Estimates of hyperspectral surface and underwater UV planar and scalar irradiances from OMI measurements and radiative transfer computations

: Quantitative assessment of the UV effects on aquatic ecosystems requires an estimate 1 of the in-water hyperspectral radiation ﬁeld. Solar UV radiation in ocean waters is estimated 2 on a global scale by combining extraterrestrial solar irradiance from the Total and Spectral Solar 3 Irradiance Sensor (TSIS-1), satellite estimates of cloud/surface reﬂectivity and ozone from the 4 Ozone Monitoring Instrument (OMI) and in-water chlorophyll concentration from the Moderate 5 Resolution Imaging Spectroradiometer (MODIS) with radiative transfer computations in the 6 ocean-atmosphere system. A comparison of the estimates of collocated OMI-derived surface 7 irradiance with Marine Optical Buoy (MOBY) measurements shows a good agreement within 5 % 8 for different seasons. To estimate scalar irradiance at the ocean surface and in water, we propose 9 scaling the planar irradiance, calculated from satellite observation, on a basis of Hydrolight 10 computations. Hydrolight calculations show that the diffuse attenuation coefﬁcients of scalar and 11 planar irradiance with depth are quite close to each other. That is why the differences between 12 the planar penetration and scalar penetration depths are small and do not exceed a couple of 13 meters. A dominant factor deﬁning the UV penetration depths is chlorophyll concentration. 14 There are other constituents in waters that absorb in addition to chlorophyll; the absorption from 15 these constituents can be related to that of chlorophyll in Case I waters using an inherent optical 16 properties (IOP) model. Other input parameters are less signiﬁcant. The DNA damage penetration 17 depths vary from a few meters in areas of productive waters to about 30-35 meters in the clearest 18 waters. A machine learning approach (an artiﬁcial neural network, NN) was developed based on 19 the full physical algorithm for computational efﬁciency. The NN shows a very good performance 20 in predicting the penetration depths (within 2 %). 21


Introduction 23
An interest in ultraviolet (UV) radiation effects on aquatic ecosystems is particularly 24 driven by increased levels of biologically harmful UV radiation (290-400 nm) resulting 25 from the depletion of Earth's ozone layer.A recent review of studies of the UV radi-26 ation effects on aquatic ecosystems and interactions with other environmental factors 27 is provided in Hader et al. [1].One of the important effects of enhanced levels of UV 28 radiation is a reduction in the productivity of phytoplankton, caused by inhibition of 29 photosynthesis due to damage to the photosynthetic apparatus [see e.g., 2].This effect 30 is described by the spectral biological weighting functions (BWF) which depend on 31 wavelength, phytoplankton species and environmental factors [3][4][5].Knowledge of UV 32 radiation penetration is important for evaluation of ecosystem properties, including 33 ecosystem health and primary productivity [1].Enhanced UV radiation can also affect 34 the photochemical decomposition of dissolved organic matter [6] and the photochem-35 ical production of carbonyl sulfide in seawater [7], thereby affecting long-term global 36 biogeochemical cycles.
the OCI extraterrestrial solar irradiance (ETS) (Figure 1).At wavelengths below 2400 nm, 90 the original TSIS-1 HSRS hybrid spectrum was constructed by adjusting the absolute 91 irradiance scale of high spectral resolution solar irradiance datasets with measurements 92 from the Spectral Irradiance Monitor (SIM) on the TSIS-1 mission aboard the Interna-93 tional Space Station (ISS).The TSIS-1 SIM instrument is a prism-CCD spectrometer with 94 SI-traceable calibration monitored carefully on-orbit [25].The uncertainties reported 95 for the TSIS-1 HSRS are 1.3% in the UV region we used in this study.Daily TSIS-1 SIM 96 measurements from one week in early December 2019 when solar activity was near 97 minimum were used to construct the reference spectrum.The TSIS-1 HSRS spectrum is 98 recommended by the PACE science team for the use in OCI L2 algorithms.We corrected 99 TSIS-1 HSRS, reported at a standard distance of 1 AU, for the variation of ETS with the 100 Sun-Earth distance (±3.5%).Figure 1a shows TSIS-1 high spectral resolution extraterrestrial solar irradiance 102 measurements at varying boxcar smoothing widths from 1 to 5 nm (OCI 5 nm resolution 103 in dark red).The spectral shape was chosen because OCI data will be collected at higher 104 resolution in orbit and averaged onboard to 5 nm resolution.Figure 1b shows spectral 105 details in the UV-A region.The high frequency structure in the irradiance spectra results 106 from solar Fraunhofer features, resulting from absorption in the Sun's photosphere.

107
The depth of the prominent Ca H and K Fraunhofer lines at 396.847 and 393.366 nm 108 diminishes rapidly as smoothing is applied, and a notable distortion and spectral shift 109 in the Fraunhofer features occurs as the smoothing width is increased from 3 to 5 nm.[31] are also obtained from the GES DISC.

137
As a proxy of the surface reflectance we use a monthly climatology of the socalled minimum Lambertian Equivalent Reflectivity (LER).Given the measured topof-atmosphere (TOA) radiance, I m , the LER is defined by inverting the following exact equation: where R is the surface LER, I 0 is the TOA path radiance calculated for a black surface, T is small enough, the atmospheric and oceanic RT problems can be treated separately.

149
Vasilkov and Krotkov [8] estimated that the separation of the atmospheric and oceanic 150 RT models produces less than 10% resulting error in UV underwater irradiance.This RT 151 scheme allows us to significantly reduce the computational burden and to calculate spec-152 tral UV penetration into the ocean using global satellite measurements with reasonable 153 computational resources.

154
RT calculations of hyperspectral surface planar irradiance, E(λ), are needed to create a boundary condition for Hydrolight calculations of underwater downwelling irradiance.E(λ) is determined in the presence of Rayleigh scattering from the molecular atmosphere, the absorption of ozone, scattering by clouds, both scattering and absorption by aerosols, and reflection from the surface.To accommodate variable BWF spectra, we extended the OMI surface UV algorithm [23] from 4 to 110 wavelengths producing E(λ) at every 1 nm from 290 to 399 nm at the OCI spectral resolution of 5 nm.The algorithm is based on interpolation of lookup tables of clear sky irradiance, E clr (λ), and cloud/aerosol transmittance factor, C T , given by ( Calculation of E clr from satellite measurements of total column ozone, Ω, and 155 Lambertian equivalent surface reflectivity, R s , is described in Krotkov et al. [35,36]  173 We use the DIScrete ORdinate Radiation Transfer (DISORT) code [41] for large τ c , where polarization can be neglected, and the Gauss-Seidel RT code [40] for τ c < 10, where polarization may have an effect on backscattered radiances.The effective τ c corre-176 sponds to the actual cloud optical thickness only in an idealized case of a homogeneous 177 plane-parallel cloud layer with complete coverage of the satellite field of view (pixel). 178 For inhomogeneous cloud fields, the τ c and C T are spatially averaged quantities that 179 depend on the sub-pixel 3D cloud structure and satellite observational geometry in a 180 more complex ways [37].The spectral independence of τ c is a good approximation in 181 the UV region and was confirmed by Mie calculations.We also neglect the spectral 182 dependence of LER in UV, which is less than 0.05 over both land and ocean in the  A C T error analysis [37] shows that the C1 cloud model with OMI-derived effective  model [11].According to Mobley [11], "These models have proven sufficiently accurate 216 for most HydroLight applications.In particular, apparent optical properties (AOPs) are 217 only weakly dependent on the details of the sky radiance distribution-that is, after all, 218 one of the main reasons for using AOPs."

219
The sea surface is assumed to be covered with waves that are parameterized as a 220 function of the surface wind speed.We assume the wind speed to be equal to 5 m/s.In  For studying physical processes in the ocean, e.g. the heating rate, downward or upward planar irradiance (i.e., energy flux through a horizontal plane) is essential.However, in biogeochemical studies, e.g.photosynthesis, photochemistry, UV effects on marine ecosystem, etc., the scalar irradiance (density of radiant energy) is more appropriate [46].The OMI UV irradiance product provides the planar irradiance, E d , at the ocean surface.The spectral planar downward irradiance (energy flux through a horizontal plane) is defined as: where I is the radiance as a function of wavelength λ, zenith angle θ, and azimuth angle φ; ω is the solid angle, integration is performed over the upper hemisphere.The upward irradiance is defined similarly with integration over the lower hemisphere.The scalar irradiance (a.k.a.actinic flux in the atmospheric optics) is defined as: where the integration is performed over the entire 4π solid angle.

In-water irradiance 279
We first present the results which show the main factors affecting the underwater

280
UV radiation field and then the results of OMI-retrieved characteristics of the radiation 281 field.

Spectral irradiance 283
Here we consider the spectral dependence of planar and scalar irradiances and

284
DNA action weighted irradiance.The latter is defined as a product of the spectral 285 irradiance and the DNA damage action spectrum [50] (see also 286 https://www.temis.nl/uvradiation/product/action.html).Figure 3 shows an example A comparison of the normalized irradiance spectra (Figure 3b) near the ocean

302
In-water attenuation of E d and E o with depth is characterized by the diffuse attenuation coefficient (K-function): where E is either E d or E o , z is the depth, and the wavelength dependence is omitted for briefness.Then, propagation of E to depth is described by the exponential function: where E(0) is the irradiance value at the surface.A penetration depth, z p , can be defined 303 as a depth at which the quantity E decreases to a pre-defined fraction of its surface value   The data in Figure 5 show that the dependences of the diffuse attenuation coefficient  In this section, OMI retrievals are shown for OMI orbit 2573 on Jan. 7, 2005.All the retrievals are limited to SZA< 80 • .The retrievals include the surface erythemal dose rates and penetration depths for the DNA damage dose rates.The DNA damage dose rate at a given depth is defined as the integral of the DNA-weighted irradiance over the UV spectral range: where E(λ, z) is either the planar or scalar irradiance, A(λ) is the DNA damage action 337 spectrum [50], and SZA is defined for each OMI pixel at the time of the satellite overpass.Figure 7 shows maps of the OMI-derived surface erythemal dose rates.The dose 349 rates were calculated using the planar and scalar irradiances convolved with the erythe-350 mal action spectrum [54] (see also As expected, the scalar erythemal dose rates are noticeably higher than the planar of SZA is similar to the so-called Umkehr effect that is related to ozone absorption in 361 the atmosphere.In general, the ratio of the scalar erythemal dose rates to the planar 362 erythemal dose rates varies from 1.5 to about 3.0.
Figure 8 shows maps of the penetrations depths of the DNA damage dose rates 364 calculated using the planar and scalar irradiance and their difference.The maps of the 365 penetration depths show that a governing parameter that mostly defines the penetration 366 depth is chlorophyll concentration.There is a strong spatial correlation between the 367 chlorophyll concentration (Figure 6c) and the penetration depths (Figure 8a   Differences between the planar penetration and scalar penetration depths are small.

372
They do not exceed a couple of meters (Figure 8c).This fact follows from Hydrolight 373 computations that show a small difference between K functions for the planar and scalar 374 irradiances for a wide range of input parameters (Figure 5).

376
Forward radiative transfer modeling from tools such as Hydrolight can be compu-377 tationally inefficient due to the large number of complex non-linear physical equations.

378
The current and future Earth observing satellites continue to provide measurements at 379 higher spectral, spatial, and temporal resolutions.As a result of the increased number 380 of measurements, traditional physically based radiative transfer models will not be 381 feasible in operational processing.Machine learning approaches have been proposed 382 to overcome these computational challenges.Machine learning models such as neural 383 networks (NNs) can learn how to represent the complex physical relationships in the 384 radiative transfer simulations through statistical equations [56,57].

385
Here we explore the feasibility of using a NN to reproduce the physics-based 386 penetration depth simulations from Hydrolight so that the retrieval algorithm can be 387 applied to an operational sensor such as OMI.The inputs used to estimate penetration 388 depth are SZA, chlorophyll concentration, total column ozone, and surface irradiance.

389
For this work we use a simple 4-layer feed-forward neural network with an input layer, 390 two hidden layers, and an output layer that predicts planar and scalar penetration depth.

391
The neural network uses a sigmoid activation function for each hidden layer and an 392 adaptive moment estimation optimizer is used to minimize the error with a learning 393 rate of 0.01.We train the NN with 80% of the samples from two orbits from January 101

Figure 1 .
Figure 1.Extraterrestrial spectral irradiance at different spectral resolutions shown for (a) the entire UV spectral range and (b) the OCI spectral range shown in the light blue cutout in (a).The color bar represents the boxcar smoothing width in nanometers.
Instrument (OMI) is a nadir-viewing spectrometer aboard 112 the United States National Aeronautics and Space Administration's (NASA's) Earth 113 Observing System (EOS) atmospheric composition (chemistry) observatory (Aura) that 114 flies in a sun-synchronous orbit with a mean local equator crossing time of about 13:45 115 (ascending node).Aura is part of the afternoon "A-train" satellite constellation.OMI 116 measures the solar irradiance daily and Earth backscattered radiance from 270-500 nm 117 with a spectral resolution of approximately 0.5 nm [22,26].It provides near global 118 coverage with a nadir pixel size of 13×24 km 2 (along and across the swath, respectively) Data and Information Services Center (GES DISC).OMI TOA radiance measurements 126 used in this study are from sensor band 2 (UV-2) and band 3 (Vis).A small angular 127 offset in pointing of the two bands results in differences in FOV location of 2-3 km in 128 rows 10-40 and 15-25 km at the very edges of the OMI swath.These larger differences at 129 swath edges are predominantly in the cross-track direction.130 To carry out atmospheric RT computations in UV, we need to know the total column 131 ozone amounts and surface reflectance.The total ozone fields used as input to the 132 atmospheric RT computations are obtained from the NASA OMI Total Ozone Mapping 133 Spectrometer (TOMS)-like product (OMTO3) that has been validated extensively up 134 to a solar zenith angle (SZA) of 80 • [30].We use operational L2 total column ozone 135 measurements from OMI in Dobson Units (1 DU = 2.69 * 10 16 molecules/cm 2 ).The 136 OMI-TOMS V8.5 total ozone data

183UV, causing < 2 %
error in E clr (see Fig.6in Krotkov et al.[35]).Even with spectrally 184 independent τ c and LER, our algorithm accounts for the spectral dependence of diffuse 185 cloud transmittance which results from interactions between the cloud and the Rayleigh 186 atmosphere and ozone absorption. 187

188 τ c at
360 nm can also be used to describe attenuation of surface UV irradiance by non-189 absorbing aerosols (e.g., sulfates and oceanic) or their mixture with clouds.The surface 190 UV radiation is more strongly attenuated by UV absorbing aerosols (e.g., smoke and dust) 191 of the same optical depth.These transitory plumes of absorbing aerosols are detected 192 using the OMI UV aerosol index (AI

221
our atmospheric RT model, we do not consider a separation of the incident light into a 222 clear-sky fraction and a cloudy fraction.This approach is similar to that described in223    Frouin et al.[47].We scale the input surface irradiance for Hydrolight computations 224 by our OMI-retrieved spectral irradiance.We do not apply the default cloud cover 225 correction in the calculations because this correction has effectively been incorporated 226 into the C T factor.227TheIOP model used here is an extension of the Case I water model[42] to the 228 spectral region 290-400 nm.The model has been described in detail in Vasilkov et al.229[10,43]; here, we briefly describe the main features of the IOP model and its verification 230 in Appendix A. The only input parameter of the model is chlorophyll concentration.231TheRT computations with Hydrolight were conducted for vertically homogeneous 232 waters.We do not account for non-elastic Raman scattering because its contribution to 233 the in-water radiation field in the UV region is small.This is due to a relatively large 234 wavelength shift between the vibrational Raman excitation and emission bands, which 235 is about 40-50 nm.Due to the sharp decrease of solar radiation at shorter wavelengths in 236 the UV region, the vibrational Raman excitation is significantly reduced at shorter wave-237 lengths, and thus the vibrational Raman emission at longer wavelengths is small.This 238 fact substantially limits the spectral performance of algorithms developed to estimate UV 239 underwater light attenuation from satellite hypespectral observations from the in-water 240 vibrational Raman scattering signal [19].Reliable results of the light attenuation retrieval 241 can be expected for longer wavelengths of the UV-A spectral range only.The attenuation 242 of the harmful UV-B radiation seems to be hardly estimated using the in-water Raman 243 signal from the theoretical point of view.It should also be noted that the Raman-based 244 approach for retrieving the light attenuation has another limitation; it is applicable for 245 cloud fraction less than 0.05 only [19].Additionally, the Raman effect is significantly 246 smoothed due to the relatively low spectral resolution of OCI.The Raman effect strongly 247 depends on the spectral resolution of an instrument.Even at the OMI spectral resolution 248 of about 0.5 nm, the Raman effect does not exceed a few percent in the deepest Ca II 249 Fraunhofer lines [44].250 Lookup tables for in-water downward and upward irradiances were generated for 251 the UV wavelength range of 290-400 nm, for chlorophyll concentrations that varied from 252 0.01 to 10 mg/m 3 , for SZAs ranging from 0 • to 80 • , and ozone column amounts from 253 150 to 550 DU.

Figure 2
Figure2shows results of comparing the OMI-derived surface irradiance with the 278

Figure 2 .
Figure 2. (a) A comparison of the smoothed E s measurements from MOBY (solid line) and OMI (symbols) using the Solar Ultraviolet Spectral Irradiance Monitor (plus signs) and TSIS (asterisks) extraterrestrial solar irradiance spectra for a selected OMI pixel.(b) The mean difference and standard deviation between the OMI-derived surface irradiance and the MOBY-measured irradiance.

287Figure 3 .
Figure 3. Spectral planar (solid lines) and scalar (dashed lines) irradiances.Left: Absolute values of the irradiances at two depths: 2 m (red lines) and 20 m (blue lines).Right: Planar and scalar irradiances normalized over their values at 400 nm.The black line shows the DNA damage action spectrum.

304ε
= E(z p )/E(0).For instance, in the case of K equals a constant and the commonly used 305 value ε = 0.1 for defining the euphotic zone depth, z 10%[53], the penetration depth is 306 z p = − ln(0.1)/K.307 The diffuse attenuation coefficient at a given depth depends on angular distribution 308 of radiance and IOPs [e.g., 46].Here we compare the diffuse attenuation coefficients for 309 downwelling planar irradiance, K d , and scalar irradiance, K o , as a function of different 310 input variables.Figure 5 shows the dependence of K d and K o on depth, wavelength, 311 chlorophyll concentration, and SZA. 312

Figure 5 .
Figure 5. Diffuse attenuation coefficient K d (red lines) and K o (blue lines) as a function of: (a) wavelength, (b) depth for two SZAs of 15• (solid lines) and 60 • (dashed lines), (c) chlorophyll concentration for two wavelengths 300 nm (solid lines) and 380 nm (dashed lines) and (d) SZA for two values of chlorophyll concentration 0.1 mg/m 3 (solid lines) and 1.0 mg/m 3 (dashed lines).

313(
of scalar and planar irradiance on depth are quite close to each other.Given the average 314 cosine of the downwelling radiance is defined as µ(z) = E d (z)/E 0 (z), this means a weak 315 dependence of µ in UV on depth in the upper layer of the ocean due to the following316 relationship dµ/dz = µ(K d − K o ).The weak dependence of µ on depth results in a weak dependence of the K functions on depth (see Figure5b) because we assume a vertically 318 uniform distribution of IOPs.This assumption is well justified for the well-mixed upper 319 layer of the ocean.The weak dependence of the K functions on depth in the upper layer 320 allows for use of a single value of the K functions averaged over the upper layer for 321 predicting the penetration depths in the UV.This is particularly important for satellite 322 estimates of the diffuse attenuation coefficients[16], because the satellite estimates are 323 based on the measurement of water-leaving radiance which is primarily formed in the 324 upper layer of the ocean.325Thewavelength dependence of the K function shown in Figure5ais determined by 326 the IOP wavelength dependence.The dominant role in this dependence is played by 327 the spectral dependence of the total absorption coefficient, which significantly increases 328 with decreasing wavelength.Similarly, the dependence of the K functions on chlorophyll 329 Figure5c) is explained by the increase of the total absorption coefficient with increasing 330 the chlorophyll concentration (see Appendix A).Figure5dshows that the K functions 331 increase slightly with increasing SZA.This is explained by the fact that the average 332 cosine of downwelling radiance decreases due to an increased fraction of the diffuse 333 light in the incident radiation.The dependence of K d and K o on ozone amount is quite 334 small and is not shown in Figure5.

338 340 Figure 6
Figure6shows maps of the main input parameters of orbit 2573 used for the

Figure 6 .
Figure 6.Maps of the main input parameters: (a) Solar zenith angle; (b) Chlorophyll concentration in mg/m 3 ; (c) Ozone amounts in DU; and (d) Effective cloud optical depth at 360 nm.

Figure 7 .
Figure 7. Maps of the surface erythemal dose rates: (a) calculated using the scalar irradiance; (b) calculated using the planar irradiance; (c) Ratio of the scalar erythemal dose rate to the planar dose rate.

353(
erythemal dose rates.Both planar-based and scalar-based erythemal dose rates obviously 354 depend on SZA and cloud cover.The erythemal dose rates exhibit a strong spatial 355 correlation with the effective cloud optical depth shown in Figure 6d.The ratio of 356 the scalar dose rates to the planar dose rates (Figure 7c) is highly correlated with SZA 357 Figure 6a) and increases with SZA except for very high SZA> 70 • in the northern 358 part of the orbital swath.For those high SZAs, the ratio decreases with increasing SZA 359 (see Figure A2b of Appendix B).This dependence of the ratio on SZA for high values 360 and b).Other 368 input parameters play an insignificant role in the spatial distribution of the penetration 369 depths.The penetration depths vary from a few meters in areas of productive waters 370 of the Southern Ocean to about 30-35 m in the clearest waters of the South Pacific Gyre. 371

375Figure 8 .
Figure 8. Maps of the penetration depths for the DNA damage dose rates: (a) calculated using the planar irradiance; (b) calculated using the scalar irradiance; (c) The difference between the planar penetration and scalar penetration depths.The color bars represent the penetration depths in meters.

394 7 ,Figure 9 .
Figure 9. Comparisons of Hydrolight penetration depth simulations and neural network estimate for January 7, 2005.Left panel shows comparisons for orbits included in neural network training while right panel shows orbits on this date not included in the training.

Figure 10 .
Figure 10.Map of planar penetration depth on January 7, 2005.Top panel shows planar penetration depth from Hydrolight, middle panel shows planar penetration depth from the neural network, and the bottom shows the percent difference of Hydrolight versus the neural network estimate.The color bars represent the penetration depths in meters and the percent difference.

Figure 9 Figure 10
Figure 9 shows comparisons of the NN estimates of penetration depth compared In practice, we calculate C T (λ) using full radiative transfer calculations for a model 162 163 of a homogeneous, plane parallel C1 cloud model [38] embedded in a Rayleigh scatter-164 ing molecular atmosphere with climatological ozone absorption profiles.The C1 cloud 165 model represents a water cloud model having the modified gamma size-distribution 166 of water droplets with the mode radius of 4 microns.The cloud effective optical thick-167 ness, τ c , assumed spectrally independent, is derived by matching pre-calculated and 168 measured OMI TOA reflectances at 360 nm corrected for non-elastic (Raman) scattering 169 and collision-induced O 2 -O 2 absorption [39].The C T (λ, Ω, τ c , R s , SZA) lookup table is , at the ocean surface by scaling the planar irradiance, E d on a basis of Hydrolight 258 computations: E o = f (λ, θ, , Chl, Ω)E d , where the scaling factor, f , that depends on