Simulation of Threshold UV Exposure Time for Vitamin D Synthesis in South Korea

School of Earth and Environmental Sciences, Seoul National University, Seoul, Republic of Korea Department of Atmospheric Sciences, Chungnam National University, Daejeon, Republic of Korea Department of Atmospheric Sciences, Yonsei University, Seoul, Republic of Korea New and Renewable Energy Resource Center, Korea Institute of Energy Research, Daejeon, Republic of Korea Department of Atmospheric Sciences, Pusan National University, Busan, Republic of Korea National Institute of Environmental Research, Incheon, Republic of Korea


Introduction
Increases in surface UV irradiance resulting from stratospheric ozone depletion have had harmful effects on human health by inducing skin damage [1,2].To assess the health risks from UV, erythemally weighted UV (UV Ery ) or the UV index (UVI; defined by UV Ery in Wm −2 divided by 25 mWm −2 ) has been developed using a weighted function related to the occurrence of skin erythema [3,4,5,6].UV Ery irradiance (or the UVI) generally varies with atmospheric conditions that include the quantity of ozone, which is an important factor in its accurate estimation.e widely used action spectrum for the erythemal dose is that of the Commission International on Illumination (CIE) [5].Because prolonged exposure to UV Ery leads to harmful erythemal dosing, UV Ery observation networks have focused primarily on UV-B (ranges from 280 to 315 nm) measurements, with some consideration of UV-A (ranges from 315 to 400 nm) measurements [7].In addition to its adverse effects, UV radiation has several beneficial effects on human health, such as perceived improved appearance, enhanced mood through endorphin release, and a reduction of blood pressure [8,9].e synthesis of vitamin D in the skin can be used as a representation of the beneficial effects of UV exposure [10][11][12][13][14].
e idea of adequate UV exposure time is defined as the UV exposure that balances the risks and benefits of UV exposure to the skin [15].e wavelengths of UV radiation for synthesizing vitamin D fall primarily in the UV-B and part of the short UV-A bands (shorter than 330 nm) [16,17], which is similar to the spectral weight of UV Ery .However, the effective range for the action spectrum is shorter than the CIE erythemal action spectrum [15,18,19,20].From previous studies, the optimized exposure time for vitamin D synthesis is normally shorter than the time required to cause erythema [15].erefore, the exposure time to solar UV radiation that results in sufficient vitamin D synthesis without damaging the skin can be determined.e threshold value of exposure time is used to minimize the risk of erythemal dosing and to secure vitamin D synthesis.erefore, exposure time calculations require accurate calculations of UV Ery and the UV irradiance spectra weighted by the action spectrum of vitamin D synthesis (UV VitD hereafter).e latter is related to the production of 25-hydroxy vitamin D. However, the solar UV irradiance at the surface changes diurnally and seasonally due to the geometrical changes in solar position.For example, the UV Ery irradiance in the midlatitudes is similar to that in the tropics during the summer, but it is lowered by approximately 90% during the winter [15,21] due to the large seasonal variation in the solar zenith angle.In addition to the solar position, atmospheric factors such as ozone concentrations [22,23], aerosol [22,23,24], and cloud coverage [25,26] diminish surface UV irradiance.Comprehensively, diminishing surface UV irradiance by the atmospheric conditions caused the "vitamin D winter" effects, which is a season with insufficient vitamin D synthesis by UV irradiance [27,28].
Focusing on studies that have calculated exposure time, the regional distribution of the levels of threshold of UV exposure for vitamin D synthesis have been determined by using the statistical relationship between UV VitD and several variables, such as global solar irradiance, total ozone, and dew point temperature [27,29].In addition, Miyauchi et al. [30] noted that the UV VitD and exposure time calculations have also been developed based on a radiative simulation combined with various elements of observation data.e latter considers the season, time, and spatial variation of atmospheric conditions.
In South Korea, the forecast system of daily maximum UV Ery is developed based on a statistical linear regression model for total ozone that uses long-term satellite datasets from the Total Ozone Mapping Spectrometer (TOMS) and the Ozone Monitoring Instrument (OMI) [31], which is similar to the UV Ery simulation systems used in other regions [24,32,33,34,35,36,37].However, the estimation of UV VitD and exposure time simulations for it, which accounts for atmospheric conditions with high temporal and spatial resolution, have not yet been reported.is study provides a simulated exposure time for vitamin D synthesis based on an improved UV calculation.During the UV calculation, we also considered to the information of total ozone prediction from statistical approach and cloud forecast from the model simulation in South Korea as shown in Section 2. Finally, Section 3 describes the simulation results of exposure time and comparison in several observation sites.

Exposure Time Calculation Based on the Simulation
Figure 1 shows a flow chart of the simulation of UV VitD exposure time.e simulated UV VitD is based on the calculation method for daily representative UVI, defined as the noon-time value, over Korea [31].In several previous studies, for clear-sky UV calculations using radiative transfer models (RTMs), total column ozone has been predicted based on results from empirical linear regression models [31,32,38] or chemical transport models [39].In this study, the simulation consists of a total ozone model based on empirical regression.As described in Section 2.1, the total ozone prediction is daily representative total ozone forecast on the next day with using parameters from the results of numerical weather predictions.A cloud modification factor is applied to the UV irradiance results to calculate the UVI and UV VitD (Section 2.2).Finally, the method of calculation of the UV exposure time is shown in Section 2.3.

Total Ozone Prediction.
e quantity of total ozone in the midlatitude region depends on the activity of the Brewer-Dobson circulation and stratosphere-troposphere exchange in the Arctic [40,41].In South Korea, Park et al. [42] have reported on the total ozone, as well as the annual, seasonal, and day-to-day variation of total ozone.Using a 25-year set of ground-and satellite-based observational data, the interannual variation was found to be less than 20 Dobson Unit (DU).e seasonal variation ranged from 51 to 106 DU, which corresponds to approximately 17%-30% of the total ozone.is large temporal variation is the result of solar activity and the natural oscillations that affect stratospheric ozone.However, according to an analysis of the daily representative total ozone dataset [42], the day-to-day ozone variation, which is defined as the relative difference in total ozone between a given day and the day prior, ranged from −30.3% to 38.6%, with a mean absolute difference of 5.2∼5.7%.In addition, variation in column amount of ozone in the stratosphere, which is known to be less variable than that in the troposphere, has been estimated to be 13.4 DU for a standard deviation from ozonesonde observations over the Korean Peninsula [41]. is short-term temporal variation is caused mainly by the heterogeneity of the distribution of stratospheric ozone and its dynamic transport.Based on these observations, total ozone variations on a daily scale must be considered when estimating surface UV irradiance.e total ozone dataset was compiled from observations from the Dobson spectrophotometer at Yonsei University, Seoul (WMO/GO3OS Station No. 252, location: 37.57 °N, 126.95 °E, 84 m above sea level).e quality of the Dobson data was validated using a dataset from the Brewer spectrophotometer at Pohang [41], overpass data from TOMS [41,43,44,45], and data from OMI [41,46,47].From the intercomparison studies, the total ozone from the other instruments agreed within 2% with that from the Dobson spectrophotometer.
e atmospheric factors, daily total ozone data, and its climatology were used to develop the daily total ozone 2 Advances in Meteorology prediction on the next day (D + 1) by using the linear regression method.e training period for the linear regression was 44 months, from May 2011 to December 2014.To account for the long-term variations of total ozone considering seasonal and annual scales, a 30-year dataset from 1985 to 2014 was used as the climatological total ozone dataset for total ozone prediction.Because total ozone variations on a daily scale are strongly related to atmospheric conditions in the stratosphere and upper troposphere, we selected u-wind, v-wind, temperature, and geopotential height from 100 to 300 hPa at the site of the Dobson spectrophotometer as variables for the empirical regression.
ese meteorological variables were derived from data from the regional data assimilation and prediction system (RDAPS) model of the uni ed model (UM) from the KMA, which has a horizontal resolution of 12 km × 12 km.Using forward stepwise selection, signicant meteorological variables were identi ed for use in the prediction of daily total ozone and the empirical regression formula is shown below: where c(D + 1) is the predicted total ozone amount on the next day (D + 1); c and c c are the observed total ozone amount and climatology of total ozone using the 30-year dataset (period: 1985-2014) for a speci c day, respectively; and u, v, T, and h are u-wind, v-wind, temperature, and geopotential height at a speci ed pressure, respectively.Based on the regression model for total ozone prediction, as shown in Figure 2, during the period from May 2011 to December 2014, the di erences in total ozone between observed and estimated have a mean of 0.3% with a root mean squared di erence of 5% (17.6 DU).

Cloud Modi cation
Factor.Clouds, including their quantity, type, and optical properties, vary in time and space in the real atmosphere, and the UV attenuation by the cloud has large variability due to the variation of cloud properties.To estimate the radiative e ect of cloud, most methods used to the cloud modi cation factor (CMF) as de ned by the ratio between actual irradiance and clear-sky irradiance [25,48,49,50].Most of CMF value is less than 1.0, which means the existence of cloud diminishes the surface UV irradiance [51,52].Otherwise, several previous studies showed that observed UV-B irradiance was signi cantly enhanced by the cloud [53,54,55], and the cloud e ect for UV-B has spectral dependence [56,57,58].e CMF value is basically related to the cloud cover (cloudiness) with empirical approaches from the observation [59].In addition, the CMF value is also dependent on the cloud altitude, cloud types, cloud thickness, and solar zenith
e UV irradiances calculated from the RTM were basically conducted under cloud-free conditions.To consider the extinction by cloud, the parameters for cloud (e.g., cloud optical depth, phase function, and cloud vertical distribution) could be used as an input of RTM simulation.However, the KMA provided the predicted cloud amounts based on the tenth-scale with high spatial resolution.Because the RTM is a one-dimensional model that does not account for spatial variation, its irradiance includes uncertainties related to the cloud extinction from the cloudiness value.Although the cloud optical depth can be used as an input to the RTM, it is di cult to directly convert from cloudiness to cloud optical depth.In this study, the CMF value is used to consider the extinction of cloud in the simulation, and the CMF is the spectrally independent value.e CMF is simply de ned by the cloud amount introduced from Lee et al. [31]: where f is the modeled cloud amount in tenths (fractional cover multiplied by ten).From the previous study in South Korea, the quantitative value of spectral di erence of CMF in 320∼360 nm is up to 0.05 [63], which is equivalent to the CMF error by cloud amount error of 1.25.
Because the meteorological forecast model provides cloud amount with 3-hour intervals, the CMF values also have a 3-hour resolution.Although the model calculates the UV irradiance with high temporal resolution, the CMF values changes every three hours.In the UV irradiance model, the CMF for a cloud amount of 0-2 is de ned to be 0.984, which is considered as the maximum value and occurs under low-cloud conditions.
e CMF from observation was estimated up to 0.95 for solar zenith angle of 40∼70 ° [63].e calculated cloud amount values have been grouped into ve cloud-coverage categories at intervals of approximately 2-3.

Exposure Time Calculation.
e clear-sky UV irradiance was calculated using an RTM for the tropospheric ultraviolet and visible (TUV) [64,65].e TUV model uses a radiative transfer method for shortwave irradiance calculations based on the two streams or discrete ordinates with multistreams.Atmospheric conditions were based on the standard atmosphere of the US including vertical pro les of molecular composition, temperature, and pressure discretized into several vertical layers.In addition to the input variables required for the RTMs used for the UV calculations, we also considered the aerosol conditions.An aerosol optical depth (AOD) of 0.5, single scattering albedo (SSA) of 0.95, and asymmetry factor (ASY) of 0.75 at 340 nm were used, which are similar to the observed optical parameters of aerosols in Seoul [66].e SSA and ASY were assumed to be constant within the UV range, while the AOD had a spectral dependence with an angstrom exponent of 1.0.
e surface albedo was used as an input parameter to represent the surface properties.e land-cover type climate modeling grid (CMG) product (MCD12C1) was used to de ne the surface conditions.e MCD12C1 provides high spatial resolution (0.05 °) coverage of the dominant landcover types along with an "urban" surface type.Based on the "urban type" from MCD12C1, the urban index was de ned as the total number of grid point for "urban type" in 4 grid points near a speci c site.Using the urban index, the surface type was categorized into urban and suburban regions.e surface albedo ranged from 0.02 over grass [67] to 0.12 over concrete surfaces [68], near regions of industrial and human activity.Based on the previous studies, the urban index can be directly converted to the surface albedo using the following formula: SUF 0.020 + 0.025 × UI, where SUF and UI are the surface albedo and urban index (ranges from 0 to 4), respectively.e reference year for the surface types is 2012, which is the most current dataset for MCD12C1.e TUV calculates the UV irradiance from 280 to 420 nm with a 1 nm resolution.e forecasted clear-sky UV irradiance, UVI, and UV VitD were estimated at one-hour intervals during the daytime.e exposure time calculation for vitamin D synthesis is based on McKenzie et al. [15] and summarized below.Accordingly, the dose of vitamin D (DUVI) can be expressed as where R UV is the ratio of UV Ery to UV VitD as a function of the solar zenith angle and total ozone because of their di erent spectral weighting functions [15], T D is the threshold exposure time for vitamin D synthesis, α is the fractional exposure area of skin, MEDF is the blocking factor relating to the minimal erythema dose (MED), which is estimated from the erythemal dose relating to the skin type, and SPF is the sun protection factor.erefore, the MEDF is de ned to be the number of standard erythemal doses (SED), which is corresponding to 100 J/m 2 for erythemal UV irradiance, for  Advances in Meteorology given skin types.e DUVI is essentially a similar concept to estimate the UVI value, but it also considers the spectral difference due to the change in action spectra.Based on the DUVI value, the T D is estimated to be e reference value of the exposure time (T D0 ) corresponds to conditions under which the exposure time for vitamin D synthesis is 1 minute as described in previous studies [15,69,70].If α and MEDF are assumed to be 0.1 and 4.5 (for Type IV skin), respectively, the equation for T D simplifies to T D � 360.0/[RUV × UVI].e α for 0.1 is assumed to be from nominal cases of wintertime exposure skin surface area, with only the hands and face exposed.In some cases, the parameters related to the skin type and exposure of the skin surface area can have large variations.For example, high deficiencies of vitamin D were found in rural areas at high sun elevations in the equatorial region for dark skinned women [71].In Youn et al. [72], the skin type of Korean mostly ranges from type III to V, and the skin type is related on the frequency of UV exposure and age.Although several factors related to the skin types can be considerable factor for accurate exposure time estimation, the factors of MEDF are applied the above assumed parameters (based on skin type IV) in this study.
Because the exposure time is estimated from the spectral UV irradiance with high spectral resolution, the R UV can be directly estimated from the RTM results with simultaneous estimation of UV Ery and UV VitD .As the UV irradiance spectrum varies during the exposure time, the R UV was defined as the average value during the exposure period.To calculate the T D , based on the results, the UV irradiance from the RTM was interpolated with one-hour interval to a one-minute interval.After interpolation of the UV irradiance with a one-minute interval, T D can be estimated with one-minute resolution.

Results and Validation
3.1.Annual and Seasonal Variation of UV. Figure 3 shows the simulated UV Ery and UV VitD before and after adopting the CMF, and, as shown in Table 1 for the six representative sites, the noon exposure time for vitamin D synthesis (T D ) and erythema dose (T E ).During the comparison period from January 2015 to September 2016, the T D clearly shows a seasonal cycle, with the longest exposure times in winter (especially December) and the shortest in summer (May to July).Generally, the T D follows the seasonal change in solar zenith angle.In summer, the minimum T D was estimated to be less than 30 minutes.However, the simulated T D was never less than 10 minutes.Although the cloud-free UV irradiance is highest in the summer season, the summertime UV VitD is similar to that of the late spring and early autumn due to the high cloud cover due to the Asian monsoon season in summer.
During the winter, the T D was generally longer than 100 minutes (December to February) and exceeded 200 minutes in December.
us, sufficient synthesis is rarely possible by solar UV exposure alone during winter.e longest T D was estimated during December, when the largest solar zenith angle occurred at noon on the winter solstice.In addition, the T D variations were greater in the winter than in the summer.ese variations were due to the low values of UV VitD in the winter leading to reduced synthesis efficiency.For this reason, the day-to-day changes in T D were largest in the winter, despite the small day-today changes in CMF.
Figure 4 shows the seasonal average of T D at the representative sites at noon.During summer (June to August, JJA hereafter), the T D was estimated to range from 12.35 to 14.10 minutes, while the T D ranged from 50.97 to 99.62 minutes during the winter (December to February, DJF hereafter).e annual variation of T D ranged from 38.62 (Gosan) to 85.52 minutes (Gangneung).Regardless of the season, the T D was the longest in Gangneung and the shortest in Gosan and depended strongly on location, particularly latitude.
e annual variation and seasonal average of T D decreased from the north to the south.Compared with the T D in spring (March to May, MAM hereafter) and autumn (September to November, SON hereafter), the six-site averaged T D during MAM was 13 minutes shorter than that during SON. is is because the seasonal mean solar zenith angle during MAM was significantly smaller than that during SON.As shown in Figure 5, the overall characteristics of seasonal and annual variations of the T D at 09:00 were similar to those at noon. e annual variation in T D ranged from 98.86 (Gosan) to 153.49 minutes (Gangneung) and showed a strong latitudinal dependence.Furthermore, the six-site averaged T D during MAM was 18 minutes shorter than that during SON, similar to the seasonal dependence seen at noon. e ratio of T D at noon to that at 09:00 ranged from 1.90 (DJF at Gangneung) to 3.08 (MAM at Gosan).e variation of the T D ratio at noon to 09:00 is related to differences in the solar zenith angle and the diurnal variations of the CMF.At all six stations, the diurnal variations of the T D were smallest during the DJF and largest during the MAM.

Comparison and Error Analysis.
To compare the simulation and observation of T D and T E , the broadband UV irradiance data from the UV biometer instruments at Seoul and Pohang are used.Because of differences in the observational periods and instrument maintenance, the comparison periods for the UV biometer were defined to be June 2015 to September 2016 in Seoul, and from January 2015 to September 2016 in Pohang.
e UV biometer at Korean observation sites is designed to provide daily maximum UV values with uncertainties up to 5% [73].However, the broadband instrument provides neither the spectral UV irradiance nor the UV VitD .To estimate the UV VitD and T D from broadband observation, an alternative parameter for estimating R UV is essential before the comparison.For this reason, an empirical approach was adopted to estimate R UV from UVI alone to be able to adopt the UV VitD estimation   Advances in Meteorology from the UV biometer.e empirical R UV was estimated by applying a t between the UVI and R UV both derived from the spectral irradiance from the Brewer spectrophotometer in Seoul for cloud covers of less than two tenths for the period of 2006-2010.As shown in Figure 6, using this approach revealed a clear relationship in R UV with UVI.

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Figure 7 shows a scatter plot of the simulated and observed T D at Seoul and Pohang.Due to the limitation of the empirical approaches for R UV , the comparison was performed only for cloud-free days, which were de ned as days during which the cloud covers from both observations and prediction from RDAPS was less than 2 (as the maximum value in 3-hour intervals).Overall, the number of data points selected for the comparison was 112 (09:00) and 91 (noon) for Seoul and 134 (09:00) and 112 (noon) for Pohang.In addition, Figure 7 represents the seasonal averaged T D with its standard deviation as an error bar.Although the comparison was only performed under clear-sky conditions, the statistical result of the correlation coe cient of determination (R 2 ) ranged from 0.86 to 0.91.e mean biases of T D between the observations and simulations ranged from −2.08 to 1.97 minutes, but compared to the bias values, the root mean square errors (RMSEs) at the two sites were relatively high.e RMSEs in Seoul were 21.70 minutes at 09:00 and 15.91 minutes at noon, and that in Pohang were 20.50 minutes at 09:00 and 9.36 minutes at noon.However, the slope is always larger than 1.0.e slope at both 09:00 and noon is 1.6 in Seoul, and 1.2 and 1.3,  Advances in Meteorology respectively, in Pohang.In particular, the T D di erences increase under the condition for simulated T D > 150 minutes.
Because the exposure time for the synthesis is inversely related to the UV intensity, the T D di erence is enhanced under low UV irradiance conditions.Figure 8 shows the UVI value between the observation from UV biometer and the simulation under cloud-free conditions.In Figure 8, the slope between the observation and simulated UVIs ranges from 0.8 to 1.0.Furthermore, small negative biases are found for the simulated UVIs.e negative biases can a ect the longer T D values in the simulation, and the di erence is greater under the cases with weak UV intensity.erefore, the overestimation of T D in the simulation is signi cant in cases where T D is large.
Large RMSEs of T D are thought to be from the error generated during the interpolation of the UV irradiance calculation and discrepancy of UV irradiance data between model and observation.T D is calculated using all UV irradiance within the time during the exposure period.Because of the variations in cloud coverage and type, the real atmosphere causes dramatic changes in the surface irradiance.For this reason, the observed UV is fully evaluated to the atmospheric conditions with a one-minute resolution.Clearly, the observation data from the UV biometer also have interpolation process for exposure time estimation because of its temporal resolution of 10 minutes.However, the simulated UV irradiance at intervals of one minute is calculated by interpolating with the one-hour simulation.In particular, the predicted cloud amount for the CMF calculation is estimated in 3-hour intervals.
e UV attenuation by the cloud is a function of cloud cover, cloud types, and cloud optical thickness and its vertical distribution.However, the CMF in the simulation is simply xed according to the cloud amount from the forecast model of KMA.erefore, the simple calculation for 8 Advances in Meteorology the CMF is one of error source in the T D calculation.In addition, the attenuation due to real cloud conditions uctuates, unlike the simulated cloud condition.Table 2 shows the CMF for the T D simulation and the ratio of the UVI between the observed and clear-sky from the RTM, with respect to the cloud categories from the RDAPS.If the clear-sky UVI from the RTM is accurately de ned to the atmospheric and surface conditions except for the clouds, the observed UVI over clear-sky UVI (CMF obs hereafter) is assumed to be the e ect of cloud attenuation, which is directly estimated for the CMF from the observation.For all the cloud categories, the standard deviation of CMF obs Advances in Meteorology ranges from 0.162 to 0.225.In addition, the CMF obs is more sensitive to the cloud amount than the CMF.For these reasons, the scatter plot of the UVI in Figure 8 shows large variations for most of the ranges of UVI, with a slight negative bias.In addition, the variation of T D is larger in high T D cases than that in small T D cases, because the tting curve for the R UV from the observation varies greatly under low UVI conditions.e predictions of total ozone are also thought to be an important source of errors in simulated T D . Figure 9 shows a scatter plot between the predicted and observed total ozone for (D + 1) during the validation period.
e correlation coe cients (R) were 0.86 and 0.84 at Seoul and Pohang, respectively, with an RMSE of approximately 22 DU.Moreover, there were high values for the mean absolute error (MAE) and mean absolute percentage error (MAPE), of approximately 16 DU and 5%, respectively.Previous study using data in Korea has shown that a 1% change in total ozone resulted in a 1.0%-1.2%change in surface erythemal UV irradiance [74].
e amplitude of the UV irradiance change due to the total ozone variation in Korea is similar to those from other model studies [75,76].erefore, Advances in Meteorology the RMSE of 22 DU corresponds to an approximate 7%-8% variation in UV.In addition, the T D variation was more sensitive to the variation in UV irradiance during the winter than the other seasons.Figure 10 shows the seasonal RMSE of total ozone between observations and predictions.e RMSE was larger during DJF and MAM than during JJA and SON, which had the weakest UV irradiance.erefore, the seasonal dependence of errors in the prediction of total ozone partially accounted for the large discrepancy in the simulated T D .
In the UV model simulation, the AOD value is assumed to be same in time and space.However, spatiotemporal distribution of aerosol is highly varied in the real atmosphere.Figure 11 shows the time series of daily AOD at 550 nm (AOD 550 hereafter) in South Korea by using the Level 2 Aerosol product from Moderate Resolution Imaging Spectroradiometer (MODIS) (MYD04 hereafter) in the year 2016.We assumed to be the South Korea region as a grid box of 33.0∼38.6 °N and 124.5∼131.0°E.To estimate the AOD 550 from MODIS in South Korea, we selected the pixels with the quality ag as "good" and "very good."Yearly averaged AOD 550 is 0.31 with temporal standard deviation of 0.17.For the spatial variation of AOD 550 , we also estimated to the spatial standard deviation of AOD 550 in South Korea, and yearly averaged spatial standard deviation is 0.17.Based on the yearly averaged AOD 550 , relative variation is 44.2% and 54.6% for spatial and temporal variation, respectively.From Kim et al. [23], relative di erence of erythemal UV irradiance by changing 1% of AOD was estimated to be 0.29 ± 0.06% from the observation in Seoul.Although the spectral de nition of AOD is di erent between MODIS and model simulation, the UV simulation error is estimated to be 12.8% and 15.8% for spatial and temporal variation of AOD, respectively, based on the sensitivity study of Kim et al. [23].

Conclusion and Discussion
In this study, the T D was estimated over South Korea using simulated UV radiation from RTM.To calculate the spectral UV irradiance from RTM, a statistical linear regression method was applied to predict total ozone amount for oneday forecasts.Satellite observations of total ozone and its climatology were used to capture the general variability of total ozone.Wind, temperature, and geopotential height from the upper troposphere to the lower stratosphere were used to estimate the short-term variability of the total ozone due to atmospheric dynamics.In addition, particularly in urban areas, surface albedo variations were assumed to be dependent on the land-cover type.Using satellite measurements, the surface albedo was classi ed according to land-cover type and applied to the observational sites.After  Advances in Meteorology these applications to surface albedo and the prediction of total ozone, an RTM was used to estimate the clear-sky UV radiation.
A CMF was applied after calculating the clear-sky UV Ery , because of the di culty in converting cloud amount to optical depth for use in the one-dimensional RTM. e CMF was calculated as a function of cloud amount applied to the forecast results of the RDAPS from the KMA.Finally, the simulated UV irradiance dataset was interpolated from a one-hour to a one-minute resolution, and the T D was estimated after considering the diurnal changes of spectral UV irradiance with high temporal resolution.Because of this high temporal resolution, the seasonal cycle and diurnal variations of T D can be determined.In addition, local weather conditions were accounted for the T D calculation by considering the cloud attenuation.
A comparison of modeled T D with data from UVI observation sites revealed that the simulated T D values had small biases with large deviations.In addition, the di erences in T D between the simulated and observed values are greater under weak UV irradiance conditions.T D discrepancies between the observations and simulations were caused by UV estimation errors due to simple interpolation for UV estimation from the one-hour to one-minute interval and the simple CMF assumption.e simulation error for the prediction of total ozone also a ected the deviations of the T D .e 22 DU RMSE for the predicted total ozone arose from short-term variations.Because of the large short-term discrepancies of the total ozone, the modeled UV irradiance varied from 7% to 8%.In addition, the modeled UV irradiance also varied between 12.8% and 15.8% due to the spatial and temporal variation of AOD in South Korea, respectively.From this validation study and error analysis, it is evident that more accurate regression methods for the prediction of total ozone, modification factors for cloud attenuation, and considering seasonal variations of aerosol are required to improve the accuracy of the simulation of T D .

Data Availability
e total ozone data from OMI, surface type data from MODIS, RDAPS model, and UV observation data from KMA were used.Brief descriptions of the data are explained in the manuscript in Section 2. (1) e Level 3 data of total ozone from OMI is provided in the Mirador Earth Science Search in NASA.(2) e surface type data named MCD12C1 is provided in the site of USGS (https://lpdaac.usgs.gov).(3) e RDAPS of the UM from the KMA are used after confirming from the Korean Meteorological Administration.(4) e UV observation data from KMA also used after confirming from the Korean Meteorological Administration.

Figure 1 :
Figure 1: Flow chart of forecast system of exposure time for vitamin D synthesis.

Figure 2 :
Figure 2: Relation between the observed and predicted total ozone amount for (D + 1) value.

6 R 2 Figure 8 :
Figure 8: Scatter plot of UVI between the observation and simulation (Predicted UVI) based on cloud-free conditions in (a) Seoul at 9 a.m. and (b) at noon and in (c) Pohang at 9 a.m. and (d) at noon.

Figure 9 :
Figure 9: Scatter plot of total ozone between the observed and forecasted values in (a) Seoul and (b) Pohang.

Figure 10 :Figure 11 :
Figure 10: Seasonal characteristics of total ozone RMSE between the observed and forecasted value (D + 1) in (a) Seoul and (b) Pohang.

Table 1 :
List of representative region for the UV calculation.

Table 2 :
Mean and standard deviation of CMF obs with respect to the cloud categories from the numerical weather prediction results.