- Email: [email protected]
Thermal vegetation canopy model studies
311
REMOTE SENSING OF ENVIRONMENT 11 311-326(1981)
Thermal Vegetation Canopy Model Studies
J A SMITH, K J RANSON, D. NGUYEN, L BALICK, College of Forestry and Natural Resources, Colorado State Umverszty, Fort Colhns, Colorado 80523
L E LINK, Enwronmental Laboratory, U S Army Corps of Engmeers Waterways Experiment Statzou, Vwksbur~ M~ss)ss~pp~39180
L FRITSCHEN, College of Forest Resources, Umvers~ty of Washington, Seattle, Washington 98115
and B HUTCHISON Atmospheric Turbulence and l~ffusmn Laboratory, Oak Rtdge, Tennessee 37830
An iteratwe-type thermal model apphcable to forest canopms was tested with data from two diverse torest types The model framework consists of a system of steady-state energy budget equataons describing the mteractmns oI short- and long-wave rachatmn within three horizontally mhmte canopy layers A state-space tormulatmn of the energy dynamics wlthm the canopy is used whtch permits a factonzataon of canopy geometrical parameters from canopy optmal and thermal coethcmnts as well as enwronmental driving variables Two sets of data characterizing a coniferous (Douglas-hr) and deciduous (oak-hmkory) canopy were collected to evaluate the thermal model The results show that the model approramates measured mean canopy temperatures to within 2°C for relahvely clear weather conditions and devaates by a mammum of 3°C for very hazy or foggy condmons
Introduction
Rapid and accurate assessment of renewable resources ~s an increasingly important task facing remote sensing speciahsts. Mathematical abstraction of energy processes of vegetahon canopies is a useful techmque for relalang sensor response to envaronment-canopy mteractrans. Such an understanchng is reqmred m order to make timely inferences about the conditmn of forestry and agricultural resources from remote sensors. In the thermal regime, several authors have re©Elsewer North Holland Inc, 1981 52 Vanderbdt Ave, New York, NY 10017
ported success m estimatmg evapotranspiration of crops from thermal sensor data (Heflman et al., 1976; Reginato et al., 1976; and Soer, 1980) Several models have been reported that describe the energy balance of vegetatmn either in terms of a single leaf (Gates, 1968; Wmbelt and Henderson, 1977, and I~mes et al., 1978), or an abstract layered canopy (Alderfer and Gates, 1971, and Deardorff, 1978). Few models have been described that characterize the energy flows wlthm vegetation canopies as a funchon of the canopy geometry (Goudnaan, 1977; Norman, 1979, and Kames et al., 1981). 00344257/81/040311+1650250
312
In this study, a modification of the thermal canopy model reported by Fames et al. (1981) that is applicable to forest canopies is described and evaluated. The model is an lteratwe type formulation of a system of steady-state energy budget equations describing a canopy as three horizontal layers. Each layer is described in terms of reflective and thermal radiation coefficients and leaf lnchnatlon angle distnbulaons. The model emphasizes the radlatwe energy processes occurnng both within and above the vegetataon canopy layers and relates these flux transfers to detaded consideration of the canopy geometry. Other energy transfer processes such as sensible heat and evapotransplratlon are included but in a farrly slmphslac manner Standard expressions from the literature are utilized. The modular form of the model makes it faarly easy to replace the existing expressions as warranted Thus, the model is capable of evaluating partacularly the ra&atwe energy processes from wadely diverse canopies There were two broad objectives of the work reported here First was to determine rf we could re-express a prevaously developed thermal exatance model (Fames et al., 1981) in a more usable form which would permit a wade variety of engineenng-type target/background stu&es to be performed in a more practacal computational fashion. The second objective was to evaluate the model wath vahdatlon data collected from two different forest types; a Douglas fir (Pseudotsuga menzzesii) canopy and a mrxed deciduous canopy. Here, we first describe the updated model structure and solutaon approach This is followed by a description of the experimental sites and methods for ob-
j A SMITH ET AL
taming the required model input data. Finally, the results and summary are given
Model Structure The updated model formulation given below differs m three major aspects from the onginal model developed by Fames et al. (1981). First, the model has been rewntten in a vector-matrix form with a state-space charactenzatlon. That is, there is a specific identification of a state vector X, the canopy layer tempera~tres, a control vector U, the meteorological driving variables, and a parameter vector P In this formulalaon, the long-wave energy budget terms have been factored into a geometnc-dependent term, the S matrix, and the long-wave thermal source terms This factonzatlon permits the precalculatmn of the S matrix for a wade variety of canopy situations and then the subsequent convolvmg of these matrices wath the U and P vectors to evaluate canopy thermal vanatlons. A second potential advantage of this factonzatlon is that it results in a hnear system of equations wath respect to S suggesting the use of hnear fdtenng theory to estimate S from X (Sorenson, 1966). The second modification is the use of more slmphfymg assumptions in the model, partacularly wath regard to the short-wave absorption calculation as discussed later. Finally, in solving the nonhnear energy budget equations, exphclt use was made of the closed form expressions for the Jacobian of the system m a Newton-Raphson technique. In the matenal that follows, mchvldual expressions for the component energy budget processes are summarized and an exphclt expression for the elements of the
THERMAL VEGETATION CANOPY MODEL STUDIES
Jacoinan matnx are given. The geometncal factonzataon of the energy budget equation for the long-wave flux transfers is derived. Energy balance framework
The model as a plane-parallel abstraction of a vegetat/on canopy davided into three honzontal layers. Two addataonal source layers are given by the atmosphere above the canopy and by the undedyang ground An energy balance framework, assumang steady-state condatxons, as formulated for each of the three vegetation layers (sinks) as a flmctlon of the five source layers. In the expressions that follow, i = 1, 2, 3 represents the sank or vegetation layers and t = 1, 2, 3, 4, 5 represents respectxvely the atmosphere, the three vegetation layers, and the ground source layers of energy flux The combination of the ,, i lnchces thus represents flux from source layer I to sank layer ~. The vector expressaon for the energy balance equations for layers 1, 2,3 consaderlng long-wave transfers, short-wave transfers, sensible heat, and evapotranspiration can be written as
313
tance of the boundary layer to ddfus~on ~s estamated from other measured parameters), S = l o n g - w a v e flux transfer matrix calculated from geometncal properties of the canopy, A=short-wave flux absorption coefficient vector, UA(ToTgWS RH SW) r is the control or input vector, To = mr temperature (°C), Tg = ground temperature (°C), WS = wand speed (m/see), R H = relatave humachty, S W - short-wave fltLX (w/m2). F may be rewritten m the following matrix form winch exphotly separates the geometrical properties of the canopy S from the remaining energy terms (Smath et al., 1981). F a~aoB(X)Ts-oB(x) + A + H(X) + L E ( X ) = 0 ,
(2) where B -- vector of long-wave emlssaon terms,
F(X,P,U) = 0 ,
(1)
where
Xa(XaXg.X3)T--the average layer temperature vector for layers 1, 2, 3, Pa(e,, ,--1,2,3, a,, ~=1,2,3, eg, RI, S, A) = t h e parameter vector characterlzmg the canopy layers, e,,a, =emassavity and absorphvity of the vegetation layers, eg, ag =emxsslvity and absorptavity of the ground layer, R t = l e a f stomatal resastanee to water vapor dfffusaon (Note that the resls-
H--vector of sensable heat, LE -- vector of evapotransp~rat/on terms, o--- Stefan-Boltzmann constant.
The slgnlficance of tins factonzatlon xs that a wade vanety of abstract or cannomcal canopaes may be characterized by precalculation of the S matrix. This matrLx table may then be convolved wath the appropriate meteorological dnving vanables to simulate diurnal behavior for a wide spectrum of scenarios. The vector equation (2) may be expanded for each layer and the exphot
l A SMITH ET AL
314
dependence on parameters or input variables may be in&cated by
where h C, the convection coefficmnt, is taken from Tibbals et al. (1964) EvapotransplraUon:
o,,o{B(To)Sn + B(T,)Sl )
LE ( X, , WS, To, R, RH ) 1
+ A , - o B ( X 1 ) + H(X 1;W$, Ta)
-- R+R------~a[s(X,)-RHs(Ta)]h(X,),
+ LE( X~, WS, ra, R t, RH) =0,
(7)
(3a) where
½a2o{B(Ta)S21 + B(X1)S9.9. --FA 2 - o B ( X 2 )
-'}-H(X2, WS,Ta)
+LE(X2, WS, Ta , R I, RH) =0, (3b)
l a30 ( B( Ta)S31-4-B( X, )S32 +B(Xe)Sa3 +B(X3)S34 +B(Tg)S35}
+ A 3 - o B ( X 3) + H(X3, WS, ra) +LE(X3, WS, T~, R z, RH) = 0 .
(3c) The formulatmn for each energy budget component used in the model is ~ven by Long-wave: Short-wave absorptmn '
n( x,)-- e,(X, --~273) 4, (4) A,-ABS(i).SW, (5)
h( X, ) = latent heat of vaponzahon of water at temperature X,; s(X,)= water vapor density mslde the leaf at saturation at the leaf temperature X, (g cm-3), s(Ta ) = water vapor density at saturation of the free mr beyond the boundary layer of the leaf at the axr temperature Ta (g cm-3), R a --resistance of the boundary layer to water vapor dtIfuslon, The terms s( X,), s(Ta), and R a are calculated from measured dnwng variables, U (Kames et al., 1981). The discusslon of the S matnx, which controls the interceptmn of long-wave flux wathm the canopy layers, ls given later. Explicit evaluation of the Jacobian
An lteratave Newton-Raphson Techtuque (Burden et al., 1978) was used to where solve the system of nonhnear thermal ABS(i) = short-wave absorplaon coeffl- equations (2) smee the Jacobian of the cxent calculated by an optacal system may be analyhcally derived m absorption model winch uses dosed form This method involves ltera Monte Carlo techmque to ahve evaluahon of the followang expresinclude multiple scattering ef- sion about an imtlal guess X 0 unttl 8X fects (Karnes and Smith, 1980; converges, Kimes et al., 1980). Sensible heat.
n ( x,; WS, Ta) =hc( WS)( X, - Ta) (6)
(8)
THERMAL VEGETATION CANOPY MODEL STUDIES
315
the geometnc matrtx S for a wide vanety of plant canopies as a means of charj = system Jacobaan = [OF/OX] x=x0" actenzmg their long-wave thermal behavior These precalculated matrices may The Jacoblan of the system is gxven by then be convolved wath the appropnate meteorologacal dnwng vanables as re0Fm qmred m order to sxmulate a multatude of L m - OX n , target/background scenarios. In addmon, the hnear form of Eq. (2) with respect to =2anemSnml(X m +273)3+~.m S suggests the possibility of applying hnear fdtenng theory to estimate S from X { 4 e m l ( X m =273) 3 + h o t ~ measurements of canopy temperature, X. The elements of the S, matrix describe the fraction of long-wave ematted flux 1 [s(Xn)_RHs(T~) ] ~h(X.) from a source layer, i (whxch includes the + R t +R-------~ OX., air above the canopy and ground layers as h(X.) Os(X.) ] well as the three vegetahon layers), that is + RI+R-------~ OX-------~' n , m = l , 2 , 3 antercepted by a sink layer , Thas flux (9) must escape the specific source layer 1 and then pass unimpeded through all m~nm IS the Dlrac delta function. Given termechate layers between the source layer specific algebraac expressmns for s(X.) i and the sank layer , before being mand h ( X . ) the partial denvatlves are easily tercepted by the canopy elements m layer z. evaluated To calculate S,1, we antegrate over all emattlng darectaons Or, q~,. the total flux Geometrical factorization--S matrix that escapes a source layer i and as inA slgmflcant slmphflcatmn of the ther- tercepted by a foliage element m layer i mal model from the development re- that has an orientation chrechon deported earher (Klmes et al., 1981) is the scribed by fohage mchnatmn angle 0k. To factonzatlon o[ the geometric-dependent calculate the total flux antercepted an layer terms from the energy related source z from a source layer i, we then sum the terms for the long-wave flux transfer energy intercepted by each fohage mprocesses. This factonzatlon is made pos- chnatlon class over the fohage lnchnatlon sable essentmlly because of the lack of angle dlstnbutmn occurnng m layer multiple scattenng m the thermal regime S p e c i f i c a l l y , between canopy components whose emls9 swmes (absorptlv~tles) are assumed nearly S,,= ]~ f, kC,,k, (10) unity and by the fact that the thermal k = l properties on both sides of a canopy component are assumed equal The mult~phcatwe separation of the geometry de- where pendent terms from the energy terms ~k = the leaf slope distribution for permRs the possabfllty of precalculatlng layer z= 1,2,3 and foliage anwhere
318
j A SMITH ET AL
canopy included acqmnng high contrast black and white shde photography of canopy silhouettes. For the purposes of our modehng, the canopies were partitioned into three layers of equal height. High contrast shdes were used as input to a laser dlffractometer and the ddfractmn patterns then optically sampled (Klmes et al, 1979). Separate branch and fohage measurements were combined to provide the lnchnahon angle dlstnbutlons for each layer. Leaf mchnatlon dlstnbuhons for the oak-hickory canopy were sampled m sltu for several leaves at 1-m intervals throughout the stand. The recorded distributions were summed and averaged over the appropriate layer-height intervals to provide the three-layer leaf-mchnatlon angle dlstnbutmns The leaf-angle dlstn-
buhons for the two canopies are compared on a layer by layer basxs m Fig. 1. Leaf-area index (LAI) is defined as the total one-sided leaf area occupying the horizontally prolected area of the canopy LAIs for the Douglas fir canopy were derived from measurements reported by Klnerson and Fntschen (1971) In this paper, graphs of canopy height z(m) versus surface area density F( z ), ( m2m- 3 ) for nine sample plots are given. Integrating F(z) over height gwes the needlesurface area mdex (NSAI) for a particular height mcrement (dz). For our modehng purposes, LAI values were determined by dlvidmg NSAI for each layer by two Data collected at the site since these measurements were made indicate no substantlal change of LAI since 1971 Values of LAI for the oak-hickory canopy layers
I0
A Oe (.~ Z I.~
0
ILl n"
06
W I--
04
.--I :::)
02 o Ook-hlckory
0 C ~'~1
I
0
I
I
I
I
I
I
I
I
20
30
40
50
60
70
80
90
LEAF INCLINATION ANGLE (degrees) FIGURE 1 Comparative plots of fohage lnehnahon angle vs cumulahve frequency for the three layer Douglas fir and oak-h~ckory canop]es A = Layer 1, B = Layer 2, C = Layer 3
THERMAL VEGETATION CANOPY MODEL STUDIES
Model Validation Experiments Data obtained at two existing research sites were utilized to evaluate the validity of the model One site is located in a Douglas fir canopy in the Cedar River watershed near Seattle, Washington. The second site, at the Walker Branch Watershed near Oak Badge, Tennessee, is typical of an Appalachaan mxxeddeciduous forest. Both research sites were being used for ongomg research in forest meteorology and had extensive instrum e n t a t i o n and c o m p u t e r i z e d data acquisition support
Cedar River, Washington site The Cedar Raver, Washington study site is located on the A. E Thompson Research Center at a mxcrometeorologacal observatory maintained and operated by the University of Washington 55 km southeast of Seattle, Washington The average elevation is approximately 215 m above sea level The dominant, naturally regenerated stand of Douglas fir [Pseudotsuga menzwsii (Mlrb) Franco] was approxamately 41 years old wath an average tree spacmg of 5.8 m. Average height of the Douglas fir stand was about 28 m wath an average leaf-area index (LAI) of approximately 7 8 Ground cover consisted of fern, salal, huckleberry, mosses, and htter Sod at the site consisted of Barneston gravelly loamy sand onglnatlng from glacial outwash (Jensen, 1976). Located at thas sate was a 28-m tall Douglas fir tree contained in a lyslmeter (Fntschen et al, 1973) The site adjacent to thas tree was instrumented to provade data for evapotransplrataon stuches These data included wet and dry bulb temperature profiles, soft temperatures, global
317
short-wave radiation, precipatatIon, and wind speed and darectlon. In addition, needle surface temperatures were monitored at several pomts around the lyslmeter tree near the top and center of the canopy
Walker Branch, Tennessee site The Walker Branch study site is located near the Walker Branch Watershed research faclhty on the U.S. Department of Energy Reservation near Oak Badge, Tennessee This research area is situated on a ndge top about 70 m above the valley floor at an elevation of 335 m above mean sea level The area is representatwe of an Appalachian deciduous forest (Hutchlson, 1977) The species composatlon of the stand is dominated by various species of oak and hickory. The average height of the codomlnant trees is about 21.5 m with lower limit of the hve crown being 15 m above the ground Basal area was approximately 26 m ~ ha -I Understory growth IS abundant and the ground is covered by a shallow accumtdatlon of litter Hutchison (1977) gives a detaaled descnptIon of the site and data available at the research faclhty.
Modeling Input Data The data collected at the two sites include fohage and background optical parameters, geometry charactenzatlon measurements, and envaronmental measurements. This section describes the data reqmred for our models and the techniques or sources used to acqmre it
Foliage geometry The procedure for determining fohage lnchnatlon angles for the Douglas fir
316
J A SMITH ET AL
chnatmn angle 0 k = 5 °, 15 °, ,85 ° C,k = fractmn of emitted flux from a source layer i that is intercepted by a fohage element mchned at angle 8 k within layer ~. If ~ represents a umt vector m the d~rectlon of an em:ttmg source element, described by /~, ~ , and d, a unit vector describing the onentatmn of an absorbing sink fohage element, then the amount of flux intercepted by tlus fohage element from dlrechon ~ 1s proportional to ]d P[ If we let CONT,~. represent the fraction of long-wave flux that is emitted from layer along dlrectmn P and IS finally intercepted m layer ,, then, C.~, the total flux intercepted by the fohage element emitted over all d~rectlons ~ in layer 1 is gwen by
elCONT,, d¢ dO . (11) Several investigators have described the calculatmn procedure for eshmatmg CONT,~ for various theorelacal canopms, e g., deW~t (1965) and Verhoef and Bunmk (1975). Basically the calculations reqmre the determmatmn of the probability of encountering a gap (or hit) in traversing a vegetahon layer winch is
populated by fohage elements possessing a leaf slope (hstnbutlon f,k and a l e a / o r fohage area mdex We have generahzed these ideas to multiple layers (Ohver and Smith, 1974). The specific expressions for these weighting coefficients for an arbitrary source darectmn ~ are summarized in Table 1 In this table, Po(~, r) represents the probabthty of encountenng a gap along dlrectmn ~ in traversmg layer z Note that the probability of traversing half a layer is gwen by Pol/2(i, r) and that the probabxhty of encountenng emlttmg fohage elements m a layer along a chrectlon ~ is gwen by 1-P0(i, r). For example, CONT:3 ~ represents the flux that :s emitted along dlrectmn f from source layer 3 (wh:ch is vegetation canopy layer 2) and is intercepted by sink layer 1 (whmh is vegetahon canopy layer 1) This is equal to the probabthty of having emlttmg elements in canopy layer 2. i e , the probab:hty of a hit m layer 2, [1-P0(2, r)], times the probabdlty that tins flux encounters a gap m traversing to the midelements of absorbing fohage m layer 1, Poll2(1, r). It is thus given by CONTI3 ~= Pol/2(1, r ) [ 1 - P o ( 2 , r)] = pol/2(1, r ) - P~)/2(1, r )Po (2, r) (12)
T A B L E 1 Expressions for contribution coefficients CONT, Ir for sink layer z, source component I and arbitrary direction 0r Po0, r ) = p r o b a b l h t y of gap in layer z m direction 0r SOURCE
SINK LAYER
LAYER
1
2
3
I
eol/2(l,r)
Po(l,r)eol/2(2,r)
Po(l r)eo(2,r)Pol/2(3,r)
2
211- e~/2(l, ,)]
e~/2(2,, ) - t'o~/2(2,r)Fo(1,r)
3 4
Po~/2(1,r)-P~/2(1, r)Po(2,r) 1'ol/2(1. r)Po(2,r) -Pd/Z(1, r)Po(2,r)P0(3,r) Po:/2(1,r)Po(2,r)Po(3,r)
2[1-pol/Z(2,r)] P~/2(2, r)-PoWZ(2, r)Po(3,r)
e~/2(3,r)eo(2, r) -10d/2(3, r)eo(2,r)eo(l, r ) PoW2(3,r)-Po~/2(3, r)Po(2,r) 211-P1/Z(3,r)]
PoWZ(2,r)Po(3,r)
P~/Z(3, r)
5
THERMAL VEGETATION CANOPY MODEL STUDIES
319
I0
B
>(.~ Z W 0
06
,~ O4 ._1
(.) 02 o Douglas-f=r o Ook-h=ckory
0
0
I I0
I 20
I 30
I 40
I 50
I 60
i 70
,I 80
I 90
LEAF INCLINATION ANGLE (degrees)
I0
(3
O8
06
04
¢.) O2 o Douglas-fir
OC
I
0
o
I
I
I
I
I
I
I
I
2o
30
40
50
eo
70
eo
9o
LEAF INCLINATION
ANGLE
(degrees)
320
j A SMITH ET AL
were denved from a graph of cumulative LAI versus height through the canopy. The graphs were generated by ATDL personnel from direct measurements. Table 2 hsts the LAIs and mldlayer heights used to model the Douglas fir and oakhickory canopies and the S matnces for each canopy.
Short-wave absorption coefficients The absorption of global short-wave radiation by canopy layers is an important component an the daytime energy budget. The radiation absorbed is a function of the global short-wave energy avadable, which is a measured input parameter to the model, and the short-wave interception coefficients for the canopy system, which in our case were estimated by a separate multiple scattenng absorptive Monte Carlo model (Fames and Smith, 1980) Strictly spealong these short-wave absorptton coefficients for the canopy and ground layers are a function of sun angle, a result borne out by the Monte Carlo analyses. However, for the thermal model reported here our objective was to slmphfy the reqmred analyses in order to
faclhtate the analysis of a multitude of canopy situations and reduce reqmred input data Extenswe analyses wath the complete treatment of short-wave energy absorption would be expensive and prewous analyses indicate that the absorption coefficients were relatively stable wathm 15-20% for sun angles ranging from nadar to zenith angles of 45 ° . It was felt that an average absorption value calculated for each canopy for these sun angles generally would be reasonable At large zenith solar angles the short-wave absorptaon coefficient becomes highly nonlinear In our treatment of this parameter we tend to underestimate this component of the energy source term significantly at early morning and late evening, but the magmtude of the insolation is relatively small at these hours. In order to estimate the short-wave flux absorption it as necessary to have estimates of the canopy and ground optical scattering properties, i e , reflectance and transmittance of fohage elements and ground layer Canopy element transmattance values were directly measured at both sites as well as average background reflectance
TABLE 2 Canopy layer heights, LAIs and S matrices for the Douglas hr and oak-hickory canopies modeled m this study DOUGLASFIR Mid-layer height (m)
Leaf-area index
Layer 1 Layer 2 Layer 3 Layer 1 Layer 2 Layer 3
OAK--HICKORY
23 3 14 0 47 15 53 10
18 3 11 0 37 34 08 04
To (1) LAYER S MATlaIX From (1)
Sky Layer 1 Layer 2 Layer 3 Ground
TO (0 LAYEB
1
2
3
1
2
0 2722 1 4484 0 2722 0 0000 0 0000
0 0006 0 0048 1 9820 0 0047 0 0007
0 0000 0 0000 0 2946 1 4035 0 2946
0 1595 1 6741 0 0470 0 0338 0 0788
0 0281 0 7914 0 3539 0 2589 0 5607
3 0 0 0 0 0
0201 5441 2574 3496 8217
THERMAL VEGETATION CANOPY MODEL STUDIES
values as described m the report (Smith et al., 1981). However, it was not prachcal to obtaan measurements of the canopy element reflectances, particularly for the Douglas fir needles Rather, hterature reflectance values for both old and new Douglas hr were obtained from Jarvas et al (1976) Similarly, measurements by Colwell (1969) were averaged for the oak-hickory leaves. In both cases the actual site measured transmittance values were used to ensure that at least physically reasonable reflectance estimates were obtained. Stomatal resistance
The resistance of the leaf to water vapor diffusion depends on many envaronmental factors Leaf stomates open and close in response to m~crocllmatlc and sod conditions and regulate the coohng of the plant through evapotransplratlon. This parameter is difficult to measure and highly vanable. For our modehng purposes average values were used as constants. The value for Douglas fir was set at 0.10 m m / c m Stomatal resistances measured for the oak-hickory canopy ranged from 0 04 to 0 07 m l n / c m for sun leaves The upper value was selected for use m the deciduous canopy simulations Stomatal resistance was set to infinity during mghthme hours for both canopies Model estimates of leaf temperatures are not very sensltwe to stomatal resistance at these values and tmder the moderate envaronmental cond~tlons encountered dunng the data collection (Smith et al., 1981). Emissivity and absorptivity The ablhty of a canopy element to emit and absorb long-wave radaahon is expressed by the emissivity and absorptivity coefficients specified in the model Emis-
321
Slvaty (e,) and absorptwaty (a,) were set to 1.0 for all three canopy layers Emissivity of the ground (eg) was also set to 1 0. Emlsslvaty of the air (e~) was calculated as a function of aar temperature by an emplncal relahonship (Hudson, 1969) Canopy temperature measurements
Since the purpose of the expenments was to collect data sets for vahdatlon of the thermal model, actual canopy fohage temperature measurements were reqtured The experimental setup at the Cedar Rwer site included temperature measurements for a number of lndlvadual Douglas hr needles The temperature sensors were located around the lys~meter tree at heights from 20 to 26 m. The measurements at a given height were averaged to gwe an average layer temperature. The 26-m measurement was assumed to represent the average canopy temperature for the top layer (Layer 1) The 20-m measurement was assumed to approximate the middle layer (Layer 2) although i t s location is closer to the boundary between Layer 1 and Layer 2. No lndlvadual leaf temperature measurements were available at the Walker Branch site, so a portable thermal radiometer 1 was used to monitor the canopy temperature throughout a 24-hr period The procedure was to position the instrument upward from the ground at the canopy and slowly move it untd the max~mum temperature was recorded. This was done to mmxmlze errors due to the presence of sky or clouds m the field of vaew. However, the referred measured temperature represents a value integrated over the entire depth of the canopy and 1Barnes Insta-Therm Barnes Engmeenng Corporation
322
j A SMITH ET AL
weighted most heavily toward the bottom of the canopy. It ~s, thus, not a precise measurement Environmental input parameters
peratures All measurements were either instantaneous or short t~me interval averages. Results
In addihon to the geometrical, optical and thermal parameters discussed above, a set of dynamic variables characterizing the microchmate of the target are reqtured to drive the thermal model. These parameters consist of aar temperature above the canopy, ground surface temperature, wand speed at the top of the canopy, relatwe hmmdlty, and global short-wave radiahon. Environmental data were provided from the automated recording systems at the two sites Air and ground temperatures and global short-wave radiatmn were measured directly. Relatwe humidity was determined from wet and dry bulb tern-
The data collected for the coniferous and deciduous canopies provided a good means of testing the thermal model under these diverse conditions. Three layer canopy temperature simulations were made over a 48-hr penod with both data sets and the results were compared w~th measured temperatures. Douglas fir canopy The thermal model was run wath envaronmental data acqmred over the 48-hr penod of 4 - 5 August 1979. The Layer 1 simulated temperatures followed the trend of air temperature
24
2C (J o
ILl
16
w t~. 12 w I..-~
8 o Layer 1~ Predicted A Layer 1,Observed
4
o
I
I
I
I
I
I
8
16
24
8
16
24
TIME (hours) 4
AUGUST
1979
I
5 AUGUST
1979
FIGURE 2 Layer 1 predicted temperatures plotted with average temperatures measured at the 26-m level m the Douglas hr canopy
T H E R M ~L VEGETATION CANOPY M O D E L STUDIES
323
20 c) 0
L,J nr
16
w n
12
ko I.-8
~
o Layer 2, Predicted A Layer 2, Observed
4
I
(
8
I
I
16
I
24
8
I
16
I
24
TIME (hours) i
4
AUGUST 1979
I
5 AUGUST 1979
FIGURE 3 Layer 2 predicted temperature plotted with average ternperature~ measured at the 20-m level m the Douglas fir canopy
throughout the 48-hr period Comparisons of measured and predicted needle temperatures are presented as Fig. 2 and 3 for Layers 1 and 2, respectively The Layer 1 predicted temperatures vaned from measured by a maximum of 3°C. These devaatlons were observed during the dayhght hours under hazy skies Nlghthme predzchons devmted from measured by 2°C or less with the maxim u m devlahons occurring under condlhans of fog. This leads us to conclude that the thermal model may be most valid for days with primarily direct solar radmhen and clear nights where radlahve coolmg 1s occurnng.
vahdate the thermal model for a deciduous oak-hzckory canopy. Nighttime slmulahons were nearly equal to mr temperature while daytime predlchons vaned by a maximum of 2°C over air temperature. Measured temperatures were compared to predicted results for Layer 2 and are shown m Fig. 4. The agreement between model and measured temperatures ~s quite good. However, as discussed earher an mdzrect measure of canopy effechve radiant temperatures was made. The largest devlahon (3°C) occurs m the afternoon whereas morning and mghtbrae predlchons vary only I ° C or less Summary
Oak-hickory canopy Enwronmental data acqmred at the Walker Branch site for the 48-hr period from 18-19 August 1979 were used to
A sunphfled thermal canopy model which treats the rachatlve flux transfers m some detaal and permits the mcorporahon of alternahve expressions for other energy
324
] A SMITH ET AL 55
50 ¢0 0
w 25 n.I,,~ ¢~ w n
20
I.aJ I--
[] Layer 2, Predicted Layer 2, Observed
10
I 8
I 16
I 24
I S
I 16
I 24
TIME (hours) I
18 AUGUST 1979
I
19 AUGUST 1979
FIGURE 4 Layer 2 predmted temperature plotted measured average temperature of oak-hickory canopy Measurements were made from the grotmd wath a thermal IR radmmeter
components has been described and shown to give reasonable results for two forest canopy situations. The model utilized detailed canopy structure charactenstms but m contrast to an earlier but more comprehensive form of the model (Kames et al., 1981) factors the long-wave energy source terms into a product of two terms, one dependent on thermal propertins only of the canopy (the Boltzmann source term) and the other on canopy geometric characteristics only. This factonzatlon has two significant apphcatlons First, as was done here, geometrical long-wave flux transfer matrices may be precalculated for a variety of targets and subsequently convolved with local meteorologmal scenarios Secondly, the hnear form of the factonzatmn suggests the use of hnear flltenng theory to estimate these flux transfer matrices gwen
measured observations This latter suggestion is currently being intensely investigated by the authors. The results of the model-experiment comparisons indicate that the model provades reasonable estimates of actual temperatures for nighttime periods to within 2°C for both canopies studied. Daytime slmulataons generally deviated from measured temperatures because, perhaps, of the slmphficatlons assumed for the shortwave flux absorption coefficients and the treatment of stomatal resistance. The results lndacate that the model may not adequately account for some of the energy transfers under more extreme environmental conditions. FmaUy, it should be noted that both in measurement situations, the model predmtmns, a~r temperature, and canopy temperature measurements all agree qmte
THERMAL VEGETATION CANOPY MODEL STUDIES
325
closely. The thermal model, however, provldes a convenient organization of the energy flow processes in a self-consistent manner which relates measured or predicted canopy temperatures to lntnnslc canopy parameters It thus permits the potential reference of canopy characteristics from measurements as suggested
Gates, D M. (1968), Energy Exchange m the Bwsphere, Harper and Row, Inc, New York, 131 p Goudxaaan, J (1977), Crop mlcrometeorology a sunulatlon study, Simulation Monographs PUDOC, Centre for Agricultural Pubhshmg and Documentation, Wagenmgen, The Netherlands, 249 p
above.
Hellman, J L, Karlemasu, E T , and Rosenberg, J j (1976), Thermal scanner measurement of canopy temperatures to estxmate evapotransplratlon, Remote Sens Enwron 5(2) 137-145
The research described m this paper was supported by the U.S. Army Corps of Engineers Waterways Experiment Station under Contract DA CW 39-77-C-0073 and, Hudson, R D, Jr (1969), Infrared System Engineering, Wdey, New York in part, by the U.S. Army Research Hutchason, B A (1977), Atmospheric turbuOffice--Durham under Grant No lence and diffusion laboratory deciduous DAAG29--79-C-0199 We wish to acforest meteorology research program, an knowledge the helpful assistance of Aloverview, ATDL, NOAA, Cont Fde 77/1, fonso Vasques of the Waterways Experillp ment Station w~th data collection experzJarvls, P G, James, G B, and Landsberg, J ments J (1976), in Vegetatwn and the Atmosphere, Vol 2 (J L Monteith, Ed), Referenees Academic Press, New York, 439 p Alderfer, R G, and Gates, D M (1971), Energy exchange m plant canopws, Ecology 52(5) 855-861
Jensen, E C (1976), The crown structure of a single codommant Douglas-fir, M S Thesis, Umverslty of Washington, Seattle, Washington, 83 p
Burden, R L, Faires, J D, and Reynolds, A C (1978), Numerical Analyses, Pnndle, Weber and Schmldt, Boston, MA Colweil, E E (1969), Seasonal change m lobar reflectance of five broadleaved forest tree species, Ph D Thesis, Umverslty of Mlchxgan, Ann Arbor, 112 p Deardorff, J W (1978), Efflcwnt prechctaon of ground surface temperature with inclusion of a layer of vegetation, ] Geophys Res (83) 1889-1904 deWlt, C T (1965), Photosynthesis of leaf canopaes Agr Res Pap 663, Wagenmgen, Netherlands, pp 1-57 Fntschen, L J, Cox, L, and IGnerson, R (1973), A 28-meter Douglas-fir in a weighmg lyslmeter, Forest Scz 19.256-261
Klmes, D S, Ranson, K J, IGrchner, J A, and Smith, J A (1978), Modehng descriptors and terraan modules Final Report under contract DACW 29-77-C-0073, Environmental Laboratory, U S Army Engineers Waterways Experiment Station, Vicksburg, Mxsslsslppl 125 p Kxmes, D S, Smith, J A, and Ranson, K J (1979), Terrain feature canopy modeling, Final Report under U S Army Research Office Grant DAAG29-78-0045, Colorado State Umverslty, Fort Colhns, CO Kxmes, D S, Smith, J A and Berry, K J (1979), Extension of the optical diffraction analysis techmque for estimating forest canopy geometry, Aust ] Bot 27 575-588 IGmes, D S, and Smith, J A (1980), Slmu-
326 latlon of solar radsatlon absorption m vegetation canopies, Appl Opt 19(16)28012811. Klmes, D S, Ranson, K J, and Smith, J A (1980), A Monte-Carlo calculation of the effects of canopy geometry on PhAR absorption, Photosynthetwa 14(1) 55-64 Klmes, D S, Smith, J A and Link, L E (1981), A thermal IR exltance model of a plant canopy Appl Opt 20(4) 623-632 Kmerson, R Jr, and Fntschen, L J (1971), Modehng a consferous forest canopy, Agr Meteor 8 439-445 Norman, J (1979), Modehng the complete crop canopy In Modification of the Energy Enwronment of Plant (B J Barfleld and J F Gerber, Eds ), ASAE Monograph Number 2, Amer Soc of Ag Engs, St Joseph, MI, 539 p Ohver, R E , and Sunth, J A (1974), A stochastic canopy model of d~umal reflectance, Final Report, U S Army Research Office, Durham, NC Regmato, R J, Idso, S B, Vedder, J F, Jackson, R D, Blanchard, M B, and Goettelman, R (1976), Sod water content and evaporation obtamed from groundbased and remote measurements, ] Geophys Res 81(9)1617-1620 Soer, F J R (1980), Estunatlon of regional evapotransplratlon and soft moisture condl-
J A SMITHET AL tlons using remotely sensed crop surface temperatures Remote Sens Enwron 9'2745 Sorenson, H W (1966), Kalman Fdtenng Techniques, Advances m Control Systems, Vol 3, 219 (C T Leondes, Ed ), Academic Press, New York
Sunth, J A, Ranson, K J, Nguyen, D, and Link, L E (1981), Thermal vegetation canopy model studies, Final Report under contract DACW39-77-C-0073, Enwronmental Laboratory, U S Army Engineers, Waterways Expenment Station, Vicksburg, MS, 297 p. Tlbbals, E C , Carr, E.K, Gates, D M, Krelth, F (1964), Radiation and convection in conffers, Amer J Bot 51(5)529-538 Verhoef, W , and Bunnd<, N J j (1975), A model study on the relations between crop characteristics and canopy spectral reflectance, NIWARS pubhcatlon No 33, 3 Knaalweg Delft, the Netherlands, 89 p Wlebelt, J A, and Henderson, J B (1977), Techniques and analysis of thermal infrared camouflage in fohated backgrounds, Final Report under contract DAAG-76-C0134, U S Army Moblhty Equipment Research and Development Command, Fort Belvolr, VA, 63 p Recewed 14 Aprz11980,revised16 January 1981
REMOTE SENSING OF ENVIRONMENT 11 311-326(1981)
Thermal Vegetation Canopy Model Studies
J A SMITH, K J RANSON, D. NGUYEN, L BALICK, College of Forestry and Natural Resources, Colorado State Umverszty, Fort Colhns, Colorado 80523
L E LINK, Enwronmental Laboratory, U S Army Corps of Engmeers Waterways Experiment Statzou, Vwksbur~ M~ss)ss~pp~39180
L FRITSCHEN, College of Forest Resources, Umvers~ty of Washington, Seattle, Washington 98115
and B HUTCHISON Atmospheric Turbulence and l~ffusmn Laboratory, Oak Rtdge, Tennessee 37830
An iteratwe-type thermal model apphcable to forest canopms was tested with data from two diverse torest types The model framework consists of a system of steady-state energy budget equataons describing the mteractmns oI short- and long-wave rachatmn within three horizontally mhmte canopy layers A state-space tormulatmn of the energy dynamics wlthm the canopy is used whtch permits a factonzataon of canopy geometrical parameters from canopy optmal and thermal coethcmnts as well as enwronmental driving variables Two sets of data characterizing a coniferous (Douglas-hr) and deciduous (oak-hmkory) canopy were collected to evaluate the thermal model The results show that the model approramates measured mean canopy temperatures to within 2°C for relahvely clear weather conditions and devaates by a mammum of 3°C for very hazy or foggy condmons
Introduction
Rapid and accurate assessment of renewable resources ~s an increasingly important task facing remote sensing speciahsts. Mathematical abstraction of energy processes of vegetahon canopies is a useful techmque for relalang sensor response to envaronment-canopy mteractrans. Such an understanchng is reqmred m order to make timely inferences about the conditmn of forestry and agricultural resources from remote sensors. In the thermal regime, several authors have re©Elsewer North Holland Inc, 1981 52 Vanderbdt Ave, New York, NY 10017
ported success m estimatmg evapotranspiration of crops from thermal sensor data (Heflman et al., 1976; Reginato et al., 1976; and Soer, 1980) Several models have been reported that describe the energy balance of vegetatmn either in terms of a single leaf (Gates, 1968; Wmbelt and Henderson, 1977, and I~mes et al., 1978), or an abstract layered canopy (Alderfer and Gates, 1971, and Deardorff, 1978). Few models have been described that characterize the energy flows wlthm vegetation canopies as a funchon of the canopy geometry (Goudnaan, 1977; Norman, 1979, and Kames et al., 1981). 00344257/81/040311+1650250
312
In this study, a modification of the thermal canopy model reported by Fames et al. (1981) that is applicable to forest canopies is described and evaluated. The model is an lteratwe type formulation of a system of steady-state energy budget equations describing a canopy as three horizontal layers. Each layer is described in terms of reflective and thermal radiation coefficients and leaf lnchnatlon angle distnbulaons. The model emphasizes the radlatwe energy processes occurnng both within and above the vegetataon canopy layers and relates these flux transfers to detaded consideration of the canopy geometry. Other energy transfer processes such as sensible heat and evapotransplratlon are included but in a farrly slmphslac manner Standard expressions from the literature are utilized. The modular form of the model makes it faarly easy to replace the existing expressions as warranted Thus, the model is capable of evaluating partacularly the ra&atwe energy processes from wadely diverse canopies There were two broad objectives of the work reported here First was to determine rf we could re-express a prevaously developed thermal exatance model (Fames et al., 1981) in a more usable form which would permit a wade variety of engineenng-type target/background stu&es to be performed in a more practacal computational fashion. The second objective was to evaluate the model wath vahdatlon data collected from two different forest types; a Douglas fir (Pseudotsuga menzzesii) canopy and a mrxed deciduous canopy. Here, we first describe the updated model structure and solutaon approach This is followed by a description of the experimental sites and methods for ob-
j A SMITH ET AL
taming the required model input data. Finally, the results and summary are given
Model Structure The updated model formulation given below differs m three major aspects from the onginal model developed by Fames et al. (1981). First, the model has been rewntten in a vector-matrix form with a state-space charactenzatlon. That is, there is a specific identification of a state vector X, the canopy layer tempera~tres, a control vector U, the meteorological driving variables, and a parameter vector P In this formulalaon, the long-wave energy budget terms have been factored into a geometnc-dependent term, the S matrix, and the long-wave thermal source terms This factonzatlon permits the precalculatmn of the S matrix for a wade variety of canopy situations and then the subsequent convolvmg of these matrices wath the U and P vectors to evaluate canopy thermal vanatlons. A second potential advantage of this factonzatlon is that it results in a hnear system of equations wath respect to S suggesting the use of hnear fdtenng theory to estimate S from X (Sorenson, 1966). The second modification is the use of more slmphfymg assumptions in the model, partacularly wath regard to the short-wave absorption calculation as discussed later. Finally, in solving the nonhnear energy budget equations, exphclt use was made of the closed form expressions for the Jacobian of the system m a Newton-Raphson technique. In the matenal that follows, mchvldual expressions for the component energy budget processes are summarized and an exphclt expression for the elements of the
THERMAL VEGETATION CANOPY MODEL STUDIES
Jacoinan matnx are given. The geometncal factonzataon of the energy budget equation for the long-wave flux transfers is derived. Energy balance framework
The model as a plane-parallel abstraction of a vegetat/on canopy davided into three honzontal layers. Two addataonal source layers are given by the atmosphere above the canopy and by the undedyang ground An energy balance framework, assumang steady-state condatxons, as formulated for each of the three vegetation layers (sinks) as a flmctlon of the five source layers. In the expressions that follow, i = 1, 2, 3 represents the sank or vegetation layers and t = 1, 2, 3, 4, 5 represents respectxvely the atmosphere, the three vegetation layers, and the ground source layers of energy flux The combination of the ,, i lnchces thus represents flux from source layer I to sank layer ~. The vector expressaon for the energy balance equations for layers 1, 2,3 consaderlng long-wave transfers, short-wave transfers, sensible heat, and evapotranspiration can be written as
313
tance of the boundary layer to ddfus~on ~s estamated from other measured parameters), S = l o n g - w a v e flux transfer matrix calculated from geometncal properties of the canopy, A=short-wave flux absorption coefficient vector, UA(ToTgWS RH SW) r is the control or input vector, To = mr temperature (°C), Tg = ground temperature (°C), WS = wand speed (m/see), R H = relatave humachty, S W - short-wave fltLX (w/m2). F may be rewritten m the following matrix form winch exphotly separates the geometrical properties of the canopy S from the remaining energy terms (Smath et al., 1981). F a~aoB(X)Ts-oB(x) + A + H(X) + L E ( X ) = 0 ,
(2) where B -- vector of long-wave emlssaon terms,
F(X,P,U) = 0 ,
(1)
where
Xa(XaXg.X3)T--the average layer temperature vector for layers 1, 2, 3, Pa(e,, ,--1,2,3, a,, ~=1,2,3, eg, RI, S, A) = t h e parameter vector characterlzmg the canopy layers, e,,a, =emassavity and absorphvity of the vegetation layers, eg, ag =emxsslvity and absorptavity of the ground layer, R t = l e a f stomatal resastanee to water vapor dfffusaon (Note that the resls-
H--vector of sensable heat, LE -- vector of evapotransp~rat/on terms, o--- Stefan-Boltzmann constant.
The slgnlficance of tins factonzatlon xs that a wade vanety of abstract or cannomcal canopaes may be characterized by precalculation of the S matrix. This matrLx table may then be convolved wath the appropriate meteorological dnving vanables to simulate diurnal behavior for a wide spectrum of scenarios. The vector equation (2) may be expanded for each layer and the exphot
l A SMITH ET AL
314
dependence on parameters or input variables may be in&cated by
where h C, the convection coefficmnt, is taken from Tibbals et al. (1964) EvapotransplraUon:
o,,o{B(To)Sn + B(T,)Sl )
LE ( X, , WS, To, R, RH ) 1
+ A , - o B ( X 1 ) + H(X 1;W$, Ta)
-- R+R------~a[s(X,)-RHs(Ta)]h(X,),
+ LE( X~, WS, ra, R t, RH) =0,
(7)
(3a) where
½a2o{B(Ta)S21 + B(X1)S9.9. --FA 2 - o B ( X 2 )
-'}-H(X2, WS,Ta)
+LE(X2, WS, Ta , R I, RH) =0, (3b)
l a30 ( B( Ta)S31-4-B( X, )S32 +B(Xe)Sa3 +B(X3)S34 +B(Tg)S35}
+ A 3 - o B ( X 3) + H(X3, WS, ra) +LE(X3, WS, T~, R z, RH) = 0 .
(3c) The formulatmn for each energy budget component used in the model is ~ven by Long-wave: Short-wave absorptmn '
n( x,)-- e,(X, --~273) 4, (4) A,-ABS(i).SW, (5)
h( X, ) = latent heat of vaponzahon of water at temperature X,; s(X,)= water vapor density mslde the leaf at saturation at the leaf temperature X, (g cm-3), s(Ta ) = water vapor density at saturation of the free mr beyond the boundary layer of the leaf at the axr temperature Ta (g cm-3), R a --resistance of the boundary layer to water vapor dtIfuslon, The terms s( X,), s(Ta), and R a are calculated from measured dnwng variables, U (Kames et al., 1981). The discusslon of the S matnx, which controls the interceptmn of long-wave flux wathm the canopy layers, ls given later. Explicit evaluation of the Jacobian
An lteratave Newton-Raphson Techtuque (Burden et al., 1978) was used to where solve the system of nonhnear thermal ABS(i) = short-wave absorplaon coeffl- equations (2) smee the Jacobian of the cxent calculated by an optacal system may be analyhcally derived m absorption model winch uses dosed form This method involves ltera Monte Carlo techmque to ahve evaluahon of the followang expresinclude multiple scattering ef- sion about an imtlal guess X 0 unttl 8X fects (Karnes and Smith, 1980; converges, Kimes et al., 1980). Sensible heat.
n ( x,; WS, Ta) =hc( WS)( X, - Ta) (6)
(8)
THERMAL VEGETATION CANOPY MODEL STUDIES
315
the geometnc matrtx S for a wide vanety of plant canopies as a means of charj = system Jacobaan = [OF/OX] x=x0" actenzmg their long-wave thermal behavior These precalculated matrices may The Jacoblan of the system is gxven by then be convolved wath the appropnate meteorologacal dnwng vanables as re0Fm qmred m order to sxmulate a multatude of L m - OX n , target/background scenarios. In addmon, the hnear form of Eq. (2) with respect to =2anemSnml(X m +273)3+~.m S suggests the possibility of applying hnear fdtenng theory to estimate S from X { 4 e m l ( X m =273) 3 + h o t ~ measurements of canopy temperature, X. The elements of the S, matrix describe the fraction of long-wave ematted flux 1 [s(Xn)_RHs(T~) ] ~h(X.) from a source layer, i (whxch includes the + R t +R-------~ OX., air above the canopy and ground layers as h(X.) Os(X.) ] well as the three vegetahon layers), that is + RI+R-------~ OX-------~' n , m = l , 2 , 3 antercepted by a sink layer , Thas flux (9) must escape the specific source layer 1 and then pass unimpeded through all m~nm IS the Dlrac delta function. Given termechate layers between the source layer specific algebraac expressmns for s(X.) i and the sank layer , before being mand h ( X . ) the partial denvatlves are easily tercepted by the canopy elements m layer z. evaluated To calculate S,1, we antegrate over all emattlng darectaons Or, q~,. the total flux Geometrical factorization--S matrix that escapes a source layer i and as inA slgmflcant slmphflcatmn of the ther- tercepted by a foliage element m layer i mal model from the development re- that has an orientation chrechon deported earher (Klmes et al., 1981) is the scribed by fohage mchnatmn angle 0k. To factonzatlon o[ the geometric-dependent calculate the total flux antercepted an layer terms from the energy related source z from a source layer i, we then sum the terms for the long-wave flux transfer energy intercepted by each fohage mprocesses. This factonzatlon is made pos- chnatlon class over the fohage lnchnatlon sable essentmlly because of the lack of angle dlstnbutmn occurnng m layer multiple scattenng m the thermal regime S p e c i f i c a l l y , between canopy components whose emls9 swmes (absorptlv~tles) are assumed nearly S,,= ]~ f, kC,,k, (10) unity and by the fact that the thermal k = l properties on both sides of a canopy component are assumed equal The mult~phcatwe separation of the geometry de- where pendent terms from the energy terms ~k = the leaf slope distribution for permRs the possabfllty of precalculatlng layer z= 1,2,3 and foliage anwhere
318
j A SMITH ET AL
canopy included acqmnng high contrast black and white shde photography of canopy silhouettes. For the purposes of our modehng, the canopies were partitioned into three layers of equal height. High contrast shdes were used as input to a laser dlffractometer and the ddfractmn patterns then optically sampled (Klmes et al, 1979). Separate branch and fohage measurements were combined to provide the lnchnahon angle dlstnbutlons for each layer. Leaf mchnatlon dlstnbuhons for the oak-hickory canopy were sampled m sltu for several leaves at 1-m intervals throughout the stand. The recorded distributions were summed and averaged over the appropriate layer-height intervals to provide the three-layer leaf-mchnatlon angle dlstnbutmns The leaf-angle dlstn-
buhons for the two canopies are compared on a layer by layer basxs m Fig. 1. Leaf-area index (LAI) is defined as the total one-sided leaf area occupying the horizontally prolected area of the canopy LAIs for the Douglas fir canopy were derived from measurements reported by Klnerson and Fntschen (1971) In this paper, graphs of canopy height z(m) versus surface area density F( z ), ( m2m- 3 ) for nine sample plots are given. Integrating F(z) over height gwes the needlesurface area mdex (NSAI) for a particular height mcrement (dz). For our modehng purposes, LAI values were determined by dlvidmg NSAI for each layer by two Data collected at the site since these measurements were made indicate no substantlal change of LAI since 1971 Values of LAI for the oak-hickory canopy layers
I0
A Oe (.~ Z I.~
0
ILl n"
06
W I--
04
.--I :::)
02 o Ook-hlckory
0 C ~'~1
I
0
I
I
I
I
I
I
I
I
20
30
40
50
60
70
80
90
LEAF INCLINATION ANGLE (degrees) FIGURE 1 Comparative plots of fohage lnehnahon angle vs cumulahve frequency for the three layer Douglas fir and oak-h~ckory canop]es A = Layer 1, B = Layer 2, C = Layer 3
THERMAL VEGETATION CANOPY MODEL STUDIES
Model Validation Experiments Data obtained at two existing research sites were utilized to evaluate the validity of the model One site is located in a Douglas fir canopy in the Cedar River watershed near Seattle, Washington. The second site, at the Walker Branch Watershed near Oak Badge, Tennessee, is typical of an Appalachaan mxxeddeciduous forest. Both research sites were being used for ongomg research in forest meteorology and had extensive instrum e n t a t i o n and c o m p u t e r i z e d data acquisition support
Cedar River, Washington site The Cedar Raver, Washington study site is located on the A. E Thompson Research Center at a mxcrometeorologacal observatory maintained and operated by the University of Washington 55 km southeast of Seattle, Washington The average elevation is approximately 215 m above sea level The dominant, naturally regenerated stand of Douglas fir [Pseudotsuga menzwsii (Mlrb) Franco] was approxamately 41 years old wath an average tree spacmg of 5.8 m. Average height of the Douglas fir stand was about 28 m wath an average leaf-area index (LAI) of approximately 7 8 Ground cover consisted of fern, salal, huckleberry, mosses, and htter Sod at the site consisted of Barneston gravelly loamy sand onglnatlng from glacial outwash (Jensen, 1976). Located at thas sate was a 28-m tall Douglas fir tree contained in a lyslmeter (Fntschen et al, 1973) The site adjacent to thas tree was instrumented to provade data for evapotransplrataon stuches These data included wet and dry bulb temperature profiles, soft temperatures, global
317
short-wave radiation, precipatatIon, and wind speed and darectlon. In addition, needle surface temperatures were monitored at several pomts around the lyslmeter tree near the top and center of the canopy
Walker Branch, Tennessee site The Walker Branch study site is located near the Walker Branch Watershed research faclhty on the U.S. Department of Energy Reservation near Oak Badge, Tennessee This research area is situated on a ndge top about 70 m above the valley floor at an elevation of 335 m above mean sea level The area is representatwe of an Appalachian deciduous forest (Hutchlson, 1977) The species composatlon of the stand is dominated by various species of oak and hickory. The average height of the codomlnant trees is about 21.5 m with lower limit of the hve crown being 15 m above the ground Basal area was approximately 26 m ~ ha -I Understory growth IS abundant and the ground is covered by a shallow accumtdatlon of litter Hutchison (1977) gives a detaaled descnptIon of the site and data available at the research faclhty.
Modeling Input Data The data collected at the two sites include fohage and background optical parameters, geometry charactenzatlon measurements, and envaronmental measurements. This section describes the data reqmred for our models and the techniques or sources used to acqmre it
Foliage geometry The procedure for determining fohage lnchnatlon angles for the Douglas fir
316
J A SMITH ET AL
chnatmn angle 0 k = 5 °, 15 °, ,85 ° C,k = fractmn of emitted flux from a source layer i that is intercepted by a fohage element mchned at angle 8 k within layer ~. If ~ represents a umt vector m the d~rectlon of an em:ttmg source element, described by /~, ~ , and d, a unit vector describing the onentatmn of an absorbing sink fohage element, then the amount of flux intercepted by tlus fohage element from dlrechon ~ 1s proportional to ]d P[ If we let CONT,~. represent the fraction of long-wave flux that is emitted from layer along dlrectmn P and IS finally intercepted m layer ,, then, C.~, the total flux intercepted by the fohage element emitted over all d~rectlons ~ in layer 1 is gwen by
elCONT,, d¢ dO . (11) Several investigators have described the calculatmn procedure for eshmatmg CONT,~ for various theorelacal canopms, e g., deW~t (1965) and Verhoef and Bunmk (1975). Basically the calculations reqmre the determmatmn of the probability of encountering a gap (or hit) in traversing a vegetahon layer winch is
populated by fohage elements possessing a leaf slope (hstnbutlon f,k and a l e a / o r fohage area mdex We have generahzed these ideas to multiple layers (Ohver and Smith, 1974). The specific expressions for these weighting coefficients for an arbitrary source darectmn ~ are summarized in Table 1 In this table, Po(~, r) represents the probabthty of encountenng a gap along dlrectmn ~ in traversmg layer z Note that the probability of traversing half a layer is gwen by Pol/2(i, r) and that the probabxhty of encountenng emlttmg fohage elements m a layer along a chrectlon ~ is gwen by 1-P0(i, r). For example, CONT:3 ~ represents the flux that :s emitted along dlrectmn f from source layer 3 (wh:ch is vegetation canopy layer 2) and is intercepted by sink layer 1 (whmh is vegetahon canopy layer 1) This is equal to the probabthty of having emlttmg elements in canopy layer 2. i e , the probab:hty of a hit m layer 2, [1-P0(2, r)], times the probabdlty that tins flux encounters a gap m traversing to the midelements of absorbing fohage m layer 1, Poll2(1, r). It is thus given by CONTI3 ~= Pol/2(1, r ) [ 1 - P o ( 2 , r)] = pol/2(1, r ) - P~)/2(1, r )Po (2, r) (12)
T A B L E 1 Expressions for contribution coefficients CONT, Ir for sink layer z, source component I and arbitrary direction 0r Po0, r ) = p r o b a b l h t y of gap in layer z m direction 0r SOURCE
SINK LAYER
LAYER
1
2
3
I
eol/2(l,r)
Po(l,r)eol/2(2,r)
Po(l r)eo(2,r)Pol/2(3,r)
2
211- e~/2(l, ,)]
e~/2(2,, ) - t'o~/2(2,r)Fo(1,r)
3 4
Po~/2(1,r)-P~/2(1, r)Po(2,r) 1'ol/2(1. r)Po(2,r) -Pd/Z(1, r)Po(2,r)P0(3,r) Po:/2(1,r)Po(2,r)Po(3,r)
2[1-pol/Z(2,r)] P~/2(2, r)-PoWZ(2, r)Po(3,r)
e~/2(3,r)eo(2, r) -10d/2(3, r)eo(2,r)eo(l, r ) PoW2(3,r)-Po~/2(3, r)Po(2,r) 211-P1/Z(3,r)]
PoWZ(2,r)Po(3,r)
P~/Z(3, r)
5
THERMAL VEGETATION CANOPY MODEL STUDIES
319
I0
B
>(.~ Z W 0
06
,~ O4 ._1
(.) 02 o Douglas-f=r o Ook-h=ckory
0
0
I I0
I 20
I 30
I 40
I 50
I 60
i 70
,I 80
I 90
LEAF INCLINATION ANGLE (degrees)
I0
(3
O8
06
04
¢.) O2 o Douglas-fir
OC
I
0
o
I
I
I
I
I
I
I
I
2o
30
40
50
eo
70
eo
9o
LEAF INCLINATION
ANGLE
(degrees)
320
j A SMITH ET AL
were denved from a graph of cumulative LAI versus height through the canopy. The graphs were generated by ATDL personnel from direct measurements. Table 2 hsts the LAIs and mldlayer heights used to model the Douglas fir and oakhickory canopies and the S matnces for each canopy.
Short-wave absorption coefficients The absorption of global short-wave radiation by canopy layers is an important component an the daytime energy budget. The radiation absorbed is a function of the global short-wave energy avadable, which is a measured input parameter to the model, and the short-wave interception coefficients for the canopy system, which in our case were estimated by a separate multiple scattenng absorptive Monte Carlo model (Fames and Smith, 1980) Strictly spealong these short-wave absorptton coefficients for the canopy and ground layers are a function of sun angle, a result borne out by the Monte Carlo analyses. However, for the thermal model reported here our objective was to slmphfy the reqmred analyses in order to
faclhtate the analysis of a multitude of canopy situations and reduce reqmred input data Extenswe analyses wath the complete treatment of short-wave energy absorption would be expensive and prewous analyses indicate that the absorption coefficients were relatively stable wathm 15-20% for sun angles ranging from nadar to zenith angles of 45 ° . It was felt that an average absorption value calculated for each canopy for these sun angles generally would be reasonable At large zenith solar angles the short-wave absorptaon coefficient becomes highly nonlinear In our treatment of this parameter we tend to underestimate this component of the energy source term significantly at early morning and late evening, but the magmtude of the insolation is relatively small at these hours. In order to estimate the short-wave flux absorption it as necessary to have estimates of the canopy and ground optical scattering properties, i e , reflectance and transmittance of fohage elements and ground layer Canopy element transmattance values were directly measured at both sites as well as average background reflectance
TABLE 2 Canopy layer heights, LAIs and S matrices for the Douglas hr and oak-hickory canopies modeled m this study DOUGLASFIR Mid-layer height (m)
Leaf-area index
Layer 1 Layer 2 Layer 3 Layer 1 Layer 2 Layer 3
OAK--HICKORY
23 3 14 0 47 15 53 10
18 3 11 0 37 34 08 04
To (1) LAYER S MATlaIX From (1)
Sky Layer 1 Layer 2 Layer 3 Ground
TO (0 LAYEB
1
2
3
1
2
0 2722 1 4484 0 2722 0 0000 0 0000
0 0006 0 0048 1 9820 0 0047 0 0007
0 0000 0 0000 0 2946 1 4035 0 2946
0 1595 1 6741 0 0470 0 0338 0 0788
0 0281 0 7914 0 3539 0 2589 0 5607
3 0 0 0 0 0
0201 5441 2574 3496 8217
THERMAL VEGETATION CANOPY MODEL STUDIES
values as described m the report (Smith et al., 1981). However, it was not prachcal to obtaan measurements of the canopy element reflectances, particularly for the Douglas fir needles Rather, hterature reflectance values for both old and new Douglas hr were obtained from Jarvas et al (1976) Similarly, measurements by Colwell (1969) were averaged for the oak-hickory leaves. In both cases the actual site measured transmittance values were used to ensure that at least physically reasonable reflectance estimates were obtained. Stomatal resistance
The resistance of the leaf to water vapor diffusion depends on many envaronmental factors Leaf stomates open and close in response to m~crocllmatlc and sod conditions and regulate the coohng of the plant through evapotransplratlon. This parameter is difficult to measure and highly vanable. For our modehng purposes average values were used as constants. The value for Douglas fir was set at 0.10 m m / c m Stomatal resistances measured for the oak-hickory canopy ranged from 0 04 to 0 07 m l n / c m for sun leaves The upper value was selected for use m the deciduous canopy simulations Stomatal resistance was set to infinity during mghthme hours for both canopies Model estimates of leaf temperatures are not very sensltwe to stomatal resistance at these values and tmder the moderate envaronmental cond~tlons encountered dunng the data collection (Smith et al., 1981). Emissivity and absorptivity The ablhty of a canopy element to emit and absorb long-wave radaahon is expressed by the emissivity and absorptivity coefficients specified in the model Emis-
321
Slvaty (e,) and absorptwaty (a,) were set to 1.0 for all three canopy layers Emissivity of the ground (eg) was also set to 1 0. Emlsslvaty of the air (e~) was calculated as a function of aar temperature by an emplncal relahonship (Hudson, 1969) Canopy temperature measurements
Since the purpose of the expenments was to collect data sets for vahdatlon of the thermal model, actual canopy fohage temperature measurements were reqtured The experimental setup at the Cedar Rwer site included temperature measurements for a number of lndlvadual Douglas hr needles The temperature sensors were located around the lys~meter tree at heights from 20 to 26 m. The measurements at a given height were averaged to gwe an average layer temperature. The 26-m measurement was assumed to represent the average canopy temperature for the top layer (Layer 1) The 20-m measurement was assumed to approximate the middle layer (Layer 2) although i t s location is closer to the boundary between Layer 1 and Layer 2. No lndlvadual leaf temperature measurements were available at the Walker Branch site, so a portable thermal radiometer 1 was used to monitor the canopy temperature throughout a 24-hr period The procedure was to position the instrument upward from the ground at the canopy and slowly move it untd the max~mum temperature was recorded. This was done to mmxmlze errors due to the presence of sky or clouds m the field of vaew. However, the referred measured temperature represents a value integrated over the entire depth of the canopy and 1Barnes Insta-Therm Barnes Engmeenng Corporation
322
j A SMITH ET AL
weighted most heavily toward the bottom of the canopy. It ~s, thus, not a precise measurement Environmental input parameters
peratures All measurements were either instantaneous or short t~me interval averages. Results
In addihon to the geometrical, optical and thermal parameters discussed above, a set of dynamic variables characterizing the microchmate of the target are reqtured to drive the thermal model. These parameters consist of aar temperature above the canopy, ground surface temperature, wand speed at the top of the canopy, relatwe hmmdlty, and global short-wave radiahon. Environmental data were provided from the automated recording systems at the two sites Air and ground temperatures and global short-wave radiatmn were measured directly. Relatwe humidity was determined from wet and dry bulb tern-
The data collected for the coniferous and deciduous canopies provided a good means of testing the thermal model under these diverse conditions. Three layer canopy temperature simulations were made over a 48-hr penod with both data sets and the results were compared w~th measured temperatures. Douglas fir canopy The thermal model was run wath envaronmental data acqmred over the 48-hr penod of 4 - 5 August 1979. The Layer 1 simulated temperatures followed the trend of air temperature
24
2C (J o
ILl
16
w t~. 12 w I..-~
8 o Layer 1~ Predicted A Layer 1,Observed
4
o
I
I
I
I
I
I
8
16
24
8
16
24
TIME (hours) 4
AUGUST
1979
I
5 AUGUST
1979
FIGURE 2 Layer 1 predicted temperatures plotted with average temperatures measured at the 26-m level m the Douglas hr canopy
T H E R M ~L VEGETATION CANOPY M O D E L STUDIES
323
20 c) 0
L,J nr
16
w n
12
ko I.-8
~
o Layer 2, Predicted A Layer 2, Observed
4
I
(
8
I
I
16
I
24
8
I
16
I
24
TIME (hours) i
4
AUGUST 1979
I
5 AUGUST 1979
FIGURE 3 Layer 2 predicted temperature plotted with average ternperature~ measured at the 20-m level m the Douglas fir canopy
throughout the 48-hr period Comparisons of measured and predicted needle temperatures are presented as Fig. 2 and 3 for Layers 1 and 2, respectively The Layer 1 predicted temperatures vaned from measured by a maximum of 3°C. These devaatlons were observed during the dayhght hours under hazy skies Nlghthme predzchons devmted from measured by 2°C or less with the maxim u m devlahons occurring under condlhans of fog. This leads us to conclude that the thermal model may be most valid for days with primarily direct solar radmhen and clear nights where radlahve coolmg 1s occurnng.
vahdate the thermal model for a deciduous oak-hzckory canopy. Nighttime slmulahons were nearly equal to mr temperature while daytime predlchons vaned by a maximum of 2°C over air temperature. Measured temperatures were compared to predicted results for Layer 2 and are shown m Fig. 4. The agreement between model and measured temperatures ~s quite good. However, as discussed earher an mdzrect measure of canopy effechve radiant temperatures was made. The largest devlahon (3°C) occurs m the afternoon whereas morning and mghtbrae predlchons vary only I ° C or less Summary
Oak-hickory canopy Enwronmental data acqmred at the Walker Branch site for the 48-hr period from 18-19 August 1979 were used to
A sunphfled thermal canopy model which treats the rachatlve flux transfers m some detaal and permits the mcorporahon of alternahve expressions for other energy
324
] A SMITH ET AL 55
50 ¢0 0
w 25 n.I,,~ ¢~ w n
20
I.aJ I--
[] Layer 2, Predicted Layer 2, Observed
10
I 8
I 16
I 24
I S
I 16
I 24
TIME (hours) I
18 AUGUST 1979
I
19 AUGUST 1979
FIGURE 4 Layer 2 predmted temperature plotted measured average temperature of oak-hickory canopy Measurements were made from the grotmd wath a thermal IR radmmeter
components has been described and shown to give reasonable results for two forest canopy situations. The model utilized detailed canopy structure charactenstms but m contrast to an earlier but more comprehensive form of the model (Kames et al., 1981) factors the long-wave energy source terms into a product of two terms, one dependent on thermal propertins only of the canopy (the Boltzmann source term) and the other on canopy geometric characteristics only. This factonzatlon has two significant apphcatlons First, as was done here, geometrical long-wave flux transfer matrices may be precalculated for a variety of targets and subsequently convolved with local meteorologmal scenarios Secondly, the hnear form of the factonzatmn suggests the use of hnear flltenng theory to estimate these flux transfer matrices gwen
measured observations This latter suggestion is currently being intensely investigated by the authors. The results of the model-experiment comparisons indicate that the model provades reasonable estimates of actual temperatures for nighttime periods to within 2°C for both canopies studied. Daytime slmulataons generally deviated from measured temperatures because, perhaps, of the slmphficatlons assumed for the shortwave flux absorption coefficients and the treatment of stomatal resistance. The results lndacate that the model may not adequately account for some of the energy transfers under more extreme environmental conditions. FmaUy, it should be noted that both in measurement situations, the model predmtmns, a~r temperature, and canopy temperature measurements all agree qmte
THERMAL VEGETATION CANOPY MODEL STUDIES
325
closely. The thermal model, however, provldes a convenient organization of the energy flow processes in a self-consistent manner which relates measured or predicted canopy temperatures to lntnnslc canopy parameters It thus permits the potential reference of canopy characteristics from measurements as suggested
Gates, D M. (1968), Energy Exchange m the Bwsphere, Harper and Row, Inc, New York, 131 p Goudxaaan, J (1977), Crop mlcrometeorology a sunulatlon study, Simulation Monographs PUDOC, Centre for Agricultural Pubhshmg and Documentation, Wagenmgen, The Netherlands, 249 p
above.
Hellman, J L, Karlemasu, E T , and Rosenberg, J j (1976), Thermal scanner measurement of canopy temperatures to estxmate evapotransplratlon, Remote Sens Enwron 5(2) 137-145
The research described m this paper was supported by the U.S. Army Corps of Engineers Waterways Experiment Station under Contract DA CW 39-77-C-0073 and, Hudson, R D, Jr (1969), Infrared System Engineering, Wdey, New York in part, by the U.S. Army Research Hutchason, B A (1977), Atmospheric turbuOffice--Durham under Grant No lence and diffusion laboratory deciduous DAAG29--79-C-0199 We wish to acforest meteorology research program, an knowledge the helpful assistance of Aloverview, ATDL, NOAA, Cont Fde 77/1, fonso Vasques of the Waterways Experillp ment Station w~th data collection experzJarvls, P G, James, G B, and Landsberg, J ments J (1976), in Vegetatwn and the Atmosphere, Vol 2 (J L Monteith, Ed), Referenees Academic Press, New York, 439 p Alderfer, R G, and Gates, D M (1971), Energy exchange m plant canopws, Ecology 52(5) 855-861
Jensen, E C (1976), The crown structure of a single codommant Douglas-fir, M S Thesis, Umverslty of Washington, Seattle, Washington, 83 p
Burden, R L, Faires, J D, and Reynolds, A C (1978), Numerical Analyses, Pnndle, Weber and Schmldt, Boston, MA Colweil, E E (1969), Seasonal change m lobar reflectance of five broadleaved forest tree species, Ph D Thesis, Umverslty of Mlchxgan, Ann Arbor, 112 p Deardorff, J W (1978), Efflcwnt prechctaon of ground surface temperature with inclusion of a layer of vegetation, ] Geophys Res (83) 1889-1904 deWlt, C T (1965), Photosynthesis of leaf canopaes Agr Res Pap 663, Wagenmgen, Netherlands, pp 1-57 Fntschen, L J, Cox, L, and IGnerson, R (1973), A 28-meter Douglas-fir in a weighmg lyslmeter, Forest Scz 19.256-261
Klmes, D S, Ranson, K J, IGrchner, J A, and Smith, J A (1978), Modehng descriptors and terraan modules Final Report under contract DACW 29-77-C-0073, Environmental Laboratory, U S Army Engineers Waterways Experiment Station, Vicksburg, Mxsslsslppl 125 p Kxmes, D S, Smith, J A, and Ranson, K J (1979), Terrain feature canopy modeling, Final Report under U S Army Research Office Grant DAAG29-78-0045, Colorado State Umverslty, Fort Colhns, CO Kxmes, D S, Smith, J A and Berry, K J (1979), Extension of the optical diffraction analysis techmque for estimating forest canopy geometry, Aust ] Bot 27 575-588 IGmes, D S, and Smith, J A (1980), Slmu-
326 latlon of solar radsatlon absorption m vegetation canopies, Appl Opt 19(16)28012811. Klmes, D S, Ranson, K J, and Smith, J A (1980), A Monte-Carlo calculation of the effects of canopy geometry on PhAR absorption, Photosynthetwa 14(1) 55-64 Klmes, D S, Smith, J A and Link, L E (1981), A thermal IR exltance model of a plant canopy Appl Opt 20(4) 623-632 Kmerson, R Jr, and Fntschen, L J (1971), Modehng a consferous forest canopy, Agr Meteor 8 439-445 Norman, J (1979), Modehng the complete crop canopy In Modification of the Energy Enwronment of Plant (B J Barfleld and J F Gerber, Eds ), ASAE Monograph Number 2, Amer Soc of Ag Engs, St Joseph, MI, 539 p Ohver, R E , and Sunth, J A (1974), A stochastic canopy model of d~umal reflectance, Final Report, U S Army Research Office, Durham, NC Regmato, R J, Idso, S B, Vedder, J F, Jackson, R D, Blanchard, M B, and Goettelman, R (1976), Sod water content and evaporation obtamed from groundbased and remote measurements, ] Geophys Res 81(9)1617-1620 Soer, F J R (1980), Estunatlon of regional evapotransplratlon and soft moisture condl-
J A SMITHET AL tlons using remotely sensed crop surface temperatures Remote Sens Enwron 9'2745 Sorenson, H W (1966), Kalman Fdtenng Techniques, Advances m Control Systems, Vol 3, 219 (C T Leondes, Ed ), Academic Press, New York
Sunth, J A, Ranson, K J, Nguyen, D, and Link, L E (1981), Thermal vegetation canopy model studies, Final Report under contract DACW39-77-C-0073, Enwronmental Laboratory, U S Army Engineers, Waterways Expenment Station, Vicksburg, MS, 297 p. Tlbbals, E C , Carr, E.K, Gates, D M, Krelth, F (1964), Radiation and convection in conffers, Amer J Bot 51(5)529-538 Verhoef, W , and Bunnd<, N J j (1975), A model study on the relations between crop characteristics and canopy spectral reflectance, NIWARS pubhcatlon No 33, 3 Knaalweg Delft, the Netherlands, 89 p Wlebelt, J A, and Henderson, J B (1977), Techniques and analysis of thermal infrared camouflage in fohated backgrounds, Final Report under contract DAAG-76-C0134, U S Army Moblhty Equipment Research and Development Command, Fort Belvolr, VA, 63 p Recewed 14 Aprz11980,revised16 January 1981