Daily from satellite OLR and the ECMWF ensembles
Tropical waves
The waves that organise tropical rain: Kelvin waves, equatorial Rossby waves, mixed Rossby–gravity waves and the MJO. The spectrum shows how the last 96 days of tropical cloudiness divide among them; the Hovmöllers and trackers show where each one is along the equator and where the forecast takes it. The MJO has its own page, MJO forecast.
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The Wheeler–Kiladis spectrum (Wheeler & Kiladis 1999) sorts tropical cloudiness by how big it is (zonal wavenumber: how many crests fit around the Earth, eastward to the right) and how fast it changes (frequency, cycles per day). Each kind of equatorial wave lives in its own part of that plane, along the curves drawn from shallow-water theory: Kelvin waves eastward and fast, equatorial Rossby waves westward and slow, the MJO eastward at the largest scales and 30–90 days, mixed Rossby–gravity waves in the antisymmetric half. Outgoing longwave radiation between 15°S and 15°N is split into the part symmetric about the equator (Kelvin, Rossby, MJO) and the antisymmetric part (mixed Rossby–gravity).
Raw power always rises toward low frequencies and large scales, so on its own it mostly shows that red background. As in the original paper, each spectrum is divided by a background: the mean power of every 96-day window in the satellite record, heavily smoothed so that only its broad shape remains. Top row: the record mean over that background, the waves that are there on average. Bottom row: the last 96 days over the same background, what is active now. Only bins whose excess is statistically significant (chi-square, Benjamini–Hochberg false discovery rate 10 %) are shaded; the record mean is credited only with the record's independent length, not with the overlap of its windows. Because a single 96-day window has few degrees of freedom per bin, each panel also tests the classic wave bands (the Wheeler–Kiladis filter regions: Kelvin, n=1 equatorial Rossby and MJO in the symmetric half, mixed Rossby–gravity and n=0 eastward inertio-gravity in the antisymmetric half) as a whole: band-summed power over band-summed background, chi-square, Benjamini–Hochberg over the five bands. Significant bands are outlined (blue dashed) and their ratio listed; a band can be significantly active while no single bin is. Each grid point's mean and trend over a window are removed first, so a standing anomaly (the seasonal cycle, or one an El Niño keeps over the central Pacific) does not appear. The record is short (from 2024) next to the 18 years WK99 used, so the top row will sharpen as the archive grows; the background is rebuilt from it.
NASA CERES FLASHFlux daily gridded TOA longwave flux from NOAA-20 (FLASH_TISA_NOAA20, 1°; NASA Langley ASDC), about four days behind, archived daily from 2024 · method as NCL wkSpaceTime: 96-day windows (60-day overlap for the background), mean and trend removed, 10 % taper, symmetric/antisymmetric split, power summed over latitude, 1-2-1 smoothing · updated daily
A longitude × time Hovmöller of deep convection along the equator. NOAA's interpolated-OLR product ended in 2022, so this derives an OLR proxy in real time from the GMGSI global longwave-IR satellite mosaic: the IR brightness temperature (cold cloud tops) is converted to outgoing longwave radiation, and the 5°S–5°N zonal mean is stacked over time. Yellow to red is low OLR (deep convection); blue is high OLR (suppressed or clear sky). An eastward (top to bottom-right) tilt is the MJO propagating east; convection parked at the dateline reflects the El Niño-shifted warm pool. Newest day at the bottom.
NOAA GMGSI longwave-IR global mosaic · McIDAS T_b + Ohring-Gruber OLR · 5°S–5°N daily mean
A longitude × time Hovmöller of the equatorial outgoing-longwave-radiation (OLR) anomaly, averaged 5°S–5°N around the globe. OLR is derived in real time from the GMGSI longwave-IR mosaic (McIDAS brightness temperature to OLR), with the anomaly taken against NOAA's interpolated-OLR daily climatology (1979–2022). The shaded field is the total anomaly: green is low OLR (deep convection), brown is high OLR (suppressed).
Each overlaid component is isolated from that anomaly field and contoured at its convective (solid) and suppressed (dashed) phase. Kelvin, MJO and equatorial Rossby are Wheeler–Kiladis wavenumber–frequency bandpass filters of the anomaly (2-D FFT in longitude and time): Kelvin is eastward wavenumber 1–14, period 2.5–30 d, equivalent depth 8–90 m; MJO is eastward wavenumber 1–5, period 30–96 d; ER is westward wavenumber 1–10, period 9.7–48 d. Low-frequency is a 120-day Lanczos low-pass in time with the zonal mean removed.
GMGSI longwave-IR proxy · Wheeler–Kiladis k–ω filtering (eq. depth 8–90 m) · climatology NOAA interp-OLR 1979–2022
Each wave isolated in its own panel — the Kelvin-filtered (5°S–5°N) and equatorial-Rossby-filtered (15°S–15°N, n=1) OLR anomaly as shading — with the active enhanced-convection packets tracked: the band's recent phase speed is fitted by day-to-day lag correlation of the filtered field, today's packet centres are located, and each characteristic is extrapolated ahead at that speed (dotted line). Below the dashed today-line the shading is a true forecast: the AIFS-ENS ensemble-mean precipitation (as a pseudo-OLR, standardized against an ERA5 1991–2020 band climatology) is appended to the record and run through the same Wheeler–Kiladis filter, so the wave field continues with the model's dynamics — where the dotted constant-speed line and the model streaks agree, confidence in the arrival time is high.
Same GMGSI OLR proxy + Wheeler–Kiladis filters as above · phase speed from lag-1-day circular cross-correlation (last 15 days) · forecast strip: AIFS-ENS ens-mean precip pseudo-OLR, identically filtered (falls back to constant-speed extrapolation if no cycle is cached)
A convectively coupled Kelvin wave is an eastward-moving pulse of tropical convection, 10–20 m/s (roughly 1,000–1,700 km a day), that crosses a basin in about a week. Its clearest large-scale footprint is in 200 hPa velocity potential: upper-level divergence (green) over the active, rainy phase and convergence (brown) over the suppressed phase. This tracker filters that field to the Kelvin band and draws where the waves are, through the analysis and the AIFS-ENS forecast.
Map, day by day: the Kelvin-filtered anomaly, ten days of analyses then each forecast day to day 15; a K marks each active crest on the equator, and grey contours give the unfiltered anomaly (the MJO and the El Niño background) for context. Along the equator: the same field averaged 5°S–5°N as a Hovmöller, time running down; a Kelvin wave is a green streak tilting down to the right, and the forecast carries each streak across the analysis line.
The forecast is the 50-member ensemble mean, so a wave the members place differently fades with lead rather than being shown with false confidence. Filtering needs a record, so the forecast is joined to the analyses and the end of the record is padded with a ramp to zero; the last forecast days therefore read weaker than they may be. Poleward of 15° the filtered field is faded out: Kelvin waves are trapped near the equator and what the filter finds there is not one. The OLR-based trackers alongside it show the same waves in observed cloudiness.
ECMWF AIFS-ENS open data (CC BY 4.0): 0-h analyses (00 and 12 UTC, averaged per day) and the ensemble-mean u, v at 200 hPa to day 15 · velocity potential by spherical harmonics (lmax 42) · anomalies against ERA5 1991–2020 with its trend · Kelvin band: eastward wavenumbers 1–14, periods 2.5–20 days, equivalent depths 8–90 m (Wheeler & Kiladis 1999) · updated each 00/12Z cycle
Below the surface, El Niño travels in oceanic Kelvin waves. A westerly wind burst in the western Pacific launches a downwelling wave: a bulge of warm water, a few centimetres of sea level and tens of metres of thermocline, that runs east along the equator at about 2.5 m/s, crossing the basin in roughly two months, and warms Niño-3 and the South American coast when it arrives. Easterly surges launch the cold, upwelling mirror image. Satellite altimetry sees each wave as a sea-level bump moving east.
Along the equator (left panel): sea level anomaly 2°S–2°N, with the Kelvin-band part in black (eastward, 1.5–3.5 m/s, 15–150 days); waves are streaks sloping down to the right. Each crest in the basin today is followed back through the record to measure its own speed, then projected east (dashed) to Niño-3 (120°W) and the coast (90°W), with the arrival dates listed underneath. Right panel: the 10 m zonal wind anomaly along the equator that launches them, observed then forecast. The broad red field is the El Niño itself, which the filter removes; the Kelvin part is a few centimetres riding on it.
Map: the same sea level over 15°S–15°N every second day for the last 200 days, with each crest marked on the equator. The arrival dates assume a wave keeps its speed and strength; a new wind burst, or the wave reflecting and dispersing near the coast, changes them.
Sea level: NOAA CoastWatch blended altimetry (Sentinel-3A/B, CryoSat-2, Jason-3, SARAL), daily, sampled at 0.5°, anomaly against its own 2017–2025 mean, trend and seasonal cycle · wind: NCEI Blended Sea Winds v2, then AIFS-ENS 0-h analyses, then the AIFS-ENS 50-member mean forecast (ECMWF open data, CC BY 4.0); anomalies against ERA5 1991–2020 · updated each 00/12Z cycle; altimetry runs one to two days behind