Calculation of dose requires the time-integration of the biological effective irradiance (Eq. 1) over an appropriate interval (hourly, daily, yearly, etc.) to get the biological effective exposure:
The exposure, via Eq. 1, is weighted by the appropriate relative biological
weighting function and the units reflect the arbitrary normalization
associated with this weighting.
Alternatively, the BWFs have been determined on an absolute basis
with biologically effective exposure expressed as the dimensionless
[Cullen Neale Lesser science 1992, Neale Lesser Cullen carbon 1994].
In either case, the biological effective exposure is a time integral of an
appropriately weighted irradiance and this raises the classic assumption of
reciprocity (that the effect is a function solely of cumulative exposure
independent of irradiance).
Reciprocity fails if, for equal weighted exposures, a short exposure to a
highly damaging irradiance causes a different effect than a long exposure
to a less damaging irradiance.
The question of reciprocity thus impacts the discussion of radiation amplification factors (see below), interpretation of experimental results, and models for assessing and predicting UV-B effects. Equally important, the time-dependent reciprocity issue almost guarantees a problem with non-linearity if carried across a sufficient range of scale. Laboratory studies [Cullen Lesser 1991, Neale Lesser Cullen carbon 1994] show that the photoinhibition of photosynthesis, when plotted against cumulative dose of UV-B, is a monotonic, nonlinear function of UV dose for any one time scale. For equal doses, however, a relatively short exposure to high UV-B irradiance is more damaging to photosynthesis than a longer exposure to lower irradiance (i.e., reciprocity fails). These results are consistent with a mechanistic model of photoinhibition as a balance between damage and recovery processes, processes that utilize different parts of the solar spectrum and are likely to operate on different time scales [Neale aquatic 1987]. These workers conclude that for their system, UV inhibition is best modeled as a function of biologically weighted irradiance, but as pointed out by Cullen and Neale (1994), the kinetics of UV-induced photoinhibition must be resolved for natural phytoplankton in a number of environments.
For example, consistent with reciprocity, Behrenfeld and co-workers (1993a,b) [Behrenfeld Chapman Hardy Lee 1993, Behrenfeld Hardy Gucinski Hanneman Lee Wones 1993], combining their own plus earlier [Ray Smith Holm-Hansen Baker Olson 1980] results of exclusion/inclusion experiments under ambient solar radiation, and using their weighted exponential BWF, found a common linear dose-response curve for all three studies. Their results, which represent data from a wide range of oceanic regimes, describe the cumulative inhibition of carbon fixation by ultraviolet radiation (UVR) as a function of total dose and suggest that reciprocity holds for their experimental conditions (4-8 hr incubations and ambient solar irradiance). Since their dose-response curve is linear with no apparent threshold, they conclude that is likely that any increase in UVR will cause additional photodamage. It is important to recognize that, as Behrenfeld and co-workers acknowledge, these studies assessed UV-B, but not UV-A, effects so that possible nonlinearity based on measurements under different UV-A exposures might not have been readily apparent.
The question of reciprocity in UV-induced photoinhibition of natural
phytoplankton has not been resolved:
reciprocity failed when Helbling et al. (1994; discussed in more detail below)
compared inhibition of photosynthesis in Antarctic phytoplankton exposed
to fixed vs. variable irradiance regimes.
Unless reciprocity can be justifiably assumed for the full range of time
scales under consideration, quantitative generalizations of UV effects
require a description of biological effects vs biologically weighted
incident irradiance and a description of the time-dependence of
the function.
The assessment of time-dependence is extremely important
[Vincent Roy 1993].
For example, if the biological effect is a function of cumulative exposure,
independent of dose (i.e., reciprocity is satisfied), then one can predict
UV effects under variable irradiance through the day, even under the
influence of vertical mixing [cf. Smith and Baker, 1982]
[Ray Smith Baker assessment 1982]).
Likewise, modelling is tractable if the effect is a function solely of
biologically weighted irradiance (dose rate), regardless of duration
[Cullen Lesser 1991].
In practice, most researchers have related effects of UV on phytoplankton
to cumulative biologically weighted exposure over the course of several
hours to a day.
Implicitly or explicitly, it has been assumed that cumulative exposure over
one day is the relevant quantity for quantifying biologically effective UV.
The bottom line (relevant also to the comparisons between laboratory and
field results) is that critical issues concerning response-versus-exposure
have been identified, but they have yet to be resolved.