GEOG 4110/5100 Advanced Remote Sensing Lecture 3

Review of Radiometric Distortion Radiometric Error Correction Temperature Retrieval Geometric Distortion

Relevant reading: Richards, sections 2.1 – 2.8; 2.10-2.15 Signal to Noise Ratio (SNR)

• What is it? • Why do we care? Dynamic Range

• What is it? • Why do we care?

Possible Combinations with: 1 bit: 0 or 1 = 2 or 21 2 bits: 0,0, 0,1 1,0 1,1 = 4 or 22 3 bits: 0,0,0 0,0,1 0,1,0, 0,1,1 = 8 or 23 1,0,0 1,0,1 1,1,0 1,1,1

N bits: = 2N Gain and Offset (Bias)

Gain is the slope Actual Sensor of the sensor Response response line

Ideal Sensor Ll = (DN x gain) + bias Response Image Brightness (Output)

Bias, Offset, Ground Scene Brightness (Input) Dark Current Contributions to Instrument Signal Distortion Distortion: a change, twist, or exaggeration that makes something appear different from the way it really is.

• What is Radiometric Distortion? • What is Geometric Distortion? Distortion Distortion: a change, twist, or exaggeration that makes something appear different from the way it really is.

• Radiometric Distortion: Errors in pixel brightness values – Instrumentation – Wavelength dependence of solar radiation – Effect of atmosphere

• Geometric Distortion: Errors in image geometry, (location, dimensions, etc.) – Platform and instrument relative motions – Scan angles and scan patterns – Rotation of the Earth – Attitude and altitude variability Basic Radiometric Terms

• Irradiance: The amount of energy incident on a given area of a surface in a given amount of time (W/m2). • Radiance: The amount of energy scattered in a particular direction (W/m2/sr). • Solid angle: The ratio of the area of a spherical surface to the square of the radius.

Ω = A/r2 r A

Ω Basic Radiometric Terms

• Spectral Irradiance: The amount of energy available across wavelength range (W/m2/µm). • Hemispherical reflectance: The ratio of the radiant flux from a surface to the radiant flux incident to it. • Hemispherical transmittance: The ratio of the radiant flux transmitted through a surface to the radiant flux incident to it. • Hemispherical absorptance: The ratio of the radiant flux absorbed by a surface to the radiant flux incident to it. Absence of an Atmosphere In Absence of an atmosphere surface irradiance between wavelengths is Wm-2

Where: Eλ = solar spectral irradiance at the earth. θ = solar zenith angle. For most remote sensing devices the wavelengths are small enough that: Wm-2 Absence of an Atmosphere

• If the surface has a reflectance of R, the radiance reflected back to the atmosphere is R L = E cosθ.Δλ Wm-2 sr-1 Δλ π • Knowing L, we can determine the Irradiance at the Sensor from a digital number C (e.g. 0-255)

-2 -1 L S = Ck + Lmin Wm sr

Where: k= (Lmax – Lmin)/Cmax and Lmax and Lmin are the maximum and minimum measureable radiances as indicated by the instrument manufacturer

Effects of the Atmosphere Bulk Atmospheric Correction

• Often it is sufficient to assume there are pixel values close to zero in the imagery (e.g. water) • In this case, any brightness observed will be a result of atmospheric contributions (Primarily LP but also ED) • Histograms of each channel will show an offset from zero as a result • Wavelength dependent • Subtracting this offset from the entire image will remove the vast majority of atmospheric effects Absorption and Atmospheric Windows

AIRS measures upwelling radiances in 2378 spectral channels covering the IR spectral band, 3.74 to 15.4 µm. A set of four channels in the Visible/Near-IR (VIS) observes wavelengths from 0.4 to 1.0 µm to provide cloud cover and spatial- variability characterization. Striping in Imagery

Southern Maruitania near the Senegal border, October 10, 1980, LANDSAT 4 Multi-Spectral Scanner (MSS). The majority of the land-cover consists of riparian vegetation, poor grassland, and barren ground

Band 1 NDVI Striping

Transfer Characteristics

Mismatches between detectors

• Ideal radiation detector has a consistent transfer function (radiation in à radiation out) • In reality, different detectors have different transfer functions – Same irradiance causes different brightness values in different detectors – 6 detectors on MSS, 16 on TM, 6000 on SPOT HRV Destriping

• Correction of radiometric mismatches can be made by adopting one sensor as a reference sensor, and adjusting the offsets of the others to match it σ σ y = d x + m − d m σ d σ i Where i i x = old brightness of a pixel y = new (destriped) brightness sd = reference value standard deviation s€i = standard deviation of detector under consideration md = reference value mean brightness mi = mean brightness of detector under consideration

Assumes brightness values don’t change significantly over distance equivalent to one scan of detectors (474 m for Landsats 1, 2, and 3) Destriping

Original Band 1 Band 1 after destriping

Example from Richards Text

Fig. 2.2 Reducing sensor induced striping noise in a Landsat MSS image: a original image, and b after destriping by matching sensor statistics

Apparent Surface Temperature Instrument Characteristics Image Characteristics

255

Lmax Transfer Function Gain Radiant Intensity

Output Signal (DN) L Offset min Bias 0 L L 0 255 min Input Signal max Digital Number (Radiant Intensity) L = Bias + (Gain × DN) Radiometric Bias = LMIN Resolution/Dynamic Gain= Range 25 True Surface Temperature • Must correct for atmospheric contribution – Attenuation of surface signal – Addition of atmospheric signal – Differs from visible in that we can’t do a bulk correction for darkest pixel: Why?

• Various techniques – Split window: uses 2 channels (windows) that overlap in spectral sensitivity – Dual window: uses 2 channels that do not overlap – Triple window: Uses 3 channels

• We will focus on AVHRR sea surface temperature – Global coverage – Good resolution – Nearly 30 years of data – Reasonably stable surface emissivity characteristics – Channel 3: 3.55-3.93 µm; Channel 4: 10.3-11.3 µm; Channel 5: 11.5- 12.5 µm 26 Transmission from Ground to the Top of the Atmosphere (TOA)

({[(I0 t’ + I1)t’ + I2]t’ + I3}t’ + I4)t’+ I5

5 {[(I0t’ + I1)t’ + I2]t’+ I3}t’+ I4

5 4 3 I5 = I0 (t’) + I1(t’) + I2(t’) 4 2 [(I0t’ + I1)t’ + I2]t’+ I3 + I3(t’) + I4t’+ I5

3 n (I0t’ + I1)t’+ I2 (n−i) Ii = ∑Iiτ' + In 0 2 I0t’+ I1

1 I0 € 27 Temperature Retrieval • Exploit the fact that attenuation and emission characteristics are different for different wavelengths • Thermal radiation emitted by the surface is absorbed by atmospheric constituents and re-emitted at all levels of he atmosphere – Primary factor at wavelengths we consider is water vapor

If we consider the atmosphere as a whole, the relationship on the previous page can be condensed for a narrow wavelength band to:

Spectral Spectral Spectral Atmospheric Atmospheric Irradiance = Radiance from + Radiance from Transmittance Emissivity at sensor ( surface )( ) (Top of Atmos. )( )

Ii = Llst + Lli(1-t) Atmospheric reflectance is negligible at thermal wavelengths Temperature Retrieval: Basic Concepts

29 Temperature Retrieval: Basic Concepts

λ2 λ2 Ii = ∫ [Bλ (Ts )]τ λ dλ + ∫ [Bλ (Ti )](1−τ λ )dλ λ1 λ1

Ii = [Bλ (Ts)](Δλ)τ λ + [Bλ (Ti )](Δλ)(1− τ λ )

Ii = Llst + Lli(1-t) 30 € Temperature Retrieval

Brightness Temperature: Brightness temperature is the temperature of a black body in thermal equilibrium with its surroundings would have to be to duplicate the observed intensity of a grey body object at a given wavelength

Split Window: A technique used to calculate land and sea surface temperatures, where corrections are made for the atmospheric modification of upwelling radiation from the surface. While a single-channel does not allow resolution of ambiguity between surface temperature and atmospheric contributions to a signal, two channels can.

31 Temperature Retrieval

If we use channels that are close in the spectral range, as with the split window, the previous relationship can be inverted to solve for surface temperature

Ts = T4 + [k4/(k4-k5)](T4-T5)

Where T4 and T5 are the brightness temperatures of channels 4 and 5 respectively, and k4 and k5 are the effective absorption coefficients at wavelengths in channels 4 and 5.

The k and t terms are calculated with radiative transfer models for a variety of conditions, and regressed against temperature data from buoys to provide a relationship between Ts and the combination of T4 and T5. They are wavelength-dependent

32 Cloud Filtering

• Maximum Temperature – all observations of a small surface area over a relatively short period of time are compared. – The highest temperature is retained as the best estimate of temperature in that area. • ocean surface features are more persistent than clouds • clouds are colder than the surface. • Caveat: This method works poorly for persistent, thin clouds.

• Two Wavelength Infrared – compare temperatures from 3.7 µm and 10.5 µm • 3.7 µm sensitive to water vapor – If the temperatures are the same, then we can assume the measured signal came from • the sea surface, OR • uniform clouds, which will probably be detected in a visual image of the area of interest. – If the temperatures at the two wavelengths are different, then there are scattered, undetected clouds in the scene. Cloud Filtering

• Infrared Variability – temperatures of clouds tend to be much more variable in space than temperature of the sea surface – all areas having a small deviation from a mean brightness temperature close to that expected of the sea in the region are accepted as good values.

• Two Wavelength Visible-Infrared – uses reflected sunlight to detect clouds on the assumption that the sea is much darker in visible wavelengths than clouds

Once cloud-free pixels have been identified, the infrared radiance of the remaining pixels must be corrected for the influence of water vapor and aerosols in the atmosphere in order to obtain accurate values for SST.