Statistical methods

Summary of conditions and change

Question. An overview available immediately after Seasonal cycle in the conditions menu: what the temperature has been, how it is changing, which extremes occurred and whether a shift is detected.

Data. The same daily series as the methods it summarises, on the selection's support and the shared analysis interval.

Method.

1. Conditions: the observed mean, median, standard deviation, minimum and maximum of the daily series, with the number of observed days and their coverage (the Daily SST series summary).
2. Trend: the slope of complete annual means in degrees per decade with its 95 per cent interval and p-value (Decadal SST trend).
3. Extremes: the marine heatwaves and cold-spells overlapping the interval, their count and days, the three strongest by maximum intensity with peak date and duration (MHW and MCS exceedance), and the trend of heatwave duration per decade (Trends in event metrics).
4. Shift: the Pettitt test for a single change in level of the daily anomalies (Single shift).

Uncertainty. Each line carries the uncertainty of its own method: the trend's interval and p-value, the event-metric trend's interval, and the Pettitt p-value. Lines whose method requirements are not met say so rather than estimating.

Requirements. Any interval; the trend lines need at least ten complete years and the shift test ten years of anomalies, otherwise they report unavailable.

Reading the result. Read the summary as orientation. Choose a method from the card's menu, or open a line, to see its figure, statistics and full disclosure.

Limits.

• The summary repeats the outcome sentences of several methods; it adds no inference of its own.
• Running several tests on one record does not make their findings independent.

Scientific reading. [1] event definitions; [2] ocean event trends; [3] ocean time-series analysis. This summary adds no estimator of its own.

Daily SST series

Question. The observed foundation sea-surface temperature of the selection, day by day.

Data. The selected SST product: 0.05° OSTIA foundation SST or 0.25° NOAA OISST v2.1. For a point, the mean of the 1, 4 or 16 native cells of the chosen support. For an area or polygon, the spherical cell-area-weighted mean of the valid cells inside the geometry: a rectangle uses exact fractional cell overlaps, a polygon or coastal buffer uses whole cells whose centres fall inside it. A day is reported only when at least 90% of the fixed ocean support is observed.

Method.

1. Each cell contributes its spherical area (proportional to the cosine of latitude) as its weight; land and ice-masked cells are excluded from the support on the first day and the support stays fixed.
2. The daily value is the weighted mean of the valid cells. Below 90% valid support the day is missing.

Uncertainty. None is fitted. The summary gives the count of observed days, the coverage and the observed range.

Requirements. Any interval inside the archive; the map date and the analysis interval are independent.

Reading the result. Gaps in the line are missing days. The footer states observed days and their share of the calendar days.

Limits.

• A regional mean smooths spatial structure; it is the temperature of the area, not of any cell in it.
• Foundation SST is free of diurnal warming by definition and is not a skin or in situ temperature.

Scientific reading. [22] OSTIA foundation SST; [11] coastal satellite/in situ differences in South Africa.

Additional method and implementation sources. Good et al. (2020), The current configuration of the OSTIA system, Remote Sensing.

SST anomaly series

Question. The departure of each day from the usual temperature for that day of the year.

Data. The daily series above and the pinned heatwave3 day-of-year climatology for 1991–2020, evaluated on the same selection.

Method.

1. Anomaly = observed daily SST minus the climatological mean for that day of year.
2. The climatology is the one that defines the event thresholds: an 11-day window (half-width 5 days) pooled across the 30 baseline years, smoothed with a 31-day running mean. It is fixed; changing the analysis interval does not move it.

Uncertainty. None is fitted.

Requirements. Both terms must be observed; either missing makes the anomaly unavailable.

Reading the result. Values above zero are warmer than the 1991–2020 normal for that date. Because the baseline is a 30-year mean and the region has warmed, recent years sit above zero more often than below.

Limits.

• The anomaly inherits any bias of the baseline; the baseline is not detrended (decision 0002).

Scientific reading. [1] day-of-year climatology; [26] baseline choices and their interpretation.

Seven-day change

Question. How much the temperature moved over the past week.

Data. The daily series.

Method.

1. Value on a day minus the value exactly seven calendar days earlier. Both days must be observed.

Uncertainty. None is fitted.

Requirements. Available on native point cards and linked rectangle cards.

Reading the result. A short-term tendency: positive values mark warming over the week.

Limits.

• Seven days is a fixed lag chosen for weekly reporting; it is not a filtered rate of change.

Scientific reading. [3] ocean time-series context. The seven-calendar-day difference is a descriptive SAOCE reporting choice.

Source uncertainty

Question. The analysis error supplied with the selected SST product.

Data. The archived per-pixel analysis standard error.

Method.

1. For one pixel the archived value is shown. For several pixels the weighted mean of the errors is reported, which is the upper bound that applies if the errors were perfectly positively correlated across the cells.

Uncertainty. This is the source product's uncertainty, not a statistic of the series.

Requirements. The archive may hold temperature without an error field for some days; those days are missing here.

Reading the result. Larger values mark days when fewer or poorer observations constrained the analysis, typically under cloud.

Limits.

• It does not include representation error near coasts or the error of the climatology.

Scientific reading. [22] OSTIA analysis and error characterisation; [3] ocean measurement/statistical uncertainty. Daily SST error is not anomaly or trend uncertainty.

Distribution of daily values

Question. The spread of daily temperatures over the interval.

Data. All observed daily values of the selection in the analysis interval.

Method.

1. Equal-width bins between the observed minimum and maximum. The number of bins is the square root of the day count, held between 8 and 18.
2. The mean, median and 10th and 90th percentiles are marked; percentiles interpolate between order statistics.

Uncertainty. None is fitted.

Settings. Period within each year: the whole year, or one calendar month or austral season (December belongs to the summer that follows it), so that a distribution can be read without the seasonal cycle.

Requirements. At least one observed day.

Reading the result. A two-humped shape usually reflects the seasonal cycle, not two regimes. For an area each day is already a spatial mean, so the histogram describes time, not space.

Limits.

• Bins are chosen for display and change with the interval; counts are days, not independent observations.

Scientific reading. [3] descriptive distributions and ocean sampling context; the display bins are a SAOCE choice.

Seasonal cycle

Question. The usual annual cycle and the thresholds that define events, with the latest two years drawn over them.

Data. The fixed 1991–2020 climatology and 10th and 90th percentile thresholds from heatwave3, and the observed daily series of the final two calendar years in the interval.

Method.

1. No calculation beyond the detector's own climatology: the mean and percentile curves are those used for detection, shown on a January to December axis.

Uncertainty. None is fitted.

Requirements. The climatology must exist for the selection.

Reading the result. Days above the dashed 90th percentile line are candidate heatwave days (five consecutive make an event); days below the 10th percentile are candidate cold-spell days.

Limits.

• The two observed years are a sample of recent conditions, not a new climatology.

Scientific reading. [1] event climatology and thresholds; [18] marine seasonal timing context.

Additional method and implementation sources. Hobday et al. (2016), A hierarchical approach to defining marine heatwaves, Progress in Oceanography.

Wind speed trend

Question. Estimate the long-term linear change in the selected wind quantity.

Data. ERA5 daily wind on the same point, rectangle, polygon or coastal-buffer support as the card. Display units are retained: m/s for speed, mN/m² for stress magnitude and 10⁻⁷ N/m³ for stress curl.

Method.

1. Form means for complete calendar years, or for the same calendar month or austral season in each year; at least 90% valid days are required. DJF is labelled by the January year.
2. Pass the supported period-year means to the shared R Prais–Winsten GLS AR(1) estimator, pw-gls-ar1-v3. Missing years retain their calendar spacing; no missing days or years are filled.

Uncertainty. The same 499-replicate parametric AR(1) bootstrap-t slope interval as the SST mean trend. Slopes and their limits are per decade; the chart draws slope limits through the fitted centre, not a fitted-line confidence band. The regression statistics give the p-value, R², sample size and AR coefficient.

Settings. Annual, a calendar month or an austral season; the card selection and shared analysis dates.

Requirements. At least ten complete period-years with 90% valid daily coverage each. A shorter result retains its observed period-year means and explains why no trend can be fitted.

Reading the result. Positive means an increase in the displayed quantity. Curl is signed; interpret its sign for the local hemisphere. These wind trends do not attribute an SST response to wind.

Limits.

• The uncertainty assumes AR(1) errors; the calibration and remaining limitations of record 0020 apply.
• Incomplete periods are excluded. Preliminary and interim contributions are counted by year. Coastal stress curl is least reliable near land.

Additional method and implementation sources. Scientific decision record 0020, shared R trend estimator; Scientific decision record 0015, ERA5 wind.

Wind stress trend

Question. Estimate the long-term linear change in the selected wind quantity.

Data. ERA5 daily wind on the same point, rectangle, polygon or coastal-buffer support as the card. Display units are retained: m/s for speed, mN/m² for stress magnitude and 10⁻⁷ N/m³ for stress curl.

Method.

1. Form means for complete calendar years, or for the same calendar month or austral season in each year; at least 90% valid days are required. DJF is labelled by the January year.
2. Pass the supported period-year means to the shared R Prais–Winsten GLS AR(1) estimator, pw-gls-ar1-v3. Missing years retain their calendar spacing; no missing days or years are filled.

Uncertainty. The same 499-replicate parametric AR(1) bootstrap-t slope interval as the SST mean trend. Slopes and their limits are per decade; the chart draws slope limits through the fitted centre, not a fitted-line confidence band. The regression statistics give the p-value, R², sample size and AR coefficient.

Settings. Annual, a calendar month or an austral season; the card selection and shared analysis dates.

Requirements. At least ten complete period-years with 90% valid daily coverage each. A shorter result retains its observed period-year means and explains why no trend can be fitted.

Reading the result. Positive means an increase in the displayed quantity. Curl is signed; interpret its sign for the local hemisphere. These wind trends do not attribute an SST response to wind.

Limits.

• The uncertainty assumes AR(1) errors; the calibration and remaining limitations of record 0020 apply.
• Incomplete periods are excluded. Preliminary and interim contributions are counted by year. Coastal stress curl is least reliable near land.

Additional method and implementation sources. Scientific decision record 0020, shared R trend estimator; Scientific decision record 0015, ERA5 wind.

Wind stress curl trend

Question. Estimate the long-term linear change in the selected wind quantity.

Data. ERA5 daily wind on the same point, rectangle, polygon or coastal-buffer support as the card. Display units are retained: m/s for speed, mN/m² for stress magnitude and 10⁻⁷ N/m³ for stress curl.

Method.

1. Form means for complete calendar years, or for the same calendar month or austral season in each year; at least 90% valid days are required. DJF is labelled by the January year.
2. Pass the supported period-year means to the shared R Prais–Winsten GLS AR(1) estimator, pw-gls-ar1-v3. Missing years retain their calendar spacing; no missing days or years are filled.

Uncertainty. The same 499-replicate parametric AR(1) bootstrap-t slope interval as the SST mean trend. Slopes and their limits are per decade; the chart draws slope limits through the fitted centre, not a fitted-line confidence band. The regression statistics give the p-value, R², sample size and AR coefficient.

Settings. Annual, a calendar month or an austral season; the card selection and shared analysis dates.

Requirements. At least ten complete period-years with 90% valid daily coverage each. A shorter result retains its observed period-year means and explains why no trend can be fitted.

Reading the result. Positive means an increase in the displayed quantity. Curl is signed; interpret its sign for the local hemisphere. These wind trends do not attribute an SST response to wind.

Limits.

• The uncertainty assumes AR(1) errors; the calibration and remaining limitations of record 0020 apply.
• Incomplete periods are excluded. Preliminary and interim contributions are counted by year. Coastal stress curl is least reliable near land.

Additional method and implementation sources. Scientific decision record 0020, shared R trend estimator; Scientific decision record 0015, ERA5 wind.

Decadal SST trend

Question. The linear rate of change of annual mean temperature, with uncertainty that allows for year-to-year persistence.

Data. Complete calendar-year means of the daily series; a year needs at least 90% observed days. Incomplete years, including the current one, are excluded. Monthly or seasonal period-years are available where stated.

Method.

1. Ordinary least squares first fits SST on calendar year, centred on the mean year.
2. The lag-one correlation ρ of the residuals is estimated from adjacent years only (gap years are not treated as neighbours), corrected for small-sample bias as ρ + (1 + 3ρ)/n, and bounded at ±0.95.
3. A Prais–Winsten transform whitens the series: the first observation is scaled by √(1 − ρ²); each later observation subtracts ρ^d times the previous one, d being the gap in years, with a matching variance correction. Least squares on the transformed series gives the slope; ρ is then re-estimated from the new residuals, corrected again, and the transform repeated until ρ settles (at most 25 iterations, tolerance 10⁻⁵). This is the estimator pw-gls-ar1-v3, run in R and shared by every annual trend in the tracker.
4. The slope is reported per decade with its standard error, a 95% interval, the two-sided p-value for zero slope, ordinary R², the fitted centre year and the value there, the AR(1) coefficient, the residual degrees of freedom n − 2 and the RMSE. The residual variance is on n − 2 degrees of freedom; the effective sample size n(1 − ρ)/(1 + ρ) is reported for orientation and is never used as degrees of freedom, because the whitening already removes the dependence.

Uncertainty. A parametric AR(1) bootstrap-t interval: 499 series are simulated from the fitted line with the fitted AR(1) errors on the same calendar axis, gaps included; each is refitted by the same estimator, and the 2.5th and 97.5th percentiles of the studentised slope deviations set the limits. The p-value is the share of replicates whose |t| reaches the observed one. The dashed lines on the figure pass through the fitted centre at the lower and upper slope limits; they are slope guides, not prediction bands.

Settings. Period within each year: whole calendar years, or one calendar month or austral season of each year, fitted as period-year means under the same 90% coverage rule; December belongs to the summer (DJF) that follows it.

Requirements. At least ten complete years.

Reading the result. A 95% interval that excludes zero is a trend the data support under the AR(1) model. R² is the share of annual variance described by the line and can be low even for a well-established slope.

Limits.

• With strong persistence (ρ near its 0.95 bound) the limits become wide; that is the honest statement of the information in the series. The bootstrap is calibrated for AR(1) errors; longer-memory noise is not covered.
• A straight line is a description over the chosen years; the sensitivity method shows how much the slope depends on them.
• The SST trend map layer and the sensitivity triangle use the same estimator with a Student-t interval on n − 2 degrees of freedom instead of the bootstrap; their slopes agree with this card, their intervals are narrower and, under strong persistence, cover the true slope less often.
• Calibration: in 300-replicate simulations of AR(1) series with a 0.2 °C per decade slope (20, 30 and 50 years with two interior gaps; ρ from 0 to 0.7) the bootstrap-t interval covered the true slope in 0.90 to 0.95 of series and rejected a true zero slope in 0.05 to 0.10. The Student-t interval of the map and the triangle covered 0.91 to 0.94 at ρ ≤ 0.3 with 30 or more years, but only 0.84 to 0.90 at ρ = 0.7, rejecting a true zero slope in up to 0.15 of series.

Scientific reading. [3] ocean regression; [39] SST trends and persistence; [40] record length, noise and trend detectability; [51] AR(1)-adjusted trend standard errors on the effective sample size n(1 − ρ)/(1 + ρ). The exact gap-aware GLS and degrees-of-freedom rules remain those stated above.

Additional method and implementation sources. Prais and Winsten (1954), Trend estimators and serial correlation, Cowles Commission discussion paper 383; Santer et al. (2008), Consistency of modelled and observed temperature trends in the tropical troposphere, International Journal of Climatology; Decision record 0004, SST anomaly and secular trend; Decision record 0020, The R analysis runner and the calibrated uncertainty layer.

Quantile regression

Question. Whether the warm and cool parts of the daily anomaly distribution are changing at different rates.

Data. All observed daily anomalies (SST minus the 1991–2020 day-of-year climatology) in the interval, with time in decimal years. Days without an observation or without a climatology are omitted.

Method.

1. Five linear quantile regressions of the daily anomaly on time at τ = 0.1, 0.3, 0.5, 0.7 and 0.9, one per quintile band, fitted by quantreg::rq in R (estimator quantreg-anomaly-block-v4).
2. The lines are fitted to anomalies, never to raw SST. A straight line through a seasonal cycle carries a slope bias that depends on where in the cycle the window starts and ends (about −6A cos φ/(πT²) per year for amplitude A, phase φ and window length T); removing the cycle removes that bias.
3. Slopes are reported per decade with the intercept at the centre year, so the lines can be drawn exactly.

Uncertainty. A residual moving-block bootstrap on the calendar axis: the residuals of each quantile fit are laid out on the full calendar of the window, blocks of 365 calendar days are drawn with replacement (absent days stay absent in every draw), added back to the fitted line on the observed days, and the fit repeated 499 times under a fixed seed. The 95% interval is the 2.5th to 97.5th percentile of the replicate slopes and the bootstrap standard error is their standard deviation; the number of usable replicates is reported. No p-value is reported: the sign statement says whether the interval excludes zero. Shading around each line is a 95% pointwise confidence interval for the fitted quantile, from the joint intercept and slope bootstrap draws. These are not prediction intervals for daily values or simultaneous bands across dates or quantiles.

Settings. Period within each year: all days, or only those of one calendar month or austral season of each year, so that a tail trend can be read within a season. A bootstrap block is then one period-year of kept days (31 for a month, about 90 for a season).

Requirements. Ten calendar years in the analysis window on every route, and at least three blocks of observed days.

Reading the result. The 0.9 slope is the trend of the warmest fifth of anomaly days and the 0.1 slope that of the coolest fifth. Because the seasonal cycle is removed, a tail is a tail of departures from the normal for the date, not a season.

Limits.

• Independently fitted quantile lines may cross within the window; this is reported, not corrected.
• The fitted-line bands are nominal 95% pointwise intervals. In 75 simulations with daily AR(1) 0.9 and 5% missing days, median-quantile coverage at the start, middle and end was 89%, 85% and 88% for ten-year records and 92% at all three positions for twenty-year records. Tail-quantile and simultaneous coverage are not established by that check.
• The bootstrap already carries daily dependence; no second AR(1) correction is applied.
• The anomaly inherits the fixed 1991–2020 baseline; in a warming region every quantile line sits above zero more often than below.
• Calibration: in 75-replicate simulations of daily anomalies with a 0.15 °C per decade trend, daily AR(1) 0.9 noise and 5% of days absent, the interval covered the true median slope in 0.93 of ten-year and 0.92 of twenty-year series, with a mean width of 0.58 and 0.23 °C per decade; the former raw-SST fit covered it in 0.42 of ten-year series.

Scientific reading. [24] dependent-data block resampling; [3] ocean statistical context. These complement the quantile-regression foundation below.

Additional method and implementation sources. Koenker and Bassett (1978), Regression quantiles, Econometrica; Decision record 0007, Quantile trends (revised); Decision record 0020, The R analysis runner and the calibrated uncertainty layer.

GAM and periods of warming or cooling

Question. A smooth curve through the annual means and the years in which its slope is distinguishable from zero.

Data. Complete annual means, at least ten.

Method.

1. A Gaussian generalised additive model with a cubic regression spline in calendar year, k knots spaced evenly over the fitted years (default 6, range 3 to 20, at most n − 2), fitted by mgcv::gamm with REML and an AR(1) residual correlation in calendar time. REML chooses the roughness penalty, so the curve can be nearly straight.
2. The knot-controlled option removes the penalty: the same cubic basis is fitted by generalised least squares with AR(1) errors, and k sets the degrees of freedom directly. It is an exploratory sensitivity setting.
3. The derivative of the curve is obtained by central finite differences of the prediction matrix (step 10⁻⁵ years) on a 241-point grid.
4. Periods of warming or cooling are the runs of grid points where the simultaneous derivative band excludes zero; their dates are rounded to that grid.
5. In automatic mode the fit is repeated at 4, 6, 8 and 10 knots inside R and a table reports, for each, the smooth degrees of freedom, the net change and the dated intervals where the band excludes zero (column band_excludes_zero); a notice appears when whether the band excludes zero anywhere depends on the number of knots.

Uncertainty. The mean curve carries a pointwise 95% band from the model covariance. The derivative carries a simultaneous 95% band whose critical value is calibrated by a 99-replicate parametric bootstrap: series are simulated from the fitted curve with the fitted AR(1) residuals, each is refitted, and the largest standardised deviation of the refitted derivative from the original is recorded; the 95th percentile of those deviations is the critical value. If fewer than 20 refits succeed, the 95th percentile of the largest standardised deviation over 2,000 joint coefficient draws is used instead, and the result says which was used. Both bands are conditional on the estimated smoothing and AR(1) correlation and on the chosen knots, because mgcv's smoothing-corrected covariance is unavailable for gamm fits.

Settings. Smoothing (automatic REML or knot-controlled) and the number of knots.

Requirements. At least ten complete years; k ≤ n − 2.

Reading the result. Smooth degrees of freedom near 1 mean the fit is close to a straight line. The reported net change is the curve's last value minus its first. A dated interval is where the band excludes zero, not a test of a bend. An AR(1) coefficient near its bound means smoothness and persistence could not be separated; compare fewer knots.

Limits.

• The bands are conditional on the estimated smoothing and correlation; the knot-sensitivity table makes the dependence on k visible rather than removing it.
• Features at the ends of the record or across long gaps are weakly supported.
• Calibration: in 60-fit simulations of 35 annual means with AR(1) 0.4 noise, the calibrated band contained a smoothly curved true derivative over the whole curve in 0.68 of fits (0.48 for the uncalibrated band) and pointwise in 0.94; on a flat truth it declared a dated interval somewhere in 0.03 of fits (0.12 uncalibrated). The whole-curve figure is well short of 0.95, so a dated interval is support under the fitted smoothing, not a calibrated test of curvature.

Scientific reading. [27] smooth trends, derivatives and simultaneous bands (general palaeoenvironmental method); [28] direct SST/autocorrelation example, but lightly cited and a conference paper.

Additional method and implementation sources. Wood (2017), Generalized Additive Models: An Introduction with R, 2nd edition, Chapman and Hall; mgcv reference: gamm; Decision record 0010, Event metric trends and GAMs; Decision record 0020, The R analysis runner and the calibrated uncertainty layer.

Robust trend and Mann–Kendall

Question. A slope that resists unusual years, with a rank test for a monotonic trend, both corrected for persistence, compared against the trend estimator.

Data. Complete annual means for the slope and annual test; complete monthly means for the seasonal test.

Method.

1. Theil–Sen slope: the median of the slopes between every pair of years. The intercept is the median of the values after removing that slope, at the mean year.
2. Mann–Kendall S: the sum over all pairs of the sign of the later value minus the earlier value. Its null distribution is an AR(1) sieve bootstrap: the residuals about the Theil–Sen line give the bias-corrected lag-one ρ and the innovation SD, 1,999 series are simulated without a trend, and the p-value is the share whose |S| reaches the observed one. The Hamed and Rao (1998) corrected-variance p-value (R package modifiedmk) is shown for reference.
3. Seasonal Mann–Kendall: the same test on each calendar month that has ten years, with S summed over the months (Hirsch, Slack and Smith 1982) and the null built by summing each month's sieve replicates.
4. The trend estimator pw-gls-ar1-v3 with its bootstrap-t interval is fitted to the same years for comparison.

Uncertainty. The slope interval is the 2.5 to 97.5 percentile of the Theil–Sen slope over the same 1,999 sieve replicates drawn around the fitted line, so persistence widens it. The Mann–Kendall p-value is the sieve-bootstrap p. Missing years are simply absent: no pair is formed across them and nothing is filled.

Requirements. At least ten complete years.

Reading the result. Agreement of the two slopes is a sensitivity check, not independent confirmation. A small Mann–Kendall p with a small Theil–Sen slope means a consistent but modest change.

Limits.

• The sieve null assumes AR(1) persistence; longer memory is not covered.
• Calibration: in 300-replicate simulations of 30-year null AR(1) series the sieve Mann–Kendall test rejected in 0.05, 0.09, 0.10 and 0.11 of series at ρ = 0, 0.3, 0.5 and 0.7, and the slope interval covered a true 0.2 °C per decade trend in 0.90, 0.89, 0.89 and 0.78; the trend estimator's bootstrap-t interval beside it is the better-calibrated statement of the slope. The analytic Hamed–Rao test, kept for reference, rejected a true null in 0.06, 0.17 and 0.26 of 30-year series at ρ = 0, 0.3 and 0.5, which is why it no longer supplies the p-value.

Scientific reading. [37] median-slope foundation; [38] autocorrelation in Mann–Kendall testing; [39] SST trends; [3] ocean regression context. Hamed–Rao’s corrected-variance p-value is reported for reference; SAOCE’s p-value and slope interval come from an AR(1) sieve bootstrap.

Additional method and implementation sources. Sen (1968), Estimates of the regression coefficient based on Kendall's tau, JASA; Hamed and Rao (1998), A modified Mann–Kendall trend test for autocorrelated data, Journal of Hydrology; Hirsch, Slack and Smith (1982), Techniques of trend analysis for monthly water quality data, Water Resources Research; Decision record 0020, The R analysis runner and the calibrated uncertainty layer.

Sensitivity to start and end years

Question. How much the fitted trend depends on which years were chosen.

Data. Complete annual means over the interval.

Method.

1. Every window with a first and last complete year and at least ten complete years between them is fitted with the trend estimator above (pw-gls-ar1-v3), all windows in one R call, with a Student-t interval on n − 2 degrees of freedom rather than the bootstrap.
2. The slopes fill a triangle of first year against last year; a dot marks a window whose individual 95% interval excludes zero; a diamond marks the window currently selected.

Uncertainty. Each cell has its own Student-t interval. Scanning many overlapping windows is not a global test, and the dots are not adjusted for the number of windows. Calibration: the Student-t interval covered the true slope in 0.91 to 0.94 of simulated series at ρ ≤ 0.3 with 30 or more years, but only 0.84 to 0.90 at ρ = 0.7 (record 0020), so dots are anti-conservative where persistence is strong.

Requirements. At least ten complete years.

Reading the result. A field of similar colours means the slope is stable to the choice of years. Strong gradients along an edge show that one end year drives the estimate.

Limits.

• Windows share most of their data; neighbouring cells are highly dependent.

Scientific reading. [40] record length, noise and trend detectability; [39] ocean trend context. These motivate sensitivity checks, not a globally adjusted test of the interval triangle.

Time of emergence

Question. When the warming signal grew larger than the year-to-year noise of the baseline period.

Data. Complete annual means of the selected interval and of the full 1991–2020 baseline.

Method.

1. Noise: the standard deviation of the 27 or more baseline annual means about their own linear fit, so that warming inside the baseline is not counted as noise. The raw standard deviation is reported beside it.
2. Signal: the fitted change since the baseline centre year (2005.5), from the trend estimator pw-gls-ar1-v3 and from an automatic GAM. The selected interval must contain the centre year.
3. Emergence year: the first year from which the signal stays beyond 1 or 2 noise SDs for every remaining year through the end of the record, with at least five such years and no missing year in between.

Uncertainty. None is attached to the emergence year itself; the linear signal carries the trend estimator's bootstrap-t interval. The two signal models are the sensitivity check.

Settings. Knots for the GAM signal.

Requirements. At least 27 complete baseline years and ten fitted years containing 2005.5.

Reading the result. Blank means not emerged by the stated criterion, not absence of change. A GAM date later than the linear date usually reflects curvature near the end of the record.

Limits.

• This is an observational adaptation of the signal-to-noise idea; it does not attribute the signal to forcing.
• No extrapolation to a future emergence date is made.

Scientific reading. [45] ocean signal-to-noise emergence; [20] SST emergence application. Modelled emergence is distinct from SAOCE’s observed five-year sustained-crossing statistic.

Additional method and implementation sources. Hawkins and Sutton (2012), Time of emergence of climate signals, Geophysical Research Letters.

Warming stripes

Question. Every complete year's departure from the baseline, in one strip of colour.

Data. Complete annual means of the full record. The baseline mean and the colour scale are fixed by the full record; the displayed years follow the analysis interval.

Method.

1. Anomaly = annual mean minus the mean of the 1991–2020 annual means (at least ten baseline years needed).
2. Colours use the published warming-stripes convention and saturate at ±2.6 standard deviations of the 1991–2020 annual anomalies.

Uncertainty. None is fitted.

Requirements. At least ten complete baseline years.

Reading the result. Hatched years fell below 90% coverage.

Limits.

• A display of annual means; no trend is fitted here.

Scientific reading. [39] ocean temperature trend context. The stripes are a descriptive visual summary, not a statistical test.

Additional method and implementation sources. Hawkins (2018), Warming stripes, Climate Lab Book.

Cumulative SST anomaly (CUSUM)

Question. Persistent warm or cool spells relative to the baseline, as a running sum of anomalies.

Data. Daily anomalies in °C·days, or calendar-month mean anomalies (months with at least 90% of days) in °C·months.

Method.

1. Sₜ = Σᵢ≤ₜ aᵢ with S₀ = 0 at the start of the interval. The reference mean is zero because the anomalies are already relative to the 1991–2020 normal. Missing steps add nothing and remain null; the sum carries across them.

Uncertainty. None is fitted; the curve is a data statement.

Requirements. An observed interval; monthly resolution needs complete months.

Reading the result. A rising curve is a spell warmer than the baseline, a falling curve a cooler one. A change of slope marks a change of regime, but no change-point test is applied here; use the Pettitt or PELT methods for that.

Limits.

• Because the region has warmed since the baseline, a steadily rising sum is expected in recent decades.

Scientific reading. [3] ocean time-series context. This cumulative anomaly is descriptive and is not a sequential change-detection test.

Additional method and implementation sources. Decision record 0005, section 10.

Multiple shifts in mean or variance (PELT)

Question. Where the level, or the level and spread, of annual temperature stepped.

Data. At least 20 consecutive complete annual means.

Method.

1. The pruned exact linear time (PELT) algorithm of the R package changepoint finds the segmentation that minimises a Gaussian cost plus the modified BIC penalty, with at least five years per segment.
2. For a change in mean the series is first divided by a robust estimate of its standard deviation (the median absolute deviation of first differences divided by √2), because the Gaussian mean cost assumes unit variance; detections are then independent of the units and of the overall spread. The mean-and-variance cost estimates each segment's variance and needs no scaling.
3. Because the detector assumes independent Gaussian noise, the result is reported in three views: the series itself, the linearly detrended series, and the series detrended and AR(1)-prewhitened with ρ from the trend estimator. A candidate that survives prewhitening is not explained by persistence alone; one that appears only in the raw series may be.
4. Segment means, standard deviations and the reduction in within-segment squared error are reported, with the first year of each new segment marked.

Uncertainty. Change-date stability, conditional on the step model: the residuals about the fitted segment means are described by an AR(1) model (bias-corrected ρ), 499 series are simulated from the segment means plus that model, PELT is run on each, and the table reports for each candidate the share of replicates that place a change within two years of it, the 2.5 to 97.5 percentile range of the nearest refitted change, and how often the replicates select more or fewer changes than the original. A linear trend with no step yields several steps, each at high stability, because stability conditions on the step fit; it is not a test against no change. Use the Pettitt method for a calibrated single-change test.

Settings. Target: mean, or mean and variance.

Requirements. 20 consecutive complete years.

Reading the result. A candidate with high stability and a narrow refitted range is well located; a candidate found in half the replicates, or one accompanied by many extra changes in replicates, is weakly supported. Serially correlated variation can itself resemble a step; compare the prewhitened view.

Limits.

• The stability measures condition on the fitted segmentation and are not a test against no change.
• The MBIC penalty assumes independent Gaussian residuals, which annual means only approximate; the robust scale MAD(Δy)/√2 used for the mean cost is biased low under persistence, which weakens the penalty in the raw view.
• Calibration: on 300 null AR(1) series of 35 years the series view found at least one change in 0.02, 0.18, 0.52 and 0.88 of series at ρ = 0, 0.3, 0.5 and 0.7; the prewhitened view found none. Candidates in the raw view of a persistent series are therefore expected without any step.

Scientific reading. [29] PELT algorithm; [30] climate/Pacific variability examples separating shifts, trends and memory. SAOCE’s MBIC, three-view and AR(1) sieve-refit settings remain local choices.

Additional method and implementation sources. Killick, Fearnhead and Eckley (2012), Optimal detection of changepoints with a linear computational cost, JASA; Killick and Eckley (2014), changepoint: An R package for changepoint analysis, Journal of Statistical Software.

Single shift (Pettitt)

Question. The single most likely date at which the daily anomaly distribution shifted, with a test that respects persistence.

Data. Observed daily anomalies, at least 3,650 of them, with at least five calendar years on each side of a candidate.

Method.

1. The Pettitt statistic Uₜ compares the ranks of the anomalies before and after each day; the candidate is the eligible day with the largest |Uₜ|.
2. The same statistic and bootstrap are computed on the anomalies after removing a linear trend in time. A gradual trend registers as a mid-record shift under the stationary null. A candidate that remains after detrending is a step beyond the trend; one that does not remain is not distinguishable from persistent variation or a trend. Both results are reported.
3. The figure shows monthly mean anomalies for readability; the test runs on the daily values.

Uncertainty. A search-adjusted block bootstrap: 499 resamples of the daily anomalies in moving blocks of three calendar years (1,095 days), laid on the calendar so that absent days stay absent. For each resample the largest eligible |Uₜ| is recorded, so the p-value is the share of resamples whose maximum reaches the observed maximum. Persistence up to three years is in the null, and the search over dates is accounted for.

Requirements. Ten years of daily anomalies.

Reading the result. A small p-value supports one shift somewhere in the record at about the marked date; the date itself has no interval.

Limits.

• The detrended variant removes only a linear trend; a smooth nonlinear change can still register as a shift.
• Persistence longer than three years is not in the null.
• A single-change test cannot describe two or more shifts.
• Calibration: on 60 simulated 35-year null series with annual AR(1) 0.2 and daily AR(1) 0.7, the stationary test rejected in 0.20 and the detrended repeat in 0.00, while a 0.4 °C step was found and dated within two years in 0.98 of series. Under that much persistence the stationary p-value remains anti-conservative; the detrended repeat is the stricter reading.

Scientific reading. [31] original single-change test; [32] ocean regime-shift methods context. The stationary-null block calibration and detrending comparison are SAOCE adaptations.

Additional method and implementation sources. Pettitt (1979), A non-parametric approach to the change-point problem, Applied Statistics; Künsch (1989), The jackknife and the bootstrap for general stationary observations, Annals of Statistics.

Sequential regime shifts (STARS)

Question. Rodionov's sequential t-test for regime shifts in annual means, as commonly used in marine ecosystem studies.

Data. At least 25 consecutive complete annual means.

Method.

1. The pinned reference R implementation of Rodionov's STARS (Stirnimann et al.), run with a ten-year cut-off, Huber weight 1, nominal p = 0.05 and MPK pre-whitening with five-year subsamples to remove red noise before testing.
2. The regime shift index and the regime means in original units are returned; a non-zero index marks the first year of a new regime.

Uncertainty. The nominal p is an algorithm setting of the sequential test, not a multiplicity-adjusted probability for the detected shifts.

Requirements. 25 consecutive complete years.

Reading the result. A shift within the last ten years is provisional because the regime after it is incomplete. The first year is lost to pre-whitening.

Limits.

• Results depend on the cut-off and the pre-whitening choice.
• No shift-date interval or cause is claimed.

Scientific reading. [33] original sequential algorithm; [34] direct STARS application to the Bering Sea.

Additional method and implementation sources. Rodionov (2004), A sequential algorithm for testing climate regime shifts, Geophysical Research Letters; Rodionov (2006), Use of prewhitening in climate regime shift detection, Geophysical Research Letters; Stirnimann, Conversi and Marini (2019), Detection of regime shifts in the environment: testing STARS using synthetic and observed time series, ICES Journal of Marine Science.

One change in slope

Question. Whether a single bend describes the record better than one straight line, and where that bend sits.

Data. At least 15 consecutive complete annual means, with five on each side of the break.

Method.

1. A continuous broken-stick regression from the R package segmented: one line before and one after a breakpoint ψ, meeting at ψ. Seven starting values spread over the admissible years (the fifth to the fifth-last) are tried and the fit with the smallest deviance is kept.
2. The two slopes are reported per decade with the common regression report.

Uncertainty. An AR(1) sieve bootstrap: the residuals about the fitted broken stick are described by an AR(1) model (bias-corrected ρ), 199 series are simulated from the stick plus that model, and the breakpoint and both slopes are refitted each time with the same estimator, giving 95% percentile intervals for the break year, each slope and the change in slope; the number of successful refits is reported. When the break interval covers 80% or more of the admissible range the summary says that the data do not constrain the break date.

Requirements. 15 consecutive complete years.

Reading the result. A narrow break interval with clearly different slopes before and after is the pattern of a real change in rate. The intervals are conditional on a one-break model: they do not test whether a break is needed at all.

Limits.

• Compare with the GAM derivative band, which asks a similar question without fixing the number of bends.

Scientific reading. [35] unknown-breakpoint regression; [32] marine change-detection context. SAOCE’s conditional bootstrap is documented above.

Additional method and implementation sources. Muggeo (2003), Estimating regression models with unknown break-points, Statistics in Medicine.

Multiple changes in slope (Bai–Perron)

Question. How many separate linear pieces the record needs, and their slopes.

Data. At least 20 consecutive complete annual means.

Method.

1. Least-squares segmentation of the regression of SST on year from the R package strucchange, with at least five observations per segment. The number of breaks is chosen by BIC.
2. Each selected segment's slope comes from the trend estimator pw-gls-ar1-v3. A segment of at least ten years carries a Student-t interval and p-value; a shorter segment reports the estimate only, because an interval on five to nine years would not be meaningful.

Uncertainty. Segment slope intervals are conditional on the chosen partition. Break-date stability repeats the BIC selection on 199 AR(1) sieve replicates simulated about the segment fits and reports how often each break recurs within two years, the range of the nearest refitted break, and how often the replicates choose a different number of breaks. BIC is a model comparison rather than a dependence-adjusted test.

Requirements. 20 consecutive complete years.

Reading the result. No break means one slope fits best by BIC; the share of replicates that nevertheless select a break shows how marginal that choice is. Several short segments with alternating slopes usually describe variability rather than structural change.

Limits.

• Serial correlation makes BIC favour more breaks than an independent series would justify; the stability share shows how often the chosen number recurs.

Scientific reading. [36] multiple structural breaks; [32] marine change-detection context. Stability frequencies are not post-selection confidence intervals.

Additional method and implementation sources. Bai and Perron (2003), Computation and analysis of multiple structural change models, Journal of Applied Econometrics; Zeileis et al. (2002), strucchange: An R package for testing for structural change in linear regression models, Journal of Statistical Software.

Seasonal amplitude and timing

Question. Whether the annual cycle is growing, shrinking or moving in the calendar.

Data. The observed daily SST of each complete calendar year.

Method.

1. For each year, least squares in R fits a mean plus two harmonics (annual and semi-annual sine and cosine) to the observed days; missing days are simply absent. Phase is day/(365 or 366) of each year and the fitted curve is evaluated on a 365-day grid of equally spaced phase days.
2. From the fitted curve on that grid: the peak-to-trough amplitude and the day of year of the maximum and of the minimum.
3. Timing is unwrapped across years so that a peak moving from late December to early January counts as a few days, not a year. The trend estimator pw-gls-ar1-v3 with its bootstrap-t interval is fitted to amplitude and to the two timings.

Uncertainty. Bootstrap-t slope intervals from the trend estimator for each annual summary. Each year's fit reports its residual SD and a delta-method standard error of the amplitude; that first-stage error is part of the year-to-year scatter about the trend line, so the slope interval includes it, with every year weighted equally.

Requirements. At least ten complete years; a year whose fitted cycle is flat has no timing.

Reading the result. Positive timing slopes mean later in the year. Double-peaked cycles can make the maximum jump between peaks; check the first and last fitted curves shown.

Limits.

• Two harmonics describe a smooth cycle; sharp seasonal fronts are smoothed.

Scientific reading. [41] annual-cycle amplitude/phase analysis; [18] marine seasonal trends; [42] SST phase changes and non-sinusoidal limits. The latter uses a different estimator.

Warm-season onset, end and length

Question. When the water first stays at or above a chosen temperature, when it last does, and for how long.

Data. Observed daily SST in July to June thermal years labelled by the July year, each with at least 90% observed days.

Method.

1. Within each thermal year, find all runs of at least five consecutive observed days at or above the threshold and keep the longest (earliest if tied).
2. Onset is the day number of the first day of that run within the thermal year, with 1 July as day 1; the last day is the day number of its final day; length is their difference. A run that touches a missing day or the thermal-year boundary has an unobserved crossing and that date is censored.
3. The trend estimator pw-gls-ar1-v3 with its bootstrap-t interval is fitted to onset, last day and length over the eligible years.

Uncertainty. Bootstrap-t slope intervals from the trend estimator.

Settings. Threshold temperature (default 18 °C).

Requirements. At least ten eligible thermal years for each trend.

Reading the result. A year with no five-day spell is missing, not a season of zero length. Negative onset slopes mean the season starts earlier.

Limits.

• This is thermal phenology of the water, not a biological or habitat forecast.
• Results depend strongly on the threshold relative to the local cycle.

Scientific reading. [18] SST threshold timing and summer duration on a continental shelf. Marine application, not validation of SAOCE’s July–June longest-spell rule.

Compare climatological cycles

Question. How the normal annual cycle and its 10th and 90th percentiles differ between the 1991–2020 baseline and a recent window.

Data. The full daily record on a 366-day leap calendar, independently of the analysis interval. The comparison window is at least 20 complete years, by default the latest 20.

Method.

1. Both climatologies are recomputed with heatwave3::ts2clm3, the production detector's own function and parameters: an 11-day pool across years for each calendar day (at least 80% observed), then the mean and the 10th and 90th percentiles, each smoothed with a 31-day circular running mean. As in the detector, the 29 February slot of a non-leap year is filled with the mean of 28 February and 1 March before pooling; that is a climatology convention, not a substituted observation.
2. The differences (comparison minus baseline) are shown for the mean and both percentiles.

Uncertainty. 199 joint resamples: residuals about day-specific linear trends are resampled as whole years from the pooled years, added to the fitted values, and both climatologies are recomputed from each resample; the pointwise 2.5 and 97.5 percentiles of the differences are drawn. Because a recent 20-year window overlaps the baseline, a shared year takes the same resampled value in both climatologies. Source-absent days stay absent in every draw.

Settings. Comparison window start and end years.

Requirements. 27 complete baseline years and 20 complete comparison years, consecutive.

Reading the result. The summary gives the year-averaged difference and names the comparison years that fall outside the baseline, because those drive the difference. The operational event baseline itself is unchanged.

Limits.

• Bands are pointwise; a band excluding zero on many days is not a single global test.
• 199 draws limit the precision of the tails.

Scientific reading. [18] seasonal SST change; [24] dependent resampling; [3] climatological/statistical comparisons. Joint year resampling and shared-year handling remain SAOCE-specific.

Thermal-envelope explorer

Question. How many days each year the regional temperature lay inside a chosen window.

Data. The daily series and an inclusive lower and upper temperature.

Method.

1. Count the observed days inside the window in each calendar year. A year is kept only with at least 90% observed days; the denominator is the full calendar year and missing days are never scaled up.
2. The trend estimator pw-gls-ar1-v3 fits the annual count on year for a slope in days per decade from ten retained years; with fewer, a descriptive OLS slope is shown without interval or p-value.

Uncertainty. The trend estimator's bootstrap-t interval and p-value from at least ten retained years; below that the slope is descriptive and carries no interval or p-value. These Gaussian diagnostics are exploratory for a bounded count.

Settings. Lower and upper temperature.

Requirements. Lower strictly below upper; at least two retained years for a slope and ten for an interval.

Reading the result. Days inside the window of the area-mean series, not a count of cells or an area fraction, and not habitat suitability.

Limits.

• Counts near 0 or 365 saturate and a straight line cannot describe them well.

Scientific reading. [19] marine degree-days and seasonal timing; [21] marine thermal limits. These motivate exposure questions; this explorer counts days and does not yet implement cumulative degree-days or a species-response model.

Additional method and implementation sources. Decision record 0005, section 4.

Changes in temperature variability

Question. Whether the spread of temperatures is changing, within years and between years.

Data. Daily anomalies in each complete year, and complete annual means.

Method.

1. Within-year variability: the standard deviation of the year's daily anomalies (at least 90% of days).
2. Day-to-day change variance: the variance of differences between adjacent observed days (at least 80% of possible adjacent pairs).
3. Between-year spread: the standard deviation of annual means in centred five-year windows of consecutive years.
4. The trend estimator pw-gls-ar1-v3 with its bootstrap-t interval for all three annual summaries, including the overlapping rolling SD.

Uncertainty. Bootstrap-t intervals from the trend estimator, with the sampling standard error of each year's SD reported beside it; that first-stage error is part of the scatter about the trend and so enters the slope interval. Neighbouring five-year windows share four of their five years, so the rolling-SD series is serially dependent; the AR(1) term absorbs only part of that dependence and its interval is approximate.

Requirements. At least ten eligible years per summary.

Reading the result. Greater spread can be relevant to extremes, but a change in spread does not by itself say why event frequency changed.

Limits.

• The rolling SD omits incomplete edge windows.
• The per-year sampling SE of the SD understates the error for persistent daily anomalies, whose effective day count is smaller.

Scientific reading. [39] SST variability across timescales; [13] separating variance and mean effects. SAOCE’s rolling-window and daily-difference estimators retain their own acceptance rules.

Persistence and memory

Question. How long a warm or cool anomaly tends to last.

Data. Daily anomalies in each complete year.

Method.

1. Lag-one autocorrelation ρ₁ of the year's anomalies over adjacent observed pairs.
2. Decorrelation time: the first lag, up to 90 days, at which the autocorrelation falls to 1/e. Pairs at each lag require every intervening day to be observed, and at least 30 pairs.
3. The trend estimator pw-gls-ar1-v3 with its bootstrap-t interval for both annual summaries.

Uncertainty. Bootstrap-t slope intervals from the trend estimator. The large-sample standard error of each year's lag-one correlation, √((1 − ρ²)/pairs), is reported; that first-stage error is part of the scatter about the trend line and so enters the slope interval.

Requirements. Years with at least 90% of days and 80% of adjacent pairs; ten eligible years for a trend.

Reading the result. A missing decorrelation time means no crossing within 90 days, not zero. Persistence is a descriptive property of the series, not a mechanism.

Limits.

• Annual autocorrelations assume stationarity within the year, which the seasonal cycle of variance only approximately satisfies.

Scientific reading. [39] direct SST persistence/decorrelation analysis; [3] autocorrelation and timescales. Search limits and unresolved crossings remain explicit local rules.

Recurring periods and wavelets

Question. Which periods of variation dominate the anomalies, and when.

Data. Complete calendar-month mean anomalies (at least 90% of days), at least 120 months over at least ten years, detrended by a linear fit in calendar time.

Method.

1. A Lomb–Scargle periodogram (lomb::lsp in R, standard normalisation, oversampling factor 4) on lomb's native frequency grid between periods of 0.25 years and the shorter of 20 years and half the record length. It uses the actual months observed; missing months are omitted, not filled.
2. A Morlet wavelet transform (biwavelet::wt, ω₀ = 6) at 40 log-spaced periods from 0.25 years to the shorter of 16 years and half the record length, run separately within each uninterrupted run of at least twelve months, with power normalised by the variance of the detrended series and the cone of influence masked.

Uncertainty. For the periodogram, 199 AR(1) red-noise surrogates with the same missing-month mask and detrending give the local 95% level at each period and a global 95% level for the largest peak; the global peak p-value counts surrogates whose maximum reaches the observed maximum. For the wavelet, each cell has a local threshold from the Gaussian AR(1) red-noise spectrum with two degrees of freedom (Torrence and Compo 1998, equation 16, through biwavelet::wt.sig); the same surrogates are transformed too, and the 95th percentile of their largest power-to-threshold ratio inside the cone is the global level. Dots mark cells above the global level, which allows for the search over all times and scales; the counts above the local and global levels are both reported.

Requirements. 120 complete months over ten years.

Reading the result. The shaded ENSO-like (2 to 7 years), IOD-like (2 to 5 years) and decadal (8 to 20 years) bands are context. Power inside a band does not attribute the variation to that climate mode.

Limits.

• Periods longer than a third of the record are weakly supported; the periodogram is capped at 20 years and the wavelet at 16, both at half the record length.
• Monthly means remove sub-monthly variation by design.
• The global level is calibrated against AR(1) red noise; structured variability that is not red noise can exceed it without being periodic.

Scientific reading. [43] ENSO wavelet tutorial, red noise and edge effects; [44] uneven-time spectral analysis and Monte Carlo significance. SAOCE’s global-search calibration remains separately recorded.

Additional method and implementation sources. Torrence and Compo (1998), A practical guide to wavelet analysis, Bulletin of the American Meteorological Society; Scargle (1982), Studies in astronomical time series analysis II, Astrophysical Journal.

Climate-mode context (one index: ENSO, IOD or SAM)

Question. How the monthly SST anomaly of a selection has co-varied with a large-scale climate mode, and at what lead or lag.

Data. Monthly means of the daily SST anomaly (90% daily coverage) and the provider's monthly index: Niño 3.4 anomaly (NOAA CPC, ERSSTv5, 1991–2020 base), the Dipole Mode Index (NOAA PSL, HadISST) or the Marshall station-based SAM index (British Antarctic Survey).

Method.

1. Pearson correlation between index(t − lag) and anomaly(t) for lags from −max to +max months; positive lag means the index leads.
2. 95% intervals from the Fisher transform with an effective sample size after Bretherton et al. (1999), N (1 − r₁r₂)/(1 + r₁r₂), from the two lag-one autocorrelations, each computed from genuinely consecutive month pairs so that a gap is never treated as an adjacent month.
3. A Bonferroni threshold, 0.05 divided by the number of requested lags, including unsupported ones, is reported beside the p-values.

Uncertainty. Approximate pointwise intervals and p-values, not a simultaneous band. Effective N is capped at observed pairs; intervals need N > 3 and three adjacent monthly pairs. The strongest lag is selected after searching. In 400 stationary AR(1) simulations per setting, coverage for r = 0.4 was 0.9425–0.9825 and family null rejection over 25 lags was 0.0025–0.065; this does not validate trend-confounded associations.

Settings. The index, one at a time (ENSO by default), and the maximum lag (0 to 24 months). Run the method again with another index to compare.

Requirements. At least 36 paired months with variation at each lag; whole SST months need 90% daily coverage. Both lagged months stay inside the selected interval; unsupported lags stay gaps.

Reading the result. A strongest lag describes timing of co-variation, not a mechanism. A shared trend or a common seasonal residual can inflate r; several modes co-vary with each other.

Limits.

• Descriptive only: no causal claim, no regression on several modes, no significance claim beyond the stated intervals.
• Indices are provider products on their own base periods. SAOCE never fills them; BAS may reconstruct missing station pressures before calculating its dimensionless SAM index. Result tables report raw monthly values, coverage and provider provenance; revisions invalidate cached results.
• The SAM index starts in 1957, the DMI in 1870 and Niño 3.4 in 1950; the SST archive starts in January 1982.

Scientific reading. [14] climate-mode associations with marine heatwaves; [15] dependence-aware environmental correlations in fisheries; [50] the effective sample size for a correlation between two autocorrelated series. SAOCE’s lag search and multiplicity correction are stated above.

Additional method and implementation sources. Bretherton et al. (1999), The effective number of spatial degrees of freedom of a time-varying field, Journal of Climate.

Marine heatwaves

Question. The detected heatwaves of the selection, their metrics and their evolution.

Data. The full-record daily series of the selection, run through the pinned heatwave3 detector with the 1991–2020 baseline.

Method.

1. Detection follows Hobday et al. (2016): a day-of-year climatology and 90th percentile from an 11-day window over 1991–2020, the threshold smoothed by a 31-day running mean; an event is at least five consecutive days above the threshold, and two events separated by at most two days are joined. Missing days are never padded.
2. Categories follow Hobday et al. (2018): the threshold minus the climatology is one unit; Moderate, Strong, Severe and Extreme are departures above one, two, three and four units.
3. Each event carries duration, onset, peak and end dates, mean, maximum and cumulative intensity (relative to the climatology, the threshold and in absolute terms), onset and decline rates, category and the fraction of days in each category.
4. The default figure shows selectable event lollipops with height given by the chosen metric; the regional workspace places each lollipop at the event start date, and the linked point chart at the peak date, held within the overview dates. Selecting an event opens its SST, climatology and threshold evolution. Daily threshold departure is a separate optional plot; overlay is opt-in.

Uncertainty. None: the detection is deterministic for the fixed parameters.

Settings. The metric shown on the lollipops; filters on duration, intensity, category and provisional status; the overview and local date search select overlapping events and keep their full values. Event-metric trends assign events by peak date.

Requirements. A climatology for the selection; events in the last seven days are provisional.

Reading the result. A regional event is an event of the area-mean SST, not a count of cells in an event. The event bar on the map shows the share of ocean area in an event instead.

Limits.

• The fixed baseline means warming alone raises event frequency; this is a documented property of the definition, not an artefact.
• Daily threshold exceedance does not by itself establish a detected event. Diamonds mark events extending outside the overview; peaks outside it are displayed at the nearest boundary.

Scientific reading. [1] event definitions and metrics; [25] intensity categories; [2] observed ocean trends.

Additional method and implementation sources. Hobday et al. (2016), A hierarchical approach to defining marine heatwaves, Progress in Oceanography; Hobday et al. (2018), Categorizing and naming marine heatwaves, Oceanography; Schlegel and Smit (2018), heatwaveR: A central algorithm for the detection of heatwaves and cold-spells, Journal of Open Source Software.

Marine cold-spells

Question. The detected cold-spells of the selection.

Data. As for heatwaves, with the 10th percentile threshold.

Method.

1. The same detector with coldSpells enabled: at least five consecutive days below the 10th percentile, gaps of at most two days joined. Plotted exceedance is the threshold minus SST, so positive values are colder than the cold threshold. Intensity metrics keep their recorded negative signs.

Uncertainty. None.

Settings. As for heatwaves.

Requirements. As for heatwaves.

Reading the result. Categories count departures below the climatology in units of the climatology-minus-threshold difference.

Limits.

• Cold-spells become rarer under a fixed baseline as the region warms.

Scientific reading. [48] marine cold-spell definitions and trends.

Additional method and implementation sources. Schlegel et al. (2021), Marine cold-spells, Progress in Oceanography.

Trends in event metrics

Question. Whether events are getting longer, more intense or more severe.

Data. The full-record event catalogue. Each event belongs to the period containing its peak date; a period is a calendar year, one calendar month or an austral season (DJF labelled by the January year). A period-year needs at least 90% valid detector days.

Method.

1. The period-year value is the unweighted mean of the chosen metric over the events peaking in it. Periods without events are missing, not zero.
2. The trend estimator pw-gls-ar1-v3 is fitted to the period-year means over the complete period-years in the interval.

Uncertainty. The trend estimator's bootstrap-t slope limits and p-value.

Settings. Event type, metric and period.

Requirements. Ten valid period-years.

Reading the result. A duration slope in days per decade describes the mean event, not the total event days; use event counts for frequency.

Limits.

• Category, fraction and rate metrics are bounded or ordinal; Gaussian limits are exploratory for them.
• Few events per year make period means noisy.

Scientific reading. [1] event metrics; [2] frequency/duration trends; [27] smooth-trend methods. Count and Gaussian mean-metric inference remain distinct.

Additional method and implementation sources. Decision record 0010.

Rapid extreme thermal transitions

Question. Describe rapid MHW/MCS reversals at fixed ocean locations using AJ Smit’s unpublished concept, and compare them with broader fixed-interval warming/cooling rates.

Data. Authoritative native-cell MHW/MCS categories and SST, plus approved 1991–2020 daily seasonal means for anomalies. Rectangle, polygon, reporting-region and coastal-buffer supports follow occupancy area weights and masks.

Method.

1. At the same cell, elapsed days run from the last categorised original-type day to the first subsequent opposite-type day. Neutral days can intervene. Returning to the original type updates departure. Both original endpoints must reach the selected minimum category; stronger earlier/later days never replace them.
2. The maximum n is 1–90 days, default 7. SST and both category archives must be observed throughout the preceding n days plus arrival, with water and no ice. Dates select arrivals. The final seven event-source days are provisional; annual recurrence requires complete stable years with 90% eligible days.
3. Report cell-transition counts, unique affected area per direction, and area-weighted elapsed time, signed SST/anomaly changes and rates. Anomaly means have their own contributing count and area. Trajectories contain observed daily values from departure to arrival, aligned on arrival day zero; each lag has its own sample count and area.
4. Persistence counts consecutive categorised days at each endpoint, not canonical event duration. Complete and censored spells are separate. Departure history ends at the read boundary or a gap. Arrival follow-up stops at an observed end, missing data, the archive edge or 30 days; censored observed durations are lower bounds.
5. Sensitivity crosses n=1,3,7,14,30,60,90 and the selected n with minimum endpoint categories I–IV, using identical fully observed 90-day histories. Its counts can differ from the main result because its observation support is stricter.
6. A separate 1–90-day rate interval k gives endpoint SST/anomaly differences divided by k for all continuously observed SST windows, including non-events. Positive and negative rates are summarised separately. Annual figures need complete stable years with 90% covered days; each included day needs 90% variable-specific ocean coverage.

Uncertainty. Descriptive results only. No confidence intervals, significance tests, formal severity scores or ecological impact claims. Overlapping windows and neighbouring cells are dependent.

Settings. Direction, maximum transition days n, minimum category at both original endpoints, and the independent fixed rate interval k. Apply changes explicitly. Explore this result selects recurrence, trajectories, annual warming/cooling rates and sensitivity. Click an annual recurrence point, or choose a Transition year, to open area evolution and spatial heterogeneity. The area view shows daily MHW/MCS occupancy, transitioning area, and cell-level maps with area-weighted spatial percentiles. Inspect individual transitions below using the paginated selector; the curve shows original endpoints, SST, climatology and thresholds. Download the separate drill-down JSON for these source values. Both directions and every diagnostic's observation support appear in detailed tables and downloads.

Requirements. Native SST and paired event categories for transitions. Fixed-interval rates need continuous observed SST; anomaly metrics additionally need the same-cell seasonal reference. Missing observations and references are not filled. Context is read automatically up to 90 days before and 30 days after the selected interval, without including later arrivals.

Reading the result. A negative MHW-to-MCS rate means cooling. Cell-transition counts are not counts of independent ocean events. Earlier trajectory positions include only longer transitions. A censored persistence value is an observed lower bound. Broader rate summaries include non-event windows and are independent of the endpoint filter.

Limits.

• Category-zero joined days are neither endpoints nor part of consecutive-category persistence. Canonical event detections are unchanged.
• Only the first 20,000 cell transitions are retained in arrival-date order. Truncation is explicit; all aggregates, trajectories, persistence and sensitivity use every eligible observation.
• Raw SST differences include seasonal progression; anomalies use the fixed native 1991–2020 seasonal mean. Each metric retains its own count and area denominator. Observed sign-specific rate summaries are not extrapolated to missing ocean area.
• Moving-patch tracking is separate work under S18. Severity definitions and inferential calibration remain research; neither is claimed by the fixed-cell suite.
• A first full-record LME calculation can take several minutes. Direction changes reuse the cache; changes to n, endpoint category or rate interval require a new calculation.

Scientific reading. [1] warm-event and [48] cold-spell definitions only. No selected paper validates the owner’s unpublished same-cell last-day-to-first-day transition definition or severity metrics.

Additional method and implementation sources. Unpublished concept supplied by AJ Smit; fixed-cell scope confirmed 2026-10-07; Decision record 0016.

Area occupied by marine heatwaves or cold-spells

Question. How much ocean area is affected, for how long, whether occupancy is changing, and how selected regions experience extremes together.

Data. Authoritative daily native-cell heatwave3 event-masked categories, paired with the native SST validity mask. Select a rectangle, imported polygon, reporting region or coastal buffer. Land is excluded from fixed first-day ocean support.

Method.

1. Area is the sum of spherical cell areas. Rectangles use fractional overlaps; polygons use complete cells whose centres fall inside, excluding holes. Percentages use the observed part of that ocean area and require at least 90% of the fixed support to be observed each day.
2. Any is the sum of exact categories I (Moderate), II (Strong), III (Severe) and IV (Extreme). Joined subthreshold days have category zero and are excluded. An event in the regional-mean SST is a separate statistic.
3. Equal-day annual means require complete calendar years with at least 90% valid daily occupancies. Years touching the final seven provisional source days are excluded. At least ten consecutive eligible years are fitted with the trend estimator pw-gls-ar1-v3. Zero-event days and years remain zero.

Uncertainty. The trend estimator's bootstrap-t 95% slope intervals, in percentage points per decade, one per category, under an AR(1) model of the annual residuals with constant variance. No multiple-category adjustment or extrapolation.

Settings. MHW or MCS, category, analysis dates and affected-area threshold (initially 10%, adjustable above 0% to 100%). Apply changes explicitly. Explore this result selects annual occupancy, threshold-day and area-day figures. To compare two to four selected areas, use Chart comparison & downloads → Regional exposure and synchrony.

Requirements. Daily: 90% observed ocean-area coverage. Trends: ten consecutive complete stable years, each with 90% valid days. Short intervals still return daily occupancy.

Reading the result. A slope of +2 percentage points per decade means an annual occupied fraction rising, for example, from 10% to 12% per decade. It is not a relative increase of 2%.

Limits.

• Sparse severe/extreme categories and saturation near 100% can make Gaussian trend intervals unreliable.
• Missing ocean area is not assumed event-free. Coverage and the observed-area denominator must accompany the percentage.
• Any category excludes joined category-zero days; it does not reproduce raw event-flag duration.
• Threshold days count valid days at or above the selected fraction. Area-days sum observed occupied km² over valid days, without filling missing dates or area; compare coverage alongside totals. Annual plots omit partial, provisional and low-coverage years.
• Combined regions count overlapping native support once. Pairwise comparisons retain the original supports, report overlap, and use only dates with 90% coverage in both. Jaccard is both/either affected days; conditional percentages use the affected days of each conditioning region. Empty denominators are unavailable.
• Raw occupancy correlation requires 30 common days and variation in both series. Shared cells, seasonality, long-term change and serial dependence can contribute. Synchrony is descriptive, without a significance test or causal interpretation.
• The first full-record comparison of large regions can take several minutes. Category/threshold changes reuse cached source reads. Downloaded comparison JSON retains the exact request and provenance; dialogue choices reset on reopening.

Scientific reading. [25] category-specific affected ocean area; [47] spatial extent; [23] spatial event evolution. The fractional-mask occupancy and descriptive synchrony rules are specific to SAOCE.

Additional method and implementation sources. Hobday et al. (2018), Categorizing and naming marine heatwaves, Oceanography; Decision record 0015.

Trends in event counts and event days

Question. Whether events, or days in an event, are becoming more frequent.

Data. Annual counts of events by peak year, or of detector-flagged event days, for at least ten consecutive years with at least 90% valid days. Zero-event years are retained.

Method.

1. A log-link Poisson regression of the count on decade with an offset log(observed days / 365.25), so that the rate is per full year of observation; its slope is the reported estimate.
2. If the Pearson dispersion exceeds 1.5 a negative binomial (NB2) with the same offset is also fitted and reported as the dispersion diagnostic.
3. The rate ratio per decade (1 = no change), its interval and the fitted rate curve with slope-limit curves are reported.

Uncertainty. A block-pairs bootstrap-t: whole (year, count, effort) rows are resampled in three-year moving blocks and the Poisson slope is refitted 1,999 times, so overdispersion and serial dependence are carried by the data rather than by a parametric covariance. The interval is the estimate plus or minus a Student-t multiple of the bootstrap standard error with degrees of freedom equal to the number of blocks minus two, and the p-value uses the same reference. The interval and p-value are reported only from 20 complete period-years: below that the degrees of freedom are two or three and the interval is uninformative, so the rate ratio is shown as an estimate only.

Settings. Event type and quantity (events or days).

Requirements. Ten consecutive complete years with at least one event overall for the estimate; 20 for an interval and p-value.

Reading the result. A rate ratio of 1.3 means about 30% more events per decade over the fitted years; an interval that excludes 1 is a change the data support under the resampling model.

Limits.

• Event-day counts are bounded by the days observed; the log-link curve can exceed that bound near saturation.
• Calibration: in 150-replicate simulations of Poisson and negative-binomial counts (mean 3, slope 0.3 per decade on the log scale) the interval covered the true slope in 0.97 and 0.93 of 35-year series, with a width of 0.46 to 0.64 on the log scale, and in 1.00 and 0.99 of 20-year series, where it is wider (1.5 to 2.2) and constrains the rate ratio per decade only to within a factor of about two to three. Shorter records have fewer blocks, and below 20 years no interval is reported.

Scientific reading. [2] ocean event-frequency trend context; [24] dependent-data block resampling. The effort-offset Poisson/bootstrap-t combination and calibration remain specific to science record 0012.

Additional method and implementation sources. Künsch (1989), The jackknife and the bootstrap for general stationary observations, Annals of Statistics; Decision record 0012, count-model calibration; Decision record 0020, The R analysis runner and the calibrated uncertainty layer.

Accumulated heat stress (degree heating weeks)

Question. Accumulated thermal stress on the map, after the NOAA Coral Reef Watch convention.

Data. Daily SST and the warmest of the twelve 1991–2020 monthly-mean climatology values per cell (the maximum monthly mean).

Method.

1. Hotspot = daily SST minus the maximum monthly mean. Hotspots of at least 1 °C accumulate over a rolling 84-day window; units are °C-weeks.

Uncertainty. None.

Requirements. Served map dates.

Reading the result. A map of the temperature product under a fixed baseline; it is not an observation of coral condition.

Limits.

• The CRW thresholds were developed for tropical reefs.

Scientific reading. [7] NOAA CRW HotSpots and Degree Heating Weeks; [8] reef-scale thermal-stress application.

Additional method and implementation sources. NOAA Coral Reef Watch, Degree Heating Week methodology.

Compare two periods

Question. How much warmer or cooler one span of years is than another.

Data. Complete annual means in two non-overlapping periods of at least ten years each; by default the two halves of the interval.

Method.

1. Differences B minus A of the mean and of the 10th, 50th and 90th percentiles of the annual means.
2. An approximate Welch interval for the mean difference uses an effective sample size for each period, n(1 − ρ)/(1 + ρ) with ρ the bias-corrected lag-one correlation of the demeaned values, and Welch–Satterthwaite degrees of freedom.
3. Every difference carries a p-value from an AR(1) sieve bootstrap: an AR(1) model is fitted to each period's demeaned values, 1,999 replicate pairs of periods are simulated about the pooled mean under the null of no difference, and the p-value is the share of replicates whose absolute difference reaches the observed one.

Uncertainty. The approximate AR(1)-adjusted Welch 95% interval for the mean, and the sieve-bootstrap p-values for the mean and the three percentile differences. The Welch interval is approximate under persistence; the sieve p-values carry the fitted AR(1) dependence of each period.

Settings. Start and end years of each period.

Requirements. Ten complete years in each period, inside the interval, non-overlapping.

Reading the result. The percentiles are of annual means, not of daily temperatures; a change in the 90th percentile of annual means is a change in warm years, not in hot days.

Limits.

• The two periods are treated as independent of each other.
• Four contrasts are reported without joint adjustment.
• A p-value cannot go below 0.0005 with 1,999 replicates.
• Calibration: on 300 null series of 15 + 15 years the sieve p-value for the mean rejected in 0.08 (ρ = 0) and 0.09 (ρ = 0.5) of series, and the Welch interval excluded zero in 0.07 and 0.04.

Scientific reading. [46] unequal-variance mean comparison; [24] dependent-data resampling background; [3] ocean sampling/statistical context. SAOCE uses an AR(1) sieve rather than blocks; annual quantile contrasts are a separate statistic.

Additional method and implementation sources. Decision record 0020, The R analysis runner and the calibrated uncertainty layer.

Compare two selections' trends

Question. Whether one place is warming faster than another.

Data. The annual means of two selections on their common complete years, at least ten.

Method.

1. The paired difference B − A is formed on exactly the same years and its trend is fitted with the trend estimator pw-gls-ar1-v3 and its bootstrap-t interval.
2. The slopes of A and B are fitted separately on the common years for comparison. Because each series carries its own AR(1) estimate, the paired slope need not equal the difference of the two separate slopes.

Uncertainty. The bootstrap-t interval of the paired difference series, which keeps both the serial dependence and the correlation between the two selections. Treating two separate slope intervals as independent would overstate the uncertainty when the selections co-vary.

Requirements. Two selections and ten common complete years.

Reading the result. A difference interval excluding zero means the rates differ; the separate slopes shown here are fitted on the common years and can differ slightly from the single-selection cards, which use each selection's own years.

Limits.

• Only two selections at a time.

Scientific reading. [3] ocean regression/covariance context; [24] dependence-preserving uncertainty. The paired B-minus-A estimator is specified in science records 0011/0012, not inferred from separate fits.

Additional method and implementation sources. Decision record 0020, The R analysis runner and the calibrated uncertainty layer.

Compare areas side by side

Question. The same analysis on two rectangles with shared dates and settings.

Data. Two drawn rectangles.

Method.

1. Each series keeps its own weights and coverage; the chosen analysis runs on each.

Uncertainty. As for the chosen analysis on each area.

Requirements. Two rectangles.

Reading the result. Side-by-side fits do not test a difference; use the trend comparison for that.

Scientific reading. [3] ocean sampling and covariance context. Side-by-side plots do not test a difference; use the paired trend comparison for that question.

Compare maps and dates

Question. Two fields on one camera.

Data. Served map layers.

Method.

1. A split display of two dates, two layers, or a day against its 1991–2020 climatology.

Uncertainty. None.

Requirements. Served map dates.

Reading the result. A spatial display, not a temporal test.

Scientific reading. [22] OSTIA source context; [26] baseline interpretation. Map comparison adds no significance test.

Agulhas front position

Question. Locate the strongest SST-gradient candidate along the fixed South, South-East or East transect each day.

Data. Native 0.05° OSTIA SST and water/ice flags. All transects are WGS84 geodesics of exactly 235 km, preserving the inshore endpoint and initial heading supplied by the owner.

Method.

1. Reuse S02 gradient magnitude: one-cell Gaussian smoothing and centred metric differences with a fully valid stencil. Search the fixed ocean support along the transect.
2. Require at least 90% of the fixed eligible samples and three valid positions. Missing dates remain null. Equal maxima have no unique position; boundary maxima and competing peaks at least 90% as strong are flagged.
3. Repeat at Gaussian widths 0.5 and 1.5 cells on the same support. Report the three positions and their range, and inspect any date's gradient profile.

Uncertainty. Smoothing sensitivity is a diagnostic, not a confidence interval. No significance or minimum-gradient threshold is claimed.

Settings. Explore → Agulhas front; choose a named transect and exact dates. Full record selects the available SST interval. Click a dated line or select a date to inspect its profile and map location.

Requirements. The source must cover the fixed transect and complete gradient stencils. A conservative coastal margin is excluded for comparable smoothing support.

Reading the result. Position is distance from the supplied inshore endpoint, not the coast. The strongest thermal gradient can belong to a different front or eddy on another day.

Limits.

• Descriptive SST front candidate, not a validated Agulhas Current boundary, core or transport estimate.
• The full 235 km is searched; no tracking continuity or physical-feature identity is imposed.
• Native-cell resolution limits position precision. Inspect boundary, ambiguity, coverage and sensitivity diagnostics.

Additional method and implementation sources. Scientific decision record 0021; Krug and Penven (2011), New perspectives on Natal Pulses from satellite observations.

Line profile

Question. Temperature along a straight line on a given day.

Data. The displayed layer's grid.

Method.

1. The straight line between the two endpoints is sampled at the nearest cell of the displayed 0.1° grid; distance is great-circle distance along the line. Land and missing cells remain gaps.

Uncertainty. None.

Requirements. Two different endpoints.

Reading the result. A nearest-cell sample, not an interpolation.

Limits.

• Resolution follows the displayed layer grid; it can differ from the product’s native archive.

Scientific reading. [3] spatial sampling of ocean fields. Nearest-cell sampling does not create additional independent observations.

Hovmöller section

Question. Temperature along a line through time.

Data. The card’s native archive cube, 0.05° OSTIA or 0.25° OISST, independently of the displayed layer and date.

Method.

1. The route is straight, or follows the coast when both endpoints lie within 25 km of the same coastline and are at least 10 km apart; a coastal route samples cells within the chosen offshore buffer.
2. Straight sections sample the nearest native cell at each point. Coastal sections aggregate eligible cells in their offshore bins. Both retain daily resolution without temporal smoothing; missing days are gaps.

Uncertainty. None.

Settings. Route, variable (SST or anomaly), number of years and end date.

Requirements. A route inside the archive.

Reading the result. Time runs along the x axis, position along the section up the y axis.

Limits.

• A nearest-cell sampler; cross-shelf gradients narrower than a cell are not resolved.

Scientific reading. [3] ocean time-space analysis. A Hovmöller section is descriptive and supplies no significance test.

Isotherm migration

Question. Where a chosen temperature contour lay in a given month across years.

Data. Monthly mean SST per cell; a month needs at least 90% of its days.

Method.

1. Contours of the monthly mean at 15, 18, 20, 23 or 26 °C are drawn for the chosen month in each year and compared.

Uncertainty. None.

Settings. Isotherm and month.

Requirements. Complete months.

Reading the result. A poleward displacement over years is the visual counterpart of warming; it is not a fitted trend.

Limits.

• Contours of a monthly mean field can fragment near fronts and coasts.

Scientific reading. [5] geographical shifts of isotherms; [6] contour-based thermal displacement. Context for the fixed-month contour comparison.

Ocean regimes

Question. Areas of the sea surface whose temperature statistics are alike, and which of them are most distinct.

Data. Fifteen statistics per 0.25° block of daily SST over 1991 to 2020: mean, annual harmonic, two variabilities, trend, front strength and the heatwave and cold-spell metrics.

Method.

1. Statistics are standardised across blocks and weighted so that each of six groups counts equally; blocks are joined by Ward's method (through 2,000 micro-clusters for the domain) and the tree is cut at 2 to 12 regimes.
2. Distinctness is the distance to the nearest other regime divided by the regime's internal spread.

Uncertainty. None reported; the variance removed by each cut is the only summary of fit.

Settings. Number of regimes, and the area (whole domain, a reporting region or a saved polygon).

Requirements. The published regimes product; inside an area, at least 20 ocean blocks of 0.25°, about 14,000 km².

Reading the result. Nested regimes; the rise of variance removed with the number of regimes guides how many an area supports.

Limits.

• All features derive from one SST product, so they are correlated views of one series, not independent evidence.
• Feature set, standardisation and weights determine the regimes and are fixed.
• Contiguity is not enforced; regimes are statistical summaries, not ecoregions.

Scientific reading. [3] ocean multivariate-analysis context. SAOCE’s feature weights and Ward clustering are specified above; this is not EOF analysis.

Same-day ranking

Question. How the latest day compares with the same calendar day in every archive year.

Data. The area-weighted value for a calendar day across all archive years; 29 February ranks only among 29 Februaries.

Method.

1. The midrank percentile of the latest value among the same calendar day across years, the observation itself included: the share of peers below it plus half the share equal to it, stated with the number of years.

Uncertainty. None; a rank is a data statement.

Requirements. An observed day.

Reading the result. A percentile near 100 in a warming region is expected to recur; it does not imply an event.

Scientific reading. [3] ocean sampling context. A same-day rank describes the available comparison record and is not a return period.