engineering, Washington State University, Pullman, WA 99164, USA b Department of Botany, Washington State University, Pullman, WA 99164, USA c Crop and Soil Science, Washington State University, Pullman, WA 99164, USA Received 7 March 1996; accepted 22 August 1996

Abstract The performance of a heat balance-based sap flow gauge design, capable of alternating variable heat input (VHI) and constant heat input (CHI), was analyzed. The gauge employs differentially wired thermocouples to monitor differences in stem temperature and radial heat losses. The VHI method employs a control circuit to maintain a constant temperature difference between a thermocouple placed upstream from the gauge heater and a thermocouple at the heated portion of the plant stem. The CHI method applies a constant voltage to the gauge heater with no control circuit. Simultaneously, on the same plants, the effect of the placement of thermocouples, either inserted into the stem structure or placed on the surface, was also investigated. Sets of 15 rain and daily integrated measurements were compared with gravimetric water losses determined by lysimetry. The evaluation included three plant species: sunflower (Helianthus), maize (Zea maize) and potato (Solanum tuberosum). The results showed that the VHI gauges tended to underestimate flows for both the 15 min and daily sap flows. The CHI gauges gave generally better results and were easier to implement and monitor. No consistent differences in the performance of the inserted and surface-mounted thermocouples were found; any differences that were noted were generally small and of no practical significance. An exception was the case of sunflower CHI at large flow rates, when the inserted thermocouples outperformed the surface-mounted ones. Important departures between gauge sap flows and lysimetric plant water losses at low flow rates were observed. Gauge performance was better for dally integrated flows (relative absolute error, RAE .-~ 10% for combined data) than for 15 min interval average flows (RAE = 32-36% for combined data). However, the performance of the short-time-interval gauge improved dramatically when low flows ( < 10 g h -1) were not included in the analysis. © 1997 Elsevier Science B.V. Keywords: heat balance; sap flow

1. I n t r o d u c t i o n Recent advancements have allowed researchers to closely approximate plant transpiration by determining the sap mass flow. This is done using gauges that

* Corresponding author.

are attached to or are inserted in the plant stem. The sap flow gauges used on herbaceous plants generally fall into three categories: heat pulse timing, heat probe, and heat balance methods (Campbell, 1991). Published studies indicate that for herbaceous plants the most popular o f these is based on the heat balance method. These gauges do not disturb the

0168-1923/97/$17.00 ~ 1997 Elsevier Science B.V. All rights reserved. PII S 0 1 6 8 - 1 9 2 3 ( 9 6 ) 0 2 3 9 7 - 0

240

J.F. Kjelgaard et al. /Agricultural and Forest Meteorology 85 (1997) 239-250

plant root medium (as lysimeters do) or cause permanent damage to the plant during measurements. For the heat balance method, a heater element is placed around the plant stem to provide energy to the system. Thermocouples are used to determine how much heat is lost by conduction up and down the stem, and also radially from the heater element. The difference between the heat input and these losses is assumed to be dissipated by convection with the sap flow up the stem, and may be directly related to mass flow. A variety of sap flow gauges employ the heat balance concept. The most popular has been a gauge based on initial designs by Sakuratani (1981); Sakuratani, 1984), further refined by Baker and van Bavel (1987) and Steinberg et al. (1989), and now commercially available (Dynamax ® Corp., Texas). Typically, the heat input voltage is constant regardless of the sap flow rate. This could potentially cause the stem to reach high temperatures that could damage

the xylem (Baker and Nieber, 1989; Ishida et al., 1991). Temperature control for this design has been attempted by Weibel and Boersma (1995) with apparently successful results. Several studies have reported gauge failure in the field (Shackel et al., 1992; Gerdes et al., 1994), but this design has been the basis of numerous studies to examine plant transpiration (Ham and Heilman, 1990b; Lascano et al., 1992; Dugas et al., 1992; Devitt and Berkowitz, 1993). An alternative gauge based on the heat balance design was presented by Ishida et al. (1991), who used three thermocouples differentially wired together; one placed at the heater element and the other two upstream and downstream from the heater. A separate set of differentially wired thermocouples monitors radial heat losses away from the stem (Fig. 1). The heat input for this configuration is usually varied (variable heat input, VHI) to maintain a constant temperature difference between the heated por-

Fig. 1. Generalschematicof the sap flowgauge wiringand insulation.

J.F. Kjelgaard et al. / Agricultural and Forest Meteorology 85 (1997) 239-250

tion of the stem and the upstream thermocouple (Cermak et al., 1976; Fichtner and Schulze, 1990; Ishida et al., 1991). This limits the amount of heat applied to the plant .,stem when the system has periods of low or zero flow; provides the proper amount of heat when sap flow fluctuates throughout the day; and minimizes the radial heat losses from the gauge. The use of differentially wired thermocouples allows more accurate measurements of temperature gradients and simplifies the wiring requirement for each gauge. The VHI approach may also provide more accurate sap flow measurements due to the reduced fluctuations in stern heat storage (Grimes et al., 1995b). However, Weibel and Boersma (1995) noted that the VHI method is computationally rigorous and limits the number of gauges that may be run by a single data logger. A constant heat input (CHI) approach allows more gauges to be monitored by a single data logger, requires less hardware, and may be more practical fo:r field studies. In this study, the gauge designed by I:shida et al. (1991) was operated in either a variable heat input (VHI) or a constant heat input (CHI) mode. An additional option for gauge design concerns the placement of thermocouples. In an analysis of simulated sap flow in dicotyledons and monocotyledons, Ishida et al. (1991) found temperature gradients between the surface and xylem within the heated portion of the stem segment, particularly in the case of monocotyledons. Similar findings were presented by Baker and Nieber (1989). In order to obtain more representative stem temperatures, Ishida et al. (1991) recommended inserting the gauge thermocouples into the stem. Sakuratani (1981) did this for larger plant stems ( > 10 mm in diameter) and Fichtner and Schulze (1990) used inserted thermocouples with vines. Weibel and de: Vos (1994) found that inserting thermocouples between the bark and xylem of apple trees gave the best representative temperatures for monitoring sap flow. Based on their work with fruit trees, Khan and Ong (1995) also recommended inserting thermocouples. However, similar heat balance gauge designs using surface-mounted thermocouples have yielded good results (Baker and van Bavel, 1987; Steinberg et al., 1989; Senock and Ham, 1993). The objective of this research was to compare the accuracy of the heat balance sap flow gauges of

241

Ishida et al. (1991) in both CHI and VHI modes with monocots (maize) and dicots (potato and sunflower) over a range of sap flows typical for mature plants. In addition, the gauge configuration allowed for the simultaneous use of thermocouples placed on the stem surface and thermocouples inserted (2 mm depth) into the stem. Thus, CHI and VIII modes, and the use of surface-mounted and inserted thermocoupies were tested on the same plants without changing the plant/gauge geometry.

2. Theory The sap flow gauge design used for this study was based on the configuration presented by Ishida et al. (1991). Fig. 1 shows a conceptual schematic of the thermocouple placement. With power applied to the heating element, the following equations may be used to partition the heat inputs to calculate sap flow for both VHI and CHI applications. The basic components of the stem energy budget components are Qn - Of -- Qup - Qdn - Qrad =

0

(1)

where Qn is the heat input, Q f represents the convective heat carried by the sap flow, Qup and Qdn represent the heat conducted upstream and downstream through the plant stem, and Q=d is the radial heat loss from the heater away from the plant stem (all components in the units J s-l). Eq. (1) represents a simplified formula. Several researchers (Baker and Nieber, 1989; Groot and King, 1992; Grimes et al., 1995a) have indicated that other heat balance components such as stem heat storage are negligible except at low or zero flows. Using Eq. (1) as the basis for calculating flow, the different heat energy components were determined as follows. The energy input from the heater is calculated with the formula

QH = Vi~/RH

(2)

where Vin is the input voltage supplied to the stem heater (V), and R H is the corresponding heater resistance ( ~ ) . For the CHI mode, Vi. may be measured directly from the heater voltage controller. The VHI mode uses a pulsed input signal to control the stem temperature between the thermocouple lo-

242

J.F. Kjelgaard et aL /Agricultural and Forest Meteorology 85 (1997) 239-250

cated at the heater and the upstream thermocouple. Therefore QH is calculated as (Ishida et al., 1991)

OH = ( VaVb)/RH

(3)

where V~ is the average of the pulsed signal, taking into account the fraction of time the signal is on, and Va is the supply voltage, usually from a car battery. Both signals are read directly from the control circuit. The heat components due to stem conduction are calculated from

QuP= " I TJ~-L-~-~p]

(4)

and Qdn = 0.54 [ 7r----~-- ) t Ldn

(5)

where 0.54 (J s-1 m - 1 oC - 1) is the approximate thermal conductivity of an herbaceous plant stem (Sakuratani, 1984), dia. is the nominal plant stem diameter (m) at the heater location, ~Tup and ~Tdn are the temperature differences between the heater and thermocouples located upstream and downstream (°C), and Lup and Ldn are the distances from the edge of the heater to the respective upstream and downstream thermocouples (see Fig. 1). To determine radial heat losses, a radial conductance (Krad) must be calculated during a time of zero or near-zero flow (usually early in the morning) K~.d =

OH - Qup - Qdn

8Trad

(6)

where Krad has the units of J s-1 oC - 1 and 8T~ad is the temperature difference between the heater element and the outside of the initial layer of foam insulation (see Fig. 1). With the Krad value determined (and assumed constant throughout the day), the radial heat loss is calculated as Qr~d = K~dSTr.d

(7)

The heat balance component due to sap flow (Qf) from Eq. (1) may he converted into an equivalent mass flow (S) 3600Qf s

-

4.19 8Tap_ dn

(8)

where S is in g h -~, 4.19 is the specific heat of liquid water ( j - 1 g-1 oC - l), 3600 is the number of seconds per hour, and ~Tup_ dn (°C) is the temperature difference between the upstream and downstream thermocouples.

3. Methodology The measurements were made at the greenhouse facilities at Washington State University. Daytime temperatures in the greenhouse were typically 25°C with nighttime temperatures around 15°C. Three plant species (potato (Solanum tuberosum), maize (Zea mays) and sunflower (Helianthus)) were grown in 10-inch diameter plastic containers. The plants were watered and fertilized on a regular basis to ensure robust growth. The measurements were made when the plants were mature, with stem diameters 8-20 mm. Individual potted plants were placed in large plastic bags and the bag opening was sealed around the base of the plant stem. Lysimetric measurements of transpiration were made by placing the bagged plants on an electronic scale (Mettler PM34, Mettler Instrument Corporation, Heightstown, N J), interfaced to a portable computer that recorded the scale readout every 15 min. The resolution of the scale readout was 0.25 g. Special gauges were constructed to accommodate the different thermocouple placements to be evaluated (inserted and surface-mounted), thus allowing simultaneous comparisons on the same plant. During the period of measurement, the sap flow gauges were provided with variable heat inputs using the VHI circuitry and control as described by Ishida et al. (1991). Typically, after two or three days of VHI measurements, CHI measurements were done by removing the VHI circuitry and control program. A constant output voltage regulator was then wired onto the heater. The gauges were allowed to run up to one week on the same plant. Prior to mounting the gauge, the stems of the potato, sunflower and maize plants required some preparation. The potato plants had knobs and stem ridges in the vicinity of the heater, which were trimmed to improve contact between stem and heater.

J.F. Kjelgaard et al. / Agricultural and Forest Meteorology 85 (1997) 239-250

The sunflowers had senesced lower leaf stems which were trimmed. Sheath leaves from lower stem sections of maize plants were removed and gauges were placed between the lowest stem nodes. Thin resistive heaters (Heater Design Inc., Cerritos CA) were placed around the plant stems, and secured with tape. Tbe heaters ranged in size from 43 mm long by 15 irma wide for potato stems (with heater resistances of 140-170 ~ ) and 73 nun long by 21 mm wide for maize and sunflower stems (heater resistances of approximately 54 fD. The inserted thermocouples for measuring the stem heat conduction and conw,~ctive flow were made of 0.25 mm type E duplex wire (Omega Engineering Inc., Stamford, CT). Twisted and soldered thermocouple tips, approximately 2 mm long, were pushed into each plant stem using a pair of needle-nose pliers. The surface-mounted thermocouples were constructed of 0.13 mm type E duplex (Omega Engineering Inc., Stamford, CT) with soldered tips approximately 1 mm long. Both the inserted and surface "middle" themaocouples were placed directly under the axial center-line of the heater element. Upstream and downstream thermocouples were placed approximately 10 mm upstream or downstream from the edges of the heater for potatoes, and 15 mm from heater edges for maize and sunflower (see Fig. 1). While mounting the gauges, precautions were taken to ensure that upstream and downstream thermocouple wires did not cross or come close to the heater element. For the determination of radial heat losses, differentially wired, 0.13, mm type E thermocouples (Omega Engineering Inc., Stamford, CT) were used. One thermocouple was placed on the outside of the heater, and the other between the inner and outer layers of insulation, directly over the heater. Two layers of insulation were used for the gauges. The inner layer consisted of adhesive vinyl foam tape weather strip (V~r.J. Dennis and Co., Elgin, IL) approximately 32 mm wide and 5 mm thick. Lengths of tape were cut so that the heater and thermocouple assemblies were wrapped under a double thickness of tape (10 mm thickness). The width of the weather strip allowed the heater and upstream/downstream thermocouples to be covered with three sections of tape. Care was taken to apply the insulation uniformly to ensure representative ~T~ad measurements

243

from the set of thermocouples measuring the radial heat loss. Additional layers of insulation were placed upstream and downstream of the initial three sections to further isolate the stem. Once the outside radial thermocouple was in place (see Fig. 1), a length of polyurethane pipe foam was placed over the inner insulation. Velcro ® straps were used to fit the pipe foam snugly over the weather strip. Aluminum foil was placed over the entire assembly to minimize the effects of solar radiation on the gauge. The thermocouples and heater input voltage were measured on a CR-10 data logger (Campbell Scientific Inc., Logan, UT). VHI measurements (temperatures and voltages) were taken every 2 s, using the control settings recommended by Ishida et al. (1991). The damping factor, controlling the response time of the heater control, was set at 0.025. The temperature differential maintained on the plant stem was 3°C, with a duty cycle of approximately 50%. Analysis of the VHI circuit control indicated some power loss through the etched circuit board and reduced supply voltage measurements compared with the actual supply voltage. Therefore, all values from Eq. (3) were divided by 0.98. For the CHI gauges the heater voltage was approximately 3-3.5 V, with the voltages and temperatures interrogated every 10 s. Average readings of all measurements were output every 15 min, and analyzed on electronic spreadsheets. Quantitative error analysis was done using the following performance parameters: the root mean square error (RMSE), the relative RMSE, and the relative absolute error (RAE). These were defined as follows: R M S E = ~ n-1

i=1 ~ (Pi--Oi)2

(9)

RMSE Relative RMSE = - -

(10)

R A E = I( Pi - O i ) / o i l

(11)

Oavg

x 100

where n is the number of observations, i denotes the ith observation, P represents the gauge sap flow, O represents the observed (gravimetrically determined) sap flow, and Oavg is the average observed sap flow. Units for RMSE are the same as the sap flow units, the RAE is a percentage value, and the relative RMSE is unitless.

244

J.F. Kjelgaard et aL /Agricultural and Forest Meteorology 85 (1997) 239-250 160

4. Results and discussion

140

Typical VHI and CHI diurnal heat energy components are shown in Fig. 2. The VHI performance (lower graph) shows the circuitry adjusting to increasing sap flow for the first half of the day, and then readjusting to lower flows later in the day. The upstream stem conduction (Q,p) shows a constant value, illustrating the ability of the VHI system to maintain a constant temperature gradient as the flow rate changes (Ishida et ai., 1991). As the flow increases, the Qf component follows the changing flow rates and is the major source of heat flow away from the heated stem section. Qrad shows slight changes. The CHI example (upper graph) shows that sufficient voltage was applied to handle the sap flow rates encountered, Qf not being limited by QH. The conduction and radial heat components all show adjustments as the sap flow changes. The difference in the magnitudes of flows between maize and potatoes accounts for the large difference in heater input energy.

A 120 ,,7, P" 100 _.o LL "cO r/)

80 60 4O 20 0 160

i i o Inserted TC (y--a + bx)

140

i

i i b) Maize CHI t 8 a..~

a= -0.94

120

b=l.00

~o~ _ 100

,,.~*r|o~ ~

40

_

20

~

~

0

20

/ "

..,If="

o ~u~ceTc _

(~-.a + bx)

"

~,=-o.9o b=l.00

= =

o! ~

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.~.~"

r2=0.94

,,-°' 80 ~- 60

i

n=284

,-

,

40

60

i 80

i 100

?;°'a4 l 120

140

160

Observed Flow (g hr "1)

0.5

I

Fig. 3. Comparison of measured and observed sap flow rates at 15 min intervals: (a) maize VHI with inserted and surface-mounted thermocouples, and (b) maize CHI with inserted and surfacemounted thermocouples.

i

I

a) Malze CHI

DOY 264 0.4

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

.......... QH

- - - Qup - - - - Qdn

~" 0.3

- - ' - - Qrad

~

"r" 0.2

o.1

-:-"z_ :--_ ~

0.0

.....

0.15

.....

*

'

i b) Potato VHI

i

DOY 286

.'/~

.......... ~r~H --Qup

0.10

.

- - ' - - Ornd

:

~ '-~..

./;~t~

~ :'"....

-r 0.05

0.00

0

6

12

18

24

Time

Fig. 2. Sap flow gauge heat balance components: (a) constant heat input (CHI), and (b) variable heat input (VIII).

Scatter plots comparing the sap flow determined by the gauges and observed water losses over 15 min periods for maize, potatoes and sunflowers are shown in Figs. 3-5, respectively. A large range of sap flow rates was observed, with potatoes having the lowest (0-35 g h-l), maize sap flow greater than potatoes (0-150 g h-l), and sunflowers the highest sap flow rates (0-200 g h-l). For maize, the data obtained using the VHI method (Fig. 3, top) indicate a general tendency for the gauges to underestimate flow, particularly at higher flow rates. Regression analysis (dotted lines) also indicates the tendency to underestimate, but the inserted thermocouples give slightly better results. Both surface-mounted and inserted CHI results for maize (Fig. 3, bottom) show good agreement with the observed flow. However, maize CHI did not have as high a range of flows as maize VHI. Regression analysis shows excellent agreement with the 1:1 line (solid line).

J.F. Kjelgaard et al. /Agricultural and Forest Meteorology 85 (1997) 239-250 4.0 o 'lnserte~lTC (y-,-.a+ bx) a--0.27 b:0.a5

35 ~30 r,..

25

'a)Pot~toYHl'

'

' / /

/ ~/~

r~=o.93

_o- -" .-°° -

Iidli~11,;

_ *

;

o~ 20 LL

,~r'a.t~JFti,

~. 15

,li~l~a

co

10

uliL

5

I

"E I

40

I

o

35 ~ 30

I

I

I

I

Inserted TC

a= -0.18 b=0.85 I

I

I

I

e:o.g, I I

li=ll ~

' l: _. = ,l . . -i f- i

2o ~15

= =

~

S o 8 _-

o-

,,

!!ll@ll~

!i Ii _ i , ~ a ~ a -

~ l l l ~ U o -o

_tl!~ il" , 0

5

10

:

o-

o=

I,¢tlMIIO o7,

5

~,~..

o ~'d.-"

. i ~'J~_~ao ~ ~

°--a95

10

I I

b) Potato CHI

b--1.00

.c 25

sua.se Tc

(y--a + bx)

a"

-o-

J~lrdlr -.--

0

o

a

=,, , ~ m ~ R ~ l

"

s

Surface TC

';,:-o,~7'

|

b=l,00

n=395

,

i

,

15

20

25

Observed

~0~, 30

35

245

for factor. Dividing the values from Eq. (3) (QH deten-nination for the VHI gauges) by a factor of 0.9 (instead of the 0.98, accounting for circuitry power loss) results in improved performance, similar to that of the CHI method. However, the use of such a factor can not be substantiated. Figs. 3-5 also indicate inconsistent and generally small (except for sunflower) differences in performance between the inserted and surface-mounted thermocouples. The CHI gauges overestimated for large flows in sunflower (over 100 g h - l ) with surface-mounted thermocouples. The maize CHI gauge measurements appear to overestimate with flows above 90 g h - l for both thermocouple mountings. These results are similar to those of Ham and Heilman (1990) and Cohen et al. (1993), who also noted the overestimation of sap flow at higher flow rates and attributed part of this error to non-equilibrium conditions between the xylem and stem surface temperatures. Numerical analyses by Baker and

40 250

Flow (g hr ~)

Fig. 4. Comparison of me~isured and observed sap flow rates at 15 min intervals: (a) potato VHI with inserted and surface-mounted thermocouples, and (b) potato CHI with inserted and surfacemounted thermocouples.

I

o 200

I

InsertedTC

I

--.

= 150

j

I

a) SunflowerVHI

=

=

D tla

~--0.,~

=

-

~/-. .."

-

~-..oi~i~9~

o

" 100 Q.

Graphs for potato VHI results (Fig. 4, top) show similar trends, with regression analysis indicating underestimates with the VHI method throughout the range of sap flow rates for both inserted and surface-mounted thermocouples. Potato CHI (Fig. 4, bottom) indicates good agreement with observed flow, similar to the maize CHI results. For sunflower VHI (Fig. 5, top), the surfacemounted thermocouples show excellent agreement with the 1:1 line, whereas the inserted thermocouples show a general tendency to underestimate. The sunflower CHI results (Fig. 5, bottom) show a regression slope and intercept near unity and zero, respectively, in the case of the inserted thermocouples, while surface measurements resulted in overestimates at high flows. The results in Figs. 3-5 show that gauge performance was better for CHI heating for all three plant species. The systematic underestimation of the VHI gauges suggests the existence of some unaccounted

. , , . ~ .o. = i , l o o

u)

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e

ra=0"95 I

0 -250

I

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o

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InsertedTC

~. 100 (O

.

I

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a

.=Bin 'e °

om , ~ ,.,~a,./~ --

50 ~ l

.

I

b) S u n f l o w e r C H I

(y=a + bx) a= -2.22 b='0.99 n=215

200

+~x)'SurfaceTC ....

~y=, a: -5.53

Surface TC

( ~- a + b x )

I

"a= -4.27" b=1.17 n=21S

imu,~'~ -

r~=o.~

O~p ,-_

0

,

I

I

I

50

100

150

200

Observed

250

Flow (g hr "1)

Fig. 5. Comparison of measured and observed sap flow rates at 15 min intervals: (a) sunflower VIII with inserted and surfacemounted thermocouples, and (b) sunflower CFII with inserted and surface- mounted thermocouples.

J.F. Kjelgaard et al. / Agricultural and Forest Meteorology 85 (1997) 239-250

246

Nieber (1989) and Ishida et al. (1991) also suggest the existence of these conditions at higher sap flows. Simulations by Ishida et al. (1991) showed that the sap flow error was significantly reduced by inserting the thermocouples into the stem. Our results with sunflower CHI suggests that inserted thermocouples may perform better at higher flow rates. To examine the effects of thermocouple placement with heat balance gauges, several studies have been conducted, mostly on trees. Weibel and de Vos (1994) found that the optimum placement of thermocouples was just under the bark. Khan and Ong (1995) also found that inserted thermocouples reduced errors in sap flow. In the case of sunflower VHI, the overestimation of flow served to improve the regression analysis for the surface-mounted thermocouples. Ham and Heilman (1990) recommended

increasing the heater width to help correct sap flow overestimation. They found that when the heater width to stem diameter ratios were small (approximately 0.6), the sap flow was more likely to be overestimated at high flow rates. Based on a limited number of trials, the overestimates were minimized with a heater width to stem diameter ratio of 1.2. In our experiments, the ratios were varied between 1.2 and 1.0. No consistent differences in the performance of monocots or dicots were noted in the results. Zhang and Kirkham (1995) found that the accuracy of the CHI gauge was more dependent on the sap flow rate than the differences in the anatomy of the stems of monocots and dicots. Table 1 shows a statistical analysis of the gauge performance results for 15 min intervals. In general, for the different plant species, heat input methods,

Table 1 Average sap flow rates, RMSE, relative RMSE and RAE for VIII and CHI sap flow gauges and inserted and surface-mounted thermocouples (TC), compared with plant water losses determined by lysimetry (observed). Analysis is for 15 min interval data between 6:00 and 20:00) SDT. Crop

Heat inputs No. of observations Location of TC

Average f l o w / ( g h - l )

Maize

VHI VHI Observed CHI CI-I/ Observed

41.6 40.9 42.9 43.4 43.1 44.1

8.0 9.2

18.6 21.4

35.6 39.5

7.6 7.4

17.2 16.8

29.6 29.3

13.9 13.5 16.1 13.4 13.5 14.3

3.3 3.6

20.5 22.4

19.0 22.0

2.9 2.5

20.4 17.6

26.2 24.4

62.2 65.7 69.8 63.6 73.5 66.7

12.9 12.9

18.5 18.5

33.9 35.7

11.0 17.4

16.5 26.0

55.9 66.2

Potato

Sunflower

Combined data

R M S E / ( g h - 1) Relative RMSE (%)

RAE

725

Inserted Surface

284

Inserted Surface

VHI VHI Observed CHI CHI Observed

283

Inserted Surface

394

Inserted Surface

VHI VHI Observed CHI CHI Observed

392

Inserted Surface

211

Inserted Surface

1400

Inserted

41.9

9.1

20.1

31.8

Surface

42.5 45.2 45.9 46.3 46.3

9.6

21.2

34.8

7.1 9.6

15.3 20.7

34.3 35.9

VHI VHI Observed CHI CHI Observed

889

Inserted Surface

Note: Slight differences between the numbers of observations in Table 1 and the regression analysis in Fig. 3 - 5 are due to the calculation of the RAE, which excludes observed flows equal to zero.

J.F. Kjelgaard et al. /Agricultural and Forest Meteorology 85 (1997) 239-250

247

Table 2 Relative absolute error (RAE) of sap flow measurements compared with plant water losses determined by lysimetry at selected flow rates. Analysis is for 15 rain interval data between 6:00 to 20:00 SDT. The numbers of observations are shown in square brackets Crop

Heat inputs

Location of TC

Maize

VHI VHI

Inserted Surface

CH/ CHI

Inserted Surface

VIII VHI

Inserted Surface

CHI CHI

Inserted Surface

VHI VHI

Inserted Surface

CHI CHI

Inserted Surface

Potato

Sunflower

RAE (%) at flow rates/(g h - l ): All

> 10

> 20

> 30

> 40

35.6 39.5 [725] 29.6 29.3 [284]

18.0 19.1 [573] 15.9 15.7 [233]

14.4 15.6 [490] 13.0 12.6 [210]

12.1 13.1 [417] 11.0 10.5 [180]

10.2 11.4 [351] 10.5 9.9 [152]

19.0 22.0 [283] 26.2 24.4 [394]

15.0 16.8 [202] 12.6 10.7 [224]

14.8 15.8 [97] 12.0 9.5 [ 118]

20.9 20.9 [13] t 1.3 9.1 [31 ]

33.9 35.7 [392] 55.9 66.2 [211]

17.4 17.8 [343] 21.6 26.1 [168]

15.3 15.9 [312] 14.9 19.8 [144]

14.1 14.7 [284] 11.9 17.1 [125]

13.6 13.9 [255] 9.4 15.2 [111]

Table 3 Average sap flow rates, RMSE, relative RMSE, and RAE for VHI and CHI sap flow gauges, and inserted and surface thermocouples (TC), compared with plant water losses determined by lysimetry (observed). Analysis is for daily integrated measurements Crop

Heat inputs

No. of observations

Location of TC

Average f l o w / (g day- l )

Maize

VHI VHI Observed CHI CHI Observed

13

Inserted Surface

6

Inserted Surface

590.3 579.8 608.7 514.6 511.0 521.8

VIII VIII Observed CHI CI-I/ Observed

5

Inserted Surface

7

Inserted Surface

VIII VHI

7

Potato

Sunflower

Observed CI-I/ CHI Observed Combined data

VIII VIII Observed CHI CHI Observed

Relative RMSE (%)

RAE (%)

62.3 78.8

10.2 12.9

10.8 11.7

40.1 31.0

7.7 5.9

7.1 5.6

197.5 192.2 228 188.3 191.3 201.4

36.3 40.2

16.0 17.6

12.6 15.3

21,3 15,8

10.6 7.8

10.9 8.4

Inserted Surface

886.8 936.3

124,2 111.2

12.5 11.2

10.5 9.2

4

Inserted Surface

994.1 854.1 988.3 896.4

54.0 127.9

6.0 14.3

11.5 17.6

25

Inserted Surface

75.4 84.9

12.5 14.0

11.1 12.1

17

Inserted Surface

37.9 65.5

7.9 13.7

9.7 9.6

565.1 563.8 605.6 460.6 491.7 478.0

RMSE/ (g day - 1)

248

J.F. Kjelgaard et al. / Agricultural and Forest Meteorology 85 (1997) 239-250

and thermocouple placements, the average flows were approximately equal to the corresponding lysimetermeasured flows. The root mean square error (RMSE) ranged from 2.5 to 17.4 g h - 1 , representing 17.226% of the average observed water losses. The relative absolute error (RAE) ranged from 19% to 66.2%. Overall, when comparing the results of measurements with inserted and surface-mounted thermocouples, the differences in performance were small and inconsistent. An exception was the case of sunflower CHI, where inserted thermocouples substantially outperformed surface-mounted thermocouples. In general, the CHI method tended to outperform VHI. Irrespective of the heating method or thermocouple placement, the RAE values for all crops appear high, prompting further analysis to determine the source of the error. Table 2 shows the RAE for sap flow measurements at selected flow rates, obtained by arbitrarily excluding the lowest flow rates. It is apparent that as the lower flow rates were discarded, the accuracy of the stem flow gauge increased. However, the most significant changes occurred when flow rates of less than l0 g h -1 were excluded, with the RAE decreasing 13 to 20% for maize, 4 to 13% for potato, and 16 to 40% for sunflower. Excluding the lowest flow rates after this arbitrary cut-off point improved the gauge accuracy even further (with the exception of the potato VHI results), but the rate of improvement slowed considerably. Zhang and Kirkham (1995) noted similar trends, with improvements in gauge performance when sap flows were greater than 20 g h - 1 . However, the largest sap flows they measured were approximately 65 g h - 1. The large error associated with low flow rate periods may arise from several sources, including the neglect of the stem heat storage component from the original heat balance equation (Groot and King, 1992; Grimes et al., 1995a). The effect of neglecting stem heat storage is diminished with plants of smaller diameters (Grimes et al., 1995a), which may explain the lower RAE seen with potatoes when sap flows of less than 10 g h -1 were included (Table 1). Another source of error could be the assumption of zero sap flow when determining the radial conductance of the gauge (Eq. (6)). This experiment assumed zero-flow between the early morning hours of 2 and 4 a.m., although at times the lysimeter indicated the occurrence of gravi-

1000 0

900 800 700

~o

,'T" (z u)

I Inserted TC

i a) l ~ I z o V H I I

'

'Z:

(y-.-a + bx)

.,~..--

8=27.4 b=0.92 n=13 r2--0.9o

~..'~. "0 p~.:: :6"" n ~.:::-'U

~ ' "

600

-

[]

=:-

500

~"

400 300 200 1000 900

J

~7a.6 b--0._aa n=13

o J"O " --j-" ,,.," I

I

,~---o.~ I

I I 0 InsertedTC (y=a + bx) a= -55.9

I

I

I

I

I I b) Maize CHI

I

I

I ." .:'~ .

.~

800 ~.~

700

r2_-0.97

600 u.

co

500

400

~

rl SurfaceTC (~-.a. bx) a= -28.8

.~,~,," ~

~o~

.::' 200 ¢,";" I 200 300

n=6

I 400

I 500

I 600

I 700

I 800

I 900

1000

Observed Flow (g day"1)

Fig. 6. Comparison of measured and observed sap flow rates for daily integrated sap flow from 15 rain interval data: (a) maize VIII with inserted and surface-mounted thermocouples, and (b) maize CHI with inserted and surface-mounted thermocouples.

metric weight losses of 1-4 g h -1. No correction for this "night" flow was made. Also, the use of one thermocouple (as opposed to a thermopile) to monitor radial losses may add to the error during low-flow periods, when this component is a more significant fraction of the heat balance, particularly for the CHI gauges. However, care was taken to ensure the application of uniform insulation and shielding of the gauges to minimize the effects of solar radiation (Groot and King, 1992; Gutierrez et al., 1994). Finally, the form of Eq. (9) results in potentially large errors at low flow rates even when the differences between observed and measured sap flow rates are small. The performance of the gauges improved when dally flow rates were analyzed. Fig. 6 shows an example plot of daily integrated sap flow versus water loss determined by the lysimeter. The data for maize are shown because the VHI and CHI systems were run on a larger number of days. The VHI results show a tendency to underestimate at higher

J.F. Kjelgaard et al. /Agricultural and Forest Meteorology 85 (1997) 239-250

daily flows, the surface-mounted thermocouples showing greater departures from the 1:1 line (solid line). The maize CHI results are very good, and mimic the trends seen with the 15 min interval data. Dally flow results of potato and sunflowers also exhibited trends similar in nature to the 15 min interval plots (Figs, 4. and 5). Table 3 presents a statistical analysis o f the results of daily integrated sap flows compared with water losses determined by lysimetry. The performance o f the gauge appeared to be independent o f crop, whether monocot (raaize) or dicot (sunflower or potato). The overall trends were similar to those found in Table 1, but the magnitudes of the relative R M S E and the R A E were significantly lower. For potatoes, the daily R A E ranged from 8.4 to 15.3%, for maize 5.6 to 11.7%, and for sunflower 9.2 to 17.6%. Except for CHI sunflower, the inserted thermocouples showed no distinct or consistent advantage compared with the surface-mounted thermocoupies. The CHI outperformed the VHI method, except for sunflower and surface-mounted thermocouples.

5. Conclusions VHI gauges showed systematic underestimation of sap flow, particularly at the higher observed sap flow rates. Better performance was obtained with CHI gauges, especially for daily periods. In addition, CHI gauges were easier to maintain and monitor, requiring fewer input channels on the electronic data logger than the VHI gauges. No consistent differences were found in the performance o f the inserted and surface-mounted thermocouples, except with the largest sap flows (up to 200 g h - l ) , where inserted thermocouples gave better results for the CHI gauges. Further research is required to determine whether inserted thermocouples should be recommended for large flows. Overall, the errors observed for the 15 min interval measurements were large, with the R A E in the range 1 9 - 6 6 % for the individual plant species, and 3 1 . 8 - 3 6 % for the combined data. A t low flow rates important differences were observed between the sap flows determined by the gauges and plant water losses observed by lysimetry. W h e n flows of less than 10 g h -1 were excluded from the analyses for

249

each gauge and plant species, the R A E improved dramatically, ranging between 11 and 26%. Gauge performance improved substantially for daily integrated flows. The R A E ranged from 5.6 to 17.6% for the different plant types, with approximately onethird of dally integrated measurements having an R A E below 10%. For the combined data, the R A E ranged from 9.6 to 12.1%.

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Ham, J.M. and Heilman, J.L., 1990. Dynamics of a heat balance stem flow gauge during high flow. Agron. J., 82: 147-152. Ham, J.M. and Heilman, J.L., 1990b. Measurement of mass flow rate of sap in Ligustrumjaponicum. HortScience, 25: 465-467. Ishida, T., Campbell, G.S. and Calissendorff, C., 1991. Improved heat balance method for determining sap flow rate. Agric. For. Meteorol., 56: 35-48. Khan, A.A.H. and Ong, C.K., 1995. Correction of systematic errors in estimates of transpiration obtained using a constant temperature heat balance technique. Expl. Agric., 31: 461-472. Lascano, R.J., Baumhardt, R.L. and Lipe, W.N., 1992. Measurement of water flow in young grapevines using the stem heat balance method. Am. J. Enol. Viticul., 43: 159-165. Sakuratani, T., 1981. A heat balance method for measuring water flux in the stem of intact plants. J. Agric. Meteorol. (Jpn.), 37: 9-17. Sakuratani, T., 1984. Improvement of the probe for measuring water flow rate in intact plants with the stem heat balance method. J. Agric. Meteorol. (Jpn.), 40: 273-277.

Senock, R.S. and Ham, J.M., 1993. Heat balance sap flow gauge for small diameter stems. Plant Cell Environ., 16: 593-601. Shackel, K.A., Johnson, R.C., Medawar, C.K. and Phene, C.J., 1992. Substantial errors in estimates of sap flow using the heat balance technique on woody stems under field conditions. J. Am. Soc. Hort. Sci., 117: 351-356. Steinberg, S., van Bavel, C.H.M. and McFarland, M.J., 1989. A gauge to measure mass flow rate of sap in stems and trunks of woody plants. J. Am. Soc. Hortic. Sci., 114: 466-472. Weibel, F.-P. and Boersma, K., 1995. An improved stem heat balance method using analog heat control. Agric. For. Meteorol., 75: 191-208. Weibel, F.-P. and de Vos, J.A., 1994. Transpiration measurements on apple trees with an improved stem heat balance method. Plant Soil, 166: 203-219. Zhang, J. and Kirkham, M.B., 1995. Sap flow in a dicotyledon (sunflower) and a monocotyledon (sorghum) by the heat-balance method. Agron. J., 87: 1106-1114.