Long-Term Trends of Astroclimatic Parameters above the Terskol Observatory

Abstract

Astroclimatic conditions characterize the quality of an astronomical site. The Terskol Observatory was founded over 42 years ago in 1980. The astronomical site (coordinates 43°16′29″ N, 42°30′03″ E) is located about 10 km from Mt. Elbrus in the northern Caucasus Mountains. The paper presents the results of an analysis of long-term variations from 1980 to 2022 of astroclimatic parameters such as total cloud cover, precipitable water vapor, and wind speed at a level of 200 hPa above the Terskol Observatory using atmospheric ERA5 Reanalysis data from the European Center for Medium-Range Weather Forecast. The probability distributions and seasonal variations of the astroclimatic parameters are also presented. Long-term trends of the astroclimatic parameters are studied with statistically significant trend analysis methods using the Mann–Kendall test and the Sen’s slope test to estimate the magnitude of the changes. The results show non-significant decreases of annual average 200-hPa wind speed and increases in precipitable water vapor, but significant (99 per cent confidence level) long-term decreasing of total cloud cover above the Terskol Observatory.

1. Introduction

The atmosphere of Earth is a major challenge for the quality of astronomical observations using ground-based optical telescopes. The studies of the atmosphere above astronomical sites are important for scheduling of observation, instrument optimization, and adaptive optics development. Astroclimate is a set of atmospheric parameters that can affect astronomical observations [1,2]. Astroclimatic parameters include such atmospheric characteristics as wind speed and turbulence distribution relevant to adaptive optics performance. In addition, one of the main atmospheric parameters is the amount of clear sky, which determines the possibility of carrying out astronomical observations. Both cloud coverage and water vapor content are key characteristics determining the fraction of photometric and spectroscopic nights. These critical parameters affect the available time of observation conditions suitable for the operation of various instruments of an astronomical observatory.

Site characterization is an essential task not only for the installation of new observatories but also for the operations of already working telescopes. One of the areas of astroclimatic study of astronomical sites is the characterization of the long-period behavior of atmospheric conditions [3]. Climate change became a challenge for the scientific throughput of ground-based astronomical observatories, for example Paranal Observatory, Chile [4]. The long-term changes of the astroclimatic parameters directly affect astronomical observations. The best astronomical observatory 40 years ago may not be the best for observation in today’s climate. Since global climate is changing, an acknowledged fact, it has become important to study the influence of climate change on each astroclimatic parameter of the observatories. If a change in an astroclimatic parameter is detected, it will be necessary to quantify the estimation of how much it contributes to the astronomical site characterizations. Then, this knowledge must be used to optimize observation strategies and instrumental upgrades of telescopes. However, this kind of atmospheric data is not often available at astronomical observatories. As an alternative, meteorological reanalysis products are used to perform analyses of long-term variations of atmospheric conditions. Reanalysis combines the model with observations through data assimilation. Meteorological reanalysis is useful for the characterization of existing astronomical observatories without atmospheric monitoring instrumentation. Long-time sets of ERA5 reanalysis after ERA-Interim with higher temporal and spatial resolution are now available from the European Center for Medium-Range Weather Forecast (ECMRWF) [5]. One of the advantages in the use of meteorological reanalysis is the long-term, uniform databases now available. Many large astronomical observatories in the world have carried out detailed studies of atmospheric parameters using reanalysis data, but mostly regarding seasonal distribution [1,6,7,8,9,10]. Long-term atmospheric changes in large astronomical observatories were analyzed using ERA-Interim reanalysis in [3] and two Russian sites using ERA5 in [10].

In the paper, we consider long-term trends of astroclimatic parameters: wind speed at 200 hPa level (V200) as parameter suitability for adaptive optics, precipitable water vapor (PWV), and total cloud cover (TCC) at the Terskol Observatory. The observatory was founded in 1980. The analysis of the averaged parameters from 1980 to 2022 is performed using ERA5 reanalysis data from the European Center for Medium-Range Weather Forecast. The long-term trends of the parameters are examined for a statistically significant trend using the non-parametric Mann–Kendall method and Sen’s slope to estimate the magnitude of the changes.

2. Materials and Methods

The Terskol Observatory has geographical coordinates 43°16‘29″ N, 42°30′03″ E. The astronomical site is located about 10 km from Mt. Elbrus in the Northern Caucasus Mountains. The altitude is 3150 m above sea level. The climate of the Elbrus region is moderate continental.

The 2-meter Zeiss astronomical telescope is the main instrument of the observatory (Figure 1). Photometric, spectral, and positional methods are used in the visible and IR ranges. The observatory has both astronomical facilities conducting night- and daytime observations. The main scientific areas of research include the study of the physical characteristics and chemical composition of stars, galactic nuclei, and star formation processes; the study of optical manifestations of gamma-ray bursts; research in the field of physics of stellar and planetary systems; research in the field of asteroid-comet hazards; and comprehensive studies of near-Earth space and ground support for space projects [11]. Now, the program of adaptive optics development is going for the 2-meter Zeiss telescope.

However, there are no regular measurements of astroclimatic parameters over a long time at the site. Some results of the measurement of astroclimatic parameters carried out before first stellar observations at the Terskol Observatory have been presented in [12]. Studies of astronomical seeing have been performed with the 2 m Zeiss telescope [13]. Recently, a seasonal study of PWV using measurements from the Global Navigation Satellite System (GNSS) and comparisons with data from ERA5 reanalysis has been reported in [14].

In this study, data from ERA5 reanalysis were used for the analysis of astroclimatic characteristics above the Terskol Observatory [5]. It is produced by the Copernicus Climate Change Service (C3S) at ECMWF. ERA5 reanalysis is the latest fifth-generation database. The database assimilates the various observational data from satellites, aircraft measurements, and ground-based monitoring with a modern numerical weather prediction model with resulting data in spatial grid 0.25°. ERA5 data have an hourly temporal resolution. ERA5 was generated utilizing 4D-Var data assimilation and model forecasts in CY41R2 of the ECMWF Integrated Forecast System (IFS) [5].

The TCC, PWV, and climate variables V200 are analyzed using the nonparametric Mann–Kendall test and Sen’s slope estimator. The Mann–Kendall (MK) trend analysis method is a non-parametric test method for estimations of significance. The approach is widely used to identify trends in series of PWV, temperature, and other atmospheric variables. Its advantage is that it does not assume a normal distribution of data.

The short descriptions of the MK and Sen’s tests are presented below from [15]. There are two hypotheses for this test. The null hypothesis is H₀, and the alternative hypothesis is H_a, where H₀ is that there is no trend, and H_a is that there is an upward trend or downward trend.

The MK test presents for the time series x₁, …, x_n, the following as

$$\mathrm{S}={\displaystyle \sum _{k-1}^{n-1}{\displaystyle \sum _{j-k+1}^n}}\hspace{1em}\mathrm{sgn}(x_j-x_k)$$

(1)

where n is the number of data points, x_k and x_j are the data values in the time series i and j (j > k), respectively, and sgn(x_j − x_k) is the function equal to

= 1 if x_j − x_k > 0

Sgn (x_j − x_k) = 0 if x_j − x_k = 0
        = −1 if x_j − x_k < 0

(2)

The variance of S (Equation (1)) is computed as follows:

$$\mathrm{VAR}(\mathrm{S}) = 1\backslash 18[\mathrm{n}(\mathrm{n} - 1)(2\mathrm{n} + 5) - {\displaystyle \sum _{p=1}^g}{\mathrm{t}}_{\mathrm{p}}({\mathrm{t}}_{\mathrm{p}} - 1)(2{\mathrm{t}}_{\mathrm{p}} + 5)]$$

(3)

where g is the number of tied groups in the data set, Σ is the summation over all tied groups, and t_p is the number of data points in the pth group. A tied group is a set of sample data that have the same value.

The standard normal test statistic Z, or test Z, is calculated for the sample size n > 30, as following

$$=\mathrm{S}-1/\sqrt{VAR(S)}\hspace{1em}\mathrm{if} \mathrm{S}>0$$

Z = 0  if S = 0

(4)

$$=\mathrm{S}+1/\sqrt{VAR(S)} \mathrm{if} \mathrm{S} < 0$$

Positive values of test Z indicate an increasing trend, and negative values of test Z indicate a decreasing trend. Testing trends are calculated at the specific significance level α. When |Z| > |Z_1−α/2|, the hypothesis H₀ is rejected, which means that a significant trend exists in the time series. In this study, α = 0.05, α = 0.01 and α = 0.001 are used.

The non-parametric Sen’s slope estimator test is used to determine the median slope statistically different from zero in the time series. The test calculated both confidence levels and the slopes of all data value pairs (Qi) as following:

Qi = (x_j − x_k)/j − k

(5)

for (1 ≤ i < j ≤ n), where i and j are indices and x_j and x_k are data values at time j and k (j > k), respectively. Sen’s slope is then calculated as the median from all slopes. In the study, the unit of Sen’s slope (Q) is the value per year. The positive value means that there is an increasing trend and the negative value means that there is a negative trend in the time series.

3. Results

3.1. Wind Speed at Level 200-hPa

A winds speed at the pressure level of 200 hPa (V200) has been proposed as the suitability of an astronomical site for adaptive optics [16]. An adaptive optics system is needed to correct the atmospheric turbulent distortions in near real time. The aim of adaptive optics is to provide a high angular resolution close to the theoretical diffraction limit for an optical telescope. A deformable mirror is used for correction in the adaptive optical system of the telescope. As a result, adaptive optics provide the best quality of astronomical observation. The correlation between V200 and astronomical seeing was found for astronomical observatories using reanalysis data [3,7,17,18].

Besides the wind at a pressure level of 200 hPa is causing the so-called ‘wind-driven halo’, where atmospheric turbulence conditions vary so quickly that the telescope’s control system cannot correct for them [19,20]. As a result, this limits the contrast capabilities of the telescope. The time lag between the analysis of the atmospheric turbulence and its correction with a deformable mirror creates a wind-driven halo. This phenomenon appears when atmospheric turbulence conditions change faster than the telescope’s control system can correct them. The effect leads to a tenfold reduction in contrast. This limits the contrast capabilities of the instrument and could potentially limit exoplanet studies.

Figure 2 shows the evolution of the wind speed at 200 hPa from 1980 to 2022 above the Terskol Observatory from the ERA5 database.

The results indicated yearly fluctuations trending to a decrease in the wind speed at level 200 hPa from 1980 to 2022 above the Terskol Observatory. The change can be useful for available time for AO operations. The average annual values of V200 range from 17 m/s to 23 m/s in the considered period.

The effect of a wind-driven halo is mainly caused by the wind speeds higher than 25 m s⁻¹ as indicated in [20]. Figure 3 shows the cumulative distribution and histogram of monthly averages values of V200.

The monthly average values of wind speed at the 200 hPa level less than 25 m/s are observed in 70% of the considered period 1980–2022, while the V200 less than 15 m/s appeared in 25% of the time.

Seasonal variations of wind speed at a height of 200 hPa are calculated via the median values for 1980–2022 using ERA5 reanalysis data (Figure 4).

The median value of wind speed V200 varies from 13 m/s to 34 m/s during the year above the Terskol Observatory. The wind speeds are highest in summer. The lowest value of V200 is 10 m/s in May. The monthly averages of V200 exceed 25 m/s from July to August above the Terskol Observatory. This means that the adaptive optics systems probably will be operating with servo-lag error during summer. The suitable season for observation is from October to June.

3.2. Precipitable Water Vapor

Atmospheric water vapor plays a critical role for ground-based astronomy. An observation from the radio wavelengths to the infrared depends on the water vapor content in the atmosphere via absorption reducing the transmission of light from an astronomical object. The quantitative classification based on precipitable water vapor (PWV) for characterization of astronomical observatory suitability for IR observation is as follows: good or excellent, PWV < 3 mm; fail or mediocre 3 mm < PWV < 6 mm; poor 6 mm < PWV < 10 mm; extremely poor PWV > 10 mm [21]. It should be noted the requirements for adaptive optics are reduced in the IR range. The PWV decreases with height in atmosphere. Therefore, high-mountain observatories are preferred for IR observations [22]. The PWV and its changes are related to radiation balance, cloud formation, and precipitation mechanism. Additionally, PWV is one of the indicators of climate changes in global and regional ranges.

The applicability of the ERA5 reanalysis for estimating PWV above the Terskol Observatory based on comparison with GNSS measurements was evaluated earlier [14]. The difference between the average annual PWV values estimated from the data of measurements of GNSS stations and reanalysis has been detected to be 0.74 mm at the Terskol Observatory.

The long-term trend of PWV over the period of 42 years at the Terskol Observatory is presented in Figure 5.

Figure 5 shows a weak trend of increasing PWV above the Terskol Observatory. An increase in the water content in the atmosphere leads to a reduction in the astronomical signal, especially in the IR range. The average annual values of PWV are the range from 6.15 mm to 8.3 mm in the considered period. The average annual value of PWV is 7.4 mm in 1980 and 7.5 mm in 2022. If taking into account the estimation error, this does not allow us to draw a conclusion about the changes.

Figure 6 shows the cumulative distribution and histogram of monthly average values of PWV for the period of 1980–2022.

During the period, about 3% of the monthly mean PWV values are less that 3 mm, which means excellent conditions for IR astronomy. A total of 45% of PWV values are less than 6 mm, which corresponded to mediocre IR conditions. The poor and extremely poor conditions are equally occurring at the site.

The seasonal variations of PWV are calculated via the median values for 1980–2022 using ERA5 reanalysis data (Figure 7).

The seasonal variation of PWV is typical for middle latitudes, with higher values in summer and lower values in winter [10,14]. The median value of PWV is more 10 mm in summer, which corresponds to extremely poor IR astronomical conditions (PWV > 10 mm). The suitable conditions (3 mm < PWV < 6 mm) for IR observations are detected from November to March. The poor conditions (6 mm < PWV < 10 mm) are detected in April–May and September at the Terskol Observatory.

3.3. Total Cloud Cover

The clear-sky time fraction is the most important characteristic of the quality of an astronomical site. The duration of astronomical observations directly depends on the quantity of cloudless time, making it one of the most crucial factors for an astronomical observatory’s operation because astronomical observation in the infrared and visible ranges is available when the sky is clear or a little cloudy. According to the European Southern Observatory (ESO), a photometric night is defined by no visible clouds; a clear sky is defined as a sky with less than 10% cloud cover. In addition, cloud cover variability plays an important role in climate via the Earth’s radiative energy balance. Some climate models suggest that warming will increase relative cloudiness.

Figure 8 presents the long-term trend of TCC for the considered period of 42 years at the Terskol Observatory.

Results from Figure 8 indicate yearly fluctuations with a trend towards less average cloud cover from 1980 to 2022. The average annual values of TCC are the range from 69.6% to 56.5% in considered period. The TCC has been decreasing by about 10 percent since the year in which the observatory was founded. This means an increase in the available time for astronomical observations at the Terskol Observatory.

The cloudiness data are fixed by AAG CloudWatcher cloud detector at the site over last years. Figure 9 shows cloudiness measurement data for 2021, where (a) is data for daytime and nighttime, (b) is nighttime. The cloudy is condition when infrared temperatures ranging between −5 °C and 0 °C.

About 40% of the time without clouds is determined for the year, which corresponds to an average annual mean TCC of 62% from ERA5 data. The longer cloudless time is recorded by the detector for October–November. According to measurements, the month with the longest time of cloudiness is April. The summer season is characterized by a small fraction of cloudless time for nighttime observations. In addition, more cloudiness is recorded during the day than at nighttime.

3.4. Mann–Kendall Test and Sen Estimator

The Mann–Kendall trend tests and Sen’s slope estimator were applied to the long-term data set of V200, PWV, and TCC for the period from 1980 to 2022 at 90, 95, and 99% confidence levels.

Table 1. The results of applying the Mann–Kendall test and Sen’s slope for long-term trends of V200, PWV, and TCC at the Terskol observatory in comparison with the nearby SAO RAS observatory [10].

Astroclimatic Parameters	Sen Estimator Q (in Year)	MK Test Significance
Long-term of TCC	−0.13%	Significantly 1
Long-term of PWV	+0.004 mm	Not significantly
Long-term of V200 Long-term of TCC [10] Long-term of PWV [10]	−0.008 m/s −0.12% +0.004 mm	Not significantly Significantly 1 Not significantly

¹ Trend at α = 0.01 of the level of significance or 99% confidence level.

provides the results for long-term trends of V200, PWV, and TCC at the Terskol observatory. The comparisons of PWV and TCC at the nearby Special Astrophysical Observatory of Russian Academy of Science (SAO RAS) are presented from work [10]. The RAS or 6 m BTA (Big Telescope Alt-Azimuthal) site has geographical coordinates 43°39′12″ N, 41°26′30″ E.

The significant trends of long-term V200 and PWV are not found in the period of 1980–2022 at the Terskol Observatory, as well as at the BTA site. The Sen’s slope for PWV is the same at both sites (0.004 mm). The negative statistically significant trends of TCC were detected at the Terskol observatory as well as at the BTA site. The significance level is 0.01 or 99% confidence level. However, the Sen’s slope of the TCC change is 0.13 per year at the Terskol Observatory and 0.12 per year at the BTA site.

Therefore, we consider the seasonal change of TCC at the Terskol observatory. Figure 6 shows the seasonal changes via three monthly averages. Where winter is the averages of TCC values for three months, December, February, and January (Figure 10a), spring is March, April, and May (Figure 10b), autumn is September, October, and November (Figure 10c), and summer is June, July, and August (Figure 10d).

The results show the decreasing trend of TCC for all seasons above the Terskol Observatory. A strong decrease is seen especially for summer from 60% to 45% (Figure 10d). Winter is characterized by strong variability from year to year in the range of 65–80% (Figure 10a). The decrease in TCC is detected in the last 5 years in spring (Figure 10b). Overall, the change of TCC has a very positive effect on astronomical observation at the Terskol Observatory, as it increases the available observation time on the telescopes. In addition, summer as a season is characterized by a lower value of TCC and is most suitable for ground-based astronomy at the site.

The Figure 11 shows the long-term changes of PWV which is split into seasons. The corresponding MK and Sens’s slope results are presented in

Table 2. The results of applying the Mann-Kendall test and Sen’s slope for seasonal long-term trends of PWV at the Terskol Observatory.

Season	Sen Estimator Q (in Year)	MK Test Significance
Winter	+0.006 mm	Not significantly
Spring	−0.002 mm	Not significantly
Autumn Summer	+0.003 mm +0.015 mm	Not significantly Significantly 2

² Trend at α = 0.05 of the level of significance or 95% confidence level.

.

The long-term change of PWV tends to increase for winter and autumn during the considered period with Sen’s slope is 0.006 mm and 0.003 mm per year, respectively. However, this trend is only significant in summer according to the MK tests at 95% confidence level. The Sen’s slope is 0.015 mm per year, that high rate compared to other seasons. Note that the decrease in cloudiness is highest also in summer. In contrast the long-term of PWV has non-significantly increasing trend in spring with Sen’s slope 0.002 mm per year.

Figure 12 shows the long-term changes of V200 which is split into seasons and corresponding MK and Sens’s results are presented in

Table 3. The results of applying the Mann-Kendall test and Sen’s slope for seasonal long-term trends of V200 at the Terskol Observatory.

Season	Sen Estimator Q (in Year)	MK Test Significance
Winter	+0.054 m/s	Not significantly
Spring	+0.048 m/s	Not significantly
Autumn Summer	−0.057 m/s −0.058 m/s	Not significantly Not significantly

.

The long-term changes of V200 are not significant trends in all seasons, according to the MK Test. The V200 decreased in winter and spring. The Sen’s slope is 0.054 m/s and 0.048 m/s, respectively. The V200 increases in autumn and summer. The Sen’s slopes are 0.057 m/s and 0.058 m/s, respectively. As a result, there are opposite tendencies in the V200 behavior, that positive and negative for astronomical observations.

4. Conclusions

In this paper, we present the long-term variations of astroclimatic conditions from 1980 to 2022 by using the data set from ERA5 reanalysis at the Terskol Observatory (coordinates 43°16′29″ N, 42°30′03″ E). The long-term trends of V200, PWV, and TCC are examined for significance using the Mann–Kendel test and Sen’s slope. For the analysis of the long-term trend of the parameters, the specific distribution of each parameter is of particular importance. As such, the probability distribution and seasonal behavior of V200, PWV, and TCC are presented.

Below, we summarize key points about the trends and parameters:

(i)

The long-term trend of wind speed V200, as a parameter determining adaptive optics operations, was not significant during the period from 1980 to 2022. The V200 had a small negative change, with a Sen’s slope 0.008 per year. This tendency of V200 is positive for the operation of adaptive optics at the telescopes of the Terskol Observatory.

(ii)

The monthly average values of wind speed at the 200 hPa level less than 25 m/s were observed in 70% of the considered period of 1980–2022, while a V200 less than 15 m/s appeared 25% of the time. The lowest median value of V200 was 10 m/s in May. The highest median value of V200 was 31 m/s in July.

(iii)

The long-term trend of PWV was not significant during the period from 1980 to 2022. The PWV had a small positive change, with a Sen’s slope of 0.004 per year. In addition, trend is significant in summer according to the MK tests at 95% confidence level. The Sen’s slope is 0.015 mm per year. The tendency of PWV may have a negative influence on IR astronomical observations with the telescopes at the Terskol Observatory.

(iv)

There were 45% of the monthly mean PWV values less than 6 mm and about 3% of PWV values less than 3 mm in the considered period of 1980–2022, corresponding to fair and excellent conditions for IR observations. The suitable season for IR observations is winter. The lowest median value of PWV was 3.4 mm in February.

(v)

The long-term trend of TCC was a significant negative trend from 1980 to 2022, with a slope of 0.133 per year. Additionally, the loss of TCC was detected in all seasons, especially in summer from 60% to 45%. As a result, the change in TCC significantly increased the available time for astronomical observation as a key parameter for characterizing the quality of the astronomical site.

(vi)

The annual average TCC was 62% on average per year. The longest cloudless time was detected by AAG CloudWatcher cloud detector in October–November. In addition, more cloudiness is observed during the day than at nighttime at the Terskol Observatory.

The long-term trends of astroclimatic parameters above the Terskol Observatory probably reflect impacts of climate change. However, the changes in climate do not have only negative effects on the operation of ground-based astronomical observatories but can also have a positive effect on the quality of astronomical observations the Terskol Observatory shows, because the scientific output capacity of the telescope and optimal scheduling are determined by astroclimatic conditions of the site.

These results will be used to optimize observation strategies and instrumental upgrades at the telescopes of the Terskol Observatory.