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c-factor BRDF normalization

Source: R/cfactor_BRDF.R
cfactor_BRDF.Rd

Calculates the c-factor proposed by Roy et al. (2016) which can be used to normalize surface reflectance data to nadir BRDF adjusted reflectance (NBAR), or to convert NBAR observations to off-nadir surface reflectance. The c-factor is calculated based on a spectral kernel-based BRDF model. The mathematical formulation of the kernels is presented in Wanner et al. (1995), Lucht et al. (2000) and Carlsen et al. (2020) .

Usage

cfactor_BRDF(SAA, SZA, VAA, VZA, NSZ, br = 1, hb = 2, band)

Arguments

SAA

SpatRaster or numeric. Solar azimuth angle in degrees.

SZA

SpatRaster or numeric. Solar zenith angle in degrees.

VAA

SpatRaster or numeric. Satellite sensor azimuth angle in degrees.

VZA

SpatRaster or numeric. Satellite sensor zenith angle in degrees.

NSZ

numeric. NBAR solar zenith angle. This prescribed NSZ is obtained from the satellite product metadata or calculated using the algorithm and code provided by Li et al. (2019) .

br

numeric. Crown relative height parameter. Defaults to 1.0.

hb

numeric. Shape parameter. Defaults to 2.0.

band

character. Spectral band to be processed. There are six bands that can be considered: "blue (0.43-0.45 um)", "green (0.53-0.59 u)", "red (0.64-0.67 um)", "NIR" (near-infrared, 0.85-0.88 um), "SWIR" (shortwave-infrared, 1.57-1.65 um), and "SWIR2 (shortwave-infrared, 2.11-2.29 um)".

Value

Returns a single numeric value or a SpatRaster with the c-factor values for a spectral band.

References

Carlsen T, Birnbaum G, Ehrlich A, Helm V, Jäkel E, Schäfer M, Wendisch M (2020). “Parameterizing anisotropic reflectance of snow surfaces from airborne digital camera observations in Antarctica.” The Cryosphere, 14(11), 3959–3978. doi:10.5194/tc-14-3959-2020 .

Li Z, Zhang HK, Roy DP (2019). “Investigation of Sentinel-2 Bidirectional Reflectance Hot-Spot Sensing Conditions.” IEEE Transactions on Geoscience and Remote Sensing, 57(6), 3591–3598. doi:10.1109/TGRS.2018.2885967 .

Lucht W, Schaaf CB, Strahler AH (2000). “An algorithm for the retrieval of albedo from space using semiempirical BRDF models.” IEEE Transactions on Geoscience and Remote Sensing, 38(2), 977–998. doi:10.1109/36.841980 .

Roy DP, Zhang HK, Ju J, Gomez-Dans JL, Lewis PE, Schaaf CB, Sun Q, Li J, Huang H, Kovalskyy V (2016). “A general method to normalize Landsat reflectance data to nadir BRDF adjusted reflectance.” Remote Sensing of Environment, 176, 255–271. doi:10.1016/j.rse.2016.01.023 .

Wanner W, Li X, Strahler AH (1995). “On the derivation of kernels for kernel-driven models of bidirectional reflectance.” Journal of Geophysical Research, 100(D10), 21077. doi:10.1029/95JD02371 .

Examples

# Using data with numeric format
cfactor_BRDF(SAA = 56.58, SZA = 35.6, VAA = 236.4, VZA = 1.00, NSZ = 34.97, band = "NIR")
#> [1] 0.9966411

# Using SpatRaster data
library(terra)
m1 <- matrix(seq(from = 56.54, to = 56.67, length.out = 9), nrow = 3, ncol = 3)
m2 <- matrix(seq(from = 35.54, to = 35.65, length.out = 9), nrow = 3, ncol = 3)
m3 <- matrix(seq(from = 221.05, to = 259.06, length.out = 9), nrow = 3, ncol = 3)
m4 <- matrix(seq(from = 0.53, to = 1.12, length.out = 9), nrow = 3, ncol = 3)
SAA <- terra::rast(m1)
SZA <- terra::rast(m2)
VAA <- terra::rast(m3)
VZA <- terra::rast(m4)
cfactor_BRDF(SAA, SZA, VAA, VZA, NSZ = 34.97, band = "NIR")
#> class       : SpatRaster 
#> size        : 3, 3, 1  (nrow, ncol, nlyr)
#> resolution  : 1, 1  (x, y)
#> extent      : 0, 3, 0, 3  (xmin, xmax, ymin, ymax)
#> coord. ref. :  
#> source(s)   : memory
#> name        :     lyr.1 
#> min value   : 0.9966314 
#> max value   : 0.9992424