On rogue La Niñas, with below-average monsoon rainfall

Abstract

Prediction of the seasonal monsoon rainfall over India relies largely on the well-known relationship with El Niño and Southern Oscillation (ENSO) and is possible because reasonably reliable seasonal predictions of ENSO are now available. Usually, the cold phase of ENSO is associated with above-normal monsoon rainfall and the warm phase of ENSO with below-normal rainfall. There are, however, exceptions: years in the cold phase of ENSO with below-normal monsoon rainfall and even drought conditions. We term these exceptional events ‘rogue La Niñas’. Clearly, an explanation of these exceptional cases will improve the predictive skill. Here we show that for the part of the Arabian Sea, east of the upwelling region and north of the equatorial belt (60°–70°E, 10°–23°N), the correlation of outgoing longwave radiation with Indian summer monsoon rainfall is even higher than that with the equatorial central Pacific associated with ENSO. Convection over this region is triggered by ENSO, but is modulated by the underlying sea surface temperature (SST). There is a minimum of SST of about 28.1°C above which the convection over the Arabian Sea is high enough and there are no rogue La Niñas. Furthermore, we show that, in this region, the SST of June–September is related to the SST of April–May. When April–May SST is >29.6°C, June–September mean SST is always >28.1°C and there are no rogue La Niñas; the monsoon rainfall is always normal or above normal as expected with a La Niña. Thus the chance of a rogue La Niña can be predicted from the April–May SST of the Arabian Sea.

Appendices

Appendix: ENSO–Monsoon associations

Siddhartha Gadgil¹ and Sulochana Gadgil²

¹Department of Mathematics, Indian Institute of Science, Bangalore.

²Centre for Atmospheric and Oceanic Sciences, Indian Institute of Science, Bangalore.

The following text and analysis are available as a Jupyter notebook on Google Colaboratory at https://drive.google.com/file/d/1tBu6btHHZb5BL9CjGTxU9yFNkJx4H7dl/view?usp=sharing.

Questions

We investigate whether for the monsoon season as a whole, is there an association between ENSO index and rainfall. To do this, we compare with the appropriate null hypothesis using appropriate distributions and compute p values.

Null hypothesis and distributions/tests

To test for association, we take the null hypothesis to be that the signs of the ENSO index and rainfall anomaly are independent. We use the Fisher exact test.

We use scipy, specifically Fisher’s exact test.

Import scipy.stats as stats.

Functions for p values

For the monsoon season, we have input a 22 matrix of frequencies, and we calculate three different p values, those for independence and for binomial on the right and left (with appropriate direction). For neatness, we capture all these in a single function, which returns these as percentages. Concretely, we return a triple with independence, positive ENSO and anomaly, and negative ENSO and anomaly.

We shall also return raw values, since we wish to correct for multiple hypotheses, i.e., cherry-picking statements that show stronger effects.

We now correct for cherry-pick. We have chosen whether to consider positive or negative associations after looking at the data. The general correction to the p-value is to observe that if we compute the probability q of an event X occurring, the $p$-value is not $q$ but the probability of at least one of $k$ independent events ${X}_{1},\dots ,{X}_{k}$ occurring, with each having probability q. This probability is

$$p=1-(1-q)^{k}$$

We define a function

Since we like to deal with percentages, it will be convenient to directly correct these.

Computations

We test associations for total rainfall, and the positive and negative cases.

Results

• The clear conclusion is that there is a significant association, since the p-value is 0.05% and there are no multiple hypotheses.

• Both sides are well below 5%. Since this applies to both sides, no cherry-picking was involved, so we can conclude associations for both negative and positive ENSO for the conventional threshold of 5%.