3.1 Factors affecting surface UV

The UV irradiance at the Earth's surface is largely determined by the solar zenith angle, clouds, total ozone column, surface albedo, aerosols, Earth–Sun distance, and altitude or pressure. The different factors affecting surface UV radiation have been discussed in the literature (see, e.g. Weatherhead et al., 2005, and reference therein). Here, we only include a brief discussion of these factors and encourage the interested reader to study the literature more in depth.

3.2 General radiative transfer set-up

The aim of the radiative transfer set-up of the TROPOMI UV algorithm is to account for the factors influencing the surface UV irradiance discussed above. VLIDORT is a one-dimensional radiative transfer model where the vertical structure of the atmosphere is represented by 30 model layers, as depicted in Fig. 2. At the very bottom, there is a surface, which in our set-up is a Lambertian reflector characterized by its albedo. The layer 1–2 km above the surface (layer 2) includes a homogeneous water cloud. In addition, all layers include Rayleigh scattering by air molecules (p is the pressure), absorption by ozone, and temperature information.

The cloud (layer 2) consists of water droplets with a size distribution following the C1 model by Deirmendjian (1969) yielding an effective cloud droplet radius of r_eff=6 µm. The same cloud model has been used in the TOMS–OMI and the AC SAF UV algorithms (Krotkov et al., 2001; Kujanpää and Kalakoski, 2015).

The temperature and the ozone density of each layer in the radiative transfer model is set according to the TOMS V7 climatology (Wellemeyer et al., 1997), which gives climatological ozone and temperature profiles for three broad latitude bands (low latitude, midlatitude, and high latitude) as a function of total ozone column.

This general set-up of the VLIDORT model is used for both (i) calculating the cloud optical depth and (ii) calculating surface UV irradiances, as described in the following subsections. All radiative transfer calculations were done using the extraterrestrial solar spectrum of OMI (Dobber et al., 2008) and assuming an Earth–Sun distance of 1 AU.

Figure 2Schematic structure of the model atmosphere.

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Table 1Node points of the cloud optical depth look-up table.

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Figure 3Cloud optical depth vs. the reflectance at 354 nm according to the look-up table. For the relationship shown here, the surface pressure was p_s=1 atm and the solar and viewing geometry was ${\mathit{\theta }}_{\mathrm{v}}=\mathrm{40}{}^{\circ }$, ${\mathit{\theta }}_{\mathrm{0}}=\mathrm{45}{}^{\circ }$, and ${\mathit{\varphi }}_{\mathrm{r}}=\mathrm{60}{}^{\circ }$.

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Table 2Node points of the look-up table for the dose rates and UV irradiances at selected wavelengths. The full 26 profile set of the TOMS V7 climatology is used. L, M, and H refer to the low-, middle-, and high-latitude profiles, respectively, while the numbers refer to total ozone columns in DU.

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3.3 Cloud LUT

The main input used to estimate the cloud optical depth (τ_c) is the reflectance at 354 nm (R₃₅₄). R₃₅₄ is available in the TROPOMI AI L2 output, as it is also used for calculating the aerosol index. R₃₅₄ is defined as (Stein Zweers, 2016, their Eq. 4-1):

where I₃₅₄ is the radiance at 354 nm reflected by the Earth (atmosphere and surface) measured by TROPOMI and E_0, 354 is the solar irradiance at 354 nm at the top of the atmosphere, and θ₀ is the solar zenith angle. E_0, 354 is measured by TROPOMI on a daily basis and is corrected for the Doppler shift in the measured spectrum due to the relative motion of the satellite with respect to the Sun. Both I₃₅₄ and E_0, 354 are the average over five consecutive spectral pixels centred at 354 nm of the TROPOMI instrument. Furthermore, they have both been normalized to correspond to an Earth–Sun distance of 1 AU.

In our radiative transfer calculations, the combined spectral response of these five consecutive pixels are represented by a 0.88 nm wide (corresponding to 5 pixels 0.22 nm apart), flat-top slit function with Gaussian tails, which have a width of 0.27 nm at half maximum.

The approach here is somewhat different from that used in the OMI UV algorithm, where the radiance of a single spectral pixel at 360 nm is used to determine the reflectance, from which the cloud optical depth is consecutively calculated. We believe the approach chosen for TROPOMI will constitute an improvement because (i) averaging over five channels will help reduce noise in the signal, and (ii) while there is some O₂−O₂ absorption at 360 nm (Thalman and Volkamer, 2013) that may influence the estimated cloud optical depth, 354 nm is free of such absorption features.

The cloud LUT was calculated using the VLIDORT radiative transfer model. R₃₅₄ was calculated by systematically varying the cloud optical depth (τ_c), the solar zenith angle (θ₀), the viewing zenith angle (θ_v), the relative azimuth angle (ϕ_r) between the sun and the satellite, the surface albedo (ρ_s), and the surface pressure (p_s). The outcome is a look-up table spanning all relevant combinations of these parameters that gives τ_c as a function of the other parameters by interpolating in the multidimensional space defined by the LUT nodes. Interpolation is performed using polynomial (Lagrangian) interpolation. The base alternative is to use 4 points from the surrounding space, resulting in third-degree polynomial interpolation. If the desired point is close to the boundary of the LUT, then 3 points are used (resulting in second-degree polynomial interpolation), while for points outside the LUT space, 2 points are used (linear extrapolation). The same interpolation scheme is also used for the UV LUT (Sect. 3.4).

Note that here τ_c is an effective optical depth in the sense that it corresponds to the cloud optical depth of a homogeneous water cloud, as specified above, that produces the best match with the measured R₃₅₄ given the other input parameters. Note that the ozone content of the atmosphere has a negligible influence on R₃₅₄. Therefore, we used a constant ozone profile in these calculations, corresponding to the midlatitude TOMS V7 profile with a total ozone column of 325 DU (i.e. M325 in Table 2).

The nodes of the cloud LUT are listed in Table 1. All inputs needed to retrieve τ_c are based on the TROPOMI AI L2 output, except the albedo, which is based on a climatology as explained above. p_s of the AI L2 output is normally based on the pressure fields of the European Centre for Medium-Range Weather Forecasts (ECMWF). In the case of missing data from the ECMWF, p_s is calculated from the altitude a.s.l. using the hydrostatic equation and assuming a scale height of 8.3 km. The altitude in the AI L2 output is based on Global Multi-resolution Terrain Elevation Data 2010 (Danielson and Gesch, 2011).

To demonstrate the idea of estimating τ_c based on the measured R₃₅₄, Fig. 3 shows τ_c as a function of R₃₅₄ for a low albedo (ρ_s=0.04) and a fairly high albedo (ρ_s=0.60) case. For the low-albedo case, R₃₅₄ increases strongly with increasing τ_c up to optical depths of around 20, whereafter the increase gradually levels off as R₃₅₄ saturates towards large τ_c. Note that for the high-albedo case, R₃₅₄ is less sensitive to changes in τ_c than for the low-albedo case. This means, in practice, that it is more difficult to accurately estimate τ_c for high-albedo cases. Finally, the figure also brings forth the strong Rayleigh scattering of radiation in the UV; for cloudless skies (τ_c=0), the low albedo R₃₅₄ is around 0.25.

3.4 UV LUT

The solar irradiance at Earth's surface is a function of wavelength. Furthermore, the effect of the incoming radiation on, for example, a specific photochemical reaction or a biological response, depends on the wavelength. In order to quantify the effectiveness of radiation with respect to a specific effect, various action spectra (weighting functions) have been introduced (e.g. Aphalo et al., 2012) that can be used to calculate effective spectral irradiances and dose rates (e.g. Kujanpää and Kalakoski, 2015, Eq. 2).

The UV LUT of the TROPOMI algorithm includes UV irradiances at four selected wavelengths, namely 305, 310, 324, and 380 nm, and erythemally (Webb et al., 2011) and vitamin-D weighted UV dose rates (CIE, 2006, the tabulated data provided in the publication were linearly interpolated to obtain a complete action spectrum). Note that both the erythemal and the vitamin-D action spectrum gives large weight to radiation of wavelengths below 320 nm (see Fig. 3 in Kujanpää and Kalakoski, 2015).

Similarly to the cloud LUT, the LUT for UV irradiances and dose rates was created by running the radiative transfer model by systematically varying the following input parameters: θ₀, Ω, τ_c, ρ_s, and p_s. Table 2 lists the nodes chosen for the UV LUT. Here, the ozone profile follows the TOMS V7 climatology as explained above.

For comparison with ground-based measurements of UV irradiances, it is worth noting that all calculations for the UV LUT were done using a triangular 1 nm full-width-at-half-maximum (FWHM) slit function, which is commonly used as a standard slit function, for example, when comparing different ground-based spectrometers (Gröbner et al., 2005). Note also that the wavelengths of the extraterrestrial spectrum used in our radiative transfer calculations (Dobber et al., 2008) have been corrected to correspond to wavelengths in the atmosphere rather than in a vacuum.

Figure 4The reflectance at 354 nm (a), the cloud optical depth (b), and the UV index at solar noon (c) of the TROPOMI UV algorithm based on OMI test data for 13 August 2007. Jokioinen (south-western Finland) and Sodankylä (northern Finland) are marked with black squares.

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3.5 Daily cycle and post-processing

The calculated UV quantities are corrected for the variation in the Earth–Sun distance (see Sect. 3.1) and the attenuation caused by absorbing aerosols in a post-processing step. After these corrections have been applied, the daily doses and daily accumulated irradiances are calculated by integrating over the 24 h time window centred at local solar noon. For this, a time step of half an hour is used. It is worth emphasizing that the TROPOMI UV algorithm does not account for variation in the cloud cover within the day, but instead assumes that the cloud optical depth inferred from the overpass measurement is valid for the whole day.

The absorbing aerosol correction follows the approach of Arola et al. (2009) used in the OMI UV algorithm. It is based on a monthly aerosol climatology by Kinne et al. (2013). The correction is a multiplicative factor (C_a) which depends on the aerosol absorption optical depth (τ_aa):

Here, the factor 3 in the denominator represents average conditions according to earlier studies on the behaviour of satellite-estimated UV compared to ground-based measurements and its dependence on τ_aa (Krotkov et al., 2005; Arola et al., 2005). Arola et al. (2009) found a significantly reduced bias in the OMI UV product compared to ground-based measurements over Europe after this correction had been applied.

The aerosol absorption optical depth depends on wavelength, but so does the aerosol correction factor (C_a) that is applied in the TROPOMI UV algorithm. Here, we utilize the aerosol optical depth and single scattering albedo at 290, 315, 345, and 380 nm, available in the aerosol climatology. These values are linearly interpolated to the wavelengths included in the TROPOMI UV algorithm, after which the wavelength-specific τ_aa is calculated. For the UV irradiances at selected wavelengths (i.e. 305, 310, 324, and 380 nm), the TROPOMI UV algorithm applies a wavelength-specific aerosol correction. For the erythemally weighted and vitamin-D weighted UV irradiances, the aerosol correction corresponding to 310 nm is applied.

Table 3TROPOMI UV output for Sodankylä 13 August 2007.

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Figure 5The UV index as measured by a Brewer spectrophotometer in (a) Jokioinen, and (b) Sodankylä on 13 August 2007 together with results from the TROPOMI UV algorithm based on OMI measurements.

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4.1 Output and example results

The TROPOMI L2 UV product includes the following UV quantities: the UV irradiance at 305, 310, 324, and 380 nm; the erythemally weighted UV; the vitamin-D weighted UV. Each of these are available as (i) a daily dose or daily accumulated irradiance, (ii) overpass dose rate or irradiance, and (iii) local noon dose rate or irradiance. In addition, all quantities are available corresponding to actual cloud conditions and as clear-sky values, corresponding to otherwise the same conditions but assuming a cloud-free atmosphere. This makes 36 UV parameters altogether (see Table 3).

The L2 aerosol index and total ozone column products used as input to the UV product are both based on measurements taken by TROPOMI's UVVIS spectrometer, band 3, which covers the wavelength range 320–405 nm (Loots et al., 2016). The ground resolution of these measurements, and thus also of the TROPOMI UV product, is 7×3.5 km² in nadir, while the largest pixels throughout the swath are foreseen to be roughly 9×14 km². The TROPOMI swath consists of 450 across-track pixels.

During the development of the TROPOMI UV algorithm, the UV processor software has been tested using GOME-2 and OMI satellite data as a surrogate for real TROPOMI measurements. The GOME-2 and OMI data have been processed using the TROPOMI aerosol index (Stein Zweers, 2016) and total ozone (Spurr et al., 2016) algorithms to produce realistic TROPOMI-like L2 output.

Figure 4 shows, as an example, the reflectance at 354 nm, the retrieved cloud optical depth, and the UV index of solar noon produced using OMI-based test data for 13 August 2007, processed to yield L2 aerosol index and total ozone output files that were given as input to the TROPOMI UV algorithm. The Finnish UV measurement stations Jokioinen (south-western Finland) and Sodankylä (northern Finland) are marked on the map. The OMI overpass time for both stations was close to 10:30 UTC and less than 15 min from local solar noon.

The figure shows relatively high reflectances (R₃₅₄) corresponding to cloudy areas over the central Baltic (east of Sweden) as well as over large parts of Sweden, Norway, Finland, and the Kola Peninsula. The cloud optical depth in these areas varies from values below 5 to values over 50. Over the western part of Russia, on the other hand, there is a rather cloud-free region extending to the south-eastern part of Finland. In this area, cloud optical depths are below 1.

The figure also shows the UV index (UVI) at local solar noon. The UVI has been introduced by the World Health Organization (WHO, 2002) as a tool for informing the public about UV radiation. Thus, here we use the UVI to demonstrate the example output of the TROPOMI UV algorithm. The UVI is formulated based on the erythemally weighted UV dose rate, scaled to reach a convenient number (i.e. the UVI is the erythemal dose rate in W m⁻² multiplied by 40).

The solar noon UVI of Fig. 4 reflects the aforementioned variations in the cloud optical depth. Also, the noon solar zenith angle has a strong influence on the UVI. UVI <2 prevails in the cloudy Scandinavian and North Atlantic areas, while UVI >4 is present in the relatively cloud-free areas of south-eastern Finland and western Russia. Further south, cloud-free areas with UVI >8 can be seen south of the Black Sea, and also in the mountainous regions between the Black Sea and the Caspian Sea, where an influence of the altitude can be observed. South of the Black Sea, in the immediate vicinity of the coast, there is a crescent-shaped area showing UVI <4, with corresponding relatively high reflectivity and cloud optical depth. Meteorological satellite products (Meteosat SEVIRI data collected by the Finnish Meteorological Institute; not shown) confirm that clouds are present over this area.

Figure 5 shows a more detailed comparison of the TROPOMI UV product with ground-based measurements taken by Brewer spectroradiometers (Lakkala et al., 2008) of the Finnish Meteorological Institute. Table 3 lists all 36 UV quantities of the L2 TROPOMI UV output for the satellite pixel closest to Sodankylä.

The UVI measured by the Brewer spectrophotometer in Sodankylä (Fig. 5) shows reduced values due to clouds during the morning and afternoon hours, while the values around noon are close to those expected for cloud-free conditions. Also for Jokionen, the Brewer-measured UVI is close to expected values for cloud-free conditions, although the midday hours in general are somewhat cloudy. The very morning and late afternoon hours in Jokioinen also appear cloud-free, with good agreement between the TROPOMI clear-sky UVI and that measured by the Brewer. The retrieved effective cloud optical depths are 2.3 and 3.0 for Sodankylä and Jokioinen, indicating the presence of a cloud over both stations during the satellite overpass. This is consistent with both the Brewer UV measurements and with supporting satellite data (AVHRR data collected by the Finnish Meteorological Institute; not shown). Finally, Fig. 5 also demonstrates the effect of assuming that the overpass cloud optical depth is valid throughout the day: while the Brewer measurements indicate significant variability in the UV irradiance caused by clouds, the TROPOMI UV (red curve) is evenly attenuated throughout the day.

4.2 Expected uncertainty

The errors associated with the estimated UV quantities using the TROPOMI UV algorithm are expected to be similar to the errors of the heritage algorithms, namely the OMI surface UV product, which is most similar to that of TROPOMI. For TROPOMI, no validation results are yet available, while OMI has been scrutinized in comparison to ground-based measurements in a number of studies presented in the literature.

For OMI, Tanskanen et al. (2007) summarized their validation results as follows:

For flat, snow-free regions with modest loadings of absorbing aerosols or trace gases, the OMI-derived daily erythemal doses have a median overestimation of 0–10 %, and some 60 to 80 % of the doses are within ±20 % from the ground reference. For sites significantly affected by absorbing aerosols or trace gases one expects, and observes, bigger positive bias up to 50 %. For high-latitude sites the satellite-derived doses are occasionally up to 50 % too small because of unrealistically small climatological surface albedo.

After inclusion of the absorbing aerosol correction in the OMI algorithm, it is expected that the overestimation due to aerosols should have reduced considerably, which indeed was the case for the European stations included in the study of Arola et al. (2009). However, even after this correction, a systematic overestimation of 20–30 % remained for Rome (Italy) and Reading (England). Furthermore, it is worth noting that the aerosol climatology represents typical or average conditions, which means that day-to-day variations in the aerosol load at polluted locations may still cause occasional strong overestimation in the surface UV.

A recent study by Bernhard et al. (2015) assessed errors in the OMI UV over high latitudes, caused by inaccuracies in the surface UV albedo climatology used in the algorithm. Their results show that the OMI UV can have a bias exceeding 50 % – in both negative and positive directions – when the OMI surface albedo is too high or too low. Note, however, that, although the percentage error may seem large, the figures of Bernhard et al. (2015) correspond to conditions with relatively low sun and therefore the errors remain small on an absolute scale.

A more comprehensive uncertainty analysis of the TROPOMI UV product is planned, which will be based on uncertainties in the inputs given to the LUTs and how the uncertainties of all input parameters combined influence the estimated surface UV.