SEBAL - Dca.ufcg.edu.br

2. The reflectivity for each band (ρ λ ) is computed (model F02). The reflectivity of asurface is defined as the ratio of the reflected radiation flux to the incident radiation flux.It is computed using the following equation given for Landsat images:ρλ=ESUNπ ⋅ Lλλ⋅ cosθ⋅d r(6)where; L λ is the spectral radiance for each band computed in model F01, ESUN λ is themean solar exo-atmospheric irradiance for each band (W/m 2 /µm), cos θ is the cosine ofthe solar incidence angle (from nadir), and d r is the inverse squared relative earth-sundistance. Values for ESUN λ are given in Table 6.3, Appendix 6. Cosine θ is computedusing the header file data on sun elevation angle (β) where θ = (90 0 - β). The term d r isdefined as 1/d e-s 2 where d e-s is the relative distance between the earth and the sun inastronomical units. d r is computed using the following equation by Duffie and Beckman(1980) 1 , also given in FAO 56 paper: Crop Evapotranspiration (Allen et al., 1998):d r⎛ 2π⎞= 1+0.033cos⎜DOY ⎟⎝ 365 ⎠(7)where; DOY is the sequential day of the year (given in Table 6.5, Appendix 6), and theangle (DOY × 2π/365) is in radians. Values for d r range from 0.97 to 1.03 and aredimensionless.To complete step 2, model F02_reflectivity, is loaded and run. Values for ESUN λ areentered into the table of the model. (Since band 6 is not shortwave, it is not used in thiscomputation and is given a dummy value of 1 for ESUN). The constants d r and cos θare also entered along with the radiance file computed in model F01. Again, the outputfile for reflectivity (ρ λ ) and the model are saved.3. The albedo at the top of the atmosphere (α toa ) is computed (model F03). This is thealbedo unadjusted for atmospheric transmissivity and is computed as follows:α toa = Σ (ω λ × ρ λ ) (8)where; ρ λ is the reflectivity computed in step 2 and ω λ is a weighting coefficient for eachband computed as follows:ω λ=∑ESUNλESUNλ(9)1 Duffie, J.A. and W.A. Beckman. 1980. “Solar Engineering of Thermal Processes.” John Wiley andSons, New York, p 1-109.17