MONTE CARLO MODELLING OF SEA ICE BEAM-SPREAD DATA

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1 Ice in the Environment: Proceedings of the 16th IAHR International Symposium on Ice Dunedin, New Zealand, 2nd 6th December 2002 International Association of Hydraulic Engineering and Research MONTE CARLO MODELLING OF SEA ICE BEAM-SPREAD DATA P.E. Bond 1 ABSTRACT Beam-spread measurements were performed on first-year sea ice, and laboratory grown NaCl ice, to determine the influence of the ice structure on light propagation at optical wavelengths. An extensive set of beam-spread profiles for both sea ice and snow-covered sea ice encompassing ice stations in McMurdo Sound, Antarctica, the Ross Sea during both winter and summer, as well as laboratory grown NaCl ice, were fitted using empirical Monte Carlo models. The transport scattering rates determined from the Monte Carlo models showed relationships with both the temperature and salinity of the upper surface of the sea ice, while those collected from the snow-covered sea ice were shown to depend on snow grain size. Fitting of beam-spread profiles, using a Monte Carlo model whose transport scattering rates were based on the physical properties of the ice, was successful for sea ice from McMurdo Sound. The model used air, brine and salt fraction profiles measured throughout the depth of the ice, and determined scattering rates for the ice using these profiles, as well as the assumed dimensions of the air bubbles and salt crystals. Brine inclusion dimensions were left as fittable parameters. A measured beam-spread profile was fitted by assuming physically realistic inclusion sizes, including elongated, vertically orientated brine inclusions, resulting in anisotropic scattering rates which allow light to propagate more easily in the vertical direction within the ice. A possible but not significant preferential direction for the horizontal propagation of light was found in firstyear ice. This direction was found to approximately coincide with the basal planes of the aligned ice platelets observed at depths greater than 0.2 m. INTRODUCTION The interaction of light with sea ice and snow affects both the atmosphere-ocean energy balance, and the organisms which make the sea ice their habitat. Understanding this interaction is formidable due to the dependence of the sea ice structure on its growth history, which can vary extensively over both distance and time scales (Weeks and Ackley, 1982). Variations in the internal structure translate to sea ice and snow having wide ranges of optical properties. A large number of studies have focussed on understanding the ice structure-light interaction, and only the briefest of overviews is given here. Using iden- 1 Department of Physics, University of Otago, PO Box 56, Dunedin, New Zealand. pbond@physics.otago.ac.nz

2 tical techniques as presented here, Buckley and Trodahl (1987) measured beam-spread profiles on first-year sea ice which were successfully interpreted using empirical Monte Carlo models (Haines et al., 1997). Grenfell (1991) developed an analytical model with physically based scattering lengths to fit measured albedos from multi-year ice. Perovich (1996) performed many sea ice-light interaction measurements, and implemented analytical models to determine the effect of the microstructure on its optical properties. Warren (1982) determined that snow thickness, rather than grain size affects visible wavelength albedo. Pegau and Zaneveld (2000) determined a preferential direction of propagation while measuring the radiance within first-year sea ice. Arrigo et al. (1991) developed a bio-optical model featuring depth dependent optical parameters, to determine the effect of algae on ice melt. This research measured beam-spread profiles from first-year sea ice grown in varying environments, comprising to the best of our knowledge, the most extensive set collected to date. The technique has the advantage that the sea ice to be measured in its in situ state without undergoing brine drainage, and also allows some depth dependent scattering information to be obtained. These profiles were subsequently interpreted using Monte Carlo models whose optical parameters were determined empirically, and where permitting, based on the measured physical properties through the ice depth. The aim would be to determine sea ice optical properties from the ice physical properties that are routinely measured in the majority of sea ice studies. EXPERIMENTAL METHOD Beam-spread profiles were measured on first-year sea ice at Cape Evans, McMurdo Sound, during the 1998 summer (MCM), in the Ross Sea during the 1998 winter (NBP98-3) and 1999 summer (NBP99-1), and on laboratory grown NaCl ice (LAB). During the Ross Sea cruises, we worked from the Nathaniel Palmer, a National Science Foundation icebreaker. In McMurdo Sound, we were based at K131, an Industrial Research Limited and Antarctica New Zealand field camp. The laboratory experiments were performed in walk-in freezers at the University of Otago, New Zealand. Source-detector separation Light source Source-detector separation Upper surface light-detector Sea-ice Underwater arm Underwater light-detector Slot in sea-ice for arm Seawater Figure 1: Schematic of experimental set-up. A beam of light is directed vertically onto the upper ice surface. The light remitted due to scattering by the internal structure of the ice is detected at varying source-detector separations. The experiment was identical to that used by Buckley and Trodahl (1987), and depicted in Figure 1. Dividing the detected irradiance by the input power of the light beam gives the relative irradiance (m 2 ), enabling comparisons with profiles generated from Monte Carlo models. Two wavelength bands of light were used to allow the absorption due to ice, and algae-detritus to be differentiated. Blue (458 nm) was close to the minimum ice absorption, while green (558 nm) was close to the nm minimum absorption for Ross Sea algae and de-

3 tritus (Fritsen, C.H., personal communication). Vertical sections of the ice were removed and photographed for analysis. Ice and snow physical property profiles were collected at the MCM and LAB sites, and were provided for the NBP sites by Dr Martin Jeffries and colleagues (M.O. Jeffries, personal communication). The 1.75 m thick MCM first-year sea ice consisted of 50 mm of frazil ice overlying columnar congelation ice, and was covered with 50 mm of wind blown snow. The upper ice surface was flat with gentle undulations approximately 2 mm high, and was mottled blue-white in appearance. A 10 mm thick layer of algae was prominent at the ice-water interface, and platelet ice was observed in the lower ice column. The 86a profile was measured on 2.1 m thick first-year ice with a 25 mm snow cover in McMurdo Sound (Buckley and Trodhal, 1987). The 0.2 m thick NaCl LAB ice consisted of a thin, 1 2 mm disordered upper layer of ice crystals with a columnar structure underneath, and a smooth upper surface. This ice was frozen from 9 PSU NaCl solution. The NBP98-3 profiles were measured on cold, first-year sea ice in the Ross Sea during winter. The ice consisted of consolidated ice pans, covered with a snow cover whose thickness rarely exceeded 50 mm. Algae was only visually apparent at one site. The NBP99-1 profiles were measured on relatively warm, first-year sea ice during thermal decay in the Ross Sea during summer. Thick layers of melting snow resulted in almost uniform temperature profiles in the ice. Algae was apparent throughout the ice, through which irregular melt channels of mm diameter were present. MONTE CARLO MODEL The Monte Carlo model written for this work modelled the ice structure as a series of horizontal layers. The air-ice interface was modelled as diffuse. Scattering angles were determined using a Henyey-Greenstein function with the asymmetry parameter set to 0.9. Scattering rates were permitted a zenith angle dependence (Haines et al., 1997), µ s = µ si + sin(θ)µ sa, where µ si is the isotropic scattering rate, and µ sa describes the zenith angle (θ) dependent scattering rate component. The transport scattering rate, µ s, relates to the scattering rate using g, the asymmetry parameter: µ s = µ s (1 g). These equations finally give: µ sv = µ si, the transport scattering rate in the vertical direction, and µ sh = µ si + µ sa, the transport scattering rate in the horizontal direction. The effects of algae and detritus were combined and modelled as layers having a uniform concentration of effective CHLα. The scattering rate and absorption of each model layer were either specified by the user, or calculated using a series of MATLAB scripts, using measured physical property profiles and assumed size distributions for air bubbles (Perovich and Gow, 1996) and salt crystals (Weeks and Ackley, 1982). Brine inclusion dimensions were left as fittable parameters. The optical parameters were optimised by the iterative fitting of the measured beam-spread profiles. RESULTS Beam-Spread Profiles All measured green beam-spread profiles, and the 86a profile (Buckley and Trodahl, 1987) are shown in Figure 2. The predominant feature is the extreme variability in the NBP profiles, particularly the NBP98-3 winter data, at large source-detector separations. This was expected due to the differing growth conditions experienced by the ice, leading to differing microstructure, and thicknesses. The variable snow cover also plays an

4 Relative irradiance (m -2 ) Uncertainty range McMurdo Sound, Antarctica (MCM) Ross Sea, winter (NBP98-3) Ross Sea, summer (NBP99-1) Laboratory NaCl (LAB) '86a' (Buckley and Trodahl, 1987) Source-detector separation (m) Figure 2: Green beam-spread profiles measured from both sea ice and snow covered sea ice during the MCM, NBP98-3 and NBP99-1 field trips, the NaCl ice LAB experiments, and profile 86a from McMurdo Sound during µ'sv µ'sh µ'sv µ'sh µ'sv µ'sh Figure 3: Photograph of 1.75 m thick vertical ice section from McMurdo Sound, and MCM021 empirical model. A wooden 1 m ruler is visible to the right of the ice. The ice section was photographed lying horizontally on the ice, and is shown in its in situ vertical orientation. important role, when it insulates the ice from both the atmosphere and incoming solar flux. The MCM sea ice profiles on the other hand, are comparable with each other, and with the 86a profile measured 12 years previously, over all source-detector separations. Two MCM profiles from snow-covered sea ice are apparent from their large slopes and short maximum source-detector separations. The LAB profiles are also consistent with each other for short source-detector separations. The six underwater profiles are apparent by their small slopes and low relative irradiance under the light spot. All measured beam-spread profiles were fitted with the simplest empirical Monte Carlo model that would fit the measured profile at all values of sourcedetector separation. Figure 3 shows the model used to fit the MCM021 profile, and a photograph of the 1.75 m thick vertical ice section removed close to the site. The scattering rates within each model layer do appear to correlate to the apparent whiteness of the upper regions of ice. The whitish ice near the ice-water interface was caused by brine drainage upon removal of the section from the ice sheet. The MCM021 ice was also fitted using a model whose parameters were based on depth profiles of physical ice properties, shown in Figure 4. An assumption made in this model was that the volume of brine inclusions would decrease, caused by a reduction in inclusion height, as the surrounding ice became colder. Initially elliptical inclusions then become progressively spherical as the ice sheet thickens. The inclusion dimensions were specified at the icewater interface. Effects of ice growth rate on inclusion dimensions were not incorporated. Air bubbles and salt crystals were assumed to reside in aligned distributions throughout the ice, the degree of alignment being proportional to the width-height ratio of the brine

5 0-0.5 Brine Depth (m) -1 Air Salt (x100) Temperature ( o C) Density (kg.m -3 ) Salinity (PSU) Impurity fraction Figure 4: Physical property profiles of sea ice from McMurdo Sound. The shaded regions indicate uncertainty limits Depth (m) -1 Height Width µ'sv µ'sh Brine Air Salt Brine inclusion dimensions (mm) Brine inclusion volume (mm 3 ) Number density (mm -3 ) µ' s (m -1 ) Figure 5: Inclusion dimensions, volume, number density and scattering rates for brine inclusions, and scattering rates for air bubbles and salt crystals used in the physical MCM021 model. inclusions. The brine inclusion dimensions, volume, number density, and both horizontal and vertical scattering rates for all impurities, used for the physical model, are shown in Figure 5. The brine inclusions required to fit the physically based model were 8 mm tall and 0.2 mm wide at the ice-water interface, within the range for sea ice (Perovich and Gow, 1996). Highly anisotropic scattering rates were required to allow sufficient light to emerge from the ice-water interface, with the horizontal scattering rate being seven times the vertical scattering rate at the upper surface, and increasing to 30 near the ice-water interface. The anisotropy was constrained by the dimensions and size distributions of the impurities, including the air bubble size distribution, assumed to be that of pancake ice (Perovich and Gow, 1996) to be constant with depth. Since ice growth rates decrease with increasing ice

6 thickness, these assumptions of size distributions may be invalid. The air volumes calculated from ice density measurements had measurement uncertainties of around 100 %, resulting in a similar uncertainty of the air bubble contribution to scattering in the ice. Empirically determining the air volume using the brine volume (Nakawo, 1983), coupled with measurements of air bubble size distribution throughout the ice thickness may lead to improvements. The anisotropic scattering rates required at the upper surface by the physical model appear to contrast to the almost isotropic scattering of the empirical model. The empirical model was fitted to mimic the presumed isotropic scattering of the granular ice comprising the upper 0.05 m of the MCM ice. The upper surface profile is not sensitive to the anisotropy of the upper layers, only to the total scattering rate. This shows that to constrain the scattering in the model, particularly the degree of anisotropic scattering, the more difficult to perform lower surface profiles are also required. Relative irradiance (m -2 ) 10 1 Measured profiles Empirical model Physical model Green Blue Source-detector separation (m) Figure 6: MCM021 beam-spread profiles from both empirical, and physically based scattering parameter models, as well as measured data. The MCM021 beam-spread profiles from both empirical and physically based models are shown in Figure 6. Both model profiles adequately fit the measured data within the uncertainty range. The lower surface green complex model profile falls below the measured data once the source-detector separation exceeds 1.0 m. Since the upper surface beam-spread profiles predominantly sample scattering at the upper surface, the physical properties of the upper 0.05 m of ice, and the upper 0.03 m of snow were plotted against the upper surface empirical model parameters to determine whether simple relationships would be evident. The expected relationships are unclear since the ice structure at the time of measurement depends on the cumulative growth and environmental history. Decreases in temperature would be expected to make brine inclusions smaller and therefore present smaller scatter cross-sections, while ice grown in colder temperatures would be expected to grow at a greater rate entrapping more brine and thus increasing the total scattering cross-section of the inclusions. Air bubbles would be unaffected by changes in temperature but would be expected to have their number density and size distribution dependent on ice growth rates. Figure 7 shows both increased salinity and decreased temperature of the upper ice correlate with an increase in the empirical model scattering coefficient. These indicate that rapid ice growth, due to colder temperatures, is accompanied by an increased salinity and has greater light scattering ability. No trend is evident for the ice brine fraction.

7 µ' s (m -1 ) MCM LAB NBP98-3 NBP Temperature ( C) Salinity (PSU) Brine fraction Figure 7: Dependence of µ s, determined from the empirical fitting of the measured sea ice and NaCl ice profiles, on the physical properties of the upper 0.05 m of ice. µ' s (m -1 ) µ' s (m -1 ) MCM NBP98-3 NBP Temperature ( C) Grain size (mm) Density (kg.m -3 ) Predicted µ' (m -1 s ) Figure 8: Dependence of µ s, determined from the empirical fitting of the measured snow covered sea ice profiles, on the physical properties of the upper 0.03 m of snow. For the snow-covered sea ice (Figure 8) there appears to be a trend for increased scattering to be accompanied by a decrease in temperature and smaller grain sizes. The association between grain size and µ s with is consistent with Warren (1982), whose calculations show albedo to increase with decreasing grain sizes. Physically this may be interpreted as due to a decrease in the role of absorption, as well as a reduction in the penetration depth into the snow, allowing greater light flux being collected in the vicinity of the light-detector. No trend is evident for the snow density. Assuming spherical snow grains, the predicted scattering rate can be calculated from the snow density and snow grain size. As shown, the actual scattering rates appear to be 0.2 those predicted. This implies that the snow structure was composed of clusters rather than separate grains, as was indeed the case (Morris, K., personal communication). The clusters reduce the scattering surface by allowing the snow grains to shadow each other.

8 Azimuthal Scattering Dependence The five MCM profiles measured within 50 m of each other, were measured at three orientations, to determine whether the ice would show an azimuthal scattering dependence. These are depicted in Figure 9, along with a horizontal thin section photograph, from a depth of 0.40 m, taken with polarised light to show crystal structure (Gribble, M.A., personal communication). Considerable alignment of the crystal basal planes can be seen, some clock-wise from the alignment arrow prominent on the right. basal planes c-axis MCM21 Normalised relative irradiance MCM23a MCM22 N MCM23b MCM23c Uncertainty range of MCM23a* MCM21* MCM22* MCM23a* MCM23b* MCM23c* Source-detector separation (m) Figure 10: Relative green MCM beam-spread profiles measured in McMurdo Sound, normalised by MCM023a profile. The shaded region corresponds to the uncertainty limit for MCM023a. Figure 9: Polarised light photograph of horizontal thin section from 0.40 m depth, and the orientations of the five MCM profiles. Relative green MCM profiles were produced by normalising by the MCM023a profile, which lay closest to 45 from the aligned ice crystal basal planes at the MCM site. Figure 10 shows for source-detector separations greater than 0.2 m, the relative profiles deviate either above, or below, the baseline, with increasing source-detector separation. The uncertainty range for the relative profiles encompasses the deviations, so this observation must be viewed cautiously. These deviations are consistent with lower scattering rates parallel with the basal planes due to the light encountering fewer platelet boundaries, compared with propagating across the basal planes, similar to observations by Pegau and Zaneveld (2000) for Arctic sea ice. For sourcedetector separations less than 0.2 m there is no evidence of azimuthal scattering dependence, since the remitted light has encountered granular and transition ice with random horizontal crystal alignment. CONCLUSION It has been shown that simple empirical Monte Carlo models are capable of modelling the optical propagation of light through first-year sea ice. Progress in determining the ice optical properties from temperature, salinity and density profile measurements has been shown to be partially successful. A model making assumptions of the dimensions

9 and alignment of the scattering impurities was able to replicate a measured profile from 1.75 m thick sea ice. The brine inclusion dimensions required to fit the measured beamspread profile were within acceptable limits, implying that the assumptions used in the model may be justified. Relationships were evident between the upper surface scattering rates determined from the empirical Monte Carlo models, and the upper surface physical properties of the sea ice, and snow-covered sea-ice. A possible azimuthal scattering dependence has been determined for the first-year sea ice in McMurdo Sound. ACKNOWLEDGEMENT We wish to thank Pat Langhorne, Tim Haskell, Martin Jeffries, Kim Morris, and Joe Trodahl for assistance and the loan of physical property data. Funding assisted by Antarctica New Zealand, Telecom Payphones, Otago University, Foundation for Research Science and Technology, the Trans Antarctic Association, The Royal Society of New Zealand and the NZ Lottery grants committee. REFERENCES Arrigo, K.R., Sullivan, C.W. and Kremer, J.N. A Bio-optical model of Antarctic sea ice. Journal of Geophysical Research 96(C6): (1991) Buckley, R.G. and Trodahl, H.J. Thermally driven changes in the optical properties of sea ice. Cold Regions Science and Technology 14: (1987). Grenfell, T.C. A radiative transfer model for sea ice with vertical structure variations. Journal of Geophysical Research 96(C9): (1991). Haines, E.M., Buckley, R.G. and Trodahl, H.J. Determination of the depth dependent scattering coefficient in sea ice. Journal of Geophysical Research 102(C1): (1997). Nakawo, M. Measurements on air porosity of sea ice. Annals of Glaciology 4: (1983). Pegau, W.S. and Zaneveld, J.R.V. Field measurements of in-ice radiance. Cold Regions Science and Technology 31: (2000). Perovich, D.K. and Gow, A.J. A quantitative description of sea ice inclusions. Journal of Geophysical Research 101(C8): (1996). Perovich, D.K. The Optical Properties of Sea Ice. CRREL Report 96-1, U.S. Army Cold Regions Research and Engineering Laboratory, Hanover, NH, USA (1996). Warren, S.G. Optical properties of snow. Reviews of Geophysics and Space Physics 20(1): (1982). Weeks, W.F. and Ackley, S.F. The Growth, Structure and Properties of Sea Ice. CRREL Report 82-1, U.S. Army Cold Regions Research and Engineering Laboratory, Hanover, NH, USA (1982).