Relevant Angles for CIPS Observing Geometry

1. Relevant Angles for CIPS Observing Geometry SV=Scattering Volume Solar Zenith Angle Sun-SV-Zenith Viewing Angle Nadir-CIPS-SV Scattering Angle (angle between original and scattered path)

2. Some Useful Descriptions of the Atmosphere I Decrease in pressure with height: Pressure is the force per unit area exerted by the atmosphere Therefore pressure could be expressed as the weight of a column of air molecules: p=pressure, n=number density, m=mean mass of individual molecules (~.8*mN2 + .2mO2 in trop.) N(z) is the “column density”, the number of molecules in a column of unit area extending from altitude z to the top of the atmosphere Ideal gas law: kB=Boltzmann’s constant, T=temperature H is called the “scale height”

3. Some Useful Descriptions of the Atmosphere II Relate pressure to height: Solve assuming constant temperature H is the distance over which the atmospheric pressure decreases by a factor e. H is also then the distance over which the atmospheric number density of molecules decreases by a factor e.

4. Some Useful Descriptions of the Atmosphere III How is column density related to scale height? (assuming constant temperature): H is also the height the atmosphere would be if it were collapsed to a layer of uniform density These relationships are useful for getting a feel for how the atmosphere behaves. Because they assume that temperature is constant, their quantitative utility is limited. They should only be applied in small altitude intervals. In practice its usually better to calculate column density by its defining equation. This is for a vertical column. Sometimes, what is needed is the slant column density for a path at angle q relative to vertical: (this version works for q < ~70 degrees)

5. Optical Depth F is irradiance s is cross section F(l,z) Z t is called optical depth and describes how far a photon is likely to travel through a column of gas. As a flux travels a distance such that t equals unity, the flux is reduced by a factor of e.

6. Cross Sections cm2 Ozone Absorption Rayleigh Scattering Cross Sections - have units of area – represent the “size of the target” for photons colliding with atoms, molecules, or ions Dependent upon photon energy There is one total cross section describing the area presented by the target atom or molecule in a collision, this cross section is the sum of many individual cross sections that represent probabilities or efficiencies of all the individual possible processes (scattering, absorption, etc.) Cross sections therefore represent the efficiency of a given process

7. CIPS Observing Geometry for a Single Observation A beam of solar photons travels along a path to the scattering volume and then to CIPS. Along the way photons are removed from the beam due to absorption by ozone. Note that there are contributions to the Rayleigh scattered signal from all points along the path (these are not shown).

8. CIPS Algorithm Overview The observed albedo from Rayleigh scattering may be written according to the single scattering formula: S ≈ 1/cos(q) + 1/cos(q0) q = viewing angle q0 = solar zenith angle X = ozone density as a function of pressure level l = wavelength (265 nm for CIPS) Il = atmospheric radiance Fl = solar irradiance b = Rayleigh scattering coefficient PR = Rayleigh phase function Q= scattering angle p = pressure in mb a = absorption coefficient of ozone

9. We have generalized the result of McPeters et al. [1980] and shown that by assuming ozone density varies exponentially with altitude and that the ratio of the ozone scale height to that of the background atmosphere is constant, then: where, Nair = the air vertical column density above 1 mb CO3 = ozone column density above 1 mb m = cos(q) m0 = cos(q0) And s = the ratio of the ozone scale height to that of the background atmosphere HALOE observations have shown that s does not deviate significantly from 0.7.

10. Ozone concentration Relative contribution to nadir viewing Rayleigh scattered radiance

11. Cloud Albedo where, APMC = is the nadir viewing albedo of the cloud if observed at Q = 90° PM = Mie Phase Function Note that although currently not implemented, this equation may need to be scaled by m = cos(q), this should be a topic for consideration

12. Phase function is the fraction of radiance emitted per unit solid angle Mie Phase function of mean particle size 0,10,20,30,40,50, 60 nm Rayleigh Phase Function Phase function for Gaussian particle distribution with width 14 nm

13. Interpreting CIPS Scattering Profile The unknowns are CO3, s, APMC, and R Option 1: Non linear least squares fit and use 7 data points to retrieve 4 unknowns - experience says this is prone to significant error bars Option 2: Assume an s, use NLSfit to retrieve CO3, APMC, and R Option 3: Have an indicator of cloud presence if cloud not thought to be present, solve only for CO3, s if a cloud is thought present, assume s, solve for CO3, APMC, and R (assumed s could be taken from observations in cloud free regions)

14. How can we determine the presence of a cloud? For the case of no cloud, y should be a simple linear function of x (with a slope of s) If a cloud is present, the slope is changed, the effect is different for small scattering angles versus large ones. For example, calculate slope at small scattering angles and compare to same calculation for large scattering angles, if ratio is significantly different from 1, then a cloud is likely to be present.

15. PMC (forward scattering) Rayleigh Background PMC (backward scattering)