On-site ‘Langley’ Style Procedures

The m easurem ent of atm ospheric transm ission is a relative m easure, so the absolute top-of-the-atm osphere spectral flux need not be known. The m ethod of Langley calibrations is based on the Bouguer-Lam bert-Beer law, which describes the reduction of m onochrom atic radiation through a m edium as a function of the extinction in the m edium and the source intensity. For ideal atm ospheric conditions this can be expressed as:

where = spectral intensity at the surface

= spectral intensity at the top of the atm osphere

= optical depth

= the optical airm ass

Assum ing the passband that represents a wavelength is relatively sm all so that the assum ption of m onochrom atic radiation is valid, the radiom eter output signal (V) can be substituted for the intensity, and a radiom eter output for the top-of-the-atm osphere (V ) can be determ ined by extrapolating a series0

of observations at different airm ass values during conditions where the atm ospheric turbidity rem ains constant. Mathem atically, this can be easily accom plished through m aking the equation linear by taking the logarithm of both sides:

Observations obtained during stable conditions can be analysed using a least-squares regression between airm ass and the logarithm of the radiom eter output signal. The zero-intercept is the logarithm of the signal that would be observed at the top-of-the-atm osphere.

Although easy to com pute, the actual evaluation of V is difficult because the atm osphere is seldom0

stable over the airm ass range needed to obtain the num ber of observations required to calculate the intercept value. The task becom es m ore difficult when a large num ber of V values m ust be obtained0

over a short tim e period.

To overcom e this problem , a variety of techniques have been developed, two of which are described following Section 7.4.2.1.

Forgan, B.W ., 1986: D eterm ination of aerosol optical depth at a sea level station - inves tigations at G ape

16

G rim m B A P S. C G BAP S T echnical R eport 5. G ape G rimm BAPS , G ape G rimm , Australia. 55 pages + figures.

H arrison, L, and J. M ichalsky, 1994: O bjective algorithms for the retrieval of optical depths from

ground-17

based m easurem ents. Appl. O ptics, 33(22), 5126 - 5132.

7.4.2.1 Quality Assurance Procedures for Langley Calibration

The acceptance of high values of the coefficient of determ ination (r ) obtained from a regression analysis² has been shown to lead to erroneous values of V . Therefore, several quality assurance procedures0

can be used to better determ ine the quality of the intercept.

Forgan , working in m id-latitude sea-level conditions, suggests the following five m ethods to help¹⁶ determ ine the quality of the intercept value:

(1) The sam pling period m ust be as short as possible but provide at least a 3-airm ass range between 2 < m < 6.5. Data around solar noon should be avoided.

(2) If a plot of the residuals of the regression shows a trend in the deviations or any of the residuals are greater than ± 0.006, the calculated V is unacceptable.0

(3) If the pressure changes by m ore than 1 hPa during the period of observations, V for wavelengths0

less than 500 nm should be discarded, or the m olecular scattering norm alized to constant pressure using a m olecular extinction m odel.

(4) The intercept m ust be less than the intercept calculated for a pure m olecular scattering atm osphere.

(5) The unbiased estim ate of the standard deviation of the regression should be less than 0.003 The work of Harrison and Michalsky , besides presenting a m eans of determ ining the quality of the¹⁷ Langley regression (see 7.4.2.3), additionally note that:

(6) The m easurem ent interval should be either in the m orning or afternoon and that the data should not be com bined.

(7) Airm ass below 2 should not be used, even when available, because the rate of change of the atm osphere is sm all causing an increased probability of contam inating the data with changing atm ospheric conditions.

Finally:

(8) As the regression is between airm ass and signal, the data should be based on airm ass observations. Many observation program s are based on tim e and not airm ass. Observations that are equally spaced in tim e lead to an increased num ber of m easurem ents at sm aller airm ass, which in turn produce a bias in the intercept toward these values. This can be overcom e by taking m easurem ents at equal airm ass or weighting the data as a function of airm ass to offset the increase in the num ber of observations as airm ass decreases.

NOTE: The Langley calibration is based on the actual sun-earth distance at the tim e the calibration is obtained. The use of these calibrations m ust correct for the change in the sun-earth distance. Com m only, individual Langley calibrations are norm alized to the m ean sun-earth distance and then converted to the sun-earth distance of the observation as part of the data analyses procedure.

7.4.2.2 Ratio-Langley Technique

The Ratio-Langley technique was developed following the observation that the responsivities of a group of wavelengths obtained over a period of tim e were found to correlate with each other. This cross-correlation for wavelengths affected by m olecules, aerosols and to a lesser extent, ozone (unaffected by strong absorption bands) is expected because of the extinction functions of each of these com ponents.

The variation in the cross-correlation com es prim arily from the change of aerosol conditions over tim e,

Forgan, B.W ., 1988: Sun photom eter calibrations by the ratio-Langely m ethod. In Baselien Atm ospheric

18

Program (Australis) 1986, edited by B.W . Foragan and P.J. Fras er, pp 22 - 26, Bureau of M eteorology, M elbourne, Australia.

which dom inates the extinction. Forgan using this observation has developed the ratio-Langley technique¹⁸ to reduce the extrapolation error associated with norm al Langley calibrations.

2 1

For a wavelength pair 8 < 8 , where neither wavelength occurs in a region of strong absorption, and the signals can be given as:

and

where i represents the ith atm ospheric attenuator.

The ratio of the two wavelengths can be given as (dropping the wavelength for clarity):

The sum of the optical depth differences is m ade up of a term com bining the constant differences in attenuation due to m olecular scattering and gaseous absorption plus the difference due to aerosol attenuation. The latter term is a function of the aerosol optical properties, prim arily the size distribution.

Using an Ångström size distribution, it can be shown that the bias error in the ratio of the I 0pair caused by system atic trends in the AOD can be less than the sm allest bias for the individual I0. Therefore, the ratio can be used to obtain inform ation on the extraterrestrial constants of the wavelength pair even when the individual extraterrestrial constants are found unacceptable by the rem oval of atm ospheric effects. This can be accom plished in a m anner sim ilar to determ ining the individual extraterrestrial constants by regressing the ratio against airm ass.

The ratio results can be utilized successfully for a variety of purposes:

(1) If a single wavelength is well-calibrated, the ratio m ethod can be used to successfully transfer the calibration inform ation to other wavelengths on the sam e instrum ent.

(2) If well-known extraterrestrial constants are known for a pair of wavelengths, the ratio technique will provide a m eans of checking the stability of the filters. By com bining a variety of filter pairs, those filters with changing responsivity can be determ ined.

(3) The transfer of the calibration from one radiom eter to a second can be im proved through the use of the ratio-Langley technique. The transfer of the extraterrestrial constant from one instrum ent to another cannot be accom plished using sim ple procedures, except when the radiom eters have identical optics and the centre wavelengths and passbands are perfectly m atched. W hile m odern m anufacturing techniques used in the construction of com m ercially available instrum ents provide the precision necessary to reproduce the optical geom etry, the passband and wavelength sim ilarity of interference filters is unlikely. Rearranging the above equation and again rem oving 8 and now t for clarity, it can be seen that:

Only if the instrum ents are identical does the )J term reduce to zero, so that the calibration transfer is no longer airm ass dependent.

7.4.2.3 Objective Algorithm

The objective algorithm described by Harrison and Michalsky provides a m eans to rem ove observations⁵ that m ay contam inate the Langley calibration m ethod using a quantitative approach. The m ethodology is used on airm ass between 2 and 6 where airm ass changes are rapid, but the problem of atm ospheric refraction increasing the uncertainty of the analyses is avoided.

The m ethod for direct pointing instrum ents consists of four steps to rem ove observations that have been contam inated:

(1) A forward finite-difference derivative filter is used to rem ove regions where the slope of the dI/dm curve is positive indicating atm ospheric variability not consistent with uniform airm ass-turbidity processes such as cloud contam ination. By determ ining the m inim um value of the derivative, the process rem oves observations for a tim e period equal to the tim e between the positive derivative and the m inim um derivative on both sides of the m inim um .

(2) A second forward finite-difference derivative filter is then used to determ ine regions of strong second derivatives. In these regions, if the first derivative is negative and the value greater than twice the m ean value of the first derivative for the observations, the regions are elim inated.

This m ethod elim inates observations that m ay have been contam inated by cloud, but m issed using Step 1 and those regions where the data has been truncated.

(3) Perform a least-squares fit to the rem aining data. The standard deviation of the residuals about the fit is calculated and all points that have a residual greater than 1.5 tim es the standard deviation are elim inated. A second least-squares fit is computed on the rem aining observations.

(4) More than a of the original observations m ust be found valid in this m anner and the standard deviation of the residuals about the regression line m ust be less than 0.006 before the Langley calibration is accepted.

The m ethods described in Sections 7.4.2.2 and 7.4.2.3 can be com bined.