ENSO.Oscillator

Conceptual model for ENSO. This is a rewrite of a Fortran program used in Choi et al (2013).

The main function is oscillator() which is a generator that yields ENSO SST anomalies indefinitely after being initialised.

ENSO.Oscillator.dT_func(h, T, a, b, e)

dT = a*h-b*T-e*(T^3.)

Parameters:

• a (positivie number) – regression coefficient between SST anomaly growth rate and thermocline depth anomaly
• b (positive number) – surface damping time scale (in /month)
• e (positive number) – cubic damping rate (i.e. $ϵ$ in Eq.1 of Choi et al. 2013)

Returns:

dT (K/month)

Return type:

numeric

ENSO.Oscillator.lag_time(ck, cr, x_W, x_E, x_force)

Compute the lag times for (1) Kelvin waves and (2) Rossby waves + reflected Kelvin waves to reach the eastern boundary.

i.e. the difference of the two is the time lag between positive feedbacks and negative feedbacks of ENSO

Parameters:

• ck (number) – Kelvin wave speed in m/s
• cr (number) – Gravest Rossby wave speed in m/s
• x_W (number) – Longitude of western boundary (in degree)
• x_E (number) – Longitude of eastern boundary (in degree)
• x_force (number) – Longitude of the wind forcing

Returns:

lag time for positive feedbacks, lag time for negative feedbacks (units: month)

Return type:

(number, number)

ENSO.Oscillator.oscillator(tstep, a, b, c, d, e, gam, r, lag_long, lag_short, T0, h0, noise_generator, noise_update_freq=0.2, warmseasonal=None, coldseasonal=None)

Generator for simulating ENSO SST anomaly under a conceptual framework and a nonlinear air-sea coupling coefficient. (see Choi et al. (2013))

Parameters:

• tstep (number) – time step size (in month)
• a (positivie number) – regression coefficient between SST anomaly growth rate and thermocline depth anomaly, as in dT_func()
• b (positive number) – surface damping time scale (in /month), as in dT_func()
• c (positive number) – regression coefficient between SST anomaly growth rate and the zonal wind stress anomaly with a time lag characterised by the positive feedbacks (i.e. $c\text{'}$ in Eq.1 of Choi et al. 2013)
• d (positive number) – negative of the regression coefficient between SST anomaly growth rate and the zonal wind stress anomaly with a time lag characterised by the negative feedbacks (i.e. $d\text{'}$ in Eq.1 of Choi et al. 2013)
• e (positive number) – cubic damping rate (i.e. $ϵ$ in Eq.1 of Choi et al. 2013)
• gam (number) –

  mean regression coefficient between wind stress and temperature anomalies (i.e. gamma in Eq.2 of Choi et al (2013).)

• r (number) – nonlinearity, greater than -1. and less than 1. Zero means no nonlinearity. Positive values mean a stronger air-sea coupling coefficient during warm condition than during cold condition
• lag_long (number) – time lag for the negative feedback to arrive (in month)
• lag_short (number) – time lag for the positive feedback to arrive (in month)
• T0 (number) – Initial SST anomaly
• h0 (number) – Initial thermocline depth anomaly
• noise_generator (generator) – to be added to the zonal wind stress anomaly
• noise_update_freq (number) – how frequently the noise is updated (in month)
• warmseasonal (scalar or an array) – see wind()
• coldseasonal (scalar or an array) – see wind()

Yields :

T (number) – SST anomaly at the current time step

ENSO.Oscillator.wave_speeds(drho, hbar, verbose=False, fout=None)

Calculate the Kelvin and Rossby wave speed

Parameters:

• drho (number) – approximate density ratio between the surface mixed layer and the deeper ocean (less than 1.)
• hbar (number) – mean thickness of the surface mixed layer
• verbose (bool) –
• fout (File Object) – if None, default is sys.stdout

Returns:

Kelvin wave speed, Rossby wave speed, in m/s

Return type:

(number, number)

ENSO.Oscillator.wind(temp, gam, r, warmseasonal=None, coldseasonal=None, mon=1)

Compute the zonal wind anomaly given an SST anomaly

Assume a piecewise linear relationship between the zonal wind stress anomaly and the SST anomaly (see Choi et al (2013).)

Parameters:

• temp (number) – temperature anomaly
• gam (number) –

  mean regression coefficient between wind stress and temperature anomalies (i.e. gamma in Eq.2 of Choi et al (2013).)

• r (number) – nonlinearity, greater than -1. and less than 1. Zero means no nonlinearity. Positive values mean a stronger air-sea coupling coefficient during warm condition than during cold condition
• warmseasonal (scalar or a numpy array of numbers) – for varying coupling coefficient in different calendar month for the warm condition. The value is to be multiplied to the wind anomaly. Length = 12 (Jan, Feb,...). Default is 1 (i.e. no seasonality)
• coldseasonal (scalar or a numpy array of numbers) – similar to warmseasonal, but for cold condition.
• mon (int) – calendar month (1-12). Only meaningful when warmseasonal or coldseasonal is not 1.