now that i know that…

Now That I Know That…

What Do I Do?

(Analyzing your Microtop Solar Radiometry Data)

Review: Transmissivity

The probability that a photon will pass through a medium without interacting with it (absorption or scattering) is:

where:

T = the “transmissivity” of the medium

τ = the “optical thickness” of the medium.

)exp( T

Review: Optical Thickness

Optical thickness τ is the (dimensionless) radiative unit of length

where:

n = the number of “extincters” (scatterers or absorbers) per unit volume in the medium

σ = the extinction cross-section (effective area per “extincter”)

s = the geometric path length

dsnd

Linear Problem Additive τ

A medium typically has several kinds of “extincters”, but their effects are additive:

where:

na1 = the number of the 1st absorber per unit volume

σa1 = the absorption cross-section (effective area per absorber) for the 1st absorber

So:

(Etc., etc.)

dsnnnnd ssssaaaa ...)( 22112211

...2121 ssaa ddddd

Beer’s Law

• Assume that your measurement consists only of solar radiation that is transmitted through the atmosphere without interacting with it.

• Then the measured spectral irradiance F can be described by Beer’s Law as:

where:

F0 = the spectral solar extraterrestrial irradiance

τs = the “optical path length” of the medium along the solar beam.

)exp(0 sFF

Geometry

Since the sun is not directly overhead, the geometric path length along the solar beam (S) is longer than a line along the zenith to the same altitude (A).

A S

Flat Atmosphere?

But as long as the sun is not too near the horizon (say, z < 80º), the atmosphere can be treated as “flat,” and S is related to A by a simple cosine law, with 1/cos z called the “air mass factor” m.

z

AS

cos

A S

AmS

Putting it all together

If we assume that the atmosphere is horizontally homogenous, then m is the only difference between a zenith line of sight and our slant line of sight, and so:

where a1 = ozone absorption,

s1 = Rayleigh (molecular) scattering, and

s2 = Mie (aerosol) scattering

0

221111 )( dznnnm ssssaas

So… what did I measure?

• The only thing the instrument really measures is F at 5 wavelengths:

305, 312, 320, 340 and 380 nm

(ozone-sensitive) (aerosol-sensitive)

• The instrument did some internal calculations to give you more information, however…

)exp(0 sFF

And the other bits come from…?

F0 = extraterrestrial solar spectral irradiance (from independent measurements)

m = air mass factor (from geometry, given your location and the local time)

σa1 = ozone absorption cross-section (from lab measurements)

τs1 = molecular scattering optical depth (using laboratory measured cross-sections, and assuming a standard atmosphere, given your location)

0

2111 ssaas mmdznm )exp(0 sFF

So… what else did I get?

• The instrument therefore also can tell you about:

Ozone column amount[ ] (in Dobson units)

and Aerosol Optical Depth (no units) [ ]

at each wavelength.

21

0

11 ssaas mmdznm

0

2111 ssaas mmdznm

And a “Dobson Unit” is…?

• Take all of the ozone in a column above a given point at the surface, and compress it to p = 1 atm, T = 0ºC.

• The resulting layer of ozone is typically ~ 0.3 cm thick, which corresponds to 0.3 “atm-cm” of ozone, or 300 “Dobson units.”

Why do I get several ozone estimates?

• The ozone estimate is made by comparing the differential absorption between 2 adjacent wavelengths whose sensitivity to ozone differs significantly.

• Each different estimate uses a different pair of wavelengths.

• If ozone is abundant, the weakly absorbed wavelengths will give a better ozone estimate; if ozone is scarce, the strongly absorbed wavelengths will give a better estimate.

Ozone Cross-Section

σa1

Aerosol Cross-Section

• Depends on the nature of the aerosol (size distribution, optical properties, etc.).

• For typical tropospheric aerosol, the following rule is often useful to estimate the variation over small wavelength intervals:

• α is the “Angstrom coefficient” for the aerosol, and is typically ~ 1 or 2.

• Compare to Rayleigh scattering:

2s

41

s

Final Adjustments

• Based on the manufacturer’s calibration, you should make the following adjustments prior to using your data:

Instrument #5: Instrument #7• Ozone is 1.2% high Ozone is 1.0% high• 340nm aer is 0.007 high 340nm aer is 0.009 high• 380nm aer is 0.048 high 380nm aer is 0.061 high

TEAM 2

Ozone Data from MICROTOPS 7

TEAM 1

Ozone Data from MICROTOPS 5

TEAM 3

AOT Data from MICROTOPS 5

(340 nm, 380 nm)

TEAM 4

AOT Data from MICROTOPS 7

(340 nm, 380 nm)

Inter-comparison

Diurnal Variation

TrendSatellite Data

Inter-comparison

Diurnal Variation

Trend

Satellite Data

OZONE

AEROSOLS

THE END

Team #1

You have 2 month-long datasets. Make ozone and aerosol plots that characterize:

• The consistency of the two datasets• The existence (or not) of diurnal trends in the retrieved

quantities• The existence (or not) of longer-term trends (weekly?

Seasonal?)• The relative skill of the various students?

Team #2

Make ozone and aerosol plots that characterize:

• The accuracy of the two instruments, as compared to satellite data (from the OMI instrument)

• Possible sources of disagreement between ground-based and satellite-based estimates of these quantities

Team #3

• Use the ozone and aerosol information to calculate the diffuse radiation (as well as the direct radiation).

• Comment on the relative contributions of diffuse vs direct radiation to the downward irradiance at the various wavelengths

Team #4

• Use the data to estimate the extraterrestrial solar spectral irradiance at each measured wavelength

• Compare your results to independent measurements

• This cross-section data might be useful

305 312 320 340 380

Ozone (1/atm-cm)

5.084 1.977 0.858 0 0

Rayleigh (1/atm)

1.126 1.029 0.930 0.718 0.450