rus
For tracing small space objects a correct estimation of solar radiation is necessary. For this purpose the photometric apparatus is subject to predetermined calibration. A improved sun photometers Langely calibration procedure is proposed.
Experts know well that the Sun photometers are the most universal instruments intended for the study of atmosphere. Sun photometers mounted at the Earth allow studying the composition of aerosols, gases with small concentrations, water vapors which are present in atmosphere. Sun photometers study the clouds, ionospheric radiations, aerosol trails occurring as a result of the sand storms, volcanic eruptions and similar objects. Sun photometers mounted on board can measure the direct and scattered radiation of the Sun. Sun photometers effectively function within the structure of different global and regional networks for the atmosphere study. Thus, for example, AERONET global network keeps more than 300 measuring stations allocated all over the world and constructed on the basis of Sun photometers of Cimel type.
Obviously, Sun photometers just as any measuring instrument must be carefully calibrated. According to the classic conception, Sun photometers must be calibrated in mountain-top geophysical laboratories where the atmosphere contains small amount of aerosol. For example, Sun photometers of AERONET global network are usually calibrated in NASA high-altitude calibration station located in Mauna Loa, Hawaiian Islands.
The main method used for the calibration of Sun photometers is Langely method. Algorithm of its procedures is briefly described below.
Bouguer-Beer law is considered; without due regard to the decay of the Sun beam intensity by distance it has the following form:
, (1)
where is the output signal of Sun photometer at the wavelength λ; m is the optical air mass; k is the calibration coefficient; τat is the optical atmosphere depth. Generally, optical atmosphere depth is determined by the sum
,
where τoz is the optical ozone depth; τR is the optical depth of Rayleigh scattering; τaer is the optical depth of atmospheric aerosol.
Taking the logarithm of the expression (1) results in the following form:
. (2)
Dependence (2) of the function lnI1(λ) of m is linear. The following procedure is used for its graphic representation (Fig. 1) which is called the Langely diagram. The intensity I1(λ) is measured with two values of the optical air masses m1 and m2. Then, the values of logarithms of both measurements and which correspond to the points A and B on two-dimensional surface are applied in the coordinate system lnI1(λ)–m. The straight line is drawn through the points A and B and extrapolated to the ordinate axis. It allows estimating the point С of intersection of AB line with ordinate axis. Using the ordinate of the point Y(C) and introducing the calibration coefficient
,
the photometer calibration is performed.
When there are no high-altitude conditions for the calibration of Sun photometers the method of Langely diagrams is usually used but due to the variability of atmospheric parameters it does not allow calibrating the device with the adequate accuracy [1]. And this is the essential fault of this method. For example, in eastern regions of China in the following provinces: Kyung Hee, Taihu and Shoxian during the Regional International Experiment for Study of Tropospheric Aerosol [2] in 2004 and 2008, the measurements which were carried out with the help of CIMEL Sun photometer showed that during the day the aerosol optical depth varies within the range . Such variability of aerosol did not make it possible to calibrate the Multi-Filter Shadow Radiometer of MFRSR type. In the paper [3] it is noted that the mistakes made during the calibration of Sun photometer cause the artificial day variations, which are symmetric relative to noon, concerning the values of aerosol optical depth and α – Angstrom index. Especially, it has impact upon the low values of aerosol optical depth. In order to calculate the calibration coefficient for the minimization of day variations of Angstrom indices and its curvature we used the Monte-Carlo method.
In order to increase the calibration accuracy when using the classic method of Langely diagrams, we suggest the new method. It is based on two well-known characteristics of aerosol physics and atmospheric optics.
The first characteristic: the results of many experimental tests show the negative correlation between Angstrom index and aerosol optical depth [4–6].
As it is reported in the paper [4], the measurements of Angstrom index and aerosol optical depth were carried out in 2004–2008 in north-west region of China in Taklimakan Desert. It was detected that maximum AOD (aerosol optical depth) occurs in April with the value of whereas the minimum Angstrom index occurs in May. Herewith, the minimum value of AOD occurs in November and the minimum value of Angstrom index occurs in May . Mutual-inverse character of the variation of Angstrom index and aerosol optical depth values during the day is shown in Fig. 2.
Mutual-inverse character of the variation of aerosol optical depth and Angstrom index is also noted in the paper [5]. In Fig. 3 the average results of AOD measurements at 57 stations of AERONET network are given, and in Fig. 4 the average results at 47 stations are given. Mutual-inverse character of the dependence of AOD and Angstrom index can be deemed the common pattern and we can cite many papers where this pattern is confirmed.
The second regularity of atmospheric physics (optics) used in the suggested modernization of the method of Langely diagrams is the mutual-inverse character or negative correlation between the visibility index and aerosol optical depth. Analysis carried out in the paper [6] showed that there is considerable negative correlation between visibility and aerosol optical depth . Table [6] gives the estimated values of some sensitivity indices at the Earth surface and aerosol optical depth.
Mutual-inverse character of the variation of visibility and aerosol optical depth is also outlined in the paper [7]. In Fig. 5 the curves of the variations of aerosol optical depth and visibility are shown for the period of 15 months obtained as a result of the measurements which were carried out in NASA Goddard Institute for Space Studies. As is seen from the graphs given in Fig. 5, the mutual-inverse character of visibility and aerosol optical depth does not give rise to doubts.
Both considered provisions of the atmospheric optics are taken as the basis of the suggested modernized method of Langely diagrams. It is about the following. Let us write the condition for the stability of aerosol optical depth using the known Angstrom formula:
, (3)
where is the aerosol optical depth; is the aerosol atmospheric turbidity; is the Angstrom index.
We receive the following from the expression (3):
. (4)
The suggested method of the stabilization of Langely diagrams is about the variation of wavelength in accordance with the expression (4).
Pursuant to the first above mentioned provision of atmospheric optics the interrelation between and has the mutual-inverse character. Therefore, the following equation can be written in the first approximation:
. (5)
Taking into account the expression (5) we obtain:
. (6)
Obviously, in the expression (6) is the growing function of .
The control of must be performed for the practical implementation of the suggested method of variation according to the expression (6); for this reason the second above-stated provision of atmospheric optics is used, in other words the value of is controlled by the ground measurement of visibility at the Earth surface.
Therefore, if we admit the mutual-inverse dependence
, (7)
where is the visibility function and , from the expressions (6) and (7) we will receive
. (8)
Thus, the obtained expression (8) allows finding the conditions for the stabilization of Langely diagram in case of the variation of aerosol atmospheric turbidity by the relevant variation of wavelength of carried out measurements.
It should be noted that Langely diagrams are usually plotted at such wavelengths where, first of all, Rayleigh scattering is negligibly small in comparison with aerosol optical depth and, secondly, the absorption lines of idles and water vapors are absent. For this reason, the suggested stabilization of Langely diagrams by the variation of wavelengths of carried out measurements does not result in additional errors. The suggested method of Langely diagrams plotting can be practically implemented on the basis of the scheme shown in Fig. 6. Operation principle of such device corresponds completely to the above described method of the stabilization of Langely diagrams and does not require the additional explanation.
Summarizing, we can formulate the following main conclusions and provisions of the carried out analysis.
1. The modernization of the Langley method designated for calibration of Sun photometers is suggested. This modernization provides for stabilization of Langley diagrams by way of variation of measurement wavelength in line with variation of visibility at the Earth surface during carrying out of calibration procedure.
2. The theoretical, physical and mathematical basics of the suggested method are outlined.
3. The functional scheme of installation for realization of the suggested method is developed.
Obviously, Sun photometers just as any measuring instrument must be carefully calibrated. According to the classic conception, Sun photometers must be calibrated in mountain-top geophysical laboratories where the atmosphere contains small amount of aerosol. For example, Sun photometers of AERONET global network are usually calibrated in NASA high-altitude calibration station located in Mauna Loa, Hawaiian Islands.
The main method used for the calibration of Sun photometers is Langely method. Algorithm of its procedures is briefly described below.
Bouguer-Beer law is considered; without due regard to the decay of the Sun beam intensity by distance it has the following form:
, (1)
where is the output signal of Sun photometer at the wavelength λ; m is the optical air mass; k is the calibration coefficient; τat is the optical atmosphere depth. Generally, optical atmosphere depth is determined by the sum
,
where τoz is the optical ozone depth; τR is the optical depth of Rayleigh scattering; τaer is the optical depth of atmospheric aerosol.
Taking the logarithm of the expression (1) results in the following form:
. (2)
Dependence (2) of the function lnI1(λ) of m is linear. The following procedure is used for its graphic representation (Fig. 1) which is called the Langely diagram. The intensity I1(λ) is measured with two values of the optical air masses m1 and m2. Then, the values of logarithms of both measurements and which correspond to the points A and B on two-dimensional surface are applied in the coordinate system lnI1(λ)–m. The straight line is drawn through the points A and B and extrapolated to the ordinate axis. It allows estimating the point С of intersection of AB line with ordinate axis. Using the ordinate of the point Y(C) and introducing the calibration coefficient
,
the photometer calibration is performed.
When there are no high-altitude conditions for the calibration of Sun photometers the method of Langely diagrams is usually used but due to the variability of atmospheric parameters it does not allow calibrating the device with the adequate accuracy [1]. And this is the essential fault of this method. For example, in eastern regions of China in the following provinces: Kyung Hee, Taihu and Shoxian during the Regional International Experiment for Study of Tropospheric Aerosol [2] in 2004 and 2008, the measurements which were carried out with the help of CIMEL Sun photometer showed that during the day the aerosol optical depth varies within the range . Such variability of aerosol did not make it possible to calibrate the Multi-Filter Shadow Radiometer of MFRSR type. In the paper [3] it is noted that the mistakes made during the calibration of Sun photometer cause the artificial day variations, which are symmetric relative to noon, concerning the values of aerosol optical depth and α – Angstrom index. Especially, it has impact upon the low values of aerosol optical depth. In order to calculate the calibration coefficient for the minimization of day variations of Angstrom indices and its curvature we used the Monte-Carlo method.
In order to increase the calibration accuracy when using the classic method of Langely diagrams, we suggest the new method. It is based on two well-known characteristics of aerosol physics and atmospheric optics.
The first characteristic: the results of many experimental tests show the negative correlation between Angstrom index and aerosol optical depth [4–6].
As it is reported in the paper [4], the measurements of Angstrom index and aerosol optical depth were carried out in 2004–2008 in north-west region of China in Taklimakan Desert. It was detected that maximum AOD (aerosol optical depth) occurs in April with the value of whereas the minimum Angstrom index occurs in May. Herewith, the minimum value of AOD occurs in November and the minimum value of Angstrom index occurs in May . Mutual-inverse character of the variation of Angstrom index and aerosol optical depth values during the day is shown in Fig. 2.
Mutual-inverse character of the variation of aerosol optical depth and Angstrom index is also noted in the paper [5]. In Fig. 3 the average results of AOD measurements at 57 stations of AERONET network are given, and in Fig. 4 the average results at 47 stations are given. Mutual-inverse character of the dependence of AOD and Angstrom index can be deemed the common pattern and we can cite many papers where this pattern is confirmed.
The second regularity of atmospheric physics (optics) used in the suggested modernization of the method of Langely diagrams is the mutual-inverse character or negative correlation between the visibility index and aerosol optical depth. Analysis carried out in the paper [6] showed that there is considerable negative correlation between visibility and aerosol optical depth . Table [6] gives the estimated values of some sensitivity indices at the Earth surface and aerosol optical depth.
Mutual-inverse character of the variation of visibility and aerosol optical depth is also outlined in the paper [7]. In Fig. 5 the curves of the variations of aerosol optical depth and visibility are shown for the period of 15 months obtained as a result of the measurements which were carried out in NASA Goddard Institute for Space Studies. As is seen from the graphs given in Fig. 5, the mutual-inverse character of visibility and aerosol optical depth does not give rise to doubts.
Both considered provisions of the atmospheric optics are taken as the basis of the suggested modernized method of Langely diagrams. It is about the following. Let us write the condition for the stability of aerosol optical depth using the known Angstrom formula:
, (3)
where is the aerosol optical depth; is the aerosol atmospheric turbidity; is the Angstrom index.
We receive the following from the expression (3):
. (4)
The suggested method of the stabilization of Langely diagrams is about the variation of wavelength in accordance with the expression (4).
Pursuant to the first above mentioned provision of atmospheric optics the interrelation between and has the mutual-inverse character. Therefore, the following equation can be written in the first approximation:
. (5)
Taking into account the expression (5) we obtain:
. (6)
Obviously, in the expression (6) is the growing function of .
The control of must be performed for the practical implementation of the suggested method of variation according to the expression (6); for this reason the second above-stated provision of atmospheric optics is used, in other words the value of is controlled by the ground measurement of visibility at the Earth surface.
Therefore, if we admit the mutual-inverse dependence
, (7)
where is the visibility function and , from the expressions (6) and (7) we will receive
. (8)
Thus, the obtained expression (8) allows finding the conditions for the stabilization of Langely diagram in case of the variation of aerosol atmospheric turbidity by the relevant variation of wavelength of carried out measurements.
It should be noted that Langely diagrams are usually plotted at such wavelengths where, first of all, Rayleigh scattering is negligibly small in comparison with aerosol optical depth and, secondly, the absorption lines of idles and water vapors are absent. For this reason, the suggested stabilization of Langely diagrams by the variation of wavelengths of carried out measurements does not result in additional errors. The suggested method of Langely diagrams plotting can be practically implemented on the basis of the scheme shown in Fig. 6. Operation principle of such device corresponds completely to the above described method of the stabilization of Langely diagrams and does not require the additional explanation.
Summarizing, we can formulate the following main conclusions and provisions of the carried out analysis.
1. The modernization of the Langley method designated for calibration of Sun photometers is suggested. This modernization provides for stabilization of Langley diagrams by way of variation of measurement wavelength in line with variation of visibility at the Earth surface during carrying out of calibration procedure.
2. The theoretical, physical and mathematical basics of the suggested method are outlined.
3. The functional scheme of installation for realization of the suggested method is developed.
Readers feedback
