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ENSO nonlinearity in a warming climate

ENSO nonlinearity in a warming climate. Julien Boucharel LEGOS / Univ. Toulouse, France Dewitte B., du Penhoat Y. LEGOS / IRD, Toulouse, France Garel B. IMT / Univ. Toulouse, France

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ENSO nonlinearity in a warming climate

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  1. ENSO nonlinearity in a warming climate Julien Boucharel LEGOS / Univ. Toulouse, France Dewitte B., du Penhoat Y. LEGOS / IRD, Toulouse, France Garel B. IMT / Univ. Toulouse, France Yeh S.-W. DEMS, Hanyang Univ., Ansan, South Korea Kug J.-S. KORDI, Hanyang Univ., Ansan, South Korea

  2. Why studying ENSO nonlinearity ? LINEAR theories have provided an understanding of the MAIN mechanisms leading to: • the growth/decay of the initial SST perturbation Bjerknes feedback (Bjerknes, 1966) • the oscillatory nature of ENSO Delayed negative feedback of oceanic dynamic adjustment (e.g. equatorial wave dynamics) (Cane and Zebiak, 1985; Schopf and Suarez, 1988; Battisti and Hirst, 1989 …) ENSO Clivar Workshop, Paris, November 2010

  3. Why studying ENSO nonlinearity ? LINEAR theories have provided an understanding of the MAIN mechanisms leading to: • the growth/decay of the initial SST perturbation Bjerknes feedback (Bjerknes, 1966) • the oscillatory nature of ENSO Delayed negative feedback of oceanic dynamic adjustment (e.g. equatorial wave dynamics) (Cane and Zebiak, 1985; Schopf and Suarez, 1988; Battisti and Hirst, 1989 …) Regular and periodic oscillatory mode over a wide range of parameters. BUT ….. ENSO Clivar Workshop, Paris, November 2010

  4. Niño3 SST anomalies from Kaplan reconstruction (Kaplan et al., 1998). SSTA [°C] Time [Year] Strongly irregular behaviour of ENSO related timeseries ENSO Clivar Workshop, Paris, November 2010

  5. Niño3 SST anomalies from Kaplan reconstruction (Kaplan et al., 1998). SSTA [°C] 12-years running mean Time [Year] Slowly varying mean state Inter-decadal variability ENSO Clivar Workshop, Paris, November 2010

  6. Niño3 SST anomalies from Kaplan reconstruction (Kaplan et al., 1998). 1976 Warm shift SSTA [°C] 1998 Cold shift 1903 Cold shift Time [Year] Inter-decadal variability reflected by the presence of abrupt transitions (Climate shifts) Bivariate test for the detection of a systematic change in mean (shift) Maronna and Yohai (1978), Potter (1981), Boucharel et al. (2009) ENSO Clivar Workshop, Paris, November 2010

  7. Niño3 SST anomalies from Kaplan reconstruction (Kaplan et al., 1998). Positive asymmetry Skewness > 0 Pseudo symmetry Skewness ~ 0 Positive asymmetry Skewness > 0 Pseudo symmetry Skewness ~ 0 SSTA [°C] Time [Year] Homogenous periods in terms of ENSO characteristics: - Variability - Frequency - Asymmetry - Predictability … ENSO Clivar Workshop, Paris, November 2010

  8. Niño3 SST anomalies from Kaplan reconstruction (Kaplan et al., 1998). SSTA [°C] Time [Year] Presence of "anomalous" Extreme Events Complexity of ENSO system on a wide range of timescales ENSO Clivar Workshop, Paris, November 2010

  9. Why studying ENSO nonlinearity ? (Inter-)decadal changes of ENSO characteristics mirror (inter-)decadal changes of nonlinearity (as measured by ENSO asymmetry). An and Wang, 2000; Wu and Hsieh, 2003; An, 2004; Ye and Hsieh, 2006…. Dynamical linkage between these changes (An, 2009) Nonlinear processes are part of the ENSO system and may be involved in ENSO low-frequency modulation ENSO Clivar Workshop, Paris, November 2010

  10. Outline: 1. Measuring the nonlinearity of ENSO 2. Interactive feedback between ENSO irregularity and low-frequency variability 3. ENSO statistics in a warming climate 4. Conclusions, perspectives ENSO Clivar Workshop, Paris, November 2010

  11. Outline: 1. Measuring the nonlinearity of ENSO 2. Interactive feedback between ENSO irregularity and low-frequency variability 3. ENSO statistics in a warming climate 4. Conclusions, perspectives ENSO Clivar Workshop, Paris, November 2010

  12. Quantifying ENSO nonlinearity • Statistical measure Summary of ENSO statistical properties: Probability Density Function Gaussian curve corresponding to the best sampled PDF fit. Number of occurences [°C] Smoothed histogram of monthly SST anomalies (1870-2009) averaged in Niño3 ENSO Clivar Workshop, Paris, November 2010

  13. Quantifying ENSO nonlinearity • Statistical measure Summary of ENSO statistical properties: Probability Density Function Presence of Extreme Events… Number of occurences [°C] Smoothed histogram of monthly SST anomalies (1870-2009) averaged in Niño3 ENSO Clivar Workshop, Paris, November 2010

  14. Quantifying ENSO nonlinearity • Statistical measure Summary of ENSO statistical properties: Probability Density Function Presence of Extreme Events… and a strong positive asymmetry Number of occurences [°C] Smoothed histogram of monthly SST anomalies (1870-2009) averaged in Niño3 ENSO Clivar Workshop, Paris, November 2010

  15. Quantifying ENSO nonlinearity • Statistical measure Summary of ENSO statistical properties: Probability Density Function Contraction of the PDF near 0 Presence of Extreme Events… and a strong positive asymmetry Number of occurences [°C] Smoothed histogram of monthly SST anomalies (1870-2009) averaged in Niño3 ENSO Clivar Workshop, Paris, November 2010

  16. Quantifying ENSO nonlinearity Hypothesis: - The "distorsion" of the PDF of tropical Pacific climate variables is a signature of the presence of nonlinearity in the ENSO system.  Quantifying this distorsion can provide insights on an integrated level of ENSO nonlinearity Up to now, only ENSO asymmetry (skewness) has been considered to document the tropical pacific nonlinearity (Burgers and Stephenson, 1999; An and Jin, 2004) But other ENSO statistical peculiarities have to be taken into account • Need to propose a quantification of the presence of EE, the leptokurtic deformation and the asymmetry of ENSO PDF • Higher order statistics ENSO Clivar Workshop, Paris, November 2010

  17. Quantifying ENSO nonlinearity • ENSO statistical specificities prompt us to consider heavy-tails laws family: ENSO Clivar Workshop, Paris, November 2010

  18. Quantifying ENSO nonlinearity • ENSO statistical specificities prompt us to consider heavy-tails laws family: The a-stable law, an example of the wide heavy-tails laws family: Lévy (1924); Mandelbrot (1960, 1963). Benoît Mandelbrot (1924-2010) ENSO Clivar Workshop, Paris, November 2010

  19. Quantifying ENSO nonlinearity • ENSO statistical specificities prompt us to consider heavy-tails laws family: The a-stable law, an example of the wide heavy-tails laws family: Lévy (1924); Mandelbrot (1960, 1963). Benoît Mandelbrot (1924-2010) Characteristic function: 4 parameters govern stable distributions a, b, g and d ENSO Clivar Workshop, Paris, November 2010

  20. Quantifying ENSO nonlinearity • ENSO statistical specificities prompt us to consider heavy-tails laws family: The a-stable law, an example of the wide heavy-tails laws family: Lévy (1924); Mandelbrot (1960, 1963). Benoît Mandelbrot (1924-2010) Characteristic function: 4 parameters govern stable distributions a, b, g and d ENSO Clivar Workshop, Paris, November 2010

  21. Quantifying ENSO nonlinearity • a-stable laws, examples Dependance on a d = 0 b = 0 g = 1 ENSO Clivar Workshop, Paris, November 2010

  22. Quantifying ENSO nonlinearity • a-stable laws, examples Dependance on a d = 0 b = 0 g = 1 • a controls the leptokurtic deformation of the PDF a associated with the kurtosis (≥ 4th-order statistical moment) ENSO Clivar Workshop, Paris, November 2010

  23. Quantifying ENSO nonlinearity • a-stable laws, examples Dependance on b Dependance on a b = 0 b = 0.5 b = 0.8 b = 1 d = 0 b = 0 g = 1 a = 1.2 d = 0 g = 1 • a controls the leptokurtic deformation of the PDF a associated with the kurtosis (≥ 4th-order statistical moment) b associated with the skewness (= 3rd-order statistical moment) ENSO Clivar Workshop, Paris, November 2010

  24. Quantifying ENSO nonlinearity • a-stable laws, examples Dependance on b Dependance on a b = 0 b = 0.5 b = 0.8 b = 1 d = 0 b = 0 g = 1 a = 1.2 d = 0 g = 1 a = 2  b = 0 • a controls the leptokurtic deformation of the PDF a associated with the kurtosis (≥ 4th-order statistical moment) b associated with the skewness (= 3rd-order statistical moment) Gaussian distribution ENSO Clivar Workshop, Paris, November 2010

  25. Quantifying ENSO nonlinearity • Estimation of a-stable parameters Koutrouvelis (1980): Regression method using the sample characteristic function: Rigorous statistical framework to quantify equivalent of high order statistical moments of ENSO timeseries Metrics of nonlinearity ENSO Clivar Workshop, Paris, November 2010

  26.  Quantifying ENSO nonlinearity • Estimation of a-stable parameters a-stable parameters inferred from Kaplan reconstruction SST anomalies on the 1870-2009 period. ENSO Clivar Workshop, Paris, November 2010

  27.  Quantifying ENSO nonlinearity • Estimation of a-stable parameters Gaussian features • During the last 130 years, most of the tropical Pacific exhibit a-stable properties. Coherent with other reconstructions (HadSST, ERSST) a-stable parameters inferred from Kaplan reconstruction SST anomalies on the 1870-2009 period. ENSO Clivar Workshop, Paris, November 2010

  28.  Quantifying ENSO nonlinearity • Estimation of a-stable parameters Gaussian features • During the last 130 years, most of the tropical Pacific exhibit a-stable properties. Coherent with other reconstructions (HadSST, ERSST) • Particularly the Warm Pool and the Cold Tongue regions a-stable parameters inferred from Kaplan reconstruction SST anomalies on the 1870-2009 period. ENSO Clivar Workshop, Paris, November 2010

  29.  Quantifying ENSO nonlinearity • Estimation of a-stable parameters Gaussian features • During the last 130 years, most of the tropical Pacific exhibit a-stable properties. Coherent with other reconstructions (HadSST, ERSST) • Particularly the Warm Pool and the Cold Tongue regions • The asymmetry map exhibits a zonal see-saw pattern a-stable parameters inferred from Kaplan reconstruction SST anomalies on the 1870-2009 period. ENSO Clivar Workshop, Paris, November 2010

  30. Outline: 1. Measuring the nonlinearity of ENSO 2. Interactive feedback between ENSO irregularity and low-frequency variability 3. ENSO statistics in a warming climate 4. Conclusions, perspectives ENSO Clivar Workshop, Paris, November 2010

  31. Inter-decadal changes of ENSO nonlinearity Estimation of a and b on each period SSTA [°C] Time [Year] ENSO Clivar Workshop, Paris, November 2010

  32. Inter-decadal changes of ENSO nonlinearity • Estimation of a-stable law main parameters (Boucharel et al., 2009): a b • Distinct nonlinear behaviours according to the tropical mean state 1870-1903: 1903-1976: 1976-1998: 1998-2009: ENSO Clivar Workshop, Paris, November 2010

  33. Inter-decadal changes of ENSO nonlinearity • Estimation of a-stable law main parameters (Boucharel et al., 2009): a b • Distinct nonlinear behaviours according to the tropical mean state • Alternation of periods favouring Extreme Events triggering in the Cold Tongue with other in the Warm Pool 1870-1903: 1903-1976: 1976-1998: 1998-2009: ENSO Clivar Workshop, Paris, November 2010

  34. Inter-decadal changes of ENSO nonlinearity • Estimation of a-stable law main parameters (Boucharel et al., 2009): a b • Distinct nonlinear behaviours according to the tropical mean state • Alternation of periods favouring Extreme Events triggering in the Cold Tongue with other in the Warm Pool • Low frequency modulation of the nonlinearity imprint in the tropical Pacific 1870-1903: 1903-1976: 1976-1998: 1998-2009: ENSO Clivar Workshop, Paris, November 2010

  35. Inter-decadal changes of ENSO nonlinearity High frequency ENSO • Asymmetry • Extreme Events Irregularity Inter-decadal Modulation Mean state Inter-decadal 20 – 50 years INTER-SHIFT periods Low frequency ENSO Clivar Workshop, Paris, November 2010

  36. Inter-decadal changes of ENSO nonlinearity High frequency ENSO • Asymmetry • Extreme Events Irregularity 2-ways feedback ? Is the ENSO irregularity associated with Extreme Events able to act back on the tropical Pacific mean state? ? Inter-decadal Modulation Mean state Inter-decadal 20 – 50 years INTER-SHIFT periods Low frequency ENSO Clivar Workshop, Paris, November 2010

  37. Inter-decadal changes of ENSO nonlinearity Decadal changes in the seasonality of the ENSO asymmetry may influence the decadal changes in the amplitude of the annual and semi-annual cycles, and therefore the tropical Pacific decadal mean state. An and Choi (2009) Fig. 1. Annual cycle of variance (dashed line; scales in the right y-axis) and skewness (solid line; scales in the left y-axis) of Niño-3 index obtained from ERSST data averaged over 1880 to 2007. ENSO Clivar Workshop, Paris, November 2010

  38. Inter-decadal changes of ENSO nonlinearity Decadal changes in the seasonality of the ENSO asymmetry may influence the decadal changes in the amplitude of the annual and semi-annual cycles, and therefore the tropical Pacific decadal mean state. This is because the season-dependent nonlinear rectification can modify the annual and semi-annual cycles. An and Choi (2009) Fig. 1. Annual cycle of variance (dashed line; scales in the right y-axis) and skewness (solid line; scales in the left y-axis) of Niño-3 index obtained from ERSST data averaged over 1880 to 2007. ENSO Clivar Workshop, Paris, November 2010

  39. Inter-decadal changes of ENSO nonlinearity SSTA [°C] season-dependant An and Choi (2009) Dewitte et al. (2007) Timmermann et al. (2003) Time [year] ENSO Clivar Workshop, Paris, November 2010

  40. Inter-decadal changes of ENSO nonlinearity ENSO High frequency • Asymmetry • Extreme Events Seasonal Cycle • skewness[SST] • Var[SST] Decadal modulation Inter-decadal modulation Phase locking NDH Residual Niño/Niña Mean state Decadal 10 – 15 years Inter-decadal 20 – 50 years SHIFT Low frequency ENSO Clivar Workshop, Paris, November 2010

  41. Inter-decadal changes of ENSO nonlinearity ENSO High frequency • Asymmetry • Extreme Events Seasonal Cycle • skewness[SST] • - a[SST] • Var[SST] Decadal modulation Inter-decadal modulation Phase locking ? Phase locking ??? NDH Residual Niño/Niña Mean state Decadal 10 – 15 years Inter-decadal 20 – 50 years SHIFT Low frequency ENSO Clivar Workshop, Paris, November 2010

  42. Inter-decadal changes of ENSO nonlinearity • Inter-decadal variability of nonlinearity as measured by [2-a] 150°E 190°E 210°E 270°E 5°N NINO3 NINO4W 5°S [2 – a]NINO3 [2 – a]NINO4W NINO4W estimation of a parameter on a 15-years running window ENSO Clivar Workshop, Paris, November 2010

  43. Inter-decadal changes of ENSO nonlinearity • Inter-decadal variability of nonlinearity as measured by [2-a] • Eastern and Western Tropical Pacific out of phase 150°E 190°E 210°E 270°E 5°N NINO3 NINO4W 5°S [2 – a]NINO3 [2 – a]NINO4W NINO4W estimation of a parameter on a 15-years running window ENSO Clivar Workshop, Paris, November 2010

  44. Inter-decadal changes of ENSO nonlinearity • Inter-decadal variability of nonlinearity as measured by [2-a] • Eastern and Western Tropical Pacific out of phase • Do these long-term variations have the ability to influence seasonal SST variations and to rectify into the inter-decadal mean state ? 150°E 190°E 210°E 270°E 5°N NINO3 NINO4W 5°S [2 – a]NINO3 [2 – a]NINO4W NINO4W estimation of a parameter on a 15-years running window ENSO Clivar Workshop, Paris, November 2010

  45. Inter-decadal changes of ENSO nonlinearity • Inter-decadal variability of nonlinearity as measured by [2-a] • Eastern and Western Tropical Pacific out of phase • Do these long-term variations have the ability to influence seasonal SST variations and to rectify into the inter-decadal mean state ? 150°E 190°E 210°E 270°E 5°N NINO3 NINO4W 5°S [2 – a]NINO3 [2 – a]NINO4W NINO4W estimation of a parameter on a 15-years running window ENSO Clivar Workshop, Paris, November 2010

  46. Inter-decadal changes of ENSO nonlinearity • Opposite behaviour between two consecutive inter-shifts periods 1903-1925 1925-1940 Mean[SST] Var[SST] NINO3 a[SST] NINO4 West ENSO Clivar Workshop, Paris, November 2010

  47. Inter-decadal changes of ENSO nonlinearity • Opposite behaviour between two consecutive inter-shifts periods • Inter-decadal changes in amplitude and phase of mean seasonal cycle 1903-1925 1925-1940 Mean[SST] Phase locking Var[SST] NINO3 Anti Phase locking a[SST] Phase locking NINO4 West Anti Phase locking ENSO Clivar Workshop, Paris, November 2010

  48. Inter-decadal changes of ENSO nonlinearity • Opposite behaviour between two consecutive inter-shifts periods • Inter-decadal changes in amplitude and phase of mean seasonal cycle • Extreme Events residual can be rectified into the inter-decadal tropical Pacific mean state 1903-1925 1925-1940 Mean[SST] Phase locking Var[SST] NINO3 Anti Phase locking a[SST] Phase locking NINO4 West Anti Phase locking ENSO Clivar Workshop, Paris, November 2010

  49. Inter-decadal changes of ENSO nonlinearity SSTA [°C] Time [year] ENSO Clivar Workshop, Paris, November 2010

  50. Inter-decadal changes of ENSO nonlinearity SSTA [°C] + = Time [year] ENSO low-frequency modulation due to its own irregularity ENSO Clivar Workshop, Paris, November 2010

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