Evaluation of Cloud Fraction Data for Modelling Daily Surface Solar Radiation: Application to the Lake Baikal Region

Abstract

Accurately modelling surface solar radiation (SSR) is essential for environmental research but remains a significant challenge in topographically complex regions like Lake Baikal, where ground measurements are sparse. This study evaluates the performance of various open-access cloud cover products—from satellite sensors (AVHRR, MODIS) and ground-based observations—for modelling daily SSR totals, using a physical radiation model validated against in-situ measurements from 10 coastal stations. The results demonstrate that the choice of cloud data critically impacts model accuracy. The AVHRR satellite product yields the most reliable estimates (R² = 0.54, RMSE = 4.538 MJ/m²), significantly outperforming both ground-based cloudiness observations and the ERA5 reanalysis dataset. This finding underscores that spatially continuous satellite data provide a superior representation of cloud attenuation for regional modelling than point-based ground observations or reanalysis. Consequently, a physical model driven by high-quality satellite cloud masks is recommended as an effective methodology for generating reliable SSR fields.

1. Introduction

Solar radiation exerts a direct and governing influence on the planetary energy equilibrium [1]. Diurnal irradiance fundamentally dictates the thermal dynamics of the terrestrial surface [2,3], drives key biogeochemical processes including the hydrological cycle, and serves as the fundamental input to both photovoltaic and thermal solar energy conversion systems [4,5]. Furthermore, through its synergistic interactions with atmospheric variables, solar radiation emerges as a pivotal parameter in climate modelling and formulation of strategic policies for agricultural and hydrological resource management [6]. Consequently, it constitutes a critical, indispensable variable for sustainable land-use planning, particularly within regions exhibiting high susceptibility to climatic changes [7,8]. Changes in surface solar radiation (SSR) directly affect climate data, the hydrologic cycle, sensible heat, latent heat, evaporation, photosynthesis, ecological life, migration, and many other important parameters.

The significant spatiotemporal variability of SSR makes estimation of total radiation challenging [9], especially in regions with complex atmospheric dynamics and sparse meteorological stations [8,10]. The SSR value depends on many parameters such as solar angle, hour angle, topography, air composition, surface morphology, and conditions [11]. All these parameters generate great uncertainties in obtaining SSR, especially for short temporal partitions such as instantaneous, hourly, or daily values.

Despite its paramount importance, establishing comprehensive and dense observational networks for SSR is often not feasible. The high cost of precision radiometric equipment, coupled with significant demands for ongoing maintenance and calibration, means that meteorological stations equipped with radiation sensors are scarce, especially in topographically complex or remote regions [12]. This spatial sparsity of direct measurements creates a critical data gap, necessitating a heavy reliance on modelled estimates to obtain a continuous understanding of solar radiation patterns across the landscape [13].

In response to this need, a wide spectrum of modelling approaches has been developed, ranging from traditional empirical and regression-based methods to sophisticated statistical, time-series, artificial intelligence, and satellite imagery-based models [14,15,16,17,18]. However, extensive reviews of the literature consistently reveal that no single model has emerged as universally superior [19,20,21]. The performance of any given model is highly contingent on local atmospheric conditions, geographic specifics, and quality of the input data [15]. This inherent regional dependency underscores the necessity for localised model development and validation, as an approach that performs well in one climatic or geographic context may prove inadequate in another [22]. Consequently, the initial aim of this paper is to develop and validate a simulation of SSR for a specific, environmentally significant region—the Lake Baikal.

Machine learning methods are widely applied for precise solar radiation forecasting. Evaluation of the performance of different machine learning methods for solar radiation prediction in Konya, Turkey [23] showed that the Long Short-Term Memory model performed best. A combined artificial neural network approach was successfully applied for forecasting solar radiation in Iran [24]. A novel aggregated model of outputs from different machine learning models demonstrates better results than a single model output [25]. A stacking model approach with categorical boosting feature selection for China revealed that the sunshine duration and ozone mass concentration significantly affect solar radiation prediction [26].

Some authors compare global radiation products and suggest correction methods to improve and reduce biases in radiation characteristics [27,28]. Saint-Drenan and Wald [29] compared ERA5, JRA-3Q, and MERRA-2 reanalyses with ground-based measurements from 28 stations located worldwide, and noted that none of the three reanalyses is reliable in space. Xian et al. [30] reaffirm that the Random Forest model is a highly effective tool for correcting ERA5 ECMWF (European Centre for Medium-Range Weather Forecasts) shortwave radiation estimates over Hubei Province, China.

Many studies rely on satellite remote sensing data from platforms such as Terra/Aqua MODIS [13,31,32], and Landsat-8 [6,33], as well as ASTER, AVHRR, ETM+/TM, GOES, MISR, POLDER, and VEGETATION [34]. Furthermore, various meteorological and solar radiation databases are commonly used, including NASA SSE, NASA POWER [35], ERA5 [27,30], SoDa [36], NOAA CLASS [34], the Baseline Surface Radiation Network [29,37], the World Bank’s ESMAP Solar Resource Mapping, and MERRA-2 [27,38].

Multiple studies focused on solar radiation using Geographic Information Systems (GIS) [39,40,41,42]. This research aims to validate its results against existing geoinformation modules [36] and apply them to specific cases. These applications include modelling snowmelt dynamics [43], optimising agricultural ecosystems [31,33,44], identifying optimal sites for solar power plants [45,46,47,48,49,50], and assessing forest fire risk [36,51]. The spatial resolution of the developed models varies from tens of metres to half a metre [51].

Among different tools, which are useful for integrating layers with different spatial resolutions, the r.sun function embedded in GRASS GIS has been selected as the most suitable to capture complex variations resulting from weather and geographical parameters [52]. The r.sun module is integrated within QGIS software version 3.36.2 [36,41,42,53]. The Area Solar Radiation tool within the ArcGIS version 10.4 Spatial Analyst toolbox is also popular [43,44,45,46,47,48]. This tool was integrated into major GIS platforms and its consequent widespread adoption, despite its reliance on 2.5D surface models for calculations.

It is widely recognised that the choice of both the modelling algorithm and, critically, the input data sources leads to substantial variations in the final radiation estimates. This study employs a well-established physical modelling approach, which explicitly and accurately accounts for extraterrestrial solar radiation and its interaction with the Earth’s movement and atmosphere. This deterministic foundation provides a robust framework for calculating potential clear-sky radiation. Within this framework, the attenuation of radiation by the atmosphere, particularly by cloud cover, becomes the most significant and variable factor determining the actual radiation that reaches the Earth’s surface. Therefore, the accuracy of the cloudiness data used as input is the single most critical element for generating valid modelling results.

The central novelty of this research is its systematic evaluation of multiple, diverse cloudiness data products within a physically coherent modelling scheme for the Lake Baikal region. This area, characterised by its immense lake, complex mountainous terrain, and unique microclimates, represents a significant gap in the existing literature, as it has not been the subject of a study that concurrently utilises in-situ observations of incoming radiation and compares the performance of various satellite-derived and reanalysis cloudiness products. Our work directly addresses this gap by rigorously testing which cloudiness data source yields the most reliable daily radiation totals when validated against a dedicated network of ground-based measurements. The aim of this paper is therefore to analyse the quality of various cloudiness data products for modelling daily SSR totals in the Lake Baikal surroundings, using a unique set of in-situ observations from 10 automated weather stations as a benchmark for validation.

Our research is positioned to address a specific literature gap. There have been no previous works that systematically combine remote sensing cloudiness data, physical radiation modelling, and a dedicated network of in-situ observations specifically for the Lake Baikal shoreline. This integrated approach is crucial for this complex environment, where the interplay between the deep lake and the surrounding topography creates highly localised microclimates that are poorly captured by generic models.

2. Materials and Methods

2.1. Materials

The study area (Figure 1) is located within the Central Ecological Zone of the Baikal Natural Territory [54]. Lake Baikal is a UNESCO World Heritage Site [55], renowned as the world’s oldest, deepest, and most voluminous freshwater lake. Its unique geomorphology, characterised by a massive water body surrounded by complex mountainous terrain, fosters highly localised and dynamic microclimates that are crucial for the region’s numerous endemic species. Solar radiation is a primary climate-forming factor. Given the sparse network of actinometric stations in the area and the complete absence of assessments of the surface radiation and heat budget under complex orographic conditions, this research is highly relevant. Data on radiation levels under natural conditions is essential for assessing changes in the coastal biodiversity of Lake Baikal amidst contemporary climate change. The territorial accessibility and the installation of automatic weather stations equipped with radiation sensors make this chosen area an ideal natural laboratory for studying solar radiation modelling.

The specific focus on the lakeshore is deliberate. The land-water interface is a critical and highly sensitive zone where sharp gradients in surface-atmosphere energy exchange occur [56]. Studying sites along this transition allows us to directly evaluate how well different cloudiness products can capture the pronounced spatial variability in solar radiation caused by the lake’s moderating influence. While the sites may be difficult to interpret, this complexity is precisely the point—it provides a rigorous test for the models.

The input data used in this study for modelling daily incoming solar radiation was: a digital elevation model (DEM) and its derivatives (slope and aspect), cloud cover, and aerosol optical thickness (AOT), which was converted into the Linke turbidity coefficient. All datasets were reprojected into the EPSG:32648 coordinate system.

Digital Elevation Model (DEM). The Shuttle Radar Topography Mission (SRTM) data [57] with a spatial resolution of 30 × 30 m was selected as the DEM. This choice was based on the findings of [10], which reported higher reliability of SRTM data due to lower levels of random errors compared to alternative DEMs.

Linke Turbidity Coefficient or AOT. Currently, instead of the dimensionless Linke turbidity coefficient (TL), the aerosol optical thickness (AOT) is widely used in meteorological and climatic calculations. For this study, the TERRA/MODIS satellite system was selected. The data is provided by NASA Earth Observations [58] and is based on the MODIS/Aqua Collection 6.1 products [59]. This data is represented as a raster layer with a spatial resolution of 0.1° by latitude and longitude, containing monthly mean AOT values per pixel in the WGS84 coordinate system. Since the solar radiation model requires TL. AOT values were converted to TL using the Ineichen–Perez model [60,61].

Cloud Fraction. Four cloud cover datasets were used as input, each representing as a raster layer of daily mean cloud fraction cover per pixel:

• TERRA\MODIS and AQUA\MODIS. Two datasets of the MOD06 product (MODIS Cloud Product) were used, namely the Cloud_Fraction datasubset, based on measurements from the Terra and Aqua satellites equipped with MODIS (Moderate Resolution Imaging Spectroradiometer) scanners. Both data sets have a spatial resolution of 0.1° by latitude and longitude in the WGS84 geographic coordinate system. The temporal resolution of the imagery for each satellite is one pass per day. The data was provided by NASA Earth Observations [47,62]. Cloud cover values are encoded as integers in the range 0 to 255, where 0 typically represents no clouds and 255 represents full cloud cover or no valid data. In the following text, data from the Terra satellite is referred to as “TERRA” and data from the Aqua satellite is referred to as “AQUA”.
• MetOp\AVHRR. The CLARA-A3 CFC (Cloud Fractional Cover, version 3.0) product, based on observations from the AVHRR (Advanced Very High-Resolution Radiometer) sensor onboard the MetOp satellite series (https://wui.cmsaf.eu/safira/action/viewProduktDetails?fid=40&eid=22257_22484 (accessed on 16 November 2024)), provides cloud cover estimates on a regular latitude–longitude grid with a spatial resolution of 0.25° in the WGS84 geographic coordinate system. Cloud fractional cover values range from 0 to 100, representing the percentage of cloud cover within each grid cell. The MetOp satellite performs, on average, two overpasses per day, yielding a temporal sampling frequency of approximately two observations per day. The data is provided by the EUMETSAT Satellite Application Facility on Climate Monitoring (CM SAF) [63,64]. Hereafter, this dataset is referred to as “AVHRR”.

The MODIS data used is the standard Level-3 daily global product (MOD06/MYD06) ‘Cloud_Fraction’ field. Similarly, the AVHRR data is the CLARA-A3 ‘Cloud Fractional Cover’ (CFC) product. Both are used as provided, without further algorithmic modification, to ensure the evaluation reflects the utility of these operational datasets.

• Weather station data. Cloud cover observations recorded every 3 h at six meteorological stations (Yelokhin, Uzur, Khujir, B. Goloustnoe, Ushkaniy, and Sarma) (Figure 1), were provided in CSV format by the Russian Federal Service for Hydrometeorology and Environmental Monitoring (Roshydromet) [65]. For consistency in modelling, daily mean cloud cover values were calculated and converted into raster format, assigning a uniform value to all pixels within each modelling site.

The spatial resolution of both the cloud cover and TL datasets was upscaled to match that of the DEM. Each cloud cover dataset was normalised to a scale where 0 corresponds to a completely clear sky and 1 represents maximum (10-point) daily mean cloud cover. Hereafter, this dataset is referred to as “Meteo”.

ERA5 reanalysis. For comparison with the modelling results, surface incoming solar radiation (ISR) data from the ERA5 reanalysis with a spatial resolution of 0.25° was also used. This data was obtained from the Copernicus Climate Data Store (CDS) [66,67].

In-situ observations. Ten automatic monitoring stations have been deployed along the Lake Baikal coast [68,69] (Figure 1).

These stations are designed to record meteorological variables and are equipped with sensors measuring air temperature and humidity, wind speed and direction, atmospheric pressure, liquid precipitation totals, snow depth, soil temperature and moisture, as well as SSR [70]. Observation points are located in open areas (deforested) to reduce the effect of the Earth’s surface on pyranometers. The lakeshore sites were deliberately selected within this heterogeneous transition zone with complex terrain. The expected scale mismatch between point measurements and satellite pixels (10–25 km) presents a rigorous, real-world test for evaluating whether the spatial average cloudiness from a product can effectively represent the cloud attenuation experienced at a point within a complex scene. The measurement range for global solar radiation is 0–1800 W/m², with an accuracy of ±5%. The spectral range of the solar radiation sensor is 400–1100 nm. The in-situ data used in this study covers the period from 1 January 2023 to 31 December 2023, with hourly temporal resolution. Daily SSR totals were calculated by integrating the hourly SSR intensity values in W/m² and converting them to MJ/m².

2.2. Methods

Physically based modelling of SSR was employed to evaluate cloud fraction data. Modelling of incoming solar radiation was accounted for the annual and diurnal variation of the Sun’s position, atmospheric extinction, terrain topography (used only for spatial comparisons), and cloud cover. The primary calculations were performed for a horizontal surface, as the pyranometers at actinometric stations are also levelled horizontally.

All computations were carried out using Python 3.11. The Rasterio version 1.4.4, PyProj version 3.7.2 and NumPy version 2.2.3 libraries were employed for processing raster geospatial data.

2.2.1. Modelling the Annual Cycle of SSR

In this study, a mathematical model described in detail in [71] was employed to calculate the SSR, accounting for astronomical, atmospheric, and topographic factors. Key astronomical parameters were computed to determine the Sun’s position on the celestial sphere:

Solar declination (δ): This is the angle between the Earth’s equatorial plane and the line connecting the centers of the Earth and the Sun. It was calculated using the empirical formula provided in [72]:

$$\delta = {23.45}^{°}·sin\left({\displaystyle \frac{{360}^{°}}{365}}·\left(n-81\right)\right),$$

(1)

where:

• δ—solar declination (in degrees),
• n—day of the year (ranging from 1 to 365).

Hour angle (ω) [72], which reflects the Sun’s position relative to local solar noon:

$$\omega ={15}^{°}·\left(t-12\right),$$

(2)

where:

• t—local solar time (in hours).

Using these, the solar zenith angle (θz) [73] was calculated, defining sun elevation above the horizon:

$$cos\theta z = sin\phi ·sin\delta + cos\phi ·cos\delta ·cos\omega ,$$

(3)

where:

• θz—solar zenith angle (in degrees),
• φ—latitude of the calculation point.

Daylight duration (ωs) is determined by the noon-centered hour angle of sunrise and sunset:

$$\omega s = arccos\left(-tan\varphi ·tan\delta \right),$$

(4)

Local solar times of sunrise and sunset are calculated using the formulas:

$$sunrise = 12 - {\displaystyle \frac{{\omega }_s}{{15}^{°}}}, sunset = 12 + {\displaystyle \frac{{\omega }_s}{{15}^{°}}},$$

(5)

where ωs—the noon-centered hour angle of sunrise/sunset.

Temporal values were converted from degrees to hours using the Earth’s rotation rate (15°/h), yielding results in the range of 0 to 23 h. All calculations were performed on an hourly basis and subsequently summed up to obtain the daily total solar radiation. The standard solar constant used in the model is I₀ = 1367 W/m² [71], while ref. [74] report on I₀ = 1361.1 W/m^2.

To account for atmospheric attenuation of solar radiation, the concept of Air Mass (AM) is used—a dimensionless quantity representing the relative path length of sunlight through the atmosphere, particularly significant at low solar elevation angles [75]:

$$AM = {\displaystyle \frac{1}{cos\theta z + 0.50572·{\left(96.07995-\theta z\right)}^{-1.6364}}},$$

(6)

The transmittance coefficient (τ), which represents the fraction of radiation that passes through the atmosphere, is calculated using the TL, proportional to AOT, along with a set of regional empirical coefficients a, c, d, f calibrated for specific meteorological stations [76]:

$$\tau = exp\left(a·TL·AM·c·{AM}^d\right) - f,$$

(7)

where AM—air mass.

The parameters of the equation a, b, c, d, f were determined by successively searching through the values of the coefficients in such a way that the curve of the annual distribution of the values of the modeled radiation under cloudless skies coincided with the values of the positive extremes of the curve of the annual distribution of natural observations (

Table 1. Coefficients for transmittance calculation.

a	b	c	d	f	Site
−0.6062	640	4.5352 × 10−3	−2.477	0	BG
−0.6062	640	4.5352 × 10−3	−2.477	0	BK
−0.6062	640	0.524535	−2.477	0	E
8.00 × 104	600	5 × 10−7	−2.477	0	L
8.00 × 104	620	5 × 10−7	−2.477	0	S
8.00 × 104	620	5 × 10−7	−2.477	0	U
−2.062 × 10−3	750	5 × 10−7	−0.077	0	U2
−2.062 × 10−3	1200	5 × 10−7	−0.077	0	Uh
−2.062 × 10−3	650	5 × 10−7	−0.077	0	X
−2.062 × 10−3	600	5 × 10−7	−0.077	−0.2	Hak

).

The influence of elevation above sea level (h in km) is accounted for through the reduced atmospheric density, which decreases radiation absorption; this effect is modelled using the atmospheric scale height H = 8.4 km [77,78]. This correction is applied to the transmittance coefficient (τ_h).

2.2.2. Cloud Cover

The effect of cloud cover on incoming solar radiation was accounted for using three models [79].

Linear model:

$$F_{cloud} = 1 - 0.9·C+0.1·C^2,$$

(8)

Exponential model:

$$F_{cloud} = exp\left(-1·C\right),$$

(9)

Clear-sky model:

$$F_{cloud} = 1.0,$$

(10)

where $C$ is the cloud cover fraction, ranging from 0 to 1.

The cloud fraction $C$ is a daily mean value for each pixel. This single daily value is used in $F_{cloud}$ for all hourly radiation calculations within that day at the corresponding location.

The cloud attenuation factor $F_{cloud}$ is applied to the clear-sky irradiance (for the relevant surface orientation) to estimate the actual global irradiance under cloudy skies. This approach implicitly incorporates the cloud-modulated diffuse component within the empirical factor $F_{cloud}$.

2.2.3. Terrain

Shadow masking. In the current implementation, explicit shading was not modelled; however, the following rules were applied: If cosθ < 0, the radiation flux on the surface was set to zero (the ray strikes the back side of the surface); if θz > 90°, the radiation was set to zero.

In its complete form, the model appears as follows:

$$R_{total}\left(\phi ,\lambda \right) = {\sum }_{t=t_{sunrise}}^{t_{sunset}}\left[I_0·{\tau }_h\left(t\right)·cos\theta z\left(t\right)\right]·Fcloud\left(C\right)·\Delta t,$$

(11)

where φ, λ are the latitude and longitude of the modelled area, respectively; t is local solar time (in hours); Δt is time interval.

To refine the calculations, a correction factor b is introduced to adjust SSR: Itotal(t) = Itotal(t) − b.

To account for topography, instead of cosθz, the cosine of the angle between the solar beam direction and the normal to the surface (cosθ) was computed, allowing the radiation intensity to be adjusted based on the slope of the surface [80].

2.2.4. Model Accuracy Assessment

The following metrics were used to evaluate the accuracy of reproducing the spatiotemporal characteristics of the modelled radiation:

The coefficient of determination (R-squared, R²) indicates the proportion of the variance in the target variable explained by the model:

$$R^2 = 1 - {\displaystyle \frac{\sum {\left(y_i - {\hat{y}}_i\right)}^2}{\sum {\left(y_i - \overline{y}\right)}^2}},$$

(12)

where y_i are observed (true) values, ŷ are predicted values, $\overline{y}$ is mean of the observed values.

In-situ SSR observation data was used as true values.

The Root Mean Squared Error (RMSE)—a measure of the root mean square deviation of predictions from true values:

$$RMSE = \sqrt[]{{\displaystyle \frac{1}{n}}{\sum }_{i=1}^n{\left(y_i - {\hat{y}}_i\right)}^2},$$

(13)

where n is number of values in time series.

The Mean Absolute Relative Error (MARE)—the mean of absolute relative errors with respect to true values:

$$MARE = {\displaystyle \frac{1}{n}}{\sum }_{i=1}^n\left|{\displaystyle \frac{{\hat{y}}_i - y_i}{y_i}}\right|,$$

(14)

The Mean Relative Error (MRE)—the mean relative error with respect to the true value:

$$MRE = {\displaystyle \frac{1}{n}}{\sum }_{i=1}^n{\displaystyle \frac{{\hat{y}}_i - y_i}{y_i}},$$

(15)

Equation (16) is used to quantitatively assess the convergence (consistency) between the directions of change in daily cloud cover and surface solar radiation (SSR) over the entire observation period. It is defined by a binary vector $V_i$ for each time step i (in our case, for each day). Specifically, $V_i$ = 1 indicates that the directions of change in cloud cover and SSR are opposite, which aligns with the expected physical relationship, whereas $V_i$ = 0 means that the directions of change are the same—contradicting physical expectations (16). Here, “convergence” refers to the degree of agreement between physical processes captured by different data sources. The higher the mean value of vector $V$ (convergence) (

Table 2. Mean convergence value for 2023 of day-to-day variations in cloud cover and solar radiation from different cloud data sources, expressed as fractions of unity.

Cloud Cover Data Source	BG	S	U	X	BK	Uh	L	U2	Hak	E	Average
AQUA	0.64	0.57	0.6	0.58	0.61	0.54	0.53	0.52	0.57	0.5	0.57
TERRA	0.61	0.64	0.64	0.62	0.57	0.52	0.52	0.49	0.6	0.52	0.57
AVHRR	0.63	0.63	0.61	0.68	0.58	0.54	0.5	0.51	0.58	0.5	0.58
MS	0.63	0.51	0.65	0.5	0.5	0.53	0.5	0.47	0.4	0.52	0.52

Note: The best metric values for each site are highlighted in bold. The best metric is the highest convergence value for each station.

), the greater the convergence.

This approach helps us preliminarily evaluate which cloud cover datasets most reliably represent real-world conditions:

$$V_i = \left\{\begin{array}{c}1,ifsign\left(C_i - C_{i-1}\right) \ne sign\left(R_i - R_{i-1}\right)\\ 0,ifsign\left(C_i - C_{i-1}\right) = sign\left(R_i - R_{i-1}\right)\end{array}\right.,$$

(16)

where $C_i$ is the cloud cover fraction at the i-th time step, and is $R_i$ is SSR at the same time step.

A preliminary conclusion can be drawn: values in the range 0.5–0.7 indicate relatively low convergence between day-to-day variations in cloud cover and in-situ SSR, particularly for cloud cover characteristics derived from meteorological station data.

3. Results and Discussion

3.1. Observations

Annual totals of SSR in 2023 across the observation sites varied widely (

Table 3. Seasonal and annual sums of SSR in MJ/m² at the actinometric stations in 2023.

BG	S	U	X	BK	Uh	L	U2	Hak	E	Season
367.47	323.99	315.06	330.54	373.42	240.46	409.64	370.65	205.90	237.65	Winter
1365.24	1418.17	1448.71	1395.43	1413.56	1373.61	1594.16	1721.12	1097.28	980.62	Spring
1524.61	1647.52	1655.59	1646.75	1474.46	1554.19	1700.08	1636.28	1270.82	1137.95	Summer
702.22	713.36	678.92	678.36	659.47	555.35	720.09	674.31	489.59	556.43	Autumn
3959.54	4103.04	4098.28	4051.08	3920.92	3723.61	4423.96	4402.37	3063.58	2912.65	Total

Note: Winter season was composed from January 2023, February 2023 and December 2023.

)—from 2641.92 MJ/m² (Uh) to 4263.58 MJ/m² (L), corresponding to a relative difference of more than 1.6 times. The mean value across all sites was 3708.47 MJ/m², with a standard deviation of 642.31 MJ/m² and a coefficient of variation of 17.3%, indicating significant spatial heterogeneity in radiation conditions.

The highest value was recorded at site L, exceeding the nearest stations (S—4103.04 MJ/m², U—4098.28 MJ/m²) by 3.9%. This site is characterised by the highest winter insolation (406.01 MJ/m²), indicating favourable insolation conditions even during the period of minimum solar illumination in this region.

Sites X (4051.08 MJ/m²), BG (3959.54 MJ/m²), and BK (3920.92 MJ/m²) form a group with moderate to relatively high SSR values, demonstrating moderate variability and high reproducibility at the seasonal scale. In contrast, stations E (2597.24 MJ/m²), U2 (2698.47 MJ/m²), Uh (2641.92 MJ/m²), and Hak (2906.13 MJ/m²) show lower SSR values, which may be attributed both to regional climatic features and to local factors [81].

Analysis of seasonal SSR variations revealed the following: the summer period (June–August) contributes the largest share to the annual total—on average 40.2% (ranging from 38.1% at Uh to 42.5% at L). Spring (March–May) accounts for 35.6%, autumn (September–November) for 18.7%, and winter (December–February) for 5.5%. The absolute winter maximum SSR was recorded at site L (406.01 MJ/m²), which is nearly 2.3 times higher than at E (179.12 MJ/m²). Sites BG (367.47 MJ/m²) and BK (373.42 MJ/m²) also demonstrate relatively high SSR values despite modest summer totals. In spring, site U leads (1448.71 MJ/m²). In summer, maximal SSR was observed at site L (1700.08 MJ/m²), followed by U (1655.59 MJ/m²) and X (1646.75 MJ/m²). Site X recorded the absolute monthly maximum in the dataset—609.62 MJ/m² in July, indicating high efficiency during the peak period. In autumn, site L leads again (720.09 MJ/m²), whereas stations with reduced insolation (e.g., Uh, E) exhibited sharp declines in daily SSR totals as early as October.

3.2. Modelling

Eight SSR calculations were performed for all days of 2023 using two cloud parameterisation models and four cloud data sources. Calculations were carried out for daily total SSR values separately for each station and then compared with in-situ observations. The average performance across all stations for all eight calculations is presented in Table 3. It demonstrates significant differences in their ability to predict actual SSR values. The highest accuracy was achieved by the exponential AVHRR_Exp model with R² = 0.54 (

Table 4. Model’s performance characteristics.

R2	RMSE, MJ/m2	MARE	MRE	Model
0.54	4.538	0.33	−0.18	AVHRR_Exp
0.48	4.872	0.35	−0.15	TERRA_Exp
0.47	4.932	0.36	−0.18	AQUA_Exp
0.40	5.189	0.36	−0.17	Meteo_Exp
0.37	4.724	0.48	0.44	ERA5
0.32	5.553	0.40	−0.34	AVHRR_Line
0.18	6.159	0.45	−0.33	TERRA_Line
0.15	6.255	0.46	−0.36	AQUA_Line
0.10	6.352	0.43	−0.31	Meteo_Line

). This model also showed the lowest absolute error (MARE = 0.33). Moreover, it has the lowest root mean square error (RMSE)—only 4.538 MJ/m². This makes the AVHRR_Exp model the best approach for describing SSR totals. The second most accurate model is TERRA_Exp, with R² = 0.48 and RMSE = 4.872 MJ/m². Third place is occupied by the AQUA_Exp model (R² = 0.47, RMSE = 4.932 MJ/m²). These three models demonstrated superior performance, outperforming the remaining linear models and the SSR data from the ERA5 reanalysis.

It should be noted that models based on a linear representation of cloud cover yielded the worst results, with R² ranging from 0.10 to 0.32, the highest errors (5.553–6.352 MJ/m²), and a significant underestimation of mean SSR values (MRE varying from −0.36 to −0.31) (Table 4). Therefore, subsequent analysis will focus on the exponential cloud cover model.

Particular interest is drawn to the ERA5 reanalysis data. Comparison of ERA5 with the exponential cloud cover model shows that, when evaluated across all observation sites, ERA5 achieves an R² of 0.37, which is 0.17 lower than that of AVHRR_Exp. Plots of the annual SSR cycle (Figure 2) reveal a systematic overestimation by ERA5 relative to observations, confirmed by an MRE of 0.44 calculated across all observation sites (Table 3). Such errors in ERA5 have been reported previously. Notably, ERA5 systematically underestimates SSR under cloudy conditions and during the cold season due to its inability to accurately parameterise cloud optical properties [27,28]. Additionally, ERA5 poorly captures the actual spatial variability of SSR, as surface conditions vary considerably from station to station [27,29]. With a spatial resolution of approximately 25 km, ERA5 is physically incapable of adequately reproducing local effects such as the influence of large water bodies (Lake Baikal), shading from mountain ranges, and other influences.

This is especially evident for the Khakusy (Hak), Yelokhin (E), and Ushkany (Uh) sites, with R² values of 0.00, 0.08, and 0.13; MARE values of 0.67, 0.82, and 0.55; and MRE values of 0.67, 0.81, and 0.54, respectively (

Table A1. Model accuracy assessment by observation site.

Meteo _Exp	Meteo _Line	Era_5	TERRA _Exp	AQUA _Exp	AVHRR _Exp	TERRA _Line	AQUA _Line	AVHRR _Line	Site
R2
0.61	0.36	0.73	0.57	0.58	0.56	0.25	0.26	0.28	BG
0.10	0.24	0.08	0.28	0.16	0.30	0.22	0.23	0.11	E
0.34	0.00	0.81	0.63	0.57	0.78	0.33	0.23	0.64	S
0.70	0.51	0.78	0.63	0.64	0.63	0.37	0.37	0.39	U
0.43	0.23	0.45	0.31	0.31	0.38	0.02	0.01	0.09	U2
0.32	0.11	0.13	0.46	0.44	0.50	0.10	0.08	0.19	Uh
0.30	0.05	0.78	0.63	0.65	0.68	0.35	0.39	0.49	X
-	-	0.78	0.60	0.56	0.71	0.32	0.27	0.57	BK
-	-	0.53	0.40	0.35	0.50	0.07	0.01	0.28	L
-	-	0.00	0.30	0.40	0.37	0.20	0.27	0.38	Hak
RMSE, MJ/m2
4.328	5.496	3.600	4.532	4.444	4.588	5.948	5.905	5.828	BG
4.671	5.972	7.392	4.183	4.505	4.118	5.435	5.860	5.175	E
6.159	7.563	3.326	4.585	4.958	3.537	6.189	6.648	4.545	S
4.180	5.327	3.521	4.611	4.533	4.605	6.040	6.029	5.950	U
5.846	6.826	5.763	6.464	6.474	6.140	7.705	7.718	7.419	U2
4.991	5.740	5.676	4.442	4.523	4.273	5.773	5.824	5.454	Uh
6.149	7.536	3.477	4.488	4.386	4.182	5.927	5.733	5.272	X
-	-	3.260	4.412	4.654	3.763	5.760	5.998	4.607	BK
-	-	5.378	6.107	6.331	5.542	7.576	7.829	6.677	L
-	-	5.846	4.893	4.508	4.637	5.234	5.004	4.603	Hak
MARE
0.30	0.36	0.32	0.34	0.35	0.34	0.44	0.46	0.43	BG
0.37	0.50	0.82	0.35	0.36	0.33	0.47	0.51	0.44	E
0.41	0.50	0.34	0.32	0.35	0.26	0.43	0.49	0.34	S
0.29	0.34	0.41	0.32	0.32	0.33	0.42	0.43	0.43	U
0.35	0.42	0.48	0.39	0.40	0.35	0.50	0.50	0.45	U2
0.37	0.41	0.55	0.31	0.30	0.30	0.41	0.39	0.38	Uh
0.42	0.50	0.36	0.31	0.30	0.31	0.42	0.40	0.40	X
		0.32	0.34	0.35	0.29	0.42	0.44	0.34	BK
		0.49	0.48	0.48	0.43	0.55	0.55	0.48	L
		0.67	0.35	0.36	0.31	0.42	0.45	0.35	Hak

Note: The best metric values for each site are highlighted in bold.

in Appendix A). However, at the remaining sites, ERA5 demonstrated some of the best results in terms of explained variance and modelling error, although its MRE values range from 0.30 to 0.43—higher than those of the exponential models (0.00 to −0.29).

Reanalysis products, such as MERRA-2, demonstrate good reproduction of the seasonal cycle of solar radiation but fail to capture local features [27,28,29,40]. This underscores the necessity of mandatory local calibration of any global products (ERA5, MERRA-2, SARAH-E) prior to their use in regional studies. This was successfully implemented in [82] for MERRA data over the Fiji Islands, where the authors performed detailed validation and correction based on ground-based measurements.

For models with exponential cloud cover parameterisation, using TERRA, AQUA, and AVHRR cloud data, the performance metrics were fairly similar, with slightly better results obtained with the AVHRR sensor (Table 4 and Table A1). The difference in model accuracy between sites using AVHRR data reached up to 0.21, 1.42, 0.09, and 0.16 for R², RMSE, MARE, and MRE, respectively, indicating spatial heterogeneity.

Considering SSR modelling results based on cloud observations (Meteo), the quality metrics were generally quite low, although at some sites (GB and U) they approach to the ERA5 results and even outperform the models based on other cloud data sources, showing better MRE values: −0.16 and −0.13, respectively.

Summarising the interim findings, it can be noted that the AVHRR daily mean cloud cover data performed better than MODIS and meteorological station data. This somewhat contradicts common perceptions of these products. A partial explanation is provided in studies [19,20]. The authors emphasise that comparisons of different models and data sources conducted in various regions worldwide over recent decades often yield contradictory and even mutually exclusive results. No existing model or sensor is universally “best”—only optimal for a specific region. Several studies note that although AVHRR offers higher observation frequency and longer data records, its cloud detection capability is limited by a smaller number of spectral channels, ultimately resulting in lower contrast between clouds and the surface compared to MODIS [13,83].

However, the observation frequency plays a critical role. AVHRR provides multiple daily overpasses, whereas Terra and Aqua satellites each provide only one. This enables CLARA-A3 to better capture the diurnal dynamics of cloud cover, which is particularly important for calculating integrated daily SSR totals. At the same time, as noted in [13,83], more sophisticated MODIS algorithms may be more sensitive to noise, aerosols, snow cover, and other local features, which under the complex topography of the Lake Baikal coastline can lead to systematic errors. In conclusion, for tasks requiring estimation of integrated daily values, the reliability, stability, and consistency of the data processing algorithm may be more important than spatial detail.

It should be noted that the high spatiotemporal variability of cloud cover in the Lake Baikal region—driven by the interaction of lake–land breeze circulation, orographic lifting, and synoptic-scale processes—is also crucial when calculating daily totals of solar radiation. Unlike monthly averages, daily integrals are highly sensitive to short-lived and localised changes in cloud cover, which can introduce considerable uncertainty when comparing different data sources. Nevertheless, the high observation frequency of AVHRR enables a more accurate capture of intraday cloud dynamics and, consequently, a more precise estimation of daily totals of SSR. Although cloud structures can be extremely heterogeneous on individual days, the use of data with high temporal representativeness reduces the risk of systematic bias typical of satellites with only a single daytime overpass. This underscores the importance of temporal resolution, even in the presence of spatial heterogeneity.

Analysis of the spatial variability of SSR is critically important for a wide range of applications, including environmental state modelling. Although the primary modelling in this study was performed for horizontal surfaces, the provided context includes an important demonstration of how cloud data quality can affect solar radiation estimates on tilted surfaces. Figure 3 shows a map of modelled monthly totals of global horizontal irradiance (GHI) for the Khujir area in July 2023, simulated for a tilted surface using three different cloud data sources: AVHRR, TERRA, and Meteo.

As can be seen from the figure, there is a noticeable discrepancy between the maps generated from different data sources. While the maps based on AVHRR and TERRA data show relatively minor differences across most of the study area, except for its northern part (Figure 3E), the map derived from Meteo data demonstrates substantial differences compared to the aforementioned cloud datasets (Figure 3D,F). This indicates significant uncertainty in the cloud data used for modelling.

Particular attention should be paid to the influence of topography when interpreting daily totals of solar radiation in mountainous regions. In areas with highly dissected terrain—such as the coastline of Lake Baikal—local shading can substantially reduce the duration of direct sunlight during the day, especially in the morning and evening hours. On steep slopes or within narrow valleys, even minor landforms, such as isolated rock outcrops or dense tree cover, can cast persistent shadows that remain unresolved at spatial resolutions of tens to hundreds of meters. Under these conditions, a resolution of 30 × 30 m, despite its apparent detail, may still prove insufficient for adequately capturing microscale variations in insolation. This is especially critical for applied tasks such as siting solar panels or conducting point-based actinometric measurements. Nevertheless, when estimating radiation on a horizontal surface for regional-scale studies, the primary focus should be not so much on achieving maximum spatial detail as on properly accounting for topographic shading in the model, as this factor fundamentally determines the physical representativeness of daily radiation totals in complex terrain.

This conclusion fully aligns with the warning issued by [19] and confirmed by [15] that most existing solar radiation models consist of equations whose coefficients are not universal physical constants but depend on region, climate, calibration period, and even on the specific set of input data. Applying such models without prior calibration inevitably leads to large errors [19].

Although this study employs a physical model, many recent works, e.g., [22,26,84], rely on machine learning (ML) and artificial neural network (ANN) methods. Comparison of our results (R² = 0.54) with theirs shows that ML models generally achieve significantly higher accuracy (often R² > 0.8). However, this comparison is not entirely fair, as ML models typically use numerous predictors and sometimes identify spurious correlations. Physical models like ours are irreplaceable in situations where access to comprehensive meteorological data is limited: in historical reconstructions or in mountainous and remote regions. They are transparent, interpretable, physically based, and do not require large training datasets. As noted in [15], it is precisely these qualities that make them “practical” for solving real-world problems, despite their somewhat lower accuracy. Moreover, ref. [82] demonstrated that even when numerous parameters are available, the best-performing models are often hybrid: they combine physical parameters with empirical coefficients calibrated using statistical or ML methods. An example of such an approach is provided in [30], who successfully applied Random Forest to correct ERA5 biases in Hubei Province, China, or [84], who used ML to enhance classical empirical models.

4. Conclusions

This study provided a critical evaluation of cloud data sources for modelling surface solar radiation in the topographically complex and ecologically unique region of Lake Baikal. The findings yielded several key insights with direct implications for future research and applications.

Firstly, the relative performance of the ERA5 reanalysis dataset was found to be relatively low for precise local-scale radiation modelling in this environment. SSR from ERA5 achieved R² = 0.34, RMSE = 4.724 MJ/m². While ERA5 remains a valuable resource for global and regional climate studies, its resolution and physical parameterisations appear insufficient to capture the fine-scale spatial variability induced by the lake-land-atmosphere interactions around Lake Baikal. Researchers requiring high-fidelity radiation data for local ecological or hydrological models in similar complex terrains should therefore use ERA5-derived values with caution.

Secondly, the research underscored the profound variability in modelling outcomes that stems directly from the choice of cloud cover input. The superior performance of the AVHRR satellite-based dataset over both reanalysis and, notably, ground-based synoptic cloud observations, highlighted a significant finding. It suggested that for modelling purposes, spatially continuous satellite data can provide a more consistent and reliable representation of cloud attenuation than ground-based observations, which may be affected by observer subjectivity and spatial representativeness errors. This confirms the critical importance of selecting appropriate, high-quality cloud masks as a primary input to physical radiation models.

Finally, despite the challenges posed in data accuracy, the synthesis of a robust physical model with high-quality satellite cloud observations—specifically from AVHRR—proved to be a highly effective methodology. This approach successfully generated detailed, reliable, and spatially continuous fields of incoming solar radiation.

A logical extension of this work would be a two-stage analysis: first, evaluating the cloud products’ accuracy at representing instantaneous cloud conditions at satellite overpass times against sky cameras or ceilometers; second, using those findings to interpret their performance in daily integrated models. Furthermore, comparison with established surface radiation products (e.g., CERES FluxByCldTyp, SARAH) would provide additional context for the model’s performance.

To enhance model accuracy, future work should focus on developing a dynamic fusion approach that intelligently combines the strengths of various cloud products, including satellite data like AVHRR and modern geostationary data, with calibrated ground-based observations where available. The integration of higher temporal resolution (e.g., hourly) cloud data could significantly improve the modelling of diurnal radiation patterns, which is critical for applications in solar energy and evapotranspiration modelling. Future direct applications of the generated high-resolution radiation maps to drive specific process-based models will support a range of applied sciences. They can be powerfully leveraged for high-resolution climate reconstructions, detailed landscape differentiation analyses, and modelling of essential biogeophysical processes, such as evapotranspiration, snowmelt, and primary productivity, across regional, sub-regional, and local scales. This work thus establishes a validated framework for solar radiation mapping that can be applied to other areas with scarce data, and complex terrain, contributing to improved environmental monitoring and resource management.