Digital Accessibility of Solar Energy Variability Through Short-Term Measurements: Data Descriptor

Abstract

A variety of factors, such as absorption, reflection, and attenuation by atmospheric elements, influence the quantity of solar energy that reaches the surface of the Earth. This, in turn, impacts photovoltaic (PV) power generation. In light of this, a digital assessment of solar energy variability through short-term measurements was conducted to enhance PV power output. The clear-sky index $\left(K_t^{*}\right)$ methodology was employed, effectively eliminating any indications of solar energy obstruction and comparing the measured radiation to the theoretical clear-sky radiation. The solar energy data were gathered in Mozambique, specifically in the southern region at Maputo–1, Massangena, Ndindiza, and Pembe, in the mid-region at Chipera, Nhamadzi, Barue–1, and Barue–2, as well as in the northern region at Nipepe-1, Nipepe-2, Nanhupo-1, Nanhupo-2, and Chomba, over the period from 2005 to 2024, with measurement intervals ranging from 1 to 10 min and 1 h during the measurement campaigns conducted by FUNAE and INAM, with additional data sourced from the PVGIS, Meteonorm, NOAA, and NASA solar databases. The analysis indicates a $K_t^{*}$ value with a density approaching 1 for clear days, while intermediate-sky days exhibit characteristics that lie between those of clear and cloudy days. It can be inferred that there exists a robust correlation among sky types, with values ranging from 0.95 to 0.89 per station, alongside correlated energies, which experience a regression with coefficients between 0.79 and 0.95. Based on the analysis of the sample, the region demonstrates significant potential for solar energy utilization, and similar sampling methodologies can be applied in other locations to optimize PV output and other solar energy projects.

Dataset: https://github.com/Muco-1990/Accessibility.git (accessed on 11 August 2025).

Dataset License: CC–BY Attribution 4.0 International.

1. Summary

To fulfill its daily requirements, human society has progressed to necessitate a continuously growing energy supply. Historically, humans have relied on their physical strength as a fundamental and adequate energy source, primarily for survival. The solar radiation that reaches the Earth’s surface plays a significant role in various natural processes, including climate change, surface erosion, hydrological cycles, and photosynthesis. As the population expands and industries and technologies advance, there is a heightened demand for energy to facilitate daily activities such as heating, cooling, lighting, and irrigation, in addition to fulfilling industrial needs like large-scale electrification and machinery operation [1,2,3].

Approximately 67% of the global energy is derived from fossil fuels, which emit harmful gases and particles into the atmosphere, leading to severe pollution. Nevertheless, initiatives are underway to significantly curtail their usage and enhance the proportion of clean, green, and renewable energy sources by the year 2050. Despite 660 million individuals lacking access to grid-connected electricity, major corporations have embraced local energy sources, which are particularly beneficial in many countries, with 85% having access to hydroelectric power for electrification. In Mozambique, for instance, 72% of the electricity provided is sourced from hydroelectric means. However, hydroelectric sources, among others, pose the disadvantage of disrupting ecosystems, which will have repercussions for future generations and species. There is a pressing need to explore alternative sources, such as solar energy, which can be harnessed wherever solar radiation is available. Nonetheless, the output of a solar power plant is influenced by the variability in solar energy [1,2,3,4,5,6].

Recent research that extrapolates the performance of solar systems across various global locations has indicated that the energy generated during periods of both high and low solar radiation exhibits significant differences [5,6]. According to recent studies, the energy produced during low solar radiation periods and during high solar radiation periods varies, highlighting the performance of solar systems in diverse regions around the globe [5,6]. The variability in solar energy and its duration across a range of time intervals, such as 24 h, 1 h, 1 min, 1 s, 0.01 s, 0.001 s, 0.0001 s, and 0.00001 s, has been shown to be strongly correlated [7,8,9]. Notable variations on intermediate days were also observed [2,4,10,11], alongside a reduction in amplitude and the identification of actual variables influenced by particle and gas dynamics, among other factors [5,12,13,14].

Utilizing cloud velocity and Global Horizontal Irradiance (GHI), researchers estimated GHI data on a horizontal surface with an optimal tilt angle based on a 5 min model, concluding that variability exists in the tilted surfaces [12,13,14]. They assessed short-term variability and determined that short-term ramp rates were diminished as the size of the plant increased during the long-term data collection [7,15]. They forecasted PV power production from GHI models for renewable resource generation and variable solar resources, discovering fluctuations in solar power variability [5,16,17]. Additionally, they examined PV systems, uncovering limited access due to environmental factors and renewable energy tariffs [18,19].

In order to improve electricity access for various requirements and to foster social development, this study aimed to examine the long-term regressive and spatio-temporal accessibility of solar energy variability through short-scale measurements. The GHI data were gathered from fifteen stations located in the Southern, Mid, and North regions of Mozambique, capturing 24 h amplitudes and short time scales at intervals of 1 and 10 min, as well as 1 h, over a thirty-year period from 1994 to 2024. Solar energy is encompassed within the Mozambique solar energy study project, which is supported by FUNAE [20], INAM [21], PVGIS [22], NASA [23], NOAA [24], and Meteonorm [25]. Some remote sensing data were directly extracted from the database, while additional data from FUNAE and INAM were collected on-site using high-resolution pyranometers, which were recorded in a data logger. Data were gathered through short-scale measurements over a long-term duration of thirty years to accurately assess the variability in solar energy, as there has yet to be a consensus on which measurement interval best captures the variability for any given location.

Throughout this period, the instruments were subjected to regular maintenance to eliminate potential obstructions and shadows [26,27], alongside documentation of rainy days that had a significant effect on solar energy behavior. The solar radiation model was utilized in place of the cloud model [10,11,28,29] to ascertain the $K_t^{*}$ [3,9,11,30,31,32,33], which mitigates the variability in solar energy caused by various factors, including spatial geometry, among others. To evaluate the regressive and spatio-temporal accessibility of solar energy variability across the Southern, Mid, and North regions of Mozambique at a short measurement scale and over an extended data collection period, it was essential to analyze the temporal variability of different types of days, establish correlations between increases at two sensor points, and develop an advisory tool for solar radiation in the regions of Mozambique.

The region can be analyzed through the experimental sampling descriptor of data gathered from the South, Mid, and North areas of Mozambique, employing the regional model, which functions at a resolution between 1 and 10 min and achieves a confidence level of 0.91 regarding overall data quality. The data demonstrate Gaussian statistical properties in relation to the frequency of daily recordings and observations, which have been corrected for inaccuracies caused by various factors such as convection current failures, shading, and obstruction by birds. This study utilizes both the Random Forest model and the Ordinary Kriging model, considering atmospheric conditions of clear skies and removing all variability associated with spatial geometry. The statistical assessment of all variability measures indicates an accessibility metric that shows energy availability surpassing 70% during the period of minimal solar incidence, characterized by predominantly clear and intermediate days. Nevertheless, a decorrelation is noted extending from the Mozambique region on an interprovincial level, revealing a regression with a coefficient of approximately 0.89, inferred from atmospheric parameters.

These results establish a series of modeling steps applicable to all global regions, requiring only local inputs such as location, climate, and acidity, among others. However, it can be demonstrated that within the study area, energy is distributed along the Nhamadzi, Barue–1, Barue–2, and Chipera study paths. As a result, based on annual observations with the highest consistency of measurements from 2005 to 2024, the stations of Nhamadzi and Chipera exhibit the highest density potential for acceptable daily total solar energy, followed by the stations of Barue–2 and Barue–1, in all instances at least 50% based on the evaluation of its radiation equivalent to its $K_t^{*}$.

2. Data Description

2.1. Data Collection and Processing

The FUNAE [20] and INAM [21] solar radiation measurement campaign, along with the PVGIS [22], NASA [23], and Meteonorm [25] solar energy data platforms, gathered the GHI data from 2005 to 2024. This initiative on solar energy variability established a monitoring network throughout the Southern, Mid, and North regions of Mozambique, which includes Maputo City, Gaza, Inhambane, Sofala, Manica, Tete, Zambezia, Niassa, Nampula, and Cabo-Delgado. The network comprised stations outfitted with 16 high-resolution pyranometers. The Campbell CR23X data logger utilized operates at a frequency of 1 Hz, capturing the instantaneous averages over 1 and 10 min. The data adhered to quality control measures (removal of erroneous values) and were later processed using programs specifically designed for calculating radiation at intervals of 1 min, 10 min, and 1 h. Satellite data collected over a span of thirty years provided insights into variability that were not captured by the short-term site data collected from 2012 to 2014, along with comparisons of variability across different range intervals.

The cumulative monitoring network predicted energy output and validated the efficiency of solar PV power installations. Enhanced operational efficiency, anomaly detection, real-time sample collection, climate assessments, and long-term performance are just a few of the benefits offered by the network. Continuous collection and analysis of GHI and DNI (Direct Normal Irradiance) enable more precise energy use planning, quicker problem resolution, and improved overall performance.

2.2. Study Area

Mozambique is located between the longitudes of 30°12′ and 40°51′ E and the latitudes of 10°27′ and 26°52′ S. The network encompassed the following stations, with their respective longitude and latitude coordinates: Chomba (39°23.3′36.16″ E and 11°32′57.57″ S), Nanhupo 1 and 2 (39°30′46.77″ E and 15°57′57.38″ S), Nipepe (32°26′12.82″ E and 13°54′25.935″ S), Chipera (31°40′3.4″ E and 14°58′28.1″ S), Nhamadzi (35°2′18.7″ E and 19°43′46.6″ S), Massangena (32°56′26.7″ E and 21°34′59.5″ S), Lugela 1 and 2 (36°42′47.51″ E and 16°28′4.45″ S), Ndindiza (33°25′22.8″ E and 23°27′37.1″ S), Pembe (35°35′35.5″ E and 22°56′44.3″ S), Barue 1 and 2 (33°13′0.8″ E and 17°47′32.5″ S), and Maputo-1 (32°9′39.8″ E and 23°55′7.8″ S). The data collected span 30 years of measurements from 1994 to 2024, encompassing the months from January to December, and include daily radiation data.

2.3. Specifications of Each Sample File

The “CSV” files, under the titles “daily_GHI_Chomba(2005–2024)”, “daily_GHI_Nanhupo-1 (2005–2024)”, “daily_GHI_Nanhupo-2 (2005–2024)”, “daily_GHI_Nipepe-1 (2005–2024)”, “daily_GHI_Nipepe-2 (2005–2024)”, “daily_GHI_Lugela-1 (2005–2024)”, “daily_GHI_Lugela-2 (2005–2024)”, “daily_GHI_Chipera (2005–2024)”, “daily_GHI_Nhamadzi (2005–2024)”, “daily_GHI_Barue-1 (2005–2024)”, “daily_GHI_Barue-2 (2005–2024)”, “daily_GHI_Pembe (2005–2024)”, “daily_GHI_Ndindiza (2005–2024)”, “daily_GHI_Massangena (2005–2024)”, and “daily_GHI_Maputo–1 (2005–2024)”, refer to the GHI measurements at the stations of Chomba, Nanhupo-1, Nanhupo-2, Nipepe-1, Nipepe-2, Lugela-1, Lugela-2, Chipera, Barue–1 and Barue–2, Nhamadzi, Pembe, Ndindiza, Massangena, and Maputo–1, between the years 2005 to 2024. In each file, column A under the reference “Time” refers to the local measurement time interval; columns B to column AF, under the reference GHI_1 to GHI_31, refer to the GHI measurements on each day of each month (1 to 30 or 31). For example, the terminology “_Jun_Cho” refers to June at Chomba station, the terminology “_Jun_Na_1” refers to June at Nanhupo–1 station, the terminology “_Jun_Na_2” refers to June at Nanhupo–2 station, the terminology “_Jun_Ni_2” refers to June at Nipepe–1 station, the terminology “_Jun_Ni_2” refers to June at Nipepe–2 station, “_Apr_Cha” refers to April at Chipera station, “_Jun_Be_1” refers to June at Barue–1 station, the terminology “_Jun_Be_2” refers to June at Barue–2 station, the terminology “_Oct_Nzi” refers to October at Nhamadzi station, the terminology “_Jun_Pe” refers to June at Pembe station, the terminology “_Jun_Ndza” refers to June at Ndindiza station, the terminology “_Jun_Mna” refers to June at Massangena station, the above with a measurement interval of 1 to 10 min, and the terminology “_MPT–1” refers to June at from Maputo–1 (with a 1-min measurement interval).

In the “CSV” files, under the terms “Chomba_A (2005–2024)”, “Nanhupo–1_A (2005–2024)”, “Nanhupo–2_A (2005–2024)”, “Nipepe–1_A (2005–2024)”, “Nipepe–2_A (2005–2024)”, “Chipera_A (2005–2024)”, “Nhamadzi_A (2005–2024)”1, “Barue–1_A (2005–2024)” and “Barue–2_A (2005–2024)”, and “Lugela–1_A (2005–2024)” and “Lugela–2_A (2005–2024)”, the sample of $K_t^{*}$ data refers to the days analyzed as acceptable days measured during the twelve months of each year among the years 2005 to 2024, with a regular amplitude of 24 h and a measurement interval of 1 to 10 min and 1 h, with the symbols “kt*_C_A” and “Δkt*_C_A” in column A and column B of each file referring to the $K_t^{*}$ and $\Delta K_t^{*}$ on clear sky days. The terms “kt*_Cy_A” and “Δkt*_Cy_A” in column C and column D of each file refer to the $K_t^{*}$ and $\Delta K_t^{*}$ on cloudy sky days; “kt*_I_A” and “Δkt*_I_A” in column E and column F of each file refer to the $K_t^{*}$ and $\Delta K_t^{*}$ on intermediate sky days (if accompanied by the following terminology: “_Cho” refers to the Chomba station, “_Na-1” and “_Na-2” refer to the Nanhupo–1 and Nanupo–2 stations, “_Ni–1” and “_Ni–1” refer to the Nipepe–1 and Nipepe–2 stations, “_Cha” refers to the Chipera station, “_Nzi” refers to the Nhamadzi station, “_Be–1” and “_Be–2” refer to the “Barue–1” and “Barue–2” stations, “_Lu–1” and “_Lu–2” refer to the Lugela–1 and Lugela–2 stations), as applied in the regressive and spatio-temporal study methodology of the variability in solar energy on unacceptable days.

The “CSV” files, under the terms “Chipera_NA (2005–2024)”, “Nhamadzi_NA (2005–2024)”, “Barue–1_NA(2005–2024)”, and “Barue–2_NA (2005–2024)”, give the sample of $K_t^{*}$ data referring to the days analyzed as unacceptable days measured during the twelve months of the 19 years 2005 to 2024, with a regular amplitude of 24 h and a measurement interval of 1 to 10 min and 1 h. The symbols “kt*_C_NA” and “Δkt*_C_NA” in column A and column B of each file refer to the $K_t^{*}$ and $\Delta K_t^{*}$ on clear sky days; “kt*_Cy_NA” and “Δkt*_Cy_NA” in column C and column D of each file refer to the $K_t^{*}$ and $\Delta K_t^{*}$ on cloudy sky days; “kt*_I_NA” and “Δkt*_I_NA” in column E and column F of each file refer to the $K_t^{*}$ and $\Delta K_t^{*}$ on intermediate sky days (if accompanied by the following terminology: “_Cha” refers to the Chipera station, “_Nzi” refers to the Nhamadzi station, “_Be–1” and “_Be–2” refer to the “Barue–1” and “Barue–2” stations). This information is applied in the regressive and spatio-temporal study methodology of the variability in solar energy on unacceptable days.

The file “CSV”, under the heading done_behavior_sigle_day_density, in column A under the symbolic specification kt* and the $K_t^{*}$ under the description of a clear day, is used to study the behavior of the daily course of a clear day in terms of its relationship with the density of the $K_t^{*}$. In the “CSV” file, concerning “location_of_study_stations”, column A under the reference to “ID” refers to the identity assigned to each station by the researcher; column B under the reference to “Name” refers to the name assigned to each station according to its location by the researcher; column C under the reference to “Num_stations” refers to the number of measuring devices (pyranometers) installed in each measuring station; column D under the reference to “Province” refers to the province in which the measuring station is installed; column E and column F, under reference to “Longitude” and “Latitude”, refer to the geographic coordinates longitude and latitude where the measuring stations are located.

Furthermore, the “CSV” files, written with the terminology “_accepted_unaccepted_unapplicable”, refer to the classification of days as acceptable, unacceptable, and not applicable. If they start with the labels “Barue_1_2005_2011”, “Barue_1_2012_2018”, and “Barue_1_2019_2024”, they refer to the classification at the Barue_1 station in the years 2005 to 2024; if they start with “Barue_2_2005_2011”, “Barue_2_2012_2018”, and “Barue_2_2019_2024”, they refer to the classification at the Barue_2 station in the years 2005 to 2024; if they start with “Nhamadzi_2005_2011”, “Nhamadzi_2012_2018”, and “Nhamadzi_2019_2024”, they refer to the classification at Nhamadzi station in the years 2005 to 2024; the labels “Chipera_2005_2011” and “Chipera_2012_2018” refer to the classification at Chipera station in the years 2005 to 2024; the labels “Massangena_2005_2011”, “Massangena_2012_2018”, and “Massangena_2019_2024” refer to the classification at Massangena station in the years 2005 to 2024; the labels “Ndindiza_2005_2011”, “Ndindiza_2012_2018”, and “Ndindiza_2019_2024” refer to the classification at Ndindiza station in the years 2005 to 2024; the labels “Pembe_2005_2011” and “Pembe_2012_2018” refer to the classification at Pembe station in the years 2005 to 2024; and the label “Maputo_1” refers to the classification at Maputo_1 station in the year 2005 to 2024. Each of the previously described files includes a full explanation of the technical specifications and significance of its constituent parameters. The vectors and instructions for managing the solar energy sample for long-term measurement and casual interactive accessibility are also explained in

Table 1. Selection of days at the Barue–1 station.

Files	Content	Interval	Sample
“daily_GHI_Chomba (2005–2024)”, “daily_GHI_Nanhupo-1 (2005–2024)”, “daily_GHI_Nanhupo-2 (2005–2024)”, “daily_GHI_Nipepe-1 (2005–2024)”, “daily_GHI_Nipepe-2 (2005–2024)”, “daily_GHI_Chipera (2005–2024)”, “daily_GHI_Nhamadzi (2005–2024)”, “daily_GHI_Barue-1 (2005–2024)”, “daily_GHI_Barue-2 (2005–2024)”, “daily_GHI_Lugela-1 (2005–2024)”, “daily_GHI_Lugela-2 (2005–2024)”, “daily_GHI_Pembe (2005–2024)”, “daily_GHI_Ndindiza (2005–2024)”, “daily_GHI_Massangena (2005–2024)”, and “daily_GHI_Maputo–1 (2005–2024)”	GHI measurements at the stations	1, 10 min, and 1 h	Input
“Chipera_A (2005–2024)”, “Nhamadzi_A (2005–2024)”, “Barue–1_A (2005–2024)”, and “Barue–2_A (2005–2024)”	$K_t^{\mathrm{*}}$ data for acceptable days measured	1, 10 min, and 1 h	Output and input
“_accepted_unaccepted_unapplicable” starting with “Barue_1_2005_2011”, “Barue_1_2012_2018”, and “Barue_1_2014” refer to the classification at the Barue_1 station in the years 2005 to 2024; “Barue_2_2005_2011, “Barue_2_2012_2018”, and “Barue_2_2019_2024”	acceptable, unacceptable, and not applicable	1 min, and 1 h	Output

.

2.4. Sample Size

Utilizing data from the FUNAE and INAM campaigns and the PVGIS, NASA, and Meteonorm databases, the projects titled MZF01-Maputo–Maputo-1, MZ17–Gaza–Ndindiza, and MZ15-Gaza-Massangena were conducted. The samples for MZ20–Inhambane–Pembe, MZ11–Sofala–Nhamadzi, MZ21–Manica–Barue–1 and –2, MZ06–Tete–Chipera, MZF01-Niassa-1 and Nipepe-2, MZF24-Nanpula-Nanhupo-1 and Nanhupo-2, and MZF03-Chomba, which encompassed a comprehensive 19 years of measurements from 2005 to 2024, were utilized to compute solar radiation from 6 to 18 h. This interval represents the incidence of solar energy on the earth’s surface across the study area. Consequently, this analysis yielded daily data for each radiation zone, amounting to approximately 147,745.00 for measurements taken at 1 to 10 min intervals and 297,402 for measurements recorded at hourly intervals.

2.5. Data Values Fluctuations

The selection process for each station is elucidated below, illustrating how the data values fluctuated on each day of every month under examination. This required an initial categorization into classes of acceptable days, during which the measured GHI spectrum was in close proximity (or closeness) to the reference spectrum; unacceptable days, when the experimental GHI spectrum deviated significantly (or farness) from the reference spectrum; and unapplicable days, characterized by the GHI spectrum reflecting approximately 60% of the measured data, which corresponded to a spectrum with values beyond the solar constant, resulting in a highly distorted spectrum in comparison to that of the Student’s T-test, considering that the daily sample follows a binomial distribution with Gaussian properties.

At the Barue–1 station, from 2005 to 2011, around 65.0% of the days were classified as acceptable, 34.0% as unacceptable, and 1.0% as unapplicable, with the definitions of each category of day presented in

Table 2. Selection of days at the Barue–1 station in 2005–2011.

Month	Acceptable Days		Unacceptable Days		Unapplicable Days
	Nr.	Id.	Nr.	Id.	Nr.	Id.
January	11	1, 17, 18, 19, 23, 24, 25, 26, 28, 30, 31	20	2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 20, 21, 22, 27, 29	0	None
February	17	1, 3, 4, 10, 15, 16, 17, 18, 19, 20, 21, 23, 24, 25, 26, 27, 28,	11	2, 5, 6, 7, 8, 9, 11, 12, 13, 14, 22	0	None
March	24	1, 2, 3, 4, 5, 6, 7, 8, 9, 12, 13, 14, 15, 17, 18, 19, 20, 21, 22, 23, 24, 25, 29, 30	7	10, 11, 16, 26, 27, 28, 31	0	None
April	25	1, 2, 3, 4, 6, 7, 8, 9, 10, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 26, 27, 28, 29, 30	4	11, 12, 5, 24, 25	0	None
May	28	1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31	3	18, 19, 20	0	None
June	22	2, 3, 4, 5, 6, 7, 8, 9, 13, 14, 15, 17, 19, 20, 22, 25, 26, 27, 28, 29, 30	8	10, 11, 12, 16, 18, 21, 23, 24	0	None
July	25	1, 2, 3, 4, 5, 7, 8, 9, 10, 12, 13, 14, 15, 16, 17, 20, 21, 23, 24, 25, 26, 27, 28, 29, 31	5	6, 11, 18, 19, 30	0	None
August	15	3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17	16	1, 2, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, m29, 30, 31	0	None
September	14	4, 5, 6,7, 8, 9, 11, 17, 23, 24, 25, 26, 27, 28	15	1, 2, 3, 12, 13, 14, 15, 16, 18, 19, 20, 21, 22, 29, 30	0	None
October	21	2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 16, 20, 21, 22, 25, 26, 27, 29, 30, 31	8	1, 7, 14, 15, 17, 19, 23, 24	2	18, 28
November	19	1, 2, 5, 6, 7, 13, 14, 15, 16, 17, 18, 20, 21, 25, 26, 27, 28, 29, 30	11	3, 4, 8, 9, 10, 11, 12, 19, 22, 23, 24	0	None
December	15	1, 2, 3, 4, 5, 9, 10, 11, 13, 23, 24, 25, 26, 27, 28	16	6, 7, 8, 12, 14, 15, 16, 17, 18, 19, 20, 21, 22, 29, 30, 31	0	None

.

In accordance with the analysis presented in Table 2, data from the Barue–1 station during the years 2012–2018 indicated that 63.0% of the days were deemed acceptable, while 36.0% were classified as unacceptable, and 1.0% were categorized as unapplicable. For the period of 2019–2024, the station recorded 55.0% of acceptable days, 31.0% of unacceptable days, and 14.0% of unapplicable days. At the Barue–2 station, the observations from 2005–2011 revealed that approximately 57.0% of the days were acceptable, 29.0% were unacceptable, and 14.0% were unapplicable. In the subsequent period of 2012–2018, around 63.0% of days were acceptable, 36.0% were unacceptable, and 1.0% were unapplicable. Furthermore, during 2012–2018 at the Barue–2 station, it was noted that about 70.0% of the days were acceptable, 29.0% were unacceptable, and 1.0% were unapplicable. At the Chipera station, the data from 2005–2011 showed that approximately 67.0% of days were acceptable, 24.0% were unacceptable, and 9.0% were unapplicable. In the period of 2012–2018, the Chipera station recorded about 40.0% of acceptable days, 48.0% of unacceptable days, and 12.0% of unapplicable days. For the years 2019–2024, the station observed approximately 52.0% of acceptable days, 39.0% of unacceptable days, and 9.0% of unapplicable days. At the Nhamadzi station, the observations from 2005–2011 indicated that around 68.0% of days were acceptable, 26.0% were unacceptable, and 6.0% were unapplicable. In the following period of 2012–2018, the Nhamadzi station reported approximately 0.0% of acceptable days, 99.0% of unacceptable days, and 1.0% of unapplicable days. During 2019–2024, the Nhamadzi station recorded approximately 0.0% of acceptable days, 38.0% of unacceptable days, and 62.0% of unapplicable days.

Across the Southern region, at the Maputo–1 station, the data from 2005–2011 indicated that approximately 42.0% of days were acceptable, 30% were unacceptable, and 28% were unapplicable, with no observations recorded for the periods of 2012–2018 and 2019–2024. At the Massangena station, the observations from 2005–2011 revealed that approximately 72.0% of days were acceptable, 23.0% were unacceptable, and 5.0% were unapplicable, as illustrated in Figure 1, obtained using for all stations, the Supplementary Material Files Barue-1_A (2012–2014).csv, Barue-1_NA (2012–2014).csv, Barue-2_A (2012–2014).csv, Barue-2_NA (2012–2014).csv, Barue_1_2012_accepted_unaccepted_unapplicable.csv, Barue_1_2013_accepted_unaccepted_unapplicable.csv, Barue_1_2014_accepted_unaccepted_unapplicable.csv, Barue_2_2012_accepted_unaccepted_unapplicable.csv, Barue_2_2013_accepted_unaccepted_unapplicable.csv, Barue_2_2014_accepted_unaccepted_unapplicable.csv, Chipera _2012_accepted_unaccepted_unapplicable.csv, Chipera _2013_accepted_unaccepted_unapplicable.csv, Chipera_A (2012–2014).csv, Chipera_NA (2012–2014).csv, Massangena_2012_accepted_unaccepted_unapplicable.csv, and Massangena_2013_accepted_unaccepted_unappplicable.csv.

At the Massangena station during the period from 2005 to 2011, it was noted that approximately 71.0% of the days were classified as acceptable, 29.0% as unacceptable, and 0.1% as unapplicable, with no data recorded for the years 2012 to 2018. In contrast, at the Ndindiza station from 2019 to 2024, around 73.0% of the days were deemed acceptable, 23.0% unacceptable, and 4.0% unapplicable. Furthermore, at the Ndindiza station for the years 2005 to 2011, approximately 68.0% of days were acceptable, 31.0% unacceptable, and 1.0% unapplicable. During the period from 2012 to 2018 at the same station, about 70.0% of days were acceptable, 29.0% unacceptable, and 1.0% unapplicable. At the Pembe station from 2005 to 2011, it was observed that approximately 18.0% of days were acceptable, 9.0% unacceptable, and 73.0% unapplicable. In the subsequent period from 2012 to 2018, the Pembe station recorded approximately 81.0% of days as acceptable, 18.0% as unacceptable, and 1.0% as unapplicable. Lastly, at the Pembe station for the years 2019 to 2024, around 81.0% of days were classified as acceptable, 19.0% as unacceptable, and 0% as unapplicable. At the Lugela–1 station during the years 2005 to 2011, approximately 64.0% of days were acceptable, 18.0% unacceptable, and 18.0% unapplicable. In the period from 2012 to 2018 at the Lugela-1 station, about 78.0% of days were acceptable, 12.0% unacceptable, and 10.0% unapplicable. Finally, at the Lugela-1 station for the years 2019 to 2024, approximately 77.0% of days were deemed acceptable, 7.0% unacceptable, and 0% unapplicable. At the Lugela-2 station from 2005 to 2011, it was observed that approximately 67.0% of days were acceptable, 27.0% unacceptable, and 6.0% unapplicable. During the period from 2012 to 2018 at the Lugela-2 station, around 71.0% of days were classified as acceptable, 8.0% as unacceptable, and 21.0% as unapplicable. Lastly, at the Lugela-2 station for the years 2019 to 2024, approximately 56.0% of days were acceptable, 22.0% unacceptable, and 22.0% unapplicable.

3. Methods

3.1. Clear-Sky Index

The horizontal direct normal radiance at clear sky was discovered after the features of the perfect development of solar radiation were investigated. It explains the day’s spectrum and discovers that, while solar incidence is high during the peak period, the incidence of GHI on the earth’s surface is lower at the start and end of the day. The curve is Gaussian [8,9,15], and the days under study include the radiation distribution that would be expected on a clear sky day (that is, with an atmosphere devoid of clouds). The $K_t^{\mathrm{*}}$ was defined by relating the GHI and the clear-sky radiation ($G_{Clear}$), providing a random values of GHI, given in Equation (1) [7,17]:

$$K_t^{\mathrm{*}}={\displaystyle \frac{GHI}{G_{Clear}}}$$

(1)

By using the e (ramp rate) pattern, the values obtained present the best fit in defining the values of the normalized model. The GHI and Total Theoretical Radiation spectra were used in combination with time to select a maximum of 10 days with the GHI behavior closest to the Total Theoretical Radiation, or acceptable, and similarly for days that were not acceptable [3,18].

3.2. Process for Clustering

With the days modeled to correspond to each quartile, including the designation of the first ($T_1$), second ($T_2$), third ($T_3$), interquartile (IQR), the lower whisker $\left(w_{low}\right)\left(T_1-1.5ITR\right)$, the upper whisker $\left(w_{up}\right)\left(T_1+1.5ITR\right)$, and the outliers $\left(data<w_{low}or>w_{up}\right)$, the probability density function was calculated using the kernel density estimator function [19,20,21]. The days chosen for each month were arranged in a table that included the reference day and the mean value. The spectrum was then plotted using the function, and, as a result, the median values were determined. In graphical terms, the sample was categorized into classes. As is customary for cloudy sky days, the days of the year in which their horizontal and vertical coordinates are located in intervals before and after the median of the values and below were designated as clear sky days; and, finally, the days in which their coordinates are located above the values, regardless of what the values are, were defined as intermediate sky days [21,22].

3.3. Regression and Correlation

Utilizing values for the various day classes (clear, intermediate, and cloudy), a correlation function based on the distance from the correlation coefficient or systematic correlation of the $K_t^{\mathrm{*}}$ and ${∆K}_t^{*}$ values was performed, as shown in Equation (2) [3,21,23]:

$${\chi }_{ij}^{{∆K}_t^{*}}={\displaystyle \frac{cov\left(∆K_{t,i}^{*}\left(t\right),∆K_{t,j}^{*}\left(t\right)\right)}{{\sigma }_{∆K_{t,i}^{*}\left(t\right)}{\sigma }_{∆K_{t,j}^{*}}}}$$

(2)

Random values, with increments $∆K_{t,i}^{*}\left(t\right),∆K_{t,j}^{*}(t)$ and metric standard deviation ${\sigma }_{∆K_{t,i}^{*}\left(t\right)},{\sigma }_{∆K_{t,j}^{*}}$, individually over a period of time $t$ between two locations $i,j$, are used to discover the relationship between two points, $x$ and $y$, with distance $d_{ij}$, both statistically and geographically. The correlation of the $K_t^{\mathrm{*}}$ values between two equally spaced measuring stations was established, highlighting the initial equidistant location at Nhamadzi, followed by Barue–1 and Barue–2, then evaluating Chipera. The systematic correlation model, initially proposed by Marcos et al. (2011) [33], given as ${\chi }_{ij}^{∆K_t^{*}}=exp\left({\displaystyle \frac{t^{-1}{d}_{ij}ln\left(\mathrm{0,2}\right)}{\mathrm{1,5}}}\right)$, was used to compare the systematic relationship of increases in the $K_t^{\mathrm{*}}$. Finally, using a set of relative velocity values for the Southern and Mid regions, Hoff and Perez (2012) [10] proposed a spatial correlation coefficient model given as ${\chi }^{∆k_t^{*}}={\left(1+{\displaystyle \frac{d_{ij}}{t.v}}\right)}^{-1}$. To analyze the accessibility of solar energy, the distribution of daily energy transfers and the number of acceptable, unacceptable, and non-applicable days were examined. According to the density estimation kernel, the best days were shown in the quantitative diagram as the most distinct and the nubs.

The computerization for analysis in terms of logarithmic regression was provided by Equation (3):

$$y^{∆K_t^{*}}=f\left({∆K}_t^{*},\beta ,\epsilon \right)=∆K_{t,j}^{*}\left(t\right)={\alpha }_l+{\beta }_{ij}^{{∆K}_t^{*}}∆K_{t,i}^{*}\left(t\right)+{\epsilon }_t$$

(3)

Taking into account the regression matrix alongside other elements such as $y^{∆k_t^{*}},K_t^{*},\beta$, and ${\epsilon }_t$ matrix residuals, one is led to observe a trend indicating a greater deviation among pairs of stations for various regression models [3,21,23]. This trend is influenced by the multiplicative atmospheric transmittance $\left(\tau \right)$ throughout the study area, as depicted in Figure 2a. The primary contributors to this transmittance are water vapor $\left({\tau }_w\right)$ and uniform mixed gases $\left({\tau }_g\right)$, which exhibit values of 0.9986 and 0.9865, respectively. This is followed by ozone $\left({\tau }_0\right)$ with a range of 0.9758, aerosols $\left({\tau }_a\right)$ at 0.9656, and 0.8992 attributed to Rayleigh/Mie scattering $\left({\tau }_r\right)$. Furthermore, Figure 2b demonstrates that during the rainy and hot seasons, the transmittance nears 1, a result of the heightened excitation of atmospheric particles and the consequent emission of absorbed energy (obtained using the Supplementary Material files, behavior_sigle_day_density.csv, daily_GHI_Barue-1 (2012–2014).csv, daily_GHI_Barue-2 (2012–2014).csv, daily_GHI_Chipera (2012–2014).csv, daily_GHI_Maputo-1 (2012–2014).csv, daily_GHI_Massangena (2012–2014).csv, daily_GHI_Ndindiza (2012–2014).csv, daily_GHI_Nhamadzi (2012–2014).csv, and daily_GHI_Pembe (2012–2014).csv). Conversely, in the dry and cold seasons, the transmittance typically hovers around 0.3, which can be attributed to the stability of atmospheric conditions and the increased absorptivity of solar energy.

3.4. Validation and Data Curation

The duration of incidence of solar radiation was extracted from the daily solar energy sample gathered from 2005 to 2024. Missing data were interpolated to fill up the gaps. After determining the theoretical clear-sky radiation and comparing it to the measured GHI, the days were classified as acceptable or undesirable. To exclude outliers and produce results with a larger margin of error, the days were statistically examined independently; eventually, the final % helped determine the $K_t^{*}$ values and the summative assessment.

The GHI and $K_t^{*}$ data sample was registered on the ePPI Reviewer 6 platform, in the link https://eppi.ioe.ac.uk/eppireviewer-web/home (accessed on 12 May 2025), used to register also the research originality as well as to access the systematic review channel, version 6.15, on 23 October 2023, under ID: 44675. Having generated around 756 of the keywords collected that interconnect from the interconnection diagram built in VOS explorer (a systematic tree generator of related keywords from a search key, consulted on 14 April 2025; available via the link https://app.vosviewer.com/), and then validated, the system presented a set of meta-analyses guiding us to the following: the determination of the clearness sky index, the determination of $K_t^{*}$ as the selected method, and, with the randomized values of this course evaluation diary of a day, its temporal deviation during a year, the temporal analysis using histograms, the analysis of the index of variability $K_t^{*}$ as a function of time of day, the rate of variability using various methods, the adjustment of normalized $K_t^{*}$, the study of the effects of $K_t^{*}$, the temporal variability of a singular measurement point and the spatial–temporal variability between two points, and the correlation and regression of $K_t^{*}$. Furthermore, the data were moved to the view potential in the STATA Software analysis, version 18.3. Several meta-analyses (ID: 36458) that highlighted suggestions for energy accessibility in various stations across the selected section were comparable.

3.5. Noise in the Solar Energy and Quality Dataset

The majority of the sample data collected on each day analyzed within the specified range included values derived from the solar constant or the extraterrestrial solar energy spectrum. Values that fell outside this spectrum, often due to various factors such as multiple solar reflections, human interference, obstacles, shading, and external lighting, were categorized as unacceptable days. These instances were rectified through interpolation utilizing Random Forest machine learning models to mitigate excessive fluctuations. In situations where more than 50% of the measurements were missing due to measurement failures, shading, power outages, or failures of mini solar power supplies connected to grounded power supplies, these days were deemed non-applicable. The final outcomes of the $K_t^{*}$ classification indicated that the majority of days exhibited intermediate sky types and clear sky conditions, with a lower frequency of cloudy sky days recorded in the study area compared to regions with high solar incidence.

4. Usefulness and Applicability of the Solar Energy Dataset

For short-scale measurements, the sample was assessed utilizing standardized pyranometers over a duration ranging from one to ten minutes. The data logger captured the sample, and the computer application “NRD” processed the results. Subsequently, Equation (1) was applied to compute the $K_t^{*}$, with classifications of clear, cloudy, and intermediate sky days assigned to the randomized $K_t^{*}$ data. Furthermore, across all seasons, clear sky days exhibit a high energy flow characterized by an index approaching 1. In contrast, cloudy sky days, which significantly obstruct the transmission of solar energy, are recorded with a clear-sky index nearing 0.2. Intermediate sky days display characteristics that are intermediate between the two previously mentioned types. An examination of all day types reveals a significant fluctuation in the clear-sky index, with values ranging from 0.2 to 1.

To determine the proportion of acceptable, unacceptable, and unapplicable days, the spectral comparison of the clear-sky radiation (ignoring all atmospheric constituents) and the GHI (radiation lowered by the various atmospheric constituents: clouds, gases, water vapor, etc.) was determined. Using clear, cloudy, and intermediate sky days as well as acceptable, unacceptable, and unapplicable days, this qualitative analysis shows the variability in solar energy. The $K_t^{*}$ development of each type of day as well as of all types of days has a central maximum close to zero, always varying in the range of −1 to 1. Intermediate sky days with intermediate characteristics between clear and intermediate sky days are potentially the ones that most affect photovoltaic production, registering an abrupt decrease at a frequency of around 0.8 and then with wide arms in which the solar radiation gradually decreases, impacting the output power in a solar PV power plant.

These data provide energy levels, as well as periods of lower and higher incidence (June and December for the study region), that constitute a tool for dimensioning PV system projects based on the energy available at each location. Knowledge and optimal handling of these energy parameters eliminate the effect of variability on the output of a solar plant, by a priori preventing the PV cells from being impacted by the high variability in solar energy, which can occasionally result in hot spots and overloads that impact the PV modules, the optimal operation of the systems, and the final PV production at the output of a solar plant, extending the useful life of the system.

The association between clear, cloudy, and intermediate sky days, as well as of all days during the full research period, was examined using Equations (2) and (3) for each class of acceptable and unacceptable days. It shows that the increasing distances, the spatial correlation structures of the three sky types along the analysis section, also differ in their decay rates: for acceptable days, the approximate values of ${\chi }_{ij}^{K_t^{*}}$ under cloudy sky conditions are 0.79565, clear 0.8783, intermediate 0.8579, and all sky types 0.8024; on unacceptable days, the values are as follows: under cloudy sky conditions 0.8524, clear 0.8828, intermediate 0.6854, and all sky types 0.6325.

The region exhibits a non-linear regression with a tendency towards logarithmic behavior, which is characterized by a regression coefficient $y^{∆K_t^{*}}$ of approximately 0.8254 and 0.9684 for all types of days. For the $K_t^{*}$ values and their increase for acceptable days, the regression coefficients are as follows: 0.8256 and 0.8483 for clear days, 0.7564 and 0.8489 for cloudy days, 0.7225 and 0.8447 for intermediate sky days, and 0.7178 and 0.7459 for all sky types. For unacceptable days, the regression coefficients are as follows: for clear days 0.7458 and 0.7248, for cloudy days 0.6487 and 0.8789, for intermediate sky days 0.7489 and 0.8789, and for all sky types 0.7885 and 0.8487.

The trajectory back to the norm is more noticeable on days with intermediate sky conditions, in comparison to other types of sky conditions. The geospatial–temporal distribution of solar energy indicates the frequency of increasing trends on clear sky days being higher in 2024 than it was in 2005. On cloudy sky days, there is a greater tendency for the clear-sky index to rise. Prior to the $K_t^{*}$ values trending higher in 2024, the frequency of occurrence density was higher in 2005 but declined thereafter. The $K_t^{*}$ value was 0.6218 in Maputo, 0.8778 in Inhambane, in Tete an average of 0.9979, 0.8211 in Sofala, 0.7258 in Manica, 0.6997 in Zambezia, 0.7320 in Niassa, 0.9287 in Niassa, 0.8616 in Nampula, and 0.7628 in Cabo-Delgado, as shown in Figure 3a, obtained using the files Ndindiza_2012_accepted_unaccepted_unapplica, Ndindiza_2013_accepted_unaccepted_unapplicable.csv, Ndindiza_2014_accepted_unaccepted_unapplicable.xlsx, Nhamadzi _2012_accepted_unaccepted_unapplicable.csv, Nhamadzi _2013_accepted_unaccepted_unappli, Nhamadzi _2014_accepted_unaccepted_unappli, Nhamadzi_A (2012–2014).csv, Nhamadzi_NA (2012–2014).csv, in Supplementary Materials.

In all measurement years, as illustrated in Figure 3b, the average values are −0.0416 in Maputo, −0.0686 in Gaza, 0.0878 in Inhambane, 0.0941 in Tete, −0.0654 in Sofala, −0.01985 in Zambezia, −0.2333 in Niassa, −0.20427 in Nampula, and 0.01537 in Cabo-Delgado province.

The region demonstrates significant potential for solar energy, as depicted in Figure 4a, based on the digital accessibility of solar energy, which is systematically organized in the database available at https://github.com/Muco-1990/digital_accessibility__solar_energy_variability.git (accessed on 11 August 2025). The average calculated $K_t^{*}$ potential for the region stands at 0.86. However, the north-central channel experiences moderate energy flows, while the south-central channel encompasses areas with exceptional flow. This predicted and digitally represented energy allows the region to generate photovoltaic (PV) energy consistently, mitigating fluctuations and ensuring the optimal long-term operation of plants while reducing potential pollution and electronic waste. When the predictor elements are aggregated in total transmittance, the coverage rate results in ∆$K_t^{*}$ as shown in Figure 4b, which is remarkably small, approximately −0.002 (analyzed using the file done_behavior_sigle_day_density.csv in the Supplementary Materials).

Conversely, this enhances the energy prediction mentioned earlier. Mozambique displays a transitive $K_t^{*}$ with a favorable solar energy incidence in comparison to other Southern African nations. However, tropical climate regions generally experience substantial fluxes of full PV solar energy incidence, around 87%, which is sufficient for optimal PV excitation, as demonstrated in Figure 4c. Nevertheless, when industrial activities, human actions, and natural resources are intensified, the introduction of gases and particles leads to a significant reduction in solar energy transmittance, posing challenges due to various atmospheric factors, as can be concluded looking at the files Pembe_2012_accepted_unaccepted_unapplicablle.csv, Pembe_2013_accepted_unaccepted_unapplicablle.csv, Pembee_2014_accepted_unaccepted_unapplicable.csv, and behavior_sigle_day_density.csv in supplementary materials.

Limitations

The challenges faced during the data collection process included the inability to install radiometers on unshaded towers, frequent interruptions in the conventional electric current connected to the solar PV-hybrid data storage base within the data logger, and bird obstructions that complicated measurements, particularly around the central region stations. However, techniques were implemented to eliminate any potential sample influence errors. The lack of access to GHI data samples measured at short intervals (less than one minute and ten minutes) hindered the ability to compare the raw samples. A binomial distribution can be utilized to classify the different types of days, akin to the study that examines cloud speed, dynamics, and hours of sunlight brightness.