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Data sets.

The primary data set for our analysis is the 1° × 1° gridded daily precipitation data from the IMD (ref. 7). This is developed from approximately 2,140 rain-gauge stations using the Shepard interpolation methodology⁷, and has been extensively used in the literature^{9, 18, 23}. We test the sensitivity of the results using the newer APHRODITE data set²⁹, which includes fewer stations over India (see Fig. 11b in ref. 29), and has not yet been used in published studies of daily precipitation characteristics over India (Supplementary Section 1).

Characteristics of extreme wet and dry spells.

Our analyses focus on the characteristics of extreme wet and dry spells during the July–August period, when the monsoon is established over the entire subcontinent⁷. Our core-monsoon region (18°–28° N and 73°–82° E) is similar to that of refs 6, 21, and is defined over central India, a region that exhibits high mean seasonal precipitation and high daily-scale precipitation variability (Supplementary Fig. 1). This region experiences wet and dry spells associated with fluctuations in the location of the continental tropical convergence zone, which lead to strong precipitation anomalies⁷. We test the sensitivity of our results by comparison with the domains of refs 1, 7.

Previous studies have used different atmospheric variables such as outgoing long-wave radiation²¹, upper-level winds³⁰ and precipitation^{1, 6, 7} to define active and break periods within the monsoon season. Following several studies^{1, 6, 7, 9}, we use precipitation anomalies to focus on extreme wet and dry spells. We define extreme wet and dry spells based on de-trended precipitation anomalies to exclude the influence of the seasonal mean precipitation trend. We first remove the time-varying mean from the area-averaged daily precipitation time series over the selected domain and normalize those anomalies by the standard deviation (daily-scale variability) of precipitation over the entire record (1951–2011 for IMD, and 1951–2007 for APHRODITE). Next, we define wet and dry spells as events of at least 3 consecutive days with precipitation anomalies consistently exceeding one standard deviation of daily precipitation⁷. We then calculate the time series of frequency, duration intensity and cumulative days of wet and dry spells, where the frequency is the total number of wet (dry) spells in a given season, the duration of each spell is the number of consecutive days with precipitation anomalies exceeding one standard deviation, the intensity of each spell is the average precipitation anomaly divided by its duration, and the cumulative days are the total number of days accumulated over all wet (dry) spells in a season.

Time dependence.

Several precipitation characteristics exhibit substantial temporal auto-correlation, although the lag time varies between characteristics (Supplementary Figs 9–11). To account for this autocorrelation (temporal dependence), we assess the time-dependence structure of the data time series using the autocorrelation function and the partial autocorrelation function (PACF) to fit an autoregressive moving-average model (ARMA). The augmented Dickey–Fuller test and Kwiatkowski–Phillips–Schmidt–Shin test confirm the validity of the assumption of stationarity in the temporal-dependence structure required for inference within the ARMA framework (Supplementary Section 2.2). We then use the Ljung–Box–Pierce (LBP) test to evaluate the adequacy of this model in capturing the autocorrelation (Supplementary Section 2.1). For example, we fit an ARMA model of order 6 (AR6) to the IMD daily precipitation time series based on the PACF showing significant temporal dependence up to 5 days (Supplementary Fig. 8). LBP statistics confirm that the residuals of this AR6 model exhibit no remaining autocorrelation. We similarly model the time dependence of other characteristics using the PACF and the LBP test to determine the appropriate auto-regressive model. (See Supplementary Section 2.1 for LBP test details.)

Significance testing.

On the basis of the Q–Q plots and the Anderson–Darling normality test (see Supplementary Section 2.3 and 2.4), we reject our null hypothesis of normal distributions of the variables (Supplementary Fig. 12). Given the temporal dependency of the variables, we use a non-parametric, moving-block bootstrap test for significance testing (Supplementary Section 2.5), which does not assume a specific underlying distribution for the test variable. The block size for this test is informed by the order (lag) of the ARMA model as discussed in Supplementary Section 2.1.

We select 1951–1980 as our primary baseline period, and apply the moving-block bootstrap test on the distributions of each characteristic in the baseline and post-baseline periods to test the null hypothesis that the mean of the distributions is equal in the two periods. Further, we test the sensitivity of our results to the selection of the baseline period by varying the cutoff year between the two periods. We also assess the significance of linear trends in the precipitation characteristics from 1951 to 2011 to test the null hypothesis that the trend is not significantly different from zero.

We report statistical significance at the 5% significance level, unless otherwise specified.