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Issue #6/2020
U. F. Mammadova
Issues of Measuring the Moisture Content in the Surface Atmosphere Layer Using an External Emitter and a Photometer with LED Emitters in The Photodetector Mode
Issues of Measuring the Moisture Content in the Surface Atmosphere Layer Using an External Emitter and a Photometer with LED Emitters in The Photodetector Mode
DOI: 10.22184/1993-7296.FRos.2020.14.6.550.558
The problem of measuring the moisture content in the surface layer of the atmosphere using an external emitter and an LED photometer is defined and solved. It is noted that the absence in many zones of the planet of automated stations for measuring the moisture content of air of the international network AERONET induces the need to develop and use simple sun photometers. The devices for measuring the moisture content in the surface layer of the atmosphere can be built on the basis of two LED light emitters operating in the mode of narrow-spectrum photodetectors. The problem of determining the optimal dependence of external thermal radiation on the wavelength at which the value of atmospheric transmission in the surface atmosphere reaches its maximum is defined and solved. An expression for determining the optimal temperature of the external radiator is obtained.
The problem of measuring the moisture content in the surface layer of the atmosphere using an external emitter and an LED photometer is defined and solved. It is noted that the absence in many zones of the planet of automated stations for measuring the moisture content of air of the international network AERONET induces the need to develop and use simple sun photometers. The devices for measuring the moisture content in the surface layer of the atmosphere can be built on the basis of two LED light emitters operating in the mode of narrow-spectrum photodetectors. The problem of determining the optimal dependence of external thermal radiation on the wavelength at which the value of atmospheric transmission in the surface atmosphere reaches its maximum is defined and solved. An expression for determining the optimal temperature of the external radiator is obtained.
Теги: moisture content optical transmission of the atmosphere optimization precipitated water sun photometer влагосодержание оптимизация оптическое пропускание атмосферы осажденная вода солнечный фотометр
Issues of Measuring the Moisture Content in the Surface Atmosphere Layer Using an External Emitter and a Photometer with LED Emitters in The Photodetector Mode
U. F. Mammadova
Azerbaijan State University of Oil and Industry, Baku, Azerbaijan
The problem of measuring the moisture content in the surface layer of the atmosphere using an external emitter and an LED photometer is defined and solved. It is noted that the absence in many zones of the planet of automated stations for measuring the moisture content of air of the international network AERONET induces the need to develop and use simple sun photometers. The devices for measuring the moisture content in the surface layer of the atmosphere can be built on the basis of two LED light emitters operating in the mode of narrow-spectrum photodetectors. The problem of determining the optimal dependence of external thermal radiation on the wavelength at which the value of atmospheric transmission in the surface atmosphere reaches its maximum is defined and solved. An expression for determining the optimal temperature of the external radiator is obtained.
Keywords: sun photometer, optical transmission of the atmosphere, moisture content, precipitated water, optimization
Received on: 04.08.2020
Accepted on: 24.09.2020
Introduction
As noted in [1], modern means of remote sensing of the atmosphere make it possible to determine the height profile of humidity based on microwave and infrared measurements. Known such satellite-based means as IR sounding devices HIRS / 3, AMSU-A, AMSU-B and others operating in the ranges of tens and hundreds of GHz. For ground measurements, SHF radiometers operating at 22 GHz and 36 GHz are used. The measurement error of such devices is not less than 15–30%. The main disadvantage of these devices is the high error in determining the profile in the surface layer.
According to [2], information on the altitude distribution of humidity in the atmosphere is needed by both meteorologists and specialists in radio wave propagation, including specialists in GPS measurements. There are empirical formulas for determining the content of water vapor by height (Gann’s formula, Sürzig-Hrgian’s formula, etc. [2]). However, the calculation error using such formulas turns out to be no less than ±(5–10%).
The methods for measuring air humidity, implemented in modern measuring systems for observing atmospheric electricity using radiosondes are known to the experts [3]. At the same time, often in the primary readings of temperature and humidity, there are unreliable values, single emissions or abrupt measurements.
In this case, operational remote sensing makes it possible to analyze the primary data of the radiosonde and eliminate the influence of unreliable values on the overall result [4]. Such operational sensing can be carried out using SIMEL sun photometers used in the international aerosol measurement network AERONET. However, the number of automated stations of the AERONET network worldwide does not exceed 500, and in many areas the automated stations of this network have not yet been installed. Consequently, an urgent question arises about the need to create and use sun photometers that are simple in design and operate in an automatic mode. Sun LED photometers, specialized in measuring the moisture content of air, can be considered as such technical means. Further in this work, a brief overview of known studies on the development of sun LED photometers is given, a method is proposed for the use of these devices, and the problem of optimal measurements is formulated and solved.
Materials and method
The research [4] describes the design of a simple LED‑photometer used to measure the total columnar amount of water vapor in air. The device was used under the GLOBE program (Program for the global study of the distribution of water vapor on the planet) and worked in the near infrared range. A photodiode with a filter (940 nm) and LED (light-emitting diode 825 nm), operating in the photodetector mode, were used as photodetectors with a narrow band of measured optical radiation. The ratio of the output signals of these sensors allows the calculation of the total columnar amount of water vapor during the daytime.
The research [5] reports on the development of a similar device. This device uses two LED‑emitters operating in the photodetector mode at wavelengths of 815 and 940 nm, respectively. The signal spectrum of these light-sensitive elements is shown in Fig. 1.
For the technical implementation of the ground-level method for measuring the moisture content in the surface layer, we built a two-channel measuring device (the optical-electronic circuit of the measuring device is shown in Fig. 2).
The created device, operating at wavelengths λ1 = 940 nm and λ2 = 870 nm, was investigated experimentally. Fig. 3 shows the experimentally taken dependence , where V1 is the signal at the output of the channel with a wavelength of 940 nm; V2 is the signal at the channel output 870 nm.
To calculate the total amount of precipitated water vapor, we used expression (1) from [5], modifying it by multiplying it by the calibration factor.
, (1)
where m is the optical air mass; I940, I815 are the signals at the outputs of the photometer; k is the calibration factor.
The results of measurements by the Butler method [6] were used as a reference value for the total amount of precipitated water vapor. The measurements have shown that the value of the coefficient k can vary within the range of 1.03–1.08, which is partially explained by a significant methodological error of the Butler method itself.
As for the temperature stability of LED diodes operating in the photodetector mode, here one should distinguish between the amplitude stability of the photodetector signal and the color shift during emission. The studies carried out in [7] showed that the amplitude stability of the radiation intensity with a change in temperature within the range of 300–350 K does not exceed 5%, and the mixing of the peak wavelength is ≈2 nm. These results allow us to conclude that the temperature instability of LED diodes in the photodetector mode will not have such a noticeable effect on the total measurement error of the total amount of precipitated water vapor, which reaches 10–15%.
Apparently, the measurement of the total amount of deposited vapors throughout the entire thickness of the atmosphere can be carried out in the daytime using the optical radiation of the Sun. However, the task of studying the moisture saturation of the surface layer of the atmosphere often becomes a more urgent task. This is important for systems for forecasting thunderstorms and lightning, as well as for sanitary purposes. To solve this problem, a method of photometric measurement of a high-temperature radiator installed on a special high-rise object can be proposed. A high-rise building, a radio antenna or special meteorological masts can be used as such a high-rise object. The process scheme of such measurements is shown in Fig. 4.
Apparently, with such ground-altitude measurements carried out in the evening / night time, the optical air mass is determined as
(2)
or
. (3)
In this case, the value of PW can be determined by the expression (1) where m is calculated by the formulas (2) or (3). The reliability of the results of such measurements will depend on the transmission of the surface layer of the atmosphere. Therefore, it makes sense to investigate the conditions under which the transmission of the surface layer of the atmosphere would reach the maximum value.
OPTIMIZATION OF THE PROPOSED GROUND-ALTITUDE METHOD
According to the studies of the authors of [8], under conditions when optical radiation is essentially nonmonochromatic and the Beer–Lambert–Bouguer equation poorly describes the measurement modes with a sun photometer, the broadband electrical signal V at the photometer output can be defined as
,
where V0 is the signal value of the photometer located at the upper boundary of the surface layer; T1 is a broadband function.
According to [10], the function of broadband transmission for the surface layer of the atmosphere can be defined as
, (4)
where λ1, λ2 are the start and end points of the measured wavelength interval; Rλ is the normalized spectral response of the detector; F0λ are the solar radiation at the upper boundary of the surface layer; ma, mR, mg are optical air masses of aerosol, Rayleigh scattering and small gases; αa,λ, αR,λ, αg,λ are the optical thicknesses of aerosol, Rayleigh scattering, and small gases, respectively.
Optimization of the T1 indicator is carried out as follows.
The function of quadratic broadband transmission is introduced for consideration.
Furthermore, according to [9], the absorption spectrum of water vapor in the visible range and in the near-IR region has a continuous character with peaks at wavelengths of 590; 650; 690; 720; 760; 820; 940 nm. This is leads the circumstance of studying the extreme nature of the atmosphere transmission broadband in the corresponding spectral zone.
. (5)
The following condition is accepted
. (6)
It is assumed that
, (7)
. (8)
Taking into account conditions (6–8), the optimization problem for T1.кв by finding the optimal value of F0λ can be expressed as a problem of unconstrained variational optimization
, (9)
where γ is the Lagrange multiplier.
According to [11], the optimal function F0λ that leads T1.кв to an extreme value should satisfy the condition
. (10)
It is easy to obtain the following solution from (10):
. (11)
It is known that the optical thickness of an aerosol is determined by the Angstrem formula [12], i. e.
, (12)
where β is the aerosol turbidity of the atmosphere; χ is the Angstrom exponent.
Taking into account (11) and (12), we obtain
. (13)
Thus, in the optimal case, F0λ.opt should decrease with increasing λ. However, according to Planck’s law, in the range of 0.5–1.2 µm, depending on the temperature of the emitter, both an increase and a decrease in the intensity along the wavelength are possible.
According to Planck’s law, the optical radiation of an absolutely black body is defined as [13]
. (14)
By equating (13) to (14), we obtain
. (15)
From equality (15), we can calculate T, at which, for a given value of λ, the parameter T1.кв would reach its maximum value. In this case, the value of λ can be chosen as .
(16)
Thus, for given values λ, χ0, ma, β, χ, the optimal temperature of the emitter in the proposed ground-based altitude method can be calculated using formula (16).
Conclusion
Thus, the absence in many zones of the planet of automated stations for measuring the moisture content of air of the international network AERONET induces the need to develop and use simple sun photometers. The devices can be built based on two LED light emitters operating in the mode of narrow-spectrum photodetectors. Such LED‑photometers make it possible to measure the moisture content in the surface layer of the atmosphere in the evening and at night using a thermal emitter installed at a high-altitude object. An optimization problem has been defined and solved, which makes it possible to determine the optimal dependence of the initial optical radiation on the wavelength at which the atmospheric transmission in the near-ground atmosphere reaches its maximum. Comparison of the revealed optimal dependence with the analytical expression of Planck’s law made it possible to calculate the expression for determining the optimal temperature of the external radiator.
AUTHOR
Mammadova Ulker Fizuli gyzy, Postgraduate, Azerbaijan State University of Oil and Industry, Baku, Azerbaijan. Area of interest: sun photometer, optical transmission of the atmosphere.
U. F. Mammadova
Azerbaijan State University of Oil and Industry, Baku, Azerbaijan
The problem of measuring the moisture content in the surface layer of the atmosphere using an external emitter and an LED photometer is defined and solved. It is noted that the absence in many zones of the planet of automated stations for measuring the moisture content of air of the international network AERONET induces the need to develop and use simple sun photometers. The devices for measuring the moisture content in the surface layer of the atmosphere can be built on the basis of two LED light emitters operating in the mode of narrow-spectrum photodetectors. The problem of determining the optimal dependence of external thermal radiation on the wavelength at which the value of atmospheric transmission in the surface atmosphere reaches its maximum is defined and solved. An expression for determining the optimal temperature of the external radiator is obtained.
Keywords: sun photometer, optical transmission of the atmosphere, moisture content, precipitated water, optimization
Received on: 04.08.2020
Accepted on: 24.09.2020
Introduction
As noted in [1], modern means of remote sensing of the atmosphere make it possible to determine the height profile of humidity based on microwave and infrared measurements. Known such satellite-based means as IR sounding devices HIRS / 3, AMSU-A, AMSU-B and others operating in the ranges of tens and hundreds of GHz. For ground measurements, SHF radiometers operating at 22 GHz and 36 GHz are used. The measurement error of such devices is not less than 15–30%. The main disadvantage of these devices is the high error in determining the profile in the surface layer.
According to [2], information on the altitude distribution of humidity in the atmosphere is needed by both meteorologists and specialists in radio wave propagation, including specialists in GPS measurements. There are empirical formulas for determining the content of water vapor by height (Gann’s formula, Sürzig-Hrgian’s formula, etc. [2]). However, the calculation error using such formulas turns out to be no less than ±(5–10%).
The methods for measuring air humidity, implemented in modern measuring systems for observing atmospheric electricity using radiosondes are known to the experts [3]. At the same time, often in the primary readings of temperature and humidity, there are unreliable values, single emissions or abrupt measurements.
In this case, operational remote sensing makes it possible to analyze the primary data of the radiosonde and eliminate the influence of unreliable values on the overall result [4]. Such operational sensing can be carried out using SIMEL sun photometers used in the international aerosol measurement network AERONET. However, the number of automated stations of the AERONET network worldwide does not exceed 500, and in many areas the automated stations of this network have not yet been installed. Consequently, an urgent question arises about the need to create and use sun photometers that are simple in design and operate in an automatic mode. Sun LED photometers, specialized in measuring the moisture content of air, can be considered as such technical means. Further in this work, a brief overview of known studies on the development of sun LED photometers is given, a method is proposed for the use of these devices, and the problem of optimal measurements is formulated and solved.
Materials and method
The research [4] describes the design of a simple LED‑photometer used to measure the total columnar amount of water vapor in air. The device was used under the GLOBE program (Program for the global study of the distribution of water vapor on the planet) and worked in the near infrared range. A photodiode with a filter (940 nm) and LED (light-emitting diode 825 nm), operating in the photodetector mode, were used as photodetectors with a narrow band of measured optical radiation. The ratio of the output signals of these sensors allows the calculation of the total columnar amount of water vapor during the daytime.
The research [5] reports on the development of a similar device. This device uses two LED‑emitters operating in the photodetector mode at wavelengths of 815 and 940 nm, respectively. The signal spectrum of these light-sensitive elements is shown in Fig. 1.
For the technical implementation of the ground-level method for measuring the moisture content in the surface layer, we built a two-channel measuring device (the optical-electronic circuit of the measuring device is shown in Fig. 2).
The created device, operating at wavelengths λ1 = 940 nm and λ2 = 870 nm, was investigated experimentally. Fig. 3 shows the experimentally taken dependence , where V1 is the signal at the output of the channel with a wavelength of 940 nm; V2 is the signal at the channel output 870 nm.
To calculate the total amount of precipitated water vapor, we used expression (1) from [5], modifying it by multiplying it by the calibration factor.
, (1)
where m is the optical air mass; I940, I815 are the signals at the outputs of the photometer; k is the calibration factor.
The results of measurements by the Butler method [6] were used as a reference value for the total amount of precipitated water vapor. The measurements have shown that the value of the coefficient k can vary within the range of 1.03–1.08, which is partially explained by a significant methodological error of the Butler method itself.
As for the temperature stability of LED diodes operating in the photodetector mode, here one should distinguish between the amplitude stability of the photodetector signal and the color shift during emission. The studies carried out in [7] showed that the amplitude stability of the radiation intensity with a change in temperature within the range of 300–350 K does not exceed 5%, and the mixing of the peak wavelength is ≈2 nm. These results allow us to conclude that the temperature instability of LED diodes in the photodetector mode will not have such a noticeable effect on the total measurement error of the total amount of precipitated water vapor, which reaches 10–15%.
Apparently, the measurement of the total amount of deposited vapors throughout the entire thickness of the atmosphere can be carried out in the daytime using the optical radiation of the Sun. However, the task of studying the moisture saturation of the surface layer of the atmosphere often becomes a more urgent task. This is important for systems for forecasting thunderstorms and lightning, as well as for sanitary purposes. To solve this problem, a method of photometric measurement of a high-temperature radiator installed on a special high-rise object can be proposed. A high-rise building, a radio antenna or special meteorological masts can be used as such a high-rise object. The process scheme of such measurements is shown in Fig. 4.
Apparently, with such ground-altitude measurements carried out in the evening / night time, the optical air mass is determined as
(2)
or
. (3)
In this case, the value of PW can be determined by the expression (1) where m is calculated by the formulas (2) or (3). The reliability of the results of such measurements will depend on the transmission of the surface layer of the atmosphere. Therefore, it makes sense to investigate the conditions under which the transmission of the surface layer of the atmosphere would reach the maximum value.
OPTIMIZATION OF THE PROPOSED GROUND-ALTITUDE METHOD
According to the studies of the authors of [8], under conditions when optical radiation is essentially nonmonochromatic and the Beer–Lambert–Bouguer equation poorly describes the measurement modes with a sun photometer, the broadband electrical signal V at the photometer output can be defined as
,
where V0 is the signal value of the photometer located at the upper boundary of the surface layer; T1 is a broadband function.
According to [10], the function of broadband transmission for the surface layer of the atmosphere can be defined as
, (4)
where λ1, λ2 are the start and end points of the measured wavelength interval; Rλ is the normalized spectral response of the detector; F0λ are the solar radiation at the upper boundary of the surface layer; ma, mR, mg are optical air masses of aerosol, Rayleigh scattering and small gases; αa,λ, αR,λ, αg,λ are the optical thicknesses of aerosol, Rayleigh scattering, and small gases, respectively.
Optimization of the T1 indicator is carried out as follows.
The function of quadratic broadband transmission is introduced for consideration.
Furthermore, according to [9], the absorption spectrum of water vapor in the visible range and in the near-IR region has a continuous character with peaks at wavelengths of 590; 650; 690; 720; 760; 820; 940 nm. This is leads the circumstance of studying the extreme nature of the atmosphere transmission broadband in the corresponding spectral zone.
. (5)
The following condition is accepted
. (6)
It is assumed that
, (7)
. (8)
Taking into account conditions (6–8), the optimization problem for T1.кв by finding the optimal value of F0λ can be expressed as a problem of unconstrained variational optimization
, (9)
where γ is the Lagrange multiplier.
According to [11], the optimal function F0λ that leads T1.кв to an extreme value should satisfy the condition
. (10)
It is easy to obtain the following solution from (10):
. (11)
It is known that the optical thickness of an aerosol is determined by the Angstrem formula [12], i. e.
, (12)
where β is the aerosol turbidity of the atmosphere; χ is the Angstrom exponent.
Taking into account (11) and (12), we obtain
. (13)
Thus, in the optimal case, F0λ.opt should decrease with increasing λ. However, according to Planck’s law, in the range of 0.5–1.2 µm, depending on the temperature of the emitter, both an increase and a decrease in the intensity along the wavelength are possible.
According to Planck’s law, the optical radiation of an absolutely black body is defined as [13]
. (14)
By equating (13) to (14), we obtain
. (15)
From equality (15), we can calculate T, at which, for a given value of λ, the parameter T1.кв would reach its maximum value. In this case, the value of λ can be chosen as .
(16)
Thus, for given values λ, χ0, ma, β, χ, the optimal temperature of the emitter in the proposed ground-based altitude method can be calculated using formula (16).
Conclusion
Thus, the absence in many zones of the planet of automated stations for measuring the moisture content of air of the international network AERONET induces the need to develop and use simple sun photometers. The devices can be built based on two LED light emitters operating in the mode of narrow-spectrum photodetectors. Such LED‑photometers make it possible to measure the moisture content in the surface layer of the atmosphere in the evening and at night using a thermal emitter installed at a high-altitude object. An optimization problem has been defined and solved, which makes it possible to determine the optimal dependence of the initial optical radiation on the wavelength at which the atmospheric transmission in the near-ground atmosphere reaches its maximum. Comparison of the revealed optimal dependence with the analytical expression of Planck’s law made it possible to calculate the expression for determining the optimal temperature of the external radiator.
AUTHOR
Mammadova Ulker Fizuli gyzy, Postgraduate, Azerbaijan State University of Oil and Industry, Baku, Azerbaijan. Area of interest: sun photometer, optical transmission of the atmosphere.
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