# How to calculate reflectance and temperature using ASTER data

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1 How to calculate reflectance and temperature using ASTER data Prepared by Abduwasit Ghulam Center for Environmental Sciences at Saint Louis University September, 2009 This instructions walk you through the calculation of top-of-the-atmosphere (TOA) reflectance at sensor and brightness temperature (also called radiometric temperature) and true kinetic temperature (also called land surface temperature, LST). At-sensor radiances measured in wavelength region is converted to Digital Numbers (DNs) using a quantification system for the sake of storage and data transfer convenience. DN values have no unit and any physical connotation, therefore, need to be converted to radiance, then to at-sensor (top-ofatmosphere) reflectance/temperature and, further, to surface reflectance and LST in order to draw quantitative analysis from remote sensing data. Part 1: Calculating spectral reflectance Step 1: DN to spectral radiance Data used here, as an example, is ASTER L1B data (version 3.0), radiometrically re-calibrated digital numbers, 8bit (1-255) for visible and near-infrared bands and 12bit (1-4095) for thermal infrared (TIR) bands (see the table 1). Where, L rad, j is ASTER spectral radiance at the sensor s aperture measured in a wavelength j; j is the ASTER band number; DN j is the unitless DN values for an individual band j; UCC j is the Unit Conversion Coefficient (W m -2 sr -1 µm -1 ) from ASTER Users Handbook.

2 Band# Table 1: Calculated Unit Conversion Coefficients Unit Conversion Coefficient (W m -2 sr -1 µm -1 ) High gain Normal Gain Low Gain 1 Low gain N 3B Notes: It is worth noting that the re-calibration aimed to correct for temporal decline of the detectors responsivity between consecutive changes in the radiometric calibration coefficient (RCC) has been applied for RCC versions of 3.x or higher. ASTER TIR products with RCC versions 1.x and 2.x (2.17, 2.18 and 2.20, respectively) need to be re-calibrated for this matter using the linear function below Where, L rad, j (c) refers to the re-calibrated spectral radiance, A and B are recalibration coefficients for a band j found at

3 Table 2: Maximum Radiance Values for ASTER Bands and Gains Muximum Radiance (W m -2 sr -1 µm -1 ) Band # High gain Normal Gain Low Gain 1 Low gain N 3B Step 2: Spectral radiance to TOA reflectance ASTER at-sensor reflectance (ρ TOA, also called as planetary reflectance or apparent reflectance or TOA reflectance) for a specific band j is calcualted using the standard Landsat equation as: Where:

4 = Unitless planetary reflectance = Spectral radiance at the sensor's aperture = = Earth-Sun distance in astronomical units from an Excel file which is calculated using the below EXCEL equation (Achard and D Souza 1994; Eva and Lambin, 1998) or interpolated from values listed in Table 3 Mean solar exoatmospheric irradiances from Table 4 = Wavelength, corresponds to the band number j = Solar zenith angle in degrees (zenith angle = 90 solar elevation angle), which is found in the ASTER header file Table 3 Earth-Sun in Astronomical Units Referenced from Landsat 7 ETM+ Data User s Handbook The calculation of E SUN is the same for whatever sensor you are using, as it is simply the convolution of the band's spectral response function (A) with the Extraterrestrial Solar Spectral Irradiance function (B). A for each ASTER band can be obtained from: or download here B can be obtained from: or download here Using this standard approach the calculated E SUN for each ASTER band is given in Table 4:

5 Table 4: ASTER Solar Spectral Irradiances (W m -2 µm -1 ) Band# Smith: E SUN Thome et al (A): E SUN Thome et al (B): E SUN 1 2 3N 3B Notes: Smith: Calculated by interpolating the ASTER spectral response functions to 1nm and convolving them with the 1nm step WRC data Thome et al (A): Calcualted by convolving the ASTER spectral response functions them with the WRC data [Unknown whether these where both interpolated to 1nm or whether a subsample of WRC data values at the ASTER spectral response function step intervals were used in the convolution] Thome et al (B): Calculated using spectral irradiance values dervied using MODTRAN. Step 3: TOA reflectance to surface reflectance Surface reflectance is calculated using empirical methods when ground truthing is available by correlating the field measured surface reflectance with synchronous pixel value, or radiative transfer models such as MODTRAN, 6S (Second Simulation of the Satellite Signal in the Solar Spectrum, Vermote, et al., 1997), etc. It is recommended to use surface reflectance products for quantitative remote sensing analysis, however, TOA reflectance based outcome is also acceptable due to the fact that land surface reflectance retrieval is complicated.

6 Part 2: Calculating temperature Step 1: DNs to radiance Refer to Part1 Step1 to convert DNs to radiance for thermal bands. There is no difference between converting DNs to radiance of thermal or optical data. Step 2: Spectral radiance to TOA brightness temperature Planck s Radiance Function Where, C 1 = W m 2 ; C 2 = m K In the absence of atmospheric effects, T of a ground object can be theoretically determined by inverting the Planck s function as follows: This equation can be reformed as Let K 1 = C 1 /λ 5, and K 2 = C 2 /λ, and satellite measured radiant intensity B λ (T) = L λ, then above mentioned equation is collapsed into an equation similar to the one used to calculate brightness temperature from Landsat TM image (detailes here) Therefore, K 1 and K 2 become a coefficient determined by effective wavelength of a satellite sensor. For example, effective wavelength of ASTER band 10, λ=8.291

7 µm = m, we can have K 1 = C 1 /λ 5 = W m 2 / ( m) 5 = W m -2 m -1 = W m -2 µm -1 K 2 = C 2 /λ = m K / m = K The method may be extended to the rest the ASTER thermal bands as shown in the following table. * Unit for Unit Conversion Coefficients (UCC) is W m -2 sr -1 µm -1 ) Table 5 ASTER thermal bands (referenced ASTER L1B Manual Ver.3.0) Bands Bandpass Effective (µm) Wavelength (µm) UCC K 1 (W m -2 µm -1 ) K 2 (K)

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