Relationship between Ultraviolet-B Radiation and Broadband Solar Radiation under All Sky Conditions in Kuwait Hot Climate

Abstract

In the present study, continuous measurements of solar global (G) and ultraviolet-B (UVB) radiation are taken in Kuwait for 2014–2019 for all weather conditions. Hourly curves show a sinusoidal behavior for both G and UVB radiation. Statistical analysis indicates that there is a good agreement between hourly G and hourly UVB as the coefficients of determination (R²) for all years are larger than 0.91 and the root-mean-square error (RMSE) and mean bias error (MBE) are very small. The hourly percentage ratio (UVB/G) is found to decrease with G due to cloudy sky conditions. In addition, the ratio (UVB/G) tends to decrease with global clearness index (K_T), indicating that a higher ratio of (UVB/G) can be obtained for a cloudier atmosphere. Another interesting finding is that K_T and the UVB index (K_TUVB) are directly proportional, and a third-order polynomial fit gives an acceptable formula (R² = 0.859). Daily G and UVB values are very well correlated as R² is very close to unity for all years. The values of RMSE and MBE obtained from daily analysis are greatly enhanced as the values of RMSE and MBE are almost zero. The maximum G and UVB radiation obtained is 27.94 MJ/m² and 0.0044 MJ/m², respectively, with both occurring in June 2015. Finally, there is an excellent linear fit between the monthly G and monthly UVB radiation as R² is almost equal to unity and RMSE and MBE are negligible. Thus, the predicted daily or monthly empirical formula can be utilized with a very high accuracy to predict both daily and monthly UVB values at locations in Kuwait where G is measured.

1. Introduction

The irradiance received by Earth is vital for the Earth–atmosphere system energy balance. Accordingly, a good understanding of irradiance and its short-term and long-term trends is essential for several applications including the verification of climate models and the use of renewable solar energy. UV radiation forms a small fraction of the solar spectrum with wavelengths in the range of 100–400 nm, making about 8.73% of the spectrum at Earth’s surface [1,2]. UV radiation is commonly categorized into three different wavelength bands depending on harmful results on the skin: UVC (100–280 nm), which is completely depleted by ozone and oxygen; UVB (280–320 nm), which is consumed by ozone, and UVA (320–400 nm), which is slightly affected by ozone. UVC, UVB, and UVA represent 1.5%, 1.33%, and 5.9% of the solar spectrum, respectively. On the one hand, a little to moderate dose of ultraviolet solar radiation is fundamental in producing vitamin D3. Conversely, extra amounts can produce harmful effects on the skin and eyes. UV radiation changes greatly with latitude and local time due to the change in the sun elevation. In addition, UV radiation is usually affected by environmental conditions. UVB is responsible for sunburns and suppression of the human immune system. Due to its double-edged-sword impact, UVB radiation has recently attracted substantial attention. Many researchers have discussed the advantage and disadvantages of UVB radiation [3,4,5].

Despite the significant interest in the biological impacts of UV radiation [6,7,8,9,10,11], sensors capable of accurately measuring UV radiation are relatively expensive, which puts constraints on research budgets. As a result of such a limitation, interest in developing models that can estimate UV from the lower-cost G irradiance measurements has grown [12,13,14,15,16,17].

Elani [18] measured UV at constant periods to investigate daily, monthly, and yearly radiation in Riyadh, Kingdom of Saudi Arabia. The author concluded that different climate factors have a significant impact on UV scattering, UV reflection, ozone, and cloud layers in Riyadh. Kudsih et al. [19] analyzed the UVB segment and employed Bouguer’s law to present UVB radiation related to optical depth and air mass. The monitored UVB was used to find the optical depth utilizing an updated Lambert–Beer’s law. The predicted results revealed reliable UVB portions. Villán et al. [20] proposed new correlations that permitted evaluating hourly UV from the measured G, K_T, and air mass. An analysis of clearness index for UVB, UVA, and G was introduced by Kudsih et al. [21] adapting measured data for the period from 1995 to 2001. Clearness indices of both G and UVA had the same values, but the clearness index of UVB radiation was twice as small. The authors showed that the mean monthly UV index did not exceed a certain limit. The authors proposed a correlation to estimate UVB at locations where G measurements were available (but not UVB). Leal et al. [22] used suitable sensors to measure daily G and UV radiation. They produced various models to evaluate daily UV radiation from daily G radiation, hence overcoming the common problem of scarcity of UVB measurements due to the high cost of UVB sensors. Hourly UVB radiation and the minimum erythemal dose (MED) utilizing humidity and G were predicted by Ghoneim et al. [23] for the period of 2010–2011 in Kuwait. They stated that relationships were affected by cloud and air mass. Statistical calculations showed values of 0.92 and 12% for R² and RMSD, respectively.

UVB/G ratio variations are related to the change in different geophysical parameters. Published data indicate a broad UVB/G ratio change (0.02–0.80%) for certain sites [24,25,26,27]. A UVB/G ratio variation is attributed to the strong spectral dependence of solar radiation transmittance on optical air mass, which results in various changes in incident solar UVB and G. The change in UVB/G ratio under several atmospheric conditions at Athalassa, Cyprus was examined by Jacovides et al. [28]. Trabea and Salem [29] reported an average of 3.5% for Cairo, Egypt, while a monthly average from 2.7% to 5.2% was recorded by Martinez-Lozano et al. [30] for Valencia, Spain.

Lee et al. [31,32,33] examined the spectral dependence of aerosols, ozone, and clouds on UVB, UV, and G in South Korea. They showed that the UVB/G ratios increased with decreasing clearness index, indicating that UVB and G were affected in different ways by various attenuating parameters. The impact of aerosols and clouds on G and UVB was studied by Kim et al. [34] utilizing measurements from various locations in South Korea. They concluded that the ratio (UVB/G) was inversely proportional to K_T, which indicated that UVB and G were influenced in different ways by different attenuating parameters. The authors also investigated the relationship between K_T and clearness index of UVB radiation (K_TUVB) for each site in their study. They illustrated that the relation between the two parameters was not exactly linear, because of the various impacts of weather conditions on G and UVB. (UVB/G) increases with cloud cover, showing that G penetrated clouds more effectively than UVB. They stated that the clouds and aerosols impacts on G and UVB were related to local climate variations.

Libra et al. [35] presented the structure of the photovoltaic (PV) system and reported the monitored data during the solar eclipse of March 2015. The PV power plant was set-up on the roof of the football stadium and the collected data were discussed in detail. Monitoring of mean UV radiation during 2003 to 2017 at various locations in Saudi Arabia are carried out by Khalil et al. [36] to determine UVB, UVBext, UVI, K_TUVB and total ozone column. The calculated UVB agree well with UVB measurements. The error between recorded and estimated UVB radiation varies from 1.27 to 3.87%.

In the present work, continuous measurements of UVB radiation and G radiation are carried out in Kuwait for 2014–2019. The primary purpose of the current research is to introduce the theoretical correlation for different sky conditions to determine UVB from G radiation in Kuwait. The variabilities of both hourly, daily, and monthly G and UVB radiation are examined to check the relationship between G and UVB radiation on hourly, daily, and monthly bases. Regression analysis is employed to derive an empirical correlation among UVB and G radiation on hourly, daily, and monthly bases. The predicted equation can be utilized to calculate UVB for other sites where G data are available (but not UVB). The derived correlations accuracy is examined using the two common statistical parameters, namely RMSE and MBE. The atmospheric attenuation significantly reduces (UVB/G) at the surface of the Earth in comparison to its magnitude at the atmospheric top. The reduction is substantial because of atmospheric parameters that attenuate UVB more efficiently than G. Thus, the second target of this work is to determine the regular change in (UVB/G) ratio employing hourly data of G and UVB radiation. Finally, the variation in the hourly ratio (UVB/G) as a function of K_T as well as the relationship between global clearness index (K_T) and UVB clearness index (K_TUVB) are studied.

2. Methodology

Uncertainties in the calculation of UVB and G radiation are decreased by adapting K_T. The clearness index or the hourly value of hemispherical transmittance (K_T) is a dimensionless factor, and it is the proportion of horizontal global radiation, G, and extraterrestrial radiation, G_ext. Thus, the hourly value of hemispherical transmittance is given by:

$$K_T=\frac{G}{G_{ext}}$$

(1)

Horizontal extraterrestrial radiation is given by the accurate relationship [37]:

$$G_{ext}=G_{SC}\left(1.000110+0.034221cosB+0.001280sinB+0.000719cos2B+0.000077sin2B\right)cos{\theta }_z$$

(2)

The parameter B is expressed as:

$$B=2\pi \left(\frac{n-1}{365}\right)$$

(3)

where:

n is the year day (a number between 1 and 365);

θ_z is the zenith angle (°).

G_sc is the solar constant (1367 W/m²);

The air mass (m) is:

$$m=\frac{1}{cos{\theta }_z}$$

(4)

The zenith angle (θ_z) is expressed as [37]:

$$cos{\theta }_z=cos\phi cos\delta cos\omega +sin\phi sin\delta$$

(5)

where:

$\phi$ is the latitude (°);

ω is the hour angle (°).

The declination angle (δ) is approximated as [37]:

$$\delta =\frac{180}{\pi }\left[0.006918-0.399912\cos B+0.070257\sin B-0.006758 \cos 2B+0.000907\sin 2B-0.002697\cos 3B+0.00148\sin 3B\right]$$

(6)

UVB transmittance (K_TUVB) can be expressed as [38]:

$$K_{TUVB}=\frac{UVB}{UV{B}_{ext}}$$

(7)

UVB_ext is extraterrestrial UVB radiation on a flat area and can be expressed as [38]:

$$UV{B}_{ext}=G_{scUVB }\left(\frac{12}{\pi }\right)E_o{{\displaystyle \int }}_{{\omega }_2}^{{\omega }_1}\sin \left(\theta \right)d\omega$$

(8)

where:

θ is the solar elevation angle;

E_o is Earth’s orbit correction factor for the eccentricity;

ω₁ and ω₂ is the solar angle at start and end, respectively;

G_scUVB is the UVB solar constant (21.51 W/m²) and it can be determined from spectral data proposed by Anton et al. [39] and Serrano et al. [40].

3. Statistical Methods

The precision of various correlations derived in this work is examined utilizing the RMSE and MBE. The RMSE indicates the differences between predicted values and measured ones; hence, a small RMSE is required. The MBE characterizes the average bias in the prediction; hence, a negative MBE implies that the calculated values are underestimated, whereas a positive MBE indicates that the calculated values are overestimated. These statistical parameters are evaluated using:

$$RMSE=\sqrt{{\displaystyle \sum }_{i=1}^n{\left(X_i-X_i^{\prime }\right)}^2/n}$$

(9)

$$MBE={\displaystyle \sum }_{i=1}^n\left(X_i-X_i^{\prime }\right)/n$$

(10)

where:

X_i is the ith evaluated value;

$X_i^{\prime }$ is the ith monitored data;

n is the observations number.

The cross-correlation coefficient (R) is a suitable indication of correlation among two variables. R illustrates the linear relation strength between any two parameters X and Y and it is expressed as:

$$R=\frac{{{\displaystyle \sum }}_{i=1}^n\left(X_i-\overline{X}\right)\left(Y_i-\overline{Y}\right)}{\sqrt{{{\displaystyle \sum }}_{i=1}^n{\left(X_i-\overline{X}\right)}^2{{\displaystyle \sum }}_{i=1}^n{\left(Y_i-\overline{Y}\right)}^2}}$$

(11)

where $\overline{X} \mathrm{and} \overline{Y}$ are the mean values of all $\overline{X} \mathrm{and} Y$ data, respectively.

where:

$\overline{X} \mathrm{and} \overline{Y}$ are the mean values of all X and Y data, respectively.

The coefficient of determination (R²) is critical as it indicates the fraction of fluctuation of one variable estimated from another one and it determines the confidence in the estimation. The range of R² is 0 ≤ R² ≤ 1, and it illustrates the linear correlation power. Thus, R² is considered as the ratio of values in the neighborhood of the best fit line, and it measures how good the regression line is. Commonly, R² higher than 0.8 is regarded as a powerful relation, while R² lower 0.5 is considered an inadequate relation.

4. Experimental Setup

4.1. UVB Radiation Measurements

A measurement center is set-up at the College of Technological Studies, Kuwait to record UVB on a horizontal surface utilizing a biometer (Model: Solar Light Company/Model: 501) to measure UVB radiation in the electromagnetic spectrum band of 280–320 nm. The biometer has 99.508% of its spectral sensitivity in the range between 280 and 320 nm. The location of the biometer is selected so that no shadows are cast on it throughout the measurements. UVB data are measured in MED/h, which results in minimum skin redness after radiation for 1 h. Effective biological dose is recorded through biological effective power integration in a certain time. The biometer is regularly calibrated by the manufacturer to ensure reliable and accurate measurements.

The theory of the Robertson–Berger meter for recording UV is employed in the 501 biometer. Solar radiation passes through filters with a Teflon sheet to enhance the detector cosine function. Light produced by the phosphor is observed by the GaAs diode and both are contained in an enclosure of metal managed by a Peltier part. Current generated by the GaAs diode is enlarged and then transferred to frequency in the detector, which is disseminated to the recorder. The biometer has a normalized spectral response. The logarithm of the normalized spectral response reduces linearly with wavelength. The biometer model 501 is lightweight with a spectral response near to erythema. The biometer includes a functions menu, alphanumeric LCD, and keypad. The detector and recorder must be properly set-up to assure correct UVB measurement. The detector position and location should be far from smoke and dust to ensure accurate measurements.

The biometer readings are linked to a precise and stable data acquisition system. An accurate data taker (Model DT80) is utilized to record and store UVB measurements. This data acquisition system is a smart device that includes several functions that permit its use under different conditions. The device is powerful and standalone with USB memory support, 18-bit resolution, substantial communications abilities, as well as a built-in display. The dual channel principle allows various inputs to be utilized in several combinations. Hourly UVB radiation measurements over a horizontal surface at Shuwaikh, Kuwait are available for 2014–2019. The continuous measurements are recorded and stored at 10 min intervals for all sky conditions.

4.2. Global Radiation Measurements

The solar radiation values are measured by a research-grade pyranometer (Make: LI-COR/Model: LI-200R), which benefit from being cosine-corrected (following Lambert’s cosine law). The LI-COR sensors are also weather-resistant with low-maintenance requirements. Long-term experience and extensive research stand behind every aspect of the sensors including, but not limited to, the crown’s shape, the photodiodes, and also the used optical filter glass. The sensors offer reduced measurement drifts and increased lifespan, thanks to its unique drain design, which is very efficient in shedding water in addition to the robust housing, which prevents ingress of water. Sensors are durable in long-term outdoor deployments. They also have detachable heads, which means replacement or factory recalibration can occur without the need to remove the cable from the mounting structure.

The LI-200R sensor is designed for outdoors use under unobstructed natural daylight conditions. It is sensitive to the broadest waveband, and it accurately detects G radiation, including diffused as well as direct solar radiation. The technical specifications of the sensor are listed in

Table 1. The technical specifications of the LI-200R UVB Sensor.

Parameter	Value
Radiation detection range	400–1100 nm
Incident angle correction	Cosine corrected up to 82°
Calibration frequency	Two years
Calibration uncertainty	±3% typical, within ±60° angle of incidence
Typical sensitivity	75 μA per 1000 W/m2
Maximum deviation	1% at 3000 W/m2
Stability	<±2% change per annum
Response	<1 µs

. The output unit is W/m², which makes it suitable for many applications including environmental, solar energy, agricultural, and meteorological research. This pyranometer offers uniform sensitivity and it is cosine-corrected. It is widely accepted that cosine-corrected sensors offer the most accurate way to measure radiation on a flat surface coming from every angle. The cosine correction helps in accurately measuring the G radiation under challenging conditions including low solar elevation angles and low light levels. The latter condition is crucial for the accurate estimation of light compensation point for plants.

The LI-200R measures G radiation with a high-stability unfiltered silicon photovoltaic detector (blue enhanced). When utilized outdoors under unobstructed natural daylight conditions, the captured data are a close match to first-class thermopiles. The sensor’s crown is dual-purpose, i.e., efficient water shedding and physical blockage of light from outside the hemisphere of sensitivity; the result is a precise cosine response. The sensor is housed in a weatherproof anodized aluminum body with stainless-steel hardware, while the sensing element is covered by an acrylic diffuser. A strict calibration protocol is followed for all Kuwait National Meteorological Network (KNMN) sensors. The LI-200R sensors are calibrated under natural daylight conditions against an Eppley Precision Spectral Pyranometer (PSP). With specifications as those listed in Table 1, this sensor is considered suitable for the reported work.

KNMN stations utilize a CR3000 Micrologger, which can handle complex applications of a wide range of sensors. The CR3000 is such a powerful and fast data-logger that it can manage extended eddy-covariance systems with full energy-balance systems and is designed for stand-alone operation under challenging conditions. The CR3000 comprises an integrated compact package that has its power supply (built-in), a 128 × 64-pixel backlit graphical/8-line numeric display, and a keyboard that has 16 characters. The CR3000 can handle serial communications with serial sensors and devices that have the support of I/O port pairs. With flexible power and communication options, it is suitable for distant places. Accurate time is guaranteed even when the data-logger is disconnected from battery power, thanks to the battery-backed clock. Finally, expansion of the CR3000 pulse count, control port, and serial communications capabilities is possible through a custom ASIC chip.

5. Error Analysis

A substantial analysis was performed to guarantee the precision of evaluated average daily and monthly UVB measurements. This task was evaluated by calculating the autocorrelation coefficient and then employing the results for standard error evaluation. The standard errors attained are smaller than the fundamental records for devices utilized in present work. Thus, mean monthly hourly and daily records were considered to characterize the sampling location. Broadband G data have an approximate error of about 3%, and errors in UVB measurements are determined to be smaller than 2.1%.

6. Results and Discussions

6.1. Hourly Analysis

Figure 1 illustrates the hourly variation in both G and UVB radiation for the continuous measurements during 2014–2019 under all sky conditions. The hourly G and UVB radiation measurements were examined to establish whether there was a precise empirical formula(s) between the two variables. Such empirical formulas, once validated, can be utilized to determine UVB values for other periods/locations where the G is measured but not UVB.

As indicated by Figure 1, the curves of hourly values show a sinusoidal behavior for both G and UVB radiation, with minimum values attained in January and December. In addition, the high variation in G and UVB radiation values during spring and summer is directly impacted by dust and sand in Kuwait at these times, while in winter, it may be attributed to the influence of cloud and rain discrepancy. Figure 1 also reveals a strong similarity between the trend of both hourly G and UVB radiation, which indicates the possibility of deriving empirical equations to estimate UVB from G. To demonstrate the resemblance between hourly G and hourly UVB radiation, a statistical test was employed to validate the link between these two parameters for each year. The validity of the correlation formulas obtained in the present study was examined by comparing the predicted value with the corresponding measured one. The criteria used for such a comparison were RMSE, MBE, and R².

Table 2. Hourly regression analysis for 2014–2019.

Year	Relationship between G and UVB	RMSE	MBE	R2
2014	UVB = G × 0.000162	0.0178	0.0046	0.949
2015	UVB = G × 0.000139	0.0183	0.0037	0.927
2016	UVB = G × 0.000133	0.0176	0.0035	0.927
2017	UVB = G × 0.000120	0.0162	0.0028	0.917
2018	UVB = G × 0.000120	0.0186	−0.0011	0.917
2019	UVB = G × 0.000133	0.0200	0.0026	0.912

presents the relationship equations between G and UVB for each year during 2014–2019. RMSE, MBE, and R² are also listed in Table 2. The coefficients of determination (R²) indicate how well the regression equation fits the data. It indicates the proportion of variance in the dependent variable (UVB) explained by the independent variable (G).

Table 2 reveals a good agreement between hourly G and hourly UVB radiation, as demonstrated by the statistical analysis parameters for each year. R² values for all years are higher than 0.91 and the regression coefficient or relationship slopes are similar for all years, except year 2014. In addition, the UVB radiation predicted in 2014 is higher than those of all other years for which the predicted UVB is nearly identical to the measured one. The reason the year 2014 is slightly different is attributed to the disturbance in the Kuwait desert climate (dust, wind speed, and visibility), which has a different impact on the transmittance and scattering of both G and UVB and, consequently, the ratio G/UVB. For 2014, the number of days for which the daily concentration of total suspended particulate (TSP) exceeded 25 µg/m³, 25 µg/m³, and 25 µg/m³ is higher than those for 2015–2019. RMSE and MBE values are smaller than the measurements errors and can be considered negligible. The presented results confirm the validity of the derived empirical equations. Accordingly, they can be used with an acceptable accuracy to estimate hourly UVB from hourly G for locations where no UVB sensors exist.

The measured versus predicted hourly values of UVB for 2014–2019 are illustrated in Figure 2a–f. These figures reveal the strong correlation between predicted and measured values. As seen from figures, the slope of the line is nearly close to unity for all years. In addition, most of the data are closely clustered around the line, demonstrating the good agreement between the measured and predicted values.

It is observed that the maximum hourly G and UVB radiation values take place in summer months at midday (12 h). The maximum values obtained for both hourly G and hourly UVB radiation are presented in

Table 3. Maximum hourly G and hourly UVB during the measured period.

Year	G (W/m2)		UVB (W/m2)
	Max	Date	Max	Date
2014	1006.4	18 June	0.247	20 April
2015	1022	17 May	0.235	17 May
2016	1007	14 June	0.205	16 May
2017	991.3	5 June	0.205	5 April
2018	974.5	18 April	0.183	26 April
2019	968.9	21 June	0.192	14 April

along with the date of maximum occurrence for each year.

Table 3 shows that except for 2015, the dates of the maximum G and UVB values are the same. In addition, the maximum G values occur between 18 April and 21 June, while the maximum UVB values are limited to a narrower period, i.e., 5 April to 17 May. In addition, the results in Table 3 illustrate that the attenuation in the maximum UVB values over the six-year period is significantly higher, i.e., about 35%, than the corresponding value for the maximum G values, i.e., about 5.5%. This behavior is linked to the large transmittance of UVB through the atmosphere [41]. In addition, the significant transmittance of UVB in comparison to the corresponding one for G can be attributed to absorbing aerosols that significantly decrease UVB but have a much lower impact on G [42]. Commonly, the reduction in radiation by clouds is higher at longer wavelengths, while at shorter wavelengths, the transmittance of aerosols is greater [43].

The hourly (UVB/G) % against G for different sky conditions from 2014 to 2019 is presented in Figure 3 to examine the influence of atmospheric conditions on this ratio. As shown from figure, this ratio decreases with G as a result of cloudy conditions. This illustrates that clouds transmit G more effectively than UVB because of the higher absorption by water vapor [44], while the attenuation by aerosols and ozone is larger for UVB radiation than for G. Thus, UVB is higher during summer due to reduced cloud cover and reduced stratospheric ozone.

The difference in the hourly characteristic of G and UVB is linked to transmittance. Accordingly, the attenuation of G and UVB radiation was examined by considering the fluctuation in the (UVB/G)%-K_T curve as it presents G radiation attenuation. The variation in (UVB/G)% with K_T implies that atmospheric parameters alter G and UVB in a different manner during their transmittance through the atmosphere. Figure 4 presents the ratio (UVB/G) as a function of K_T. The ratio (UVB/G) tends to decrease with K_T, indicating that higher ratios (UVB/G) are obtained for higher cloud cover conditions.

Generally, both G and UVB decrease with the atmosphere turbidity due to attenuating factors, e.g., clouds, ozone, and aerosols. Several researchers have attributed this behavior to the different effect of sky conditions on G and UVB. In addition, some researchers have claimed that clouds dominate the variability in K_T. Hence, future efforts of the authors will focus on investigating the individual effects of different atmospheric parameters on G and UVB radiation variation. The relationship between global clearness index (K_T) and UVB clearness index (K_TUVB) was examined to establish an empirical correlation between them. Figure 5 presents hourly K_T and K_TUVB during 2014–2019 for all sky conditions in Kuwait.

As depicted in Figure 5, K_T and K_TUVB are directly proportional. A linear fit between K_TUVB and K_T gives the following equation:

$$K_{TUVB}=0.0077 K_T \left(R^2=0.836\right)$$

It should be noted that atmospheric conditions also play a role in the correlation between K_TUVB and K_T. Wang et al. [45] proposed that the attenuation of G and UVB is better presented by a polynomial of the third order instead of a linear relation. A third-order polynomial fit between K_TUVB and K_T for the present dataset gives the following empirical formula:

$$K_{TUVB}=0.020 K_T-0.059 K_T^2+0.062 K_T^3$$

The determination coefficient (R²) is improved from 0.836 to 0.859. Tena et al. [45] indicated that K_TUVB was strongly dependent on solar zenith angle, while this is not the case for K_T. Considering that K_TUVB and K_T should have similar behavior, and to prevent the dependency on solar zenith angle, the measurements of the four central hours, i.e., noon ± 2 h, were considered. Following their procedure, the determination coefficient (R²) was greatly improved, i.e., from 0.859 to 0.933, as presented in Figure 6.

6.2. Daily Analysis

Figure 7a,b present the variation in daily G and daily UVB radiation during 2014–2019 for all sky conditions. The daily measurements were examined to derive an emperical relationship between the two parameters, similar to what was carried out for hourly G and UVB radiation. The two graphs show a strong agreement in the general behavior, which can be described as being sinusoidal. In addition, the figures show high fluctuations in daily G and UVB values observed in the winter season, for all years. On the other hand, there are less fluctuations during the summer season due to clear sky conditions on most days in Kuwait. These figures again confirm the similarity between the behavior of daily G and daily UVB radiation, which was noticed in Figure 1 for hourly values. It is suggested that high fluctuations during the spring months are mostly due to unsteady weather conditions.

As was the case for hourly data, daily G and UVB values are strongly correlated, which indicates that daily UVB can be estimated from the readily available daily G data. Peak data of daily G and daily UVB radiation occur at midday (12 h) during summer months. The maximum values obtained for both G and UVB radiation are presented in

Table 4. Maximum daily G and UVB during 2014–2019.

Year	G (MJ/m2)		UVB (MJ/m2)
	Max	Date	Max	Date
2014	29.63	18 June	0.0053	18 June
2015	29.83	21 June	0.0052	17 May
2016	29.69	14 June	0.0047	22 May
2017	29.23	5 June	0.0042	5 April
2018	27.37	14 July	0.0041	18 June
2019	28.41	22 June	0.0040	23 May

along with the date for the maximum value for each year.

Table 4 also shows that the date of maximum daily G radiation does not match that for the maximum daily UVB radiation. In general, maximum values of daily G are observed during June, except for 2018 for which the maximum daily G radiation occurs during July. On the other hand, the maximum daily UVB radiation is attained during April to June. Another observation is that the maximum daily G value is about the same for 2014–2017, but it decreases slightly for 2018–2019. The degradation in daily G radiation during the study period is about 8.99%, while for UVB radiation, the degradation is more significant with the corresponding value being about 32.5%. The reason behind such phenomena was discussed before (refer to the hourly data part).

To demonstrate the resemblance between the behavior of both daily G and daily UVB, we examined the correlation between these two parameters using MBE and RMSE to validate the derived correlation formula.

Table 5. Daily regression analysis for 2014–2019.

Year	Relationship between G and UVB	RMSE	MBE	R2
2014	UVB = G × 0.000152	0.00067	$5.67\times {10}^{-5}$	0.985
2015	UVB = G × 0.000131	0.00072	$4.92\times {10}^{-5}$	0.966
2016	UVB = G × 0.000126	0.00063	$5.57\times {10}^{-5}$	0.966
2017	UVB = G × 0.000114	0.00067	$5.38\times {10}^{-5}$	0.951
2018	UVB = G × 0.000125	0.00062	$2.91\times {10}^{-5}$	0.966
2019	UVB = G × 0.000127	0.00061	$3.35\times {10}^{-5}$	0.975

presents the relationship equation between daily G and UVB for each year during 2014–2019, along with the statistical relative parameters, i.e., MBE, RMSE, and R².

A quick examination of the values listed in Table 5 shows a very good agreement between the daily G and UVB radiation, as demonstrated by the statistical analysis parameters for each year. The coefficient of determination is significantly improved, and it is very close to unity for all years. The regression coefficient or relationship slopes are nearly the same for all the years (except the year 2014, which is slightly higher).

In addition, the values of RMSE and MBE are greatly enhanced compared to the values obtained for the hourly dataset as the values of RMSE and MBE are almost zero. The above results confirm the validity of the predicted models. Thus, the daily predicted correlations give a higher accuracy in comparison to the hourly ones. Accordingly, they can be utilized with an improved accuracy to estimate daily UVB from daily G for locations where no UVB sensors exist.

6.3. Monthly Analysis

Figure 8 and Figure 9 show the monthly average of the daily sum of G and UVB radiation for 2014–2019 in Kuwait.

Generally, G and UVB have similar monthly behaviors for all years (refer to Figure 8 and Figure 9). Minimum monthly values of G and UVB occur during the cold months, i.e., November to January, while the maximum monthly G and UVB values occur in June, except for 2018 when it occurs in August. The minimum monthly G radiation is 9.51 MJ/m² and occurs in January 2019, while the minimum monthly UVB radiation is 0.00089 MJ/m² and occurs during November 2017. On the other hand, the maximum monthly G and UVB radiation values are 27.94 MJ/m² and 0.0044 MJ/m², respectively, both occurring in June 2015. These observations again confirm the similarity between the behavior of monthly G and UVB radiation, which was previously demonstrated for hourly and daily values.

To further check the similarity between the monthly average G and UVB radiation, the relationship was examined for each month.

Table 6. Monthly regression analysis for 2014–2019.

Month	Relationship between G and UVB	RMSE	MBE	R2
January	UVB = G × 0.000111	$0.00005$	$-6.88\times {10}^{-8}$	0.999
February	UVB = G × 0.000123	$0.00023$	$-1.29\times {10}^{-5}$	0.992
March	UVB = G × 0.000135	$0.00044$	$-3.70\times {10}^{-5}$	0.998
April	UVB = G × 0.000149	$0.00078$	$-5.73\times {10}^{-5}$	0.998
May	UVB = G × 0.000151	$0.00092$	$-7.76\times {10}^{-5}$	0.999
June	UVB = G × 0.000143	0.00087	$-6.96\times {10}^{-5}$	0.998
July	UVB = G × 0.000132	0.00055	$-4.54\times {10}^{-5}$	0.999
August	UVB = G × 0.000120	0.00026	$-1.83\times {10}^{-5}$	0.998
September	UVB = G × 0.000105	0.00014	$1.01\times {10}^{-5}$	0.999
October	UVB = G × 0.000101	0.00019	$1.30\times {10}^{-5}$	0.996
November	UVB = G × 0.000108	0.00010	$2.28\times {10}^{-6}$	0.995
December	UVB = G × 0.000112	0.00004	$-6.62\times {10}^{-7}$	0.999

presents the relationship equations between the monthly G and UVB values for each month. RMSE, MBE, and R² are also listed in Table 6.

Table 6 reveals an excellent agreement between the monthly G and monthly UVB radiation, as demonstrated by the statistical analysis parameters for each month. The relationship is linear with the coefficient of determination (R²) almost equal to unity. The values of RMSE and MBE are significantly less than those for the hourly dataset as RMSE and MBE are almost zero. The above results confirm the validity of the predicted models. Previous predictions indicate that the predicted daily or monthly empirical formula can be utilized with a very high accuracy to predict both daily and monthly UVB values from both daily and monthly G for locations where no UVB sensors exist.

7. Conclusions

UVB and G radiation are continuously monitored in Shuwaikh, Kuwait through the period 2014–2019 for all sky conditions. The experimental data are analyzed to predict a relationship between G and UVB radiation. In addition, K_T and K_TUVB indices are evaluated and examined. The derived daily and monthly empirical formulas show a well-understandable relation, being able to predict UVB in the future relying on the lower-cost G measurements. This is a great advantage as UVB sensors are more expensive.

Based on current predictions, the following conclusions can be stated:

• Hourly curves show a sinusoidal behavior for both G and UVB radiation, with minimum values in January and December.
• The higher changes in G and UVB radiation in spring and summer seasons are related to frequent dust storms as well as dust/sandstorms in Kuwait at these times of the year.
• Maximum hourly G and UVB radiation takes place in summer months at midday (12 h).
• There is a good agreement between hourly G and hourly UVB radiation as R² values for all years are greater than 0.91. In addition, RMSE and MBE values are very small and smaller than the measurement errors.
• The measured versus predicted hourly curves of UVB for all years reveal the strong correlation between both factors. The slope of the line for these curves is very close to unity for all years, and most of the data are situated close to the best-fit line, showing good consistency between measured and predicted UVB.
• The attenuation in maximum G is about 5.5% during the whole period of measurements, while it is about 35% for UVB, which is much higher.
• The hourly percentage ratio (UVB/G) decreases with hourly G as a result of cloudy sky variations.
• High absorption by water vapor attenuates G radiation more efficiently than UVB, while the attenuation by aerosols and ozone is greater for UVB than G radiation.
• The (UVB/G) ratio tends to decrease with K_T, indicating that a higher ratio of (UVB/G) can be obtained for cloudier conditions.
• K_T is directly proportional to K_TUVB with a third-order polynomial giving an acceptable formula, i.e., determination coefficient = 0.859.
• Measurements for the four central hours of each day are utilized to avoid the dependency of clearness indices on solar zenith angle. Relying on these four hours only, the determination coefficient of the linear correlation between the two indices is greatly enhanced from 0.859 to 0.933.
• The graphs of daily G and UVB radiation for all years show the same behavior. In addition, these graphs indicate a sinusoidal behavior.
• G and UVB values are very well correlated on a daily basis, as demonstrated by the statistical analysis parameters for each year. The coefficient of determination is significantly improved, and it is very close to unity for all years.
• The values of RMSE and MBE obtained from daily analysis are greatly enhanced compared to the values obtained for hourly analysis as the values of RMSE and MBE are almost zero.
• G and UVB have similar monthly behavior for all years. Minimum values of G and UVB occur in the cold months, i.e., November to January.
• The minimum G radiation obtained is 9.51 MJ/m² in January 2019 and the minimum UVB radiation attained is 0.00089 MJ/m² in November 2017.
• The maximum G and UVB radiation obtained are 27.94 MJ/m² and 0.0044 MJ/m², respectively, both of which occur in June 2015.
• There is an excellent linear fit between the monthly G and UVB radiation as R² is almost equal to unity. In addition, the values of RMSE and MBE are greatly decreased compared to the values obtained for hourly analysis.
• The present results indicate that the derived daily and monthly empirical formulas can be utilized, with a very high accuracy, to predict both daily and monthly UVB values from G values for locations with no UVB sensors.