Learning Objectives
By the end of this knowledge development session, student divers will be able to:
- State the difference between the diffuse attenuation coefficient and the beam attenuation coefficient, and name the measurement that produces each.
- Explain why the two coefficients differ for the same water, and state the approximate ratio expected between them.
- Explain what it means when both coefficients change but their relationship does not.
- Explain what a change in the relationship itself indicates about the water.
- State one condition under which the two measurements should not be compared, and describe how the logger array detects that condition.
- Explain why the expected value of this relationship was established in water unlike a reef, and what that means for a measurement made at one.
Presentation Notes
a. You now have two independent measurements of the same water. The logger array gives Kd, from light falling vertically through the water column. The black disc gives c, from light travelling horizontally along a straight path to your eye. Both describe how the water removes light. They are not the same number, and the difference between them is useful.
b. They differ because scattered light is treated differently by each. When a particle scatters a photon slightly off course, that photon still continues broadly downward and still reaches a downward-facing sensor lower in the column. As far as Kd is concerned, it was never lost. But that same photon has left the straight line between the disc and your eye, and as far as the black disc is concerned it is gone. The horizontal measurement counts every scattering event as a loss; the vertical one forgives most of them.
c. So c is always the larger of the two. In natural water the beam attenuation coefficient typically runs something like three to five times the diffuse attenuation coefficient. That is not a coincidence or a calibration — it follows directly from the physics in note (b), and the size of the ratio is set by how much of the loss is scattering rather than absorption.
d. Multiply one by the other and something useful happens. Because Kd has units of one over distance and the black disc extinction distance has units of distance, multiplying them gives a pure number with no units at all. Published relationships from freshwater and coastal work suggest that number should land somewhere near 1.2. The Technical Supplement, section A.7, shows the two separate routes by which that figure is reached, and they agree — which is a reason to trust it rather than a coincidence.
e. A pure number is something you can test. Every station occupation in this course produces a Kd and an extinction distance. Their product is a number you can compute in a minute, and compare against the expectation, and compare against your own previous stations. If it lands near the expected value, your two optical measurements are telling a consistent story and both are probably sound. If it does not, something is wrong or something is interesting, and it is worth finding out which.
f. Here is the part that matters most. Suppose you occupy the same station twice and both optical measurements change — the water is murkier, Kd is up, the disc vanishes sooner. Two cases must be distinguished.
g. Case one: the product is unchanged. Both coefficients moved together, in proportion. This means the balance between absorption and scattering is the same as before — there is simply more of whatever was already there. More of the same sediment, stirred up by more wave action.
h. Case two: the product itself has shifted. The two coefficients did not move in step, so the mixture has changed character. Something is in the water now that was not there before, or was there in different proportion — a different particle size, a plankton bloom rather than mineral sediment, or dissolved colour from land runoff, which absorbs strongly while scattering very little.
i. That distinction is worth more than either measurement alone. "Cloudier" is not a diagnosis. "Cloudier in the same way as before" and "cloudier in a different way" point at different causes and different consequences for the reef. Suspended sediment and a plankton bloom do different things to coral. Two inexpensive measurements, taken together over time, can begin to tell them apart — and neither can do it alone.
j. Do not compare the two when the column is layered. The vertical measurement samples the whole span of the array. The horizontal measurement samples one depth. If the water is optically uniform these describe the same water and the comparison is valid. If there is a cloudy layer between the loggers, the two instruments are looking at different water and their product means nothing.
k. The intermediate loggers are what tell you. This is the linearity test from Topic 5, doing a second job. If the light readings fall on a straight line when plotted as the appendix describes, the column is optically uniform and the comparison holds. If a middle reading departs from the line, the column is layered, and the Station Report should say so and treat the comparison as unreliable. Record the depth at which the disc measurement was made; ideally it is near the middle of the array.
l. The two instruments happen to share a weighting, which is fortunate. As Topic 5 noted, the logger's light sensor responds roughly the way a human eye does rather than the way a plant does. The black disc is judged by human eyes. So both of these measurements are weighted the same way across the spectrum, and comparing them is more defensible than it would be if one instrument measured the light that algae use and the other did not. What looks like a limitation of the logger, in the context of this comparison, is an advantage.
m. The expected value comes from other water than this. Every published figure behind the expectation was measured in rivers, lakes and coastal water — turbid, mineral-laden, often stained with organic colour. Clear ocean water over carbonate sand is optically unusual: very little absorption, and a bright reflective bottom. So the number you are comparing against was established somewhere quite unlike a reef.
n. Which means your measurement is not an exercise. You have not measured this before. Nor, in all likelihood, has anyone measured it at your station — the ocean is vast, reefs are many, and the number of places where anyone has put a light logger and a black disc in the same water on the same day is very small.
So when you compute the product, you are producing a value for a particular reef at a particular time that did not exist before you made it. If it lands near the freshwater expectation, you have evidence that the relationship travels further than the water it was measured in. If it does not, you have evidence that reef water is optically different in a way worth explaining. Either result is worth having, and it came from a disc and a handful of loggers.
This is the clearest example in the course of the difference between following a protocol and contributing to a body of knowledge.
o. And do not import the rest of the freshwater relationships. There is published work relating black disc visibility to suspended solids in rivers, with an equation that fits well. It should not be used here. The authors themselves found that the relationship differed significantly between five rivers in a single region, and had to fit each river separately. A relationship calibrated in water an order of magnitude murkier than a reef, on different particles, cannot be extrapolated to a reef and trusted. The physics — the definitions of Kd and c, and the reason they differ — travels anywhere. Fitted equations do not travel at all. Knowing which is which is one of the more valuable things this course teaches.
Appendix reference. The definitions of both coefficients, the derivation of the expected product by two independent routes, the linearity condition for a valid comparison, and the propagation of uncertainty into the product are given in the Technical Supplement, section A.7. Sources are listed in Supplement D.
p. If the disc never disappeared, the product is a bound, not a blank. A censored clarity observation — "greater than 30 m" — does not stop you reporting Π. It makes the report one-sided, which is weaker than an equality and much stronger than silence.
The reasoning is short. If y > 30 m then, since c = 5/y, the beam attenuation coefficient is less than 5/30 = 0.167 m⁻¹. And since Π = Kd × y, with Kd measured normally, the product is greater than Kd × 30.
So a station that could not resolve its extinction distance still reports a value: "Π > 1.4", together with the separation that produced the bound. A reader comparing stations can use that. They cannot use a blank cell.
This is the same discipline as "below detection limit" for a concentration, and it is worth pointing out that the two are the same idea from opposite ends. The measurement did not fail. It told you something less specific than you wanted, and the honest response is to report exactly what it told you — no more, and no less.