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METEOSAT SECOND GENERATION (MSG)

CONVERSION FROM COUNTS TO RADIANCES AND FROM RADIANCES TO BRIGHTNESS TEMPERATURES AND REFLECTANCES

Author: D. Rosenfeld (HUJ)

Contributors: I. Lensky (HUJ), J. Kerkmann (EUM), S. Tjemkes (EUM)

Y. Govaerts (EUM), HP. Roesli (MeteoSwiss)

Conversion from Countsto Radiances

The relation between the binary pixel value and the physicalradiance is fully defined for each spectral band by the relation:

R = CAL_offset + CAL_slope * Count (1)

R = spectral radiance in mWm-2sr-1(cm-1)-1

CAL_offset = offset constant between the pixel count and the physical radiance extracted eitherfrom the on-board calibration (for IR channels) or from other sources (e.g. SEVIRI Solar ChannelCalibration (SSCC) for solar channels). The units are mWm-2sr-1(cm-1)-1

CAL_slope = linear calibration coefficient extracted either from the on-board calibration(for IR channels) or from other sources (e.g. SEVIRI Solar Channel Calibration (SSCC)for solar channels). The units are mWm-2sr-1(cm-1)-1

Count = binary pixel value (pixel count, between 0 and 1023)

More info: www.eumetsat.de, MSG/MSG Documentation (under Quick Links)/Level 1.5 Data Format Description (MSG/ICD/105)

Conversion from Countsto Radiances

Detailed structure of the Level 1.5 Header: the calibration info (slope, offset) can be found in the radiometric processing sub-header !

Conversion from Radiancesto Brightness Temperatures

In the MSG-MPEF the following analytic relation between the equivalent brightness temperatures (Tb) and the SEVIRI radiances (R) is adopted:

(2)

With: C1 = 1.19104 10-5 mW m-2 sr-1(cm-1)-4

C2 = 1.43877 K(cm-1)-1

c = central wavenumber of the channel

A, B coefficients (see next slide)

More info: www.eumetsat.de, MSG/Data Products & Services/Image Data/Calibration/

Conversion from BrightnessTemperatures to Radiances

Viceversa, the analytic relation between the radiances (R) and the equivalent brightness temperatures (Tb) for the MSG infra-red channels is given by equation (3):

(3)

With: C1 = 1.19104 10-5 mW m-2 sr-1(cm-1)-4

C2 = 1.43877 K(cm-1)-1

c = central wavenumber of the channel

A, B coefficients (see next slide)

More info: www.eumetsat.de, MSG/Data Products & Services/Image Data/Calibration/

Conversion from Radiancesto Brightness Temperatures

Values for the central wavenumber (in cm-1), and the parameters A, and B (in K) for the analytic relationship between radiance and equivalent brightness temperature for the thermal IR SEVIRI channels on MSG-1:

Channel No. Channel ID c A B

04 IR3.9 2569.094 0.9959 3.471

05 WV6.2 1598.566 0.9963 2.219

06 WV7.3 1362.142 0.9991 0.485

07 IR8.7 1149.083 0.9996 0.181

08 IR9.7 1034.345 0.9999 0.060

09 IR10.8 930.659 0.9983 0.627

10 IR12.0 839.661 0.9988 0.397

11 IR13.4 752.381 0.9981 0.576

Conversion from Radiancesto Reflectances for VIS Channels

A simple way to calculate the reflectances for channels VIS0.6, VIS0.8 NIR1.6 and HRV is:

REFL(i) = 100 * R (i) / TOARAD (i ) / cos(TETA) i=1, 2, 3, 12 (4)

REFL Reflectance [in %] for channel i, i = 1, 2, 3, 12

R measured Radiance [in mW m-2 ster-1 (cm-1)-1] for channel i, i = 1, 2, 3, 12

TOARAD solar constant at Top of the Atmosphere [in mW m-2 ster-1 (cm-1)-1] for channel i, i = 1, 2, 3, 12

TETA solar zenith angle (to be calculated from date, time, lat, lon); for twilight condition (i.e. TETA > 80°) TETA is set to 80° to avoid problems

i number of the channel (1 = VIS0.6; 2 = VIS0.8; 3 = NIR1.6; 12 = HRV)

TOARAD (i=1, VIS0.6) = 20.76 / ESD**2

TOARAD (i=2, VIS0.8) = 23.24 / ESD**2

TOARAD (i=3, NIR1.6) = 19.85 / ESD**2

TOARAD (i=12, HRV) = 25.11 / ESD**2

ESD is the earth-sun-distance (in Astronomical Units), which varies during the year according to the following equation:

ESD (JulianDay) = 1.0 - 0.0167 cos ( 2p (JulianDay - 3) / 365) (5)

Conversion from Radiancesto Reflectances for VIS Channels

An IDL (Interactive Data Language) tool to calculatebrightness temperatures and reflectances is offered at:

- www.eumetsat.de
- Data, Products and Services
- Useful Programs and Tools (under Quick Links)
- SEVIRI Pre-processing Toolbox

Conversion from Radiancesto Reflectances for Channel IR3.9

During daytime, Channel IR3.9 receives energy both from emitted thermal radiation and from reflected solar radiation. One possibility to calculate the reflectance for channel IR3.9 is:

REFL = 100 * (R_tot - R_therm) / (TOARAD - R_therm) (6)

with:

REFL Reflectance [in %] for channel IR3.9

R_tot measured total Radiance [in mW m-2 ster-1 (cm-1)-1] for channel IR3.9

R_therm CO2-corrected, thermal component of Radiance [in mW m-2 ster-1 (cm-1)-1] for channel IR3.9

TOARAD CO2-corrected, solar constant at Top of the Atmosphere [in mW m-2 ster-1 (cm-1)-1]

for channel IR3.9

Conversion from Radiancesto Reflectances for Channel IR3.9

The CO2-corrected thermal component of the radiance in Channel 04 (IR3.9) can be estimated from the IR10.8 channel by equation (7):

R_therm = R(IR3.9, BT(IR10.8)) * R3.9_corr (7)

Using equation (2) to calculate the brightness temperature for channel IR10.8 and equation (3) to convert this temperature back to radiance (using the coefficients A and B for channel IR3.9 !)

R3.9_corr is the CO2 correction factor to account for the attenuation of the emitted thermal radiation by CO2 absorption (see next slide).

Conversion from Radiancesto Reflectances for Channel IR3.9

The CO2 correction factor of IR3.9 total radiation, R3.9_corr, can be estimated usingthe IR10.8 and the IR13.4 brightness temperatures:

(8)

Conversion from Radiancesto Reflectances for Channel IR3.9

The CO2-corrected, solar constant at the Top of the Atmospherein Channel 04 (IR3.9) can be estimated from:

TOARAD = 4.92 / ESD**2 * cos(TETA) * exp[-(1-R3.9_corr)] * exp [-(1-R3.9_corr)* cos(TETA) / cos(SAT)] (9)

ESD earth-sun-distance (in Astronomical Units), see equation (4)

TETA solar zenith angle (to be calculated from date, time, lat, lon); for twilight condition (i.e. TETA > 80°) TETA is set to 80° to avoid problems

SAT satellite zenith angle

4.92 / ESD**2 solar constant [in mW m-2 ster-1 (cm-1)-1] in channel 4 without CO2 correction

exp[-(1-R3.9_corr)] is the CO2 attenuation of the reflected solar radiation from cloud to satellite

exp[-(1-R3.9_corr)]* cos(TETA) / cos(SAT)) is the CO2 attenuation of the solar radiation from the sun to cloud

CO2 Correction of BrightnessTemperature of Channel IR3.9

T4_CO2corr, the CO2-corrected brightness temperature at IR3.9,can be estimated using the IR10.8 and the IR13.4 brightness temperatures:

T4_CO2corr = ( BT(IR3.9)4 + Rcorr )0.25 (10)

Where:

Rcorr = BT(IR10.8)4 - (BT(IR10.8) - DT_CO2)4

And: DT_CO2 = (BT(IR10.8) - BT(IR13.4)) / 4.

CO2 Correction of BrightnessTemperature of Channel IR3.9

In equation (10), the CO2-correction of BT(IR3.9) depends non-linearly on T_CO2,the difference between IR10.8 and IR13.4, which depends on (in order of priority):

I. Temperature difference between surface and air mass at about 850 hPa (T_CO2 is very large for hot desert surfaces during daytime (see next slide))

II. Height of the cloud (T_CO2 is small for high clouds (see next slide))

III. Satellite viewing angle (so called "limb cooling" effect, T_CO2 is large for large satellite viewing angles)

IV. Differences in surface emissivity at 10.8 and 13.4 m

CO2 Correction of BrightnessTemperature of Channel IR3.9

2 March 2004, 12:00 UTC 2 March 2004, 24:00 UTC

MSG-1, T_CO2 [i.e. (BT(IR10.8) - BT(IR13.4)) / 4.], Range = 0 / +10 K, =1.0

IR3.9 Solar Reflectance: Summer Example

IR3.9 Brightness Temperature IR3.9 Reflectance Difference IR3.9 - IR10.8

Range = 243 K / 333 K, =1.0 Range = 0 / 25 %, =1.7 Range -5 / +65 K, =1.0

(for comparison)

MSG-1, 13 June 2003, 12:00 UTC

IR3.9 Solar Reflectance: Summer Example... close up view

IR3.9 Brightness Temperature IR3.9 Reflectance Difference IR3.9 - IR10.8

Range = 243 K / 333 K, =1.0 Range = 0 / 25 %, =1.7 Range -5 / +65 K, =1.0

(for comparison)

MSG-1, 13 June 2003, 12:00 UTC

IR3.9 Solar Reflectance: Winter Example

IR3.9 Brightness Temperature IR3.9 Reflectance Difference IR3.9 - IR10.8

Range = 243 K / 303 K, =1.0 Range = 0 / 20 %, =1.0 Range 0 / +50 K, =1.0

(for comparison)

MSG-1, 26 January 2004, 10:00 UTC

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