A method to determine atmospheric optical depth using observations of direct solar radiation

Abstract

[1] The proposed method of atmospheric total optical depth (TOD) determination is based on the assumption that TOD is an arbitrary smooth function of time. Any small section of this function can be approximated by a linear relationship. A redundant system of Bouguer equations corresponding to n solar observations (where n > 3) can be written for each linear section. This procedure is successively applied to each section of the TOD curve and yields (N À n + 1) systems of Bouguer equations, where N is the total number of solar observations during a day. Solving these systems of Bouguer equations gives an extraatmospheric value of the solar flux and TOD curve parameters. The accuracy of the method depends on the accuracy of TOD curve approximation, i.e., on the character of TOD variation with time and a total number of observations during a day. The new method (named approximation by linear sections (APLS)) has been used for TOD investigations in the Crimea (a peninsula in Ukraine) since 1996. In comparison with the classical Bouguer-Langley method the new method allows us to achieve higher accuracy, when the conditions of astroclimate at the observational site are not very good and especially when the observations are carried out for a half day, i.e., only before noon or after.

Comment on “On Langley plots in the presence of a systematic diurnal aerosol cycle centered at noon: A comment on recently proposed methodologies” by F. Marenco

“…The readers must bear in mind that the requirement for the application of the Langley method is that the total optical depth remains constant, or at least with only slight random fluctuations around a mean value during the measurements interval, usually morning or afternoon. Langley calibration problems under varying AOD conditions have been widely discussed for many years by different authors, who developed variants of the Langley method ( Shaw [1983], Forgan [1994], and Terez and Terez [2003], to cite some authors; for more details, see the extensive review given by Cachorro et al [2008]).…”

An “in situ” calibration correction procedure (KCICLO) based on AOD diurnal cycle: Application to AERONET–El Arenosillo (Spain) AOD data series

“…[28] It is concluded that the observed AOD diurnal cycle is fictitious and associated with an incorrect calibration constant. We further assert that it is not always an atmospheric effect, as discussed in several papers [Shaw, 1976[Shaw, , 1983Terez and Terez, 2003;Marenco, 2007]. Moreover, we take advantage of this diurnal cycle behavior and its dependence on the air mass to propose an improved ''in situ'' correction-calibration procedure called KCICLO method.…”

“…The KCICLO method is more intuitive than the CLM (or its variants) method, because it uses AOD values instead of some other “uncalibrated” quantity (counts, voltage, etc.). It allows a better control over the variation of the slope of the regression than in the CLM, as argued by Terez and Terez [2003, p. 4704], who state with respect to the AOD diurnal cycle: “regression lines remain straight during monotonic (linear) variation of the atmospheric transmission but their slopes give different and fictitious values of AOD, not affecting this to the error of the slopes respect to random AOD variations.”…”

On Langley plots in the presence of a systematic diurnal aerosol cycle centered at noon: A comment on recently proposed methodologies

“…This means that if an experimentalist wishes to calibrate a Sun photometer or a Brewer spectroradiometer at sea level and does not have an independent knowledge of the optical depth cycle for his observational site, he must use more elaborate techniques than Langley extrapolation to deal with atmospheric variations. These techniques can be based, for instance, on circumsolar radiance measurements, such as proposed by Tanaka et al [1986] and Nieke et al [1999], or on the approximation by linear sections introduced by Terez and Terez [2003]. The methodology introduced with the latter paper is an algorithm based on the hypothesis that optical depth is a smooth function of time, releasing the constant atmosphere assumption of the Langley method; and it yields a solution for the extraterrestrial constant I 0 which is free of the type of systematic errors that has been discussed in this paper.…”

“…In the latter case, nonlinear Langley plots would be found for the morning (afternoon), while only afternoons (mornings), which would present a monotonic optical depth behavior, can have a chance to pass linearity criteria and be considered for Langley extrapolation; they would however yield an altered extraterrestrial constant I 0 ′ as their result. Other intermediate cases can occur with an optical depth extreme at local noon but different slopes for the morning and afternoon, as shown by Terez and Terez [2003, Figure 1]; in that case, again, averaging the morning and afternoon results does not solve the problem.…”