Backscatter (bb) and scattering efficiencies (bb/b) were calculated using Mie theory and anomalous diffraction approximation (ADA) based on particle size distributions (PSD) and absorption coefficients measured in East Sound, Washington in August 1998. Particle size distributions were obtained using a Coulter counter and slopes were determined to extrapolate into size ranges that were not detected with our methods. Absorption measurements were made on discrete water samples via spectrophotometry and in situ with an AC-9. A real index of refraction (n) of 1.05 was assumed and the imaginary part of the refractive index (n’) was calculated at each of five wavelengths based on the absorption and PSD. The phase functions were calculated based on Mie theory with inputs of n, n’, PSD, and wavelength. Efficiency factors for absorption, scattering, and attenuation (Qa, Qb, and Qc) were derived from ADA, and then Qbb was determined from Qb and the calculated phase functions. The bulk optical coefficients (a, b, c, and bb) were determined based on the efficiency factors and PSD.
By allowing each of the input parameters n, n’, and PSD to vary independently, it was possible to observe the changes in the inherent optical properties (IOPs). Results suggest that an increase in n or gamma (PSD slope) or a decrease in n’ leads to an increase in bb. An increase in n or gamma also results in enhanced bb/b; however, changes in n’ lead only to slight alterations of bb/b. Particles with a higher real index of refraction appear more efficient at backscattering, whereas the more absorbing particles (i.e. phytoplankton) with a high imaginary index of refraction are less efficient backscatterers. These patterns, based on theoretical approximations, were used to interpret the results of a comparison between the modeled and measured IOPs from East Sound.
Measured filter pad absorption agreed well with the modeled estimate between 500 and 650 nm. They did not converge in the blue and red wavelengths suggesting that a portion of the larger sized phytoplankton had been omitted from the PSD, a reasonable assumption since the samples were pre-filtered through a 73 m m mesh before being analyzed in the Coulter counter. Backscattering efficiencies calculated from theory matched well with those measured using the Hydroscat and AC-9. However, the backscatter coefficients based on theory were an order of magnitude lower than those measured by the Hydroscat. One potential reason is that inappropriate indices of refraction may have been assumed for the model inputs; having knowledge about the particles present will aid in better determination of these values. Again the problem with the exclusion of larger particles in the PSD may be responsible for the poor agreement between the bb coefficients. By making more accurate particle size measurements and by gaining some knowledge of the types of particles present the input parameters can be adjusted such that better approximations can be made.
Figure Captions:
Figure 1. Particle Scattering Efficiency as a Function of the Real Part of the Refractive Index. Calculated from Mie theory and ADA using n’=0.005, PSD at 1 m in East Sound on 04 August 1998 (gamma = -3.2), and l = 442 nm. This shows that small particles and particles with higher indices of refraction are more efficient at backscattering.
Figure 2. IOP Variations with Changes in the Real Part of the Refractive Index. Calculated from Mie theory and ADA using n’=0.005, PSD at 1 m in East Sound on 04 August 1998 (gamma = -3.2), and l = 442 nm. Changes in n do not effect absorption; however, an increase in n results in enhanced scattering and attenuation. Backscatter follows the same trend as scattering as n changes.
Figure 3. Bulk Scattering Efficiencies as a Function of the Real Part of the Refractive Index. Calculated from Mie theory and ADA using n’=0.005, PSD at 1 m in East Sound on 04 August 1998 (gamma = -3.2), and l = 442 nm. Backscattering Efficiencies increase as the particle index of refraction increases.
Figure 4. Particle Scattering Efficiency as a Function of the Imaginary Part of the Refractive Index. Calculated from Mie theory and ADA using n=1.05, PSD at 1 m in East Sound on 04 August 1998 (gamma = -3.2), and l = 442 nm. Particles with higher imaginary indices of refraction are more absorbing, and are thus less efficient at backscattering.
Figure 5. IOP Variations with Changes in the Imaginary Part of the Refractive Index. Calculated from Mie theory and ADA using n=1.05, PSD at 1 m in East Sound on 04 August 1998 (gamma = -3.2), and l = 442 nm. Absorption increases as the imaginary index of refraction increases, whereas scattering decreases. Again the backscattering follows the same trend as the scattering when n changes.
Figure 6. Bulk Scattering Efficiencies as a Function of the Imaginary Part of the Refractive Index. Calculated from Mie theory and ADA using n=1.05, PSD at 1 m in East Sound on 04 August 1998 (gamma = -3.2), and l = 442 nm. Changes in the imaginary part of the refractive index only lead to slight changes in scattering efficiency.
Figure 7. Bulk Scattering Efficiencies as a Function of Gamma. Calculated from Mie theory and ADA using n=1.05, PSD at 1 m in East Sound on 04 August 1998 (gamma = -3.2), as well as a gamma of —2 and -4. The imaginary part of the refractive index was calculated from absorption measurements at each of five wavelengths. Increases in gamma (the result of having more small particles) leads to enhanced backscatter efficiencies.
Figure 8. Measured versus Modeled Spectral Absorption Coefficients. Absorption calculated from theory (n=1.05, n’ calculated, and gamma = -3.2) versus absorption measured spectrophotometrically. Reasonable agreement between the measured and modeled absorption. It is important to note that the n’ which was an input into the model was determined based on the absorption measurements; therefore, they are not independent of each other. The discrepancy in the blue and red wavelengths could be the result of a missing phytoplankton fraction from the PSD since it was pre-filtered through a 73 m m mesh while the spectrophotometric absorption was for total particulate.
Figure 9. Measured versus Modeled Spectral Backscattering Efficiency. Calculations from theory versus measurements of backscatter and scattering from the Hydroscat and the AC-9, respectively. Remarkable agreement between the independently measured and modeled data.
Figure 10. Measured versus Modeled Spectral Backscattering Coefficients. Calculations from theory versus measurements of backscatter from the Hydroscat. The measured and modeled bb were different by an order of magnitude. Potential explanations for this discrepancy are that the slopes from the PSD were not accurate in that we may have been missing some of the larger cells not sampled by the Coulter counter or the chosen indices of refraction may have been inappropriate.
Table 1. Theoretical Determination. Input and output for Mie theory and equations for the anomalous diffraction approximation. Qbb was then calculated using the phase functions from Mie theory. Bulk IOP coefficients were then determined using Qs and PSD.
