The retrieval of snow properties from SLSTR Sentinel-3 – Part 1: Method description and sensitivity study

The eXtensible Bremen Aerosol/cloud and surfacE parameters Retrieval (XBAER) algorithm has been designed for the top-of-atmosphere reflectance measured by the Sea and Land Surface Temperature Radiometer (SLSTR) instrument on board Sentinel-3 to derive snow properties: snow grain size (SGS), snow particle shape (SPS) and specific surface area (SSA) under cloud-free conditions. This is the first part of the paper, to describe the retrieval method and the sensitivity study. Nine pre-defined SPSs (aggregate of 8 columns, droxtal, hollow bullet rosette, hollow column, plate, aggregate of 5 plates, aggregate of 10 plates, solid bullet rosette, column) are used to describe the snow optical properties. The optimal SGS and SPS are estimated iteratively utilizing a look-up-table (LUT) approach. The SSA is then calculated using another pre-calculated LUT for the retrieved SGS and SPS. The optical properties (e.g., phase function) of the ice crystals can reproduce the wavelengthdependent and angular-dependent snow reflectance features, compared to laboratory measurements. A comprehensive study to understand the impact of aerosols, SPS, ice crystal surface roughness, cloud contamination, instrument spectral response function, the snow habit mixture model and snow vertical inhomogeneity in the retrieval accuracy of snow properties has been performed based on SCIATRAN radiative transfer simulations. The main findings are (1) snow angular and spectral reflectance features can be described by the predefined ice crystal properties only when both SGS and SPS can be optimally and iteratively obtained; (2) the impact of ice crystal surface roughness on the retrieval results is minor; (3) SGS and SSA show an inverse linear relationship; (4) the retrieval of SSA assuming a non-convex particle shape, compared to a convex particle shape (e.g., sphere), shows larger retrieval results; (5) aerosol/cloud contamination due to unperfected atmospheric correction and cloud screening introduces underestimation of SGS, “inaccurate” SPS and overestimation of SSA; (6) the impact of the instrument spectral response function introduces an overestimation into retrieved SGS, introduces an underestimation into retrieved SSA and has no impact on retrieved SPS; and (7) the investigation, by taking an ice crystal particle size distribution and habit mixture into account, reveals that XBAERretrieved SGS agrees better with the mean size, rather than with the mode size, for a given particle size distribution.

Satellites offer an effective way to understand the surface-atmosphere processes and 40 corresponding feedback mechanisms on the regional, continental and/or global scales (Konig 41 et al., 2001;Pope et al., 2014). Satellite derived snow products (e.g., SGS, SPS, and SSA) are 42 particularly important for short-term hydrological, meteorological and climatological 43 modelling (Livneh et al., 2009). A high-quanlity snow property data product can also be applied 44 to derive Aerosol Optical Thickness (AOT) over cryosphere (Mei et al., 2020a). High-quality 45 satellite derived snow products and their by-products are also important for the creation of long-46 term "Climate Data Records" (SSMC, 2014), which enable a better investigation and 47 interpretation concerning global climate change (Konig et al., 2001). shows a strong impact on TOA reflectance at visible channels (Warren and Wiscombe, 1980). The above analysis shows that accurate retrieval of SGS requires adequate information 269 about SPS and accounting for the dependence of the phase function on SGS. To better illustrate 270 the impacts of SGS on ice crystal phase function, we calculated reflectance at 1.6 μm with 271 https://doi.org/10.5194/tc-2020-269 Preprint. Discussion started: 7 October 2020 c Author(s) 2020. CC BY 4.0 License.
different SGS values. The right panel of Fig. 3   To reproduce the spectral BRF by SCIATRAN, we use the setup described above in this section 304 and adjust the SGS for each SPS by minimizing the deviation between simulated and measured 305 reflectance at 1.6 μm. Figure 4 shows the simulated BRF in the principal plane at 0.55 μm of 306 fresh and aged snow samples, as well as the respective measurements. The BRF is defined as 307 πI/F, where I is the reflected radiance and F is the incident irradiance. According to Fig. 4(a), 308 for fresh snow, plates are the best shape to reproduce the measured BRF in the vicinity of the 309 forward scattering peak but plates underestimate the BRF at higher viewing zenith angles in the 310 backscattering region. Here, shapes of hollow bullet rosette, hollow column, aggregate of 10 311 plates exhibit better potential to simulate the fresh snow layer BRF. In the case of aged snow, 312 shapes of solid and hollow column, hollow bullet rosette, and aggregate of 5 and 10 plates 313 provide BRF values in conformity with respective measurements. However, they slightly 314 underestimate the BRF at high zenith angles in the backscattering region where aggregate of 8 315 columns can simulate the aged snow BRF better.  According to the above analysis, we can formulate the general algorithm to retrieve SGS 329 and SPS from satellite observations. Satellite provides the wavelength-dependent TOA 330 reflectance, for a given SGS and SPS pair, the minimization between satellite observed TOA 331 reflectance and theoretical simulation is performed. The optimal SGS and SPS are obtained 332 when the difference between observations and simulations reaches the predefined criteria. The 333 SSA is then calculated by the retrieved SGS and SPS. The simulation of snow reflectance (components of vectors Rs(r)) was performed using 345 the radiative transfer package SCIATRAN (Rozanov et al., 2014) as described in Section 3. 346 The optical properties of nine ice crystal shapes, listed in Table 1, were used for radiative 347 transfer calculations. 348 The minimization problem formulated by Eq. (1) was solved separately for each crystal 349 shape using Brent's method (Brent, 1973). The solution of the minimization problem for 350 each crystal habit is characterized by the following residual: The second stage is the selection of such i (crystal shape) for which i  is minimal. 355 This completes the retrieval process and enables the optimal SGS and SPS to be obtained. 356 The third stage is to calculate SSA for the retrieved SGS and SPS. To this end, let us 357 rewrite the SSA introduced above in the following equivalent form: SSA = 3/ρr·(At/4Ap), 358 where r is the effective radius. According to Cauchy's surface area formula (Cauchy, 1841; contain information about At, the total area of non-convex particles can be calculated 365 employing geometric parameters of ice crystal habits presented in Table 1 of Yang et al. 366 (2013). The details of such calculations for non-convex ice crystal habits are given in the 367

Appendix. 368
The relationship between SSA and SGS for different SPS is presented in Fig shape. For a better illustration, the realistic range of specific surface area is limited to 100 m 2 /kg. 386 387 5 Impact of model parameters uncertainty 388 The accuracy of any retrieval algorithm depends not only on measurement errors but also on 389 the uncertainty of parameters which cannot be retrieved. In our case, such parameters are ice 390 crystal roughness, aerosol, and cloud contamination. The impacts of these factors on XBAER-391 derived SGS and SPS have been investigated and will be discussed in this section. The TOA 392 reflectances at selected channels (0.55 and 1.6 μm) and observation directions for SZA, VZA, 393 and RAA of 70°, 30°, and 135° for nadir 70°, 55°, and 135° for oblique, respectively, were 394 calculated using radiative transfer model SCIATRAN. The details of each scenario will be 395 presented in the corresponding sub-section below. of SGS depending on the ice crystal shape used in retrieval. However, in most cases, an 419 incorrect SPS leads to an underestimation of SGS. In particular, the maximal effect can be seen 420 when ice crystals of plate shape, rather than the correct aggregate of 8 columns, is used (yellow 421 solid line). This result can be easily explained coming back to the right panel of Fig. 2. Indeed, 422 one can see that the same reflectance of the snow layer can be obtained using the plate shape, The systematical error of ±16% for SGS was obtained as the maximal relative difference 437 between XBAER retrieved SGS and both in-situ and aircraft measured SGS (as presented in 438 the companion paper). This represents the worst case of SGS error propagation into SSA. 439 The impact of SPS on SSA is demonstrated in the right panel of Fig. 7. As a reference 440 shape, we have selected in this case the plate, which provides the same SSA as other convex 441 particles. One can see that the SSA of non-convex particles overestimates the SSA of convex 442 particles, which is in line with the results presented in Section 4. For instance, for the same 443 https://doi.org/10.5194/tc-2020-269 Preprint. Discussion started: 7 October 2020 c Author(s) 2020. CC BY 4.0 License. 20 SGS, the SSA for aggregate 8 columns (non-convex particle) is about 3 times larger than that 444 for doxtal (convex particle). Since the assumption of the sphere (convex particle) is used to  in SGS of less than 3% for SGS ≤150 μm, and less than 7% for 150≤SGS<300 μm. The 518 maximal errors introduced by the aerosol contamination increase to 30% and 37% in the case 519 of average and pollution conditions for AOT=0.08 and 0.11, respectively. Please be noted that 520 the AOT values in the Arctic can be even smaller than 0.05, for instance, AOT over Greenland. 521 Thus, the analysis with respect to aerosol contamination is the worst case for a typical Arctic 522

condition. 523
For the case of AOT = 0.05, SPSs have been correctly retrieved for all SGS values, 524 indicating that under a typical Arctic clean condition, the impact of aerosol is not so large to 525 disturb SPS retrieval. In order to demonstrate the two stages retrieval process and illustrate the 526 AOT, should be introduced in the retrieval of real satellite data. It is interesting to see that "solid 545 bullet rosettes" is the preferable SPS for very strong aerosol contamination cases. This is due 546 to similar scattering properties (shape) of ice crystal and weakly absorbing aerosol, defined in 547 forward simulation. The impact of aerosol contamination, for typical Arctic conditions, 548 introduces less than 5% error in SSA. However, for large aerosol contamination, the around 30% 549 underestimation in SGS linearly introduced about 25% overestimation in SSA, which agrees 550 with the analysis as presented in Fig.7.  XBAER derived SGS becomes saturated for COT larger than 0.5. Due to limited photon 579 penetration depth for optically thicker clouds (e.g., COT = 5), the XBAER algorithm retrieves 580 the effective radius of ice crystal in the cloud. This demonstrates that theoretically, the XBAER 581 algorithm can retrieve an ice cloud effective radius without a pre-processing of cloud screening. 582 And this can be further used as post-processing to avoid cloud contamination. 583 584 https://doi.org/10.5194/tc-2020-269 Preprint. Discussion started: 7 October 2020 c Author(s) 2020. CC BY 4.0 License.

27
The impact of the cloud on the retrieval of SPS is similar to the impact of aerosol 585 considered above. In short, the cloud plays a larger role for larger SPS (darker TOA) and this 586 impact increases with the increase of COT. However, cloud with large COT can be much easier 587 detected and excluded by the cloud screening algorithm (e.g for the cases with COT > 0.5). 588 SPSs are correctly picked up due to the same SPS used for both the snow layer and the cloud 589 layer. Similar to the impact of aerosol, the underestimation of SGS introduced by the cloud 590 leads to an overestimation of SSA (Fig. 11 (lower panel)). The increase of COT results in 591 saturation of the ice cloud SSA, with a value of 100 m 2 /kg in the case of aggregate of 8 columns. scale, no publication has been found to derive SGS, SPS, and SSA simultaneously. To our best 607 knowledge, this is the first paper, attempting to retrieve these parameters using satellite 608

observations. 609
The new algorithm is designed within the framework of the XBAER algorithm. The 610 XBAER algorithm has been applied to derive SGS, SPS, and SSA using the newly launched 611 SLSTR instrument onboard Sentinel-3 satellite. This is the first part of the paper, to describe 612 the algorithm, and to present the sensitivity studies. 613 The SGS, SPS, and SSA retrieval algorithm is based on the recent publication by Yang et The volume of a hollow bullet rosettes is given by 690 Using Eq. (A16), we have 692 Substituting H as given by Eq (A15), we obtain The expression (A18) can be rewritten as:  The total area of solid bullet rosettes is calculated as;   The volume of aggregates of 5 or 10 plates is given by 751 The total surface of the aggregate on relative scale is given by 785