Aquatic photoreactions can be modeled using kinetic and spectroscopic properties derived from laboratory and field studies as well as empirical relationships derived from field observations [141]. Here the former approach is discussed. The rate at a given depth z, rate(z), can be computed using equation (5):

where E0(z, A) is the scalar irradiance at z and wavelength A, a(A) is the absorption coefficient,/p(A) is the fraction of absorbed radiation that is absorbed by the photoreactive chromophores (usually assumed to be unity in the absence of more detailed information about system composition), Oa(A) is the apparent quantum yield for the photoproduction of DIC, CO, or other photoproducts (see below), and the integration is across the range of photochemically-effective wavelengths. Note that photon scalar irradiance (e.g., photons cm-2 s-1 nm_1) is used for simulations involving quantum yields in contrast to energy-based irradiance (e.g., watts cm-2 nm_1) that usually is used for estimating the dose rates employing BWFs. Also, although many recent modeling efforts have assumed that all the absorbed radiation in the UV and blue region is photoactive (and hence that /p is unity in this spectral region), this may not be the case for long-wavelength UV-A and blue radiation at the very low concentrations and absorbance of CDOM in bluewater regions of the ocean. Various recent studies have been conducted to provide data concerning the wavelengths responsible for photoproduction of DOC photoproducts in natural waters. As in the case of biological endpoints, such data are required in models that extrapolate measured photoproduct fluxes to unmeasured situations and estimate the changes in photoproduction in response to changes in atmospheric composition such as ozone depletion.

The data obtained in these studies have been presented as both apparent quantum yields and action spectra. Quantum yields are a useful indicator of the efficiency of a photoreaction, i.e. the fraction of absorbed radiation that results in chemical change. The term 'apparent' is used to signify that the nature of the light absorbing chromophores in the system has not been identified and likely could be a mixture. Apparent quantum yields are usually determined using monochromatic radiation. The quantum yield, ®a(A), which is the fraction of absorbed radiation that results in formation (unitless) of the photoproduct, is defined by the following equation:

h Fx where Rate(>l) is the observed formation rate of photoproduct (e.g. in molecules cm-3 s-1), Fx is the fraction of light absorbed at wavelength X, and Ix is the number of photons that enter the photoreaction cell per unit volume and unit time (units of photons cm-3 s-1). The latter is determined by chemical actino-metry or by some physical light detecting device such as a calibrated thermopile or spectroradiometer. Quantum yields can also be determined using the Rundel approach that was discussed earlier for UV effects on aquatic photosynthesis. The Rundel approach involves measurement of both rates, absorption spectra and spectral irradiance of the light source with a series of filters in place that block out parts of the UVR. A light source with spectral irradiance close to that of solar radiation at the Earth's surface is used for the experiments. Using a modified version of the rate equation (equation 5) in conjunction with the production rates, measured spectral irradiance, and spectral absorptivity a bestfit solution for <Da(/l) can be obtained with a MATLAB® program based on Rundel's statistical approach for the optimization of action spectra [67,78,115]. Usually, the data are fitted assuming that the quantum yields decrease exponentially with increasing wavelength but other types of fitting equations, e.g. linear, also can be readily employed. The primary strength of the Rundel approach is conservation of effort and time; the monochromatic approach requires a large number of experiments whereas a quantum yield spectrum can be determined with one experiment using the Rundel approach. On the other hand, the required ad hoc assumption of a fitting equation to estimate the spectral dependence of the quantum yields can lead to imprecise estimates of quantum yields in spectral regions beyond where the wavelength cutoffs are applied (e.g. the visible region) or where the spectral irradiance of the light source is relatively low and rapidly changing with wavelength (the UV-B region). It is reasonable to assume that photoreactions are not affected by interactions between various parts of the spectrum, such as photorepair in the case of aquatic organisms, so both the monochromatic and Rundel approaches should yield similar quantum yield spectra. A recent study has indicated that the quantum yield spectra for CO determined by the monochromatic approach is nearly the same as that determined using the Rundel approach [67].

It can be shown that the quantum yield is related to the response function by the following relationship:

where ax is the mean absorption coefficient (equation 1) of the water sample (e.g., in units of m-1) during the irradiation period. When defined using these units, the response function has units of m_1. Plots of XP(X) versus wavelength represent action spectra for photoreactions. The photoproduction rate at wavelength a is the cross product of the irradiance and the response function.

Although it has been generally assumed that aquatic photoreactions obey reciprocity, evidence in support of this assumption is mixed and can depend on the measured endpoint used to follow changes in irradiated system composition Fractional loss of the UV-absorbing CDOM component of DOC per unit time [38], as well as apparent quantum yields for photoproduct formation such as CO production [103], have been found to be conversion independent (and thus obey reciprocity). On the other hand, some photoreactions do not obey reciprocity because apparent quantum yields for photoreactions of CDOM are conversion dependent, i.e. dependent on the extent of photoreaction. For example, <Da(A) for DIC photoproduction [70] and photochemical oxygen demand [68] can be conversion dependent. Conversion dependence of quantum yields can result from changes in CDOM composition that, for example, involves depletion or creation of more photoreactive chromophores as photoreaction proceeds. Other changes such as a shift in mechanism from predominantly indirect (photosensitized) to direct decomposition or a buildup or decrease in excited state quenchers (such as molecular oxygen) also can contribute to conversion dependence. A general consequence of conversion dependence is that predictions based on first order models are likely to overestimate the photochemical removal rates.

Conversion dependence of <D>a(A) is not the only cause of apparent deviation from first order kinetics in photoreactions of DOC. If total DOC loss (not CDOM) is used to follow photoreaction kinetics, first order kinetics does not provide an adequate fit over long irradiation periods. For example, Moran et al. [38] reported that the amount of sunlight required to bring about an equivalent proportional loss of the DOC pool in water samples from coastal rivers in the Southeastern United States increased as photodegradation progressed, even when delayed DOC mineralization that occurred via enhanced bacterial activity was considered. The total DOC pool may have included a component in the original material (about 65% in this case) that was especially refractory to photochemical degradation, perhaps because it only weakly absorbed solar UVR. Alternatively, UVR may have induced photoreactions that converted the original material into refractory compounds, possibly simply by photobleaching the reactive chromophores or, alternatively, by other structural modifications that reduced photoreaction quantum yields.

Models can also be used to provide estimates of depth-integrated production of photoproducts in aquatic environments. Under well-mixed conditions in a water column of depth z, the average irradiance at wavelength I can be computed using equation 8:

Kd{A)z where Eo(X,0) is the irradiance just below the water surface and Kd(X) is the diffuse attenuation coefficient. Under conditions in which all the radiation is absorbed this reduces to (E0(A,0) / Kdz), the average rate becomes light-limited and inversely proportional to depth, and photoproduction can be described as depth-integrated "fluxes". These "fluxes," which are expressed, for example, in units of moles photoproduct per unit area and time are obtained by integrating the cross product of the net downwelling spectral irradiance just under the water surface [£(0,/)] [39,41] and the apparent quantum yields <Da(A) over the range of photoactive wavelengths (i.e., 280-450 nm) (equation 9).

Because the upwelling irradiance is generally much lower than downwelling irradiance, the net downwelling irradiance approximately equals the downwelling irradiance [39,41]. This equation only provides a rough estimate of depth-integrated photodecomposition, because mixing effects, poor knowledge offp{X), lack of reciprocity, and other factors can render this approach inapplicable. Nonetheless, such flux estimates can provide a useful initial assessment of the potential impact of UVR on various chemical and biological processes.

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