Studies on the measurements of crop emissivity and sky temperature

Agricultural and Forest Meteorology, 49 (1989) 23-34

23

Elsevier Science Publishers B.V., Amsterdam - - Printed in The Netherlands

STUDIES ON THE MEASUREMENTS AND SKY TEMPERATURE

OF C R O P E M I S S I V I T Y

JING-MING CHEN and REN-HUA ZHANG

Institute of Geography, Academia Sinica, Beijing 100012 (People's Republic of China) (Received July 19, 1988; revision accepted April 4, 1989)

ABSTRACT Chen, J.-M. and Zhang, R.-H., 1989. Studies on the measurements of crop emissivity and sky temperature. Agric. For. Meteorol., 49: 23-34. A method is presented for measuring crop thermal emissivity in situ by changing the environmental longwave irradiance. The thermal environment of wheat canopy was modified using a bottomless hemispherical cover which can be swiftly opened and closed by hand. An extrapolation technique is used to determine the step change in the crop brightness temperature immediately after the environment is modified so that the effect of the response of the real leaf temperature to the environmental change is removed. The mean sky temperature, which determines the natural environment, was obtained from multiangular measurements of an infrared thermometer with a narrow field of view of 2.0 °.

INTRODUCTION

Estimation of evapotranspiration is one of the important uses of remotely sensed plant canopy temperature. In energy balance measurements of evapotranspiration it is the difference between air and canopy temperature which is important. Since plant temperature is generally within a few degrees (3°C) of air temperature (Smith et al., 1981) the accuracy of its measurements is critical in any successful estimation of evapotranspiration as the residual of an energy budget. The information extractable from the thermal remote sensing data may be very limited when the measurements and interpretation of the data are subject to errors comparable to the plant-air temperature difference. One of the problems in the interpretation of infrared temperature measurements is the lack of knowledge of the emissivity of the surface of interest. The brightness temperature (Tb) given by a thermal detector may differ substantially from the true temperature (Tt) when the emissivity of the surface is slightly smaller than unity. Longwave irradiance coming from a surface is a combination of emission from and reflection by the surface, i.e. 0168-1923/89/$03.50

© 1989 Elsevier Science Publishers B.V.

24

aT~ = e a T ; ' + ( i - e)aT,',

J,.M. CHEN AND }¢,-!,t. Z H A N (

ii ;

where a is the Stefan-Boltzmann constant (5.67X i0-SWm-~K -)~ ~ is the emissivity, and Te is the environmental temperature. All temperatures are in kelvin K. Emissivity of vegetative targets falls within the range 0.90-0.98 (idso et aL 1969 ) and are usually greater than 0.95 when plants are free from water stress (Smith, 1983). A complex vegetation surface may have an emissivity greater than that of individual components because multiple reflection is expected to take place among plant components. Sky brightness temperature, which largely determines the thermal environment of the upper surface, is usually more than 30°C cooler than the ground surface. We are therefore involved with a temper ature correction due to the grayness of the vegetation surface. According to eq. i, this correction is usually in the range of 0.5-2.0°C, which is comparable t;~ the difference between plant and air temperatures. Emissivity of a complex vegetative surface depends on not only the emissiv ity of individual plant components but also the geometrical arrangement o~ them. Therefore emissivity should be measured in situ during the relevam growing periods since both optical and geometrical properties of plants may change with time. In spite of its importance, few studies have been reported in this respect. Fuchs and Tanner (1966) conducted a classic study on ~he emissivities of tall sudangrass and alfalfa using a bottomless, hemispherical tent covered on the inside with aluminium foil. The tent was used as a blackbody cavity and it was assumed that the measured temperature of the crop surface under the tent represented the true temperature. The brightness temperature was measured after the tent was removed. In their studies the sky temperature was obtained from an aluminium plate of a known temperature and emissivity. The same principle of measurement was adopted by Huband and Monteith (1986). There are a few problems which have not been made clear in these reports: ( 1 ) the tent may not have represented a blackbody cavity; this would require either a highly reflective inside wall or a large length/diameter ratio; (2) the measurements of the blackbody temperature of the vegetal surface were made at 5-15 s after the tent was put in position, but the temperature may have increased significantly in the short period after the surface was blocked away from the coldness of the sky; (3) there is an inherent difficulty in measuring the sky temperature with a reflective plate: the reflectivity of the plate should be large in order to measure the reflected irradiance but specular reflection from such a reflective surface may make the measurements strongly angle dependent. In this report, an improved technique of changing environmental irradiance is presented for the studies of crop emissivity. Using this technique, the change in crop brightness temperature is measured instead so that the blackbody caw

MEASUREMENTSOF CROPEMISSIVITYANDSKYTEMPERATURE

25

ity assumption is avoided. Success of this method depends on removing the systematic bias resulting from the subsequent change in the crop real temperature. This is done by extrapolating temperature measurements made after the crop is covered back to the m o m e n t of covering. The method of measuring sky temperature with a reflective plate is replaced by a technique of applying a weighting function to the multiangular measurements of sky temperature using an infrared thermometer. The advantages of the direct measurements are explored. THEORY

Since the spectrum of sky longwave radiation deviates greatly from Planck's law (Monteith, 1973), the apparent sky temperature would depend on the measuring waveband. If we denote the waveband-dependent apparent sky temperature as Tew then eq. 1 can be written as a T E = ~aT4t + (1 - e ) aT4,~

(2)

When this equation is used to determine the emissivity, all three temperatures Tb, Tt and Tew should be known. In order to avoid the difficulty in measuring the true plant temperature, brightness temperatures were measured instead for the same surface under natural and modified environments. A pair of equations for the longwave energy balances under these two thermal regimes, denoted with subscripts 1 and 2, can be given as follows

T~I =eT41 + ( 1 -

4 e)Tewl

T~,2 = eT4tz + (1 -

4 ) Tew2

(3)

These equations can be solved for the emissivity provided Ttl -- Tt2. In order to satisfy this requirement, the measurement of the brightness temperature Tbl and Tb2 should be made immediately before and after a sudden change in thermal radiation environment so that the plant surface temperature would not change significantly during the measurements. Assuming this is true, then the following equation can be derived ~=1

T~I-T42 4 4

T~

(4)

- Tew2

In practice it is not possible to measure temperature immediately after the change in the radiation environment because thermometers do not respond instantly. Figure 1 sketches three curves showing how the brightness temperatures are determined. Curve a is the response of true canopy temperature when a cover is suddenly removed. The true temperatures are slightly higher than the brightness temperatures when the thermal environment is cooler. Curve b is the expected variation of radiometric temperature with an instru-

'.2)6

,I M, CHEN AN[:,'t~.H. ZHANI;

t i

l ~,L, i

i ~

' l i m~,

Fig. 1. Response of leaf true and brightness temperatures to a step change in the e n v m m m e m a i thermal irradiance. ATe,is the change in vegetation brightness temperature required for calculat il~ the emissivity. Curve a is the response of the true temperature; curve b is the variati¢m ~)f b r i g h l ness temperature measured by an IR t h e r m o m e t e r with a typical time constant; curv~- c is !.h~ idealized variation of brightness t e m p e r a t u r e as would be measured with instantm~e()u: in.~trL~ mental r e s p o n s e

mental response time. Curve c is the true response of brightness temperature as would be measured by an instrument with an instantaneous response. Curve c is parallel to curve a. The true step change in the brightness temperature i~ not observed directly. It must be determined by extrapolating the measure~ ments obtained a few seconds after the change back to the instant of u n c o v ering. To understand how to do this accurately the variation of true teal temperature should be studied in more detail. The temperature change of a leaf with time after an adjustment of the energy input level can be described in terms of leaf time constant (2) and the possible range of change ( T t e l - - T t e 2 ) , Le. AT(t) = T ( t ) - T t e = (T,e~ - " 1 ~ 2 ) [ 1 - e x p ( - t / 2 ) ]

i5

where t is the time after te (Fig. 1 ) and Ttel and Tte,~are the equilibrium tern, peratures under two energy balances. They can be determined from the follow. ing leaf energy budget equations for the condition at night when solar radiatio~ has vanished and neither transpiration nor condensation occurs

½ea(T~, + T~, ) = eaT~o, +P()A 7't,~ - Ta)/r~

t6 !

½ea( T ~ + T~,2)=eaT~e~ + pQ,( T~¢2 - T ~ ) / r ~ where Ta is the apparent ground surface temperature, p is the air density, C,~ is the specific heat of air at constant pressure and ra is the boundary layer resistance of the leaf. These two equations can be merged together to solve for the difference between the equilibrium leaf temperatures ( Ttol- Tt~ ). The final expression is

MEASUREMENTSOF CROP EMISSIVITYAND SKY TEMPERATURE

Ttel-Tte2

where

-

rRH =

27

2pCp ( Te41 -- Te2)rRn 4 1/ 1 + 1 in which \rR r a / '

(7) r R --

4ca'/i3

a n d T = (Tte 1 +

Tte 2 ) / 2 .

When

T-- 300 K, rR = 195 s m - 1. According to eq. 7, ( T t ~ - Tte2) would fall in the range from 1 to 10 K when ( Tel - Te2 ) varies in the range from 20 to 40 K and rRH from 20 to 200 s m - 1. The time constant for a leaf can be derived from the following formula (Linacre, 1964) _ cdTt dt

pCp(Tt - Te) rRH

(8)

dT. where dt- is the rate of leaf temperature (Tt) change with time, C is the heat storage capacity for unit leaf area, and Tte is the leaf equilibrium temperature. By integrating eq. 8 with respect to Tt and t, one finds that T t - Te = ( T t o -

Tte)exp [ - - t / ( e r R H / f l C p ) ]

(9)

where Tto is the original leaf temperature at t = 0. The time constant, 2, is given by 2=CrRH/pCp

(10)

According to Linacre (1964) and Watson (1934) C varies from 460 to 680 J m - Z K -1 for thin green leaves. If we take a m e a n value of C = 5 7 0 J m - 2 K -1 then 2 = 570rRH/pCp = 0.475rRH

( 11 )

It can be seen from Table I t h a t leaf time constant is of the order of tens of seconds and the magnitude of the temperature change increases with rRH at t = 2 , but the a m o u n t of change at a given time interval of t = 5 s is almost independent of rRH. The reason can be seen in the following inference. TABLE I Leaf time c o n s t a n t and temperature changes AT(2) and AT(5) at t = 2 and t - - 5 s when Tel - Te2 = 20°C rp,a (ms -1 )

2(s) zlT(2 ) (°C) AT(5) (°C)

20

50

100

200

9.5 0.53 0.36

23.8 1.40 0.42

47.5 3.73 0.44

95.0 5.60 0.45

28

.L-M. CHEN AND R,-H, ZHAN~

According to eqs. 7 and 11 we can write T,~ ~- Tto2 =C~ rr~H ).

! !2!

= C~ rml

whereC1 is a constant depending on the change in the environmental t e m p e r ature and C~ is another constant depending on leaf heat storage capacity. Using these relations, eq. 5 can be written as AT(t)=ClraH{1-exp

~1:~

[--t/(C~reH)]}

For the purpose of this analysis, we may replace A T ( t ) with AT(t,rm~) in eq. 13. Differentiation of eq. 13 with respect to rail results in

OAT(t,rRH)

C1

0 rRH

,

t ±t/(C2rRH) exp [t/ (C.2rRH) ]

x.

W h e n t is small compared with CzrRH, the term [ l + t / ( C 2 r ~ H ) ] / e x p it/ (C2rRH) ] is approximately equal to unity so that OAT/OrRH is very close ~o zero. This weak dependence o f A T ( t , r a n ) on ran has the important implication that the amount of change in leaf temperature in a given small time interval tbllowing uncovering or covering is controlled only by the change in energy input and has little to do with the conditions of wind and leaf size. This change should be considered carefully in order to improve the reliability of the emis~ sivity measurements. Since during the exponential change described by eq. 9 the difference b e tween the true and brightness temperature would remain the same when the environmental temperature does not change (Curve a parallel to Curve c it~ Fig. 1), the true temperatures in eq. 9 can be replaced in pairs by brightness temperatures, i.e. Tb -- Tb~ = ( Tb2 -- Tb~ ) exp ( -- t/2 ) where Tb2 and The are initial it is calm at night 2 is in the within 15 s it is roughly true practical purposes to use the

( 15 )

and equilibrium brightness temperatures. When range from 50 to 100 s. If we take measurements that t/2 < < 1 and it may be accurate enough for approximation that

exp ( - - t / 2 ) = l - - t / 2

i I6

With this approximation eq. 15 is simplified to Th =Tb2 -- ( Tb,~ -- Tb~)t/)~

i17

Using this linear relation between Tu and t, the value of T~)2required tbr determining the step change ATb can be obtained by extrapolating the measurements of Tb back to the point where t = 0 (i.e. to in Fig. 1 ).

MEASUREMENTS OF CROP EMISSIVITY AND SKY TEMPERATURE

29

EXPERIMENTS Experiments were conducted in the Yucheng Comprehensive Experimental Station in China on winter wheat of cultivar No. 5 Lumai during heading and grain filling stages, at about 2100 h on May 5 and M a y 28, 1987, respectively. The measurements of radiometric temperature were made with an infrared thermometer (National ER-2007, Matsushita Communication Ind. Co. Ltd., J a p a n ) which has a field view of 2.0 ° and a spectral response region of 8-12.5 ttm. A hemispherical cover was used to modify the thermal environment of the wheat canopy under investigation. The cover had a diameter of 1 m and was mounted on a metal frame. It consisted of two equal parts which could be opened and closed by hand in less than 1 s. A 10-cm-diameter viewing hole was made at the apex of the cover for reading the IR thermometer in the vertical direction. The thermometer was fixed at 70 cm above the bottom of the cover. The voltage output of the infrared thermometer was recorded twice a second by an electronic notebook Polycorder (Omnidata International). This technique allowed the wheat canopy brightness temperature to be continuously observed while closure and disclosure of the cover was exercised. The sky temperature was measured with the IR thermometer at six elevation angles. For each elevation angle, there were four readings corresponding to four orientations. A weighting scheme was introduced to obtain the mean sky temperature (see Appendix). The temperature distribution within the cover was uniform and one or two readings were enough to represent the mean cover temperature. The measurements of the sky and cover temperatures were made at the beginning and end of each emissivity experiment so that the effects of temporal variation could be removed. The mean sky temperature in the entire longwave band (3-50 j~m ) was measured with a pyrgeometer (Model PIR, The Eppley Laboratory Inc.). RESULTS AND DISCUSSION

Emissivity The change in brightness temperature Figure 2 shows a step change in Tb when a wheat canopy under a cover was suddenly exposed to the sky. Both temperature and time are on a linear scale. In drawing the lower line, the first four points were neglected to remove the effect of instrumental response. In this figure and the following figure an overshoot point appears. We are not able to determine whether there is a physical or instrumental reason for the overshoot. (A numerical study with the consideration of temperature gradient across leaf thickness does not show the overshoot. ) The straight line fitted using the remaining points is extrapolated to the changing point to determine the size of the step change in Tb. In this case

;:;(I

J..M. ('HEN A ND i H. ZHAN(

22,4 ~ - - - - ' : 22.3~-°

[ - - .......... L_e_ _:: '

22.2F

i

22.1 22,0 /t-

;:

/

21.7!21,6~ 21.~ 21,4r21.3L ~ - ~ . o

-~. . . . . . . .

~---~

~

i

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

- - i A

t0

5

riME

~_

i

I

_

I

15

I

2'0

I

_ _ _ 9

(S)

Fig. 2. T h e v a r i a t i o n of wheat brightness temperature Tb when a hemispheric cover ~)ver Ih~ canopy was opened during heading stage.

20.2 20.1 ! 20.Op 19.9 to oo

19,7F ~9-6F 19.SF

19.4L. 19.3! 19.21 19.1~

()

i::)

20 TIME

30

40

iS)

Fig. 3. The v a r i a t i o n of wheat brightness temperature T b f b l l o w i n g closure and disc]o,-ur(: (d ~ cover over the surface during late. grain filling stage.

ATb is 0.44°C. The slope of the lower line was gentle, indicating a small decrease in Tb by 0.13°C in the first 15 s. The decrease was small because the sky ternperature measured by a pyrgeometer was only 7°C cooler than the cover temperature, though the apparent sky temperature measured by the thermometer was 30°C cooler. Even though the variation is small, it is still comparable to the step change, and can not be ignored. Under the same condition, ATb was determined to be 0.53°C when the cover was successively closed. Figure 3 shows a section of a record of wheat brightness temperature measured during late grain filling stage when the cover was repeatedly opened and closed and the radiometric temperature was sampled continuously. In this experiment the longwave sky temperature measured by the pyrgeometer was 13°C

MEASUREMENTS OF CROP EMISSIVITY AND SKY TEMPERATURE

31

lower than the cover temperature. The temperature variation in this case had an upward trend when the cover was closed and a downward trend when the cover was opened. The downward trend was greater than the upward trend because the general trend of decreasing in air temperature would have some effect. The step changes in Tb resulting from the opening and closure of the cover were 0.32 and 0.33°C, respectively. Other successive results were, in order, 0.32, 0.43, 0.35, 0.30, 0.42 and 0.38°C. The standard deviation of these eight numbers is 0.04°C and the mean is 0.356°C. We are aware that the determination of the step changes might have been subjected to an error due to the linearizing treatment. However, the error should be small because the time constant 2 was estimated to be in the range from 50 to 90 s and the condition of t/2 < < 1 for the linearizing treatment is approximately satisfied. It was calm during the experiments.

The change in environmental temperature The change in the environmental temperature due to the use of the cover is the difference between the sky and cover temperature. The sky temperature is referred to the irradiance in the measuring window 8-12.5 ~tm of the thermometer. The apparent sky temperature in the window region varied considerably with elevation angle, and many observations should be made in order to determine a mean sky temperature. Table 2 gives an example of such observations. In consideration of the hemispherical radiation geometry, a weighting function is used to calculate the mean sky temperature (Appendix). Using the data in Table 2, the calculated result is Tew= -9.12 ° C. All sky temperatures used in this study were calculated with the same method. In later investigation it was found that the measurement at the single elevation angle of 37 ° can represent the mean sky temperature (see Appendix).

Emissivity results All the experimental results are concluded in Table 3 in which the emissivities are calculated with eq. 4 with Tb2 replaced by (Tbl --ATb), Tbl by Tbl,Tewl TABLE2 The distribution Azimuth

of window sky temperature

(°C) with elevation and azimuth

angles

Elevation 5°

15 °

30 °

45 °

60 °

75 °

N

22.8

4.1

-6.9

- 14.9

- 18.3

- 19.2

E

20.7

3.7

- 7.7

-

12.9

-- 17.5

-

S

24.6

4.6

-4.8

-

12.0

-

16.7

-

19.0

W

22.0

5.1

-4.2

-

10.5

-

15.0

-

18.2

18.7

J,-M. (:;HEN AND R.H. ZHAN{;

;:12

by Tcove,and Tew2by Te~, where ,-4Tb is the step changes of brightness temper ature of the crop as shown in Fig. 1. There is a systematic difference between the emissivities measured in head ing and late grain filling stages. Near the end of the grain filling stage, the ears were outstanding in height and were very visible by the thermometer. Since an ear surface is rougher than a leaf surface, it is expected to have a greater emissivity. The alfalfa emissivity measured in situ by Fuchs and Tanner (1966) and wheat emissivity by Huband and Monteith (1986) are 0.976. Compared with this value, the figures from the present experiments are large. It is likely that these blackbody temperatures of wheat might have a positive bias because they were measured at 5-15 s after the tent was mounted. During this period the crop temperature should have increased by a small amount. The difference between the two techniques must be considered to explain their smaller values for the emissivity. A positive bias of 0.15 K in the blackbody temperature would explain the difference between the emissivities 0.981 and 0.976 when the en vironmental temperature is changed by 30 K. Huband and Monteith made their measurements 5-15 s after the tend was mounted; a bias of about 0.15 K in this period is consistent with our measurements. CONCLUSIONS

The thermal emissivity of a wheat canopy was measured to be 0.981 + 0.002 and 0.986 + 0.002 for the heading and late grain filling stages, respectively. These values are slightly larger than the value of 0.976 reported by Fuchs and Tanner (1966) for alfalfa and Huband and Monteith (1986) for wheat. Although the present experiments were conducted under rather humid cti matic conditions in which the apparent difference between the sky" and the ground surface temperature at night was less than 30°C in the 8-12.5 pm wave band, and less than 15°C in the entire thermal waveband, we can still see the significant step changes and the subsequent exponential changes (approxL mated by linear change in this study) in the wheat brightness temperature when the thermal surroundings of the upper hemisphere were modified with a simple cover. In dry climates, both changes are expected to be much larger. TABLE 3 Results o f w h e a t emissivities

Heading Late grain filling

.17'h(K)

"l'b, ( K )

T.,.,(K )

T, . . . .

0.485 ± 0.05 0.356 + 0.04

294.2 291.9

264.01 262. l l

294.8 292.4

(K)

( 0.98i 2_: 0.0(~,4 ().986 -~:0.002

33

MEASUREMENTS OF CROP EMISSIVITY AND SKY TEMPERATURE

APPENDIX: M E T H O D S FOR E S T I M A T I N G T H E W I N D O W SKY T E M P E R A T U R E

If the azimuthal variation of sky radiation is ignored, the mean sky temperature in the window region is defined by the following equation 4 I 7~/2 Tew=jo T4(fl)

sinflcosfldfl

(hl)

where T(fl) is the sky temperature at elevation ft. The discrete form of this equation is

Tew =

~s~nfl ~oos~

(A2)

In these equations the term sinfl cosfl is the weight for averaging the temperatures measured at various elevation angles. Since this weight is symmetric about fl= 45 ° we used the sky temperatures measured at 15 °, 30 °, 45 °, 60 ° and 75 ° for calculating the mean. Although the apparent sky temperature varies considerably with elevation, the variation is often smooth when the atmospheric humidity distribution is horizontally uniform. This condition can be found in clear, foggy or overcast days. Since the variation is smooth, there might be an angle at which measurements represent the mean sky temperature. Elsasser (1942) derived that emission to a horizontal surface from an atmospheric column of length h is equivalent to the emission from a slab of atmosphere of thickness h/1.66. At an elevation angle of 37 ° the length of an air column through the atmosphere °C 30

%x

2O

F-

10

j

-10

x x×

x -20

I

I

q

L

-10

0

10

20

!

30 °C

T37o

Fig. A1. Comparison of mean IR sky temperature using a weighting scheme (Tew) and IR measurements at a single elevation angle 37 ° (TsT.).

:{4

J.-M. CHENANI)P,. H. ZHAN~

is 1.66 times the thickness of the atmosphere, i.e, cosec 37 ° --1.66, so thai measurements at 37 ° may represent the mean sky temperature. Figure A1 shows the relation between the IR measurements at angle 37 ° an(i the mean window sky temperature for a horizontal surface. These two sets ot temperatures are in very good agreement. The points are within 3 K of the ] : line.

REFERENCES Elsassar, W.M.. 1942. Heat transfer by infra-red radiation in the atmosphere. Harv~td Mete~-¢ logical Studies, 6: 107. Fuchs, M. and Tanner, C.B., 1966, Infrared thermometry of vegetation. Agmn. J. ;i~: .,!~ --6iii Huband, N.D.S. and Monteith, J.L., 1986. Radiative temperature and energy balance. ,:~!a wh~a~ canopy. Part I: Comparison of radiative and aerodynamic canopy temperature, Boundar~ Layer Meterol., 36: 1-17. Idso, S.B., Jackson, R.D., Ehler, W.L. and Mitchell, S.T., 1969. A method lor determinati¢m ,~ infrared emittance of leaves. Ecology, 50: 899-902. Linacre, E.T., 1964. Determination of the heat transfer coefficient of a leaf. Plant Phy~iol,. :~!!: 687-690. Monteith, J.L., 1973. Principles of Environmental Physics. Edward Arnold, Lond, m Smith, J.A., 1983. Matter-energy interaction in the optical region. In: ASP Manual ¢~t Remol~. Sensing, 2nd edn. Falls Church, VA, Ch. 3. Smith, J.A., Ranson, K.J., Nguyen, D. and Balick, L., 1981. Thermal vegetation canopy mode studies. Remote Sensing Environ., 11:311-326. Watson, A.N., 1934. Further studies on the relation between thermal emissivity an(t plato tern perature. Am. J. Bot., 21: 605-609.