Calculation of Optimal Times for Exposure to Sunlight

The optimal time for exposure to sunlight that is needed to receive adequate UV for vitamin D production, but without inducing erythema, depends strongly on latitude and season. Here we develop algorithms for calculating the time in terms of the widely used UVI.

We can calculate the time taken (tE in minutes) to induce skin damage (one minimum erythemal dose) using

E 60 UVI

where the factor 4000/60 accounts for the conversions from UVEry to UVI and seconds to minutes; UVI is the UV Index (= 40 x UVEry, where UVEry has units of W m_2); and MEDF is a factor to take into account the differences in skin color. It is expressed as the number of SED (1 SED = 100 J m of erythemally-

1 However, higher vitamin D levels have been associated with winter UV exposures among Tasmanian school children (Jones et al., 1999) suggesting that vitamin D synthesis can occur in winter at latitudes higher than 40°S.

weighted UV) required to induce erythema (Diffey et al., 1997) according to the Fitzpatrick skin classification (Fitzpatrick, 1988), (see Table 2.2), and SPF is the sun protection factor of any sun block applied.

Table 2.2 Skin type classifications according the Fitzpatrick scale (Fitzpatrick, 1988)

Skin Type


SED to Burn (MEDF)


Celtic (always burns)

2 - 3


Pale (burns easily)

2.5 - 3


Caucasian (may burn)

3 - 5


Mediterranean (burns rarely)

4.5 - 6


S. American (rarely burns)

6 - 20


Negroid (rarely burns)

6 - 20

For example, for unprotected type II skin (SPF = 1), assuming 1 MED = 2.5 SED, the time taken to receive an erythemal dose at UVI = 12 would be 13.9 minutes. Under the same conditions, with a correctly-applied sun block of SPF = 20, it would take approximately 278 minutes (> 4.5 hours) for damage to occur. Two caveats should be mentioned here. Firstly, over such a large period, there will be changes in the UVI, so the mean UVI value should be applied. Second, it is implicitly assumed that reciprocity between time and UVI applies; meaning that a constant UVI dose of 10 for one hour, say, would give the same erythemal effect as a constant UVI value of 1 for 10 hours. This reciprocity has not been demonstrated for sunlight, although it does seem to apply for a range of UVI values greater than ~5 using artificial lamps that emit much higher proportions of UV-B (UV radiation in the range 280 nm - 315 nm) and UV-C (UV radiation in the range 100 nm - 280 nm) radiation (Meanwell and Diffey, 1989). According to the current WHO guidelines, some protection to avoid sunburn is advised whenever the UVI exceeds 3. At this UV level, for a fair skinned person, that corresponds to a period of approximately one hour before skin damage is detectable as mild erythema (skin reddening). On the other hand, our dietary intake of vitamin D is generally far below the level required to maintain optimal levels of blood serum vitamin 25(OH)D, so some UV exposure is desirable to maintain healthy vitamin D levels. Unlike the risk of erythema, the beneficial effects of UV radiation depend on the area of skin exposed. If twice the area is exposed, then twice the benefit is received (assuming all skin areas have a similar capacity for producing vitamin D). We use relationships derived from published physiological considerations to estimate the range of optimal exposures for various skin types as a function of UVI. We could also develop a similar relationship as a function of SZA, but that would ignore the effect of ozone, which can be appreciable.

Following the procedure described in more detail elsewhere (McKenzie et al., 2008), the time (tD) required to photosynthesize sufficient vitamin D for a given value of UVIy can be expressed in terms of the corresponding time (tD0) at some reference condition (UVI0), as follows:


where R (SZA, TOZ) is the ratio of UVEry/UVVitD for that value of UVI, as discussed above; A is the area of skin surface exposed; and the remaining terms are as defined above.

We assume that optimal vitamin D levels are easily maintained by a daily intake of 1,000 IU of vitamin D3. If an intake of 400 IU is sufficient, as some have suggested, then the times to achieve the desired UV dose would be decreased by a factor of 2.5 over those that we calculate. From the figures provided earlier (Holick, 2002; 2007), a full body exposure of type II skin under high sun conditions (UVI = 10) produces 1,000 IU in less than one minute.

In that case, the reference conditions are as follows:

UVI0 = 10 (peak UV for mid latitudes in the NH)

A0 = 1 (full body exposure)

SPF0 = 1 (no sunscreen applied).

With these substitutions, Eq. (2.3) simplifies to:

which should be compared with Eq. (2.2) for erythema.

The resulting times are shown graphically in Fig. 2.13 (McKenzie et al., 2008). The shaded area at top right gives times when erythema occurs on exposed skin for each UVI value. The shaded area at bottom left gives the times when there is insufficient UV to maintain optimal levels of vitamin D, even for full body exposures. The other three curves give the approximate exposure times needed to maintain vitamin D for different areas of the exposed body. For full body exposures, there is a wide window between the time for sufficient UV and the time for too much UV. As the fraction of body that is exposed decreases, the window of optimum UV exposure times also decreases. If only hands and face are exposed, there is generally only a small window between receiving insufficient UV for vitamin D production and too much UV for skin damage (erythema).

1 Total ozone column (in Dobson Units, where 1 DU = 2.69 x 1016 molecule cm 2 in a vertical column). 40

Figure 2.13 Range of exposure times required for optimal UV (white region), plotted as a function of UVI. The area labeled "UV damage" represents times when too much UV is received, leading to erythema (skin-reddening). The region marked "Insufficient UV" represents the time when insufficient amounts of UV are received to maintain an intake of 1,000 IU for full body exposure. For skin type W, these exposure times should be multiplied by 2, and for skin type "W they should be multiplied by approximately 5

Figure 2.13 Range of exposure times required for optimal UV (white region), plotted as a function of UVI. The area labeled "UV damage" represents times when too much UV is received, leading to erythema (skin-reddening). The region marked "Insufficient UV" represents the time when insufficient amounts of UV are received to maintain an intake of 1,000 IU for full body exposure. For skin type W, these exposure times should be multiplied by 2, and for skin type "W they should be multiplied by approximately 5

For SZA = 63°, which corresponds to noon on a mid-winter day at latitude ~41°,the UVI is typically between 2 and 3 (i.e., UVI "low"), and the ratio of UVVitD/UVEry is about 1.6. The time to produce a minimum erythemal dose for skin type II is between one and two hours. The time to achieve 1,000 IU of vitamin D is about six minutes for full body exposure (A = 1.0), and about one hour if only the hands and face are exposed (A = 0.1).

These optimal exposure times calculated above should be considered as very approximate. In particular, there is some uncertainty regarding the applicability of the action spectrum for vitamin D, and the possible role of temperature in converting pre-vitamin D to vitamin D3 (Matsuoka et al., 1989). If the action spectrum were confined to shorter wavelengths, then the R values would be reduced commensurately. For example, if the upper limit were reduced from 330 nm to 315 nm, the R values would typically be 5% - 10% lower, so the required exposure time would be increased by a similar factor. There is also the question of how well the radiation received by the skin relates to that incident on a horizontal surface. We also note that the relationships derived here are from high quality spectral measurements and they are specific to a single location with its own particular conditions. Although we consider the results should be generally applicable elsewhere, the minimum R values do depend on the range of ozone variability. At locations where ozone amounts are higher (such as at high northern latitudes), the minimum R values would be smaller, and at locations with lower ozone amounts (such as within the tropics), the minimum R values would be larger.

As the UVI becomes smaller, it becomes more difficult to produce sufficient vitamin D without inducing erythema. For low sun conditions typical of midday in the mid-latitude winter (SZA ~65°), where Rj ~1, the skin area exposed must be more than 12%. This means that for these low sun conditions, it is difficult to receive sufficient vitamin D from exposing the hands and face alone since that area is less than 12% of the full body—though the radiation received may significantly exceed that on a horizontal surface assumed here (Moan et al., 2008). For still larger SZA, larger fractions of the body would have to be exposed to produce sufficient vitamin D without erythema. However, that is of academic interest only, because at those low UVI values, there is insufficient time in a day to produce either of those outcomes.

During the winter, when cold temperatures may preclude exposures of large areas of skin, it may not be possible to receive adequate UV for optimal vitamin D synthesis. When exposures are limited to the hands and face, there is a relatively small margin of error between getting sufficient UV for vitamin D production and not getting too much for sunburn. The calculations show that the best advice would be to expose as much area as possible for the minimum time necessary. For high sun conditions, the time for skin damage is about twice the time for sufficient vitamin D production if only the hands and face are exposed. And when the UVI is 1 or less, it is not possible to get sufficient UV for vitamin D without acquiring a mild erythemal dose. Under such conditions, of course, there will generally be substantial changes in UVI over the long periods of exposure needed.

Finally, we note that this margin between UV sufficiency (for vitamin D) and UV excess (for sunburn) depends critically on the assumption that sufficient vitamin D is made in one minute. In Fig. 2.13, we assumed that one minute of exposure to UVI = 10 provided sufficient UV to maintain vitamin D levels. In that case, whenever the UVI is less than 2, one cannot manufacture sufficient vitamin D from exposure to hands and face alone without inducing erythema. If, for example, the time was 1.5 minutes, then the vitamin D curves in Fig. 2.13 all move up, and the curve for exposure to hands and face intersects the curve for erythema when UVI = 6. Conversely, if lower doses of vitamin D are sufficient, then those curves move downward.

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