# Umkehr effect

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The Umkehr is the time variation of the ratio of the scattered intensity at two different wavelengths. The word means 'reversal' in German. The Umkehr effect is observed when measurements are made with ultraviolet spectrophotometer of the ratio of the zenith sky light intensities of two wavelengths in the solar ultraviolet when the sun is near the horizon. The shorter of two wavelengths (intensity I) is strongly absorbed and other (intensity I' ) is weakly absorbed. If the value of log(I/I' ) is plotted against the sun's zenith angle, it is observed that this log-intensity ratio decreases as the zenith angle increases until a minimum is reached for a zenith angle of about 80 (when the wavelengths are 3114 and 3324 A0). [1] This effect was first noticed by Götz in 1930. The Umkehr measurement is known as customarily N-value and is given by the logarithm base 10 of the ratio of cloudless zenith sky intensities at two different wavelengths scaled by a multiplicative factor 100 plus a constant which depends on instruments and extraterrestrial radiation. Methods for deriving vertical distribution from the umkehr measurements were developed by Götz, Dobson and Meetham in 1934, [2] using the Dobson ozone spectrophotometer developed by Gordon Dobson. In 1964 Carlton Mateer provided analysis on information content in umkehr measurements.

Ultraviolet (UV) designates a band of the electromagnetic spectrum with wavelength from 10 nm to 400 nm, shorter than that of visible light but longer than X-rays. UV radiation is present in sunlight, and contributes about 10% of the total electromagnetic radiation output from the Sun. It is also produced by electric arcs and specialized lights, such as mercury-vapor lamps, tanning lamps, and black lights. Although long-wavelength ultraviolet is not considered an ionizing radiation because its photons lack the energy to ionize atoms, it can cause chemical reactions and causes many substances to glow or fluoresce. Consequently, the chemical and biological effects of UV are greater than simple heating effects, and many practical applications of UV radiation derive from its interactions with organic molecules.

The zenith is an imaginary point directly "above" a particular location, on the imaginary celestial sphere. "Above" means in the vertical direction opposite to the apparent gravitational force at that location. The opposite direction, i.e. the direction in which gravity pulls, is toward the nadir. The zenith is the "highest" point on the celestial sphere.

The Dobson spectrophotometer, also known as Dobsonmeter, Dobson spectrometer, or just Dobson is one of the earliest instruments used to measure atmospheric ozone.

${\displaystyle N(\theta )=100\log _{10}{\frac {I(\lambda ',\theta )}{I(\lambda ,\theta )}}+K}$

Considering light which is scattered only once in the atmosphere, the light received by the instrument at surface is contributed by light scattered downward from all the levels in the atmosphere. The amount of light contributed by scattering at any particular level depends on (a) the number of air molecules at that level and (b) the absorption by ozone and scattering by air molecules both before and after scattering. As the height increases contribution of effect (a) decreases and contribution of effect (b) increases. For a given zenith angle, the scattered light contribution comes from well defined layer of atmosphere, which can be termed as an effective scattering height. The effective scattering height depends on the ozone absorption coefficient and on the solar zenith angle, increasing as with each of these. The effective scattering height will always be higher for shorter wavelength which is more strongly absorbed. As the sun approaches the horizon, the two intensities decreases, but intensity I decreasing more rapidly than I' . However, when the effective scattering height for the short wavelength is above the ozone maximum, I decreases more slowly than I' , because the ozone absorption occurs mostly in the shorter vertical path after the scattering event, and the ratio I/I' increases until the effective scattering height for I' is also above the ozone maximum. This reversal (Umkehr) or inversion implies the existence of maximum of ozone concentration at some level in the atmosphere. [1]

The resulting ozone profile derived from reduction of these measurements is quite dependent on the algorithm used. The most current algorithm is I. Petropavlovskikh and P.K. Bhartia (2004). [3] Current description can be found here: http://www.esrl.noaa.gov/gmd/grad/research/umkehr/

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In optics, Lambert's cosine law says that the radiant intensity or luminous intensity observed from an ideal diffusely reflecting surface or ideal diffuse radiator is directly proportional to the cosine of the angle θ between the direction of the incident light and the surface normal. The law is also known as the cosine emission law or Lambert's emission law. It is named after Johann Heinrich Lambert, from his Photometria, published in 1760.

Compton scattering, discovered by Arthur Holly Compton, is the scattering of a photon by a charged particle, usually an electron. It results in a decrease in energy of the photon, called the Compton effect. Part of the energy of the photon is transferred to the recoiling electron. Inverse Compton scattering occurs when a charged particle transfers part of its energy to a photon.

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Static light scattering is a technique in physical chemistry that measures the intensity of the scattered light to obtain the average molecular weight Mw of a macromolecule like a polymer or a protein in solution. Measurement of the scattering intensity at many angles allows calculation of the root mean square radius, also called the radius of gyration Rg. By measuring the scattering intensity for many samples of various concentrations, the second virial coefficient A2, can be calculated.

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The Rayleigh sky model describes the observed polarization pattern of the daytime sky. Within the atmosphere Rayleigh scattering of light from air molecules, water, dust, and aerosols causes the sky's light to have a defined polarization pattern. The same elastic scattering processes cause the sky to be blue. The polarization is characterized at each wavelength by its degree of polarization, and orientation.

In atmospheric chemistry, differential optical absorption spectroscopy (DOAS) is used to measure concentrations of trace gases. When combined with basic optical spectrometers such as prisms or diffraction gratings and automated, ground-based observation platforms, what we have is a cheap and powerful means for the measurement of such trace gas species as ozone and nitrogen dioxide. Typical setups allow for detection limits corresponding to optical depths of 0.0001 along lightpaths of up to typically 15 km and thus allow for the detection also of weak absorbers, such as water vapour, Nitrous acid, Formaldehyde, Tetraoxygen, Iodine oxide, Bromine oxide and Chlorine oxide.

Polymerscattering experiments are one of the main scientific methods used in chemistry, physics and other sciences to study the characteristics of polymeric systems: solutions, gels, compounds and more. As in most scattering experiments, it involves subjecting a polymeric sample to incident particles, and studying the characteristics of the scattered particles: angular distribution, intensity polarization and so on. This method is quite simple and straightforward, and does not require special manipulations of the samples which may alter their properties, and hence compromise exact results.

Chappuis absorption refers to the absorption of electromagnetic radiation by ozone, which is especially noticeable in the ozone layer, which absorbs a small part of sunlight in the visible part of the electromagnetic spectrum. The Chappuis absorption bands occur at wavelengths between 400 and 650 nm. Within this range are two absorption maxima of similar height at 575 and 603 nm wavelengths. Compared to the absorption of ultraviolet light by the ozone layer, known as the Hartley and Huggins absorptions, Chappuis absorption is distinctly weaker. Along with Rayleigh scattering, it contributes to the blue color of the sky, and is noticeable when the light has to travel a long path through the atmosphere. For this reason, Chappuis absorption only has a significant effect on the color of the sky at dusk, during the so-called blue hour. It is named after the French chemist James Chappuis (1854–1934), who discovered this effect.

## References

1. Mateer, C. L. (April 1964). A study of the information content of umkehr observations (PDF) (PhD). University of Michigan. pp. 4–6. Retrieved 28 October 2014.
2. Götz, F. W. P., A. R. Meetham, and G. M. B. Dobson, Proc. Roy. Soc. A 145, 416, 1934.
3. Petropavlovskikh, I., P. K. Bhartia, and J. DeLuisi (2005), New Umkehr ozone profile retrieval algorithm optimized for climatological studies, Geophys. Res. Lett., 32, L16808, doi:10.1029/2005GL023323.