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28 February 2026

Daytime Atmospheric Turbulence Intensity and Distribution at the Fuxian Lack Solar Observatory During Winter

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1
National Laboratory on Adaptive Optics, Chengdu 610209, China
2
Institute of Optics and Electronics, Chinese Academy of Sciences, Shuangliu, Chengdu 610209, China
3
School of Electronics and Information Engineering, Guang’An Institute of Technology, Guang’an 638500, China
4
University of Chinese Academy of Sciences, Beijing 100049, China
Atmosphere2026, 17(3), 254;https://doi.org/10.3390/atmos17030254
This article belongs to the Section Atmospheric Techniques, Instruments, and Modeling
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Abstract

Atmospheric turbulence is a critical factor limiting the imaging resolution of ground-based solar telescopes. This study presents a systematic investigation of the intensity and vertical distribution of daytime atmospheric turbulence during winter at the Fuxian Solar Observatory, using data acquired from the 1-meter New Vacuum Solar Telescope (NVST) with its Ground Layer Adaptive Optics (GLAO) system and a custom-developed wide-field Shack–Hartmann wavefront sensor. Statistical results reveal a median Fried parameter ( r 0 ) of 8.25 cm at 500 nm, indicating generally favorable daytime observing conditions. A distinct diurnal variation in r 0 was observed: values were higher in the morning and afternoon but decreased significantly around noon due to enhanced ground-layer heating. Vertical turbulence profiling showed that approximately 52.8% of the total turbulence strength originates from the ground layer, and 93.1% is confined below 4 km, with only weak turbulence detected at higher altitudes. This study establishes the first statistical turbulence profile model for the Fuxian Solar Observatory site during winter daytime, providing crucial insights for optimizing high-resolution solar observations and the design of multi-conjugate adaptive optics systems.

1. Introduction

Atmospheric optical turbulence poses fundamental limitations for ground-based astronomical observations by significantly degrading image quality through random wavefront perturbations [1,2,3]. These perturbations are induced by temperature fluctuations and consequent refractive index variations in the atmosphere, manifesting as image blurring, jitter, and distortion that severely constrain telescope resolution [4,5,6,7,8]. For solar observations specifically, daytime turbulence intensity typically exceeds nocturnal levels and exhibits more rapid temporal variations, presenting enhanced challenges for high-resolution solar imaging [9,10,11,12].
The Fuxian Solar Observatory [13,14], situated on the shores of Fuxian Lake in Yuxi City, Yunnan Province, China (geographic coordinates: 24°34′48″ N, 102°53′01″ E; altitude: 1720 m), represents a premier solar physics research facility housing advanced instruments including the NVST [14,15]. The site’s exceptional atmospheric conditions, characterized by low water vapor content and abundant clear-sky days, make it particularly suitable for high-precision solar observations. To fully exploit NVST’s capabilities for high-resolution solar studies, comprehensive investigation of local atmospheric turbulence properties particularly daytime intensity and vertical distribution characteristics is essential [16].
The vertical distribution of atmospheric turbulence, typically described by the refractive index structure constant C n 2 ( h ) as a function of altitude h, characterizes how optical turbulence strength varies along the propagation path. This distribution is crucial for wide-field adaptive optics design, as it determines the altitude and intensity of turbulent layers that adaptive optics systems must correct. Integrated turbulence parameters, such as the Fried parameter r 0 , offer a single statistical measure of the overall turbulence strength. However, the vertical distribution of turbulence reveals the altitudes at which it is concentrated. This information is essential for multi-conjugate adaptive optics (MCAO), which enlarges the corrected field of view by addressing turbulence in distinct layers separately. Thus, knowledge of vertical distribution enables the optimization of deformable mirror conjugate heights and control strategies, which is key to overcoming the isoplanatic angle limitation and achieving wide-field high-resolution imaging. Additionally, turbulence profile information provides valuable input for telescope site evaluation, observational strategy formulation, and post-processing algorithms.
The vertical distribution of atmospheric turbulence plays a crucial role in the design and performance evaluation of wide-field adaptive optics systems [16]. Since turbulence contributions vary significantly across different altitude layers, detailed understanding of vertical turbulence structure facilitates optimized design of multi-conjugate adaptive optics systems, thereby enhancing correction performance.
In recent years, extensive atmospheric turbulence profiling campaigns have been conducted at major astronomical observatories worldwide [7,9,11,17,18,19,20,21,22]. Internationally renowned facilities including Mauna Kea Observatory [17,18,19] in Hawaii and Paranal Observatory [20,21,22] in Chile have established systematic turbulence monitoring programs. These studies consistently demonstrate that superior astronomical sites typically exhibit low boundary layer heights and weak free-atmosphere turbulence.
Significant progress has also been achieved in site characterization studies within China [6,8,12,23,24]. Site testing campaigns at potential premium locations including Lenghu in Qinghai [25,26,27] and Ali in Tibet [28,29] have revealed internationally competitive atmospheric conditions. Specifically, the Lenghu site on Saishiteng Mountain demonstrates median seeing of 0.75 arcseconds, establishing it as a promising astronomical location [30].
Despite these advances, studies focusing specifically on vertical turbulence distribution at solar observatories, particularly during daytime conditions, remain relatively limited. Solar observations face unique challenges including pronounced ground-layer thermal effects and complex atmospheric convection patterns. Therefore, detailed investigation of daytime turbulence vertical distribution at Fuxian Solar Observatory holds significant importance not only for enhancing NVST’s observational capabilities but also for providing valuable reference for the international solar physics community.
This research employs NVST’s GLAO system [31] coupled with an independently developed turbulence measurement system to conduct continuous monitoring of atmospheric turbulence at Fuxian Solar Observatory during winter daytime conditions. The study focuses on statistical characterization of turbulence intensity and evolution patterns, with the objective of establishing a comprehensive daytime turbulence model for the site. This study presents the first systematic report on the characteristics of daytime vertical turbulence distribution during winter at the observatory, thereby filling a significant gap in the atmospheric optical parameters previously available for this site. The identified patterns of daytime turbulence variation offer direct guidance for optimizing the performance of adaptive optics systems in solar observations, enabling the determination of optimal observation windows. Furthermore, the findings provide valuable quantitative knowledge for the real-time optimization of GLAO systems. This advancement can effectively reduce the burden on wavefront sensors and enhance the efficiency of atmospheric correction.

2. Instrumentation and Data Acquisition

2.1. NVST GLAO System

The NVST is specifically designed to achieve high spatial and temporal resolution solar observations. To compensate for wavefront distortions induced by atmospheric turbulence, NVST incorporates a GLAO system capable of correcting turbulence effects over an extended field of view.
The core of NVST’s GLAO system comprises a real-time wavefront sensing and correction subsystem. Wavefront sensing is accomplished using a Shack–Hartmann wavefront sensor (SH-WFS) configured with an 8 × 8 subaperture array, corresponding to different regions of the telescope entrance pupil. The system employs high-frame-rate CMOS cameras for wavefront slope measurements at rates up to 2000 Hz, enabling effective tracking of rapid atmospheric turbulence variations.
In this study, we utilize wavefront slope data recorded by the GLAO system, combined with atmospheric turbulence inversion algorithms, to derive integrated turbulence intensity information and distribution characteristics. A detailed description of this real-time measurement instrumentation is provided by Ran et al. [32].

2.2. Custom-Developed Turbulence Profiling System

Given the limitations of GLAO-based systems for comprehensive monitoring tasks, we implemented a dedicated turbulence measurement system to serve as NVST’s primary observational tool for atmospheric characterization. Incorporating atmospheric turbulence statistical parameter measurement capabilities enables enhanced long-term turbulence monitoring objectives.
The wide-field SH-WFS constitutes the core hardware for atmospheric turbulence parameter measurements. To meet the stringent requirements of this task, we developed a custom-built wide-field SH-WFS. This sensor was specifically designed and fabricated for this study, incorporating optimized optical and detection elements tailored to the needs of atmospheric turbulence characterization. Although the design draws upon prior experience with similar systems, the entire assembly—from the microlens array to the detector has been redesigned to ensure optimal performance for the present application.
After comprehensive evaluation, we selected 705 nm as the operational wavelength for the wide-field SH-WFS. The selection of 705 nm as the operational wavelength was primarily based on three practical considerations: the physical size constraints of the instrument, the available space on the optical platform, and the suitable wavefront sensing bands accessible within NVST’s optical system. This band is situated at the rear section of the imaging system, minimizing interference with other instrumental components. Additionally, the pupil plane position at this wavelength facilitates straightforward integration of the wide-field SH-WFS. The WFS installation schematic is presented in Figure 1.
Figure 1. Schematic diagram of WFS installation on NVST’s optics system. The numbers in the figure represent wavelengths in picometers (pm).
Leveraging experience from GLAO SH-WFS design, we selected the Mikrotron EoSens 3CL as the detection camera, with microlens subapertures sized at 0.576 mm and focal length of 14 mm. The Hartmann subaperture arrangement projected onto the 1-m telescope aperture forms a 9 × 8 configuration, with each subaperture covering a 42 arcsecond field of view, as illustrated in Figure 2. Considering the dimensions of the microlens array and the pupil size in the 705 nm band, we designed a collimating beam reduction system to match the pupil dimensions to the microlens array. Furthermore, accounting for available space on the optics platform and predetermined WFS location, we completed the optical support structure design while maintaining acceptable tolerances. Corresponding optical and mechanical components were integrated onto a single steel baseplate to facilitate subsequent alignment procedures.
Figure 2. The microlens arrangement of the SH-WFS. The outer large red circle represents the pupil of the telescope, while the inner small circle is the obscuration of the pupil by the secondary mirror.
Following fabrication, optical and mechanical components underwent integrated alignment and calibration. System calibration was performed using collimated laser beams to characterize optical performance. Additionally, calibration aberrations, pixel resolution, and Zernike aberration coefficients were determined during this process. After successful commissioning, the SH-WFS was permanently installed within NVST’s optics system. Using solar illumination, the WFS was positioned appropriately with microlens array conjugate to the pupil plane.
For computational requirements associated with real-time atmospheric turbulence measurements, we selected a Lenovo ThinkStation M540 host computer, balancing service scalability and cost-effectiveness. The host provides PCIe connectivity for interfacing with the Mikrotron EoSens 3CL camera. Additionally, considering camera power management, we implemented a relay module-based power control system enabling remote power control, as depicted in Figure 3.
Figure 3. Schematic of camera–computer interface and power control system.
We developed comprehensive software infrastructure to support SH-WFS wavefront measurement and atmospheric turbulence characterization. The data acquisition and processing system, whose architecture is illustrated in Figure 4, was developed on the Qt open-source platform. The core software runs on a combination of C++ 11 and Matlab R2018b, and implements functionality for camera power control, parameter configuration, image acquisition, flat/dark field correction, wavefront computation, and atmospheric turbulence parameter measurement. Apart from utilizing some standard libraries, the image processing codes are primarily in-house developed.
Figure 4. Real-time processing tasks for wavefront sensing and turbulence characterization.
For wide-field SH-WFS wavefront sensing, considering subaperture field size and guide star requirements for turbulence measurements, we implemented a 3 × 3 guide star configuration. The core software features one-click initiation and termination to facilitate extended monitoring campaigns. It executes real time processing tasks including wavefront sensing, turbulence measurement, and data storage concurrently through multi-threading. Additionally, camera control is fully integrated into this same graphical interface software and is implemented via serial communication with relay modules for power management.
The wavefront measurements from multiple targets and sub-apertures obtained via wide-field Shack–Hartmann wavefront sensors (SH-WFS) can be processed using various methods such as SLOpe Detection and Ranging [21,33] (SLODAR) and Solar-Differential Image Motion Monitor+ [9,11] (S-DIMM+) to derive information on the strength and altitude distribution of atmospheric turbulence. These methods share similar principles: first, the correlations between wavefront data from different targets and sub-apertures are analyzed; then, the results are fitted using classical turbulence statistical models to estimate the turbulence strength and altitude distribution. Prior to this correlation analysis, the raw SH-WFS images underwent standard preprocessing, including dark frame subtraction, flat-field correction, and bad pixel masking. AutoCorrelation-SLODAR [34] (AC-SLODAR) is an algorithm that does not rely on classical turbulence statistical models. It directly extracts the turbulence strength and altitude distribution from correlation analysis, offering higher precision and robustness. Therefore, our software employs the AC-SLODAR method to process the preprocessed wavefront measurements. The derived turbulence parameters subsequently underwent postprocessing, involving temporal smoothing, outlier removal, and data quality flagging. This pipeline ultimately yields the strength and altitude distribution of atmospheric turbulence.

3. Results and Discussion

3.1. Measurement System Validation

Using coordinated measurements from both systems, we characterized statistical properties of the Fried parameter r 0 , also known as the atmospheric coherence length or coherence diameter, during winter daytime at Fuxian Solar Observatory. The Fried parameter serves as a key metric describing integrated atmospheric turbulence effects, with larger values indicating superior atmospheric conditions.
Figure 5 presents simultaneous turbulence measurements acquired on 10 December 2023 by the two independent systems described in Section 2: the enhanced GLAO processing system (which extends the functionality of the existing GLAO facility) and the custom-designed standalone system (developed specifically to collect extended temporal data). The profiles in Figure 5 represent real-time measurements from two independent systems over a short time period, in contrast to statistically averaged turbulence parameters. Results demonstrate strong correlation and consistency (Pearson correlation coefficient of r = 0.9361) between the two measurement systems, validating measurement reliability through cross-verification. Minor discrepancies observed at certain intervals likely originate from the differing sampling rates (i.e., image acquisition and processing frequency) between the two systems. Specifically, the GLAO system operates at a high working frequency of 2000 Hz, while the custom-designed standalone system runs at a significantly lower average rate of approximately 30 Hz. It should be noted that this value represents the mean sampling frequency; as the standalone system is not strictly designed for real-time operation, the actual sampling rate may exhibit minor fluctuations. This difference in temporal sampling can lead to the observed mismatches in capturing the dynamics of atmospheric turbulence.
Figure 5. Comparative atmospheric coherence length measurements from dual systems on 10 December 2023.

3.2. Case Study: Turbulence Evolution on 28 November 2023

3.2.1. Meteorological Conditions

A characteristic winter day with stable meteorological conditions suitable for detailed diurnal turbulence analysis was chosen (in this case, 28 November 2023). Weather conditions included: partly cloudy to clear skies with cloud cover <10%, minimum temperature 9 °C, afternoon maximum 19 °C, and light southerly winds (Beaufort scale 2) during morning hours transitioning to calm conditions (light winds) in the afternoon.

3.2.2. Atmospheric Coherence Length Variation

Our turbulence measurement system recorded continuous r 0 data throughout the day, as shown in Figure 6. During the morning period (10:08–10:38 Beijing Time, UTC+8), r 0 values remained elevated and stable. As solar elevation increased and ground heating intensified, r 0 began declining noticeably after 10:30, reaching minimum values of 4–6 cm around local noon (12:00). During the afternoon, as solar radiation diminished and wind conditions transitioned to calm, r 0 gradually recovered, returning to approximately 10 cm after 15:00.
Figure 6. Temporal evolution of atmospheric coherence length ( r 0 ) on 28 November 2023.
Statistical analysis of daily data reveals a mean r 0 value of 8.48 cm for 28 November 2023. As evident from Figure 6, significant differences exist between morning (08:00–13:00 Beijing Time, UTC+8) and afternoon (13:00–18:00 Beijing Time, UTC+8) values. Accordingly, we conducted separate statistical analyses for these periods, resulting in the atmospheric coherence length distribution histograms presented in Figure 7. Comparative histogram analysis indicates mean r 0 values of approximately 7.1 cm during morning hours and 9.8 cm during afternoon hours.
Figure 7. Comparative histograms of atmospheric coherence length ( r 0 ) for morning and afternoon periods on 28 November 2023.

3.2.3. Evolution of Turbulence Distribution

Figure 8 illustrates the temporal evolution of atmospheric turbulence distribution with altitude, derived from the AC-SLODAR method. In this technique, the turbulence profile is modeled as a series of discrete layers. The vertical resolution is primarily determined by the configuration of the Shack Hartmann wavefront sensor used in the measurements. The color map represents the Fried parameter r 0 (in cm), which quantifies the turbulence strength at each corresponding altitude. The data gap around local noon is due to an observational adjustment: during this period, increased turbulence often leads to a shift in telescope tasks toward observing prominences at the solar limb. Under such conditions, the standard Shack–Hartmann wavefront sensor faces significant challenges in achieving reliable wavefront detection, resulting in no valid data being collected during that interval. The figure displays local time on the horizontal axis, turbulence altitude layers on the vertical axis, and color-coded r 0 values representing turbulence strength at corresponding altitudes. Figure 8 indicates that around 10:00, turbulence was primarily concentrated within the lower 4 km atmospheric layer, with relatively calm conditions aloft. Beginning around 10:30, as ground heating intensified, weak turbulence developing above 5 km altitude. During the afternoon, turbulence intensity diminished, with conditions above 4 km returning to calm states, while near-surface turbulence (below 4 km) exhibited gradual weakening trends.
Figure 8. Evolution of atmospheric coherence length with altitude and local time on 28 November 2023. The color bar on the right-hand side represents the atmospheric coherence length (cm).
Statistical analysis of daily data yields the atmospheric turbulence intensity distribution for 28 November 2023, presented in Figure 9. The turbulence intensity is aggregated over the entire day. Specifically, for each altitude layer, the atmospheric coherence length is first converted into the refractive index structure constant C n 2 , as C n 2 is an additive and averageable quantity. By averaging C n 2 across different layers, the average turbulence intensity at various altitudes is obtained. Figure 9 displays the relative proportions of turbulence intensity between different layers, calculated by dividing the C n 2 value at each layer by the sum of C n 2 across all layers. Results indicate that approximately 40% of turbulence occurred at the ground layer (modeled as a discrete layer near 0 km altitude), with 94% of total turbulence intensity concentrated below 4 km altitude. Only sporadic weak turbulence was observed above 4 km.
Figure 9. Vertical distribution of turbulence intensity on 28 November 2023.
This case study provides important implications for observational planning at Fuxian Solar Observatory: (1) atmospheric conditions deteriorate significantly around local noon, making this period unsuitable for observations highly sensitive to atmospheric conditions, such as solar granulation and prominence studies; (2) calm wind conditions may represent a necessary condition for superior seeing at this site.

3.3. Statistical Turbulence Model for Winter Daytime at Fuxian Solar Observatory

This study employed the NVST’s GLAO system coupled with an independently developed turbulence measurement system to conduct systematic atmospheric turbulence monitoring at the site from November 2022 to January 2024. Figure 10 shows the distribution of valid observation dates, which are predominantly concentrated between November and February each year. This concentration provides a solid statistical foundation for establishing a winter atmospheric turbulence model at the site. The relatively limited quantity of valid measurements is primarily due to several observational constraints: (1) telescope scheduling, which allocates most available time to winter periods; (2) limitations of the Shack–Hartmann wavefront sensor, which requires specific solar targets to deliver reliable wavefront detection—not all observing conditions or targets yield usable data; and (3) instrument readiness and weather-related interruptions. As the atmospheric turbulence characteristics are known to differ significantly between seasons, particularly between winter and summer at this location, the reported patterns should not be generalized to other times of the year. It is worth noting that under conditions of successful wavefront sensing, the method for statistical turbulence parameter extraction is well-established and has been validated through numerous simulations and references. In total, over 120 h of valid observational data were collected, encompassing diverse weather conditions and daytime periods, thereby ensuring robust statistical analysis. Data from different years were pooled together, as the climatic variations at the Fuxian Solar Observatory site are minimal between years and far less pronounced than those between seasons, such as the differences between winter and summer.
Figure 10. The distribution of valid observation dates. The light blue highlighted dates in the figure indicate the days on which valid data were collected. The red, blue, and green bars within the light blue boxes represent the years 2022, 2023, and 2024, respectively.

3.3.1. Statistical Characteristics of Atmospheric Coherence Length

Statistical analysis reveals that winter daytime conditions at Fuxian Solar Observatory exhibit a median r 0 of 8.25 cm and mean value of 8.58 cm (at 500 nm wavelength), indicating generally favorable daytime observing conditions. For natural atmospheric turbulence averaged over long-term monitoring, the typical value of the atmospheric coherence length generally ranges from 5 cm to 20 cm. A smaller value indicates stronger turbulence, with approximately 5 cm representing strong turbulence and values as low as 2–3 cm occurring under extreme conditions. In contrast, values greater than 15 cm, indicating weaker turbulence, are typically observed during nighttime at excellent astronomical sites.
Distinct diurnal variation is evident in the r 0 values. The temporal evolution and corresponding statistics, which are derived from all valid observation days, are presented in Figure 11 and Table 1. Note that for short-term, real-time monitoring data such as these, the occurrence of occasional outliers (both low and high values) is considered normal and is reflected in the statistical ranges provided. Optimal conditions occur during morning hours (10:00–10:30) with mean r 0 reaching 9.38 cm; around local noon (12:00–12:30), r 0 decreases to 7.75 cm due to enhanced ground-layer heating; during afternoon hours (14:00–16:00), conditions gradually recover with mean values approaching 9 cm.
Figure 11. Diurnal evolution of atmospheric coherence length (cm) during winter daytime at Fuxian Solar Observatory.
Table 1. Atmospheric coherence length across different daytime periods during winter at Fuxian Solar Observatory.
These statistical patterns demonstrate an inverse relationship between atmospheric coherence length and solar radiation intensity: stronger solar radiation corresponds to smaller r 0 values. During morning hours, increasing solar radiation produces declining r 0 trends, while afternoon conditions show gradual recovery as solar radiation diminishes. Regarding weather conditions, we observed no strong correlation between r 0 and specific weather patterns, though it should be noted that telescope operations are restricted to non-precipitation conditions, limiting observable conditions to clear or partly cloudy skies.

3.3.2. Statistical Model of Turbulence Distribution

Based on measurements collected between November 2022 and January 2024, we compiled a statistical characterization of the atmospheric turbulence altitude distribution across different daytime periods during winter at Fuxian Solar Observatory, as presented in Figure 12. The analysis integrates all valid measurement data. For each altitude layer, the turbulence strength is characterized by the refractive index structure constant C n 2 , derived from the atmospheric coherence length. We first convert the coherence length values to C n 2 for each layer, then average the C n 2 values to obtain the mean turbulence intensity per layer. Each column in Figure 12 represents the relative contribution of turbulence at different layers during a specific time period, calculated as the ratio of the layer C n 2 to the sum of C n 2 over all layers. The figure displays time periods on the horizontal axis, turbulence altitude layers on the vertical axis, and color-coded values representing the proportional contribution of each altitude layer to total turbulence intensity.
Figure 12. Temporal evolution of vertical turbulence distribution during winter daytime at Fuxian Solar Observatory. The color bar on the right-hand side represents the normalized turbulence intensity (relative contribution, ranging from 0 to 1).
Figure 12 reveals similar turbulence intensity distributions during morning (10:00–11:00) and afternoon (14:00–16:00) periods, while the interval between 11:00 and 14:00 exhibits a characteristic pattern of concentration toward the surface layer followed by gradual dispersion, with ground-layer (0 km) turbulence contribution reaching maximum values of 62.6%. Above 4 km altitude, only weak turbulence is consistently observed.
Figure 13 and Table 2 present the integrated vertical turbulence intensity distribution derived from all statistical data during winter daytime at Fuxian Solar Observatory. Results indicate that approximately 52.8% of turbulence is concentrated at ground layer (0 km), with 93.1% of total turbulence intensity occurring below 4 km altitude. Weak turbulence layers are identified around 7–8 km altitude, contributing approximately 2% of total intensity, while the 11 km altitude layer contributes approximately 1%.
Figure 13. Integrated distribution of turbulence intensity during winter daytime at Fuxian Solar Observatory.
Table 2. Distribution of turbulence intensity during winter daytime at Fuxian Solar Observatory.

4. Conclusions

This study presents a comprehensive characterization of atmospheric optical turbulence during winter daytime conditions at the Fuxian Solar Observatory, utilizing coordinated measurements from the NVST GLAO system and a custom-developed turbulence measurement system.
Our analysis reveals that the site exhibits generally favorable daytime seeing conditions with a median atmospheric coherence length ( r 0 ) of 8.25 cm at 500 nm wavelength. A distinct diurnal pattern emerges, characterized by optimal conditions during morning hours (mean r 0 = 9.38 cm), progressive degradation around local noon (minimum r 0 = 7.75 cm), and gradual recovery during afternoon periods. This temporal evolution demonstrates a clear inverse relationship between solar radiation intensity and atmospheric coherence length.
The vertical distribution analysis indicates strong turbulence concentration in the lower atmospheric layers, with 52.8% of total turbulence occurring at ground level and 93.1% confined below 4 km altitude. The temporal evolution of turbulence stratification reveals similar distribution patterns during morning and afternoon periods, while the midday hours (11:00–14:00) exhibit enhanced ground-layer concentration with surface contributions reaching 62.6%.
The case study of 28 November 2023, provides additional insights into turbulence behavior under specific meteorological conditions, suggesting that calm wind conditions may represent a necessary condition for superior seeing at this site. The established statistical model of turbulence distribution provides valuable reference data for optimizing observational scheduling, designing future adaptive optics systems, and developing advanced image reconstruction techniques at Fuxian Solar Observatory.
This study presents the first systematic report on the characteristics of daytime vertical turbulence distribution during winter at the Fuxian Solar Observatory, thereby filling a significant gap in the atmospheric optical parameters previously available for this site. The identified patterns of daytime turbulence variation offer direct guidance for optimizing the performance of adaptive optics systems in solar observations, enabling the determination of optimal observation windows. Furthermore, the findings provide valuable priori knowledge for the real-time optimization of GLAO systems. This advancement can effectively reduce the burden on wavefront sensors and enhance the efficiency of atmospheric correction.

Author Contributions

Conceptualization, L.Z. and C.R.; methodology, X.R.; software, X.R. and H.B.; validation, X.R., and L.Z.; investigation, C.R.; writing—original draft preparation, X.R.; writing—review and editing, X.R., L.Z., D.Y.K., V.P.L. and C.R.; visualization, X.R.; supervision, C.R.; project administration, L.Z. and C.R. All authors have read and agreed to the published version of the manuscript.

Funding

This work was supported by the National Natural Science Foundation of China (Grant Nos. 12261131508 and 11727805), as well as by the Ministry of Science and Higher Education of the Russian Federation and the Russian Science Foundation (RSF) (Grant No. 23-42-00043).

Data Availability Statement

The original contributions presented in this study are included in the article. Further inquiries can be directed to the corresponding author.

Acknowledgments

The authors express sincere gratitude to the entire staff of Fuxian Solar Observatory for their support during data acquisition, particularly the NVST operations team for assistance with GLAO system data collection. We acknowledge technical support from Yunnan Observatories, Chinese Academy of Sciences, and valuable suggestions from colleagues during data processing and analysis.

Conflicts of Interest

The authors declare no conflicts of interest.

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