Equatorial Waves and Tropical Cyclogenesis

1. Equatorial Waves and Tropical Cyclogenesis Carl J. Schreck, III University at Albany

2. Equatorial Waves • Wheeler & Kiladis (1999) and others have shown the importance of equatorial wave in tropical convective variability • The Madden–Julian Oscillation (MJO) • Kelvin waves • Equatorial Rossby (ER) waves • Mixed Rossby-gravity (MRG) waves • Tropical Depression (TD-type) disturbances Spectrum of TRMM multisatellite precipitation analysis Eq–15°N, May–Nov, 1998–2007, divided by a red background following Roundy & Frank (2004)

3. Influences of Equatorial Waves on Tropical Cyclone (TC) Genesis • Equatorial waves can modulate the background conditions for cyclogenesis (e.g., Liebmann et al. 1994; Bessafi & Wheeler 2006; Frank & Roundy 2006; Camargo et al. 2009) • Convection • Low-level vorticity • Low-level convergence • Vertical wind shear • Mid-level relative humidity • Low-level confluence associated with the MJO can also amplify higher frequency modes (e.g., Sobel and Maloney 2000) • What fraction of tropical cyclone formations may be attributed to each wave type?

4. Time–Longitude Composite of Western Pacific Tropical Cyclogenesis • The westward moving developing TC is the dominant feature • The genesis location anomaly is 89 mm/day • Weaker (< 16 mm/day) eastward and westward envelopes of precipitation could indicate equatorial waves Composite unfiltered precipitation for 145 TC formations during the warm season (May–Nov) in the western Pacific (0°–20°N; 120°E–180°)

5. Time–Longitude Composite of Western Pacific Tropical Cyclogenesis MJO Kelvin ER MRG TD • The westward moving developing TC is the dominant feature • The genesis location anomaly is 89 mm/day • Weaker (< 16 mm/day) eastward and westward envelopes of precipitation could indicate equatorial waves Contours indicate filtered anomalies of the shaded composite unfiltered field

6. Artificial Precipitation Maximum MJO Kelvin ER MRG TD • A stationary precipitation anomaly of the same magnitude as the composite TC can project onto many different wave modes • How do we determine whether anomalies are associated with TCs or equatorial waves? Contours indicate filtered anomalies of the shaded Gaussian precipitation field

7. Artificial Precipitation Maximum MJO Kelvin ER MRG TD • A stationary precipitation anomaly of the same magnitude as the composite TC can project onto many different wave modes • How do we determine whether anomalies are associated with TCs or equatorial waves? Contours indicate filtered anomalies of the shaded Gaussian precipitation field

8. Time–Longitude Composite of Western Pacific Tropical Cyclogenesis MJO Kelvin ER MRG TD • A stationary precipitation anomaly of the same magnitude as the composite TC can project onto many different wave modes • How do we determine whether anomalies are associated with TCs or equatorial waves? Contours indicate filtered anomalies of the shaded composite unfiltered field

9. Removing TC-related Anomalies • Calculate the anomalies by removing the first four harmonics of the annual cycle • NCDC’s global best tracks are used for TC locations • Only fixes with maximum winds ≥ 13 m/s are used 21 Aug 2000 Range rings every 500 km

10. Removing TC-related Anomalies • A Gaussian centered on the storm is used to determine which anomalies are TC-related • The anomaly at the TC center is assumed to be completely TC-related • Anomalies at large radii are assumed to be entirely associated with the environment • Anomalies at a radius of 500 km are considered to be half from TC and half from environment 21 Aug 2000 Range rings every 500 km

11. Removing TC-related Anomalies • This removal process greatly reduces the intense precipitation in the core of the TCs • Precipitation is slightly increased farther away from the storm where compensating subsidence may suppress rainfall • Some potentially TC-related features remain, but the results are not sensitive to expanding the radius for the Gaussian 21 Aug 2000 Range rings every 500 km

12. 5 m/s TC-related Spectrum • The removed TCs produce power in a broad region associated with westward propagation at roughly 5 m/s • Another maximum in TC-related power lies in the MJO band • The TCs produce power in most of the equatorial wave bands, but it is much smaller than the total power Spectrum of removed TC anomalies, Eq–15N, May–Nov, 1998–2007

13. TC-related Spectrum Percent of total spectrum that is associated with removed TC signal Total Spectrum, Eq–15N, May–Nov, 1998–2007

14. Method for Attribution • Remove the TC-related anomalies • Filter the remaining rainfall rates for a given wave type • Test the filtered anomaly at the 1° box containing the genesis location against some threshold • At Lingling’s genesis location, the MRG-band anomaly is 3.97 mm/day • How large should the anomaly be to attribute a storm to that wave type? Map of Typhoon Lingling’s genesis. Shading indicates remnant unfiltered rainfall rates following removal of all TCs. MRG-band anomalies are contoured.

15. Method for Attribution • Remove the TC-related anomalies • Filter the remaining rainfall rates for a given wave type • Test the filtered anomaly at the 1° box containing the genesis location against some threshold • At Lingling’s genesis location, the MRG-band anomaly is 3.97 mm/day • How large should the anomaly be to attribute a storm to that wave type? Map of Typhoon Lingling’s genesis. Shading indicates remnant unfiltered rainfall rates following removal of all TCs. MRG-band anomalies are contoured.

16. Method for Attribution • Remove the TC-related anomalies • Filter the remaining rainfall rates for a given wave type • Test the filtered anomaly at the 1° box containing the genesis location against some threshold • At Lingling’s genesis location, the MRG-band anomaly is 3.97 mm/day • How large should the anomaly be to attribute a storm to that wave type? Map of Typhoon Lingling’s genesis. Shading indicates remnant unfiltered rainfall rates following removal of all TCs. MRG-band anomalies are contoured.

17. Selecting the Attribution Threshold • More than one wave type may exceed the threshold for a given tropical cyclone • For each wave type, the majority of TCs develop in association with convective anomalies (consistent with Frank & Roundy 2006) • The number of storms attributed to each wave type decreases as threshold increases • The relative importance of the wave types is generally insensitive to the threshold The percent of 145 Western Pacific TCs May–Nov, 1998–2007 that form where the filtered anomaly exceeds a given threshold

18. Summary • TCs can contaminate the filtered anomalies for many equatorial wave types • The influence of TCs on wave climatologies is relatively small • TC contamination can be mitigated by removing the TC-related anomalies using a Gaussian function centered on the best track position before filtering

19. Summary • Even following the TC removal, each wave type produces favorable convective anomalies at most genesis locations (consistent with Frank & Roundy 2006) • The number of storms attributed to each wave type decreases as the attribution threshold increases • For a wide range of thresholds, TD-type disturbances are attributable for the most TC developments

21. Sensitivity of attributions to radius used to remove TCs • This figure uses a 3 mm/day threshold • The attributions are relatively insensitive to the removal radius beyond 500 km

22. Composite WestPac TC before and after removal Rings every 500 km

23. Mean Rainfall RateOriginal TC-related Original TC-relatedRainfall Variance

24. Genesis locations for storms attributed to each wave type using a 3 mm/day threshold overlaid on the filtered variance for that wave May–November 1998–2007 145 total TCs TD 51% Kelvin 23% MRG 26% MJO 13% ER 29% None 19%