1. In the past thirty five years NOAA, with help from NASA, has established a remote sensing capability on polar and geostationary platforms that has proven useful in monitoring and predicting severe weather such as tornadic outbreaks, tropical cyclones, and flash floods in the short term, and climate trends indicated by sea surface temperatures, biomass burning, and cloud cover in the longer term. This has become possible first with the visible and infrared window imagery of the 1970s and has been augmented with the temperature and moisture sounding capability of the 1980s. The imagery from the NOAA satellites, especially the time continuous observations from geostationary instruments, dramatically enhanced our ability to understand atmospheric cloud motions and to predict severe thunderstorms. These data were almost immediately incorporated into operational procedures. Use of sounder data in the operational weather systems is more recently coming of age. The polar orbiting sounders are filling important data voids at synoptic scales. Applications include temperature and moisture analyses for weather prediction, analysis of atmospheric stability, estimation of tropical cyclone intensity and position, and global analyses of clouds. The Advanced TIROS Operational Vertical Sounder (ATOVS) includes both infrared and microwave observations with the latter helping considerably to alleviate the influence of clouds for all weather soundings. The Geostationary Operational Environmental Satellite (GOES) Imager and Sounder have been used to develop procedures for retrieving atmospheric temperature, moisture, and wind at hourly intervals in the northern hemisphere. Temporal and spatial changes in atmospheric moisture and stability are improving severe storm warnings. Atmospheric flow fields are helping to improve hurricane trajectory forecasting. Applications of these NOAA data also extend to the climate programs; archives from the last fifteen years offer important information about the effects of aerosols and greenhouse gases and possible trends in global temperature.
This talk will indicate the present capabilities and foreshadow some of the developments anticipated in the next twenty years.
Quick Review of Remote Sensing Basic Theory Paolo Antonelli SSEC University of Wisconsin-Madison Monteponi, September 2008

2. Outline
Planck Function
Infrared: Thermal Sensitivity
Bit Depth

3. Spectral Distribution of Energy Radiated
from Blackbodies at Various Temperatures

4. Radiation is governed by Planck’s Law
In wavelenght:
B(,T) = c1 /{  5 [e c2 /T -1] } (mW/m2/ster/cm)
where  = wavelength (cm)
T = temperature of emitting surface (deg K)
c1 = x 10-8 (W/m2/ster/cm-4)
c2 = (cm deg K)
In wavenumber:
B(,T) = c13 / [e c2/T -1] (mW/m2/ster/cm-1)
where  = # wavelengths in one centimeter (cm-1)
c1 = x 10-5 (mW/m2/ster/cm-4)

5. B(max,T)~T5 B(max,T)~T3 max ≠(1/ max) B(,T) versus B(,T) B(,T)
100 20 10
6.6 5 4
3.3
wavelength [µm]

6. wavelength  : distance between peaks (µm)
Slide 4
wavenumber  : number of waves per unit distance (cm)
=1/ 
d=-1/ 2 d 

7. Using wavenumbers
Wien's Law dB(max,T) / dT = 0 where (max) = 1.95T
indicates peak of Planck function curve shifts to shorter wavelengths (greater wavenumbers) with temperature increase. Note B(max,T) ~ T**3. 
Stefan-Boltzmann Law E =   B(,T) d = T4, where  = 5.67 x 10-8 W/m2/deg4. o
states that irradiance of a black body (area under Planck curve) is proportional to T4 .
Brightness Temperature
c13
T = c2/[ln(______ + 1)] is determined by inverting Planck function B
Brightness temperature is uniquely related to radiance for a given wavelength by the Planck function.

8.   c13 c1 Using wavenumbers Using wavelengths c2/T c2 /T
B(,T) = c13 / [e ] B(,T) = c1 /{  5 [e ] }
(mW/m2/ster/cm-1) (mW/m2/ster/cm)
(max in cm-1) = 1.95T (max in cm)T =
B(max,T) ~ T**3. B( max,T) ~ T**5.
 
E =   B(,T) d = T4, E =   B(,T) d  = T4,
o o
c1 c1  
T = c2/[ln(______ + 1)] T = c2/[ ln(______ + 1)]
B 5 B

9. Temperature sensitivity
dB/B =  dT/T
The Temperature Sensitivity  is the percentage change in radiance corresponding to a percentage change in temperature
Substituting the Planck Expression, the equation can be solved in :
=c2/T

10. ∆B11> ∆B4
∆B11
T=300 K
Tref=220 K
∆B4

11. ∆B4/B4= 4 ∆T/T ∆B11/B11 = 11 ∆T/T ∆B4/B4>∆B11/B11  4 > 11
(values in plot are referred to wavelength)

12. (Approximation of) B as function of  and T
∆B/B= ∆T/T
Integrating the Temperature Sensitivity Equation
Between Tref and T (Bref and B):
B=Bref(T/Tref)
Where =c2/Tref (in wavenumber space)

13. B=Bref(T/Tref)  B=(Bref/ Tref) T   B T 
The temperature sensitivity indicates the power to which the Planck radiance depends on temperature, since B proportional to T satisfies the equation. For infrared wavelengths,
 = c2/T = c2/T.
__________________________________________________________________
Wavenumber Typical Scene Temperature Temperature Sensitivity

14. Non-Homogeneous FOV N Tcold=220 K 1-N Thot=300 K
B=NB(Tcold)+(1-N)B(Thot)
BT=NBThot+(1-N)BTcold

15. For NON-UNIFORM FOVs:
Bobs=NBcold+(1-N)Bhot
Bobs=N Bref(Tcold/Tref)+ (1-N) Bref(Thot/Tref)
Bobs= Bref(1/Tref) (N Tcold + (1-N)Thot)
For N=.5
Bobs/Bref=.5 (1/Tref) ( Tcold + Thot)
Bobs/Bref=.5 (1/TrefTcold) (1+ (Thot/ Tcold) )
The greater  the more predominant the hot term
At 4 µm (=12) the hot term more dominating than at 11 µm (=4) N
1-N
Tcold
Thot

16. Consequences At 4 µm (=12) clouds look smaller than at 11 µm (=4)
In presence of fires the difference BT4-BT11 is larger than the solar contribution
The different response in these 2 windows allow for cloud detection and for fire detection

17. Low Gain Channels Band 14 low 0.68 µm Vegetated areas Are visible
Saturation over Barren Soil
Visible details over water

18. High Gain Channels Band 14 hi 0.68 µm Saturation over Vegetated areas
little barely visible
Saturation over Barren Soil
Visible details over water

19. Range for Band 14 low
0.68 µm
Range for Band 14 high
0.68 µm

20. Bit Depth and Value Range
With 12 bits 212 integer numbers can be represented
Given ∆R, the range of radiances we want to observe, the smallest observable variation is ∆R/ 212
Given dR smallest observable variation, the range of observable radiances is dR* 212
For this reason Band 14low (larger range) is used for cloud detection and Band 14hi (smaller range) is used for ocean products dR ∆R

21. Conclusions
Planck Function: at any wavenumber/wavelength relates the temperature of the observed target to its radiance (for Blackbodies);
Thermal Sensitivity: different emissive channels respond differently to target temperature variations. Thermal Sensitivity helps in explaining why, and allows for cloud and fire detection;
Bit Depth: key concepts are spectral range and number of bits.