P&s. Chem .Earth (B), Vol. 25, No. 2, pp. 147-157,200O 0 2000 Elsevier Science Ltd All rights reserved 1464-1909/00/S - see front matter
Pergamon
PII: S1464-1909(99)00128-S
S-SEBI: A Simple Remote Sensing Algorithm to Estimate the Surface Energy Balance G. J. Roerink,
Z. Su, M. Menenti
DLO-Winand Staring Centre for Integrated The Netherlands.
Land, Soil and Water Research (SC-DLO), P.O. Box 125,670O AC Wageningen,
Received 24 April 1999; accepted I I October 1999
surface energy balance were measured by several techniques and for several field sites. Together with the LANDSAT-TM scene of 23 August 1997 of the same area this gives an excellent opportunity for a profound study of interaction between the radiation and energy fluxes. A new relative simple method to derive the surface energy fluxes from remote sensing measurements, called the Simplified Surface Energy Balance Index (S-SEBI), is developed, tested and validated with the in-situ flux measurements. Basically it determines a reflectance dependant maximum temperature for dry conditions and a reflectance dependant minimum temperature for wet conditions, whereafter the sensible and latent heat fluxes are partitioned according to the actual surface temperature. The major advantages over other remote sensing flux algorithms, such as presented by Choudhury (1989), Moran and Jackson (1991), Kustas and Norman (1996) and Bastiaanssen (1995) are: (I) no additional meteorological data is needed to calculate the fluxes if the surface hydrological extremes are present and (ii) the extreme temperatures for the wet and dry conditions vary with changing reflectance values, where the other methods try to determine a fixed temperature for wet and dry conditions for the whole image and/or for each land use class.
Abstract. A small field campaign was conducted during August 1997 in the Piano di Rosia area in Tuscany, Italy. The terms of both the radiation balance and the surface energy balance were measured by several techniques and for several field sites. Together with a LANDSAT-TM scene of 23 August 1997 of the same area, these data give an excellent opportunity for a profound study of interaction between the radiation and energy fluxes from point to regional scale. A new method to derive the surface energy fluxes from remote sensing measurements, called the Simplified Surface Energy Balance Index (S-SEBI), is developed, tested and validated with the available data. If the atmospheric conditions over the area can be considered constant and the area reflects sufficient variations in surface hydrological conditions the fluxes can be calculated without any further information than the remote sensing image itself. The results of this case study show that with the relative simple S-SEBI method the surface energy balance parameters can be estimated with a high precision. The measured and estimated evaporative fraction values have a maximum relative difference of 8%. 0 2000 Elsevier Science Ltd. All rights reserved 1 Introduction The exchange processes occurring at the land surface are of crucial importance for the re-distribution of moisture and heat in soil and atmosphere. The land surface connects the radiation, energy and water balances of the soil and atmosphere. To improve the understanding of these exchange processes the utilisation of satellite remote sensing is indispensable to extrapolate in-situ measurements to a regional scale. LANDSAT-TM data can be compared directly with field measurements, because of its high resolution. A small field campaign within the framework of the Sensing of Mediterranean RESMEDES (Remote Desertification and Environmental Stability) project was conducted during August 1997 in the Piano di Rosia area in Tuscany, Italy. The terms of both the radiation balance and the
Correspondence
Table 1. Brief description Image Characteristic Sensor Path/Row Acquisition Date Acquisition Time Number of Rows Number of Columns Reference System Resolution Min. Max. Min. Max.
to: G.J. Roerink 147
X-Coordinate X-Coordinate Y-Coordinate Y-Coordinate
of the LANDSAT-TM
image.
value LANDSAT5TM l92/30 23 August 1997 9:30:54 GMT 2540 3104 UTM-32N Band
1.2.3.4S.7:
Band 6: 120 m 608970 702120 4742960 4819160
30 m
G.Roerink el al.: S-SEBI: An Algorithm to Estimate the Surface Energy Balance
148
Fig. 1. Colour coqosite of LANDSAT-‘TMbands 4 (red), 5 (green) and 3 (blue), Tuscany, Italy, 23 August 1997. The enlarged subset encompasses the Piano di Rosia area, where the field campaign took place.
Table 2. Overview of available DEM sources. DEM map Map_Tuscany Map62_476 Map63_476 Map65478 Map66_478 Map66_479 Map67_478 Map68-478
Reference System UTM-32N UTM-32N UTM-32N UTM-32N UTM-32N UTM-32N UTM-32N UTM-32N
Resolution 250 m 20 m 20 m 20m 20m 20 m 20 m 20m
2 Material and method 2.1 LANDSAT-TM data During the RESMEDES field campaign in the Piano di Rosia area in Tuscany, Italy the LANDSAT-TM sensor passed by on 23 August 1997, 9:30:54 GMT. A colour composite of bands 4, 5 and 3 is shown in Fig. 1, together with a subset of the Piano di Rosia area, where the field campaign took place. Table 1 gives the main characteristics of the image. 2.2 DEM data Tuscany is a hilly area; therefore a Digital Elevation Model (DEM) is necessary to correct for the solar incidence angle at the surface and the cooling effect of altitude on temperature. Two types of DEM’s are available. The first one covers the whole LANDSAT-TM area with a resolution of 250 m, the second type are DEM’s of several Tuscany sub-areas of approximately 10x10 km with a resolution of 20 m. Table 2 gives an overview of available DEM sources. To make use of all available DEM sources slope and aspect are calculated first for every DEM, whereafter they are
UL-comer 494001,4929056.5 620000,477OCOO 630000,4770000 65oooO,4790500 660000,4790000 660000,48OOOOO 670000,4795000 68COOO,4795000
LR-comer 810501,4678556.5 630000,4760000 64OOQO,4760000 660003,4780500 670000,4780000 670000,4790000 680000,478500 690000,4785OCO
resampled to the LANDSAT-TM resolution of 30 m. Finally the 10x10 km sub-areas (of 20 m resolution originally) are mozaiked with the DEM, covering the whole area (of 250 m resolution originally). 2.3 Field campaign Ground truth data were collected during a small field campaign in the Rosia di Piano area in Tuscany, August 1997. The terms of the radiation and the surface energy balance were measured at 4 sites: sugar beet, maize, sunflower and wheat stubble. Table 3 shows the measured values. Fig. 1 shows the LANDSAT-TM image overlaid with the boundaries of the field sites. The surface energy balance parameters were measured with eddy correlation and bowen ratio method (respectively indicated as eddy and bowen in Table 3). On a larger scale the sensible heat flux was measured with a scintillometer (indicated as LAS in Table 3); this is a device measuring the refraction index of air, which can be related to temperature fluctuation and subsequently to the sensible heat. For a detailed description, see De Bruin et al. (1995). The term ‘residual’indicates that the surface parameter is not actually measured, but is derived as the rest term of the radiation or energy balance.
wxa uv .saxnj3 Ghaua aql30 uoypyhi .103uam am sarqeA asay) ‘uo!$e~p~?~lau pa%elahe lilmoq aql Y]!M sa!cwdams!p lsalp2urs aql aheq saxnU &aua 30 sanphi ~mg 0~:6-00:6 aql aw!s wuauIamseauI pIarJ aqj Buga&alu! uaqhi uoywap!suo3 olu! uayal aq pInoqs s!q~ Wq3 ivaq iuaiel pue aIq!suas) saxnu iuaInqmi aqi 30 amieu ~goaq3 aql . .saaaruopy Ma3 c 01 saqaw p2Jar\as uro13 uoyaqp puydn aqi u! lupdloo3 e alley xnu isay lualE1 pue alq!suas aqi pue ,urp Ma3 e 01 Zw3 Ialalzas 30 van2 UBIaAo xnj3 way pas aql ‘pamseaw LlIey~aqds!ruaq s! uo~~wpw !al!s pIag a@+ e ug!M 101v Ja33!p seam pamsvaur ayl30 saz!s aqJ . +saym338 luala33!p a,wq put? saldgpd lualajj!p uo paseq am qcnqm ‘pasn an? sanb!uqDal iuawamseatu iuaJa33g .
:sa!wedams!p a%.mI asay ls!xa su0sea.I Ic?.‘anaS‘,w/M 091 01 dn s! aDualag!p aql ai!s az!euI aql JOT .palzalap aq uw say,wdams!p ahI amso a3ug”q ICiGaua aql 01 pamduro3 SF uogwpw lau aql 31 ‘pawadxa SFuo!wpvl iau aql 01 paiyal aseamu! ue IaAaMoH .asealDap slay10 ‘aurp qi!M aseamu! atuos :aIqss ssaI am swai a3uyaq L%aua aqJ, .al!s iaaq .m%ns aql 103 a1qelyv rCIu0 am satyalz ainuy-au0 aql aDu!s ‘sanp2A paPelaht! dlmoq am suopeInye3 xnu flJ-LvsaNvy aqi 30 uog~pqe~ puv uopwqgw 103 pasn surlal a3uyeq uogwpe-1 aqL yun aql ql!M puodsano:, ,UI/M Ma3 B U!ql!M SatlI”A IE:(j-OS:6 sanlw oo:o~-f~o:6 warn aqi SE aug u! alqeis am a3ualeq uogmpw aqi 30 surrai aql mg uaas aq ue3 i! 11” 30 1s.u~ wep pIa! aql30 /Clyenb aql lnoqe alaq apew am symmal Ma3 v
IV0 SS'O 16'0
6b'O lb'0
S9'0 LL'O
_L.I40lE:6-OE:6 .L.I4f)00:01-0f:6 _LJ'IDOE%-0016 p=fs PU!M
3ZYUl
svoun?s
191 5x1 wfw
ELI soz (4w)
OLt: ZIP (fwW 262 IEE
E8b 9bb (ww4
ZII 001 @=w
85 E9 Gwa)
LEI 281 (4W
8ZE 606 (uafioq)
Gwa)
SLI 8LI 0wW
b9b
Z9b
Z8b WPW
89b ILP
ELP
66b
96b
b8b
SES
PIS
oz 81
zs
8S
Eb Le:
LOS EZS 18b (wPw4
WPW
ESE laaqJ&ns
laaqJc%ns s1!awes
iaaqJc%ns
911
801
EEI SE1
IZI
911
PSE 8bt:
SI! aUm
SF awes
6ZT
.LI4Vt)OO:OI-OE:6 .LWD OE:6-00:6 amsol:, acmp2q r(haug .LPlOOO:OI-OE:6 .LvIOOE:6-00:6
-
xnv maq iuawy LPI~00:01-OE:6 .Lwo OE:6-00:6 xnu lcaq alqyag IVIE) OO:Ol-OE:6 .L.Ix~OE:6-00:6 xnv waq I!os 1&w IE:6-0t:6 .LNVf)OO:Ol-OE:6 .LJw OE:6-00:6 UO~K?!pl?J 19N LPI!3 lE:6-OE:6 IiW00:01-OE:6
-
uwOE:6-00:6 UO!lC!pOJaAEM%lo[ pall!rua
IN9
lE:6-0t:6
-
JJW00:01-OE:6 II&lOE:6-00:6
-
uo!lF!pEJ?AL?M%UO~ %uyoXlI JJW
IE:6-OE:6
-
IPIt)OO:Ol-056 uoy~pw
IWO OE:6-00:6 ar\muoqs pal3apaa
WIvf) lE:6-OE:6 WI0 OO:Ol-OE:6 IvlVf)OE:6-00:6 uoy?!pUJ aAvMlIoqs BU~rnOXl~
G. Roerink et al.: S-SEBI: An Algorithm to Estimate the Surface Energy Balance
150
fraction,
A, which is determined
A=
hE
as:
A Radiation controlled 2 3 g TH
hE+H
To f
..
To .,_.,__,.,. ~~~~ ma Evaporation/controlled > r0
Surface reflectance Fig. 2. Schematic representation of the relationship between surface reflectance and temperature together with the basic principles of S-SEBI.
data point for validation is created by using the energy balance closure values of maize also for sugar beet. The maize values are taken, because they are based on the eddy correlation method, like the sensible heat flux measurements in the sunflower site. Probably the real sunflower values would be a bit smaller than the maize values, because the sunflower site is much warmer and thus dryer than the maize site, which results in less available energy.
2.4 S-SEBI algorithm The Simplified Surface Energy Balance Index (S-SEBI) has been developed to solve the surface energy balance with remote sensing techniques on a pixel-by-pixel basis. It is given by:
R,=G,+H+hE
(1)
where: & GO
H LE
= net radiation = soil heat flux = sensible heat flux = latent heat flux
[W [W [W [W
me*] mm’] mm’] mm’]
S-SEBI requires scanned spectral radiances under cloudfree conditions in the visible, neat-infrared and thermal infrared range to determine its constitutive parameters: surface reflectance, surface temperature and vegetation index. With this input the energy budget at the surface can be determined. First the net radiation term is calculated as the rest term of all incoming and outgoing shortwave (SW) and longwave (Iw) radiation, some of which can be detected directly by remote sensing techniques. Secondly the soil heat flux is derived with an empirical relationship of the vegetation and surface characteristics. The sensible and latent heat flux are not calculated as separate parameters, but as the evaporative
hE = R, -Go
(2)
It has been observed that surface temperature and reflectance of areas with constant atmospheric forcing are correlated and that the relationships can be applied to determine the effective land surface properties (Menenti et al., 1989; Bastiaanssen, 1995). By assuming constant global radiation and air temperature, a formal explanation can be given to the observed surface reflectance and temperature. At low reflectance, surface temperature is more or less constant with increasing reflectance. These concern water saturated surfaces like open water and irrigated lands, where all available energy is used for the evaporation process. At higher reflectance, surface temperature starts to increase with increasing reflectance. Up a certain point, surface temperature may be termed as ‘evaporation controlled’ because the change in temperature is a result of the decrease of the evaporation as a consequence of less soil moisture availability. Here the increase in excess sensible heat flux exceeds the decrease in net radiation due to increase of reflectance. Beyond a certain threshold value of reflectance, surface temperature decreases with increasing reflectance. This is due to the fact that the soil moisture has decreased to such an extent that no evaporation can take place in this case. Hence the available energy is purely used to heat up the surface. However, due-to the increase of reflectance, the available energy decreases as a result of the decrease of net radiation (more is reflected away). This process leads to the decrease of temperature with increasing reflectance. Here the temperature is said to be ‘radiation-controlled’. A schematic representation of S-SEBI is given in Fig. 2. In the case where the two reflectance-to-temperature relationships for hEm,(ro) and H,,,,(ro) can be determined, S-SEBI then calculates the evaporative fraction as follows: For each pixel the surface reflectance, ro, and surface temperature, TO, are determined; where temperature is related to soil moisture and thus the fluxes. Together with a reflectance dependant temperature, ThE, where L?Z,,,,(ro) = R, - Go and H = 0 and a reflectance dependant temperature, TH, where H,,,,(ro) = R, - GO and 3LE= 0 the evaporative fraction is calculated as the ratio of: *
TY-To =T, -Tu
(3)
The S (of Simplified) in the S-SEBI model stands for the case where the extreme temperatures TM and TH can be determined from the image itself. This is possible when the atmospheric conditions are constant over the image and sufficient wet and dry pixels are present throughout the reflectance spectrum. Note that a different wind speed will
G. Roerink et al.: S-SEBI: An Algorithm
change the values of the extreme temperatures TU and TH, but as long as the wet and dry pixels are present the S-SEBI method will work. The complete SEBI version (Menenti and Choudhury, 1993) has to be used when the previous terms are not met. To give a few examples where SEBI has to be used: if images of England (no dry areas), the Saharan desert (no wet areas) or larger areas like Europe (no constant atmospheric conditions) are considered. SEBI calculates the extreme temperatures ThE and TH from an external data source, such as meteorological data (radio soundings) or numerical weather prediction model output.
151
to Estimate the Surface Energy Balance Table 4. LANDSAT-TM Band
1 2 3 4 5 7
band specific constants
(1
b
-0.15 -0.28 -0.12 -0.15 -0.037 -0.015
15.21 29.68 20.43 20.62 2.719 I.438
weight
f&b, 19.5.7 182.9 155.7 104.7 21.93 1.452
0.293 0.274 0.233 0.156 0.033 0.011
0.25 -
3 Results 3.1 Input parameters Surface albedo The surface albedo is determined from the 6 TM bands which measure the spectral reflectance in the visible and near and middle i&a-red part of the electro-magnetic spectrum. First the broadband planetary albedo is calculated by means of a spectral weighing procedure and adjusted for the incidence angle. Afterwards the planetary albedo is plotted against measured surface albedo and the transmittance and path radiance of the atmosphere is calculated. With aid of this transmittance, finally all pixels are given a surface albedo value depending linearly on their planetary albedo. For each band first the spectral radiance is calculated using constant values:
L(h)=a+-bu) 255 where: L(h) DN
= spectral radiance for wavelength h [mW cmm2ster-’ pm’] = Digital Number 1-l
The constants a and b are given by Markham & Barker (1987) and are presented in Table 4. The corresponding planetary albedo for each band is:
Y,,
@I=
7cL(h)d2
KLw ox
,y
(5)
where: d
= relative earth-sun distance
d(b)
SWradiation at TOA for band b [mW cmm2ster-’ urn“] = solar zenith angle WI
cp.!
= incoming
L-1
0’ 0
1
I
0.05
0.1
Planetary
reflectance
0.15 (-)
Fig. 3. Relationship between the calculated broadband planetary allxdo and the measured broadband surface albedo, Tuscany, 23 Aug. 1997.
The slope and aspect maps derived from the DEM provide the necessary information to calculate the solar zenith angle, e.g. the angle between the incoming solar ray and the normal to the (hilly) surface. For flat surfaces the solar zenith angle is 38.7”. The incoming SW radiation at TOA (top of atmosphere) differs per band, according to Table 4. The broadband planetary albedo is being calculated as the total sum of the different in-band planetary albedos according to different weights for different bands, which can be found also in Table 4. Now the relation between surface albedo and planetary albedo can be established by plotting measured surface albedos (ratio of measured reflected SW radiation over measured incoming SW radiation, see Table 3) against corresponding calculated planetary albedos and perform a linear regression through the points. For open water (Mediterranean sea) a surface albedo value of 0.05 is assumed (Stull, 1988), in order to enlarge the calibration range. The result is shown in Fig. 3. The fitted relationship is: r0 = 1.864*r,, - 0.030. In order to retrieve the atmospheric transmissivity, which is necessary later on to derive the net radiation, this relationship is rewritten as: Y.. J-0 =
I’
r2
I-.
U=
Y.. -0.016 I’
0.536
(R2 = 0.96)
G. Roerink et al.: S-SEBI: An Algorithm to Estimate the Surface Energy Balance
152
440
420 Outgoing
460
Iw radiation
0
460
0.2
0.4
0.6
0.6
1
NDVI (-)
at TOA (W/m2)
Fig. 4. Relationship between the outgoing Iw radiation at TOA and the outgoing Iw radiation at the surface, Tuscany, 23 Aug. 1997, 9:30 GMT.
Fig. 5. Relationship between NDVI and surface emissivity.
where: broadband surface albedo
r0
=
‘;J r, 3
= broadband planetary albedo = atmospheric albedo = two-way atmospheric transmittance
i-1 I-l r-1 L-1
With known solar zenith angle for flat surfaces (cps= 0.676 rad) the two-way atmospheric transmittance can be split into the sun to ground transmittance, r,Ys-g = 0.705, and the ground to sensor transmittance, T~_,~ = 0.761.
L6,ToA (h) = 0.1238 + 1*560;5; 1238 DN Satellite temperature radiance by:
1260.56 60.776
T.wr= W
(r,,)
is derived
(8)
from the spectral
(9)
+I>
J&VA(V Normalised
Difference
The Normalised calculated as:
Vegetation
Difference
Index
Vegetation
Index, NDVI, is
The different constants in Eqs. (8) and (9) can be found in Markham and Barker (1987). Applying the law of Stefan Boltzmann, the outgoing lw radiation at TOA, L’,, is:
(10)
Where r,,3 and r,A are the planetary reflectances in band 3 and 4 respectively. No atmospheric correction is applied to the NDVI, since it is only used as one of the inputs for the empirical relationships of surface emissivity and soil heat flux, which have to be established anyway. Surface temuerature Band 6 (10.4 - 12.5 pm) of LANDSAT-TM measures emitted lw radiation from the earth surface and atmosphere. DN-values of band 6 are converted to spectral radiance at TOA
G~,ToA@))
W
Where o is the Stephan Bolzmann constant (5.67*10e8 W rn’ Kw4). Now the outgoing lw radiation at TOA can be atmospherically corrected by linking the outgoing lw radiation at TOA to the outgoing lw radiation at the surface, Lt (Fig. 4). A value for open water (20 “C - 419 W me2) is added in order to enlarge the calibration range, it is taken from http://nodaac.iol.nasa.gov/sst/, as the mean Sea Surface Temperature of August, 1997. The measured Maize value is not used in the fit, because it is measured as the rest term of the radiation balance, and therefore an accumulation of all measured errors. The linear regression gave:
LT = 0.607 GoA + 170.405 The radiative
surface temperature,
(11) TaR, is calculated
by
G. Roerink et a/.: S-SEBI: An Algorithm to Estimate the Surface Energy Balance inverting the Stephan Boltzmann
law:
T,” =dfi
153
60 + mean temperature
(12)
The next step is to correct the radiative surface temperature for emissivity effects of the surface:
To =dz
(13)
Where To is the surface temperature and E+,is the surface emissivity, which is an empirical relationship of the NDVI, using the vegetation cover method of Valor and Caselles (1996): 0
E, =E”Pv
+EJ1-PP,,)+4(d&)P,(1-PJ
with:
P, =
NDVI - NDVI, (15)
NDVI,, - NDVI,
= = = = = =
emissivity emissivity fractional vegetation NDVI of NDVI of
of full vegetation cover of bare soil vegetation cover structure parameter full vegetation cover bare soil
L-1 [-I L-1 f-1 [-I [-I
With no additional information available the aR, E, and (de) terms in the spectral 8-14 pm region (band 6) are set at respectively 0.91, 0.99 and 0.02, according to Valor and Caselles (1996). From the NDVI histogram NDVI, and NDVI, were set at 0.1 and 0.8. Figure 5 shows the relationship between NDVI and the surface emissivity. The last step is a temperature correction for the cooling effect of altitude on temperature. One of the assumptions of S-SEBI is that the atmospheric conditions are constant in space, which is not valid in mountaneous areas, since the air pressure decreases with altitude. A correction to sea level of 6 “C per 1000 m is applied. Relation between surface albedo, 3.2 temperature and evaporative fraction
surface
Figure 6 shows the feature space plot of the surface reflectance and the surface temperature together with the mean surface temperature per reflectance unit. According to the theory (see $ 2.4) at low reflectance the average temperature is more or less constant. At ro > 0.06 the average temperature rises with increasing reflectance and between r. = 0.2 and r. = 0.28 the temperature stabilises. At
0.4
0.6
0.8
1
Surface reflectance (-) Fig. 6. Feature space plot of reflectance and temperature for the Tuscany case, overlaid with the two reflectance-to-temperature relationships for hE,,,&,,) and H,,,,,&o) and the mean surface temperature per reflectance unit.
Table 5. Regression relationships.
where:
NDVI,, NDVI,
0.2
(14)
Relationship TH TIC
coefficients
of the reflectance
to temperature
b -37.78 10.97
r. > 0.28 most of the pixels are radiation controlled, since the average temperature starts to decrease. However, it is also clear that the feature space plot represents a wide variety in hydrological conditions, i.e. also pixels with low reflectance and high temperature (dry dark soils) and vice versa (wet white sands) are present. Easily a slightly increasing lower limit, where maximum latent heat flux is assumed, and a steep decreasing upper limit, where maximum sensible heat flux is assumed, can be recognized. The triangular shape of the feature space plot reveals the two reflectance to temperature relationships for hE_(re) and H,,(r,), which are plotted in Fig. 6. They can be described by:
TH =aH +b,r,,
(16)
(17) Where the regression variables a and b can be found in Table 5. Note that these variables are site and time specific. Substituting Eqs. (16) and (17) in Eq. (3) gives:
G. Roerink et al: S-SEBI: An Algorithm to Estimate the Surface Energy Balance
154
aH +b,r,
A= aH
-To
-aLE + @, -&&-,
(18)
Where r (-) is the soil heat / net radiation flux density ratio, which is an empirical relationship of the surface reflectance, surface temperature and NDVI. The used constants in Eq. (21) were established by Bastiaanssen (1995). Figure 7B is the resulting map of the soil heat flux.
3.3 Surface energy balance parameters Sensible heat flux Net radiation The energy source for the land surface flux densities G,, H and hE is the net radiation flux density R,, defined as the resultant of all incoming and outgoing radiation. The radiation balance can be expressed as:
The sensible heat flux is the heat transfer between the ground and the atmosphere, enhanced by forced or free convection. It is calculated from the net available energy and the evaporative fraction as: H =
(19)
(l-A)(Rn -Go)
(22)
Figure 7C is the map of the sensible heat flux. Latent heat flux
Where the incoming SW radiation, d, is calculated as the resultant of the atmospheric transmissivity times the exoatmospherical incoming solar radiation, d,Y,,, which is determined by its geographic location, daynumber and daytime. The reflected SW radiation, K’, is defined by the surface albedo, and the emitted lw radiation, L’, is defined by the surface temperature (Stefan Boltzmann equation). The only unknown term, the incoming lw radiation, L’, is measured in the field and is 350.75 W mm2(mean value from 9:00-10:00 GMT, see Table 3). Figure 7A is the resulting map of the net radiation.
hE==A(R,, -Go)
(23)
Figure 7D is the map of the latent heat flux.
4 Validation
Soil heat flux The soil heat flux, Go, is the energy used for warming or cooling the subsurface soil volume. It is determined by the thermal conductivity of the soil and the temperature gradient of the topsoil. This cannot be directly determined through remote sensing techniques. Many investigations have shown that mid-day soil heat flux / net radiation fraction is reasonably predictable from remote sensing determinants of vegetation characteristics (Daughtry et al., 1990). However, the attenuation of radiative and conductive heat transfer in canopy and soil respectively changes significantly with soil type. The expression used to define the soil heat flux density is:
Go = I-R,
r=
The latent heat flux is the amount of energy used for the evaporation process of the soil and the transpiration process of the plants. It is calculated from the net available energy and the evaporative fraction as:
To -273.15
* (0.32~~ -I- 0.62$)
(21)
r0
* (1- 0.978AmP)
In Fig. 8 the S-SEBI calculated results are plotted against the measured values in the field for the sensible and latent heat fluxes and the evaporative fraction. The 1: 1 line is also plotted in the graphs, The S-SEBI values of the different field sites are the area-averaged values according to the field site boundaries in Fig. 1. No attention is paid to the calculation of a footprint for the sensible and latent heat flux, since the wind speed was very Iow (see, Table 3). The field measurements of the sensible and latent heat flux values are the 30 minutes averaged values from 9:00-9:30 GMT, because during the next 30 minutes the eddy correlation measurements show some unexplainable decreases. The graph of sensible heat flux shows that the S-SEBI values are systematically too high. These systematically higher S-SEBI values can be explained by the fact that there exists also a similar difference between the net radiation and the energy balance closure. S-SEBI starts with solving the radiation budget, the calculated net radiation is the basis for the partitioning of the energy budget, i.e. the S-SEBI calculations cannot be compared directly with the energy budget measurements. Similar discrepancies can be detected for the eddy correlation measurement of the latent heat flux.
155
G. Roerink et al.: S-SEBI: An Algorithm to Estimate the Surface Energy Balance
0
100
B.
Soil Heat Flux
600
Fig. 7.
Maps of the surface energy balance parameters.
156
G. Roerink et al: S-SEBI: An Algorithm
250 A,E 5
200
2 g
150
X
/ / 0
50 Sensible
“E g 400
•I bowen
I
I
I
100
150
200
heat flux [measured]
250
(W/m*)
ratio
= m ;
300
a ; c 200 ti; 2 & 100
to Estimate the Surface Energy Balance
The sunflower field has a measured value (indicated as ‘estimated’ in Fig. S), which is derived as the residual of the energy budget, where the sensible heat flux is an eddy correlation measurement and the energy balance closure is taken from the maize field. Probably the energy balance closure value is over-estimated, since sunflower has a higher surface temperature than maize (see Table 3). This is the reason that the ‘estimated’ value lies perfectly on the 1:l line. If the energy balance closure of sunflower is indeed smaller than maize, the S-SEBI derived latent heat flux will be larger than the measured one and a similar discrepancy will show up as for the eddy correlation value. To overcome these systematic differences it is better to compare the evaporative fraction, which is independent of the magnitude of the different energy and radiation budget measurements. The results in the corresponding graph match well. The difference between the bowen ratio measurement, which was located in the sugar beet site, and the S-SEBI value is the largest and has a value of 8%, which lies within the accuracy of the present energy flux measurement techniques of approximately 10%. The difference between the eddy correlation measurement and the S-SEBI value is 2% and the difference between the ‘estimated’ and S-SEBI value is 5%, which would be smaller if a smaller value for the energy balance closure would be used, as explained above.
5 Conclusions
‘tii _I 0 0
loo Latent
200
300
heat flux [measured]
500
400 (W/m*)
x eddy correlation
0
0.2 Evaporative
0.4 fraction
0.6
0.8
[measured]
1 (-)
Fig. 8. Validation of the S-SEBI calculated results against the field measurements for the sensible heat flux, latent heat flux and evaporative fraction, together with the 1: 1 line.
This case study to map the energy balance terms in Tuscany, Italy with LANDSAT-TM data gave very promising results. If the input images of surface albedo and surface temperature show a lot of variation in surface conditions (wet/dry, dark/bright) and the atmospheric conditions are constant over the image, the S-SEBI model is a rather simple method to partition the surface energy balance terms without additional (field) data. In general can be said that the S-SEBI method works appropriate for high-resolution images like LANDSAT-TM of heterogeneous somewhat drier areas, like the Mediterranean area. Problems will occur if more humid areas are selected, since the remote sensing data will not contain any dry pixels. This problem will appear less for the occurrence of wet conditions in dry areas, since most of the time an image will contain a lake or a part of an ocean or sea. The S-SEBI method is also applicable for lower resolution data, like NOAA/AVHRR or METEOSAT images. However special attention has to be paid to the fact that the atmospheric conditions are not constant anymore over larger continental areas, i.e. a location specific atmospheric correctionYs needed for the input images and the determination of the extreme temperatures for the wet and dry conditions has to be location specific as well. A second problem with lower resolution images is that a larger pixel reflects a combination of land surface types and at a certain resolution no pixel will be completely dry or wet anymore. If any of the previous
G. Roerink er al.:
conditions cannot be fulfilled the complete SEBI code can be used to calculate the energy balance parameters. The calculated heat fluxes are in good accordance with the measured values, however the S-SEBI calculated heat fluxes are systematically higher than the measured values. This is the result of the large discrepancies between the net radiation measurements and the measured energy balance closure values. Since S-SEBI first calculates the net radiation balance and then partitiones it into the energy balance terms, the systematically lower energy balance measurements will never match the S-SEBI results. To overcome these problems the evaporative fraction should be used for validation purposes. When this is done all S-SEBI calculated values match the measured values within the measurement accuracy of approximately 10%. Acknnw/edgemenfs. The authors would like to thank: (I) Ce.S.1.A. of the Accademia dei Georgofili, Florence, Italy, for the provision of the the LANDSAT-TM scene and the DEM data; (ii) the Dept. of Geography of the University of Basel, Switzerland, for the provision of the ground truth data at the maize, sugar beet and sunflower sites; (iii) the University of Padova, Italy, for the provision of the ground truth data of the wheat stubble site and (iv) the Dept. of Meteorology of the Wageningen Agricultural University, the Netherlands, for the provision of the scintillometer flux measurements.
References Bastiaanssen, W.G.M.,
157
S-SEBI: An Algorithm to Estimate the SurfaceEnergy Balance
1995. Regionulizution of’surjixe,flux
densith
und
moisture indicurors in composite terruin. Ph.D. Thesis, Wageningen Agricultural University (appeared also as Report 109, DLO-Winand Staring centre), Wageningen, The Netherlands: 273 p.
Brest, C.L. and Goward,S.N.,
1987. Deriving surface albedo measurements
from narrow band satellite data, Bruin,
H.A.R. de,
ht.
J. Remote Sensing 8 (3): 35 I-367.
Hurk, B.J.J.M. van den, and Kohsiek, W.. 1995. The
scintillation method tested over a dry vineyard area. Boundury-hyer Meteorhgy
76: 25-4.
Choudhury, B.J., 1989. Estimating evaporation and carbon assimilation using infrared
temperature
data. In: Asrar,
G.
(Ed.).
Vistus in
modeliiq, in theory und upplicuticm ofopticul remote sensing. Wiley, New York: 628-690. Daughtry, C.S.T., Kustas, W.P., Moran, M.S.. Pinter, P.J., Jackson, R.D., Brown, P.W., Nichols, W.D., and L.W. Gay, 1990. Spectral estimates of net radiation and soil heat flux. Rem. Sens. Qj’Env. 32: 11I-124. Kustas, W.P.
and J.M.
Norman,
1996.
Use of remote sensing for
evapotranspiration monitoring over land surfaces. J. of Hydrologicul Sciences. 41 (4): 495-5 16. Menenti, M., Bastiaanssen, W.G.M.,
Eick D. van, and Abl El Karim, M.A.,
1989. Linear relationships between surface reflectance and temperature and their application to map evaporation of groundwater. Adv. Spuce Rex Vol. 9, No. I: 165-176. Menenti, M. and Choudhury, B.. 1993. Parameterization of land surface evaporation by means of location dependent potential evaporation and surface temperature range. Proceedings of IAHS conference on Land Surface Processes, IAHS Publ. 212: 561-568. Moran, M.S. and Jackson, R.D.. 1991. Assessing the spatial distribution of evapotranspiration using remotely sensed inputs. J. Environm. Quu/. 20: 525-737. Stull, R.B., 1988. An introduction to boundury luyer meteorology. KIuwer Academic Publishers, Dordrecht, The Netherlands, 666 pp. Valor, E. and Caselles, V., 1996. Mapping land surface emissivity from NDVI: application to European, African, and South American areas. Remote Sens. Environ. 57: 167- 184.
