The atmospheric electrical index for ENSO modoki: Is ENSO modoki one of the factors responsible for the warming trend slowdown?

Like the southern oscillation index (SOI) based on the pressure difference between Tahiti (17.5°S, 150°W) and Darwin (12.5°S, 130°E), we propose the new atmospheric electrical index (AEI) taking the difference in the model calculated atmospheric electrical columnar resistance (Rc) which involves planetary boundary layer height (PBLH) and aerosol concentration derived from the satellite measurements. This is the first non-oceanic index capable of differentiating between the conventional and modoki La Niña and El Niño both and may be useful in the future air-sea coupling studies and as a complementary to the oceanic indices. As the PBLH variation over Darwin is within 10% of its long term mean, a strong rise in the Rc over Darwin during the modoki period supports modoki’s connection with aerosol loading. Our correlation results show that the intensity of El Niño (La Niña) event is almost independent (not independent) of its duration and the possibility of ENSO modoki being one of the factors responsible for the warming trend slowdown (WTS).


Composite Atmospheric Circulation Patterns
(supplementary figures given below) includes composite atmospheric circulation patterns supporting our discussion in the manuscript. These are anomalies of the geo-potential height (GPH) at 500 hPa, vertical velocity (ω) at 500 hPa , sea level pressure (SLP) and upward long-wave flux at top of atmosphere. The climatology period for calculating the anomalies is from year 1980 to 2011. The anomaly of parameter 'P' at latitude 'i' and longitude 'j' is given by, (Pi,j) = average (Pi,j)│ T1 -average (Pi,j)│ T where T1 is the total period of the events of a particular type and T is the total period 1980-2011.
For all the above parameters the means of the CP (modoki) and the EP (conventional) events are significantly different at statistical significance level α =0.05 using Student's t test.   Figure S1: The scattered plots showing the correlation statistics between the filtered series of the columnar resistance (R c ) and the Sea Level Pressure (SLP) at Tahiti and Darwin on the ENSO time scale of 2-7 years using the FFT band pass filter. This plot has been made using Origin 6.1 software. Figure S2: Composite atmospheric circulation patterns. Origin 8.5 software has been used for making these plots.

Supplementary Equations
The equations used to calculate atmospheric electrical columnar resistance are as follows: where H is the PBLH, S is the scale height of conductivity (= 4340 m) and λ(∞) is the average atmospheric electrical conductivity of the planetary boundary layer.
where e is the electronic charge = 1.6 × 10 -19 C, n(∞) is the calculated steady state concentration of small ions and k is the mobility of small ions, assumed to be equal to 1.2 × 10 -4 m 2 V -1 s -1 .
where b is a constant involving attachment coefficients between the oppositely charged aerosol and between the charged aerosol and the uncharged particles. Q(∞) is the ionization at the top of the boundary layer and it is calculated using ionization profile given below (equations S5a-S5d).
MODIS AOD values at 550 nm have been converted to those at 500 nm using the following expression 4 : where α is an Angstrom exponent (440-870 nm) Total aerosol concentration (Z) is derived from AOD data using the following expression 5 : The average ionization rate (Q(∞)) at the top of the boundary layer is obtained using the following expression 6 : Q (z) = Q a exp [(z-z a ) / S a ] × 10 6 (z < z a ) (S5a) Q a = 15 + 17.778 cos 4 (θ) × 10 6 (S5b) Q 0 = 1.5 + 0.533 cos 4 (θ) × 10 6 (S5c) where Q(z) is the ionization rate at altitude z due to cosmic rays. Q a and Q 0 are the ionization rates at reference altitude z a (= 6 km) and at sea level respectively. θ is the co-latitude and S a is the scale height.
From the calculated Q(∞) at the top of the planetary boundary layer and derived Z, steady state conductivity λ (∞) is calculated. R c is calculated using (S1).