1. Nonlinearity of atmospheric response
to ENSO and MJO
Hai Lin
Recherche en Prévision Numérique,
Environment and Climate Change Canada
BIRS Workshop 17w5061, November 19-24, 2017
Banff, Alberta

2. Outlines Extratropical response to El Nino and La Nina Observations
Numerical experiments
Extratropical response to MJO

3. ENSO
Leading source of seasonal forecasting skill in the extratropics → El Niño & La Niña
Is the extratropical response to El Niño a mirror image of that to La Niña?
Why?

4. Composite of T2m anomaly for 5 El Nino winters and 5 La Nina winters
Hoerling et al. 1997, JCLIM

5. Composite of Z500 anomaly for 5 El Nino winters and 5 La Nina winters
Hoerling et al. 1997, JCLIM

6. Composite of SST anomaly for 5 El Nino winters and 5 La Nina winters
Hoerling et al. 1997, JCLIM

7. Composite of precip anomaly for 5 El Nino winters and 5 La Nina winters
Hoerling et al. 1997, JCLIM

8. Explanation for extratropical nonlinearity
One possible explanation is the nonlinear relationship between SST and precipitation in the tropics:
Positive SST anomalies can initiate deep convection within the core of the east Pacific cold tongue,
whereas negative SST anomalies will have their largest effect in the west Pacific warm pool region.
Any other dynamical reason?

9. Numerical experiments
Primitive equation model (Hall 2000)
Specified tropical diabatic heating anomaly similar to ENSO,
Fixed location
61 experiments with different heating amplitudes from negative to positive
30 members of 120 day integrations for each amplitude

10. Ensemble mean Z550 anomaly response

11. Dominant response patterns

12. Transient response Three sets of experiments:
Each set has 50 integrations from different initial conditions
Each integration lasts 30 days
Daily ensemble difference → response
Control run ─ climatological forcing;
El Niño run ─ climatological forcing + tropical heating anomaly
La Niña run ─ climatological forcing + tropical cooling anomaly
The same 50 initial conditions for all three sets of experiments, so that the only difference is the thermal perturbation.

13. Forcing anomaly
Only in temperature equation
Maximum at 350 mb

14. Day 1

15. Day 2

16. Day 3

17. Day 4

18. Day 5

19. Day 6

20. Day 7

21. Day 8

22. Day 9

23. Day 10

24. Day 11

25. Day 12

26. Day 13

27. Day 14

28. Days 16-30

29. W vector
Days 16-30

30. ω’ = - h’ / [α – cp(∂T/ ∂p + ∂T’/ ∂p)]
Tropical circulation
Why La Niña has a stronger response?
→Stronger vertical motion due to changes in static stability _
ω’ = - h’ / [α – cp(∂T/ ∂p + ∂T’/ ∂p)]
In the center of response, adiabatic process tends to balance the diabatic heating anomaly
El Nino: ∂T’/ ∂p < 0
La Nina: ∂T’/ ∂p > 0

31. Asymmetric development of tropical waves
To the west of thermal forcing:
El Nino, upper troposphere easterly  suppress Rossby wave development
La Nina, upper troposphere westerly  favors Rossby wave development
In the center of response, adiabatic process tends to balance the diabatic heating anomaly

32. Feedback from transients
Modified storm track
Vorticity flux convergence by transients

33. Days 16-30
Anomaly of Z550 rms for transients
El Niño
La Niña

34. Days 16-30
Z550 tendency by transients
El Niño
La Niña

35. MJO Leading source of skill for subseasonal predictions
Is there difference between extratropical response pattern to +MJO and that to -MJO?

36. Composites of tropical
Precipitation rate for 8 MJO phases, according to Wheeler and Hendon index.
Xie and Arkin pentad data,

37. Lagged probability of the NAO index Positive: upper tercile; Negative: low tercile
Phase 1 2 3 4 5 6 7 8
Lag 0
+45%
−42%
Lag +1
+47%
−46%
Lag +2
+50%
+42%
−41%
Lag +3
+48%
−48%
Lag +4
−39%
Lag +5
(Lin et al. JCLIM, 2009)

38. Z500 anomaly composites
following MJO phase 3 and 7

39. Wintertime North Atlantic weather regimes
From Cassou (2008)

40. Observed nonlinearity

41. Dominant tropical subseasonal OLR patterns

42. MJO forcing structure

43. Experiments with MJO forcing
Three sets of experiments:
Each set has 360 integrations from different initial conditions
Each integration lasts 20 days
Daily ensemble difference → response
Control run ─ climatological forcing;
+MJO run ─ climatological forcing + MJO
-MJO run ─ climatological forcing - MJO
The same 50 initial conditions for all three sets of experiments, so that the only difference is the thermal perturbation.

44. Z500 ensemble mean response

45. Spread Z500 response

46. Z500 response to +MJO

47. Z500 response to -MJO

48. STRM200 response to +MJO
STRM200 response to -MJO

49. Summary Asymmetric response to El Nino and La Nina
In addition to the nonlinear relationship between SST and precipitation, there are dynamical mechanisms.
Mechanisms include: 1) changes in static stability; 2) aymmetric development of tropical waves; and 3) feedback from synoptic-scale transients.
The extratropical response to MJO is also nonlinear
A better representation of such nonlinearity in numerical models would be helpful for subseasonal to seasonal predictions.