3 THEORETICAL BACKGROUND THERMAL REMOTE SENSING
3.3 Fire quantification via satellite analysis
Space-borne remote sensing has been widely used to quantify vegetation fires (e.g. Matson and Dozier, 1981; Flannigan and Vonder Haar, 1986; Lee and Tag, 1990; Setzer and Pereira, 1991; Kaufman et al., 1998). Infrared spectro-radiometers can be used directly to measure the radiative energy released by a
3 Theoretical background thermal remote sensing
fire source. It is important to note here though, that satellite sensors can only register that part of the total fire energy emission that is released as radiation.
When observing fires from space, the pixel that corresponds to a ground segment that includes a fire (in the following referred to as a ’fire pixel’) will usually not be homogeneous and will contain both fire and other background information. A ground segment that corresponds to a fire pixel will thus consist of a background and a fire-related, thermal component covering different portions of an image pixel. Taking into consideration equation 3-5 (Stefan-Boltzmann law) the total radiative energy release of the sub-pixel fire component can be described as:
Mfire = Asampl σεf qfnTfn 4
(3-10)
where:
Mfire = radiative energy release of the fire (FRE) [W]
Asampl = ground sampling area [m
2
]
σ = Stefan-Boltzmann constant: 5.67x10-8 [W m-2 K-4]
εf = fire emissivity
qfn = fractional area of the nth fire thermal component within the ground
pixel
Tfn = temperature of the nth fire thermal component [K]
Several remote sensing techniques were developed to derive sub-pixel fire information from a heterogeneous image pixel. A common and widely used technique is the so-called bi-spectral method (Dozier, 1981), whereby two measurements of thermal radiances at different wavelength intervals are used to calculate the fire temperature and fire area. Wooster et al. (2003) have recently demonstrated that the bi-spectral fire temperature and area retrievals can be used to estimate the total amount of energy that is emitted as radiation from a fire (the so-called fire radiative energy or FRE). Kaufman et al. (1998) and Wooster et al. (2003) have presented two different approaches, the so-called MODIS and MIR method, to derive FRE of a sub-pixel fire component directly via the analysis of a single infrared measurement. For a detailed review of remote sensing techniques used to compute radiative energy releases of vegetation fires see Wooster et al. (2003).
3.3.1 The bi-spectral technique
The bi-spectral technique is based on the assumption that a hot portion within an image pixel will contribute more to the total energy emitted in the short wave infrared range than in the long wave infrared range (figure 3-1). So, the equivalent fire temperature (Tf) and equivalent proportion of a fire
3 Theoretical background thermal remote sensing
Ls1 = qf Lbb,s1 (Tf) + (1- qf) Lbg,s1 (3-11)
Ls2 = qf Lbb,s2 (Tf) + (1- qf) Lbg,s2 (3-12)
where:
Ls1 = atmospherically-corrected pixel radiance of first infrared channel
[W m-2 sr--1 m-1]
Ls2 = atmospherically-corrected pixel radiance of a second infrared channel
[W m-2 sr--1 m-1]
Lbb,s1 = band-integrated Planck Function first infrared channel [Wm -2
sr--1 -1
] Lbb,s2 = band-integrated Planck Function second infrared channel
[W m-2 sr--1 m-1]
Lbg,s1 = atmospherically-corrected mean background radiances of first infrared
channel [W m-2 sr--1 m-1]
Lbg,s2 = atmospherically-corrected mean pixel radiances of second infrared
channel [W m-2 sr--1 m-1]
The equivalent fire temperature and fire area are the temperature and area of a fire component that would produce the same signal observed in the investigated spectral regions. Thus, the values of fire temperature and size returned by the bi-spectral technique are a clear simplification owing to the fact that real fires will have many different thermal components. The mean pixel radiances of the background (Lbg,s1, Lbg,s2)are estimated as the mean radiances of neighbouring non-fire pixels in the
vicinity of the anomaly pixel. The band-integrated Planck Function is given by equations 3-2 and 3-4.
The energy release of a sub-pixel fire (Mfire, bi-spectral) can be estimated using the temperature (Tf) and
area (Af) provided by the bi-spectral technique according to equation 3-5 (Stefan-Boltzmann law) as:
Mfire, bi-spectral = f
4
– Tbg4) Af (3-13)
where:
Mfire, bi-spectral = radiative energy release of the fire derived via the bi-spectral
technique [W]
Tbg = background temperature that is assumed to be equal to the
mean temperature in the vicinity of the investigated fire pixel [K]
Af = qf Asampl = equivalent fire area [m 2
]
The bi-spectral method is a common tool used to calculate the temperature and area of a sub-pixel hot spot (e.g. Prins et al., 1998; Robinson, 1991). Nevertheless, Giglio and Kendall (2001) reviewed the bi-
3 Theoretical background thermal remote sensing
spectral method and found large errors if careful consideration is not taken with respect to the accuracy of the inter-channel co-registration of the two input channels and of background characteristics (Wooster et al., 2003).
A further disadvantage of the bi-spectral technique is the fact that it is restricted to image pixels that show anomalous and unsaturated pixel values in at least two input channels, at well-separated wavelength intervals. In addition, the bi-spectral retrievals are very sensitive to background temperature variations, resulting in for example a temperature retrieval error of a few hundreds of Kelvin for small fires (qf < 0.005 % of the pixel area), if the background temperatures varies about +/- 5
K (Wooster et al., 2003). Due to these error sources, Giglio and Kendall (2001) suggest that reliable bi- spectral estimates can only be derived if the fire size qf exceeds 0.005 % of the pixel area. According to
Wooster et al. (2003) the error induced by background temperature variations can be reduced, if the bi- spectral technique is applied to hot pixel clusters rather than to individual single pixels. In addition, a clustering of anomaly pixels reduces the potentially large bi-spectral retrieval errors due to interchannel geometric co-registration errors (Wooster et al., 2003).
3.3.2 The MODIS method
Kaufman et al. (1996, 1998) first introduced the concept of FRE derivation via the analysis of a single infrared measurement. The so-called MODIS method is based on semi-empirical relationships between the fire spectral radiances measured in the 3.9 ! #"$&%')(*+,-./0, 132547698*:;<;6>=@?BA6C/DBEFE-GDHA6EI6+JK,;ML&NOQPRL6TSUOVXW8ZYLDJJ6E[GD\N*N]6>EI6Y+;6>=^D\N;L6_:$J\`ba\;YLDJJ6>E-c?C5;ML6dc:ICe6
analysis, since this spectral range is very sensitive to 600 K to 1000 K hot vegetation fire (see figure 3- 1, Planck Function of a 600 K and 1000 K blackbody).
Kaufman et al. (1998) carried out simulations of vegetation fire scenarios each containing different
fMghij*k,l0mnFioh#kpq^fMgh>i)jrkBlts&kBuv\wiox,ybpqzuxBj/{&xBph9pHfo|*}n~fMgn$pk^{&xfh9p,fnIk,l0! 3X Fo_&$&>QR+
plotted brightness and temperature differences between simulated fire and neighbouring background pixel, against the total FRE release and found, within the limits of the MODIS sensor saturation, very good linear correlations. Thus, a constant factor could be computed that relates the brightness temperature difference of a detected fire and neighbouring background pixel directly to the fire total radiative energy release:
Mfire, MODIS = a Asampl (T MIR,p 8
– T MIR,bg 8
) (3-14)
where:
3 Theoretical background thermal remote sensing
MODIS method (W)
TMIR,p = brightness temperature of potential fire pixel [K]
TMIR,bg = mean brightness temperature of neighbouring non-fire image
pixels (K)
a = constant factor derived through a best-fit relationship of simulated fire scenarios between the FRE and the composite-
! "$#&%('*),+.-0/2134
Wooster et al. (2003) adapted the MODIS method to the BIRD MIR channel, where it was seen to have large errors in cases where fire temperature is below 600 K.
3.3.3 The MIR method
Wooster et al. (2003) recently presented an alternative technique, the so-called MIR method, to compute FRE directly from spectral radiances recorded in the BIRD MIR channel. The MIR radiance method is based on the assumption that the total FRE is linearly proportional to the fire pixel radiance recorded in the MIR spectral range:
Mfire,MIR = b Asampl (LMIR,P - LMIR,BG) (3-15)
where:
Mfire,MIR = radiative energy release of the coal fire derived via the MIR
method [W]
b = constant derived through a best-fit relationship between
blackbody temperature and emitted spectral radiance in the BIRD MIR range
LMIR,P = atmospherically-corrected MIR radiance of image pixel
[W m-2 sr--1
1
m-1]
LMIR,BG = atmospherically-corrected mean radiance of neighbouring
non-fire image pixel [W m-2 sr--1 1
m-1]
It is important to note that in contrast to the MODIS method the constant factor b is derived through a best-fit relationship, between blackbody temperature and emitted spectral radiance in the BIRD MIR range, and not through a semi-empirical relationship. Analogous to the MODIS method, the MIR method is only applicable in the case where fire temperature is higher then ~600 K (Wooster et al., 2003). A major advantage of single-band fire quantification methods (MODIS and MIR methods) is the fact that they do not rely on an exact geometric co-registration of different instrument channels.