Sea surface temperature associations with the late Indian summer monsoon

Abstract

Recent gridded and historical data are used in order to assess the relationships between interannual variability of the Indian summer monsoon (ISM) and sea surface temperature (SST) anomaly patterns over the Indian and Pacific oceans. Interannual variability of ISM rainfall and dynamical indices for the traditional summer monsoon season (June–September) are strongly influenced by rainfall and circulation anomalies observed during August and September, or the late Indian summer monsoon (LISM). Anomalous monsoons are linked to well-defined LISM rainfall and large-scale circulation anomalies. The east-west Walker and local Hadley circulations fluctuate during the LISM of anomalous ISM years. LISM circulation is weakened and shifted eastward during weak ISM years. Therefore, we focus on the predictability of the LISM.

Strong (weak) (L)ISMs are preceded by significant positive (negative) SST anomalies in the southeastern subtropical Indian Ocean, off Australia, during boreal winter. These SST anomalies are mainly linked to south Indian Ocean dipole events, studied by Besera and Yamagata (2001) and to the El Niño-Southern Oscillation (ENSO) phenomenon. These SST anomalies are highly persistent and affect the northwestward translation of the Mascarene High from austral to boreal summer. The southeastward (northwestward) shift of this subtropical high associated with cold (warm) SST anomalies off Australia causes a weakening (strengthening) of the whole monsoon circulation through a modulation of the local Hadley cell during the LISM. Furthermore, it is suggested that the Mascarene High interacts with the underlying SST anomalies through a positive dynamical feedback mechanism, maintaining its anomalous position during the LISM. Our results also explain why a strong ISM is preceded by a transition in boreal spring from an El Niño to a La Niña state in the Pacific and vice versa. An El Niño event and the associated warm SST anomalies over the southeastern Indian Ocean during boreal winter may play a key role in the development of a strong ISM by strengthening the local Hadley circulation during the LISM. On the other hand, a developing La Niña event in boreal spring and summer may also enhance the east–west Walker circulation and the monsoon as demonstrated in many previous studies.

Appendix 1

The goal of composite analysis is to highlight the space-time evolution of a time series or a gridded dataset according to the variations of some index time series. The first step of the method consists in defining groups of years according to the values of the index time series. The second step involves the description of each group of years with the help of the gridded dataset or other time series. Usually, this description is obtained by computing composite means for each group of years. As the years used in the composite means are restricted to those years belonging to each group, the resulting maps may be useful to describe the spatial variability associated with each group of years identified by the index time series. While it is easy to compute composite means, assessing the significance of these composite maps is a more difficult task. This is often done with the help of a classical Student’s two sample t-test (Morrison 1990), where one sample consists of the years belonging to one group and the second sample of the other years (or the years belonging to another group). In the usual context of statistical inference, this procedure is used to test the hypothesis of equal population means on the basis of two random samples independently drawn from two normal populations with a common variance s ², but possibly different means. The assumptions of random selection and normality are essential for the validity of the test. As noted by Brown and Hall (1999), this classical test cannot be used for statistical inference in composite analysis since composite means are computed from groups of years which are not randomly selected but rather by the value of the index time series. The assumption of normality is also difficult to verify and inappropriate here since the data distribution in each composite is unknown even if the original data distribution is assumed to be Gaussian. Finally, the Student’s t-test is inappropriate in exploratory studies which are very common in climate research (Nicholls 2001). Therefore, we need an alternative procedure for significance testing of our composites. In order to overcome the drawbacks of the Student’s t-test, we suggest the following approach to assess chance of occurrence of the composite maps.

Let x ₁, x ₂, …, x _n be the raw time series of one grid point X in the dataset observed during the n years included in the composite analysis. $\bar{x}$ and s are the sample mean and the sample standard-deviation calculated on these n values. Suppose now that the n years are classified by means of an index time series into k groups and let C ₁, C ₂, …, C _k be the k groups of years. In common applications k is less than or equal to 3. Finally, let n ₁, n ₂, …, n _k be the number of years in each group and $\bar{x}_{1} ,x_{2} , \ldots ,\bar{x}_{k}$ be the means computed from the years belonging to each group. Suppose now that we want to assess if the n _j values for the grid point X observed during the years in class C _j are significantly different from the values observed on all the years.

This problem can be treated as the statistical testing of an hypothesis. The null hypothesis H ₀, as usually stated, is that these n _j values were allocated in class C _j at random and without replacement among the population of the n years included in the composite analysis. In order to test this hypothesis, we may compare the actual mean $\bar{x}_{j}$ with the expected value of the mean, assuming the null hypothesis H ₀ is true. More precisely, it may be shown with the help of the theory of random sampling without replacement in a finite population, that $\bar{x}$ is the expected value of the mean for the years in class C _j and $\sqrt{(n - n_j)/(n_j \times (n - 1))} \times s$ is the standard-error of the mean for the years in class C _j if the null hypothesis H ₀ is true. In order to assess the validity of this null hypothesis, we may then compute the following sample criterion for each grid-point X in the dataset:

$$ U(X) = (\bar{x}_j - \bar{x})/s_j \quad \text{with}\ s_j = \sqrt{(n - n_j)/(n_j \times (n - 1)} \times s $$

(1)

In statistical terms, large absolute values of this statistic indicate a strong departure from the null hypothesis. For example, U(X) = 8 means that the overall mean $\bar{x}_j$ in class C _j deviates from the sample mean $\bar{x}$ by over 8 standard-deviations under the null hypothesis of a random selection of years in group C _j in the finite population of the n years.

Finally, the statistic U may be used to compute critical probability, that is to say, the probability that, under the null hypothesis of a random selection of group C _j in the finite population, the statistic U takes values more discordant than the observed sampled criterion U(X). More precisely, this critical probability is

$$ {\text{PROB}}({\text{abs}}(U) > {\text{abs}}(U(X)))\quad {\text{if }}H_{0} {\text{ is true}} $$

(2)

For this purpose, we need to find the null distribution of the U statistic. This null distribution may be estimated by means of simulation, as in bootstrapping techniques and (approximate) randomisation tests (Noreen 1989), or approximated since it is possible to demonstrate that U(X) is approximately distributed as a Gaussian distribution with mean zero and standard-deviation unity if H ₀ is true by the use of an extension of the central limit theorem. This is the approximation which is used here since simulations indicate that this approximation is good enough if at least 5 or 6 observations belong to the class C _j .

In other words, the statistic U(X) may be compared with a critical value λ_α based on the theory of random sampling in a finite population to determine whether the null hypothesis H ₀ is to be retained or rejected as in a classical statistical test. This critical value corresponds to the value of the criterion U which would be exceeded by chance with some specified and small probability α (say 0.01 or 0.05) if the null hypothesis is true. α represents the significance level of the test. Intuitively, this significance level is the risk of erroneously rejecting the null-hypothesis (statistical type I error) as in a formal statistical test.

The procedure outlined may be applied to each grid-point in the dataset and to each group of years defined in the composite analysis in order to assess the significance of the composite maps. Finally, it should be noted that if there is only two groups in the composite analysis, our test procedure may also be used to test the difference between the means in the two groups. In other words, testing the significance of the mean in one group is the same as testing the mean in the other group, or the difference between the two group means in this case. Finally, it should be mentioned that our procedure does not solve the problem of multiple tests since the procedure is applied separately to each group in the composite analysis rather than to all the groups together.