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Station Report Tools

Your measurements in, a defensible verdict out

Everything the Station Report asks you to compute — all in your browser, no login, nothing sent anywhere, and it keeps working offline once the page has loaded. Each calculator shows the formula it used and the numbers it put into it, so you can check it by hand — and you should, at least once. A calculator you have never checked is a rumour with a rounded edge.

The pre-filled figures are under review. Most reproduce the worked example in the Technical Supplement exactly. A few are illustrative values built to match the supplement's stated magnitudes rather than lifted from it, and each is labeled where that is so. The formulas are the document's in every case; some of the example inputs are not yet, and will be replaced as the course completes review.

Every threshold in the report descends from this one number. Put every instrument — loggers and dive computers together — in one shaded bath of site water, let it settle, then read them all at the same moment, three times, five minutes apart. Snapshot 1 sets each instrument's offset bᵢ = Tᵢ − T̄; snapshots 2 and 3 measure whether that offset stays put. What is left over is u(T), and the threshold a difference must beat is C = 2√2 · u(T).

SNAPSHOT 1 SNAPSHOT 2 SNAPSHOT 3 t = 0 min t = 5 min t = 10 min group mean offsets b = T − T̄ residual ≡ 0, always defined here — so it cannot be tested here u(T) measured from these residuals an offset that holds can be corrected and trusted; one that wanders on deck will wander on the dive
An offset cannot be both defined and tested at the same reading — which is why the bath needs three snapshots and not one.

Bath readings

Every instrument that will carry a temperature into the reef, in °C as read. Minimum three loggers; dive computers belong here too.
InstrumentSnap 1Snap 2Snap 3
Why C is not u(T). Every question the report asks is about a difference between two readings, and a difference between two independent quantities carries more uncertainty than either alone — √2 times as much when both come from this array on this day. A threshold also needs a coverage factor, and the course uses k = 2, the ordinary metrological convention for about 95 % confidence. So the number a difference must beat is 2√2 ≈ 2.83 times the bath figure. Fewer differences resolve under this rule than under the sloppy one. That is the intent, not a defect.

On Dive 3 the array stays put and you travel. Every observation is matched against the stationary array at the same depth and the same moment — so a difference measured forty minutes into a survey is not simply the morning warming up. Depth is controlled by working at a common nominal depth; time is controlled here. The threshold is C = 2√(u²obs + u²ref), built from the two things actually being compared — not from the bath figure, and not from the Dive 2/4 thresholds.

Positions

Two clock times per position, as Slate C records them: when you arrived and when you took the reading. Reference is the array's sample nearest that reading.
PosArrivedReadObs °CRef timeRef °C
Times as hh:mm:ss, exactly as the computer shows them. “~10:15” cannot be matched.
The equal dwell matters more than the long one. Whatever lag remains is common to every position and largely cancels in a comparison between them — but only if the dwell was the same everywhere. A dwell that varies puts a varying error into the very differences you are measuring. Two positions properly settled beat six done in a hurry, and if the arithmetic does not fit the gas plan you reduce positions, never dwell.

Example figures are illustrative. The Technical Supplement's worked example does not cover Dive 3, so the four positions pre-filled here are made up to exercise the tool. The arithmetic and the thresholds are the course's; these particular times and temperatures are not.

Dive 2 against Dive 4 — the same station, the same hour, one day later, with nothing expected to have changed. Each parameter gets an empirical threshold R = max(|x₄ − x₂|, C₂₄), where C₂₄ = 2√(u₁² + u₂²) combines the two days' bath figures. The max is the whole point: on a quiet day the observed differences can be smaller than the instruments can resolve, and carrying one forward would hand Dive 5 a bar it clears for free.

Two occupations

Each day's u(T) from its own bath, then each parameter as measured on Dive 2 and Dive 4.
ParameterDive 2Dive 4Own C
Leave Own C blank for temperatures — they use C₂₄ from the two bath figures. Fill it for Kd, y and Π, whose thresholds come from their own propagated uncertainties, not from the bath.
Nothing resolving is the good outcome here. Dive 4 asks whether the procedure repeats, and a day on which nothing exceeded its threshold means the method reproduced itself to within what the instruments could see. That is the cleanest possible result, and the thresholds it yields are the ones Dive 5's claim about change has to clear.

Two questions, strictly in order. First: is the optical product stable at the home station — do any two of its occupations differ by more than their threshold? If a pair resolved, there is no single reference value to carry, and the second question cannot be asked. Only then: does it travel? Compare the reference against the new station using C₆ = 2√(s² + u₆²).

Home station — Π per occupation

One value per occupation of the first station. At least two; three is the usual case.

Second station

“No resolved shift” is not “the same.” It is a statement about what this equipment, on these days, could distinguish — never a claim that the two values are equal. And when the propagated uncertainty of a single occupation dominates C₆, that is itself a finding: the way to test whether Π travels is not more occupations, but a tighter y.

A temperature reported at depth z inherits an error from any uncertainty in z, scaled by how fast temperature changes with depth: σT,depth = |dT/dz| · σz. Combined with the array's own figure, the station temperature carries σT = √(u(T)² + (|dT/dz|σz)²). In any water with real vertical structure the second term dominates — and it is the only term in the whole error budget the diver personally controls.

Depth log

Paste the depth samples your dive computer recorded over the station interval, separated by spaces, commas or newlines. σz is their standard deviation.

The gradient

Two loggers spanning the station depth, from the same occupation.
An isothermal column can be measured more precisely than a stratified one. Where dT/dz is zero the depth term vanishes and the uncertainty is the array's alone. That is not a trick of the arithmetic — it is why the same instruments, held equally well, give a tighter number in mixed water than across a thermocline.

Example figures under review. The depth log and logger pair pre-filled here are illustrative — built to reproduce the magnitudes A.9 states (a 1 °C per 3 m gradient with σz around 0.3 m contributing about 0.1 °C, roughly two and a half times the array's own figure) rather than lifted from the worked example. Equations (A-34) and (A-35) are the supplement's exactly.

Light falls off exponentially, so ln E = ln E₀ − Kdz is a straight line in a uniform column. The reported coefficient comes from the endpoints only — Kd = ln(E₁/Eₙ) / (zₙ − z₁) — because surface brightness cancels and only the longest baseline has a signal that clears the sensors' scatter. The middle loggers are a test, not extra data: their residuals say whether one coefficient describes the column at all.

The array

Depth and illuminance for each logger, shallowest first. Three minimum; more improves the linearity test, not the coefficient.
LoggerDepth mE lux
The 10 % default is the guide's planning figure for uncalibrated channels. The light channels get the same three-snapshot treatment as the bath — gains become additive offsets in ln E by (A-38) — and the number belonging here is the u(lnE) measured that morning. A quoted figure is not a measured one.
A failed linearity test is not a failed dive. Residuals larger than the sensors' own scatter mean the column is layered — a turbid or clear stratum between loggers — and a single Kd would misdescribe it. That is a real finding about the water, and it is also the validity condition for the optical product: on a layered column, Π must not be computed at all.

The figures here are the worked example's: four loggers at 2.1 to 11.4 m, giving Kd = 0.0600 m⁻¹ at 12.7 %, with a least-squares slope of 0.0609 — within 1.5 % of the endpoint value. Note the default light-channel spread is 5.0 %, the figure measured in that example's intercomparison, not the 10 % planning figure for uncalibrated channels.

Both Teams swim apart, so each extinction event measures the whole separation, not half of it — the part most easily got wrong. The Team still swimming has its count interpolated to the other Team's moment by n(t) = n × Δt₁/Δt₂, and the two independent estimates are averaged. Their difference is the observer spread; half of it enters u(y).

Kick-cycle calibration

Three timed runs over the measured course, per diver, from Dive 1. u(k) = 1.15 s — the disc swim is a new swim, not the calibration average.
DiverRun 1Run 2Run 3

The swim

Seconds from the start of the separation swim to each Team's extinction event, and the observer's kick count at that moment.
Why the larger relative uncertainty is used. The two divers calibrate separately and the less consistent kicker sets the term — the whole optical measurement inherits it. And u(k) uses 1.15× the standard deviation of the runs, not the standard error of the mean: the disc swim is one new swim, not an average of three. A spreadsheet's default would offer s/√3, which in the worked example halves the figure and reports about twice the precision the measurement has.

A coefficient with units of inverse distance times a distance: Π = Kd · y, dimensionless. Two independent routes put it near 1.15 to 1.25 — but every constant behind that came from fresh and temperate coastal water. Over a reef it is an expectation to be tested, not a constant to assume.

Inputs

Kd from tab 03 — photopic weighting only — and the extinction distance with its propagated uncertainty.
Why the gate matters. Π pairs a coefficient measured across the whole array with a distance measured at one depth. They describe the same water only if the column is optically uniform. And the spectral weighting must match on both sides — the distance was judged by a human eye, so only a photopic Kd may enter.

Everything entered in the tabs above, assembled into a Station Report you can print or save as a PDF — including the accuracy-and-limitations statement the course requires. Nothing is uploaded; the sheet is built in your browser from what you typed.