Summary

The model takes the DTN forecast sea state and the measured vessel heading and predicts the standard deviation (σ) of heave, pitch and roll. These predictions were compared with the rig MRU (TrendData export, one sample every 5.6 min) in ±3-hour windows around each forecast step with lead time ≤ 30 h. Heave and pitch are reproduced with correlations of 0.87 and 0.83 and about seven in ten cases within ±30 %. Roll correlation is 0.46 in-sample and 0.16–0.49 when one month is held out, so roll is reported as indicative only. The rig cannot measure waves, so the comparison tests the forecast and the model together; the forecast wind against the rig anemometer (correlation 0.85, ratio 1.06) supports the forecast as input. This is the second calibration round (v1.3): the first used 207 steps from 37 issues; doubling the data left the physical parameters unchanged and moved only the scale factors (heave 0.92 → 0.99, pitch 1.08 → 1.19).

Blind test (18 Oct 2026). The calibrated model was then run, unchanged, on 11–28 August, a period it had never seen: two rough-weather spells with Hs up to 4.0 m and rig headings all round the compass, so the swell came from ahead, astern, the quarter and the beam. In rough seas 90 % of heave and pitch predictions fell within ±30 % of the MRU. Heave and pitch are now validated from calm to rough seas and from all directions; the one weakness found is a small over-prediction of pitch with the swell on the beam (details below).

Model vs MRU, step by step

Values are the most probable maximum in a 3-hour window, the same "max" the calculator shows: heave peak-to-peak at the MRU, pitch and roll single amplitude. The trend export samples only every 40 s to 5.6 min, too slowly to catch each crest, so the measured maximum is worked out from the measured σ with the same wave statistics the model uses (σ·√(2 ln N), N = waves in 3 h); the 0.45-second check further down confirms this against the real largest waves. Left: measured (dots) and model from the forecast (line) over the period; the red band is the blind test. Grey bands are periods without both a DTN forecast and an MRU extract in the archive. Right: scatter with the 1:1 line (yellow) and ±30 % band (dotted). Pitch and roll were detrended with a 6-hour rolling mean before computing σ, to remove slow trim/heel changes; heave was not.

Statistics

Blind test: 11–28 Aug 2026, data the model never saw (365 steps, 141 distinct MRU windows)

Largest values in the blind period: heave max 4.5 m p-p measured (model 5.3 m at its peak step), pitch 2.2° (model 2.2°), roll 3.0° (model 3.0°). Same model and coefficients as the calculator (v1.3, calibrated on September–October only). Two spells: 11–22 Aug (Hs 1.6–4.0 m, rig headings 200°, 30°, 146°, 122°, 89°, 60°, so swell from every side) and 23–28 Aug (Hs 2.0–3.9 m, bow-on to a long S/SSW swell, Tp up to 15 s). Data from before 11 Aug were left out because the rig was still moving onto this location.

Known weakness: pitch with the swell on the beam. When the dominant swell is 45–135° off the bow the model over-predicts pitch by about 33 % (127 steps). In absolute terms this is small, 0.05° on average and 0.11° at most (σ), and most of it falls on 17–20 Aug when the measured pitch was only 0.07–0.08°, close to the sensor floor. With the swell ahead or astern pitch has no bias (238 steps). Narrower swell spreading and an oblique-sea correction were both tested and did not remove it, and the error is on the safe side, so the model was left unchanged.

High-rate check (25 Aug 2026, two 1.5-hour windows sampled every 0.45 s)

The fast samples resolve each wave (418 and 442 waves), so here the measured maximum is the real largest wave, not a statistic. The model's most probable maximum (for the 93-minute window) was 9–13 % above it, slightly on the safe side, as expected of that statistic. They also check the motion periods, not only the amplitudes. Roll is about 30 % high and the measured roll spectrum peaks near 16–17.5 s, which suggests the real roll period is a little longer than the model's 14.8 s. These windows also give the first estimate of the helideck heave rate: about 25–40 % below what the switched-off helideck function predicted. The helideck function has since been calibrated against a month of HMS records (section below).

In-sample (September–October, 411 steps, calibration applied; values in σ, ratios are the same in max)

Prediction = √(floor² + (scale·σ_model)²). The floor is what the MRU shows when the sea is nearly flat (sensor noise plus slow heel/trim changes from DP and ballast). Scale factors (0.99 heave, 1.19 pitch, 0.88 roll) were chosen so that the largest 25 % of events are matched, which makes the model run ~15 % high in calm weather; a pure least-squares fit would under-predict the big events. For an operational tool the big events matter more, so the conservative choice was kept.

Hold-out tests, both directions

October was calmer than September; the heave over-prediction there is mostly the floor dominating small motions. Reference points: using forecast Hs alone (no motion model) gives correlations of 0.37 / 0.37 / 0.35 on this set, and the uncalibrated model gives 0.87 / 0.82 / 0.45, so the skill comes from the physics, not from the calibration.

Where the data came from

• Forecasts: 132 DTN Marine Daily Planner issues (10 Aug – 17 Oct 2026), position 22.59 S 40.23 W from 11 Aug; only rows with lead time ≤ 30 h were used (776 steps, of which 365 in the blind test).
• Motions: rig MRU heave, pitch, roll and IAS heading, exported from the trend system at 2.6 min (8–30 Aug), 5.6 min (30 Aug – 17 Oct), 40 s (23–28 Aug), 13.5 s (24–26 Sep) and 0.45 s (two windows on 25 Aug). The trend values are instantaneous samples: over the same hours the 5.6-min and 13.5-s exports give the same σ (ratio 0.93–1.04), so the coarse rate adds noise (about ±9 % per 6-hour window) but no bias.
• Wind: IAS anemometer vs DTN 10-m wind: correlation 0.85, median ratio 1.06 (anemometer is higher than 10 m).
• Vessel data: CargoMax stability reports of 15 Oct (TRT connected) and 18 Oct 2026 (disconnected), General Arrangement PBS-J-XD-00027, topside Operations Manual.
• Independent wave data: none available for the period. Campos Basin buoys BM02 and AX24 (PNBOIA/REMObs) are offline; the nearest live buoy is the Watchkeeper at Cabo Frio, 227 km away, behind a token-gated API. A GFS-Wave or Copernicus hindcast at the rig position is the next step.

Validated envelope

Hs 1.1–4.0 m; heave up to 4.5 m most probable 3-hour maximum peak-to-peak (2.4 m significant); swell from ahead, the quarter, the beam and astern, with periods up to 15 s. The calculator's colour thresholds (2.0 m p-p, 1.0°, 1.5°) are at or above the largest motions seen, so red cells sit at the edge of what has been checked. Helideck: Hs up to 3.3 m and heave rate up to 1.1 m/s, against one month of HMS records (18 Sep – 18 Oct 2026), day limits, AW139 and S-92.

Helideck vs HMS (18 Sep – 18 Oct 2026)

The helideck status light was tested against one month of the rig's own HMS records (Seatex HMS, 720 hours replayed with ibReader, 165 000 ten-second records of pitch, roll, inclination and the NORMAM-27 heave rate MAHR). Each forecast step is compared with the share of time the HMS showed GREEN in that 3-hour step, because what matters for a landing is the 20 minutes before it, not the whole step. The HMS was set to NORMAM-27, day, AC-B (AW139) most of the time and AC-A (S-92) when an S-92 was expected; both aircraft were checked by applying their limits to the same records (this reproduces the HMS status 99.9 % of the time). The test is independent: each week was predicted with coefficients fitted only on the other weeks.

Top two rows: share of each 3-hour step the HMS was green (dots) and the model probability of a green deck (line), AW139 and S-92 limits. Right: the same grouped by model probability; a perfect model sits on the yellow line. Bottom: helideck heave rate, the quantity that drove every red period of the month. 28 Sep – 6 Oct is left out because no DTN forecasts issued in that period were available.

Heave rate (MAHR), model 20-minute most probable maximum vs HMS step median: correlation 0.84, median ratio 1.02, 69 % within ±30 %. The HMS went red only on 24 Sep (four spells of 10–20 minutes at about 03:00, 05:00, 14:00 and 16:00, heave rate 1.06–1.10 m/s), and even then the deck was green 71–87 % of each step; no step of the month was mostly red, so the model's red calls have not yet been tested against a real red period. On the roughest steps the model is slightly cautious (where it gives below 80 %, the deck was green about 88 % of the time). The 24 Sep forecasts were 54–72 hours old, because no DTN issues from 22–23 Sep were available.

How the probability is built. The model gives the most probable 20-minute maxima of pitch and roll (plus the static trim 0.57° and list 0.3° the HMS reads) and of the heave rate. The spread between those values and the HMS (log-normal: heave rate ±32 %, pitch ±12 %, roll ±36 %, inclination ±14 %) was measured over the month. The deck is only as green as its weakest limit, so the probability shown is the lowest of the four; multiplying them would count the same swell several times, since the errors move together (correlation 0.57–0.80).

Independent review

Before delivery the model, code and statistics were re-checked by a separate reviewer who had not seen them being built. Everything quantitative was recomputed from the delivered files: Python and JavaScript implementations agree to 1.4·10⁻¹⁵; JONSWAP spectra integrate to Hs within 0.3 %; heading conventions, unit conversions and the significant/maximum definitions are consistent; the statistics above reproduce to the last digit. Findings and what was done:

• criticalBest heading picked stern-to-swell. At zero speed the model is symmetric, so a heading and its reciprocal tie; the sweep kept the first one. Fixed: ties resolve to the bow-to-weather side and the page says so.
• criticalRoll hold-out skill not shown. Added here and on the calculator; roll is labelled indicative.
• should fixIn-sample statistics on a half-duplicated sample; only the flattering bias shown. Both tables above now carry the overall bias, the hold-out hit rates and the 108-window count.
• should fixValidated range narrower than the colour thresholds. Stated on both pages.
• should fixParser dropped rows with "CALM" wind. Fixed; the page now warns when lines are missing.
• should fixBroad swell spreading (cos²) and a roll damping ratio of 0.22 are effective, not physical, values. Kept, documented; the heading sensitivity of the index is modest (0.55–0.90 across all headings in the tests).
• minorkyy shown but unused (removed from the display); wind-sea partitions with Tp < 4 s partly outside the frequency grid (no motion effect); roll natural period 13.7–14.8 s depending on solid vs corrected GM.

Full review text and all data files are in the model package kept by the author.

Method in brief

Heave and pitch: closed-form box-hull expressions of Jensen, Mansour & Pedersen (2004, Ocean Engineering 31, 61–85) with block/waterplane corrections and an effective sectional added-mass ratio of 0.8 (fitted). Roll: linear one-degree-of-freedom response, ω_n = √(g·GM)/k′xx with kxx = 16.2 m from the item-level weight distribution of the stability reports, effective wave-slope excitation, equivalent damping ratio 0.22 (fitted). Sea state: wind sea plus two swells as JONSWAP spectra (DNV-RP-C205 γ from Tp/√Hs) with cos² spreading; wind-sea period from Tp = 4√Hs bounded by the fully developed sea. Point motions at the MRU (30 m from CG, fitted), the main well (7 m) and the helideck (113 m) as root-sum-square of heave and x·pitch, which is exact for this model because heave and pitch are in quadrature. Statistics: σ = √m0, significant = 2σ (4σ peak-to-peak for heave), most probable maximum = σ√(2 ln N). Helideck HMS probabilities: limits from NORMAM-27/DPC Rev 2 Table 1 (Class 3 helideck, AW139 as Category B, S-92 as Category A, day and night, maxima of the last 20 minutes), heave rate as the NORMAM-27 VArf (largest vertical oscillation of the helideck centre divided by half its period); the probability of a green deck comes from the log-normal spread between model and HMS measured over 18 Sep – 18 Oct 2026, taking the weakest of the four limits (see Helideck vs HMS).