Measurements and Evaluations of the Atmospheric Transparency at Short Millimeter Wavelengths at the Candidate Sites for Millimeter and Submillimeter Wave Telescopes

1. Introduction

Radio astronomical observations at millimeter and submillimeter wavelengths are a very important tool of astrophysical research (e.g., [1]). They provide a unique opportunity for detailed investigations of the interiors of the cold dense interstellar clouds of gas and dust which represent cradles of new stars. The emission peak of these clouds lies in this band. Millimeter and submillimeter waves are very rich in the spectral lines of various molecules, atoms and ions, which can serve as diagnostic tools of physical conditions and chemical content. At these wavelengths the highest angular resolution can be achieved which is very important for studies of compact objects, in particular active galactic nuclei. These studies are facilitated by a lower interstellar scattering in comparison with longer radio wavelengths. Bright examples of such a study are recent images of the “shadows” of supermassive black holes in the centers of M87 and our Milky Way galaxies [2,3]. These results have been obtained with the Event Horizon Telescope (EHT), which is a global VLBI network of sufficiently large millimeter-wave observatories operating at the 1.3 mm wavelength. Nowadays there are about 10 such observatories in the world. The success of the EHT stimulates the project of its extension, known as the next-generation EHT (ngEHT) [4]. Many locations in the world are considered as candidate sites for new EHT telescopes (e.g., [5]). There is a huge area in the northern Eurasia, including the whole Russian territory, which lacks such facilities although many years ago a construction of the 70-m radio telescope intended for operation at short millimeter wavelengths started on the Suffa plateau in Uzbekistan[6] (it was frozen after the USSR collapse) and there are relevant new projects and proposals [7,8,9,10].

The main obstacle to ground-based radio astronomy observations at short millimeter and submillimeter wavelengths, in addition to the technical challenges, is the atmospheric opacity, caused primarily by water and molecular oxygen. The observations are possible only in the so-called “atmospheric transparency windows” – the bands of relatively high transparency between the strong spectral lines of these molecules. The main windows discussed here are those centered at ∼90 GHz, ∼140 GHz, ∼225 GHz and ∼350 GHz. They are usually referred to as the 3 mm, 2 mm, 1.3 mm and 0.8 mm windows, respectively. However, even in these windows the opacity can be quite high. Radio astronomical observations at the sea level are possible only in the 3 mm and 2 mm windows. At higher frequencies high-altitude locations should be used.

While the oxygen absorption is stable and can be rather easily evaluated, the water content is highly variable. Water in the atmosphere is present in two forms – water vapor and liquid water (the latter one mainly in clouds). The amount of water vapor is usually characterized by the PWV (Precipitable Water Vapor) parameter, which is the vertically integrated amount of water vapor in the atmosphere. It is usually measured in millimeters. The amount of liquid water is parameterized by Liquid Water Path (LWP) measured in g m${}^{-2}$ or in $\mu$m (e.g. [5]). The zenith opacity (optical depth) of the atmosphere in dependence on frequency ($\nu$) is related to these parameters by the following expression:

$$\tau \left(\nu \right)={\tau }_{\mathrm{O}2}\left(\nu \right)+\beta \left(\nu \right)PWV+\gamma \left(\nu \right)LWP,$$

(1)

where ${\tau }_{\mathrm{O}2}\left(\nu \right)$ is the molecular oxygen contribution to this opacity, $\beta \left(\nu \right)$ is the specific absorption coefficient per PWV unit and $\gamma \left(\nu \right)$ is the specific absorption coefficient per LWP unit. The suitability of a site for radio astronomy observations is primarily characterized by the opacity statistics in atmospheric windows or by the PWV statistics, which are related to each other under clear sky conditions, although the LWP statistics is also important.

Both ${\tau }_{\mathrm{O}2}\left(\nu \right)$ and $\beta \left(\nu \right)$ are determined by the vertical distributions of the atmosphere physical parameters (pressure and temperature), molecular oxygen and water vapor. They can be derived empirically for a certain site or calculated using the existing models of the atmosphere in conjunction with spectroscopic databases (e.g., [11,12]). Then, nowadays global dynamic models of the atmosphere with a high spatial and temporal resolution are available (see below). The dependencies of the microwave absorption by molecular oxygen and water vapor on physical parameters and altitude in the atmosphere were analyzed many years ago [13]. In paper [14] the dependencies of ${\tau }_{\mathrm{O}2}\left(\nu \right)$ and $\beta \left(\nu \right)$ on altitude for the 1.3 mm window were calculated. The dependence of the molecular oxygen optical depth on altitude (h) is well described by the exponential function:

$${\tau }_{\mathrm{O}2}\left(\nu \right)=\alpha \left(\nu \right)e^{-\frac{h}{h_0}},$$

(2)

where $\alpha \left(\nu \right)$ is the O${}_2$ optical depth at the sea level and $h_0$ is the characteristic height usually adopted to be 5.3 km [15], although it can be somewhat different in different seasons [13].

Atmospheric transparency research is important not only for radio astronomy but also for telecommunications and radars. Millimeter-wave communication channels can provide the highest throughput (e.g., [16,17,18,19,20,21,22]) but are strongly affected by the atmosphere. Millimeter-wave radars are promising facilities for monitoring space debris and dangerous asteroids (e.g., [23,24,25,26]).

There are several ways to measure the atmospheric opacity and PVW, which are described in Section 2. In Section 3 we present some results of such investigations. They are discussed in Section 4.

2. Instruments and Methods

2.1. Methods for measuring atmospheric opacity

The optical depth of the atmosphere in zenith can be measured by several methods. Direct measurements of the opacity in a flat layered atmosphere are based on the Bouguer’s law:

$$I\left(\nu \right)=I_0\left(\nu \right)e^{-\frac{\tau \left(\nu \right)}{cos\theta }},$$

(3)

where $I_0\left(\nu \right)$ is the intensity of cosmic source emission within the antenna beam, as it would be measured without atmosphere, $I\left(\nu \right)$ is the measured intensity of this emission and $\theta$ is the zenith angle. By measurements of $I\left(\nu \right)$ at different zenith angles, the optical depth in zenith $\tau \left(\nu \right)$ can be retrieved. This method requires a long time for a substantial change of the zenith angle, stable atmospheric conditions during this time and negligible or well known dependence of the antenna response on the zenith angle. The flat layered model is valid at $\theta \lesssim {85}^{\circ }$ (e.g. [15]).

In practice the value of the zenith opacity (optical depth) at millimeter wavelengths is usually derived from measurements of the atmosphere emission [15]. The sky brightness temperature in a flat layered atmosphere, neglecting the cosmic microwave background, equals to

$$T_{\mathrm{s}}(\theta ,\nu )=T_{\mathrm{a}}\left(\nu \right)\left[1-e^{-\frac{\tau \left(\nu \right)}{cos\theta }}\right],$$

(4)

where $T_{\mathrm{a}}$ is the mean temperature of the atmosphere:

$$T_{\mathrm{a}}\left(\nu \right)=\frac{{\int }_0^{\infty }\kappa (\nu ,l)T\left(l\right)exp[-{\int }_0^l\kappa (\nu ,l^{\prime })d{l}^{\prime }]dl}{{\int }_0^{\infty }\kappa (\nu ,l)exp[-{\int }_0^l\kappa (\nu ,l^{\prime })d{l}^{\prime }]dl},$$

(5)

where $T\left(l\right)$ is the air temperature along the line of sight and $\kappa (\nu ,l)$ is the total air absorption coefficient, $dl=dh/cos\theta$ and h is the height. The value of the mean temperature of the atmosphere is discussed in [27]. At a relatively low opacity $T_{\mathrm{a}}\sim (0.90\cdots 0.95)T_0$, where $T_0$ is the ambient temperature. At a higher opacity the mean temperature increases, as expected, to $\sim T_0$. Therefore, $T_{\mathrm{a}}$ depends on the zenith angle.

In principle the zenith optical depth can be derived using Eq. (4) from the absolute measurements of the sky brightness temperature. However this method requires a precise absolute calibration of the brightness measurements, which can be challenging. A typical widely used approach, known as a “sky dip” (described below), is based on relative measurements of the sky brightness at several (minimum two) zenith angles.

2.2. Measurements of the atmosphere optical depth by the “sky dip” method

2.2.1. Basics of the “sky dip” method

From the measurements at two zenith angles (${\theta }_1$ and ${\theta }_2$) the optical depth of the atmosphere in zenith in the first approximation can be obtained as [15]

$$\tau ={\displaystyle \frac{1}{sec{\theta }_2-sec{\theta }_1}}ln{\displaystyle \frac{u_0-u_1}{u_0-u_2}}.$$

(6)

Here $u_1$ and $u_2$ are the receiver responses at the zenith angles ${\theta }_1$ and ${\theta }_2$, respectively, while $u_0$ is the response for the input emission with the brightness temperature $T_0$. Most frequently a reference angle near the horizon, where the optical depth should be high, is used for this purpose. Some variants of this method, which use measurements at 3 zenith angles and a reference area near the horizon, are considered in [28]. From measurements of the sky brightness in a range of zenith angles the optical depth can be derived by fitting the measurement results with a function corresponding to Eq. (4) (which can be also expressed in the logarithmic form) assuming a constant mean atmosphere temperature. In this case a reference signal is needed anyway. Some examples of such devices are the 225 GHz tipping radiometers at the site of the 30-m IRAM radio telescope (D.L. John, private communication) and at the Large Millimeter Telescope (LMT) site [29].

2.2.2. A dual-band radiometer for measuring the atmospheric opacity developed at the Institute of Applied Physics RAS

About 10 years ago a dual-band radiometer MIAP-2 for measuring the atmospheric opacity was developed and manufactured at the Institute of Applied Physics of the Russian Academy of Sciences and GYCOM company [30]. The radiometer operates in the 3 mm and 2 mm atmospheric windows.

At the front-end of the 3 mm channel a broad-band millimeter wave amplifier is used with the specified frequency range 84–99 GHz. In fact, it has no rejection of lower frequencies, which leads to contamination of the measurements by the strong contribution of the molecular oxygen absorption band near 60 GHz. The problem was partly fixed by installation of a waveguide filter with the cross-section of $1\times 2$ mm${}^2$, which has the cutoff frequency of ∼75 GHz [31]. Nevertheless, the contribution of the low frequencies remains significant and its consequences are discussed below.

The front-end of the 2 mm channel includes the local oscillator on a Gunn diode with a built-in frequency doubler, a balanced mixer on Schottky-barrier diodes (SBDs), an intermediate-frequency amplifier (IFA), and a detector for a range of 4–8 GHz. The local oscillator frequency is 140 GHz. The channel detects the emission in both lower and upper sidebands, which are 132–136 GHz and 144–148 GHz, respectively.

At the front-ends of both channels the modulator-calibrators are used. This device is described in detail in [32]. It is based on chains of series–parallel connected SBDs, placed into the standard cross-section waveguide. It can serve as a modulator of the input signal or as a source of a calibration signal. Depending on the current, it can be in 3 states: (1) open (transmitting the input signal with low losses), (2) locked with the equivalent brightness temperature of 155–180 K (“cold” calibration level) and (3) locked with the equivalent brightness temperature of ∼300 K (“warm” calibration level). These features enable both sky-dip measurements and absolute measurements of the sky brightness temperature.

Both channels are equipped with the lens antennas, which are misphased conically-shaped feed horns with a bent fracture and lenses. The half-power beam width of the antennas (with lenses) in both bands is about 2.5${}^{\circ }$. The elevation scan is provided by the rotating common mirror in front of both horns, oriented at the angle of 45${}^{\circ }$, and a mirror drive system, which is based on a stepper motor. The zenith angle range is from 0${}^{\circ }$ to 90${}^{\circ }$, and the step is 0.7${}^{\circ }$.

Three measurement modes are possible. In the first one the measurements are performed at two zenith angles and at the angle near the horizon as a reference (see Section sec:basics). In the second mode the data at 5 zenith angles are acquired. The angle near the horizon is not mandatory. At last, the absolute measurements of the sky brightness are possible.

As mentioned above, the frequency responses of the channels, especially in the 3 mm band, are not well defined. This can create problems with the interpretation of the measurement results. In [33] an attempt is done to determine the effective frequencies of the channels by comparison of the experimental values of the coefficients in Eq. (1) with the values obtained from the model calculations for a range of frequencies. The experimental values were obtained using independent measurements of the PWV amount. As a result, it was found that the effective frequencies of the 3 mm and 2 mm channels are 79.7 and 134 GHz, respectively. The effective frequency of the 3 mm channel is lower than the specified frequency range of the 3 mm amplifier. It shows that the contribution of the molecular oxygen absorption band near 60 GHz is significant in this channel and should be taken into account.

Two pieces of such a radiometer have been manufactured, however the second one lacks the 2 mm channel. At the same time it has a better constrained frequency response of the 3 mm channel.

2.3. Measurements of the precipitable water vapor (PWV) by water vapor radiometers

In some cases the information on the PVW value and its fast variations is of primary interest. They lead to phase shifts and fluctuations, which should be taken into account in radio interferometry. Although such information can be retrieved from the measurements of the opacity in the atmospheric windows described above, a more effective approach is to perform such measurements at frequencies near the H${}_2$O transitions. Usually for this purpose the transitions at ∼22 GHz and ∼183 GHz are used. For example, all 12-m ALMA antennas are equipped with the 183 GHz water vapor radiometers [34]. At the Institute of Applied Astronomy of the Russian Academy of Sciences a dual-band water vapor radiometer operating at ∼21 GHz and ∼31 GHz was developed [35]. It is actively used for atmospheric measurements (e.g., [36,37]).

2.4. Evaluation of the atmospheric opacity from global atmospheric models

Atmospheric transparency can be estimated on the basis of the approach used for modeling path delay in the neutral atmosphere [38]. The publicly available data provided by the NASA Global Modeling and Assimilation Office model GEOS-FPIT1 are used [8]. They evaluate atmosphere parameters (in particular, air temperature, total atmospheric pressure, and partial pressure of water vapor) using various ground, air-born, and space-born measurements that are assimilated into a dynamic model. Current models have 72 levels in altitude, $0.{25}^{\circ }\times 0.{31}^{\circ }$ spatial grid and 3 hours resolution in time. Atmospheric absorption at any frequency can be calculated for any selected location by using standard spectroscopic parameters as described in [8]. The values of the zenith opacity obtained in this way are in good agreement with the results of sky-dip measurements at the LMT and other sites, including measurements with the MIAP-2 radiometer at 2 mm on Suffa plateau [39].

Similar data are provided by the Modern-Era Retrospective Analysis for Research and Applications, Version 2 (MERRA-2) [40,41] and the European Center for Medium-Range Weather Forecast ReAnalysis (ERA5) [42].

2.5. Evaluation of the precipitable water vapor (PWV) from the Global Navigation Satellite System (GNSS) data

The development of the Global Navigation Satellite Systems (GNSS) provides an opportunity for estimations of PWV from measurements of delays of the navigation signals [43,44,45]. Taking into account the surface temperature and pressure, the PWV values can be estimated from these delays with a low uncertainty. Nowadays this method is widely used for this purpose, including evaluation of results obtained from the global atmospheric models mentioned above (e.g., [46,47,48,49,50,51,52,53,54,55,56,57]).

2.6. Evaluation of the precipitable water vapor (PWV) from the sky-dip data by the artificial neural network

The direct comparison of the results obtained by the different methods may be problematic. The low PWV values in dry atmosphere are barely detectable by humidity sensors in aerosonde. Wet conditions and high opacity lead to small variations in brightness temperature on different angles, leading to higher errors in $\tau$ and PVW estimations. The spatial-temporal resolution of the dynamic atmospheric models is limited, it is lower than typical sizes of the topographic features such as mountains and typical times of the variations of the PWV values. Since that, different methods should be cross-validated and extrapolated to the same scale.

Recently we proposed the statistical approach for the determination of the PWV values based on machine learning algorithms and MIAP-2 data [58]. The idea was to use non-linear regression to calculate PWV values from the MIAP data using the receiver responses on different angles in the 2 mm and 3 mm bands as the input data, without addressing to the physical model. The training set is based on the one year monitoring session near the Badary observatory (2016–2017). The observatory was equipped with the water vapor radiometer (WVR) and GNSS receivers capable for tropospheric delay estimations. We found that the GNSS and WVR data are consistent. We use the GNSS data as the target values for the statistical model fitting and the k Nearest Neighbors (kNN) [59] and artificial neural network (ANN) as the regression models. We utilize the individual component analysis to speed up the learning process. As a result, the regression model encapsulates the instrumental transfer function and the PWV fraction in the microwave absorption (Eq. eq:tau). The bias introduced by the flat layered atmospheric model was also excluded. The coefficient of determination $R^2$ on the validation part of the dataset was 0.8 for kNN and 0.86 for ANN with symmetrical deviations from the trend line [58]. The result of this findings was that the PWV may be consistently determinated from the sky dip data using the statistical approach.

We use similar approach to construct statistical model based on the two sessions obtained in Svalbard (2018-2019) and Badary (2016-2017). The target values are based on publicly available MERRA-2 model’s PWV data and ANN regressor. The input data was the MIAP-2 measurements 2×6×3 vector (bands, angles, $n_m=t_{\mathrm{MERRA}}/t_{\mathrm{MIAP}}$, number of MIAP measurements per MERRA-2 timestamp). We found that PWV estimations based on WVR data are biased from MERRA-2 data in dry conditions (Figure 1). The resulting $R^2$ was 0.98 on validation dataset trained on Badary data only and 0.96 for Svalbard and Badary combined dataset. The time-series and scatter plot are presented in Figures 1 and 2. The results show a good agreement between the predicted and the PWV MERRA-2-based and GNSS-based values. The lower $R^2$ value is probably caused by the different impact of the absorption in O${}_2$ and LWP in different sites that cannot be represented by the single regression model. Still, the predictive ability of the model is very high at the full variety of the atmospheric conditions during the sessions.

Figure 1. Left panel: the scatter diagram between the WVR and MERRA-2. Right panel: correlation between the target PWV values (MERRA-2) and the predicted values on the validation dataset.

Figure 1. Left panel: the scatter diagram between the WVR and MERRA-2. Right panel: correlation between the target PWV values (MERRA-2) and the predicted values on the validation dataset.

Figure 2. Time-series plot of the PWV in MERRA-2 data (target values), GNSS-based data and predicted by ANN from Badary session, one month partial selection.

Figure 2. Time-series plot of the PWV in MERRA-2 data (target values), GNSS-based data and predicted by ANN from Badary session, one month partial selection.

This approach can be applied to different types of the data acquiring methods and should produce the statistically coherent results. The $R^2$ traces the predictive ability of the statistical model and can test the validity of the different non-direct methods testing astroclimatic measurements or atmospheric model predictions in specific places. We assume the MERRA-2 model as the reference, but it can also be tested by different direct PWV drone-based measurements or aerosonde that is too rare to serve as training set.

3. Results

3.1. Monitoring of the millimeter-wave atmospheric opacity at selected sites

To date, atmospheric absorption studies with the MIAP-2 radiometers have been carried out at several sites in Russia and Uzbekistan [31,60,61,62,63,64,65]. However, a long-term monitoring covering all seasons is limited to the RT-70 radio telescope construction site on the Suffa plateau in Uzbekistan (altitude 2400 m), site of the BTA telescope of the Special Astrophysical Observatory (SAO) in the North Caucasus (altitude 2040 m) and the Badary observatory in the Baikal region (altitude 813 m). Among these sites, the best atmospheric transparency has been observed on the Suffa plateau. From these measurements the PWV values were derived, which are in good agreement with the satellite and aerosonde data [31]. Then, expected optical depth in other atmospheric transparency windows was evaluated. The monthly averaged values of the optical depth in zenith at 1.3 mm are ∼0.3 in winter and ∼0.8 in summer. The corresponding monthly averaged PVW values are ∼4 mm in winter and ∼14 mm in summer.

In addition to long-term monitoring, short-term measurements of atmospheric absorption have been carried out in several locations: the Muus-Khaya peak in Yakutia (altitude 1950 m), the Terskol peak in Caucasus (altitude 3150 m), Svalbard (altitude 36 m), Caucasian Mointain Observatory (altitude 2112 m), Mondy, Sayans in Buryatia (altitude 2006 m), Karadag in Crimea (altitude 105 m). Measurements have recently begun in the eastern Caucasus [65]: in Dagestan (Mount Mayak, 2700 m and Mount Shalbuzdag 4142 m) and in North Ossetia (Stolovaya Mountain, ∼3000 m).

The Muus-Khaya peak is located in the region of the “Pole of Cold”. The measurements were done in July and gave quite good results for this season: PVW∼5 mm [60], which is significantly better than at the RT-70 site on the Suffa plateau in summer. The expected PWV value in winter is 1–2 mm, which makes this peak a promising site for millimeter and submillimeter astronomy. The short measurement on the Terskol peak did not show good results. The one day measurements on Elbrus in August 2021 gave rather high opacity, too. Promising preliminary data were obtained for the eastern Caucasus. In May 2023, a long (over half a year) expedition ended in the vicinity of Kurapdag (Chirag village), which basically confirmed the previously formulated hypothesis about the lower humidity of the eastern Caucasus compared to the western one. An interesting feature was observed on Karadag. The millimeter-wave absorption there strongly depends on the wind direction and can drop to quite low values when dry air enters from the steppe Crimea [28].

All the data collected during numerous expeditions, including the semi-annual expedition to Dagestan that ended in May 2023, where the results have not yet been processed or published, are posted in the open access archive [66].

3.2. Some results of the opacity evaluations from the NASA data

Evaluations of the atmospheric opacity from the NASA data as described in Section sec:nasamethod have been performed for more than 40 sites around the globe [8]. They include analysis of the seasonal variations of the opacity. The main conclusion of this research is that the best place for submillimeter astronomy in the Eastern hemisphere is the high-altitude (4300–4500 m) plateau in Eastern Pamirs. The atmospheric transparency at this site is comparable to that in the Atacama desert in Chile and is much better than on the Suffa plateau in Uzbekistan, where the 70-m radio telescope is constructed. Typical PWV values in winter are as low as 0.8–0.9 mm. The extent of the plateau is rather large, baselines up to ∼130 km are possible. Similar conditions exist in Tibet.

4. Discussion

4.1. Degradation of the telescope sensitivity due to atmospheric opacity

Atmospheric opacity leads to deterioration of the telescope sensitivity in any case. However, it is worth obtaining numerical estimates of this deterioration. In particular it can help to understand better an acceptable value of the opacity in various conditions. For this purpose we will estimate the quantity, which can be called a “degradation factor”:

$$R_{\mathrm{D}}=\frac{T_{\mathrm{SYS}}^{*}}{T_{\mathrm{RX}}},$$

(7)

where $T_{\mathrm{RX}}$ is the receiver noise temperature and $T_{\mathrm{SYS}}^{*}$ is the system temperature “above the atmosphere”, i.e. calculated from the system temperature at the receiver front-end taking into account the attenuation in the atmosphere. Neglecting antenna losses and background emission

$$T_{\mathrm{SYS}}^{*}=T_{\mathrm{RX}}{e}^{\frac{\tau }{cos\theta }}+T_{\mathrm{a}}\left(e^{\frac{\tau }{cos\theta }}-1\right).$$

(8)

In case of no opacity $R_{\mathrm{D}}=1$. The plot of the degradation factor $R_{\mathrm{D}}$ in dependence on the receiver noise temperature $T_{\mathrm{RX}}$ and zenith opacity $\tau$ for the zenith angle $\theta ={45}^{\circ }$, assuming $T_{\mathrm{a}}=250$ K, is presented in Figure 3. For example, if the degradation factor of 1.5 is considered to be acceptable and the receiver noise temperature is $T_{\mathrm{RX}}\sim 100$ K, then the required zenith opacity is $\tau \lesssim 0.1$. It is worth noting that the integration time required to achieve the same sensitivity, varies as $R_{\mathrm{D}}^2$. In case of $T_{\mathrm{RX}}\gg T_{\mathrm{a}}$, which happens at very high frequencies, the degradation factor approaches $e^{\tau /cos\theta }$. Then, $R_{\mathrm{D}}=1.5$ implies $\tau \approx 0.29$ at $\theta ={45}^{\circ }$.

Figure 3. The degradation factor $R_{\mathrm{D}}$ (gray scale) in dependence on the receiver noise temperature $T_{\mathrm{RX}}$ and zenith opacity $\tau$ for the zenith angle $\theta ={45}^{\circ }$, assuming $T_{\mathrm{a}}=250$ K. The curves correspond to $R_{\mathrm{D}}=1.2$, 1.5 and 2 (from bottom to top).

Figure 3. The degradation factor $R_{\mathrm{D}}$ (gray scale) in dependence on the receiver noise temperature $T_{\mathrm{RX}}$ and zenith opacity $\tau$ for the zenith angle $\theta ={45}^{\circ }$, assuming $T_{\mathrm{a}}=250$ K. The curves correspond to $R_{\mathrm{D}}=1.2$, 1.5 and 2 (from bottom to top).

4.2. The effect of cloudiness

The coefficient $\gamma$ in Eq. (1) is approximately $2.5\times {10}^{-3}$ and $3.5\times {10}^{-3}$$\mu$m${}^{-1}$ at 230 and 345 GHz, respectively, with weak temperature dependence [67]. It means that LWP of 100 $\mu$m (which is equivalent to 100 g m${}^{-2}$) contributes about 0.25 to the opacity at 230 GHz. The median values of LWP for different cloud classes are from ∼10 to ∼40 g m${}^{-2}$[68,69]. In [5] the LWP statistics is presented for the existing and candidate EHT sites. The median values are well below 100 $\mu$m for most sites. Therefore, in most cases the opacity in clouds at 1.3 mm is ≲0.1 and cannot fully prevent the radio astronomical observations.

However the problem is that clouds are usually very inhomogeneous, which leads to spatial and temporal fluctuations of the opacity and of the sky brightness. Their influence can hardly be sufficiently suppressed even by the usual beam switching technique. As a result, these fluctuations make practically impossible observations of weak sources, especially in continuum. Spectral line observations are less affected because the fluctuations are synchronous in all channels and can be subtracted at the data reduction. However, a more frequent calibration is needed.

4.3. Comparison of the candidate sites for millimeter-wave telescopes in Eurasia

A long-term monitoring of atmospheric opacity with the MIAP-2 radiometers has been performed at several sites in Russia and Uzbekistan, as described in Section sec:monitor (the RT-70 radio telescope construction site on the Suffa plateau, site of the BTA telescope in Caucasus and the Badary observatory). Among these sites, the best conditions for millimeter-wave astronomy have been observed on the Suffa plateau. However, these conditions are far from being excellent and hardly allow for regular observations at wavelengths $\lambda \lesssim 2$ mm. At 1.3 mm only episodic observations can be possible in winter, when the monthly averaged value of zenith opacity at this wavelength drops to ∼0.3 (somewhat lower estimates of the opacity for this site are obtained in [5]).

Promising results have been obtained in the short summer measurements on the Muus-Khaya peak in Yakutia (Section sec:monitor). However, a long-term monitoring at this site is needed. Short measurements on the Terskol peak are not conclusive.

Investigations with various methods (e.g., [8,39,65,70,71,72,73,74]) reveal other promising sites in Eurasia with better conditions in comparison with the Suffa plateau. In paper [8] based on the NASA GEOS-FPIT model, the Eastern Pamirs and Tibet are shown to be the best places. According to [71] based on the ERA5 re-analysis, very good conditions exist at the Ali 1 site in Tibet (PWV ∼0.4 mm in winter) and at Muztag-Ata in the Chinese Pamirs (PWV ∼0.7 mm in winter). Comparable conditions exist in the Sayan Mountains. The Khulugaisha peak, in terms of its characteristics, is close to the sites of Tibet and Pamirs (PWV ∼0.6 mm in winter). There are promising sites in Altai and Dagestan, in particular the Khorai and Kurapdag mountains [71]. The Terskol peak is also rather good in terms of PWV [39,75] but not so good concerning cloudiness. The Aktashtau peak in Uzbekistan (3383 m) located near the RT-70 construction site, has PWV statistics similar to Terskol [71]. With PWV $\lesssim 2$ mm, astronomical observations at least in the 1.3 mm and 0.85 mm atmospheric windows can be quite efficient. Even lower PWV values, ∼0.5 mm, make possible observations in the higher frequency windows.

It is worth noting that in rugged terrains the spatial resolution of the global models can be insufficient to characterize atmospheric conditions on certain sites (e.g. on local peaks). This emphasizes the importance of local measurements with radiometric systems or GNSS devices. So far, our measurements have been performed at 3 and 2 mm. Measurements in the 1.3 mm window would be very important.

In this consideration of the candidate sites for new millimeter and submillimeter wave telescopes we have taken into account only the atmospheric opacity. However, there are other criteria which should be also considered. One of them is stability of the atmosphere [76,77]. Enhanced instability can lead to strong phase fluctuations [78] and anomalous refraction (e.g., [79]). This factor is still poorly investigated.

A new large millimeter wave telescope should be an efficient part of the global VLBI network (EHT). The estimates show that from this point of view the Caucasus region is the most effective with the existing EHT configuration (Andrey Lobanov, private communication). However, the situation will change if a large millimeter wave telescope is built in eastern Asia. In this case, places like the Pamirs and Tibet will have an advantage.

5. Conclusions

Our studies of the atmospheric transparency at the candidate sites for millimeter and submillimeter telescopes continue for about 10 years already by various methods. The considered sites are located in Russia and in the nearby surroundings (in particular, in Uzbekistan). The atmospheric optical depth has been measured with the dual-band tipping radiometer and evaluated from the global atmospheric models. Several sites have been selected, which can be effectively used for astronomical observations at least in the major atmospheric transparency windows at 1.3 mm and 0.85 mm. The investigations continue. More detailed studies of several recently suggested sites are planned as well as an extension of the measurements to the 1.3 mm atmospheric window.