Investigation of the Global Spatio-Temporal Characteristics of Astronomical Seeing

Abstract

Astronomical seeing is important for monitoring the atmospheric environment, observation scheduling and management, and selecting astronomical sites. This study first attempts to establish a near-global astronomical seeing map by employing the fifth European Centre for Medium-Range Weather Forecasts Reanalysis (ERA5) data combined with the estimated model. Then, some example sites’ results from ERA5 were compared against the astronomical seeing results from the balloon-borne microthermal measurements and the differential image motion monitor (DIMM) instrument. The global astronomical seeing variations exhibit large spatial dependence. The best seeing areas are generally discerned over the mid-latitude regions, consistent with the regions of the European Southern Observatory and Tibetan Plateau. In addition, the astronomical seeing values of the Tibetan Plateau in spring are better than in the other seasons. The site results from ERA5 show that the astronomical seeing values of some example sites are generally consistent with the measurements. Overall, the global astronomical seeing map presented in this study can provide a reference and basis to further understand the astronomy site selection and optoelectronics equipment observation path selection.

1. Introduction

The Earth’s atmospheric turbulence is a key parameter in determining the performance of ground-based telescopes and interferometers. Atmospheric turbulence is caused by random fluctuations of the atmosphere, mainly due to wind shear caused by the drag of airflow on the Earth’s surface, differences in the heating of different locations on the Earth’s surface by solar radiation, or thermal convection [1,2]. Additionally, knowledge of the atmospheric optical turbulence characteristics is equivalent to knowing the variability of astronomical seeing. Astronomical seeing (called ’seeing’ in the following) represents the angular size of stellar images blurred by atmospheric turbulence. It is defined in terms of the full width at half-maximum of a star image on the focal surface of a large aperture telescope measured in arcseconds. Seeing is an essential parameter for assessing the quality of astronomical sites at optical/infrared wavelengths and selecting astronomical observations [3,4,5]. Therefore, it is necessary to know global seeing data to evaluate astronomical seeing conditions. Weaker turbulence will correspond to a small seeing.

Atmospheric optical turbulence represents the characteristics of the refractive index structure constant $C_n^2$. Several techniques have been implemented to measure the atmospheric turbulence profile [$C_n^2\left(h\right)$] [6,7,8,9,10,11,12]. The most widely used is balloon-borne microthermometry [13], which has the characteristics of high vertical resolution. In addition, seeing is a function of $C_n^2$ integrated over the light’s propagation path, which can be acquired from $C_n^2$ vertical profiles [14,15]. The measurement instruments such as the differential image motion monitor (DIMM) [16,17,18,19,20,21] and the multi-aperture scintillation sensor (MASS) [22,23] are widely used to measure seeing data. Although many site-testing programs have been carried out worldwide, global long-term seeing data are unavailable and impractical by employing instruments due to observation difficulties and financial issues. Alternatively, adopting reanalysis data combined with turbulence estimate models is convenient, available, and economical. There are many typical accessible global-scale atmospheric reanalysis data, including ERA5 (the fifth European Centre for Medium-Range Weather Forecasts Reanalysis) data [24], the MERRA-2 (Modern-Era Retrospective analysis for Research and Applications, version 2) reanalysis data [25], JRA-55 (Japanese 55-yr) reanalysis data [26], and CFSv2 (Climate Forecast System Reanalysis, version2) data [27]. Compared to these global reanalysis products, the ERA5 dataset provides atmosphere parameters every hour with a horizontal resolution of 31 km and 137 vertical pressure levels, which exhibits higher temporal and spatial resolution [28,29].

Based on measurement experiments, scholars have summarized different atmospheric optical turbulence estimation models to model realistic atmospheric turbulence conditions. The simplest models of atmospheric optical turbulence are empirical models [30,31,32], which only require the altitude parameter. However, this kind of model lacks spatial and temporal characteristics. Another model is the optical turbulence parameterization model, such as the Tatarskii [1], which incorporates more meteorological parameters. According to Tatarskii’s theory, scholars have conducted vast research analysis [33,34]. In addition, considering the complexity and variability of atmospheric turbulence, more meteorological parameters need to be accounted for in the atmospheric estimation models. Subsequently, several outer-scale models have been developed to calculate the $C_n^2$ profile based on the Tatarskii theory, including the Dewan model [35], the HMNSP99 model [36], and the Thorpe model [37]. However, the Thorpe model only contains temperature variables, while the Dewan model includes wind shear. It is worth noting that the HMNSP99 model contains temperature gradients in addition to wind shear. Meanwhile, early efforts show that the HMNSP99 model has been widely used in different conditions [14,24,38,39], such as marine environments and plateau areas. Although the results of turbulence detail changes that deviate from the measurements at some altitudes, the HMNSP99 model can be used as a practical method to convert the global meteorological reanalysis data into global three-dimensional quantitative astronomical seeing characteristics.

Considering the complexity of turbulence instrumentation measurements and the spatial-temporal measurement limitations for the large-scale experimental area, this study quantified and visualized the global astronomical seeing data based on the REA5 reanalysis data, providing a reference for ground-based astronomy to select the best candidate sites and schedule the best observation time. Subsequently, worldwide seasonal seeing variation characteristics are presented. Additionally, some example site seeing values from the ERA5 data, such as Da Qaidam, Haikou, Rongcheng, Ali, Daocheng, Muztagh-ata, and Lenghu, are validated by comparison with corresponding radiosonde measurements and DIMM data.

This paper is organized as follows: Section 2 describes the measurement of in situ balloon-borne microthermal and DIMM, the ERA5 data and the methodology in this study. In Section 3, the results based on the global astronomical seeing map are presented. In addition, some statistical site results from REA5 data are compared to the measurements. Finally, the conclusions are provided in Section 4.

2. Data and Methodology

2.1. Balloon-Borne Microthermal and DIMM Measurements

High-resolution micro-thermometer radiosonde measurements were performed in Da Qaidam, Haikou, and Rongcheng in August 2020, from March to April 2018, and November 2018, respectively. The detailed distribution of geographical locations and terrain heights are displayed in Figure 1. Da Qaidam, Haikou, and Rongcheng are marked by black spots. The Da Qaidam site (37.74$°$N, 95.35$°$E, Qinghai) is located on the northern edge of the Qaidam Basin above the Tibetan Plateau and has a typical inland highland desert climate, with an altitude of about 3200 m above sea level (ASL). The Haikou site (20.05$°$N, 110.19$°$E, Hainan) is located in the northern region of Hainan Island, with an altitude of about 15 m ASL. It is located at the northern edge of the low tropics and has a tropical monsoon climate. The Rongcheng site (36.46$°$N, 122.11$°$E, Shandong) is located in the eastern-most region of the Shandong Peninsula, surrounded by the Yellow Sea to the north, east, and south, with an altitude of about 80 m ASL. In addition, the site has a warm temperate continental monsoonal humid climate.

The micro-thermometer are balloon-borne payloads that measure the in situ temperature structure coefficient ($C_T^2$) using a pair of fine wire probes separated horizontally by 1 m. For visible and near-infrared wavelengths, the random fluctuations in the refractive index is mainly caused by the temperature effect. $C_T^2$ is a proportional constant in the inertial sub-range form of the temperature structure function $D_T(r,h)$ [40], defined by

$$C_T^2(r,h)=\frac{D_T(r,h)}{r^{2/3}},l_0\ll r\ll L_0,$$

(1)

where $C_T^2$ is the temperature structure constant in ${\mathrm{K}}^2{\mathrm{m}}^{-2/3}$. $D_T(r,h)$ is defined as one of the statistics describing temperature disturbance from two micro-temperature probes with distance r (in m), and is given by

$$D_T(r,h)=\langle {[T\left(\overrightarrow{x}\right)-T(\overrightarrow{x}+\overrightarrow{r})]}^2\rangle ,l_0\ll r\ll L_0,$$

(2)

where $D_T(r,h)$ denotes the temperature structure function, with units $K^2$. The angle bracket $\langle \rangle$ represents the ensemble average, $T\left(\overrightarrow{x}\right)$ and $T(\overrightarrow{x}+\overrightarrow{r})$ in K denote the temperature at the two points separated by r, while $l_0$ and $L_0$ are the inner and outer scales of the atmospheric turbulence, in metres.

Considering the Gladstone formula [41], the relationship between the index of refraction structure constant ($C_n^2$) and the temperature structure constant ($C_T^2$) are expressed as

$$C_n^2\left(h\right)={\left[79\times {10}^{-6}\frac{P\left(h\right)}{T^2\left(h\right)}\right]}^2{C}_T^2(r,h),$$

(3)

where $C_n^2\left(h\right)$ is the index of the refraction structure constant, with units ${\mathrm{m}}^{-2/3}$, T is the absolute atmospheric temperature in K, and P is the air pressure in hPa.

In this study, the micro-thermometer is attached to the meteorological micro-thermometer measurement system and is carried into the atmosphere by a balloon to carry out meteorological radiosonde measurements at Da Qaidam, Haikou, and Rongcheng. Figure 2 displays the balloon-borne micro-thermometer measurement system. The device comprising two platinum wire sensors of 10 $\mathsf{\mu }$m in diameter employed for micro-thermometer radiosonde measurements is shown in the left panel in Figure 2. Two resistance wire probes are employed to measure the temperature difference across a 1 m horizontal distance as the instrument ascends through the atmosphere at around 5 m s${}^{-1}$. In addition, two probe wires have a linear resistance-temperature coefficient and can be seen as two legs of a Wheatstone bridge. The bridge output voltage is amplitude-modulated based on the temperature difference between the probes. Subsequently, this voltage is amplified, bandpass filtered and then averaged. The frequency response range of the micro-thermometer is 0.05–30 Hz, and the noise level of the sensors and electronic processing of the signals corresponds to a temperature difference of 0.002 K [14,15,38,42].

In the sounding experiment, the altitude range of the micro-thermometer measurements is from the surface to about 30 km above sea level. Since the balloon-borne payload is attached to a meteorological radiosonde, air temperature, wind speed, air pressure, and relative humidity information are also relayed to the ground station. Then, the signal is transmitted to the ground station along with the standard meteorological data. In addition, all of the flights were released during the early morning or late evening at local time. During the sounding measurements, some data were abnormal with insufficient height because of the strong winds. After eliminating the abnormal data, 29, 30, and 14 profiles from measurements were reserved at the Da Qaidam, Haikou, and Rongcheng field campaign sites, respectively.

The DIMM is now a widely accepted instrument and has become a standard assessment for integrated atmospheric optical turbulence and a good integrated seeing measurement. DIMM measures the integrated optical turbulence through the entire atmosphere, providing an estimate of the total atmospheric seeing [16]. Note that the DIMM instruments were installed on a roof or tower several metres above the ground to avoid near-ground turbulence at the different testing sites.

The DIMM instrument at the Ali observatory is displayed in Figure 3. The DIMM at the Ali observatory is a small transportable instrument that uses a differential technique to accurately measure astroclimatic seeing conditions. Seeing is measured via the differential image motion in two sub-aperture images of a star. In particular, this measurement technique has the advantage of being insensitive to telescope and ground vibrations [43,44,45]. DIMM measures the integrated seeing from the telescope pupil to the top of the atmosphere. In addition, DIMM instruments have been widely used for many other different site-selection campaigns, such as Daocheng, Muztagh-ata and Lenghu [5,44,45,46]. The locations and topographic distribution of Ali, Daocheng, Muztagh-ata and Lenghu are shown in Figure 1. The DIMM measurements were carried out from March 2017 to February 2019 at Ali, Daocheng, and Muztagh-ata. In addition, the site testing campaign of Lenghu was conducted between October 2018 and 2020.

2.2. Methodology

Atmospheric optical turbulence is detrimental to ground-based astronomy. The estimated models of optical turbulence have been widely used to calculate vertical profiles of $C_n^2$, the refractive index structure constant from standard radiosonde meteorological parameters [35]. Based on the locally uniform isotropic theory, $C_n^2$ can be estimated using the Tatarskii equation as below [1]

$$C_n^2=2.8{\left[\frac{79\times {10}^{-6}P}{T^2}\left(\frac{\mathrm{d}T}{\mathrm{d}h}+\gamma \right)\right]}^2{L}_0^{4/3},$$

(4)

where T is the absolute atmospheric temperature in K, P indicates the pressure in hPa, $\gamma$ denotes the dry adiabatic lapse rate ($9.8\times {10}^3$ K/m), and h denotes the height above ground. $L_0$ is the outer scale of atmospheric turbulence.

Ruggiero [36] summarized the HMNSP99 outer-scale model based on the sounding data. The HMNSP99 model is the function of wind shear (S) and the temperature gradient (dT/$dh$). Its specific expression is

$$L_0^{4/3}=\left\{\begin{array}{c}{0.1}^{4/3}\times {10}^{0.362+16.728S-192.347\frac{\mathrm{d}T}{\mathrm{d}h}},\mathrm{Troposphere}\hfill \\ {0.1}^{4/3}\times {10}^{0.757+13.819S-57.784\frac{\mathrm{d}T}{\mathrm{d}h}},\mathrm{Stratosphere}\hfill \end{array}\right.$$

(5)

where S represents the vertical shear of horizontal velocity, defined as

$$S=\sqrt{{\left(\frac{\partial u}{\partial h}\right)}^2+{\left(\frac{\partial v}{\partial h}\right)}^2},$$

(6)

where u and v are the north–south and east–west wind components, respectively.

Adaptive optics (AO) and diffraction-limited infrared instruments are planned as future upgrades to the telescope. To maximize and optimize the performance of the telescope and its instrument suite, it is crucial to find more candidate sites that are excellent both in terms of their astronomical performance and operation as well as maintenance. Astroclimatic seeing plays an important role in the design and optimization of AO systems. Seeing stands for the angular size of stellar images influenced by atmospheric turbulence and is usually computed by integrating the optical turbulence profiles with respect to the zenith [3]. Seeing is referred to as the zenith direction, and its specific parameter is given as follows:

$$\epsilon =5.25{\lambda }^{-1/5}{\left[{\int }_0^{\infty }{C}_n^2\left(h\right)\mathrm{d}h\right]}^{3/5}.$$

(7)

where $\epsilon$ denotes astronomical seeing in arcseconds. Small values better represent astronomical seeing. $\lambda$ is the optical wavelength, and $\lambda$ = 550 nm for this study.

2.3. ERA5 Data

ERA5 is the fifth generation ECMWF reanalysis data for the global climate and weather, replacing the ERA-Interim reanalysis data publicly available from 1950, with climate data store entries for 1950–1978 (preliminary back extension) and from 1959 onwards. ERA5 adopts Cycle 41r2 of the integrated forecasting system (IFS) and is based on the 4D-Var data assimilation method. ERA5 presents global data with flexible regional options for extended periods, assimilated by combining model data with observations from across the world into a globally complete and consistent dataset using the laws of physics. ERA5 data contain a variety of atmospheric parameters with a horizontal resolution of 31 km, 137 vertical levels from the surface to 0.01 hPa, and an hourly output, encompassing absolute temperature, relative humidity, and horizontal wind speed components (u and v). The specific information on the ERA5 data is listed in

Table 1. The specific information of ERA5 data.

Horizontal Coverage	Horizontal Resolution	Vertical Resolution	Vertical Coverage	Temporal Coverage	Temporal Resolution
Global	0.25$°$ × 0.25$°$	137 level	1000 hPa to 1 hPa	1959 to present	Hourly

.

In addition, ERA5 data in the free atmosphere have quite good reliability and resolution, both horizontally and vertically (137 levels) [28], and capture more detailed atmospheric parameters than previous lower-resolution global reanalysis data. In this study, ERA5 data from some example sites have a resolution of 0.25$°$ latitude and 0.25$°$ longitude. The specific information of ERA5 data at different example sites is tabulated in

Table 2. The specific information of ERA5 data at different example sites.

Name	Site (lon, lat)	ERA5 (lon, lat)	Time (UTC)
Da Qaidam	95.35$°$E, 37.74$°$N	95.25$°$E, 37.75$°$N	Aug. 2020
Haikou	110.19$°$E, 20.05$°$N	110.25$°$E, 20.00$°$N	Apr. 2018
Rongcheng	122.11$°$E, 36.46$°$N	122.00$°$E, 36.50$°$N	Nov. 2018
Ali	80.06$°$E, 32.31$°$N	80.00$°$E, 32.25$°$N	Mar. 2017 to Feb. 2019
Daocheng	100.11$°$E, 29.11$°$N	100.00$°$E, 29.00$°$N	Mar. 2017 to Feb. 2019
Muztagh-ata	74.90$°$E, 38.33$°$N	75.00$°$E, 38.25$°$N	Mar. 2017 to Feb. 2019
Lenghu	93.89$°$E, 38.61$°$N	94.00$°$E, 38.50$°$N	Oct. 2018 to 2020

.

3. Results and Discussion

3.1. Global Distribution Characteristics of Seeing

Figure 4 depicts the spatio-temporal distribution characteristics of astronomical seeing worldwide with zonal mean seeing. The first row corresponds to the seeing results in DJF and MAM; while the second row shows the JJA and SON seeing results. Note that the blue colour indicates the good-seeing areas in each sub-graph. It is observed from Figure 4 that the worldwide seeing map exhibits large spatial dependence. The western part of China, such as the Tibetan Plateau (latitude of ∼30$°$N), shows significantly smaller seeing values. Additionally, there is a blue zonal band surrounded by the Andes (at a longitude of ∼70$°$W) in South America. The regions of low seeing values are broadly located in the mid-latitude regions within Asia, North America, and South America, such as the Tibetan Plateau and Cordillera Mountains, including the Andes in all seasons. These are regions where important astronomical stations are located, such as Ali, Daocheng, and Cerro Paranal, and are consistent with the locations of the important astronomical observatories from the European Southern Observatory (ESO) and Tibetan Plateau. In addition, it is evident that the seeing values over the Tibetan Plateau are smaller than those of other areas during all seasons. Particularly, the astronomical seeing values over the Tibetan Plateau are better in spring than in other seasons, seen in Figure 4. Furthermore, the seeing in Africa, North America, and South America notably depicts good-seeing areas, especially in the Cordillera Mountains. In comparison, seeing over the Cordillera Mountains appears to slightly change during the seasons.

Here the spatio-temporal distribution characteristics of astronomical seeing can be quantified by computing with zonal mean seeing in each sub-graph (right panel) from Figure 4. It is clear that most of the zonal mean seeing values are consistent with spatial distribution of the astronomical seeing, particularly in the mid-latitude regions. The zonal mean seeing results also show that the best-seeing areas are generally consistent with the regional scope of international observatory stations. Moreover, the Antarctic has small seeing values, which exhibited a similar distribution during all seasons.

3.2. Verification of the Example Sites

As we all know, it is difficult to validate global-scale seeing values due to the lack of seeing values from instrumental measurements. In this section, statistical analysis of the seeing values between the measurements and ERA5 data was conducted at some example sites to verify the model’s reliability. Note that the actual seeing values which were used for comparison were computed from in situ balloon-borne micro-thermometer measurements and reported from previous papers. The measured seeing values at Ali, Daocheng, Muztagh-ata, and Lenghu were acquired from the DIMM instrument [5,44,45].

Table 3. Comparison of the astronomical seeing values between the measurements and the ERA5 data at some example sites. Note that 25% and 75% refer to the first and third quartiles of the seeing values from the statistical data. In addition, the measured seeing values at Da Qaidam, Haikou, and Rongcheng are calculated from the sounding measurements; while the seeing values at Ali, Daocheng, Muztagh-ata and Lenghu are measured from the DIMM instrument.

Site Name	Seeing (Arcseconds) (Median [25%, 75%])
	Measurement	ERA5
Da Qaidam	1.06 [0.72, 1.75]	0.88 [0.85, 0.93]
Haikou	1.15 [0.74, 2.32]	1.17 [1.15, 1.20]
Rongcheng	1.09 [0.98, 1.38]	1.23 [1.17, 1.30]
Ali	1.08 [0.88, 1.39] [44]	0.87 [0.79, 1.00]
Daocheng	1.01 [0.84, 1.22] [44]	0.96 [0.85, 1.10]
Muztagh-ata	0.82 [0.64, 1.06] [44]	0.85 [0.78, 0.92]
Lenghu	0.75 [0.61, 1.03] [5]	0.96 [0.88, 1.07]

lists the statistical median and the first and third quartile values of the astronomical seeing values from the measurements and ERA5 data at several sites. The median seeing values from sounding measurements are 1.06, 1.15, and 1.09 arcseconds, and the corresponding values from ERA5 are 0.88, 1.17, and 1.23 arcseconds, at Da Qaidam, Haikou, and Rongcheng, respectively. The statistical median seeing values from ERA5 generally revealed the local seeing characteristics at Da Qaidam, Haikou, and Rongcheng. However, the scope of the first and third quartile values from the sounding measurements appear to be wider compared with the ERA5 data. This may result from the wider variety of climatic conditions during balloon measurements and the differences in maximum detection height in the calculation process. A clearer picture will emerge from the acquisition of a bigger dataset.

In addition, from Table 3, the median seeing from DIMM measurements are 1.08, 1.01, 0.82, and 0.75 arcseconds at Ali, Daocheng, Muztagh-ata, and Lenghu, respectively. Next, the distribution characteristics of the seeing results from ERA5 are introduced in detail at Ali, Daocheng, Muztagh-ata, and Lenghu. Firstly, the statistical seeing results from the ERA5 data at Ali, Daocheng, and Muztagh-ata are shown in Figure 5. The left panel of Figure 5 shows the histogram of all seeing data for each site. The statistical seeing values follow a log-normal distribution. The median seeing value from ERA5 at Ali is 0.87 arcsecond, and about 75% of the data are below 1 arcsecond.

Additionally, the median seeing values from ERA5 at Daocheng and Muztagh-ata are 0.96 and 0.85 arcseconds, respectively. The histogram distribution of seeing from ERA5 generally reveals the measured distributional features at the three sites, although the median values deviate slightly from the DIMM measurements [44]. Moreover, Figure 5 (right panel) illustrates the monthly statistical boxplot of the seeing values from ERA5 at the three sites. In contrast, the seeing values from the boxplots from ERA5 and DIMM measurements [45] are consistent with the general changing trend at the three sites. Note that the median seeing values from ERA5 do not exhibit the good characteristics of the measured seeing values in May 2017 at Ali from the boxplot. As reported in [45], the DIMM was previously installed on the 3 m rooftop, and after May 2017, DIMM measurements were carried out on a 5 m tower. Nevertheless, the cross-comparison results from the DIMM measurements indicate that the seeing values at 3 m and 5 m are not noticeable different. As for the monthly statistical results of seeing at Daocheng, the ERA5 results generally showed the seeing characteristics in August 2017. In addition, the seeing results from the ERA5 data at the Muztagh-ata site exhibited poor seeing characteristics in July and August, consistent with the actual DIMM measurement results at the Muztagh-ata site. Similarly, the scope of the first and third quartile values of the seeing values from the DIMM measurements in Table 3 seem to be slightly wider than the ERA5 data results. The reason for this may be that the DIMM data obtained in the process is affected by the wider variety of climatic conditions. Furthermore, the DIMM instruments are installed on top of a tower or observation building several metres from the ground. In addition, a few months of seeing data were missing due to reinforcing the tower.

Moreover, the statistical histogram of the seeing data from ERA5 at Lenghu is displayed in Figure 6. The seeing results from ERA5 have a similar distribution compared with the DIMM measurements [5]. From the figure, one can see that the median seeing value from ERA5 is 0.96 arcseconds. Although the median value obtained by ERA5 is higher than the median measured seeing value of 0.75 arcseconds, about 75% of the statistical seeing values from ERA5 are lower than 1.07 arcseconds, similar to the statistically measured results of the DIMM measurements. The seeing distribution from ERA5 in Figure 5 and Figure 6 visualizes the general distribution of the astronomical seeing values at Ali, Daocheng, Muztagh-ata, and Lenghu compared to the DIMM measurements, showing a certain ability to reconstruct the distribution of the seeing values at these sites, thus providing a potential reference for selecting optoelectronic equipment observation path selection. It also provides a new idea for finding promising astronomy sites, and then evaluating them by balloon-borne microthermal and DIMM measurements.

4. Conclusions

In this study, the global astronomical seeing distribution map was presented from the ERA5 reanalysis data combined with the estimated model. Subsequently, the spatio-temporal distribution characteristics of astronomical seeing worldwide were analysed with the seasonal variation results. Furthermore, the verification of the seeing results from ERA5 and the corresponding measurements, including sounding measurements at Da Qaidam, Haikou, Rongcheng sites and DIMM data at Ali, Daocheng, Muztagh-ata, and Lenghu. The results are summarized as follows.

The global median seeing areas generally display a large spatial dependence, discerned over the mid-latitude regions such as the Andes in South America and the Tibetan Plateau in the western part of China. The seeing values over the Tibetan Plateau and the Andes are smaller than the other areas in all seasons. The astronomical seeing values on the Tibetan Plateau are better in the spring than in other seasons. Additionally, several areas such as the Cordillera Mountains from North America and some areas in Africa also exhibit potential candidate sites for observatory stations. The results of the zonal mean seeing values demonstrate its capabilities by capturing the best seeing areas generally located in the mid-latitude regions, such as the Tibetan Plateau and the Cordillera Mountains, including the Andes in all seasons, remarkably coherent with international observatory stations at the ESO and Tibetan Plateau.

For the statistical seeing results at some example sites, the results from the ERA5 data are generally reasonable compared to the sounding and DIMM measurements. Although the seeing values from the ERA5 data are not completely consistent with the measured values at these sites, the results achieved here provide an attempt at acquiring seeing values worldwide from the high spatio-temporal resolution ERA5 data, which provides a reference for research and the selection of observatories.