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Determination of stomatal conductance by means of infrared thermography
Infrared Physics & Technology 46 (2005) 429–439 www.elsevier.com/locate/infrared
Determination of stomatal conductance by means of infrared thermography P. Bajons b
a,*
, G. Klinger b, V. Schlosser
a
a Department of Material Physics, University of Vienna, Strudlhofgasse 4, A-1090 Vienna, Austria Department of Meteorology and Geophysics, University of Vienna, Althanstrasse 14, A-1090 Vienna, Austria
Received 22 December 2003
Abstract The leaf energy balance equation is extended to obtain the boundary layer resistances to heat transfer and the stomatal resistance, the stomatal conductance respectively, of leaves in vivo. Calculations are based on the determination of temperature rise and fall times (thermal time constants of leaves in different states) which are caused by a sudden change of irradiation intensity. The change in the irradiation was performed by turning on/off a laser diode (675 nm). To measure the temperature and its changes without direct contact with the leaves, a commercial IR-imaging system (thermo-camera) was employed. Experiments were made on ivy leaves under laboratory conditions. The advantages and the applicability of the new method are demonstrated and experienced experimental difficulties are discussed. 2004 Elsevier B.V. All rights reserved. PACS: 87.63.Hg; 44.20.+b; 87.10.+e; 06.60.Mr Keywords: Active thermography; Boundary layer resistance; Plants and leaves
1. Introduction Passive infrared thermography has been widely used in industrial test procedures and engineering as a non-destructive method for the detection of heat transfers, heat losses, hot spots or temperature distributions. In recent years this basic method has *
Corresponding author. Tel.: +43 1 4277 51359; fax: +43 1 4277 9513. E-mail address: [email protected] (P. Bajons).
expanded by the development of active methods such as the application of additional heat fluxes to the sample surface or the generation of additional heat pulses within the material followed by the measurement and analysis of the resulting surface temperature changes. Applications span from large area investigations such as buildings [1] to small scale studies as for example the determination of functional or structural defects of electronic devices or of solid materials [2]. While these investigations are centered on non-biotic
1350-4495/$ - see front matter 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.infrared.2004.09.001
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substances, studies on living bodies such as plants are performed mostly by using passive [3–9] and frequently by using active [10] thermographic methods. Stomatal activity is one of the vital mechanisms which regulates the thermal interaction of a plant with its environment [3,4]. Though affected by meteorological circumstances this activity is manifested through the rate of heat transfer and the resulting leaf temperature. At equilibrium the rate of radiation energy absorbed by a body equals the energy losses by re-radiation, the sensible heat exchange between the body and the surrounding air and the heat energy stored in the body. For living biological substances additional heat losses due to evapo-transpiration have to be taken into account. The width of the aperture of the stomata influences and regulates transpiration and thus the stomatal resistance to evaporation. Its inverse the stomatal conductance respectively, is a leading indicator of related heat transfer. Energy losses due to metabolic processes (necessary for photosynthetic or catabolic reactions) which may take place, are in most situations relatively small and are therefore neglected in the calculations. The solution of the leaf surface energy balance equation relates the temperature with the non-biotic (physical) parameters, i.e. the boundary layer resistance for heat transfer by convection and radiation and the boundary layer resistance to water vapor, as well as with the biological parameter, i.e. the actual stomatal resistance. For the quantitative determination of the stomatal resistance additional measurements to calculate (eliminate respectively) the physical parameters are necessary. Reported approaches [8,9] measure simultaneously the temperature of a similar non-biotic surface, usually a micro-porous membrane (‘‘reference leaf’’), where the resistance to heat transfer is known. Additionally, the temperature difference between the leaf in vivo and a wetted leaf and the difference with the leaf in vivo and a leaf with closed stomata (‘‘dry leaves’’) have to be measured. While these experiments are passive thermographic approaches, in the present study active thermography is the method used for the determination of boundary layer resistances and of stomatal resistance. Here temperature changes due to the action of defined light
pulses are studied. Based on an extension of the above mentioned theory of energy balance the evaluation of the data is performed by considering temperature rise and fall times (thermal time constants) caused by a sudden change of irradiation intensity.
2. Theory Although the interaction between leaves and their environment can be extremely complex, a simplified approach that serves to introduce basic concepts in single leaf energy budgets and thus serves to explain leaf surface temperature changes is now fairly well established [3,4,9]. This approach starts with the assumption that—due to the principle of the conservation of energy—the rate of radiation energy absorbed by a leaf equals the heat energy stored in tissues (S) as well as the energy losses by re-radiation, by sensible heat exchange between the leaf and the surrounding air (C), by conductive heat exchange, by transpiration (kE, where E is the transpiration rate and k is the latent heat of vaporization) and by metabolic processes necessary for photosynthetic or catabolic reactions. For leaves the conduction term is negligible. Further for most situations in nature the metabolic term is relatively small and thus also can be neglected. This allows to write the leaf surface energy balance equation as U ¼ S þ C þ kE
ð1Þ
where U is the net heat gain from radiation (absorbed radiation minus re-radiation). With respect to unit surface area of the leaf and based on the concept [3,4] of isothermal net radiation (the net radiation that would be received by an equivalent surface at air temperature, Rni) Eq. (1) can be rewritten as S ¼ Rni qa ca ðT l T a Þ=rR qa ca ðT l T a Þ=raH ð0:622qa k=pÞðes ea Þ=ðraw þ rs Þ ð2Þ where qa is the density of air, ca is the specific heat of air, Tl is the actual leaf temperature, Ta is the air temperature, p is the atmospheric pressure, es is the saturated vapor pressure at leaf temperature, ea is the vapor pressure of ambient air, rR is the ÔresistanceÕ to radiative heat transfer, raH is the mean leaf
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boundary layer resistance to heat, raw is the mean leaf boundary layer resistance to water vapor and rs is the mean stomatal resistance to water vapor (more precise: mean leaf resistance to water vapor which in the given study is assumed to be dominated by the stomatal resistance). When either one of the components of the energy balance changes then the temperature of the leaf is also changed. The rate of this temperature change depends on the heat capacity per unit area of the tissue and it was shown [4] that the following approximation can be applied ð3Þ
with 1=rHR ¼ 1=rR þ 1=raH
ð4Þ
where t is the time, ql is the density of leaf tissue, cl is the specific heat capacity of leaf tissue, d is the leaf thickness (volume to area ratio), Tend is the equilibrium temperature attained in the steady state and ea is the ratio of the increase of latent heat content to increase of sensible heat content of saturated air. In the case of an instantaneous change in the incident radiation the solution of the differential equation will be T l ¼ T end DT expðt=sÞ
ð5Þ
with
ð8Þ
Rearrangement of Eq. (7) 1=rHR ¼ ðql cl d=qa ca Þ=sdry
ð9Þ
and combination with Eq. (8) will lead to 1=raw ¼ ðql cl d=qa ca Þðsdry swet Þ=ðea sdry swet Þ
ð10Þ
Similarly rearrangement of Eq. (7) and combination with Eq. (6) leads to an expression for (raw + rs). Substitution of the term raw (as defined in Eq. (10)) finally gives
swet =ðsdry swet ÞÞ
ð11Þ
While the above calculations were based on the assumption that the leaves are amphistomatous, for hypostomatous leaves the calculations are slightly different. Now evapo-transpiration takes place on only one side of the leave and thus with respect to unit surface area of the leaf the respective term in Eq. (2) is half as large. This changes Eq. (6) according to sleaf ¼ ðql cl d=qa ca Þ=ð1=rHR þ ea =ð2ðraw þ rs ÞÞÞ ð6aÞ Eqs. (7)–(10) remain unchanged when the leave is still wetted on both sides and thus Eq. (11) finally changes to rs ¼ ðea qa ca =ql cl dÞsdry ðsleaf =ð2ðsdry sleaf ÞÞ
s ¼ sleaf ¼ ðql cl d=qa ca Þ=ð1=rHR þ ea =ðraw þ rs ÞÞ
swet =ðsdry swet ÞÞ ð6Þ
where sleaf is the thermal time constant of the leaf responding to this change. For the same leaf in the dry state or for a dry surface with the same aerodynamic properties as the leaf under observation the mean stomatal conductance, i.e. the inverse of the mean stomatal resistance rs, will be equal to zero. This gives a thermal time constant (sdry) according to sdry ¼ ðql cl d=qa ca Þ=ð1=rHR Þ
swet ¼ ðql cl d=qa ca Þ=ð1=rHR þ ea =raw Þ
rs ¼ ðea qa ca =ql cl dÞsdry ðsleaf =ðsdry sleaf Þ
dT 1 =dt ¼ S=ðql cl dÞ ¼ qa ca ðT end T l Þ ð1=rHR þ ea =ðraw þ rs ÞÞ=ðql cl dÞ
431
ð7Þ
On the other hand, for a corresponding wet surface the mean stomatal resistance will equal zero and thus a thermal time constant (qwet) will be obtained according to
ð11aÞ
Summarizing it may be stated that the stomatal and the boundary layer resistances are now given as functions of the thermal time constants of the leaf in its different states. The resistance values may now be deduced from the measurement and the analysis of thermal rise and decay behavior. 3. Experiment The experiments were performed under laboratory conditions, i.e. the temperature and the humidity of the air was controlled and monitored and air movements were restricted (no wind conditions).
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The temperature distribution on the leave surfaces was measured by a thermo-camera AGEMA-570 (focal plane array with 320 pixel · 240 pixel, spectral range: 7.5–13 lm). The nominal temperature resolution of the IR—camera is 0.1 K. By means of a close up lens a spatial resolution as low as 0.1 mm is possible. The camera was operated remote controlled. The software to communicate with the camera is based on LabVIEW and was developed at the Institute. The value of each image pixel either could be exported in the as given state (followed by an algorithm to transfer it to temperature data) or could be exported directly as temperature values by using the internal conversion of the camera. The internal software requires to take a priori into account the object emissivity (which was set to 0.97 in the experiments—a mean value of green leaf long wave infrared emissivity [11,12]), the object distance, the ambient temperature and the relative humidity of the air. The repetition rate of image generation and collection was approximately 1.33 s when a single pixel was exported and increased when predefined areas, or the whole image respectively, were exported. Measurements of leaf temperature changes were made in the dark and under illumination. The intensity of light was regulated by using different lamps at changing distance from the tested leaves and was measured (before or after the test) in the plane of the leaves by means of a photometer (photodiode) and/or a star pyranometer. To measure the thermal time constants the leaves were additionally illuminated by turning on and off a red monochromatic light source (InGaAIP/GaAS multimode laser diode Type RTL 67100G [16]: 675 nm, rectangular radiation characteristic, 55 mW peak irradiation), which acts in the range of maximum chlorophyll absorption and—as will be discussed later in this publication—did not significantly influence the actual opening of the stomata. In all the experiments performed within the scope of this study the leaf to air temperature difference resulting from the combined action of the laser and the lamp was kept within 3–7 K, while the leaf temperature increase which only resulted from the illumination of the laser was kept in the range of 1–3 K.
Leaves of ivy (Rhaphidophora) were studied. This kind of leaves was chosen because of its simple geometry and fairly flat surface topography. When transported into the laboratory leaf temperature changes were measured continuously and by this the plant could be given appropriate time to accommodate to the test conditions. To obtain wetted surfaces water containing a wetting agent (washing up liquid) was sprayed upon the leaf in first experiments. However, in the present study a hand held highly diffusing sprayer containing pure water was used when thermal time constants (swet) were measured. This raised the effort in measuring the time constant considerably, but on the other hand this procedure had the advantage that destruction of the wetted leaves could be avoided. Dry surfaces were obtained by covering the leaf with a thin coating of petroleum jelly (Vaseline). To measure the leaf thickness the leaves, part of the leaves respectively, were put between two glass plates. By means of a micrometer the leaf thickness between larger veins (=d according to the nomenclature used in the previous chapter) was then determined.
4. Results 4.1. Images The thermal behavior of ivy leaves was tested over a period of several months. Within this period several plants with different age and leaf size were studied. Fig. 1 shows a part of the abaxial surface of an ivy leaf giving information on the cell structure and thus on the surface waviness in a microscopic scale. Three elliptically shaped stomata are embedded. Thus also information is given on the length and the distribution of the stomata which allows to estimate its density. A typical example for the visualization of temperature distributions on an ivy plant is shown in Fig. 2. The color scale is chosen such that the temperature range between the minimum temperature (background temperature Tmin = 298 K) and the maximum temperature on the leaves of the plant (Tmaxleaf = 303 K) is covered. The plant was illuminated by a lamp. Additionally a leaf (on the right
P. Bajons et al. / Infrared Physics & Technology 46 (2005) 429–439
Fig. 1. Microscopic image of the abaxial surface of an ivy leaf.
433
physiological processes are in most cases the aim of related studies. However, besides such physiological reasons, the temperature distributions are also strongly influenced by physical conditions—a well known fact which is usually treated theoretically in applications of non-biotic heat exchanging bodies and sometimes for artificial model leaves [3,13]. In the shown example the thickness of the boundary layer which strongly influences the heat loss from the leaf surface to the surrounding medium, decreases—at least in principle—from the center to the edges of the leaf. This results in temperatures lower at the edges than in the middle of the leaf. Further, the topography of the leaf surface is not a flat plane, i.e. the leaf is vaulted. Therefore the angle of light incidence varies upon its surface which results in a locally varying amount of absorbed radiation energy leading to locally varying temperature increase. This effect of illumination geometry may be noticed even more pronounced when looking at the laser induced hot area. 4.2. Determination of thermal time constants
Fig. 2. False color thermal infrared image of the leaves of an ivy plant illuminated by the lamp. The vertical hot area bar visible on the right front leaf is caused by the additional illumination with a rectangular emitting red laser diode.
hand side in front of Fig. 2) was partly illuminated by the red laser light. The laser created in the plane of the leaf an illumination rectangle of 12 mm width and 50 mm height. This radiation caused on the leaf surface a vertical hot area bar which is clearly detectable against the background. Looking first on the parts of the plant which were not hit by the laser light it may be recognized that the leaf surface temperatures are not uniform. For example the vein structure and different absorption behavior of the tissue becomes visible. The detection and interpretation of the underlying
The uncertainties in the determination of a ÔtrueÕ leaf temperature strengthen the necessity of time resolved temperature measurements. Especially the measurement of the thermal time constants which can be determined independently from the magnitude of the change of the temperature level, makes one independent on locally varying incident radiation intensity. Figs. 3 and 4 gives information on the temporal development of the leaf surface temperature which is obtained by a sudden turn on, turn off respectively, of the laser. It represents the mean of an area consisting of 12 pixels, which are located in the center of the hot area. As the observed thermal behavior is typical for the ivy leaves tested in this study, these figures may serve for the demonstration of the applicability of the proposed method as well as a basis for the discussion of associated problems. Room temperature and also the temperature of the leaves in the dark were 298 K. Turning on the laser raised the temperature by approximately 2.5 degrees and turning off the laser lowered the temperature again to the former level (lower curve in Fig. 3).
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304
Temperature [K]
302
300
298
296 0
200
400
600
Time [s]
Fig. 3. Temporal development of the leaf surface temperature in the center of the hot area due to a sudden turn on, turn off respectively, of the laser. The lower curve is obtained under dark room conditions (thermal rise time constant 43.3 s), the upper curve by illumination of the plant with the lamp (thermal time constant 34.5 s).
Illumination of the plant with a lamp increased the temperature of the leaf to approximately 301 K, while the combined action of the lamp and the laser raised the temperature well above 303 K (upper curve in Fig. 3). In both examples the moment of the laser turn on and the laser turn off is clearly detectable. After spraying water on the leaf the temperature was lowered considerably. Under dark room conditions the temperature of the leaf fell to approximately 291.5 K, while—when illuminated by the laser—the temperature was approximately 293 K. This can be seen from Fig. 4 where after stabilization of the leaf temperature at 292.8 K, i.e. after 54 s, the laser was turned off. Giving the leaves sufficient time to dry the leaf under consideration was coated with Vaseline. After stabilization of the temperature the leaf was again subjected to the laser action and a behavior of the leaf similar as shown in Fig. 3 was observed. Data evaluation and thermal time constant determination was performed by the use of commercial software (Grapher, Golden Software). This is shown in Fig. 5 where for example the ther-
294
Laser off
301
293
Temperature [K]
Temperature [K]
300
292
Fit Results Fit 1: ANab Equation Y = A-B*exp(-X/t) A = 300.6813464 B = 2.559141214 t = 43.34197891
299
Number of data points used = 112 Average X = 113 Average Y = 300.2 298
Residual sum of squares = 0.338159 Coef of determination, R-squared = 0.991978
291 0
50
100
Time [s]
150
200
250
Fig. 4. Hot area surface temperature changes of the wetted leaf obtained under dark room conditions (the time span of cooling down to wet leaf temperature as well as of drying is shaded). During stabilization at wet leaf temperature a further temperature decrease was caused by a sudden turn off (54 s after the start of the measurement cycle) of the laser.
297 0
50
100
Time [s]
150
200
250
Fig. 5. Exponential fit of the temperature rise of the leaf illuminated by the laser under dark room conditions giving a thermal time constant of 43.3 s (measurement data taken from Fig. 3).
P. Bajons et al. / Infrared Physics & Technology 46 (2005) 429–439 293.2
Temperature [K]
Fit Results
292.8
Fit 1: Bi-exponential Equation Y = A-B*exp(-X/u)+C*exp(-X/v) A = 291.603069 B = -0.7370331158 u = 17.61344228 C = 0.7370211746 v = 17.61343796
292.4
Number of data points used = 50 Average X = 51 Average Y = 291.847 Residual sum of squares = 0.170697 Coef of determination, R-squared = 0.970096
292
291.6
291.2 0
20
40
Time [s]
60
80
100
Fig. 6. Bi-exponential fit of the temperature decay of the wet leaf illuminated by the laser under dark room conditions giving a thermal time constant of 17.6 s (measurement data taken from Fig. 4).
mal rise time for the leaf under dark room conditions was calculated as 43.3 s. However, to crosscheck the programÕs ability and to avoid possible errors due to the cameraÕs performance (noise and system drifts) or errors due to hidden physiological long term processes, calculations usually were performed by introducing a bi-exponential term into the calculation procedure. The equation used is given in Fig. 6 in which u and v stand for the time constants. Experimental results in which the values of u and v (and also of B and C) differed were reinvestigated or even eliminated. In Fig. 6 for example where these values practically do not differ, the thermal decay time for the wet leaf was calculated as 17.6 s. 4.3. Determination of stomatal resistance and conductance During the given experiment the air temperature was kept at 298 K. The thickness of the leaf between the stronger veins was measured as d = 0.26 mm. Evaluation of the data of the leaf illuminated by the lamp (Fig. 3) gave a thermal time constant sleaf = 34.5 s. Evaluation of the data of the coated ivy leaves yielded similar results for
435
the time constants as were obtained under dark room conditions and thus for the dry state the value sdry = 43 s was taken. According to Fig. 6 and based on further measurements in case of the wet state the value of swet = 17 s was obtained. For the determination of a mean value of ql cl we followed the arguments given in previous publications [4], i.e. the product of the average leaf density and the average specific heat capacity for leaves was assumed to be qlcl = 2.7 MJ/K m3. Also the tabulated values given in this book were used which resulted in the ratio of the increase of latent heat content to increase of sensible heat content of saturated air ea = 2.82, in the specific heat of air ca = 1010 J/kg K and in the density of air qa = 1.184 kg/m3. Based on Eq. (11a) the stomatal resistance to water vapor was calculated (in the area under consideration) as 284 s/m and its inverse, the stomatal conductance, as 3.5 mm/s. Calculations and results are based on mass units, which are mostly used in the micrometeorological literature. However, for compatibility with much of the physiological literature stomatal conductance will also be given in molar units. Approximate conversion [4,9], i.e. multiplication by 40, gives the stomatal conductance as 140 mmol m2 s1.
5. Discussion From an experimental point of view the accurate measurement of the thermal time constant for leaves in the wet state (swet) is a crucial point, because the time span, during which the heating or the cooling caused by the laser action can be measured accurately, is limited and because the formation of water droplets obscures the results. Similar to the known behavior of the wet-bulb thermometer the leaf—after being wetted with the sprayer—must be given time enough to cool down until the leaf temperature reaches the wetleave temperature. After stabilization at this level the laser can be turned on, turned off respectively, as for example is shown in Fig. 4. Here stabilization was reached after 30 s and the laser was turned off after 54 s. However, data collection necessary for the determination of the time constant must
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be finished before the water film upon the leaf is completely evaporated and warming up of the now dry part of the leaf starts. This is demonstrated in the given example where the temperature again starts to increase after 230 s. In principle, by using water containing a wetting agent the time span for data collection can be lengthened and also the formation of water drops can be minimized. However as this procedure lastly results in the destruction of the leaf under consideration it will not be a good choice for practical applications. Therefore only pure water was used in the experiments. Also the determination of the time constant was usually performed under darkroom condition, because the radiation energy emitted by the lamp enhanced evaporation and droplet formation and thus reduced considerably the accuracy of the results. Less difficult, but still problematic is the determination of the thermal time constant in the dry state (sdry). The coating of the leaf with petroleum jelly (Vaseline) may smooth the surface waviness (which can be seen from the microscopic image given in Fig. 1). A change in the surface roughness may influence the stream of air which flows over the surface. Also the optical properties, like the absorption and transmission of light and the thermal properties of Vaseline differ from the respective properties of the leaf. However, in many cases the stomata of the leaves are closed in the dark and thus the leaves measured under dark light conditions are representative for the dry state. Therefore values obtained on coated leaves illuminated by the lamp were compared to values obtained under dark room conditions. In the given example both values correspond to each other. Finally it may be reminded that besides of the basic problems mentioned above the evaluation of the thermal data is limited by the accuracy of the equipment used. With the given equipment repeated measurements of the rise times and/or the decay times usually yielded a scatter of the values in the range of ±1.5 s. The uncertainties in the determination of dry and wet state thermal time constants make it necessary to find some cross checks. One of these may be based on the fact that the resistances within the boundary layers are not independent of each
other. In still air and in boundary layers with laminar flow these entities depend on molecular diffusion coefficients, while in a fully turbulent boundary layer both heat and water vapor are transported equally efficiently [3,4]. Thus depending on the state of the boundary layer the theoretical value of the quotient (raw/raH) ranges between 0.89 and 1. Because of the fact that the approximations made in this study overestimate the quotient (raw/raH) its real value should be slightly above this range. Multiplication of Eq. (4) with raw as given by Eq. (10) and rearrangement leads to raw =raH ¼ ðea =sdry ea qa ca =ql cl drR Þ=ð1=swet 1=sdry Þ ð12Þ which in the given example gives raw/raH = 1.17, a value which satisfies the expectations. Based on Eq. (10) raw can be calculated which also gives raH. The knowledge of the latter allows to estimate the velocity of the airstream to which the tested leaf surface was exposed. Though this proof is by far less good than the cross check described above, it gives a qualitative hint and thus it may be just mentioned without going deeper into detail (details may be taken from Ref. [4]). In the present example the resistance values were calculated as raw = 135 s/m and raH = 116 s/m. This gives a flow velocity lower than 0.1 m/s, a limit which is in accordance with the experimental conditions. A basic assumption in the determination of the stomatal resistance, the stomatal conductance respectively, is that the action of the red laser light does not change significantly the stomatal aperture. In studies of bean leaves [14] it was shown that the stomatal conductance of leaves irradiated with white light was higher than the conductance of leaves illuminated with red light of the same intensity. Irradiation with blue light leads to even higher (approximately 10 times larger) conductance values. Thus some evidence for the presence of a specific blue radiation absorbing receptor, which activates the guard cells much more than the chloroplast absorption mechanism, is given. Similar results were found in a study [15] on ivy (Hedera helix). Though there is undoubted some influence of red light on stomatal conductance it is shown on bean leaves that the time constants
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Finally, in the context of the laser illumination procedure, it may be stated that illumination of the whole leave or only illumination of a larger part of the leaf, as shown in Fig. 2, did not lead to different results. Once the thermal constants in the wet (swet) and dry (sdry) state are determined the stomatal conductance as a function of varying leaf behavior sleaf may be calculated according to Eq. (11a) and drawn. This is shown in Fig. 7 (large dots), where also the experimental value (cross) was added. To get an impression of the sensitivity and of the error range which in the given example had to be expected, the stomatal conductance with the error in the determination of the thermal time constants of wet and dry surfaces (rounded to ±2 s) was drawn additionally. As can be seen from Fig. 7 in the range of low stomatal conductance the method is more sensitive, i.e. changes of stomatal conductance will result in larger changes of thermal time constants than in the region of higher conductance. Further, when caused by errors in
120
20
80
10
40
-2 -1
Calculated stomatal conductance [mmol m s ]
30
-1
Calculated stomatal conductance [mms ]
for the change in the aperture are in the order of one hour. Similar behavior, at least time constants in the range of several minutes, can be deduced from the data given for the ivy leaves. Thus time constants for unwanted additional stomatal activity can be assumed to be large in comparison to the thermal time constants measured for the leaves. Evaluation of the thermal time constants (Fig. 3) of the leaf illuminated by the lamp shows that the rise and the decay time are the same, while under dark room conditions the rise time is in the order of 43 s and the decay time is in the order of 41 s. These results support the assumption of negligible influence of red laser irradiation. Generally the comparison of rise and decay times was used as a possibility for a cross check in this study. Further confirmation was obtained in case of repeated measurements with varying laser intensity. When the thermal time constants remained the same it was taken as an indication that heat fluxes were not altered neither by stomatal activity nor by changing boundary layer conditions.
437
0
0 24
28
32 36 Leaf time constant [s]
40
44
Fig. 7. Calculated stomatal conductance as a function of varying leaf thermal time constants sleaf (large dots are calculated values and the cross mark is the value of the given experiment). The stomatal conductance assuming an error in the determination of the thermal time constants of the wet and the dry surfaces as large as ±2 s is drawn additionally (small dots).
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the determination of swet and sdry, also smaller absolute stomatal conductance errors can be expected at lower conductance. Performing thermographic studies a broad range of possible leaf shapes and of different environmental circumstances must be considered. Changes of circumstances will result in changes of the leaf boundary layer resistance to heat raH and in the leaf boundary layer resistance to water vapor raw. By this also swet and sdry are changed. Though it is difficult to estimate these leaf resistances accurately the dependence of leaf resistance on windspeed and dimension and their calculation assuming forced as well as free convection is discussed widely in the literature [3–5,8,9]. For laminar forced convection typical resistance values of flat leaves [4] range from raH = 500 s/m (at low windspeed) down to raH = 5 s/m. Table 1 gives estimated dry and wet leaf thermal time constants as a function of different boundary layer resistance to heat raH. The calculations are performed according to Eqs. (7) and (8). They are based on the theoretical value of raw/raH = 0.89, an air temperature of 298 K and a leaf thickness (volume to area ratio) of 0.26 mm. As may be seen decreasing boundary layer resistance leads to lower thermal time constants. A fact that qualitatively might be expected as decreasing boundary layer resistance is caused for example by increasing air circulation. With the given equipment measurements down to values of approximately raH = 20 s/ m make sense. The influence of air temperature on swet and sdry is shown in Table 2. Calculations are performed for 288 K and 308 K, thus spanning a range of 20 K. The leaf thickness which is directly proportional to the time constant, is now assumed to be Table 1 Estimated dry and wet leaf thermal time constants as a function of different boundary layer resistance to heat raH (sample leaf thickness is 0.26 mm) Air temperature [K]
raH [s/m]
sdry [s]
swet [s]
298
5 20 50 100 200
2.9 11 23 39 59
0.7 2.8 6.6 12 23
Table 2 Estimated dry and wet leaf thermal time constants as a function of different boundary layer resistance to heat raH (the leaf thickness is assumed to be 1 mm, which allows estimation of swet and sdry by multiplication with the thickness of the tested leaf) Air temperature [K]
raH [s/m]
sdry [s]
swet [s]
288
5 50 100 200 500
11 89 152 232 341
3.8 35 66 117 215
308
5 50 100 200 500
11 90 148 217 301
1.9 18 34 63 128
1 mm. This allows a quick estimation of swet and sdry from Table 1 just by multiplication with the leaf thickness (in mm). In the present example the resistance value was calculated as raH = 116 s/ m, which is close to raH = 100 s/m. For the latter (Table 1) swet = 12 s and sdry = 39 s, while in case of an air temperature of 288 K the respective values deduced from Table 2 yield swet = 17 s and sdry = 39.5 s and at 308 K swet = 9 s and sdry = 38.5 s. Thus changes of the air temperature of 20 K lead to small changes of sdry, i.e. only one second in the given example, while swet is remarkably influenced when air temperature changes. Summarizing, to determine the aperture of the stomata—for example as a function of different stress situations—there are in principle two possibilities to proceed. Either three leaves with similar properties are selected, i.e. a wet, a dry and the sample leaf are all in one field of view simultaneously, or one leaf is observed sequentially. In the latter case the leaf response should be measured in the darkness first. The wetted leaf response should also be measured in the darkness and corrections due to environmental changes should be made either by estimation or when possible by additional measurement at appropriate time. After application of stress the leaf response should be measured and the stomatal resistance calculated using Eq. (11) for amphistomtous leaves or Eq. (11a) for hypostomatous leaves. Lastly the deci-
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sion which procedure (or a combination of them) is chosen will mainly depend on the need of corrections due to environmental changes as well as on the specifications of the used instruments. 6. Conclusions The capability of infrared thermovision as an innovative method to measure convective heat fluxes over solid bodies has been discussed during the past several years. Studying plant status passive thermographic methods were usually employed. In the present study these methods are extended by taking active thermometry into account. Based on considerations of the heat transfer between the leaves of a plant and its environment the biotic and the non-biotic parameters of the boundary layer resistances are calculated. This affords to determine the thermal time constants of the leaf in the wet state and in the dry state first. Once obtained the activity of the stomata can be followed by measuring the thermal rise and decay behavior of the leaf in vivo, where temperature changes are caused by a sudden change in the illumination of the leaves. The basis of optimal performance is not only given by the knowledge of the underlying thermal mechanisms, but also by the associated experimental handling. On examples it was shown that cross checks are possible which strengthen the reliability of the experimental results. Basically the method is not invasive. This is an advantage compared to the methods usually applied for the determination of stomatal aperture. Though in the present investigation the principle mechanisms were studied, an extension of the method may serve as a basis for the early detection of plant stress or plant disease in the future. Acknowledgment The Senate of the University of Vienna and the Hochschuljubila¨umsstiftung (Contract H-141/ 2000) are acknowledged for supporting the study.
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References [1] H. Wiggenhauser, Active IR-applications in civil engineering, Infrared Phys. Technol. 43 (2002) 233–238. [2] T. Sagakami, S. Kubo, Applications of pulse heating thermography and lock-in thermography to quantitative nondestructive evaluations, Infrared Phys. Technol. 43 (2002) 211–218. [3] J.L. Monteith, M.H. Unsworth, Principles of Environmental Physics, second ed., E. Arnold, London, New York, Melbourne, Auckland, 1992, transferred to digital printing: Butterworth-Heinemann, Oxford, 2001. [4] H.G. Jones, Plants and Microclimate, Cambridge University Press, Cambridge, 1992. [5] G.S. Campbell, J.M. Norman, An Introduction to Environmental Biophysics, second ed. New York, 1998. [6] L. Chaerle, D. Van Der Straeten, Seeing is believing: imaging techniques to monitor plant health, Biochim. Biophys. 1519 (2001) 153–166. [7] L. Chaerle, D. Van Der Straeten, Imaging techniques and the early detection of plant stress, Trends Plant Sci. 5 (2000) 495–501. [8] H.G. Jones, Use of thermography for quantitative studies of spatial and temporal variation of stomatal conductance over leaf surfaces, Plant Cell Environ. 22 (1999) 1043–1055. [9] H.G. Jones, Use of infrared thermometry for estimation of stomatal conductance as a possible aid to irrigation scheduling, Agric. Forest Meteorol. 95 (1999) 139–149. [10] B. Ku¨mmerlen, S. Dauwe, D. Schmundt, U. Schurr, Thermography to measure water relations of plant leaves, in: Handbook of Computer Vision and Applications, in: B. Jahne (Ed.), Systems and Applications, vol. 3, Academic Press, New York, 1999, pp. 763–781. [11] J.R. Ehleringer, Temperature and energy budgets, in: R.W. Pearcy, J.R. Ehleringer, H.A. Mooney, P.W. Rundel (Eds.), Plant Physiological Ecology Field Methods and Instrumentation, Chapman and Hall, London, New York, 1989, pp. 117–135. [12] J.W. Salisbury, D.M. DÕAria, Emissivity of terrestrial materials in the 8–14 lm atmospheric window, Remote Sens. Environ. 42 (1992) 83–106. [13] A. Roth Nebelsick, Computer-based analysis of steadystate and transient heat transfer of small-sized leaves by free and mixed convection, Plant Cell Environ. 24 (2001) 631–640. [14] S. Maleszewski, E. Burchacka, M. Rakus, B. KoslowskaSzerenos, Stomatal response of bean leaves to changing irradiance air humidity and water potential of root medium, Photosynthetica 37 (1999) 39–46. [15] P.E. Karlsson, S.M. Assmann, Rapid and specific modulation of stomatal conductance by blue light in ivy, Plant. Physiol. 94 (1990) 440–447. [16] Roithner-Lasertechnik, http://www.roithner-laser.com.
Determination of stomatal conductance by means of infrared thermography P. Bajons b
a,*
, G. Klinger b, V. Schlosser
a
a Department of Material Physics, University of Vienna, Strudlhofgasse 4, A-1090 Vienna, Austria Department of Meteorology and Geophysics, University of Vienna, Althanstrasse 14, A-1090 Vienna, Austria
Received 22 December 2003
Abstract The leaf energy balance equation is extended to obtain the boundary layer resistances to heat transfer and the stomatal resistance, the stomatal conductance respectively, of leaves in vivo. Calculations are based on the determination of temperature rise and fall times (thermal time constants of leaves in different states) which are caused by a sudden change of irradiation intensity. The change in the irradiation was performed by turning on/off a laser diode (675 nm). To measure the temperature and its changes without direct contact with the leaves, a commercial IR-imaging system (thermo-camera) was employed. Experiments were made on ivy leaves under laboratory conditions. The advantages and the applicability of the new method are demonstrated and experienced experimental difficulties are discussed. 2004 Elsevier B.V. All rights reserved. PACS: 87.63.Hg; 44.20.+b; 87.10.+e; 06.60.Mr Keywords: Active thermography; Boundary layer resistance; Plants and leaves
1. Introduction Passive infrared thermography has been widely used in industrial test procedures and engineering as a non-destructive method for the detection of heat transfers, heat losses, hot spots or temperature distributions. In recent years this basic method has *
Corresponding author. Tel.: +43 1 4277 51359; fax: +43 1 4277 9513. E-mail address: [email protected] (P. Bajons).
expanded by the development of active methods such as the application of additional heat fluxes to the sample surface or the generation of additional heat pulses within the material followed by the measurement and analysis of the resulting surface temperature changes. Applications span from large area investigations such as buildings [1] to small scale studies as for example the determination of functional or structural defects of electronic devices or of solid materials [2]. While these investigations are centered on non-biotic
1350-4495/$ - see front matter 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.infrared.2004.09.001
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substances, studies on living bodies such as plants are performed mostly by using passive [3–9] and frequently by using active [10] thermographic methods. Stomatal activity is one of the vital mechanisms which regulates the thermal interaction of a plant with its environment [3,4]. Though affected by meteorological circumstances this activity is manifested through the rate of heat transfer and the resulting leaf temperature. At equilibrium the rate of radiation energy absorbed by a body equals the energy losses by re-radiation, the sensible heat exchange between the body and the surrounding air and the heat energy stored in the body. For living biological substances additional heat losses due to evapo-transpiration have to be taken into account. The width of the aperture of the stomata influences and regulates transpiration and thus the stomatal resistance to evaporation. Its inverse the stomatal conductance respectively, is a leading indicator of related heat transfer. Energy losses due to metabolic processes (necessary for photosynthetic or catabolic reactions) which may take place, are in most situations relatively small and are therefore neglected in the calculations. The solution of the leaf surface energy balance equation relates the temperature with the non-biotic (physical) parameters, i.e. the boundary layer resistance for heat transfer by convection and radiation and the boundary layer resistance to water vapor, as well as with the biological parameter, i.e. the actual stomatal resistance. For the quantitative determination of the stomatal resistance additional measurements to calculate (eliminate respectively) the physical parameters are necessary. Reported approaches [8,9] measure simultaneously the temperature of a similar non-biotic surface, usually a micro-porous membrane (‘‘reference leaf’’), where the resistance to heat transfer is known. Additionally, the temperature difference between the leaf in vivo and a wetted leaf and the difference with the leaf in vivo and a leaf with closed stomata (‘‘dry leaves’’) have to be measured. While these experiments are passive thermographic approaches, in the present study active thermography is the method used for the determination of boundary layer resistances and of stomatal resistance. Here temperature changes due to the action of defined light
pulses are studied. Based on an extension of the above mentioned theory of energy balance the evaluation of the data is performed by considering temperature rise and fall times (thermal time constants) caused by a sudden change of irradiation intensity.
2. Theory Although the interaction between leaves and their environment can be extremely complex, a simplified approach that serves to introduce basic concepts in single leaf energy budgets and thus serves to explain leaf surface temperature changes is now fairly well established [3,4,9]. This approach starts with the assumption that—due to the principle of the conservation of energy—the rate of radiation energy absorbed by a leaf equals the heat energy stored in tissues (S) as well as the energy losses by re-radiation, by sensible heat exchange between the leaf and the surrounding air (C), by conductive heat exchange, by transpiration (kE, where E is the transpiration rate and k is the latent heat of vaporization) and by metabolic processes necessary for photosynthetic or catabolic reactions. For leaves the conduction term is negligible. Further for most situations in nature the metabolic term is relatively small and thus also can be neglected. This allows to write the leaf surface energy balance equation as U ¼ S þ C þ kE
ð1Þ
where U is the net heat gain from radiation (absorbed radiation minus re-radiation). With respect to unit surface area of the leaf and based on the concept [3,4] of isothermal net radiation (the net radiation that would be received by an equivalent surface at air temperature, Rni) Eq. (1) can be rewritten as S ¼ Rni qa ca ðT l T a Þ=rR qa ca ðT l T a Þ=raH ð0:622qa k=pÞðes ea Þ=ðraw þ rs Þ ð2Þ where qa is the density of air, ca is the specific heat of air, Tl is the actual leaf temperature, Ta is the air temperature, p is the atmospheric pressure, es is the saturated vapor pressure at leaf temperature, ea is the vapor pressure of ambient air, rR is the ÔresistanceÕ to radiative heat transfer, raH is the mean leaf
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boundary layer resistance to heat, raw is the mean leaf boundary layer resistance to water vapor and rs is the mean stomatal resistance to water vapor (more precise: mean leaf resistance to water vapor which in the given study is assumed to be dominated by the stomatal resistance). When either one of the components of the energy balance changes then the temperature of the leaf is also changed. The rate of this temperature change depends on the heat capacity per unit area of the tissue and it was shown [4] that the following approximation can be applied ð3Þ
with 1=rHR ¼ 1=rR þ 1=raH
ð4Þ
where t is the time, ql is the density of leaf tissue, cl is the specific heat capacity of leaf tissue, d is the leaf thickness (volume to area ratio), Tend is the equilibrium temperature attained in the steady state and ea is the ratio of the increase of latent heat content to increase of sensible heat content of saturated air. In the case of an instantaneous change in the incident radiation the solution of the differential equation will be T l ¼ T end DT expðt=sÞ
ð5Þ
with
ð8Þ
Rearrangement of Eq. (7) 1=rHR ¼ ðql cl d=qa ca Þ=sdry
ð9Þ
and combination with Eq. (8) will lead to 1=raw ¼ ðql cl d=qa ca Þðsdry swet Þ=ðea sdry swet Þ
ð10Þ
Similarly rearrangement of Eq. (7) and combination with Eq. (6) leads to an expression for (raw + rs). Substitution of the term raw (as defined in Eq. (10)) finally gives
swet =ðsdry swet ÞÞ
ð11Þ
While the above calculations were based on the assumption that the leaves are amphistomatous, for hypostomatous leaves the calculations are slightly different. Now evapo-transpiration takes place on only one side of the leave and thus with respect to unit surface area of the leaf the respective term in Eq. (2) is half as large. This changes Eq. (6) according to sleaf ¼ ðql cl d=qa ca Þ=ð1=rHR þ ea =ð2ðraw þ rs ÞÞÞ ð6aÞ Eqs. (7)–(10) remain unchanged when the leave is still wetted on both sides and thus Eq. (11) finally changes to rs ¼ ðea qa ca =ql cl dÞsdry ðsleaf =ð2ðsdry sleaf ÞÞ
s ¼ sleaf ¼ ðql cl d=qa ca Þ=ð1=rHR þ ea =ðraw þ rs ÞÞ
swet =ðsdry swet ÞÞ ð6Þ
where sleaf is the thermal time constant of the leaf responding to this change. For the same leaf in the dry state or for a dry surface with the same aerodynamic properties as the leaf under observation the mean stomatal conductance, i.e. the inverse of the mean stomatal resistance rs, will be equal to zero. This gives a thermal time constant (sdry) according to sdry ¼ ðql cl d=qa ca Þ=ð1=rHR Þ
swet ¼ ðql cl d=qa ca Þ=ð1=rHR þ ea =raw Þ
rs ¼ ðea qa ca =ql cl dÞsdry ðsleaf =ðsdry sleaf Þ
dT 1 =dt ¼ S=ðql cl dÞ ¼ qa ca ðT end T l Þ ð1=rHR þ ea =ðraw þ rs ÞÞ=ðql cl dÞ
431
ð7Þ
On the other hand, for a corresponding wet surface the mean stomatal resistance will equal zero and thus a thermal time constant (qwet) will be obtained according to
ð11aÞ
Summarizing it may be stated that the stomatal and the boundary layer resistances are now given as functions of the thermal time constants of the leaf in its different states. The resistance values may now be deduced from the measurement and the analysis of thermal rise and decay behavior. 3. Experiment The experiments were performed under laboratory conditions, i.e. the temperature and the humidity of the air was controlled and monitored and air movements were restricted (no wind conditions).
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The temperature distribution on the leave surfaces was measured by a thermo-camera AGEMA-570 (focal plane array with 320 pixel · 240 pixel, spectral range: 7.5–13 lm). The nominal temperature resolution of the IR—camera is 0.1 K. By means of a close up lens a spatial resolution as low as 0.1 mm is possible. The camera was operated remote controlled. The software to communicate with the camera is based on LabVIEW and was developed at the Institute. The value of each image pixel either could be exported in the as given state (followed by an algorithm to transfer it to temperature data) or could be exported directly as temperature values by using the internal conversion of the camera. The internal software requires to take a priori into account the object emissivity (which was set to 0.97 in the experiments—a mean value of green leaf long wave infrared emissivity [11,12]), the object distance, the ambient temperature and the relative humidity of the air. The repetition rate of image generation and collection was approximately 1.33 s when a single pixel was exported and increased when predefined areas, or the whole image respectively, were exported. Measurements of leaf temperature changes were made in the dark and under illumination. The intensity of light was regulated by using different lamps at changing distance from the tested leaves and was measured (before or after the test) in the plane of the leaves by means of a photometer (photodiode) and/or a star pyranometer. To measure the thermal time constants the leaves were additionally illuminated by turning on and off a red monochromatic light source (InGaAIP/GaAS multimode laser diode Type RTL 67100G [16]: 675 nm, rectangular radiation characteristic, 55 mW peak irradiation), which acts in the range of maximum chlorophyll absorption and—as will be discussed later in this publication—did not significantly influence the actual opening of the stomata. In all the experiments performed within the scope of this study the leaf to air temperature difference resulting from the combined action of the laser and the lamp was kept within 3–7 K, while the leaf temperature increase which only resulted from the illumination of the laser was kept in the range of 1–3 K.
Leaves of ivy (Rhaphidophora) were studied. This kind of leaves was chosen because of its simple geometry and fairly flat surface topography. When transported into the laboratory leaf temperature changes were measured continuously and by this the plant could be given appropriate time to accommodate to the test conditions. To obtain wetted surfaces water containing a wetting agent (washing up liquid) was sprayed upon the leaf in first experiments. However, in the present study a hand held highly diffusing sprayer containing pure water was used when thermal time constants (swet) were measured. This raised the effort in measuring the time constant considerably, but on the other hand this procedure had the advantage that destruction of the wetted leaves could be avoided. Dry surfaces were obtained by covering the leaf with a thin coating of petroleum jelly (Vaseline). To measure the leaf thickness the leaves, part of the leaves respectively, were put between two glass plates. By means of a micrometer the leaf thickness between larger veins (=d according to the nomenclature used in the previous chapter) was then determined.
4. Results 4.1. Images The thermal behavior of ivy leaves was tested over a period of several months. Within this period several plants with different age and leaf size were studied. Fig. 1 shows a part of the abaxial surface of an ivy leaf giving information on the cell structure and thus on the surface waviness in a microscopic scale. Three elliptically shaped stomata are embedded. Thus also information is given on the length and the distribution of the stomata which allows to estimate its density. A typical example for the visualization of temperature distributions on an ivy plant is shown in Fig. 2. The color scale is chosen such that the temperature range between the minimum temperature (background temperature Tmin = 298 K) and the maximum temperature on the leaves of the plant (Tmaxleaf = 303 K) is covered. The plant was illuminated by a lamp. Additionally a leaf (on the right
P. Bajons et al. / Infrared Physics & Technology 46 (2005) 429–439
Fig. 1. Microscopic image of the abaxial surface of an ivy leaf.
433
physiological processes are in most cases the aim of related studies. However, besides such physiological reasons, the temperature distributions are also strongly influenced by physical conditions—a well known fact which is usually treated theoretically in applications of non-biotic heat exchanging bodies and sometimes for artificial model leaves [3,13]. In the shown example the thickness of the boundary layer which strongly influences the heat loss from the leaf surface to the surrounding medium, decreases—at least in principle—from the center to the edges of the leaf. This results in temperatures lower at the edges than in the middle of the leaf. Further, the topography of the leaf surface is not a flat plane, i.e. the leaf is vaulted. Therefore the angle of light incidence varies upon its surface which results in a locally varying amount of absorbed radiation energy leading to locally varying temperature increase. This effect of illumination geometry may be noticed even more pronounced when looking at the laser induced hot area. 4.2. Determination of thermal time constants
Fig. 2. False color thermal infrared image of the leaves of an ivy plant illuminated by the lamp. The vertical hot area bar visible on the right front leaf is caused by the additional illumination with a rectangular emitting red laser diode.
hand side in front of Fig. 2) was partly illuminated by the red laser light. The laser created in the plane of the leaf an illumination rectangle of 12 mm width and 50 mm height. This radiation caused on the leaf surface a vertical hot area bar which is clearly detectable against the background. Looking first on the parts of the plant which were not hit by the laser light it may be recognized that the leaf surface temperatures are not uniform. For example the vein structure and different absorption behavior of the tissue becomes visible. The detection and interpretation of the underlying
The uncertainties in the determination of a ÔtrueÕ leaf temperature strengthen the necessity of time resolved temperature measurements. Especially the measurement of the thermal time constants which can be determined independently from the magnitude of the change of the temperature level, makes one independent on locally varying incident radiation intensity. Figs. 3 and 4 gives information on the temporal development of the leaf surface temperature which is obtained by a sudden turn on, turn off respectively, of the laser. It represents the mean of an area consisting of 12 pixels, which are located in the center of the hot area. As the observed thermal behavior is typical for the ivy leaves tested in this study, these figures may serve for the demonstration of the applicability of the proposed method as well as a basis for the discussion of associated problems. Room temperature and also the temperature of the leaves in the dark were 298 K. Turning on the laser raised the temperature by approximately 2.5 degrees and turning off the laser lowered the temperature again to the former level (lower curve in Fig. 3).
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304
Temperature [K]
302
300
298
296 0
200
400
600
Time [s]
Fig. 3. Temporal development of the leaf surface temperature in the center of the hot area due to a sudden turn on, turn off respectively, of the laser. The lower curve is obtained under dark room conditions (thermal rise time constant 43.3 s), the upper curve by illumination of the plant with the lamp (thermal time constant 34.5 s).
Illumination of the plant with a lamp increased the temperature of the leaf to approximately 301 K, while the combined action of the lamp and the laser raised the temperature well above 303 K (upper curve in Fig. 3). In both examples the moment of the laser turn on and the laser turn off is clearly detectable. After spraying water on the leaf the temperature was lowered considerably. Under dark room conditions the temperature of the leaf fell to approximately 291.5 K, while—when illuminated by the laser—the temperature was approximately 293 K. This can be seen from Fig. 4 where after stabilization of the leaf temperature at 292.8 K, i.e. after 54 s, the laser was turned off. Giving the leaves sufficient time to dry the leaf under consideration was coated with Vaseline. After stabilization of the temperature the leaf was again subjected to the laser action and a behavior of the leaf similar as shown in Fig. 3 was observed. Data evaluation and thermal time constant determination was performed by the use of commercial software (Grapher, Golden Software). This is shown in Fig. 5 where for example the ther-
294
Laser off
301
293
Temperature [K]
Temperature [K]
300
292
Fit Results Fit 1: ANab Equation Y = A-B*exp(-X/t) A = 300.6813464 B = 2.559141214 t = 43.34197891
299
Number of data points used = 112 Average X = 113 Average Y = 300.2 298
Residual sum of squares = 0.338159 Coef of determination, R-squared = 0.991978
291 0
50
100
Time [s]
150
200
250
Fig. 4. Hot area surface temperature changes of the wetted leaf obtained under dark room conditions (the time span of cooling down to wet leaf temperature as well as of drying is shaded). During stabilization at wet leaf temperature a further temperature decrease was caused by a sudden turn off (54 s after the start of the measurement cycle) of the laser.
297 0
50
100
Time [s]
150
200
250
Fig. 5. Exponential fit of the temperature rise of the leaf illuminated by the laser under dark room conditions giving a thermal time constant of 43.3 s (measurement data taken from Fig. 3).
P. Bajons et al. / Infrared Physics & Technology 46 (2005) 429–439 293.2
Temperature [K]
Fit Results
292.8
Fit 1: Bi-exponential Equation Y = A-B*exp(-X/u)+C*exp(-X/v) A = 291.603069 B = -0.7370331158 u = 17.61344228 C = 0.7370211746 v = 17.61343796
292.4
Number of data points used = 50 Average X = 51 Average Y = 291.847 Residual sum of squares = 0.170697 Coef of determination, R-squared = 0.970096
292
291.6
291.2 0
20
40
Time [s]
60
80
100
Fig. 6. Bi-exponential fit of the temperature decay of the wet leaf illuminated by the laser under dark room conditions giving a thermal time constant of 17.6 s (measurement data taken from Fig. 4).
mal rise time for the leaf under dark room conditions was calculated as 43.3 s. However, to crosscheck the programÕs ability and to avoid possible errors due to the cameraÕs performance (noise and system drifts) or errors due to hidden physiological long term processes, calculations usually were performed by introducing a bi-exponential term into the calculation procedure. The equation used is given in Fig. 6 in which u and v stand for the time constants. Experimental results in which the values of u and v (and also of B and C) differed were reinvestigated or even eliminated. In Fig. 6 for example where these values practically do not differ, the thermal decay time for the wet leaf was calculated as 17.6 s. 4.3. Determination of stomatal resistance and conductance During the given experiment the air temperature was kept at 298 K. The thickness of the leaf between the stronger veins was measured as d = 0.26 mm. Evaluation of the data of the leaf illuminated by the lamp (Fig. 3) gave a thermal time constant sleaf = 34.5 s. Evaluation of the data of the coated ivy leaves yielded similar results for
435
the time constants as were obtained under dark room conditions and thus for the dry state the value sdry = 43 s was taken. According to Fig. 6 and based on further measurements in case of the wet state the value of swet = 17 s was obtained. For the determination of a mean value of ql cl we followed the arguments given in previous publications [4], i.e. the product of the average leaf density and the average specific heat capacity for leaves was assumed to be qlcl = 2.7 MJ/K m3. Also the tabulated values given in this book were used which resulted in the ratio of the increase of latent heat content to increase of sensible heat content of saturated air ea = 2.82, in the specific heat of air ca = 1010 J/kg K and in the density of air qa = 1.184 kg/m3. Based on Eq. (11a) the stomatal resistance to water vapor was calculated (in the area under consideration) as 284 s/m and its inverse, the stomatal conductance, as 3.5 mm/s. Calculations and results are based on mass units, which are mostly used in the micrometeorological literature. However, for compatibility with much of the physiological literature stomatal conductance will also be given in molar units. Approximate conversion [4,9], i.e. multiplication by 40, gives the stomatal conductance as 140 mmol m2 s1.
5. Discussion From an experimental point of view the accurate measurement of the thermal time constant for leaves in the wet state (swet) is a crucial point, because the time span, during which the heating or the cooling caused by the laser action can be measured accurately, is limited and because the formation of water droplets obscures the results. Similar to the known behavior of the wet-bulb thermometer the leaf—after being wetted with the sprayer—must be given time enough to cool down until the leaf temperature reaches the wetleave temperature. After stabilization at this level the laser can be turned on, turned off respectively, as for example is shown in Fig. 4. Here stabilization was reached after 30 s and the laser was turned off after 54 s. However, data collection necessary for the determination of the time constant must
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be finished before the water film upon the leaf is completely evaporated and warming up of the now dry part of the leaf starts. This is demonstrated in the given example where the temperature again starts to increase after 230 s. In principle, by using water containing a wetting agent the time span for data collection can be lengthened and also the formation of water drops can be minimized. However as this procedure lastly results in the destruction of the leaf under consideration it will not be a good choice for practical applications. Therefore only pure water was used in the experiments. Also the determination of the time constant was usually performed under darkroom condition, because the radiation energy emitted by the lamp enhanced evaporation and droplet formation and thus reduced considerably the accuracy of the results. Less difficult, but still problematic is the determination of the thermal time constant in the dry state (sdry). The coating of the leaf with petroleum jelly (Vaseline) may smooth the surface waviness (which can be seen from the microscopic image given in Fig. 1). A change in the surface roughness may influence the stream of air which flows over the surface. Also the optical properties, like the absorption and transmission of light and the thermal properties of Vaseline differ from the respective properties of the leaf. However, in many cases the stomata of the leaves are closed in the dark and thus the leaves measured under dark light conditions are representative for the dry state. Therefore values obtained on coated leaves illuminated by the lamp were compared to values obtained under dark room conditions. In the given example both values correspond to each other. Finally it may be reminded that besides of the basic problems mentioned above the evaluation of the thermal data is limited by the accuracy of the equipment used. With the given equipment repeated measurements of the rise times and/or the decay times usually yielded a scatter of the values in the range of ±1.5 s. The uncertainties in the determination of dry and wet state thermal time constants make it necessary to find some cross checks. One of these may be based on the fact that the resistances within the boundary layers are not independent of each
other. In still air and in boundary layers with laminar flow these entities depend on molecular diffusion coefficients, while in a fully turbulent boundary layer both heat and water vapor are transported equally efficiently [3,4]. Thus depending on the state of the boundary layer the theoretical value of the quotient (raw/raH) ranges between 0.89 and 1. Because of the fact that the approximations made in this study overestimate the quotient (raw/raH) its real value should be slightly above this range. Multiplication of Eq. (4) with raw as given by Eq. (10) and rearrangement leads to raw =raH ¼ ðea =sdry ea qa ca =ql cl drR Þ=ð1=swet 1=sdry Þ ð12Þ which in the given example gives raw/raH = 1.17, a value which satisfies the expectations. Based on Eq. (10) raw can be calculated which also gives raH. The knowledge of the latter allows to estimate the velocity of the airstream to which the tested leaf surface was exposed. Though this proof is by far less good than the cross check described above, it gives a qualitative hint and thus it may be just mentioned without going deeper into detail (details may be taken from Ref. [4]). In the present example the resistance values were calculated as raw = 135 s/m and raH = 116 s/m. This gives a flow velocity lower than 0.1 m/s, a limit which is in accordance with the experimental conditions. A basic assumption in the determination of the stomatal resistance, the stomatal conductance respectively, is that the action of the red laser light does not change significantly the stomatal aperture. In studies of bean leaves [14] it was shown that the stomatal conductance of leaves irradiated with white light was higher than the conductance of leaves illuminated with red light of the same intensity. Irradiation with blue light leads to even higher (approximately 10 times larger) conductance values. Thus some evidence for the presence of a specific blue radiation absorbing receptor, which activates the guard cells much more than the chloroplast absorption mechanism, is given. Similar results were found in a study [15] on ivy (Hedera helix). Though there is undoubted some influence of red light on stomatal conductance it is shown on bean leaves that the time constants
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Finally, in the context of the laser illumination procedure, it may be stated that illumination of the whole leave or only illumination of a larger part of the leaf, as shown in Fig. 2, did not lead to different results. Once the thermal constants in the wet (swet) and dry (sdry) state are determined the stomatal conductance as a function of varying leaf behavior sleaf may be calculated according to Eq. (11a) and drawn. This is shown in Fig. 7 (large dots), where also the experimental value (cross) was added. To get an impression of the sensitivity and of the error range which in the given example had to be expected, the stomatal conductance with the error in the determination of the thermal time constants of wet and dry surfaces (rounded to ±2 s) was drawn additionally. As can be seen from Fig. 7 in the range of low stomatal conductance the method is more sensitive, i.e. changes of stomatal conductance will result in larger changes of thermal time constants than in the region of higher conductance. Further, when caused by errors in
120
20
80
10
40
-2 -1
Calculated stomatal conductance [mmol m s ]
30
-1
Calculated stomatal conductance [mms ]
for the change in the aperture are in the order of one hour. Similar behavior, at least time constants in the range of several minutes, can be deduced from the data given for the ivy leaves. Thus time constants for unwanted additional stomatal activity can be assumed to be large in comparison to the thermal time constants measured for the leaves. Evaluation of the thermal time constants (Fig. 3) of the leaf illuminated by the lamp shows that the rise and the decay time are the same, while under dark room conditions the rise time is in the order of 43 s and the decay time is in the order of 41 s. These results support the assumption of negligible influence of red laser irradiation. Generally the comparison of rise and decay times was used as a possibility for a cross check in this study. Further confirmation was obtained in case of repeated measurements with varying laser intensity. When the thermal time constants remained the same it was taken as an indication that heat fluxes were not altered neither by stomatal activity nor by changing boundary layer conditions.
437
0
0 24
28
32 36 Leaf time constant [s]
40
44
Fig. 7. Calculated stomatal conductance as a function of varying leaf thermal time constants sleaf (large dots are calculated values and the cross mark is the value of the given experiment). The stomatal conductance assuming an error in the determination of the thermal time constants of the wet and the dry surfaces as large as ±2 s is drawn additionally (small dots).
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the determination of swet and sdry, also smaller absolute stomatal conductance errors can be expected at lower conductance. Performing thermographic studies a broad range of possible leaf shapes and of different environmental circumstances must be considered. Changes of circumstances will result in changes of the leaf boundary layer resistance to heat raH and in the leaf boundary layer resistance to water vapor raw. By this also swet and sdry are changed. Though it is difficult to estimate these leaf resistances accurately the dependence of leaf resistance on windspeed and dimension and their calculation assuming forced as well as free convection is discussed widely in the literature [3–5,8,9]. For laminar forced convection typical resistance values of flat leaves [4] range from raH = 500 s/m (at low windspeed) down to raH = 5 s/m. Table 1 gives estimated dry and wet leaf thermal time constants as a function of different boundary layer resistance to heat raH. The calculations are performed according to Eqs. (7) and (8). They are based on the theoretical value of raw/raH = 0.89, an air temperature of 298 K and a leaf thickness (volume to area ratio) of 0.26 mm. As may be seen decreasing boundary layer resistance leads to lower thermal time constants. A fact that qualitatively might be expected as decreasing boundary layer resistance is caused for example by increasing air circulation. With the given equipment measurements down to values of approximately raH = 20 s/ m make sense. The influence of air temperature on swet and sdry is shown in Table 2. Calculations are performed for 288 K and 308 K, thus spanning a range of 20 K. The leaf thickness which is directly proportional to the time constant, is now assumed to be Table 1 Estimated dry and wet leaf thermal time constants as a function of different boundary layer resistance to heat raH (sample leaf thickness is 0.26 mm) Air temperature [K]
raH [s/m]
sdry [s]
swet [s]
298
5 20 50 100 200
2.9 11 23 39 59
0.7 2.8 6.6 12 23
Table 2 Estimated dry and wet leaf thermal time constants as a function of different boundary layer resistance to heat raH (the leaf thickness is assumed to be 1 mm, which allows estimation of swet and sdry by multiplication with the thickness of the tested leaf) Air temperature [K]
raH [s/m]
sdry [s]
swet [s]
288
5 50 100 200 500
11 89 152 232 341
3.8 35 66 117 215
308
5 50 100 200 500
11 90 148 217 301
1.9 18 34 63 128
1 mm. This allows a quick estimation of swet and sdry from Table 1 just by multiplication with the leaf thickness (in mm). In the present example the resistance value was calculated as raH = 116 s/ m, which is close to raH = 100 s/m. For the latter (Table 1) swet = 12 s and sdry = 39 s, while in case of an air temperature of 288 K the respective values deduced from Table 2 yield swet = 17 s and sdry = 39.5 s and at 308 K swet = 9 s and sdry = 38.5 s. Thus changes of the air temperature of 20 K lead to small changes of sdry, i.e. only one second in the given example, while swet is remarkably influenced when air temperature changes. Summarizing, to determine the aperture of the stomata—for example as a function of different stress situations—there are in principle two possibilities to proceed. Either three leaves with similar properties are selected, i.e. a wet, a dry and the sample leaf are all in one field of view simultaneously, or one leaf is observed sequentially. In the latter case the leaf response should be measured in the darkness first. The wetted leaf response should also be measured in the darkness and corrections due to environmental changes should be made either by estimation or when possible by additional measurement at appropriate time. After application of stress the leaf response should be measured and the stomatal resistance calculated using Eq. (11) for amphistomtous leaves or Eq. (11a) for hypostomatous leaves. Lastly the deci-
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sion which procedure (or a combination of them) is chosen will mainly depend on the need of corrections due to environmental changes as well as on the specifications of the used instruments. 6. Conclusions The capability of infrared thermovision as an innovative method to measure convective heat fluxes over solid bodies has been discussed during the past several years. Studying plant status passive thermographic methods were usually employed. In the present study these methods are extended by taking active thermometry into account. Based on considerations of the heat transfer between the leaves of a plant and its environment the biotic and the non-biotic parameters of the boundary layer resistances are calculated. This affords to determine the thermal time constants of the leaf in the wet state and in the dry state first. Once obtained the activity of the stomata can be followed by measuring the thermal rise and decay behavior of the leaf in vivo, where temperature changes are caused by a sudden change in the illumination of the leaves. The basis of optimal performance is not only given by the knowledge of the underlying thermal mechanisms, but also by the associated experimental handling. On examples it was shown that cross checks are possible which strengthen the reliability of the experimental results. Basically the method is not invasive. This is an advantage compared to the methods usually applied for the determination of stomatal aperture. Though in the present investigation the principle mechanisms were studied, an extension of the method may serve as a basis for the early detection of plant stress or plant disease in the future. Acknowledgment The Senate of the University of Vienna and the Hochschuljubila¨umsstiftung (Contract H-141/ 2000) are acknowledged for supporting the study.
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