DZDDPZ4 – Preprocessing of image records – radiometric and atmospheric corrections

Doc. Dr. Ing. Jiří Horák – Ing. Tomáš Peňáz, Ph.D.

Institute of geoinformatics

VŠB-TU Ostrava

References and recommendations • Eastman, J.R.: Idrisi Andes Guide to GIS and Image

Processing

• Eastman, J.R.: Idrisi Andes Tutorial

• Liang, S.: Quantitative Remote Sensing of Land Surfaces

• Horák J.: Dálkový průzkum Země. Skripta VŠB-TU Ostrava, 2014. 137 stran.

• Rees, W.G.: Physical Principles of Remote Sensing. Cambridge Univ. Press, 2012 (kap.11 Data processing)

• Schläpfer, D.: ATCOR. On-line: http://www.rese.ch/products/atcor/index.html

• UNESCO Bilko Lessons, Module 7, Lesson 3: Radiometric Correction of Satellite Images: When and Why Radiometric Correction is Necessary. On-line: http://cwcaribbean.aoml.noaa.gov/bilko/module7/

Radiometric and atmospheric corrections (image restorations)

• Incorrect DN values are caused by the fact that the carrier position changes as well as the state of atmosphere, altitude of the Sun, look angle, seasons, etc.

• We use the approximation of natural conditions in the model or try to eliminate errors.

• DN values of individual pixels are adjusted.

• The aim is to ensure that DN values of the image recording correspond to the actual reflective or radiant properties of the objects as much as possible.

Types of corrections

Types of radiometric corrections :

• Corrections using the calibration of measuring equipment

• Corrections of errors due to the direction of irradiation (Sun-Angle Correction)

• Corrections of errors resulting from the flight geometry

• Removal of random radiometric errors Atmospheric corrections: • Corrections of errors due to the state of atmosphere

Corrections using the calibration

• usually performed automatically, directly on the satellite.

• use periodic scanning of reference areas with known characteristics (calibration lamps, the Sun, dark universe)

• measured values are corrected on the basis of the observed bias.

• Information about the calibration of sensors or correction coefficients are recorded in the image header

Corrections of errors due to the direction of irradiation Sun-Angle Correction

• compensate for seasonal differences

• Usually not performed by the RS system provider

• required especially in the study of temporal changes in the same area

• the same surfaces provide different DNs at different times due to different altitudes of the Sun.

• DN values are therefore converted for imaginary irradiation from zenith

Opravy ze směru ozáření:

Corrections

• DN values are converted for imaginary irradiation from zenith • In a simple scenario, we assume Lambertian surface and thus the

dependence of the intensity of reflected radiation on the cosine of the angle of incidence

• Landforms may introduce errors in the change of radiation, especially in high-resolution images. Therefore, the shape of topography is also included.

• It is also necessary to use correction coefficients to compensate for the fact that most of the objects do not have Lambertian surface

• Usually combined corrections for both radiometric and atmospheric – see atmospheric CSR according to NIKM.

• The most simple solution – use the ratio of original bands.

cos

),(),(

jiDNjiDN

orig

Corrections of errors resulting from the flight geometry

• remove changes in the irradiation angle occurring even in the scan line,

• shadows of vertically segmented objects associated with the flight direction relative to the Sun (especially in aerial photographs),

• forward slopes versus exterior slopes causing varying brightness

Removal of random radiometric errors

• found in the majority of image recordings,

• reasons:

– sensor malfunctions,

– failures in transmitting the signal to Earth,

Kind of random radiometric errors

• striping of the image recording

• Vertically oriented inaccurate or missing data

• Bit errors.

Striping of the image recording

• mechanooptic scanners – whiskbroom (cross-track) scanning

• horizontal orientation of striping is manifested

• Strips occur repeatedly in a regular period.

• caused by a failure, inaccurate calibration or sensitivity of the sensor.

• visible in large homogeneous areas of the image such as water bodies

Striping

• irregular or regular

• caused by a failure, inaccurate calibration or sensitivity of the sensor

Vertically oriented inaccurate or missing data

• electro-optical scanners -pushbroom scanning.

• vertical orientation of errors

Bit errors

• irregularly distributed in the area of image

• missing or inaccurate radiometric DN values of individual picture elements (very bright, very dark pixels)

Corrections of random radiometric errors

• remove stripping of the image recording – elimination is carried out before the geometric correction.

– adapt the histogram of the different line or

– Fourier transformation

• vertically oriented inaccurate or missing data – Irregular type and skewing orientation after correction of Earth’s

rotation – more demanding issue

– Fourier transformation,

• Bit errors – elimination by filtration

Top left: extract of a Landsat MSS image exhibiting severe six-line striping. Bottom left: Fourier transform of the striped image. Note the prominent peaks corresponding to the striping. Bottom right: Fourier transform of the image with the peaks corresponding to the striping manually removed. Top right: inverse Fourier transform of the edited transform

© Rees, 2012

Korekce náhodných radiometrických chyb (korekce

páskování)

Korekce náhodných radiometrických chyb (páskování před úpravou)

Korekce náhodných radiometrických

chyb (páskování po úpravě)

Saturation Striping saturation striping in Level-1 Radiometric (Corrected) (L1R) imagery, Landsat 7 Enhanced Thematic Mapper Plus (ETM+) Band 3 data

•https://landsat.usgs.gov/detector-striping

Saturation Striping • visible only over bright, saturated targets, such as snow or

clouds

• expected in Landsat Level-1R products, as there will be minor differences in detector calibration when the 8-bit raw data are converted to 16-bit radiometrically corrected data

• Also some Landsat 7 ETM+ gain-change scenes

• Rounding error (change of radiometric resolution)

• Level-1 Radiometric (Corrected) (L1R) scenes or L1G gain-change scenes is expected (no concerns)

• in a normal L1G product – recalibration of of the instrument

•https://landsat.usgs.gov/detector-striping

Band 6 Striping

striping in Landsat 7 ETM+ Band 6 high gain data, processed before Nov. 23, 1999

a software bug in the ground processing systems

•https://landsat.usgs.gov/detector-striping

Transmission Striping

Landsat 2 MSS Red Green and Blue value (RGB) data

• data could be lost from a single detector at a time due to the format in which data were downlinked from the satellite.

• Usually, several of these losses occurred at the same time, creating coloured stripes when viewed as part of an RGB image.

• striping is not correctable

•https://landsat.usgs.gov/detector-striping

Atmospheric corrections • The most complicated

• Specification of transfer function of the atmosphere

• DN values are modified due to scattering, absorption (influence of wavelength λ) and atmospheric emissivity.

• The content of pollutants in the atmosphere (smoke and haze) can greatly contribute to the signal measured by the sensor (up to 80% in the range of visible light wavelengths).

• The solution is based on the existence of differences in the radiance of the monitored object on the Earth's surface and the radiance sensed on the carrier

)()0()()()()( xLLxxLxLxL AZAZ

m 2,5 ;4,0

Types of atmospheric corrections

• Method of the darkest pixel,

• Regression analysis,

• method of 5S

• method of correction for NOAA

• Models – usually to derive real radiometric variables: • Model MODTRAN

• Model ATCOR (ERDAS Imagine, Geomatica)

• Model ATMOSC (Idrisi Andes)

• Model ATREM

• Model MODIS

Corrections using models of atmospheric influence

• Parametrization of atmospheric influences in the time of image observation

• Input of parameters into numerical models

• Take into account time of the year, geographical location

• Better to use direct measurements of water vapour, oxygen and ozone (NOAA)

• parameters expressing various meteorological influences (cloudiness, precipitation, ...)

Method of the darkest pixel

• finding the contribution of the atmosphere based on the evaluation of the measured signal corresponding to the water surface.

• radiation of water objects in the NIR band is almost zero.

• any measured signal is a contribution of the atmosphere

• this contribution is subtracted from DN values in the image recording

• method is rather imprecise - does not consider the horizontal changes in the contribution within the measured area

Regression analysis

1. between individual bands of multispectral image – assuming the compensation of local topography effects

on the emergence of differences in reflective properties of objects

2. between data measured by remote sensing methods and data from ground measurements – relatively expensive and time consuming

Regression analysis based methods

• a regression analysis between pixel values for the red and near-infrared band (TM3 and TM4).

• The regression equation then intersects the TM3 axis (i.e. TM=0) at a point (A) corresponding to the contribution of the atmosphere

Model of 5S (6S) • Simulation of the Sensor Signal in the Solar Spectrum (Second ..)

• Tanre et al., 1986

• Predict apparent reflectance out of atmosphere using information about the ground reflectance (on the surface) and atmospheric conditions

• It is possible to turn over the calculation and obtain the contribution of atmosphere

• 3 stages:

1. Process 5S for each band of the image

2. Calculation of the inverse coefficients and the spherical albedo

3. Apply inverse model to the image

(Spherical albedo = the albedo of a surface when the incident radiation is isotropic.)

Process 5S for each band of the image • Inputs are in the table. Minimal requirements are in bold (parameters of the

sensor and visibility in kms)

1. Process 5S for each band of the image Example

• Inputs:

• Outputs in the following table:

2. Calculation of the inverse coefficients and the spherical albedo

• Calculate AI and BI for each band (use 4 decimal places) (they are in the table yet)

• subsequently to create new images of Y for each band (reflectance ρ out of atmosphere)

3. Apply inverse model to the image

• Use appropriate spectral albedo S calculated in the 1st stage (course of 5S calculation) and image Y (for the given band)

• Calculate the ground reflectance (on the Earth surface)

Correction for NOAA

• Sensor AVHRR (2 bands)

• HIRS – High Resolution Infrared Radiometric Sounder – sounding of atmosphere for corrections

• V, NIR; corrections of NDVI – elimination of molecular scattering, effect of ozone absorption 5-15% in 1st band, effect absorption of H2O 10-30% in NIR.

• Thermal corrections (band 4 and 5, NOAA 11)

MODTRAN Model

• MODerate resolution atmospheric TRANsmission

• Enable to solve radiation equations describing transfer of radiation with consideration of following effects:

– Absorption/emittance and scattering

– Reflectance and emissivity of Earth surface

– Illumination by Sun and Moon

– Spherical refraction

• For wavelengths λ 0,2-100 μm

UV + VIS + IR

• Suitable for smaller heights

ATCOR model

• Atmospheric and topographical corrections – to eliminate atmospheric and topographical effects

• Enable to obtain following parameters of the ground (Earth’s surface):

– reflectance

– emissivity

– temperature

• Model variants:

ATCOR2/3 – for dig. image records from satellite sensors with a narrow field of view

ATCOR4 – for dig. image records from airborne sensors with a wide of view

ATCOR calculations for VIS and SWIR radiation

• Output signal from a sensor is influenced by:

– 1st component – radiation scattered in the atmosphere

– 2nd component - radiation reflected by the surface relevant to the observed pixel

– 3rd component - radiation reflected by the surroundings of the observed pixel scattered to the direction of observation

m 2,5 ;4,0

Průchod záření atmosférou • výsledný signál ze senzoru ovlivněn zářením:

1. rozptýleným v atmosféře (komponenta 1)

2. odraženým plochou sledovaného pixelu (komponenta 2)

3. odraženým okolím sledovaného pixelu a rozptýleným do směru sledování (komponenta 13)

ATCOR2 model

• The model intended for a flat terrain

• DN of the pixel for the given band is transformed into a reflectance by iterative calculation: 1st step – 1st component is subtracted (external radiation of the

atmosphere), the rest (2nd and 3rd component) are transformed into reflectance equivalent on the ground (the influence of surrounding is neglected)

2nd step – calculation of average reflectance in surroundings (low-

pass filters) using diameter R ‹0.5,1›[km]

3rd step – adding 3rd component (influence of surrounding), calculated as a difference between 2nd step and 1st step

4th step – (spherical albedo effect) evaluate spatially variable average reflectance (in the surrounding of 1 km) of the current scene, overall flux

– Depends on the average reflectance,

– Calculated for the fixed reflectance = 0,15

Model ATCOR2

• In case of neglecting the influence of the

surrounding, R=0 and we can omit steps 2, 3, 4

Model ATCOR2 • Elimination of the mist from the image LANDSAT 5 TM

ATCOR2 model application

Primary data LANDSAT TM data after corrections with real values of reflectance

ATCOR calculations for TIR

• Also 14.5 i 15

• Valid for:

– LANDSAT 4/5 TM band 6

– LANDSAT 7 ETM+ band 6

– ASTER

m 13 ;8

ATCOR calculations for TIR

• Output signal from a sensor is influenced by:

– 1st component – radiation emitted by the atmosphere

– 2nd component - radiation emitted by the surface (with temperature T and emissivity ε) – basic info about the observed pixel

– 3rd component – thermal radiation reflected by the ground to the direction of observation(L3) where

• r = 1-ε (reflectance)

• F (atmospheric thermal flux)

FrL

.3

Signál TIR záření

• .

ATCOR calculations for TIR

• For sensors with n thermal bands it is necessary to solve n

equations with n+1 unknowns (n values of emissivity +1

temperature of the surface) – cannot be calculated

• Thus, it is required to specify the emissivity value

• Result – image of temperature (in degrees, but usually

multiply by some constant, i.e. default 4).

• In case of negative values – recommendation to shift values

by offset to protect the value range 0-255.

ATCOR calculations for TIR

• Recommended value of emissivity:

– Fixed value specify by user for the whole scene.

– i.e. ε=0,98 for

• TM band 6: 10,5-12,5μm

• ASTER band 13: 10,3-11,0μm

– emissivity values determined according to the land

cover (LC obtained from classification of other bands):

• ε=0,96 (soil for εRED>10%, dále asphalty, sand, mixed pixels)

• ε=0,97 (vegetation for NIR/RED>2)

• ε=0,98 (water and non-classified pixels)

– emissivity values (in %) are stored in an independent

file (i.e. „*._emi3.bsq“)

ATCOR3 Model

• The model for hilly (mountain) terrain

• Output signal from a sensor is influenced by: – radiation scattered in the atmosphere

– radiation reflected by the surface relevant to the observed pixel

– radiation reflected by the surroundings of the observed pixel

– radiation of the terrain reflected towards the observed pixel

• Atmospheric conditions are calculated using the module SPECTRA: – Humidity content

– Type of aerosol

– visibility

Model ATCOR3

• model pro členitý terén

ATCOR3 Model • For hilly (mountain) terrain

• DN of the pixel for the certain band is transformed into

reflectancy using iterative calculation:

1. step – the influence of the neighbourhood is neglected. A start value for the ground reflectance of the surrounding topography is employed whilst the path radiance component is subtracted from the signal. Shadow cast from surrounding topography is included (result of SHADOW program).

2. step – calculation of a low pass filtered reflectance image of step 1. The filter size can be specified by the user (typically 1-2 km, corresponding to a range of R = 0.5 - 1 km for the adjacency effect).

3. step – results of the SKYVIEW program are employed to calculate the contribution of the reflected terrain radiation (component 4) averaging over a box of size 0.5 km. The terrain view factor equals (1 - skyview factor). This step is iterated three times to cause convergence.

https://www.rese-apps.com/software/atcor-3-satellites/atcor-

2-3-method.html

ATCOR3 Model

4. step – Adjacency effect: the atmospheric scattering of radiation between adjacent fields of different reflectances is taken into account (component 3).

5. step – Spherical albedo effect: the global flux on the ground depends on the large-scale (1 km) average reflectance. The global flux in the atmospheric LUT's is calculated for a fixed reflectance=0.15 . This iteration performs the update for the spatially varying average reflectance map of the current scene, if the adjacency range R > 0 .

6. step – (optional) empirical BRDF correction (Correction for Bi-

Directional Effect) in areas of steep slopes or low illumination

If the adjacency range R is selected as R=0 then steps 2 to 5 are omitted. For flat terrain processing (ATCOR-2), step 3 and step 6 are not relevant

ATCOR3 Model • The haze elimination from the images of IKONOS bands

4,2,1

• Dresden, Germany

ATCOR3 Model • Elimination of shadows caused by clouds LANDSAT 7 ETM+

bands 4,5,3

• The influence of the Sun elevation (41°) is taken into account

• Agricultural land in Meklenburg, Germany

Application of the ATCOR model

Original data IKONOS

data with reduces haze

Data with real values of reflectancy

ATCOR4 Model • Atmospheric Correction of Small and Wide FOV Sensors (airborne)

• For computational efficiency, there are separate modules for flat and rugged terrain imagery

• large "monochromatic" database of atmospheric correction functions comes with the ATCOR-4 model - compiled with the Modtran-5 code

• It comprises the altitudes 0 km to 10 km and 20 km (1 km increment)

• Implementation of an atmospheric/topographic correction algorithms for airborne scanner data for the solar (0.35-2.55 um) and thermal (8-14 um) spectral region:

– solar region: calculation of surface reflectance cube

– thermal region: calculation of surface (brightness) temperature & emissivity

• Self contained determination of aerosol map and spatial water vapor map

• Haze and cirrus cloud removal (low altitude haze)

• Inflight sensor calibration using ground reference targets

• operational applicability with DAIS, AVIRIS, HyMap, CASI, AISA, Daedalus, and Hyspex, Hyperspec, imagery has been proven

Model ATCOR4 - process • Same components of radiation as for ATCOR3, ATCOR2. Steps:

1. Resampling of required atmospheric files (flight altitudes) from the monochromatic atmospheric database (if new sensor is introduced).

2. Geocoding or ortho-rectification, optional for flat terrain

3. For rugged terrain, the slope, and the orientation of DEM pixels have to be calculated, as well as the sky view factor and cast shadow images

4. Testing - before processing the image cube, surface reflectance spectra of small boxes can be taken from different surface covers in the scene to assess whether the atmospheric input parameters were appropriate. A comparison with ground measured spectra or library spectra is supported.

5. If ground reflectance measurements and atmospheric data (radiosonde, visibility, optical depth, or solar irradiance) are available for the scene, an in-flight calibration can be performed to determine the radiometric calibration coefficients (offset and slope).

6. The atmospheric/topographic correction (ATCOR4) of the image cube is performed based on the assumption of Lambertian surface elements. Visibility and water vapour column can be specified by the user (constant atmospheric conditions) or can be calculated by the program - provided the required spectral bands exist

7. In the case of strong bidirecional effects (viewing in the principal solar plane) an empirical correction method can be selected to normalize the results to nadir reflectance

ATMOSC Model

• model in Idrisi Andes

• The target is to remove or eliminate of atmospheric

influences:

– haze

– … and more

• The model includes:

– Parameters of the atmosphere in certain time

(RRRRMMDD)

– Frequency of the processed band

– offset, gain

– Sun elevation

– viewing angle

Preprocessing Levels for SPOT Images

Processing

level

description

1A Radiometric correction of distortions due to differences in sensitivity of the elementary detectors of the viewing instrument. Intended for users who wish to do their own geometric image processing

1B Radiometric correction identical to that of level 1A. Geometric correction of systematic effects (panoramic effect, Earth curvature and rotation). Internal distortions of the image are corrected for measuring distances, angles and surface areas. Specially designed product for photo-interpreting and thematic studies

2 More geometrical correction, for GIS and cartography

2A Radiometric correction identical to that of level 1A. Geometrical correction done in a standard cartographic projection (UTM WGS84 by default) not tied to ground control points.

2B Using GCPs

Preprocessing Levels for SPOT Images

Processing

level

description

S Radiometric corrections and geometrical resampling for

double scene registration

S1 One input scene is processed in 1B level

S2 One input scene is processed in 2 level

3 Map projection based on ground control points and a DEM based on Reference3D data to eliminate distortions due to relief.

Combined method of compensation of seasonal effects

• For calculation of radiometric and atmospheric corrections compensating seasonal influences we can use the algorithm (NIKM):

Rλ spectral reflectance on the ground

D distance Earth - Sun

Lλsensor apparent spectral radiance

Lλhaze radiance of atmosphere

TAUν transmissivity of atmosphere Earth – sensor

Esunλ illumination by diffused radiation of atmosphere

ϴ zenith angle of the Sun

TAUz transmissivity of atmosphere Sun-Earth

Real reflectance of the

Earth’s surface (combination

of radiometric and

atmospheric corrections)

• Sequential process – 3 steps:

1. Conversion of DN values to spectral

radiance (at the sensor)

2. Conversion of the spectral radiance to

apparent reflectance (at the sensor)

3. Removal of atmospheric effects (i.e.

model 5S) -> reflectance at the Earth’s

surface

Conversion of DN values to spectral radiance

(at the sensor)

• Transformation of the DN value of the pixel for certain

band into spectral radiance according to:

• where c0 = additive component (offset, bias)

c1 = multiplicative component (gain)

Easy linear calculation

DNccL 10

Conversion of the spectral radiance to

apparent reflectance (at the sensor)

• Calculation of c0 (bias) and c1 (gain) for each band:

• Use values Lmin and Lmax for each band (provided by the

system operator) and calculate parameters of linear interpolation c0 and c1

• Lmin=c0+c1*0=c0

• Lmax=Lmin+c1*DNmax, tj. c1=(Lmax-Lmin)/DNmax

• For Landsat DNmax = 255.

• Other authors (Bilko) use slightly different calculation: C1

= (Lmax/254)-(Lmin/255) (almost no difference).

Lmin and Lmax for TM bands

Demonstration of LandSat-7 ETM+ metadata

© Rees, 2012

• Calculation of the radiance (at the sensor) using linear interpolation from min/max values for the given band:

Conversion of the spectral radiance to apparent reflectance (at

the sensor)

• apparent reflectance (for satellite it means the reflectance outside the atmosphere) is calculated:

Determination of the zenith angle of the Sun SZ

Sun height (zenith angle) SZ:

• SPOT and LANDSAT provide the elevation angle of Sun in parameters, therefore the zenith angle is calculated as 90 – elevation angle (and change to radians)

Determination of the distance between Earth and Sun d

• distance Earth-Sun (d):

d2=(1-0.01674*cos(0.9856*(JD-4)))2

• where JD is Julian’s day (number of days from the beginning of the year)

Determination of the solar irradiance ESUN

Example of calculation with metadata for LandSat-7 ETM+

• It shows that the image was acquired on 22 July 2001, and that the Sun’s elevation angle (at the centre of the image) was 41.1 at the time. The Sun’s zenith angle Θ was thus 48.9, and the distance from the Sun to the Earth on this date was 1.016 AU (this is the distance from the Sun to the Earth’s centre, not its surface, but since the radius of the Earth is only 0.000 04 AU the difference can be ignored). The mean exoatmospheric spectral radiance in the ETM+ band 1 is 1969 Wm-2μm-1, so a band 1 radiance of 70.9 Wm-2sr-1μm-1 corresponds to a planetary reflectance of

© Rees, 2012

Removal of atmospheric effects and

determination of ground reflectance

• Various methods of removal of atmospheric effects – see before

• Recommended model of 5S

Calculation of surface temperature (NIKM)

Algorithms used for surface temperature calculation can be divided into:

• split-window algorithms (use 2 thermal bands) and multispectral algorithms (use more thermal bands)

• mono-window algorithms use only one thermal band as an input

Calculation of surface temperature according to NASA (NIKM)

• Typical application of the mono-window algorithms is to calculate temperature from the thermal band of LandSat satellite.

• Simple algorithms for calculation of temperature - NASA.

• Algorithms using only one thermal band has one common disadvantage – the determined temperature are not without atmospheric influence, that is why NASA experts developed and applied for data from LandSat TM6 satellite algorithms, which models the state of the atmosphere using two basic meteorological indicators of the atmosphere status – the transmissivity and the mean temperature of the atmosphere

• 3 steps:

1. Transformation of DN into spectral radiance

2. Calculation of radiant temperature using Planck function

3. Calculation of the surface temperature

Transformation of DN into spectral radiance (NIKM)

• Where Qmax is maximal DN value (Qmax = 255), Qdn is DN value of the pixel, Lmin(λ) and Lmax(λ) are minimal and maximal recorder values of spectral density for Qdn = 0 and Qdn = 255

• For the scene of Landsat 7 ETM+ recorded in the mode „low gain“ the relevant values are Lmin(λ) = 0 and Lmax(λ) = 17,04 Wm-2sr-1μm-1,

• more simple relationship is:

max

)min()max()min(

)(

)(

Q

QLLLL

dn

dnQL 06823529,0)(

Calculation of radiant temperature using Planck function (NIKM)

• Where K1 and K2 are calibration constants. Values for ETM+ K1 = 666,09 Wm-2sr-1 and K2 = 1282,7 [K].

• If you know the emissivity of surfaces in the mapped area, you can calculate directly the temperature of the surface using:

• Where λ is wavelength of the emitted radiation, in our case the average value between wavelengths for thermal band of the Landsat, thus λ = 11,45 μm, α = hc/K = 1,438 x 10-2 mK, where K is Stefan-Boltzmann constant (1,38 x 10-23 JK -1), h is Planck constant (6,26 x 10-

34 Js), and c is the velocity of the ligth (2,998 x 108ms -1).

)(

1

2

1lnL

K

KTrad

ln1

rad

radkin

T

TT

Calculation of radiant temperature using Planck function (NIKM) - 2

• If you can correct temperature by an atmospheric correction, you can use the relationship:

• where a, b are coefficients according to the table, Ta is the average effective temperature of the atmosphere

• C and D are calculated:

where ε is the emissivity of the surface, τ is the transmittance of the atmosphere.

C

DTTDCDCbDCaT aradkin

11

C 111D

Calculation of the surface temperature (NIKM)

• It is clear, that you may calculate the surface temperature (corrected by the atmosphere influence). But you need to know the surface emissivity. To specify atmosphere influence you need the mean temperature of the atmosphere and the transmissivity. The surface emissivity can be calculated e.g. from NDVI (normalised differential vegetation index), or set the values from the table with classification of each type of the surface

• Concerning the mean temperature of the atmosphere – you may calculate (without more precise data) from the air temperature above the ground (values in the height of 2 meters) using the model of standard atmosphere. Similarly it is possible to calculate the transmissivity from the values of the water wapour content.

• http://www.intelligence-airbusds.com/en/195-preprocessing-levels-and-location-accuracy