The irradiance fields calculated by GEM use the CCCmarad radiative transfer model. CCCmarad is an in-house radiation scheme based on a modified version of the Canadian Centre for Climate Modelling and Analysis (CCCma) atmospheric general circulation model , which uses a correlated-k distribution method for gaseous transmission detailed by and . The radiation scheme has four wave number intervals for the shortwave and nine intervals for the longwave. The visible and UV portion of the shortwave is further subdivided into nine sub-bands. The four sub-bands of relevance to the calculation of the UV Index cover the following spectral ranges: 280.11–294.12, 294.12–310.70, 310.70–330.03, and 330.03–400.00 nm. For convenience, the remainder of the text will instead refer to the integer values of 280, 294, 311, and 400 nm. The irradiances of the sub-bands, i.e., the broadband irradiances, consist of direct and diffuse components, which are available in addition to their sum. This paper involves use of all three irradiance terms of these four sub-bands. It will separately consider the clear-sky and all-sky cases in the calculation of the irradiances as well, with all-sky conditions implying the possible presence of clouds.

The GEM dynamical core is described in , while basic descriptions of the physical parameterizations and detailed references can be found in . Model runs were performed using a 7.5 min time step for a uniform 1024 × 800 longitude–latitude grid (0.352∘ × 0.225∘) and a Charney–Phillips vertically staggered grid with 80 thermodynamic levels extending from the near surface (at η=1) to ∼ 0.1 mbar (η≈0.0001). The analyses, serving as initial conditions for providing the forecasts used in this study, are a composite of the already available ECCC weather analysis and separately generated ozone analyses. The GEM forecast products used as input for the simulations performed with Cloud-J are detailed in Sect. .

Prognostic ozone is solved with a linearized photochemistry scheme called LINOZ , which was implemented online within the GEM NWP model . For this work, the ozone analyses stem from assimilation of total column ozone data obtained from the National Environmental Satellite, Data, and Information Service (NESDIS/NOAA) for the Global Ozone Monitoring Experiment-2 (GOME-2) instruments of the MetOp-A and MetOp-B satellites . Assimilations were performed with the incremental three-dimensional variational approach with the first guess at appropriate time (FGAT; ) using elements of the system described in , and the references therein, adapted for chemical data assimilation.

For the treatment of cloud, GEM employs a prognostic total cloud water variable with a bulk-microphysics scheme for non-convective clouds. The radiative transfer impact from clouds is primarily dictated by the liquid and ice water mixing ratios (LWCR and IWCR) and cloud fraction (CLDR). Fractional cloudiness is based on a relative humidity threshold, which varies in the vertical. Individual cloud layers are assumed to overlap in the vertical using a maximum random cloud overlap .

The GEM model currently does not assimilate aerosol measurement data. The radiative effects associated with background aerosols are based on a climatology produced by . This climatology specifies maximum aerosol loading at the Equator and a decrease toward the poles, with different values for continents and oceans. These distributions also include a latitudinal gradient. Aerosols are assumed only to affect the solar absorption properties of the clear-sky atmosphere .

Cloud-J, a recent release of the Fast-J program , is a multi-scattering, eight-stream, radiative transfer model for solar radiation developed for integration into three-dimensional chemical transport models to calculate photolysis rates (J values) in the atmosphere. The version of the program used for this work is Cloud-J v7.4. The program is developed and maintained by Michael Prather in the Department of Earth System Science at the University of California, Irvine (http://www.ess.uci.edu/group/prather/scholar_software/cloud-j, last access: 23 March 2018).

To calculate photolysis rates, the standard Cloud-J code uses 18 interpolated wavelength bins covering a spectral range of 187–599 nm. The integrated radiative transfer model uses a plane-parallel atmosphere assumption and a full scattering phase function. Rayleigh and isotropic scattering are taken into consideration. Numerous cloud types and aerosol species of varying sizes are accounted for in the calculations by making use of look-up tables containing the scattering functions for water droplet size, ice crystals of various phases, dust, absorbing soot (black carbon), stratospheric sulfates (background and volcanic), and water haze at 0.1 and 0.4 µm. Optical depth properties include extinction optical depth, single scatter albedo, and a scattering phase function.

Cloud-J provides numerous options for the treatment of clouds in its radiative transfer calculations. Option 1 is the calculation for clear-sky conditions. Options 2 and 3 are variations of the direct use of the cloud water content, which employs cloud fraction and separate liquid and ice water paths. The remaining five options (4–8) employ different variations in the correlated, overlapping cloud scheme. The approach seeks to represent the fractional cloud cover in the model layers through the calculation of numerous independent cloud atmospheres (ICAs), where each ICA would be either 100 % cloudy or clear in each cell of the cloud model layer. This fractional cloud-overlap model serves to determine the layer structure, weighting, and number of ICAs that best represent the actual cloud distribution in the model layers.

Originally designed to calculate tropospheric and stratospheric photolysis rates in 3-D global models, the Cloud-J program was adapted to input three-dimensional fields from the GEM model and output direct and diffuse, high-spectral-resolution surface irradiances instead of mean photolytic intensities. The resultant surface spectral irradiances are, in turn, used to calculate UV Index fields.

To produce the high-spectral-resolution output for UV Index calculations, the number of wavelength bins was increased to 241 with 0.5 nm intervals over the 280–400 nm spectral range. Having augmented the number of wavelength bins to perform the high-resolution calculations, additional spectroscopic data were required for integration into Cloud-J. These spectral parameters were interpolated onto a 0.5 nm resolution grid and reformatted for reading into the program along with the GEM model forecasts. The spectral data incorporated into Cloud-J include

a set of UV–visible temperature–pressure absorption cross sections for O3 obtained from the GEISA spectroscopic database ;

The O3 cross sections obtained from the GEISA database (http://cds-espri.ipsl.upmc.fr/etherTypo/index.php?id=950&L=1, last access: 23 March 2018) were recorded by on a Bruker IFS 120HR Fourier-transform spectrometer at a spectral resolution of 5.0 cm-1. The measurements were performed as a follow up to the cross-sectional data initially recorded by on the GOME-FM instrument. The new data sets recorded by offer precise reference spectra where the spectral accuracy of the data is better than 0.1 cm-1 (∼ 0.5 pm at 230 nm and ∼ 7.2 pm at 850 nm), which was validated by recording visible absorption spectra of gaseous diatomic iodide (I2) in a reference cell using the same experimental set-up. The agreement between observed and modelled data was determined to be 1 % and better within the 255–310 nm region. Sets of O3 absorption spectra were recorded using total pressures of 100 and 1000 mbar at five different temperatures ranging from 203 to 293 K. The spectra in the UV range at 100 and 1000 mbar are nearly identical to larger differences at higher wave numbers. Three O3 absorption spectra from this data set were used for incorporation into Cloud-J (1000 mbar at 293 K and 100 mbar at 246 and 223 K). The selection of the three spectra was based on consideration of the typical temperature distribution as a function of pressure.

In addition to the O3 temperature cross sections, the O1D quantum yields associated with ozone photolysis were also required by the Cloud-J radiative transfer model. Values for the quantum yields were calculated using the prescribed method outlined by for the same three temperatures associated with the GEISA O3 cross sections.

The albedo data were interpolated from their native grid onto the 1024 × 800 GEM global grid. A linear interpolation was then performed on the data from the 23 re-gridded wavelength channels to obtain the intermediate albedo global fields corresponding to 0.5 nm intervals over the 328–400 nm spectral range to be subsequently used in the high-resolution irradiance calculations. Albedo values for the bins corresponding to the missing wavelength range of 280–328 nm were obtained by linearly interpolating the data between the 328 nm OMI channel and the UV-B values published by . According to the experimental data reported in Table 2 of , snow and/or ice are the primary reflectors of UV-A and UV-B radiation, where surface reflectivity for these spectral regions is 94 and 88 % respectively, representing a drop in reflectivity of 6.38 % in the shorter wavelength region. To emulate the experimental data, the reflectivities for the 328 nm OMI channel were linearly reduced by 6.38 % over the 280–328 nm spectral range.

The OMI solar reference spectrum produced by was used to provide the TOA solar flux values required for the high-resolution irradiance calculations performed by Cloud-J. Currently, there are no high-resolution solar spectra that cover the UV-A and UV-B wavelength ranges. Most UV–vis TOA spectra are pieced together from different sources in order to provide a continuous, unbroken spectrum. The OMI reference spectrum was created to validate the radiometric calibration of OMI measurements and to monitor potential optical degradation of the instrument. Also a combined spectrum, it was produced by employing the approach used by . It merges the balloon spectrum of , which covers a shortwave UV region between 200 and 310 nm, with a ground-based spectrum obtained from the McMath–Pierce solar telescope at Kitt Peak National Observatory . The broadband Kitt Peak spectrum covers a spectral range of 296–1200 nm. The final derived spectrum is at 0.01 nm sampling and at 0.025 nm resolution.

This spectrum was chosen for use in this work because the OMI composite spectrum uses high-resolution (0.01 nm) UV measurements made in the stratosphere from a balloon at ∼ 40 km in altitude to avoid affects of the strong atmospheric absorption below 300 nm . The solar reference spectrum produced by was also considered since it is composed of measurements made from the SOLSPEC and SOSP satellite instruments with a resolution of 1 nm. With both spectra being similar, the former was selected due to its higher spectral resolution even though the resolution of the latter is only a factor of 2 coarser than our simulation resolution. A moving boxcar averaging window covering ±0.25 nm about sampling points at intervals of 0.5 nm was applied to the OMI composite spectrum to generate the simulation spectrum.

Consideration was also given to high-resolution spectra based on accurate models of the Sun using the spectrum, such as those by and , which provide excellent spectral range, sampling, and resolution. These spectra unfortunately neglect optimization in the UV-B region for radiometric accuracy. The SAO96 and re-calibrated SAO96 (SAO2010) reference spectra described by both utilize the original Kitt Peak spectrum for UV-B, where O3 structure was not fully removed. reported that efforts were focused on intensity calibration of the wavelength range where most application to satellite measurements is performed. Intensities for portions of the spectrum shortward of 305 nm may be in substantial disagreement, by as much as 20 %, with both and . These spectra were deemed unsuitable for use in the calculation of the UV Index.

It should be noted that the solar spectrum used in this work is representative of a yearly average value of the Earth's TOA flux. Changes in the Earth–Sun distance and associated solar fluxes during the Earth's annual cycle are taken into account and are corrected for by Cloud-J in the high-resolution simulations.

The input atmospheric conditions provided to Cloud-J for this study consist of a set of 6 h forecasts from the GEM model output for the dates of 23–29 August 2015, at 18:00 UTC with daytime over North America. The GEM fields provided as input are surface pressure, and the three-dimensional fields of temperature, pressure (derived from the vertical coordinate and surface pressure), ozone, specific humidity (converted to relative humidity), LWCR and IWCR, and CLDR. For the all-sky conditions, the parameters LWCR, IWCR, and CLDR determine the liquid and ice water partial column amounts (g m-2) of each model layer in the presence of clouds.

Cloud-J was run individually for each day during the period of 23–29 August 2015 to produce irradiance fields representing the direct, diffuse, and total surface flux under both clear-sky and all-sky conditions. Weekly (7-day) averages of the direct, diffuse, and total spectral irradiances served as reference spectra in the least-squares minimization for evaluation and adjustment of GEM broadband irradiances, with individual forecast values used in the scatter plot comparisons. While the choice of 7 days was arbitrary as fewer or more days could also have been selected, the averaging was performed for computational efficiency in the minimization. The UV indices produced with Eq. () from the weekly averages of total spectral irradiances served as reference in optimizing broadband irradiances based on UV Index estimation models. The UV Index field from the clear-sky weekly averages is shown in Fig. .

In addition to measuring total column ozone, Brewer spectrophotometers provide ground-based measurements of the UV spectrum in the range of 290–325 nm with a full width at half maximum of about 0.58 nm and a sampling interval of 0.5 nm. The data processing scheme used to generate spectral irradiances at each 0.5 nm interval, which includes calibration and corrections for various factors, is described in the work detailed by and the references within. A sample inter-comparison of three Brewer instruments by (see , for other inter-comparison sources) showed relative overall differences between instruments within 6 % with an average of 3 % for wavelengths longer than 300 nm; uncertainties are larger at shorter wavelengths.

Cloud-J clear-sky surface UV irradiances were compared to Brewer spectra obtained from six different measurement stations belonging to ECCC's ozone monitoring network and identified to be under clear-sky to optically thin cloud conditions. The applied TOA solar spectrum used here for the Cloud-J simulations, as well as for optimizing use of the GEM broadband irradiances in UV Index calculations, has the same sampling interval of 0.5 nm as the Brewer measurements and a similar effective resolution of 0.5 nm. For the latter, a boxcar averaging window was applied instead of the approximately triangular-shaped Brewer slit function. Figure  depicts 5-day averages of Brewer measurements taken at 18:00 UTC on random days in the months of July and August of 2015 and the equivalent counterpart irradiance spectra calculated from Cloud-J. The locations were chosen to provide in situ measurements for different solar zenith angles in addition to varying geographic locations to evaluate the level of agreement between the Cloud-J model application and the Brewer spectra. Only 5-day averages were used, partly due to the limited number of coincident Brewer measurements made during the July–August 2015 period which met the selection criteria for the comparative analysis. Brewer measurements not only had to have been made under clear-sky or near-clear-sky conditions but also had to have been recorded within ∼ 2 min local time of the analogous 18:00 UTC model data.

The Cloud-J derived spectral irradiance curves largely follow those recorded by the Brewer spectrophotometers. The differences between the sets of curves give an overall root-mean-square relative error between the Cloud-J and Brewer spectra of ∼ 16 %. This reflects the level of varying differences over the range of measurement wave numbers. Some sources that might be contributing to the spectral variability in the differences would include differences between the boxcar averaging for the simulations and an approximately triangular instrument slit function, measurement random errors, and or errors in the TOA spectra for the simulations, if not others. Having large differences visually seen in Fig. 4 to often appear at relative extrema points suggests that the differences of averaging functions may play a notable role in the differences. Investigating this further, including a comparison of applying a triangle-shaped window instead of a boxcar with the simulations, was not carried out as the overall consistency in spectral shape was considered sufficient for this work.

The overall differences in the Cloud-J and Brewer data were also quantified by integrating the spectra of each of the six stations to produce sets of broadband irradiances covering the 295–310 and 310–325 nm regions and the 310 nm node denoting the approximate transition point between the similarly corresponding GEM irradiance broadbands.Ideally, for our comparative analysis, the wavelength ranges for the these broadbands should be analogous to the GEM UV broadbands representing 294–311 and 311–330 nm, but due to limitations in the Brewer wavelength range, broadbands for 295–310 and 310–325 nm were produced for the Cloud-J and Brewer comparison. The resultant mean percent differences of the Cloud-J broadband irradiance values compared to the ground-based measurements for the 295–310 and 310–325 nm bands are -1.6 ± 3.8 and 2.9 ± 1.8 %, respectively. The band mean differences are in the range of uncertainties from the three Brewer inter-comparisons by and provided above, and within the spread of mean differences in over the different Brewer spectrophotometers and instruments of other types from the SUSPEN inter-comparison for wavelengths above 300–305  nm. Sources affecting the smaller band differences might include disparities in clear-sky to light cloud conditions, surface reflectivities, air pollution, column ozone, and in the actual locations and heights between the Brewer stations and the nearest corresponding model grid points used to represent these locations. Differences in height above sea level between the model grid points and station locations are under 30 m except for Saturna (Fig. e) at 26 m vs. 202 m and Eureka (Fig. c) at 159 m vs. 9 m. These differences would imply differences in UV Index that are no greater than ∼ 1.5 % with similarly sized differences for the UV irradiances.

Average differences in total column ozone between the GEM model ozone fields provided to Cloud-J simulations and the Brewer measurements for the sample data set of the figure in the range of 2.8 to 4.4 % for the four non-Arctic stations and 0.5 and 0.4 % for the two Arctic stations of Eureka (Fig. c) and Resolute (Fig. d). It was determined that the GOME-2 column ozone data used in the assimilation to generate the model forecasts were similarly biased relative to Brewer spectrophotometers for that period; satellite data bias can be reduced through corrections such as in . Correcting for the larger ozone differences of the non-Arctic stations would increase the Cloud-J irradiances by 3–5 % in the lower band, correspondingly changing differences with the Brewer spectra. The higher band would be less affected as absorption from ozone is comparatively weaker for the upper wavelengths. This would bring the 295–310 nm band irradiance mean differences in percentage closer to the 310–325 nm differences.

The solar irradiance changes due to the changing orbital Earth–Sun distance are reflected in the simulations and so would not be a cause of notable differences. The Sun itself displays cyclical short-term (solar rotation) and long-term (solar cycle) solar spectrum irradiance variability. In the UV Index spectral range, these changes are within roughly 0.2 % and 0.6–1.5 % based on measurements over the recent decades ; the total irradiance has a weaker solar cycle change of ∼ 0.1 %. These variations are within the standard deviations of the mean differences over the six stations.

Further analysis of the data sets depicted in Fig.  reveal that the ratio of the 310–325 to 295–310 nm bands used in the Brewer comparative analysis is ∼ 25 for the two Arctic stations and 15 to 17 for the four non-Arctic stations. This illustrates the relative increase in irradiances above vs. below 311 nm for increasing solar zenith angles associated with the stronger increased atmospheric attenuation by ozone in the lower band. As the contribution of the 294–311 nm band to large UV Index values (low solar zenith angles) is more dominant, the impact of differences above 311 nm would become more visible for low UV Index values (high solar zenith angles). Implications of the differing sizes of differences between the broadbands referenced in Sect.  and in model ozone forecasts are briefly further examined in Sect. .

Two UV Index estimation approaches using the four broadband irradiances were considered. One consists of linear fitting directly to three of the four UV broadband irradiances, i.e., UVI=w1I280–294+w2I294–311+w3I311–330+w4I330–400, with IΔλ in watts per square metre and fit coefficient wi. With this equation, the contribution from the lowest band can be neglected unless the total column ozone is less than roughly 210 DU to contribute at least 0.1 units to the UV Index. Its coefficient value w1 is analytically derived to be 40 m2 W-1 since the erythemal action spectrum is constant over the spectral range of the lowest band.

The other approach involves applying the integral of Eq. () to piecewise interpolated spectra. Both fits are intended to have the UV Index values derived from the broadband irradiances be consistent with the values obtained from the integrated high-resolution effective spectra. UV Index values larger than 3 are used in the minimization to focus the weighting on regions of moderate to high UV Index values. The fitting over points with UV Index values larger than 3 does not exclude points and regions with isolated outlier differences and includes both land, water, and snow/ice surfaces. Minimization was performed using an amoeba downhill simplex method employing a least-squares fitting of the UV Index fields from the scaled GEM broadband irradiances to those from the high-resolution spectra produced by Cloud-J.

For the integral approach, the available irradiances in watts per square metre over the four UV spectral broadbands must be transformed to spectral irradiances for multiplication to the erythemal function prior to spectral integration. The approximate conversion to spectral irradiances is performed as follows:

The band irradiances are divided by the band widths to generate average spectral irradiances.

The selected order of the logarithmic interpolations and initial estimates of the spectral reference positions were chosen through trial and error. The optimized spectral positions are determined through least-squares fitting to the UV Index values calculated from the Cloud-J high-spectral-resolution irradiances.

Interpolations and weighted integrations are performed over four segments covering the ranges 294–298, 298–311, 311–328, and 328–400 nm. The irradiance for 280–294 nm is simply added to the sum of the integrations over the four ranges above as the erythemal function is constant with a value of unity over that spectral range; its contribution over this integration segment could alternatively be omitted as it is negligible. Determination of a reference spectral irradiance for this first band in step 2 above is still carried out to provide a required interpolation node for the other integration segments. The specification of the segments is dictated by the band widths and the two positions, 298 and 328 nm, of the slope changes in the erythemal function. The applied interpolations are of second order for the ranges 294–298 and 311–328 nm and are linear in the other ranges. The simple interpolations do not strictly preserve the original broadband irradiance values nor accurately replicate high-resolution spectra since the main interest is the fast computation of good estimates of the resultant integral value. The integrations for the last three segments are performed using Simpson's rule with two subintervals (five interpolation nodes) and that for 294–298 nm is performed with one interval (three interpolation nodes).

As described in Sect. , the Cloud-J model possesses a number of options for the treatment of clouds in its radiative transfer calculations. Cloud-J broadband irradiances were produced for each of the cloud options representing cloudy-sky conditions, 2–8, using the GEM parameters for liquid and ice water partial column amounts of each model layer in the presence of clouds and the associated cloud fractions, which are required input for Cloud-J. The simulated broadband irradiances produced by Cloud-J for each cloud option were then compared to the GEM analogs to determine which Cloud-J cloud flag produces output that best reproduces the GEM cloud-sky surface irradiances.

Prior to performing the comparative study, it was recognized that fundamental differences existed between Cloud-J and GEM with respect to the handling of clouds, particularly with respect to the scattering of light with parameters specific to water droplet and ice crystal size. Unlike GEM, the Cloud-J model does not specifically differentiate water droplets and ice crystals into different size bins and determine the scattering contribution accordingly. Instead, for water, an average droplet size is determined for the total water content in a particular model layer depending on the temperature and pressure associated with the model layer. Ice crystals are not differentiated by size at all, only by crystal shape (hexagonal, amorphous), which is also determined by the given temperature and pressure of the model layer. Ultimately, it was determined that Cloud-J cloud option 3 produced cloudy-sky surface irradiances that best emulated the GEM analog. This option was therefore applied for the UV Index comparisons in this section.

The estimation and evaluation of the UV Index estimated under cloudy conditions in this study has been limited to the consideration of two points. One is whether or not the UV Index equations derived from clear-sky conditions are appropriate for cloudy conditions. The other determines the level of impact of radiative transfer differences in the treatment of clouds on differences in derived UV Index values.

The validity of the clear-sky UV Index equations for cloudy conditions was tested using Cloud-J simulations. The clear-sky equations were applied to the Cloud-J broadband irradiances for comparison to the UV Index values derived from the high-resolution Cloud-J spectra for the actual sky conditions from GEM-LINOZ, the latter being a mixture of clear-sky and cloudy-sky conditions. It was found that the equations derived for clear-sky conditions and applied to cloudy conditions with Cloud-J broadband irradiances give essentially the same results as the UV Index values from the high-resolution spectra, i.e., no visible scatter about the diagonal is observed for the corresponding differences in Fig. a. Therefore, these equations would also be valid under cloudy conditions and do not require further adjustment.

The remainder of this section examines the impact of differences in cloud radiative transfer. Figure a shows the analogous correlations of the UV Index fields generated from the Cloud-J and GEM broadband irradiances under all-sky conditions using the Cloud-J cloud option 3. The weighting was performed using the values obtained though the integration approach of the GEM broadband irradiances under clear skies. Weighting of the all-sky broadband irradiances using the values obtained from the linear fitting approach produce similar results. The overall correlation of the Cloud-J data is in fairly good agreement with the GEM data, but there is an overall increase in error between the two data sets with increasing values of the cloud fraction. To better visualize the distribution density of the correlation, a density plot is also provided in Fig. b. We observe that the vast majority of points that fall along or near the regression line, largely, but not entirely, represent those surface irradiances under cloudless or light-cloud conditions. The probability of deviation from the regression line typically increases with increasing cloud cover. This is demonstrated in Fig. .

Figure  contains a series of probability density plots to visualize the dependence of differences in surface irradiances on cloud cover for the 330–400 nm band. Relative differences are observed between the Cloud-J and GEM surface irradiances under unattenuated, clear-sky conditions, as well as for different total effective cloud fraction intervals. To filter for cloud cover, we used the GEM variable for total effective cloud cover (ECC), which reflects the product, the cloud fraction, and opaqueness. ECC is employed in the plots to display the relative differences of the GEM and the Cloud-J irradiance values for a given range of cloud cover from clear sky (0.0) to completely overcast (1.0). Only surface irradiances pertaining to zenith angles < 70∘ were included to remove larger systematic relative differences at high zenith angles where irradiance values are smaller. The Cloud-J cloud option 3 is used to calculate cloud attenuation in all cases. Output from two different settings of the GEM radiative transfer package for cloudy skies separately provided for Cloud-J simulations and compared to the corresponding GEM irradiances.

Overall, the resultant differences in UV Index values from the high-spectral-resolution irradiances and the GEM broadband irradiances have a distribution for ECC < 0.3 similar to that for clear-sky conditions (Fig. b). Under stronger attenuation due to clouds, a substantial increase in the root-mean-square relative error of up to 33 % is observed due to differing cloud radiative transfer models, this involving UV Index values of 1 or larger.

The modification made to the GEM code from its reference settings of Sect.  was to increase the overall size of the effective radii for the ice clouds from a constant of 15 µm to values in the range of 20–50 µm to determine if it made any difference in relation to the Cloud-J output. As noted earlier in this section, Cloud-J does not differentiate between particle sizes in ice clouds. In the plots, we observe the increase range of relative differences with increasing cloud cover, where differences can reach as high as 100 % and above where the cloud fraction is ≥ 0.7 (Fig. d). This implies that different cloud radiative transfer settings (and models) can result in very large differences in UV Index in the presence of optically thick clouds. Also notable is the overall improvement on the left-hand side of the distributions when the ice particle size was increased. This illustrates the sensitivity of irradiances to cloud-related model parameters. To quantify this sensitivity, the percentage contribution of the total discrete densities are compared for the relative differences in the ranges of -0.2 to 0.2 for cases representing 0.3 ≤ ECC < 0.7 (moderate to heavy cloud) and ECC ≥ 0.7 (heavy cloud to completely overcast) conditions, Fig. c and d, respectively. Under moderate to heavy cloud cover, the density distributions are similar in nature, where the percent contributions for both the modified and unmodified versions of the GEM model are ∼ 76 %. For heavy cloud to completely overcast skies, there is a marked difference in the percent contributions. The unmodified GEM model cloud scheme produces a distribution in which 50 % of the discrete density is located within the -0.2 to 0.2 range for the absolute relative differences. Using the modified scheme, this value is increased to 62 % stemming from more relative differences of smaller absolute size. These results and percentages provide some general sense of the potential uncertainties of the UV Index values given possible uncertainties in the accuracy of the cloud radiative transfer models.