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Overview Algorithm Data Access

The forward model (physical interpretation of the measurement; measurement dependency on the true atmospheric state)

Also see: APARC Report: Umkehr Ozone

The Dobson Umkehr method uses zenith sky measurements taken at twelve nominal solar zenith angles (60,65,70,74,77,80,83,85,86.5). Each measurement is representative of the difference of the ratio of transmitted zenith sky radiances to the extra-terrestrial radiances at the ‘C’ pair of wavelengths located in the ultraviolet (311.5nm and 332.4 nm). This ratio is called the “N” value of the Dobson instrument and is defined as:
Umkehr N formula Where: I0 and I’0 are the extraterrestrial solar radiance at the ‘short’ (311.5 nm) and the ‘long’(332.4 nm) wavelengths *(note that the slits of the Dobson reject all light except for a bandpass centered at these wavelengths).

I and I’ are the transmitted solar radiance at the surface.

(adapted from the WMO GAW Operations Handbook - Ozone Observations with a Dobson Spectrophotometer (GAW report No. 183)).

As solar light passes through the Earth’s atmosphere, some light is scattered by molecular and aerosol scattering, some is absorbed, most is transmitted to the surface. In the vicinity of the ‘C’ pair of wavelengths, the primary absorber is ozone. However, ozone absorption is quite variable and absorption by ozone is much stronger at the short wavelength than at the long wavelength. Therefore at sunrise and sunset, when the sunlight path length changes rapidly, the ratio of scattering to absorption is also changing rapidly. The information content of the amount of scattering vs absorption depends on the amount of ozone in the path. For each solar zenith angle, the contribution of scattered light is a function of absorption and height above ground. From this an effective scattering height can be calculated. Since ozone absorption is stronger at the short wavelength, its effective scattering height will be higher than with the long wavelength. There comes a point (around a solar zenith angle of 86.5), the effective scattering height of the shorter wavelength will pass above the maximum in the ozone layer. Log (I/I’) will reverse sign and the N values will begin to increase (decrease) for the measurements taken during sunset (sunrise). If you plot the N values during a single measurement set (during sunrise or sunset), you will see a curve like what is shown in Figure 1. This curve is called the “Umkehr” N-value curve as “Umkehr” is German for “reversal.”

Trends of Umkehr ozone profile sites
Figure1: Climatological N value curve for Boulder (40N) for April 8th and a total column ozone value of 329 DU. Plotted with the WinDobson software.

The Inverse Model (Retrieval of vertical profile from measurements)


The current retrieval algorithm (called UMK04) is published in the following paper:

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.

The UMK04 retrieval algorithm extends the optimal estimation technique for ground-based retrievals from Rodgers 2000.

Rodgers, C. D. (2000). Inverse methods for atmospheric sounding: theory and practice (Vol. 2). World scientific.

First guess / a priori

The retrieval algorithm is optimized for long-term trend analysis by 1) fixing the first guess (a priori) profile across time using an ozone climatology in five degree latitude bands. This is so long-term changes are not c. The climatology was derived by NASA/Goddard (private communication with G. Labow). The a priori file can be downloaded here:

Readme file     First Guess (version 11b)

Corrections for multiple scattering and refraction

Next, since the assumption of single scattering is made in the forward model, a correction factor is applied to the measured N-values for multiple scattering. Corrections for atmospheric refraction were calculated using TOMRAD radiative-transfer code (based on Dave-Mateer code) and using U.S. standard atmosphere temperature profile.

tabulated multiple-scattering correction for N-values

tabulated refraction correction for N-values

tabulated multiple-scattering correction for Jacobian

The columns are data at 12 SZAs: from 60 to 90 SZA These are for the ‘C’ pair only. A and D wavelength pairs can be made available upon request.

Ozone Absorption and Rayleigh Scattering Coefficients

Ozone absorption is calculated from Bass and Paur 1980 ozone cross-sections over the Dobson slit functions. We use standard ozone profiles, representative of typical ozone distribution at low, middle, and high latitudes (the same as in SBUV V8 algorithm). The files below are the temperature dependent ozone abortion coefficients.

Short wavelength: coef_dobacdl.txt
Long Wavelength: coef_dobacdh.txt

How to read the files above:

There are 3 blocks in high and low wavelengths data (3x161 and 3x61 respectively). The line format is as following: wavelength *10 (nm), quadrature weights (from 0 to 1) , Extra-Terrestrial solar flux (W/m2/sec), α0,α1,α2,Rayleigh extinction coefficient,

de-polarization coefficient

where ozone absorption coefficient = α0+a1(Temp) + α2(Temp)2

Inverse procedure

The N-values, having been corrected for multiple scattering and refraction, are normalized to the lowest measured solar zenith angle (either 60,65, or 70). The integrated retrieved profile is constrained to be close to the observed total column ozone (nearest observed measurement). The a priori profile is multiplied terms that include information on the difference between the a priori and the retrieved profile, the difference between the measured and calculated measurements, the error covariance matrix for the measurements, and the a priori error covariance matrix. This new retrieved profile is substituted for the a priori in the step above and the process is iterated again. This iterative process continues until:

  1. A maximum of five iterations is reached.
  2. The profile converges on a solution, which is defined as the difference between retrieved profiles between iterations is less than 0.04 in all layers, the root mean squared error of the changes is less than 0.01.
Quality Assurance

The datasets archived above are fully quality assured. The QC process is performed at NOAA-GML for the five NOAA-GML Dobson stations in Boulder, CO. Profiles are flagged and removed from the long-term operational record using the following criteria:

  1. There are more than five or more iterations in the inversion procedure
  2. Measurements were not taken or were invalid for at least one of these solar zenith angles: 60,65,70
  3. Less than 9 of the 12 nominal solar zenith angles were observed and valid.
  4. The residual between the integrated retrieved profile and the observed total column ozone is more than 1.0 DU
  5. The shape of the retrieved profile is significantly different than expected.
  6. It was determined that there was significant interference present during the measurement (clouds or aerosols making the scattering assumptions invalid; absorption by large amounts of SO2 present).
  7. Known instrumental or human error.
Final product:

Here is an example of a profile from April 9th, 2025 at Boulder, CO:
Climatological N curve
Figure 2: The solid black line is the climatological N-value curve, the black line with the red dots are the measured N values. The red line with red dots is the difference between the two. Green dots indicate clouds.
retrieved ozone profile
Figure 3: Retrieved ozone profile from the above measurements using the UMK04 algorithm. The red line is the retrieved profile. The shaded gray area is climatology. Green is the difference between the two.

History and References:

  • The method of Umkehr data analysis was originally developed by Götz, Meetham and Dobson (1934).

  • Götz, F. P., Meetham, A. R., & Dobson, G. M. B. (1934). The vertical distribution of ozone in the atmosphere. Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character, 145(855), 416-446.

  • As radiative transfer work was advanced and computing power increased, the retrievals were updated with the following major work:

  • Ramanathan, K. R., and J. V. Dave. "The calculation of the vertical distribution of ozone by the Gotz Umkehr Effect (Method b)." Ann. Int. Geophys. Year, V (1957): 23-45.
  • Walton, G. F. (1957). The Calculation of the Vertical Distribution of Ozone by the Götz Umkehr Effect (method A). Ann. IGY, 5(1), 9.
  • Dütsch, H. U. (1959). Vertical ozone distribution from Umkehr observations. Archiv für Meteorologie, Geophysik und Bioklimatologie, Serie A, 11, 240-251.
  • Mateer, C. L. (1965). On the information content of Umkehr observations. Journal of Atmospheric Sciences, 22(4), 370-381.
  • DeLuisi, J. J. (1979). Umkehr vertical ozone profile errors caused by the presence of stratospheric aerosols. Journal of Geophysical Research: Oceans, 84(C4), 1766-1770.
  • DeLuisi, J. J. (1979). Shortened version of the Umkehr method for observing the vertical distribution of ozone. Applied Optics, 18(18), 3190-3197.
  • Dütsch, H. U., & Staehelin, J. (1992). Results of the new and old Umkehr algorithm compared with ozone soundings. Journal of atmospheric and terrestrial physics, 54(5), 557-569.
  • Petropavlovskikh, I., Bhartia, P. K., & DeLuisi, J. (2005). New Umkehr ozone profile retrieval algorithm optimized for climatological studies. Geophysical Research Letters, 32(16).
  • Maillard, E., Schill, H., Stübi, R., & Ruffieux, D. (2008). Re-evaluation of Arosa Umkehr serie: ozone profile measurements from 1931 up to now. In Quadrennial Ozone Symposium, Tromsø, Norway, June 29th-July 5th (Vol. 505).
  • Miyagawa, K., T. Sasaki, H. Nakane, I. Petropavlovskikh, and R. D. Evans (2009), Reevaluation of long-term Umkehr data and ozone profiles at Japanese stations, J. Geophys. Res., 114, D07108, doi:10.1029/2008JD010658.
  • Petropavlovskikh, I., Evans, R., McConville, G., Miyagawa, K., & Oltmans, S. (2009). Effect of the out-of-band stray light on the retrieval of the Umkehr Dobson ozone profiles. International Journal of Remote Sensing, 30(24), 6461-6482.
  • Petropavlovskikh, I., Evans, R., McConville, G., Miyagawa, K., & Oltmans, S. (2009). Effect of the out-of-band stray light on the retrieval of the Umkehr Dobson ozone profiles. International Journal of Remote Sensing, 30(24), 6461-6482.
  • Stone, K., Tully, M. B., Rhodes, S. K., and Schofield, R.: A new Dobson Umkehr ozone profile retrieval method optimising information content and resolution, Atmos. Meas. Tech., 8, 1043–1053, https://doi.org/10.5194/amt-8-1043-2015, 2015.
  • Petropavlovskikh, I., Miyagawa, K., McClure-Beegle, A., Johnson, B., Wild, J., Strahan, S., ... & Godin-Beekmann, S. (2022). Optimized Umkehr profile algorithm for ozone trend analyses. Atmospheric Measurement Techniques, 15(6), 1849-1870.

  • The bolded papers are the papers that outline the current algorithm in use to produce the records archived here.