Help and methods

Wind–SST relationships

Use the Wind–SST relationships section of the map workspace to examine coincident long-term changes, the delay between wind forcing and SST response, individual forcing episodes and nonlinear relationships. Every result names its observed support, dates and model assumptions.

One selection per card

1. Under Wind–SST relationships, choose Trends, Lagged response, Forcing events or Coupled GAM. This opens Add Wind–SST analysis.
2. Choose Point, Area, Coastal buffer or Ocean regime. A point needs one map click; an area needs two opposite corners; a buffer needs two coastal endpoints and an offshore width. Existing selection reuses a point, area, imported polygon or other selection already open in the workspace.
3. The new card identifies its selection as W1, W2, W3 or W4. Review the wind metric, SST response, dates and month or season, then Run analysis. For alongshore stress, supply the coastline bearing clockwise from north.
4. Use Add Wind–SST card to compare up to four selections. Each card retains its own settings and result. Arrange, Dock, Minimise and individual resize/close controls use the common workspace. Matching daily series share their date cursor; dates and model settings remain independent.

Change selection replaces only that card’s spatial support and requires a fresh analysis. Changing a metric or date also requires a rerun. Adding or closing another card keeps completed results intact unless it removes a reference used for coastal-minus-offshore SST. For that response, choose another open selection or reporting region as the explicit offshore reference.

Analyse an ocean regime

1. In Add Wind–SST analysis, choose Ocean regime, then Choose ocean regime.
2. Use Within to choose an LME, an open area/coastal buffer, a saved region or the whole classification domain. Choose the number of regimes.
3. Select Use regime in the row you want. Its analysis card opens with that regime as the fixed selection. Review settings and Run analysis.

The analysis retains every mapped part and hole of the chosen regime and selects ERA5 ocean-cell centres inside that geometry. Whole domain in the picker defines where the classification was made; the coupled analysis uses only the selected regime. The card and JSON identify its number, classification area, cut and source generation. The reported matched ocean area can differ from the classification’s area because the wind and regime grids have different cell centres.

Regimes are defined from SST statistics. Relationships within them are exploratory and conditional on that classification; selecting a regime does not provide an independent test that wind caused its thermal characteristics. The mapped polygons already omit small enclaves according to the classification settings.

What is being compared?

SST is averaged onto the 0.25° ERA5 ocean cells in the selection. Wind is not interpolated into independent 0.05° observations. Both area means use the same observed cells and spherical ocean-area weights, with at least 90% coverage. Missing days remain gaps. A point represents the matched ERA5 cell, not the original single SST pixel. Interim IFS forecast days shown on the map are excluded; these analyses use ERA5 and flagged preliminary ERA5T days only.

Wind metrics include scalar speed, maximum hourly speed, steadiness, stress components/magnitude and curl. Alongshore and cross-shore stress depend on the bearing you supply. Trailing sums require every constituent day; units include days. Direction in degrees is not regressed. SST responses are temperature, backward temperature change, or primary minus offshore-reference temperature.

Trends

Linear GLS and GAM fits use the same complete annual, month-within-year or seasonal means. Each period needs 90% paired daily coverage; at least ten period-years are required. DJF is labelled by its January/February year. Linear slopes are per decade. GAM mean-curve limits are pointwise; the derivative limits are simultaneous over the displayed year grid. Separate trends show coincident change and do not demonstrate wind attribution.

Lagged response and spatial variation

Positive lag means wind precedes SST. A fitted linear trend and three annual harmonics are removed before correlation. This adjustment requires 60 paired observations spanning two years. 399 calendar-year bootstrap resamples give a 95% simultaneous band over the displayed lag family, drawn only when at least 20 calendar years are represented; with fewer years the correlations are shown without limits and the result states why. The coverage of the band depends on the number of represented years: in a null simulation over lags ±7 it excluded zero somewhere in 27.5% of 8-year records, 13.7% of 12-year records and 5.3% of 35-year records. The band does not adjust for trying many different areas, metrics or periods. Correlation requires 30 pairs.

The spatial figure uses one fixed chosen lag in each ERA5 cell. It reports pair counts and the fraction of supported ocean area with a negative relationship. This is a descriptive account of heterogeneity, not a cellwise significance map. It can reveal opposing responses that disappear in an area mean.

Forcing events and relaxation

Default episodes are two or more days above the 90th percentile of the selected forcing score. Choose positive/high or negative/low forcing, threshold, minimum duration and response window explicitly. These are wind-forcing episodes, not a storm or marine-heatwave classification. A local upwelling interpretation requires a reviewed coastline bearing and favourable direction.

The composite shows adjusted SST response relative to the day before onset, with seven preceding days and a default 14 following days. Only fully observed, non-overlapping windows are retained. Individual episodes report duration, integrated forcing, relaxation, response magnitude and timing. Relaxation reaching a gap or the record end is censored. Pointwise event-year bootstrap limits require ten windows across five years. The event selector opens paired wind/SST evolution figures.

Coupled GAM

Compare three models on exactly the same dates: season and long-term time alone, then linear wind response distributed across lag days, then a nonlinear wind-by-lag response. The nonlinear model can also let coupling vary over time or the seasonal cycle. At least 730 complete daily histories spanning eight years are required. Lag zero is included. The lag dimension is smoothed by a basis of at most five functions, so the lag surface shows a smooth lag profile and does not resolve single-day structure; a response confined to one lag is spread over its neighbours.

Five chronological blocks are withheld in turn with at least a 30-day surrounding buffer. Each model is refitted to the remaining days. Compare held-out RMSE, where lower values indicate better prediction. These tests include interpolation and endpoint extrapolation; they do not represent operational forecasts.

The response curve compares sustained forcing with sustained median wind. The strength-by-lag figure changes one day of a median history. Changing coupling compares sustained 90th- and 10th-percentile histories. These are conditional model contrasts; some such histories may be uncommon. Approximate pointwise intervals condition on estimated smoothing and AR(1), and omit model-selection uncertainty and unmodelled dependence.

Check residual autocorrelation, effective degrees of freedom and concurvity, which measures overlap between model terms. The card flags substantial residual dependence, strongly overlapping terms and AR(1) near its fitted boundary. A better fitted curve alone is insufficient evidence; inspect the withheld-block performance.

Downloads and reproducibility

Each figure uses the shared format, physical size and resolution settings in Setup. The evidence disclosure contains source generations, exact support, diagnostics, matched daily CSV and a complete JSON result with every setting and fitted output. The JSON also contains the complete wind-by-lag surface and cell statistics.

Method sources

Implementation definitions are in scientific record 0018. Statistical foundations include mgcv large-data GAMs and AR(1), matrix-predictor lag histories and Gasparrini (2011), distributed-lag linear and nonlinear models. SAOCE uses mgcv directly; these references do not independently validate its forcing-event thresholds.