Ok. The issue is resolved:
d(t) = 1/ ((1-0.01673cos(0.0172(t-2)))^2) = 1/d^2
d(t) – this is value from metadata!
Distance of Earth-Sun: d = SQRT(1/d(t)).
Thank you.
Ok. The issue is resolved:
d(t) = 1/ ((1-0.01673cos(0.0172(t-2)))^2) = 1/d^2
d(t) – this is value from metadata!
Distance of Earth-Sun: d = SQRT(1/d(t)).
Thank you.
Can you please explain how to get the values to calculate the TOA or BOA reflectance ?
L = (rToa * e0__SOLAR_IRRADIANCE_For_band * cos(Z__Sun_Angles_Grid_Zenith_Values)) / (PI * U__earth_sun_distance_correction_factor) (Equation 1)
I know that :
rToa is the band we need to calculate its reflectance
e0__SOLAR_IRRADIANCE_For_band can be obtained from the metadata as below for Band 4 for example :
U__earth_sun_distance_correction_factor from the metadata as below :
But how to obtain:
1- cos(Z__Sun_Angles_Grid_Zenith_Values))
2- PI ( what is it ?)
I have calculated the d(t) according to the equation :
As t= 0.98358 (for the day for day 358, the earth-sun distance is 1.00992).
d(t) = 1.03431890515045328251315
But do not know where to insert d(t) in the (Equation 1)
Another question regarding :
(Equation 2)
Another question, why using the Equation 1 and not Equation 2 for calculating the reflectance? Also would be more appreciate if you could give an example of how to fine the parameters in Equation 2 from Sentinel 2 metadata.
Thanks a lot for your help and time,
D
Hi, Daniel
Data Sentinel-2A L1C MSI already have TOA Reflectance. According to the documentation, You must divide the pixel value by the value of QUANTIFICATION_VALUE:
rTOA = DN / QUANTIFICATION_VALUE
Possible also some deviation in DN from the desired range. For example:
For BOA Reflectance – use, for example, SEN2COR package:
L – this is the TOA spectral radiance – the formula is the reverse formula for finding TOA spectral reflectance. For example:
http://yceo.yale.edu/how-convert-landsat-dns-top-atmosphere-toa-reflectance
d = SQRT(1/d(t)) or d =SQRT(1/U)
ESUN = SOLAR_IRRADIANCE for Band
Theta = Z__Sun_Angles_Grid_Zenith_Values – the interpolated value from the matrix from the metadata:
GRANULE \ … granule.xml, tags: “Tile_Angles Sun_Angles_Grid Zenith… Values_List…”
L = (rToa * e0__SOLAR_IRRADIANCE_For_band * cos(Z__Sun_Angles_Grid_Zenith_Values)) / (PI * U__earth_sun_distance_correction_factor)
Please note that earth_sun_distance_correction_factor – this value U.
@Igor thanks a lot for the reply and for the explanation.
Just still on question: what is PI in L equation ?
L = (rToa * e0__SOLAR_IRRADIANCE_For_band * cos(Z__Sun_Angles_Grid_Zenith_Values)) /** (PI** * U__earth_sun_distance_correction_factor)
The correct expression for the radiance should be the following:
L = (rToa * e0__SOLAR_IRRADIANCE_For_band * cos(Z__Sun_Angles_Grid_Zenith_Values) * U__earth_sun_distance_correction_factor) / PI
because U=1/d^2
It’s the same formula!
Because:
rToa = (PILd^2)/(ESUNcos(theta));
L = (rToaESUNcos(theta))/(PId^2);
U=1/d^2;
d^2 = 1/U;
L = (rToaESUNcos(theta))/(PI/U);
L = (UrToaESUN*cos(theta))/PI;
Now it is correct. In previous posts you’ve used the following expression:
L = (rToaESUNcos(theta))/(PI*U)
see also in this topic “Radiometric convertion of sentinel 2 images”
I was misled by help to sen2three.
Now the link is unavailable:
http://s2tbx.telespazio-vega.de/sen2three/html/r2rusage.html?highlight=quantification
But in the program sen2tree has the following lines:
===================
def refl2rad(self, indataArr):
‘’’ Converts the reflectance to radiance.
:param indataArray: the digital numbers representing TOA reflectance.
:type indataArray: a 2 dimensional numpy array (row x column) of type unsigned int 16.
:return: the pixel data converted to radiance.
:rtype: a 2 dimensional numpy array (row x column) of type unsigned int 16, representing radiance.
Additional inputs from L1 user Product_Image_Characteristics metadata:
* QUANTIFICATION_VALUE: the scaling factor for converting DN to reflectance.
* U: the earth sun distance correction factor.
* SOLAR_IRRADIANCE: the mean solar exoatmospheric irradiances for each band.
Additional inputs from L1 tile Geometric_Info metadata:
* Sun_Angles_Grid.Zenith.Values: the interpolated zenith angles grid.
'''
# This converts TOA reflectance to radiance:
nrows = self.config.nrows
ncols = self.config.ncols
# The digital number (DN) as float:
DN = indataArr.astype(float32)
xp = L3_XmlParser(self.config, 'UP1C')
pic = xp.getTree('General_Info', 'Product_Image_Characteristics')
qv = pic.QUANTIFICATION_VALUE
c0 = 0
# The quantification value for the DN from metadata:
c1 = float32(qv.text)
# TOA reflectance:
rtoa = float32(c0 + DN / c1)
rc = pic.Reflectance_Conversion
# The earth sun distance correction factor,
# apparently already squared:
u2 = float32(rc.U.text)
# The solar irradiance:
si = rc.Solar_Irradiance_List.SOLAR_IRRADIANCE
e0 = float32(si[self._bandIndex].text)
# The solar zenith array:
x = arange(nrows, dtype=float32) / (nrows-1) * self.config.solze_arr.shape[0]
y = arange(ncols, dtype=float32) / (ncols-1) * self.config.solze_arr.shape[1]
szi = rectBivariateSpline(x,y,self.config.solze_arr)
rad_szi = radians(szi)
sza = float32(cos(rad_szi))
rtoa_e0_sza = float32(rtoa * sza * e0)
???–>> pi_u2 = float32(pi * u2 )
# Finally, calculate the radiance and return array as unsigned int, this is multiplied by 100,
# to keep resolution - glymur only allows integer integer values for storage.
L = (rtoa_e0_sza / pi_u2 ) * 100.0
return (L + 0.5).astype(uint16)
===================
Link:
It seems to me that this formula is correct:
L = (UrToaESUN*cos(theta))/PI;
And in their program - error.
L = (UrToaESUN*cos(theta))/PI is correct expression, but you’ve written in other posts L = (rToa * e0__SOLAR_IRRADIANCE_For_band * cos(Z__Sun_Angles_Grid_Zenith_Values)) / (PI * U__earth_sun_distance_correction_factor)
perhaps it would be appropriate to correct
In sen2cor formula is correct!
Their review:
. . .
. . .
. . .
They use d^2:
L = (rToaESUNcos(theta))/(PI*d^2);
Link:
How do you calculate theta?
Hello, fifauzan!
How do you calculate theta?
To get there:
Or get from file S2A_PRODUCT_NAME.SAFE/GRANULE/TILE_NAME/MTD_TL.xml (tag: Sun_Angles_Grid).
Hello, How do i write a band math expression to convert TOA Reflectance to TOA Radiance in SNAP.
Thank you. I am using this expression
1512.9 * 1.028880315 * B3 * cos(sun_zenith) / PI
u = 1.028880315
ESUN = 1512.9
ERROR: Referenced raster must all be of the same size.
Hello.
There is already an operator doing the conversion from reflectance to radiance, for Sentinel-2 products. You can find it under the menu Optical > Thematic Land Processing > Reflectance to Radiance.
The earth-sun distance in astronomical units excel spreadsheet file link is down, i find excel file at :
Download link is below:
https://prd-wret.s3.us-west-2.amazonaws.com/assets/palladium/production/atoms/files/Earth-Sun_distance.xlsx