, (1)
The contribution of a given particle size range to bb is a function of the backscattering efficiency, the number, and the cross-sectional area of particles within that size range. This relationship is given by
, (1)
where Qbb is the backscattering efficiency, N is the number of particles of size x in size range dx. The backscattering efficiency as a function of particle size, given a complex index of refraction, can be determined from Mie theory. In addition, the number of particles of a given size can be modeled by a Junge distribution, thereby linking its value to particle size. Since efficiency and concentration of particles per unit size are both linked to particle size, the relative contribution of particles to bb can subsequently be modeled as a function of particle size and slope of the Junge distribution. Normalizing this function to create a percentage weighting function allows for assessment of the percentage contribution of a given particle size range xd(x) to bb. The slope of the assumed Junge distribution, the single degree of freedom in the system, is varied to allow for interpretation of the effect of particle size distribution of the weighting function.
Variation in the slope of the Junge distribution profoundly affects the particle size weighting function of bb. In particle size distributions involving a significant percentage of large particles, the weighting function is fairly uniform. However, as the particle size distribution is biased toward smaller particles the signal comprising a measurement of bb originates entirely from particles less than 0.2 microns in diameter. This suggests that in most natural waters the majority of information contained in a measurement of bb pertains to particles that fall under the operational definition of colored dissolved organic material (CDOM).
This finding was field tested by attempting to find a correlation between bb and CDOM absorption. Data was collected in the Strait of Juan de Fuca and in nearby East Sound, Washington. Profiles of CDOM absorption were obtained from a <0.2 micron filter attached to a WETLabs AC-9 meter. This data was compared to bb data as measured by the HOBILabs Hydroscat-6. The two instruments compared at four wavelengths; 442nm, 488nm, 532nm, and 671nm. Data from 671nm was not considered, due to low CDOM absorption signal at that wavelength. Data collected in East Sound showed reasonable correlation for 488nm and 532nm, with r^2 values of 0.63 and 0.73 respectively. This correlation was not seen for the data from the Strait. Analysis of particle size distribution data from a Coulter counter showed similar Junge slopes for both locations. Comparison of these slopes to the distribution functions suggested that 9% of the bb signal existed in the less than 0.2 micron range. However, East Sound data showed a drastic increase in the Junge slope for particles less than 0.3 microns. Use of the higher slope to extrapolate to smaller particle sizes, changed the distribution function predicted 73% of the bb signal as coming from the CDOM. This higher slope did not exist in the Straits where their was no correlation between bb and CDOM.
