Estimating Underwater Light Regime under Spatially Heterogeneous Sea Ice in the Arctic
<p>Spatial configuration used for the 3D Monte Carlo numerical simulations. (<b>A</b>) Surface view showing the percentage of the total area covered by the melt pond over the areas described by the black lines. For each of these areas, light profiles were averaged (see Figure 7). For visualization purpose, lines of the horizontal sampling distances from the centre of the melt pond have been plotted only at 5 m intervals. (<b>B</b>) 2D side view showing the 3D volume for which simulated data were extracted and how photon detectors were placed in the water column. Orange arrows indicate incident light sources.</p> "> Figure 2
<p>Comparison of the under-ice measured downward radiance distribution (the average cosine is ≈0.61, [<a href="#B18-applsci-08-02693" class="html-bibr">18</a>]) and the angular distribution of light-emitting source used in the paper.</p> "> Figure 3
<p>Examples of in situ downward irradiance (<math display="inline"><semantics> <mrow> <msub> <mi>E</mi> <mi>d</mi> </msub> <mrow> <mo>(</mo> <mi>z</mi> <mo>)</mo> </mrow> </mrow> </semantics></math>) and upward radiance (<math display="inline"><semantics> <mrow> <msub> <mi>L</mi> <mi>u</mi> </msub> <mrow> <mo>(</mo> <mi>z</mi> <mo>)</mo> </mrow> </mrow> </semantics></math>) profiles measured under-ice on 20 June 2016. Note the presence of subsurface maxima in the downward irradiance profiles and the absence of subsurface maxima in the upward radiance profiles.</p> "> Figure 4
<p>Comparison of downward irradiance (<math display="inline"><semantics> <mrow> <msub> <mi>E</mi> <mi>d</mi> </msub> <mrow> <mo>(</mo> <mi>z</mi> <mo>)</mo> </mrow> </mrow> </semantics></math>) and upward radiance (<math display="inline"><semantics> <mrow> <msub> <mi>L</mi> <mi>u</mi> </msub> <mrow> <mo>(</mo> <mi>z</mi> <mo>)</mo> </mrow> </mrow> </semantics></math>) for one example light profile measured under-ice. Profiles were normalized to the measured radiometric value at 10 m depth (under the subsurface light maximum) in order to emphasize the similar shape between <math display="inline"><semantics> <mrow> <msub> <mi>E</mi> <mi>d</mi> </msub> <mrow> <mo>(</mo> <mi>z</mi> <mo>)</mo> </mrow> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi>L</mi> <mi>u</mi> </msub> <mrow> <mo>(</mo> <mi>z</mi> <mo>)</mo> </mrow> </mrow> </semantics></math>.</p> "> Figure 5
<p>Scatter plots showing the relationships between the measured <math display="inline"><semantics> <msub> <mi>K</mi> <mi>d</mi> </msub> </semantics></math> and <math display="inline"><semantics> <msub> <mi>K</mi> <mrow> <mi>L</mi> <mi>u</mi> </mrow> </msub> </semantics></math> in the spectral range between 400 and 580 nm at different depths (numbers in gray boxes). Red lines represent the regression lines of the fitted linear models. Regression equations and determination coefficients (<math display="inline"><semantics> <msup> <mi>R</mi> <mn>2</mn> </msup> </semantics></math>) are also provided in each plot. Dashed lines are the 1:1 lines.</p> "> Figure 6
<p>Cross-sections of simulated downward irradiance and upward radiance fields under a melt pond with a 5 m radius. The logarithm of the normalized number of photons has been used to create the scale for visualization. The normalization has been done using the values modelled at a 0.5 m depth and at a horizontal distance of 50 m from the centre of the melt pond.</p> "> Figure 7
<p>Simulated reference downward irradiance and upward radiance profiles (<math display="inline"><semantics> <mrow> <mover> <msub> <mi>E</mi> <mi>d</mi> </msub> <mo>¯</mo> </mover> <mrow> <mo>(</mo> <mi>z</mi> <mo>)</mo> </mrow> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mover> <msub> <mi>L</mi> <mi>u</mi> </msub> <mo>¯</mo> </mover> <mrow> <mo>(</mo> <mi>z</mi> <mo>)</mo> </mrow> </mrow> </semantics></math> in relative units) for six different areas with varying proportions of the surface occupied by the melt pond (see <a href="#applsci-08-02693-f001" class="html-fig">Figure 1</a>). Note that none of the averaged irradiance profiles show the same subsurface light maxima as observed with in situ data (see <a href="#applsci-08-02693-f003" class="html-fig">Figure 3</a>).</p> "> Figure 8
<p>Simulated local downward irradiance and upward radiance profiles (expressed in relative units) at different horizontal distances from the centre of the melt pond (see <a href="#applsci-08-02693-f001" class="html-fig">Figure 1</a>) used to compute <math display="inline"><semantics> <msub> <mi>K</mi> <mi>d</mi> </msub> </semantics></math> and <math display="inline"><semantics> <msub> <mi>K</mi> <mrow> <mi>L</mi> <mi>u</mi> </mrow> </msub> </semantics></math>. These attenuation coefficients were used to propagate surface reference downward irradiance (<math display="inline"><semantics> <mrow> <msub> <mi>E</mi> <mi>d</mi> </msub> <mrow> <mo>(</mo> <msup> <mn>0</mn> <mo>−</mo> </msup> <mo>)</mo> </mrow> </mrow> </semantics></math>, the surface values of the lines in <a href="#applsci-08-02693-f007" class="html-fig">Figure 7</a>) through the water column.</p> "> Figure 9
<p>Diffuse attenuation coefficients calculated from local downward irradiance and upward radiance profiles simulated at different distances from the centre of the melt pond (see <a href="#applsci-08-02693-f008" class="html-fig">Figure 8</a>).</p> "> Figure 10
<p>Reference downward irradiance profiles (thick black lines, in relative units) and propagated irradiance through the water column (coloured lines, in relative units) using local values of <math display="inline"><semantics> <msub> <mi>K</mi> <mi>d</mi> </msub> </semantics></math> and <math display="inline"><semantics> <msub> <mi>K</mi> <mrow> <mi>L</mi> <mi>u</mi> </mrow> </msub> </semantics></math> (see <a href="#applsci-08-02693-f008" class="html-fig">Figure 8</a>). Light was propagated using the surface reference downward irradiance.</p> "> Figure 11
<p>Relative errors of the predictions calculated as the relative differences between the depth integral of the reference and predicted irradiance profiles.</p> "> Figure A1
<p>The field campaign was part of the GreenEdge project (<a href="http://www.greenedgeproject.info" target="_blank">www.greenedgeproject.info</a>) which was conducted on landfast ice southeast of the Qikiqtarjuaq Island in the Baffin Bay (67.4797 N, 63.7895 W).</p> "> Figure A2
<p>Examples showing the number of downward irradiance (<b>A</b>) and upward radiance (<b>B</b>) photons captured by the detectors of the Monte Carlo simulation at different depth ranges (numbers in gray boxes) as a function of the horizontal distance from the melt pond. The red lines represent the fitted Gaussian curves.</p> "> Figure A3
<p>Scatter plots showing the relationships between downward irradiance (<math display="inline"><semantics> <mrow> <msub> <mi>E</mi> <mi>d</mi> </msub> <mrow> <mo>(</mo> <mi>z</mi> <mo>)</mo> </mrow> </mrow> </semantics></math>) and upward radiance (<math display="inline"><semantics> <mrow> <msub> <mi>L</mi> <mi>u</mi> </msub> <mrow> <mo>(</mo> <mi>z</mi> <mo>)</mo> </mrow> </mrow> </semantics></math>) between 400 and 700 nm at different depths (numbers in gray boxes). Red lines represent the regression lines of the fitted linear models. Dashed lines are the 1:1 lines. Note the large deviations between the data points and the 1:1 line occurring in the orange and red regions (≥600 nm).</p> "> Figure A4
<p>Average determination coefficient <math display="inline"><semantics> <msup> <mi>R</mi> <mn>2</mn> </msup> </semantics></math> and standard deviation (shaded area) of the regressions between normalized (at 10 m depth) <math display="inline"><semantics> <mrow> <msub> <mi>E</mi> <mi>d</mi> </msub> <mrow> <mo>(</mo> <mi>z</mi> <mo>)</mo> </mrow> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi>L</mi> <mi>u</mi> </msub> <mrow> <mo>(</mo> <mi>z</mi> <mo>)</mo> </mrow> </mrow> </semantics></math> profiles between 400 and 700 nm. At each wavelength, average values were computed from the 83 COPS measurements. A sharp decrease of <math display="inline"><semantics> <msup> <mi>R</mi> <mn>2</mn> </msup> </semantics></math> occurred at wavelength longer than approximately 575 nm, suggesting a gradual decoupling between <math display="inline"><semantics> <mrow> <msub> <mi>E</mi> <mi>d</mi> </msub> <mrow> <mo>(</mo> <mi>z</mi> <mo>)</mo> </mrow> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi>L</mi> <mi>u</mi> </msub> <mrow> <mo>(</mo> <mi>z</mi> <mo>)</mo> </mrow> </mrow> </semantics></math> profiles at longer wavelengths, possibly due to the effect of inelastic scattering.</p> "> Figure A5
<p>Scatter plots showing the relationships between <math display="inline"><semantics> <msub> <mi>K</mi> <mi>d</mi> </msub> </semantics></math> and <math display="inline"><semantics> <msub> <mi>K</mi> <mrow> <mi>L</mi> <mi>u</mi> </mrow> </msub> </semantics></math> calculated from the downward irradiance and upward radiance profiles modelled with and without Raman scattering. The dashed lines represent the 1:1 lines.</p> ">
Abstract
:1. Introduction
2. Material and Methods
2.1. Study Site and Field Campaign
2.2. In Situ Underwater Light Measurements
2.3. 3D Monte Carlo Numerical Simulations of Radiative Transfer
2.3.1. Theory and Geometry
2.3.2. Estimation of Reference and Local Light Profiles
2.4. Statistical Analysis
3. Results
3.1. Comparing In Situ Downward Irradiance () and Upward Radiance () Measurements
3.2. 3D Monte Carlo Numerical Simulations
3.3. Inelastic Scattering
4. Discussion
5. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
Appendix A
Appendix B. Smoothing Radiance Data
Appendix C. Raman Inelastic Scattering
HydroLight Simulations
- A surface free of ice.
- A surface without waves.
- Sun position at noon for May 1st (solar zenith angle = 45.39 degrees).
- A cloudless sky.
- No fluorescence.
- Using HydroLight default atmospheric parameters.
- The scattering phase function of water was described by a Fournier-Forand analytic form with a 3% backscatter fraction.
- EcoLight option was run.
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Massicotte, P.; Bécu, G.; Lambert-Girard, S.; Leymarie, E.; Babin, M. Estimating Underwater Light Regime under Spatially Heterogeneous Sea Ice in the Arctic. Appl. Sci. 2018, 8, 2693. https://doi.org/10.3390/app8122693
Massicotte P, Bécu G, Lambert-Girard S, Leymarie E, Babin M. Estimating Underwater Light Regime under Spatially Heterogeneous Sea Ice in the Arctic. Applied Sciences. 2018; 8(12):2693. https://doi.org/10.3390/app8122693
Chicago/Turabian StyleMassicotte, Philippe, Guislain Bécu, Simon Lambert-Girard, Edouard Leymarie, and Marcel Babin. 2018. "Estimating Underwater Light Regime under Spatially Heterogeneous Sea Ice in the Arctic" Applied Sciences 8, no. 12: 2693. https://doi.org/10.3390/app8122693