The algorithm used to estimate E in this study is a fast polynomial fit algorithm FP (Herman, 2010, 2018) based on calculations using the scalar TUV radiative transfer program (Madronich, 2007, 1993a, b; Madronich and Flocke, 1997) with a reduction factor for clouds CT. The FP algorithm used to estimate E has been enhanced to include the effect of aerosol absorption on UV irradiance based on derived 354 nm aerosol optical depths and single scattering albedo from OMI-measured radiances (Torres et al., 2007). The measured absorbing OMI aerosol optical depths τA (354 nm) corresponding to the locations in Table A4 are available from https://avdc.gsfc.nasa.gov/pub/DSCOVR/TimeSeries_Absorbing_Aerosol_Data/ (last access: 16 June 2020). The accuracy of OMI-retrieved aerosol properties has been evaluated by comparison to AERONET (AErosol RObotic NETwork) ground-based observations (Ahn et al., 2014; Jethva et al., 2014).

The wavelength λ dependence of τA is approximately given by using the absorption Angström exponent AAE=1.8 derived from data obtained over Seoul, Korea, in a manner similar to that derived for Santa Cruz, Bolivia (Mok et al., 2018). 1τA(λ)τA(354nm)=λ354-1.8

The reduction factor CA for irradiance E caused by absorbing aerosols is given by Eq. (2). 2CA=E(τA(λ))/E(0)=1/(1+3τA(λ))

For the purposes of estimating the absorption optical depth for erythemal irradiance, a single wavelength, λ=310 nm, is used approximately corresponding to the maximum of the product of solar flux at the Earth's surface and the erythemal action spectrum (Eq. A2). 3τA(310nm)=1.27τA(354nm)

Table 1 shows a comparison of the June maximum local noon UVI values estimated from OMI TCO3 and LER data with June ground-based measurement data. June was selected for the comparisons, since the SZA changes slowly near solstice, permitting at least a week's data to be considered selecting a maximum that can be compared with comparable calculated erythemal irradiance calculated from OMI data. The day-to-day measured and calculated variation at solar noon during June is greater than 10 % for nearly clear-sky days. Calculated values are 14-year June average maximum values that vary slightly year to year.

The FP-calculated erythemal irradiance from this study is compared to previous calculations, reference algorithm RA https://avdc.gsfc.nasa.gov/pub/data/satellite/Aura/OMI/V03/L2OVP/OMUVB/ (last access: 16 June 2020), for a few sites in common with those listed in Table A4. For the five sites shown in Figs. 1 and 2, the two algorithms produce similar results (Fig. 1a and b for Beltsville, MD, and Fig. 2 for Atlanta, Georgia, Lauder, New Zealand, Seoul, Korea, and Havana, Cuba). The comparison is in terms of the dimensionless UVI = E / (25 mW m-2).

Point-by-point comparison is difficult because of different temporal selection criteria where even small time differences produce rapid changes in E(t). To help with the comparison, the outputs from both algorithms are interpolated onto a common timescale (Figs. 1a and 2a). Differences are formed using the interpolated time series (Figs. 1b and 2). For Beltsville, Maryland (Fig. 1), with low absorbing aerosol amounts, the two algorithms agree to within a UVI mean of 0.39±1.5. A similar analysis is shown for four additional sites (Fig. 2). The OMI time series for RA (Fig. 1a) has many more points than for FP because of much stricter elimination of row-anomaly (Schenkeveld et al., 2017) points in the FP analysis. Approximately 1-year average Loess(0.1) fits to the difference data are shown. Loess(f) is a locally weighted least squares fit to a fraction f of the data points (Cleveland, 1981).

The site at Santiago, Chile, shows an overestimation case where the effect of absorbing and scattering aerosols may not be properly considered in calculations using OMI data for a city located in a depression surrounded by complex high terrain (Cabrera et al., 2012). Calculations in this paper (see Table A4) show a maximum summer value of UVI = 14, when ground-based measurements within the city show peak values near 12. The overestimate is consistent with calculations made previously using other satellite data (Cabrera et al., 2012). Another analysis of erythemal irradiance estimates from OMI satellite data in the New York City area (Fan et al., 2015) found that the calculated UVI overestimates the measured UVI under cloudy conditions, a result that might affect estimated trends.

Trends B(t) were determined for erythemal time series E(t) (similar for total column ozone and cloud transmission time series) using a generalized multivariate linear regression (MLR) model (e.g., Randel and Cobb, 1994, and references therein): 5E(t)=A(t)+B(t)⋅t+R(t), where t is the daily index (t =1 to 5113 for 2005–2018), A(t) is the seasonal cycle coefficient fit, B(t) is the linear LS trend coefficient fit, and R(t) is the residual error time series for the regression model. A(t) involves seven fixed constants, while B(t) is a single constant. The harmonic expansion for A(t) is 6A(t)=a(0)+∑p=13a(p)cos⁡(2πpt/365)+b(p)sin⁡(2πpt/365), where a(p) and b(p) are constants. Statistical uncertainties for A(t) and B(t) were derived from the calculated statistical covariance matrix involving the variances and cross-covariances of the constants (e.g., Guttman et al., 1982; Randel and Cobb, 1994). The linear deseasonalized trend results for various sites are listed in Tables 2–4 and A4 in percent per year with 1 standard deviation (1σ) uncertainty. For comparison of the trends and trend uncertainties derived from (5), trend analysis was also done using monthly average data (one data point per month). The trends and 1σ trend uncertainties derived from the monthly averages were found to be nearly identical to trends and 1σ uncertainties derived from the daily time-series data with gaps. The trends ΔE are expressed in % yr-1 with ΔE=100dE/<E>, where <E> is the average value over the considered period.

Figure 3 and Table 2 show erythemal irradiance E(ζ,φ,z,t) time series (mW m-2) and their LS linear trends (in percent change per year along with their 1σ standard deviation) at six sites with various altitudes z within the United States from 2005 to 2018 (14 annual cycles). The right-hand side axis shows the proportional values of the standard UV index, UVI = E / (25 mW m-2). Erythemal time series are truncated to start and stop at the same point in their 14-year annual cycles (1 January 2015 to 31 December 2018).

The time series depicted in Fig. 3 are non-uniform in time, with gaps, mostly from the row anomaly, between some adjacent points. In all cases the gaps are small enough to properly represent the SZA dependence of the erythemal irradiance. Of the six United States sites listed in Table 2, Albuquerque, NM, and Honolulu, HI, have trends, ΔE=100dE/<E>, with better than 2-σ standard deviations 0.64±0.19 % yr-1 and -0.30±0.12 % yr-1, respectively. These sites have small changes in TCO3 (-0.03±0.05 % yr-1 and -0.00±0.03 % yr-1) but significant changes in cloud + haze transmission CT, 0.35±0.16 % yr-1 and -0.25±0.12 % yr-1, and absorbing aerosol transmission (0.09±0.12 % yr-1 and -0.04±0.17 % yr-1), respectively (see Table 2).

Of human health interest are the maximum values that occur during the summer months when the solar zenith angle is near a local minimum reducing the slant column ozone absorption and Rayleigh scattering for clear-sky days. In terms of the UV index, a value of 6 will produce significant skin reddening in light-skinned people in about an hour of unprotected exposure (Diffey, 1987, 2018; Italia and Rehfuess, 2012). In local shade, there is reduced but significant exposure from atmospheric scattering (Herman et al., 1999), with shorter more damaging wavelengths scattering the most. For three low-latitude US sites in Table 2, the 14-year average maximum UVI reaches 12, with Tampa, FL, reaching 11. For sites with extremely high UVI (10–18), even shaded areas can produce damaging exposure from scattered UV. Table 2 shows the 14-year average maximum UVI and the 14-year average UVI.

For the mid-latitude site, Greenbelt, MD, at 39∘ N, summer values between 8 and 9 are frequently reached, with a few days reaching 10 and 1 d reaching 11 on 6 June 2008. The cause of UVI = 11 was a low ozone value of 283 DU on a clear-sky day compared to more normal values between 310 and 340 DU. The basic annual cycle follows the SZA, with the minimum angle and maximum E occurring during the summer solstice. For Greenbelt, MD, this angle is approximately 39–23.45∘ = 15.55∘. Sites with fewer clouds plus haze and closer to the Equator have higher maximum UV-index values, 12 for White Sands, NM, and 11 for Tampa, FL. Trend results corresponding to Fig. 3a are summarized in Table 2 and Appendix Table A4. The last four columns give the estimated LS trend B(t) from Eq. (4) for each time series and the standard deviation 1σ. Graphs summarizing the more extensive Table A4 are given in Sect. 2.5, which show the expected change in UVI for a wide range of locations at various latitudes. Since the purpose is estimating changes in E from all causes, the effects of the quasi-biennial oscillation (QBO), ENSO (El Niño–Southern Oscillation), and the 11-year solar cycle are not removed from the ozone time series. Figure 3b shows the increases in erythemal irradiance for Greenbelt (UVI = 11) and Rural Georgia (UVI = 12) when the effects of clouds and aerosols are removed from the calculations.

When θ(t) = SZA, CA(t), and CT(t) (transmission) are held constant for calculating E(θ(t), O3(t), CT(t), and CA(t)), a 1 % change in total column ozone amount Ω = TCO3 produces approximately a 1.2 % change ΔE in erythemal irradiance. The exact amount of change is dependent on the SZA selected (Eq. 6). The values for ΔO3, ΔCA, and ΔCT change (% yr-1) are given in Table 2, which shows that a significant amount of the erythemal irradiance change over 14 years is caused by changes in cloud cover except for White Sands, NM.

A numerical solution of the radiative transfer equation for the erythemal action spectrum can be approximated by a power-law form as a function of θ = SZA and Ω = TCO3 (Eq. 6 and Appendix Eq. A4), where the cloud and aerosol transmission are given by CT and CA. This form gives an improved version of the radiation amplification factor (Madronich, 1995) R(θ) that is independent of TCO3 (Herman, 2010). With cloud and aerosol absorption represented by CT and CA factors, 0<CT or CA<1. 7E(Ω,θ)=U(θ)(Ω/200)-R(θ)CTCA For a given time, t, the sensitivities of E to changes in Ω, θ, CT, and CA are 8dEE=-R(θ)dΩΩ+dCTCT+dU(θ)U(θ)-R(θ)ln⁡Ω200dR(θ)R(θ)+dCACA, where, for example, dU(θ)=U(θ+dθ)-U(θ) and dR(θ)=R(θ+dθ)-R(θ).

For θ=0, R(0)=1.2 and R(θ) gradually decrease to 0.85 for θ=80∘ (Herman, 2010, and Appendix Fig. A1). SZA variation is the primary anti-correlated driver for the annual cycle of erythemal irradiance (Fig. 3) at each location, except when there is heavy cloud cover. The cycle for E(θ,φ,z,t) is perturbed by the smaller effect of short-term changes in Ω,CT, and CA that are shifted in phase from θ(t). The result is that the separately estimated 14-year linear trends for CT and Ω are not necessarily additive when using Eqs. (4) and (5). For example, for the Albuquerque, NM, site (Fig. 3), the erythemal trend is statistically significant at 0.64±0.19 % yr-1. Contributing factors are the cloud transmission function CT trend ΔCT=0.35±0.16 % yr-1 (positive means more transmission), aerosol absorption function CA trend Δ CA=0.09±0.12 % yr-1, and small Ω(t) trend ΔΩ=-0.03±0.05 % yr-1. The ΔE trend for Albuquerque without cloud reflectivity and aerosol absorption is 0.04±0.3 % yr-1, corresponding to the small change in just ozone, ΔO3=-0.03±0.05.

The equatorial region is unique for erythemal irradiance, since TCO3 is a minimum and the SZA has a twice-yearly minimum as the solar declination angle changes between ±23.45∘. Four selected equatorial sites (Fig. 4 and Table 3) show very different behavior compared to mid-latitude sites (Fig. 3 and Table 2).

Equatorial sites listed in Table A4 have very high UVI maximum values (e.g., Darwin, AU 12.5∘ S, 0 km, UVIM = 14; Lima, PE, 12∘ S, 0.2 km, UVIM = 15; Kinshasa,CD, 4.3∘ S, 0.3 km, UVIM = 14; Nairobi, 1.1∘ N KE, 1.9 km, UVIM = 15; Bogota, CO, 4.6∘ N, 2.5 km, UVIM = 15) with a significant number of clear-sky days. There are exceptions where there is considerable cloud cover on many days, such as Manaus, Brazil, and Quito, Ecuador. The average E(ζ, φ, z) is higher (mean <UVI>=9, UVIM = 14) for the near-sea-level site in Manaus, Brazil (1.8 million people), than the equally populated city of Quito, Ecuador (1.85 million) at 2.9 km altitude (mean <UVI>=7, UVIM = 12). The lower average Quito value is caused by the presence of additional cloud cover (mean transmission <CT>=0.34) compared to Manaus (mean transmission <CT>=0.68) even though the Quito altitude is considerably higher. The effect of high altitude, 5.2 km with relatively clear skies, is seen for the Mt. Kenya site at 0.1∘ S with UVIM = 18.

Figure 5a shows the effect of altitude causing an increase in clear-sky E(ζ,φ,z,t) for Quito (2.9 km) compared to Manuas (0.1 km) plus a small difference in average TCO3 (2 %) between the two locations. Without clouds, Fig. 5, both sites show a double peak corresponding to SZA = 0∘ twice a year near the March and September equinoxes. Figure 5b has an expanded timescale for 2005 showing the double peak for Quito and the strong effect of clouds in the region. The 14-year average cloud-free value for Quito is <UVI>=16 and a maximum UVI = 19. The minimum cloud-free value is <UVI>=15 instead of 3 when cloud cover is included. Compared to Quito, the cloud effect is less at the Manaus, Brazil, and Mt. Kenya sites, and even at the coastal Makassar, Indonesia site. The 20 DU variation in TCO3 causes the autumn peak in E(ζ,φ,z,t) without clouds to be smaller than the spring peak. Note that there are only 90 points in 2005 because of data gaps in OMI equatorial data and the effect of losing points because of the row anomaly.

The calculations based on 1∘×1∘ (100×100 km2) spatial resolution can obscure an important health-related result. In Quito, there are frequent localized clear periods when the UV index can rise to the clear-sky values (13 < UVI < 18), an increase of about 10, which is a serious health threat for skin cancer and cataracts all year. At all sites, ground-based measurements show that UV irradiance at the ground can briefly exceed the clear-sky value because of reflections from nearby clouds (Sabburg and Wong, 2000). In Honolulu (21.3∘), the double peaks in E(ζ,φ,z,t) are not significantly separated in time (15 d) to be easily discernable, but it causes the slightly different shape in the annual cycle (Fig. 3a). In general, equatorial sites have increased E(ζ,φ,z,t) compared to higher latitudes because of both lower SZA values and less ozone near the Equator, giving reduced UV absorption and increased E(ζ,φ,z,t).

Two of the four equatorial sites in Fig. 4 and Table 3 show significant linear trends B(t) (Makassar, Indonesia, and Mt. Kenya, Kenya), with the Makassar, Indonesia, site showing the largest linear trend, -0.55±0.2 % yr-1. For Makassar, ozone is increasing at a rate of 0.17±0.02 % yr-1, which by itself would cause UVI to decrease at a rate of -0.20±0.01 % yr-1. Atmospheric transmission (Table 3) is decreasing at a rate of -0.16±0.19 % yr-1, causing E(ζ,φ,z,t) to have a net decrease. In the absence of clouds, the percent decrease in ozone amount causes an increase in E(ζ,φ,z,t) at approximately a 1.2:1 ratio. Figure 5a shows the approximate anti-correlation between ozone amounts and E(ζ,φ,z,t) for Quito and Manaus. This is modified by the 6-month shifting of the sub-solar point (SZA = 0). When all four periodic and quasi-periodic effects are combined, the result is the aperiodic function shown in Fig. 5b for Quito, Ecuador. Similar analysis applies for Manaus, Brazil, located near the Amazon River, which is dominated by variable cloud-driven atmospheric transmission, but less than for Quito, Ecuador. The other two equatorial sites Makassar, Indonesia, and Mt. Kenya, Kenya have smaller cloud effects and show periodic structures driven by SZA and ozone absorption.

Time series for the Southern Hemisphere are represented by six sites shown in Fig. 6 ranging in latitude and altitude (12.5 to 54.8∘ and 0 to 2.5 km). The maxima occur close to the December solstice date, with the exact date shifted by cloud cover, and the minima occur near the June solstice date. Of these, Darwin, Australia, is within the equatorial zone (12.5∘ S) and shows the double-peak structure with peaks separated by about 85 d. The site furthest from the Equator, Ushuaia (54.8∘ S), has the lowest UVI peak value of 9.6 (14-year average maximum UVI = 8) and the lowest 14-year minimum average UVI = 2. Occasionally the Antarctic ozone depletion region passes over Ushuaia, giving rise to increased UV amounts, but these episodes (September–October) usually do not correspond to the maximum UVI values that occur with the minimum SZA in January. The 20-year historical ground-based measurement record at Ushuaia starting in 1988 (Bernhard et al., 2010) shows higher values, 11.5, when the Antarctic ozone hole moved overhead in October, even though the SZA is not a minimum.

For the sites in Fig. 6, the populated sites San Pedro de Atacama, CL, and La Quiaca, AR, have the largest UVI maximum (17 and 18) and average (11), since they are at significantly higher altitudes (2.5 and 4.5 km) and are located at the southern edge of the equatorial zone (23 and 22∘ S) with a relatively clear cloud-free atmosphere. More than half of the days each year have 10 < UVI < 18. This 14-year average UVIM is higher than for equatorial Darwin, Australia, UVI < 15.5. The frequent June minima for Darwin are UVI = 8, with occasional days at UVI = 2 caused by clouds, while the almost cloud-free San Pedro de Atacama has minima of UVI = 4 corresponding to a June noon SZA = 46∘ compared to Darwin June SZA = 36∘. Both sites have about the same typical TCO3, 255 DU.

Previous estimations of erythemal irradiance from ground-based measurements (1997–1999) and calculations (using Total Ozone Mapping Spectrometer data) at Ushuaia (Cede et al., 2002, 2004) show very similar values, with UVI < 1 in the winter (June) and with 14-year average maximum values up to 8. The OMI data show an occasional day reaching UVI = 10 during the summer (December–January). Buenos Aires at lower southern latitudes has values of UVI from 1 to 2 in the winter and up to 12–13 in the summer. These values approximately agree with those in Table 4. Cede et al. (2004) give ground-based results for eight sites that also include a higher-altitude equatorial site, La Quiaca, AR (22.1∘ S), at 3.46 km altitude, with very high summer values up to UVI = 20. The corresponding calculated estimates using OMI data (2005–2018) also have the maximum UVI = 20 occurring in 2010 with a 14-year average maximum of UVIM = 18 (Table 4). None of the ΔE in Table 4 are statistically significant at 2σ.

Figure 7 shows the 14-year LS trends (Eq. 4) (% yr-1) ΔE, ΔΩ, ΔCT, and ΔCA and the 1σ error estimate for land (Table A4 and Fig. A3) plus Atlantic and Pacific Ocean sites distributed in latitude from 60∘ S to 60∘ N. The colored solid lines are a Loess(0.1) fit to the trend data that is approximately equivalent to a 15∘ latitude running average with least squares weighting. Figure 8 contains the same Loess(0.1) fits on an expanded common scale. The 1σ error estimates are large enough to conclude that there are few significant changes in E at the 2-σ confidence level for many of the individual sites (see sites prefaced with ∗ in Table A4). However, the Loess(0.1) curves show significant correlation with each other, suggesting that the increases and decreases from combining sites within a 15∘ latitude band are significant and not just noise.

For the UV portion of the spectrum represented by the erythemal irradiance action spectrum, the ΔE is affected by changes in TCO3 that change relatively slowly with latitude (Fig. 7a, b). ΔTCO3 drives changes (1±0.5 % per decade 40∘ S to 30∘ N, 0.3±0.3 % per decade 25 to 45∘ N, 1.4±0.6 % per decade 45 to 60∘ N). The ozone changes (Fig. 7b) obtained from OMI observations include the effects of the 11.3-year solar cycle, the quasi-biennial oscillation QBO, and the El Niño–Southern Oscillation (ENSO) effects, and, as such, are not the standard ozone trend amounts (Weber et al., 2017; WMO, 2018). There are significant increases of 1.1±1.2 % per decade in ΔCT at high southern latitudes (mostly cloud reflectivity) for a latitude range, 60 to 45∘ S (Fig. 7c) with a significant decrease around 22 and 35∘ N and an increase near 22.5∘ N.

Atmospheric transmission CT increased (cloud reflectivity decreased) by 1±0.9 % per decade for 35 to 60∘ N for the period 2005 to 2018, implying that solar insolation has also increased for all UV (305–400 nm), visible (400–700 nm), and near-infrared wavelengths (700–2000 nm). Atmospheric transmission in the presence of absorbing aerosols CA has decreased in the equatorial zone by -1.9±0.9 % per decade for 20∘ S to 5∘ N (panel d) and at southern latitudes by -1.8±1.3 % per decade for 60 to 30∘ S. CA in the Northern Hemisphere shows two peaks centered on 5 and 18∘ N and oscillates about zero -0.1±1 % per decade for 5 to 60∘ N. ΔE is correlated with changes in cloud transmission ΔCT and absorbing aerosols associated with cities ΔCA (Fig. 7b). Since ΔTCO3 changes slowly with latitude compared to ΔCT and ΔCA, the effect of ΔTCO3 is more of an offset compared to the stronger latitudinal variation effect of aerosols and clouds.

Figures 7a, b, and 8 are limited to ±60∘ latitude, since estimating E(ζ,φ,z,t) over the Arctic or Antarctica snow and ice from OMI data is likely not accurate because the LER of the scene is approximately treated as if there were a cloud instead of a bright surface. In Antarctica's Palmer Peninsula, the annual erythemal irradiance cycle ranges from 0 in winter (May to August) to a variable maximum in the spring and summer months depending on the year. For example, estimates from OMI data with CT=1 (clear sky) are 125 mW m-2 (UVI = 5) in 2013 and 175 mW m-2 (UVI = 7) in 2016. The year-to-year variation in the maximum E(ζ, φ, z, t) is driven by the highly variable Antarctic TCO3 hole.

Figure 8 shows a latitudinal plot of the maximum and average UVI over 14 years from 105 of the land sites listed in Appendix Table A4. The maximum values over 14 years show the high summertime UVI levels that can be expected at individual sites, especially for the four indicated high-altitude sites. The maximum summer values at all latitudes between 60∘ S and 60∘ N exceed UVI = 6, which is considered high enough to cause sunburn for unprotected skin (Sánchez-Pérez et al., 2019) in 20 to 50 min depending on skin type. Higher values of UVI can produce sunburn in much shorter times. For example, for UVI = 10, sunburn can be produced in as little as 15 min for Type 1 and Type 2 skin (Caucasian and Asian) to 30 min unprotected exposure for Type 4 skin (Sanchez-Perez, 2019).

The highest UVI values in Table A4 and Fig. 8 are associated with four high-altitude sites. Two of these are populated cities, San Pedro de Atacama (2.5 km, population = 11 000), Chile, and La Paz, Bolivia (3.8 km, population = 790 000). These two high-altitude sites have very high UVI associated with their low latitudes and relative lack of clouds on some days. Over the 14 years of this study, the UVI at San Pedro de Atacama has remained approximately constant (-0.06±0.10 % yr-1), while at La Paz, Bolivia, the UVI has decreased at a rate of -0.59±0.16 % yr-1 caused by an increase in ozone amount (0.1±0.02 % yr-1), a decrease in atmospheric transmission CT from increasing cloud cover (-0.48±0.14 % yr-1), and a decrease in absorbing aerosol transmission CA (-0.24±0.13 % yr-1) from increasing amounts of absorbing aerosols. The height dependence of UVI for Mt. Everest (8.8 km) is linearly extrapolated from calculations for 0 to 5 km (Eq. A4 and Table A3). Radiative transfer calculations of the height dependence to 8 km show that this is a good approximation.

For the June solstice view (Fig. 10), the EPIC view includes the entire Arctic region and areas to about 55∘ S. The center longitude of the image is close to local solar noon. The view is with north up and from sunrise (west or left) to sunset (east or right). The effect of the orbital distance from the Earth–Sun line can be seen in the asymmetry of the near-sunrise and sunset regions, implying that the 6-month orbit was off to the southwest of the Earth–Sun line. The images were selected to give estimates of erythemal irradiance over Asia, Africa, and the Americas as a function of latitude, altitude, and longitude (time of the day) for a specific Greenwich Mean Time (GMT) for each map.

In Fig. 10 high UVI is seen over the Himalayan Mountains (06:13 GMT) and central western China, reaching over UVI = 18 for 22 June on Mt. Everest (28.0∘ N, 86.9∘ E; 8.85 km). For the same conditions, except for artificially setting the altitude at sea level, the maximum UVI is 13. The sea-level mean UVI value is 7. The estimated UVI neglects reflections from snow and ice. For Everest, the extrapolated (from 5 km) average net altitude correction for a maximum UVI of (18–13) / (13×8.8 km) = 4.3 % km-1 and 5.6 % km-1 for the mean UVI, including reduced TCO3 and Rayleigh scattering (Eq. A7). With calculations to 8 km the value is 4.5 % km-1. The reason for the difference between UVI maximum and UVI mean is that the mean UVI contains clouds and aerosols, while the maximum UVI is nearly clear sky.

In the next view in Fig. 10 over central Africa (11:21 GMT) there are elevated UVI = 11, and in the third image in Fig. 10 (19:00 GMT) there is an elevated UVI area over the mountainous regions of Mexico (UVI = 16). Elevated UVI = 11 is also seen over the US Southwest. The effect of significant cloud cover at moderate SZA can be seen (blue color), where the UVI is reduced to 2 near noon (e.g., Gulf of Mexico at 19:00 GMT).

There are reductions in E(ζ,φ,z,t) from lower-reflectivity clouds in the center of the Fig. 10 images that are not easily seen in the UVI image with the expanded scale (0 to 20). The effects of higher-reflectivity clouds (see Fig. 9) are easily seen in Fig. 10 in blue color representing low amounts of E(ζ,φ,z,t) at the ground. There are only small percent change features in the ozone distribution, so that few ozone-related structures are expected in the E(ζ, φ, tO) images for such a coarse UVI scale.

Figure 11a shows the latitudinal distribution, ζ=0∘ to 80∘ N, of erythemal irradiance estimated from the synoptic EPIC measurements on a line of longitude passing through San Francisco, CA, at 19:37 GMT or 11:37 PST. The main driver of the decrease in E(ζ) from the Equator toward the poles is the increased optical path from increasing SZA(ζ) and increasing TCO3(ζ) absorption. The smaller structure near 10, 21, and 37∘ N is caused by small amounts of cloud cover reducing the transmission CT(ζ). This day, 30 June 2017, near the 22 June solstice was selected based on the data from DSCOVR-EPIC showing that there were few clouds present in the scene (Fig. 11b) with CT near 1. All the E(ζ) estimates in Fig. 11a are at or near sea level and yield a maximum UVI = 12 near 13∘ N latitude. Similarly, Fig. 11c shows the latitudinal distribution of E(ζ) for the line of longitude passing near Greenwich, England, at 0.25∘ E. E(ζ) is reduced because of cloud cover starting at 40∘ N in addition to the increasing ozone absorption at higher latitudes. The accompanying images in Fig. 11b and d show the distribution of E(ζ) and the location of significant cloud cover.

Near the September and March equinoxes (Fig. 12a and b) the Sun is overhead near the Equator, giving high UVI = 12 in many areas, with higher values (16 to 18) in the mountain regions (e.g., southern Indonesia, Peru's Andes Mountains, and some high-altitude regions in Malawi and Tanzania). While the Sun–Earth geometry is nearly the same for both equinoxes, there is considerable difference in seasonal cloud cover for the 2 equinox days. The area of sub-Saharan Africa near Nigeria has particularly high UVI values caused by nearly cloud-free conditions over a wide region, implying a considerable heath risk for midday UV exposure. Other high UVI values occur over smaller elevated areas. This is particularly evident in the nearly cloud-free high-altitude Peruvian Andes at about 28∘ S even with SZA = 28∘.

During the December solstice the Sun is overhead at 23.45∘ S (Fig. 13). The reduced SZA causes high UVI levels throughout the Southern Hemisphere mid-latitude region, Fig. 13, between 20 and 40∘ S, especially in elevated regions such as the Chilean Andes, Western Australia and elevated regions of southeastern Africa (South Africa, Tanzania, Kenya). For the case where Western Australia is near local solar noon, the UVI levels reach about 13 to 14 between 20 and 34∘ S, a region that includes the city of Perth with more than a million people and several smaller cities and towns. These high UVI values represent a considerable health risk for skin cancer, since the UVI stays above 12 for nearly a month. This is also true for eastern Australia (Fig. 14) during December, which implies a high skin cancer risk for the entire Australian continent. The same comments apply to New Zealand, eastern South Africa and elevated areas further north (e.g., Tanzania, Africa). Even higher values occur in the Andes Mountains in Chile and Peru that include some small cities (see Fig. 6 for San Pedro de Atacama, Peru time series).

Figure 14a shows the latitudinal distribution, 0 to 80∘ S, of erythemal irradiance on a line of longitude passing near Sydney, Australia (population 5.3 million), at 02:24:36 GMT or 13:24 NSW (New South Wales). The main driver of the decrease in E(ζ) from the Equator toward the poles is the increased optical path from increasing SZA(ζ) and the increasing TCO3(ζ). The smaller structures near 40, 50, and 60∘ S are caused by small amounts of cloud cover reducing the transmission CT(ζ). The 31 December day near the solstice was selected based on data from DSCOVR-EPIC showing that there were few clouds present over Australia (Fig. 6b). All the E(ζ) estimates in Fig. 14a are near sea level, with a maximum UVI = 14 near 25∘ S latitude. Figure 14b shows the distribution of high E(ζ, φ) over Australia and Indonesia, with the highest values in Australia for 31 December 2017.

The erythemal irradiance differences between the northernmost city (Darwin, population 132 000) and the southernmost city (Melbourne, population 4.9 million) are quite large in terms of UV exposure because of differences in SZA, ozone amount, and cloud cover leading to a larger number of days per year with high UVI, a few weeks for Melbourne and 3 months for Darwin. This is reflected in the non-melanoma skin cancer statistics published by the Australian Institute of Health and Welfare (2016) for the different regions, with the Northern Territories (containing Darwin) having double the rate per 100 000 people compared to Victoria containing Melbourne (Pollack et al., 2014).

The longitudinal dependence of E(ζ, φ, tO) is illustrated in Fig. 15, where sunrise to sunset slices have been taken for an equatorial latitude, ζo=0.1∘ N, and mid-latitude, ζo=30.85∘ N. The estimated E(ζo, φ, tO) includes the effect of clouds and haze (panels c and d) included in the atmospheric transmission function CT(ζo, φ, tO) and the effects of local terrain height. The maximum E(ζo, φ, tO) is to the east of the sub-satellite point because the satellite orbit about the Lagrange-1 point L1 is displaced to the west of the Earth–Sun line on 14 April 2016. The northward displacement is caused by the Earth's declination angle of about 9.6∘. This corresponds to the minimum SZA shown in Fig. 15a of 9.5∘. Panels a–d show the effects of cloud transmission for all values of LER that are not easily seen in the global erythemal color maps (bottom color panels of Fig. 15). The distribution of clouds is easily seen in the color image and LER image for 14 April at 04:21 GMT (Fig. 16a and b).

The main cause of the decrease in E(ζ, φ, tO) with latitude (Fig. 15a, b, e) between 0.1 and 30.85∘ N is the increased SZA followed by the latitudinal increase in TCO3. The difference is modulated (panels a and b) by the presence of clouds and haze (Figs. 15c, d and 16a, b) and haze in CT(ζ, φ, tO). There are nearly clear-sky patches for the equatorial slice (Fig. 15c) leading to very high UVI = 14 compared to the mid-latitude maximum of UVI = 9 because of the effect of clouds near the time of minimum SZA. The distribution of clouds is shown in the true color picture (Fig. 16a) of the Earth obtained by EPIC on 14 April 2016 at 04:12:16 GMT centered on 104∘ E. The bright white portions of cloud images are the optically thick clouds of high reflectivity and low transmission. Comparing the color image to the LER image (Fig. 16b) illustrates how dark (unreflective) the land and oceans are in the UV compared to the visible wavelengths, even though clouds are reflective in both wavelength ranges. This allows cloud reflectivity and transmission CT to be determined without complicated corrections for surface reflectivity for scenes free of snow and ice once Rayleigh scattering is removed.

Figure 17 shows a summary of the zonal average of maximum UVI (UVIM panel a) and zonal average of the mean UVI (UVIA panel b) values from EPIC on 14 April 2016 at 04:21 GMT from Fig. 14a for longitudinal band plots from -75∘ < latitude < 75∘. The solid lines are a smooth Akima spline fit (Akima, 1970) to the data points. Depending on the day of the year, the location of the maximum shifts between -23.45 and +23.45∘ following the position of the overhead Sun. The zonal average UVIM (Fig. 17a) of about UVI = 14 is approximately the same for any day of the year. This includes longitudes containing high-altitude sites at moderately low latitudes where the local UVI maximum can reach 18 to 20. The US Environmental Protection Agency classifies exposure at UVI = 6 to 7 as high, which requires protection for extended exposure (e.g., 1 h). For low latitudes <30∘, UVI > 6 occurs several hours around local solar noon. For equatorial latitudes at sea level, UVI > 6 occurs for about 6 h (Fig. 15). The zonal average values UVIA (Fig. 17b) are considerably smaller, since they are more affected by clouds than the mostly clear-sky maxima in Fig. 17a.