## Introduction

The ultraviolet index, UVI, formulated using the spectrum of erythematic action induced by UV radiation on human skin, of the CIE (Commission Internationale de l’Eclairage, acronym in French), is a simple index that informs the population of the risk of solar radiation2.

$${\rm{UVI}}={{\rm{k}}}_{{\rm{er}}}{\int }_{250\,{\rm{nm}}}^{400\,{\rm{nm}}}{\rm{I}}({\rm{\lambda }}){\rm{\varepsilon }}({\rm{\lambda }})d{\rm{\lambda }}$$
(1)

where I(λ) is the solar spectral irradiance in W/(m2·nm) and ker a constant equal to 40 m2/W. The erythema reference action spectrum coefficient, ε(λ), values are given by Madronich et al.5.

$$\begin{array}{ll}\lambda < 298\,{\rm{nm}} & {\rm{\varepsilon }}({\rm{\lambda }})=1\\ 298\,{\rm{nm}}\le {\rm{\lambda }} < 328\,{\rm{nm}} & {\rm{\varepsilon }}({\rm{\lambda }})={10}^{0.0940\cdot (298-1000{\rm{\lambda }})}\\ 328\,{\rm{nm}}\le {\rm{\lambda }}\le 400\,{\rm{nm}} & {\rm{\varepsilon }}({\rm{\lambda }})={10}^{0.0150\cdot (139-1000{\rm{\lambda }})}\\ \lambda > 400\,{\rm{nm}} & {\rm{\varepsilon }}({\rm{\lambda }})=0\end{array}$$

As shown in Table 1, the ultraviolet index, UVI, a dimensionless number, can vary between 0 and 16 and it has been divided into five ranges of danger for the population according to exposure2,10.

Numerous organizations inform the population about the daily values of this index. The prediction provides the maximum UV index value that matches the UV index at noon for clear skies. On cloudy days, the value of the UV index would be lower. In addition, it also sets up information of hourly values. In Spain, it can be consulted in the Agencia Estatal de Meteorología (AEMET)11. You can consult the UV index of any country through the website of the Finnish Meteorological Institute12.

The intensity of ultraviolet radiation B, IUVB, in the range of 280–315 nm wavelength, and measure in W/m2, is the main component of the solution to the integral given in expression (1), since the values for this range of the erythema reference action spectrum coefficient ε(λ) nearly occupy the entire wavelength of the ultraviolet index, UVI. Thus, some authors like MacKenzie et al.13 established the following relationship between ultraviolet index, UVI, and intensity of ultraviolet radiation B, IUVB:

$${{\rm{I}}}_{{\rm{UVB}}}=18.9\cdot {\rm{UVI}}\,{({\rm{W}}/{\rm{m}}}^{2})$$
(2)

As it is known, solar radiation can cause skin burns after prolonged exposure. Many authors relate skin temperature with the burn-degree, which in turn depends both on exposure time and on radiant intensity. Thus, these authors, Buettner or Hardee and Lee14,15, relate exposure time with skin temperature at different depths. However, temperature is not the correct parameter to establish the damage level, but a parameter that relates damage to exposure time (te, s) and UV radiation intensity (I, W/m2) as it is the “UV radiation dose”. Equation (3) shows the most recognized expression for the dose (D, (W/m2)4/3 s)16,17.

$${\rm{D}}={{\rm{I}}}^{4/3}{{\rm{t}}}_{{\rm{e}}}$$
(3)

## Skin Types

Not all skin types react in the same way to Sun exposure. In this regard, the World Health Organization (WHO)2 has classified phototypes or skin types into six categories according to their tolerance to solar radiation, as described in the Table 2, so that skin type I is the most sensitive and type VI is the most tolerant to UV radiation.

One of the goals of public health is to protect the most vulnerable population groups. Given that the finding that more than 90% of non-melanoma skin cancers occur in people of skin type I and II, protection messages should be focused on people of these skin types, who tend to get burnt easily. In addition, special mention should be made of children, who are more sensitive to UV radiation. Therefore, it is understood that the development of equivalence between the UVI and the percentage of population affected by different degree sunburn will promote awareness of solar radiation among that population. Although dark-skinned people have a lower risk of cancer, they can suffer from other harmful consequences, such as burns to the eyes, solar retinopathy, photo conjunctivitis or photo keratosis.

Thus, to advise on the dangers of solar radiation, several cultural and climate differences must be taken into account, namely, the population’s perception of UV radiation risks and their education2. Therefore, we believe that the relation between UVI and the percentage of population affected by different degree burns is a useful tool for raising awareness of solar radiation harm among the population.

## Effects of Solar Radiation on Human Population

The generation of skin sunburn, in its different degrees, is a significant effect of UV radiation, which generates free radicals leading to inflammation. The seriousness varies depending on the proportion of burned skin and the depth of the most severe burn.

The effects caused by UV radiation in humans can be divided into two types. First, physiological effects: increased heart rate, increased transpiration or body temperature. Second, pathological effects, which are more serious and include skin burns. These burns are divided into three categories depending on the seriousness of the damage: first degree, second degree and third degree burns.

First-degree sunburn produces redness, swelling, pain and superficial damage. These burns only affect the skin surface (epidermis) and cause negligible tissue damage. This kind of burn does not require medical attention, since they do not end up in blisters and their effects might be reversible in a period of 1 or 2 days.

The approximate value of the dose established for the appearance of first-degree sunburn is 115 (kW/m2)4/3s, given by Sanchez-Perez et al.18 and adjusted from the values given by Buettner and Bagster and Pitblado19,20.

In several studies on the ultraviolet index10,21,22,23, UVI, an association between skin type and maximum exposure time (in minutes) in which first-degree sunburn would appear is established (Fig. 1).

For skin type II and a value of 9 for UV index, using expression (2), the corresponding dose value is 113 (kW/m2)4/3s, next to value 115 (kW/m2)4/3s, given by Sanchez-Perez et al.18 and adjusted from the experimental values given by Buettner and Bagster and Pitblado19,20 for the beginning of first-degree burns. However, if we use expression (2) given by MacKenzie et al.13, for the dose calculation for lower values of UV index we do not obtain an approximate value of 115 (kW/m2)4/3s. Thus, adjusting the curve for a type II to an approximate dose value of 115 (kW/m2)4/3s, Table 3, and using equation (3), we get a new expression that relates the ultraviolet index, UVI, and the intensity of ultraviolet radiation, IUV, (Fig. 2).

The proposal for an expression that relates the ultraviolet index, UVI, and the intensity of ultraviolet radiation, IUV, is given by:

$${{\rm{I}}}_{{\rm{UV}}}=15.1\cdot {\rm{UVI}}+35.5({\rm{W}}/{{\rm{m}}}^{{\rm{2}}})$$
(4)

This expression, which mainly includes ultraviolet B radiation, covers the wavelength from 250 nm to 400 nm, so it is closer to the UVI calculation given by expression (1) than the expression proposed by MacKenzie et al.13, since it encompasses the variability of the erythema reference action spectrum coefficient ε(λ).

Considering that each skin type has a different dose for the beginning of first-degree sunburn (Fig. 1), a dose can be established for each type using expressions (3) and (4), and the values of the UV index and exposure times in Fig. 1.

The value for skin type II coincides with the value of 115 (kW/m2)4/3s given by Sanchez-Perez18 validating the use of these expressions for solar radiation. For the rest of skin types, new dose levels are established for the initiation of first-degree burns, (Table 4).

Second-degree burns affect the epidermis (outer-layer) and the dermis (underlying layer of the skin), causing blisters, pain, swelling and redness. Contrary to first-degree burns, in this kind of burns a medical treatment is required to heal the damaged area24. Using data collected by Stoll and Greene25 and Metha et al.26, a value of dose is established for the beginning of second-degree burns of 250 (kW/m2)4/3s.

Third-degree burns affect the deep hypodermis, dermis and epidermis, causing skin carbonization or a translucent white color, with coagulated and visible vessels under the skin surface. The healing of these burns occurs slowly due to tissue destruction. Consequently, people with these types of burns are more vulnerable to infections24.

## Probit Equations to Determine Solar Effects

Probit equations27 relate the percentage of population affected by a certain damage level (e.g., first-, second- or third-degree sunburn) and solar radiation. The dimensionless number Probit (Y) and its interpretation allow calculating the population percentage affected by this radiation, Sánchez-Pérez et al.18 and TNO (1989)16:

$$\mathrm{First} \mbox{-} \mathrm{degree}\,{\rm{burns}}\,{\rm{Y}}=-\,11.7+6.95\,\mathrm{log}({\rm{D}})$$
(5)
$$\mathrm{Second} \mbox{-} \mathrm{degree}\,{\rm{burns}}\,{\rm{Y}}=-\,13.9+6.95\,\mathrm{log}({\rm{D}})$$
(6)
$$\mathrm{Third} \mbox{-} \mathrm{degree}\,{\rm{burns}}\,{\rm{Y}}=-\,36.4+2.56{\rm{In}}({\rm{D}})$$
(7)

In the case of first-degree sunburn, an adjustment must be made depending on the skin type. Given that the value of population affected by first-degree sunburn is 1%, Y = 2.67, and using the values given in Table 4, for each skin type the following expressions are proposed:

$$\begin{array}{cc}\mathrm{First} \mbox{-} \mathrm{degree}\,{\rm{burns}}\,{\rm{Probit}}\,{\rm{equation}}\,{\rm{for}}\,{\rm{skin}}\,{\rm{type}}\,{\rm{I}} & {\rm{Y}}=-\,10.8+6.95\,\mathrm{log}({\rm{D}})\end{array}$$
(8)
$$\begin{array}{cc}\mathrm{First} \mbox{-} \mathrm{degree}\,{\rm{burns}}\,{\rm{Probit}}\,{\rm{equation}}\,{\rm{for}}\,{\rm{skin}}\,{\rm{type}}\,{\rm{II}} & {\rm{Y}}=-\,11.7+6.95\,\mathrm{log}({\rm{D}})\end{array}$$
(9)
$$\begin{array}{cc}\mathrm{First} \mbox{-} \mathrm{degree}\,{\rm{burns}}\,{\rm{Probit}}\,{\rm{equation}}\,{\rm{for}}\,{\rm{skin}}\,{\rm{type}}\,{\rm{III}} & {\rm{Y}}=-\,12.3+6.95\,\mathrm{log}({\rm{D}})\end{array}$$
(10)
$$\begin{array}{cc}\mathrm{First} \mbox{-} \mathrm{degree}\,{\rm{burns}}\,{\rm{Probit}}\,{\rm{equation}}\,{\rm{for}}\,{\rm{skin}}\,{\rm{type}}\,{\rm{IV}} & {\rm{Y}}=-\,13.2+6.95\,\mathrm{log}({\rm{D}})\end{array}$$
(11)

The expressions given by Sánchez-Pérez et al.18 and TNO16 are maintained for the calculation of the rest of the affected population percentage, that is, second- and third-degree burns. For the interpretation of the Probit value, the Probit tables can be used, which establish a relation between Probit number and the percentage of population affected16,18,27,28,29,30,31,32 or the following equation27,28,29,30,31,32:

$${\rm{R}}=-\,3.25{{\rm{Y}}}^{3}+48.8{{\rm{Y}}}^{2}-\,207{\rm{Y}}+270$$
(12)

where R is the percentage of affected population and valid for a percentage range between 5 and 95%, that is, valid for Probit values between 3.36 and 6.64.

The interpretation of the results obtained from the previous equations is done through the corrected tables for doses and Probit given by Sanchez-Perez et al.18, thus determining the percentage of people affected by the different degrees of burns.

## Relationship Between UVI and Percentage of Population Affected by Each Type of Burn

Following the proceeding established by Sanchez-Perez et al.18 for the calculation of percentages of affected population using the Probit equations and expressions (2) and (3), the following table (Table 5) is established, which relates the percentage of population affected for each UVI, exposure time and skin type.

From Table 5 it can be concluded that the results for the first-degree sunburn are in accordance with reality. However, for the second degree there is a high percentage of affected population for types of skin, which are more resistant to burns, such as Type III and IV. This is because only the values given by Stoll and Greene25 and Metha et al.26 for the initiation of second-degree burns are irrespective of skin type. In order to distinguish the start of second degree burns for each skin type, experimental results obtained by Stoll and Greene25 and Metha et al.26, who do not distinguish the type of skin, are adjusted using the experimental data of first degree burns, which do distinguish skin type.

Thus, it is proposed that set the start of second-degree burns up 250 (kW/m2)4/3s18, for skin type II, and the start of second-degree burns for the rest of skins type is adjusted with the data of each skin type of first-degree burns. Therefore, the values of Table 6 can be obtained.

These values are in the range of those given by different authors for the initiation of second-degree burns, 236–390 (kW/m2)4/3s, without specifying the skin type16,18,20,33. Thus, the following expressions of Probit equations can be proposed adjusting the value of 1% population affected by second-degree burns, Y = 2.67, for each type of skin using the values given in Table 6.

$$\begin{array}{cc}\mathrm{Second} \mbox{-} \mathrm{degree}\,{\rm{burns}}\,{\rm{Probit}}\,{\rm{equation}}\,{\rm{for}}\,{\rm{skin}}\,{\rm{type}}\,{\rm{I}} & {\rm{Y}}=-\,13.6+6.95\,\mathrm{log}({\rm{D}})\end{array}$$
(13)
$$\begin{array}{cc}\mathrm{Second} \mbox{-} \mathrm{degree}\,{\rm{burns}}\,{\rm{Probit}}\,{\rm{equation}}\,{\rm{for}}\,{\rm{skin}}\,{\rm{type}}\,{\rm{II}} & {\rm{Y}}=-\,13.9+6.95\,\mathrm{log}({\rm{D}})\end{array}$$
(14)
$$\begin{array}{cc}\mathrm{Second} \mbox{-} \mathrm{degree}\,{\rm{burns}}\,{\rm{Probit}}\,{\rm{equation}}\,{\rm{for}}\,{\rm{skin}}\,{\rm{type}}\,{\rm{III}} & {\rm{Y}}=-\,14.3+6.95\,\mathrm{log}({\rm{D}})\end{array}$$
(15)
$$\begin{array}{cc}\mathrm{Second} \mbox{-} \mathrm{degree}\,{\rm{burns}}\,{\rm{Probit}}\,{\rm{equation}}\,{\rm{for}}\,{\rm{skin}}\,{\rm{type}}\,{\rm{IV}} & {\rm{Y}}=-\,14.8+6.95\,\mathrm{log}({\rm{D}})\end{array}$$
(16)

Therefore, using the above expressions, Table 5 can be rewritten in the following table (Table 7).

The results obtained are more in line with reality, both for first and second-degree burns, since a distinction is made between the different types of skin and its resistance to sunburn. Therefore this information is relevant for preventing further potential conditions on a sporadic occurrence (photokeratosis, photo conjunctivitis or solar retinopathy) or more severe skin affections such as melanoma or non-melanoma skin cancer (squamous cell carcinoma or basal cell carcinoma)34.

To facilitate its handling, Table 7 could be included in a mobile application, where users could see the probability of suffering burns through their location and the choice of their skin types, and depending on their exposure time to UV radiation.