Can We Predict Rossby Wave Breakings Without Running Weather Forecasts?
← Blocking Plots | Northern Hemisphere forecast viewer | Interactive β-plane model
Question. When a large-scale wave on the jet stream “breaks”, the contours of potential vorticity (PV, a measure of the rotation and stability of the air that each air parcel carries with it; unit PVU) fold over like a breaking ocean wave. Rossby wave breaking builds blocking highs (highs that stall for days) and cut-off lows (lows detached from the jet) and steers storms. A breaking is anticyclonic when the fold rolls up clockwise (a trough leaning from south-west to north-east) and cyclonic when it rolls up anticlockwise. Can a new breaking be predicted a day ahead from the analysed flow alone, that is, from the observed state of the atmosphere up to now, without running a weather forecast? Every day this page scores three methods against ERA5, the European Centre for Medium-Range Weather Forecasts’ reanalysis (a reconstruction of past weather from observations).
Methods compared. At 00 and 12 UTC each method marks alarm regions on the map, where it expects a new breaking to start within the next 24 h. (1) U − c matching: the classical criterion that a wave breaks where the eastward speed c of its crests and troughs (the phase speed) equals the eastward wind U carrying the air (a critical line); the region lies within 500 km of the pieces of contour where |U − c| ≤ 2 m s−1. (2) Opus model: a predictor variable computed from the analysed winds and potential temperature on the dynamical tropopause (2 PVU) over the past 60 h, with no forecast; its one set of alarm regions is scored on all three surfaces; the region covers the places where it has dropped to a tenth of its value 1.5–2.5 days earlier (method unpublished). (3) GFS 24-h forecast: the run of the Global Forecast System of the US National Oceanic and Atmospheric Administration (NOAA) started at the issue time, the benchmark that does run a weather model; the region lies within 500 km of the new breakings it forecasts.
Truth and scoring. Breaking is found every 6 h in ERA5 (about five days behind real time) from contours at fixed values on three surfaces near the jet stream, 8–14 km up: PV every 0.5 PVU on the 330-K and 350-K isentropes (surfaces of constant potential temperature, the temperature air would have if brought adiabatically to 1000 hPa, along which air moves when it neither heats nor cools) and potential temperature every 5 K on the dynamical tropopause (the 2-PVU surface that separates the troposphere below from the stratosphere above). The onset of a breaking is the first 6-hourly time it is detected. Its flank is the side of the jet axis it lies on, equatorward or poleward; the jet axis is the latitude of the strongest wind on the surface. A breaking is a hit when an alarm region issued 0–24 h before its onset lies within 1000 km of it, and a miss otherwise; the hit rate is hits divided by breakings. An alarm region with no breaking within 1000 km in its 24 h is a false alarm; the false alarm ratio is false alarm regions divided by alarm regions. For a fair comparison with random guessing, the hemisphere north of 10°N is also divided into about 210 boxes of equal area (about 1000 km across): the false positive rate is the share of the boxes without a breaking that an alarm region touched, and the box hit rate minus the false positive rate is zero for alarms placed at random with the same coverage and positive for alarms with skill.
Method notes
Fields. Hourly ERA5T winds and temperature on ten pressure levels (70–500 hPa) on a 1° grid, 0–90°N, from the Copernicus Climate Data Store; GFS 1° forecasts (00–24 h, every 6 h) of the same variables from the NOAA Open Data bucket. Ertel PV is computed from the pressure-level fields with the same code for both sources and interpolated to 330 K and 350 K; potential temperature is taken where PV first falls below 2 PVU going down from the stratosphere.
Breaking. The field is smoothed with a 3° Gaussian (wider in longitude toward the pole). Contours that circle the pole are traced at the fixed values; a meridian that crosses a contour three or more times lies in a fold; folds whose envelope covers at least 300 square degrees are kept and called anticyclonic or cyclonic from the order in which the contour visits its highest and lowest crossings (after the method of the pvtend package). Folds within 1000 km of each other form one breaking. A breaking is new when no breaking of the same type lay within 1500 km 6 h and 12 h earlier. Its flank is set by the jet axis, the latitude of the strongest wind on the surface (20–70°N), smoothed over ±30° of longitude.
U − c matching. Contours at ten equivalent latitudes (25–70°N; an equivalent latitude encloses the same area as the contour). Every 15° of longitude the phase speed is the eastward shift, within ±30°, that best matches the contour’s undulation 24 h earlier (used only where the correlation reaches 0.5); U is the zonal wind along the contour.
Opus model. The predictor variable is computed on the 2-PVU surface, whose potential temperature air parcels keep when they neither heat nor cool, in local cells 3° of equivalent latitude by 15° of longitude from the analysed winds and potential temperature of the past 60 h; the same alarm regions are scored against the breakings of all three surfaces; the method is not yet published and is not described here.
Tolerance. Alarm regions extend 500 km around what triggered them (except for the Opus model, whose regions are its cells), and a hit needs an alarm region within 1000 km, so a hit only requires the right part of the hemisphere. Large alarm regions are penalised by the false positive rate and by the box score, which is why both are shown.
Scores. Hit rate = hits / breakings; false alarm ratio = false alarm regions / alarm regions; false positive rate = alarmed boxes without breaking / boxes without breaking. Large alarm regions catch more breakings but also raise the false positive rate, so the alarmed area is listed too. The pipeline code is in the site repository (pipelines/rwb_prediction); results are published to the Hugging Face dataset yanxingjianken/rwb-prediction.
Data credits. Contains modified Copernicus Climate Change Service information (ERA5). GFS data from NOAA.