Diffuse attenuation

The combination of the two maps is then a map that covers the full velocity range and includes small velocities, but has a fine resolution at low velocities and a coarse resolution at high velocities. With this two step strategy, shorter gradient pulses can be used and a substantial decrease in the diffusive attenuation of the signal can be achieved [10]. 

The rate of photolytic transformations in aquatic systems also depends on the intensity and spectral distribution of light in the medium (24). Light intensity decreases exponentially with depth. This fact, known as the Beer-Lambert law, can be stated mathematically as d(Eo)/dZ = -K(Eo), where Eo = photon scalar irradiance (photons/cm2/sec), Z = depth (m), and K = diffuse attenuation coefficient for irradiance (/m). The product of light intensity, chemical absorptivity, and reaction quantum yield, when integrated across the solar spectrum, yields a pseudo-first-order photochemical transformation rate constant. 

Diffusive attenuation is not merely of academic interest because it will probably be an inherent cause of echo attenuation in on-line NMR sensors whenever the sample moves through gradients and inhomogeneities in the main sensor field. It is therefore important to understand their potential effect and possible use in assessing quality of horticultural products. 

Note that S(A) is a function both of ctD(A)(the diffuse attenuation coefficient near the surface) and of aD(k) (the average diffuse attenuation coefficient for the whole water column of depth zmix). Using 5(A), we may express kf k) as ... 

Why can one not just use the decadic light absorption coefficient, a(A), to describe light attenuation in a given water body How is the diffuse attenuation coefficient, aD(A), related to a(A) ... 

Which water constituents primarily determine the magnitude of the diffuse attenuation coefficient D(A) ... 

Light attenuation effects were computed by using equation 6, assuming typical diffuse attenuation coefficients at 350 nm for the different oceanic types (20, 24). 

UV transparency of natural waters can be described empirically by two measures that are wavelength-specific and inter-related the downwelling diffuse attenuation coefficient, K, and the percent attenuation depth, Z o/ . A downwelling diffuse attenuation coefficient is nominally proportional to the concentration of substances in the water that absorb or scatter UVR [17,42]. It is typically calculated for specific wavelengths (A) from measurements of downwelling irradiance ( d,A) by fitting the following equation (in units of m ) [8] to irradiance versus depth data ... 

Figure 2. Spectral diffuse attenuation of downwelling irradiance from Figure 1 compared with for pure seawater estimated by Smith and Baker [18], The phytoplankton concentration (based on chlorophyll a fluorescence) was highest in the upper 30 m. The curve labeled 1-30 m minus phytoplankton was calculated by regression of spectral Xjj against chlorophyll fluorescence for a range of depths, a method that also removes effects of scattering and absorption (including that of CDOM) that covary with phytoplankton fluorescence.

The diffuse attenuation coefficient (K ) is one of several apparent optical properties (AOPs) of natural waters described by Preisendorfer [25]. Unlike inherent optical properties (lOPs) described below, AOP s depend on the quality of incident light as well as the optical qualities of the water. In spite of this apparent limitation (and in part because the differences between AOP s and lOP s were said to be small in many instances [26]), a case was argued for the standard use of to characterize natural waters for purposes of optical comparisons and bio-optical models [27,28]. Gordon [17,29] provided a practical means to adjust measurements to remove much of its dependence on the ambient light field. In particular, Gordon [17] established that, after adjustment (described below), averaged from surface to Zio% is proportional to the summed concentrations of constituent optical compounds. 

Bio-optical models have been developed to predict spectral attenuation as a function of conveniently measured parameters and are discussed extensively in Mobley [5] and Kirk [6]. Since the pioneering work of Smith and Baker [42], bio-optical models typically break down diffuse attenuation into optical constituents of natural waters. In an approach covering UV-B and UV-A wavelengths summarized by Baker and Smith [9,43], these components are represented as partial attenuation coefficients (A for each term not shown for simplicity) ... 

Figure 4. Examples of direct and diffuse solar irradiance and a correction factor for diffuse path length in measurements (Hargreaves, unpublished). (A) Diffuse fraction of irradiance as a function of solar zenith angle during summer, 1996, L. Lacawac, Pennsylvania (41.3°N) and August 2001, Crater Lake, Oregon (42.9°N). (B) Calculated correction [17] to remove effects of irradiance field from near-surface diffuse attenuation (K ) measurements, based on data in part (A).

A similar exponential treatment has also been applied to spectral modeling of UV diffuse attenuation coefficients for natural waters [57,61,76] but this seems ill-advised unless the absorption spectrum of phytoplankton or other particles is insignificant or has been observed to follow the same exponential pattern as CDOM that may be present,... 

Smith and Baker [18] are also included for comparison, and two new estimates of that will be discussed in section 3.3.4. LI-COR values for Crater Lake have been replicated using PRR-800, PUV-501, and PUV-2500 instruments (Biospherical Instruments, Inc.) on several dates. The accuracy of the LI-COR and PUV-501 instruments for measuring UV diffuse attenuation has... 

H.R. Gordon (1989). Can the Beer-Lambert law be applied to the diffuse attenuation coefficient of ocean water Limnol. Oceanogr., 34,1389-1409. 

K.S. Baker, R.C. Smith (1979). Quasi-inherent characteristics of the diffuse attenuation coefficient for irradiance, Ocean Optics VI, SPIE, 208, 60-63. 

Figure 1. Percent of surface irradiance present at depth in the clearest ocean waters. Percent surface irradiance was determined using diffuse attenuation coefficients derived from Smith and Baker [22]. Measurements of irradiance were taken with a submersible spectoradiometer in the Sargasso Sea and the Central Equatorial Pacific.

K, diffuse attenuation coefficient for downwelling irradiance organic-water partitioning coefficient Ku, diffuse attenuation coefficient for upwelling irradiance LMW, low molecular weight LUMO, lowest unoccupied molecular orbital MAA, mycosporine-like amino acid MCH, melanin-concentration hormone MDR, mean damage ratio MPB, microphytobenthos... 

Fig. 7. (A) The spectral loadings calculated by PARAFAC and (B) diffusion attenuation profiles resulting from the PARAFAC model.

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