1 Atmospheric Radiation – Lecture 13 PHY Lecture 13 Remote sensing using emitted IR radiation

2 Atmospheric Radiation – Lecture 12 Liou 7.4.1:Revision Solution: Where Can assume: emissivity = 1,  =1 Why?

3 Atmospheric Radiation – Lecture 12 Liou 7.4.1:Monochromatic transmittance, T, and weighting function Change to pressure co-ordinates: Recall Giving:

4 Atmospheric Radiation – Lecture 12 Liou 7.4.1: Instrument response function Need to convolve the emitted radiance with a function to represent the instrument response: a “slit” function instrument has only a limited spectral bandwidth Assume spectral interval is small so replace with Then With

5 Atmospheric Radiation – Lecture 12 Surface temperatureTemperature profiles Atmospheric window: cm -1 Gas phase profiles Liou 7.4.1: Temperature and gas retrievals CO2, 15um, 4.3um O3 9.6um H2O 6.3um

6 Atmospheric Radiation – Lecture 12 Liou 7.4.2: Surface temperature determination Define mean atmospheric temperature and simplify for the case where you are measuring in the window region: Where i=v, and transmission, is mainly reduced by water vapour and can be approximated by To subtract the atmospheric component (eliminate ) we take two measurements: the “split window” technique

7 Atmospheric Radiation – Lecture 12 Liou 7.4.2: Split window technique Applying the window equation to two channels Want in terms of T 2 Expand Planck function in terms of Taylor series with respect to T a Applying Taylor series expansion and eliminating T-T a Now replacing T by T b2 and T s and using equation for I 2 get Radiance expressed as Brightness temperature

8 Atmospheric Radiation – Lecture 12 Liou 7.4.2: Split window technique Now replacing T by T b2 and T s and using equation for I 2 get With Gives where In practical use, the Planck function is replaced by the Brightness temperature and T s estimated by Equation for I 2

9 Atmospheric Radiation – Lecture 12 Liou 7.4.2: Application to sea surface temperatures From NOAA AVHRR data: Retrieval from regression: In three channels (sum and difference): 10.9, 12.0, 3.7um Satellite measures SKIN temperature (first few mm) In situ buoys are used to provide the coefficients a, b and c, which relate these skin temperatures to bulk temperature of water… (McClain et al, 1985)

10 Atmospheric Radiation – Lecture 12 Liou 7.4.3: Remote sensing of temperature profiles Kaplan (1959): Vertical resolution of the temperature field can be inferred from spectral distribution of atmospheric emission. Wings in a band see deep into the atmosphere while centre sees only the top layer: absorption is strongly peaked in centre, so the mean free path of radiation is less for centre than wings.. Can select different sounding wavelengths each to be sensitive to different layers..

11 Atmospheric Radiation – Lecture 12 Liou 7.4.3: Illustration of concept Assume (find T s in practice from preceding analysis) Write Solve for this time taking into account variation across spectral interval using reference wavenumber, v r Express equation for I v as Fredholm Integral where

12 Atmospheric Radiation – Lecture 12 Liou 7.4.3: Choosing spectral region There are two gases that occur in uniform abundance at altitude up to 100km, which also show emission bands in regions convenient for measurements CARBON DIOXIDE (365ppm) and OXYGEN (volume mixing ratio 0.21)

13 Atmospheric Radiation – Lecture 12 Liou 7.4.3: 15um CO 2 band as measured by IRIS NIMBUS Decrease of tropospheric temperature as altitude increases Warming due to stratosphere

14 Atmospheric Radiation – Lecture 12 Liou 7.4.3: Weighting functions An ideal weighting function would be a delta function: all the contribution from that measurement at a single altitude.. Weighting functions are constructed from where T can be calculated using a line-by-line code taking pressure and temperature proilfes into account CO2 transmittances in the 15um band are due to a number of different lines: the v2 fundamental and hot bands..

15 Atmospheric Radiation – Lecture 12 Liou 7.4.3: Example weighting functions corresponding to 15um band intervals