Journal of Geophysical Research: Atmospheres

Trend and spectral analysis of rainfall over India during 1901–2000

Authors


Abstract

[1] The spectral analysis of gridded rainfall data obtained from 1384 rain gauge stations by India Meteorological Department demonstrates not much change in low-frequency components of decadal spectra of all India and its four subregions, namely, southwest, southeast, central, and northwest, during the last 10 decades. However, the dominant as well as the significant cycles lying between the periods 10–20 days, 20–30 days, 30–40 days, and 40–50 days are highly variable on an interdecadal basis. On close inspection, it can be inferred that the 40–50 day oscillations that corresponds to Madden-Julian Oscillations is mainly associated with the southern Indian region, namely southwest and southeast, and the 30–40 day oscillation of southeast region is gradually increasing on a decadal scale during the last 4 decades. The physical context of interdecadal variability of rainfall in India can be linked with the warm phase of Atlantic multidecadal oscillations and the cold phase of interdecadal Pacific oscillations. The correlogram analysis shows the presence of 15, (17, 19), and 17 year cycles for the southwest, central, and northwest regions, respectively. No significant trend is discernable during the last 10 decades, when the linear least squares fitting method and Mann-Kendall statistic to identify the trend and the normalized test statistic and statistical probability to quantify the significance of the trend are applied, on the annual rainfall data for all India and its subregions.

1. Introduction

[2] Rainfall is the end product of a number of complex atmospheric processes, which vary both in space and time [Luk et al., 2001]. Knowledge of the space-time variability of rainfall is important for meteorology, hydrology, agriculture, telecommunications, and climate research as rainfall and its variability are not only important constituents of the global hydrological cycle, but also influences the course of development of all living organisms on our planet [Kishtawal and Krishnamurti, 2001].

[3] Rainfall variability occurs over a broad range of temporal scales. Knowledge and understanding of such variability can lead to improved risk management practices in agricultural and other industries. In the tropics, the most important climate parameter, i.e., the rainfall, has a high degree of variability on temporal and spatial scale, as compared to the other atmospheric indicators. Apart from the short-term fluctuations that are day-to-day variations or weeks to months, there are longer-term fluctuations that range from a few years to even decades.

[4] Among the wide ranges of time scales, the interannual variability is most extensively studied. It is reasonable to expect that the nature of the interannual variability of seasonal averages will depend upon the spatial and temporal domains for which the averages are calculated [Shukla, 1987]. Part of the interannual variability may be due to changes in the intensity of mean atmospheric circulation systems, and part of it may be simply due to shifts in location and timing of those circulation systems [Shukla, 1987].

[5] The predictability of the seasonal mean monsoon depends on the nature of interannual variability of the monsoon. Various components of the Asian monsoon also exhibit significant interdecadal variability [Mooley and Parthasarathy, 1984; Kripalani et al., 1997; Mehta and Lau, 1997; Parthasarathy et al., 1991; Wu and Wang, 2002]. A better understanding of interdecadal variability may therefore be very important in improving the predictability of the seasonal monsoon climate.

[6] Krishnamurti and Bhalme [1976] reported the presence of the spectral peaks at 10–20 days in pressure and other data while Krishnamurti and Ardanuy [1980] observed 10–20, 20–30, and 30–40 day variability in longer surface pressure data. Murakami [1977] reported the existence of 5 day and 15 day peaks in the spectral analysis of Indian monsoon. Hartmann and Gross [1988] studied the seasonal variability of spectral peaks in the 40–50 day range for winds and precipitation in the tropical Pacific and Indian Ocean region. Hartmann and Michelsen [1989] performed spectral analysis of a 70 year record of daily precipitation, to search for such periodicities on subseasonal time scales, during the summer monsoon and noticed the presence of 40–50 day spectral peak, corresponding to Madden-Julian oscillation (MJO) over most of south India.

[7] The seasonal monsoon rainfall is found to consist of two dominant intraseasonal oscillations with periods of 45 and 20 days and three seasonally persisting components, by using Multichannel Singular Spectrum Analysis (MSSA) of daily rainfall anomaly [Krishnamurthy and Shukla, 2007].

[8] Kane [1995] subjected the summer monsoon rainfall time series for 29 subdivisions of India from 1951 to 1991 to maximum entropy spectral analysis and reported the periodicities in a wide range, including quasi-biennial oscillation (QBO, 2–3 years) and quasi-triennial oscillation (QTO, 3–3.9 years). Rangarajan [1994] analyzed Homogeneous Indian Monsoon (HIM) region rainfall for the epoch 1871–1990 using Singular Spectral Analysis (SSA) and reported that the HIM time series is simple in structure with only the annual oscillation and its first two harmonics accounting for almost the entire variability. Vijayakumar and Kulkarni [1995] applied SSA to the white noise of the Indian Summer Monsoon Rainfall (ISMR) series for extracting the statistically significant oscillations with periods 2.8 and 2.3 years.

[9] Laughlin et al. [2003] analyzed rainfall by means of standard statistics such as average value, variance, coefficient of variation, and percentiles. Peters et al. [2002] has presented a power law behavior in the distribution of rainfall over at least 4 decades. In recent years, Lihua et al. [2007] used Scargle periodogram and wavelet transform methods to study the periodicity of ISMR changes between 1871 and 2004 and reviewed the possible influence of solar activity on the rainfall.

[10] Munot and Kothawale [2000] used the daily rainfall data of 30 years (1960–1989) period and clearly delineated the preactive, active, and postactive phases of the summer monsoon (June-September) for all India and homogeneous regions of India. It was observed that the monsoon is active for 103 days over northeast (NE India) India, for 75–78 days over central-northeast (CNE India) India and so on for all the regions.

[11] Rajeevan et al. [2008] examined the variability and long-term trends of extreme rainfall events over central India and reported that interannual, interdecadal, and long-term trends of extreme rainfall events are modulated by the SST variations over the tropical Indian Ocean.

[12] Periodogram or Fourier line spectrum, also referred as power spectrum, is used to examine graphically the characteristics of the time series that has been Fourier transformed into a frequency domain [Wilks, 1995], where the Fourier series represents the signal, such as atmospheric and oceanic parameters, namely, rainfall, winds (which include both zonal and meridional winds), pressure, cloud cover, outgoing long-wave radiation and many others in both spatial and temporal domain, by emphasizing how much information is contained at different frequencies. The Fourier transform decomposes the observed field into independent components referred as harmonics and the spectral analysis of space harmonics (zonal waves) explains the energetic, while the time harmonics (frequency) provides information regarding the variability.

[13] NASA scientists have detected the first signs that the tropical rainfall is on the rise with the longest and most complete data record available. Guojun Gu, a research scientist, reported that the total amount of rainfall has changed very little during the period 1979–2005. But in tropics, where nearly two thirds of the rain falls, there has been an increase of 5%. This rainfall increase was mainly concentrated over the tropical oceans, with a slight decline over the land. Climate scientists predicted that a warming trend in Earth's atmosphere and surface temperatures would produce an accelerated recycling of water, between land, sea, and air. Warmer temperatures increase the evaporation of water from the ocean and land and allow air to hold more moisture. Eventually, clouds form that produce rain and snow (http://www.scientificblogging.com/news_account/long_term_increase_in_rainfall_seen_in_tropics).

[14] Scrutinizing global model warming projections in models used by the Intergovernmental Panel on Climate Change (IPCC), a team of scientists headed by meteorologist Shang-Ping Xie, finds that ocean temperature patterns in the tropics and subtropics will change in ways that will lead to noteworthy changes in rainfall patterns. Scientists have mostly assumed that the surfaces of Earth's oceans will warm rather evenly in the tropics. This assumption has led to “wetter-gets-wetter” and “drier-gets-drier” regional rainfall projections. Xie reported that “Compared to the mean projected rise of 1°C, such differences are fairly large and can have a pronounced impact on tropical and subtropical climate by altering atmospheric heating patterns and therefore rainfall” (http://desertification.wordpress.com/2010/03/01/tropics-global-warming-likely-to-significantly-affect-rainfall-patterns-science-daily).

[15] The main objective of this paper is to observe what will be the consequence of this increasing trend in global sea surface temperature (SST), which is generally referred to as global warming, on the trend of annual rainfall along with the variations in the power spectra in each decade for all India and its subregions during the analysis period (1901–2000). Further, an attempt has been made to study all India and its subregions annual rainfall series to identify the climate changes (i.e., the epochs of increasing/decreasing trends).

[16] The data used in the present study are described in section 2. The method of analysis is given in section 3. Section 4.1 provides the results obtained from the trend analysis, whereas section 4.2 discusses the variations in the power spectra in each decade. Section 5 provides the summary and conclusion.

2. Data

[17] The gridded rainfall data used for the present study was obtained from 1384 stations observed by India Meteorological Department (IMD) which had a minimum 70% data availability during the analysis period (1901–2004) in order to minimize the risk of generating temporal inhomogeneities in the gridded data due to varying station densities. Before interpolating station rainfall data into regular grids of 1° latitude × 1° longitude, multistage quality control of observed data was carried out [Rajeevan et al., 2008]. The detailed description of the development of a high-resolution daily gridded rainfall data for the Indian region is given by Rajeevan et al. [2008]. The Shepard's interpolation scheme [Shepard, 1968] is used for interpolating station rainfall data into regular grids, including the directional effects and barriers. The geographical area covered in this data is 6.5°N–38.5°N and 66.5°E–100.5°E.

[18] The SST data used in this study came from the HadISST v.1.1 data set created by the Hadley Centre for Climate Prediction and Research [Rayner et al., 2003]. The monthly mean SST data are provided on a 1° × 1° latitude/longitude global grid and data used in present study covers the period 1901–2000.

[19] Atlantic multidecadal oscillations (AMO) index was obtained from http://www.esrl.noaa.gov/psd/data/timeseries/AMO/, whereas the interdecadal Pacific oscillations (IPO) index was taken from Met Office Hadley Centre for Climate Change.

3. Method of Analysis

[20] The 100 year (1901–2000) IMD gridded rainfall data has been spectrally analyzed on decadal scale to find out the periodicity in rainfall of all India, southwest (11.5°N–21.5°N, 73.5°E–76.5°E), southeast (8.5°N–16.5°N, 77.5°E–80.5°E), central (20.5°N–26.5°N, 79.5°E–85.5°E), and northwest (23.5°N–31.5°N, 71.5°E–76.5°E) regions as shown in Figure 1 was first defined by Krishnamurthy and Shukla [2000]. The selection of these regions was based on the geographical uniformity in the rainfall.

Figure 1.

Geographical subregions chosen for the study. The subregions are: subregion a, southwest (11.5°N–21.5°N, 73.5°E–76.5°E); subregion b, southeast (8.5°N–16.5°N, 77.5°E–80.5°E); subregion c, central (20.5°N–26.5°N, 79.5°E–85.5°E); and subregion d, northwest (23.5°N–31.5°N, 71.5°E–76.5°E).

[21] The climatology of data for the period of analysis is limited to calendar day, and the grid boxes without data are excluded from the area averages. The time series of the area averages for all India and its subregions is shown in Figure 2 and is in conformity with the results of Krishnamurthy and Shukla [2000].

Figure 2.

Daily climatological mean (mm/d) of 5 day running mean of rainfall area averaged over all India, southwest, southeast, central, and northwest regions.

[22] The 10 year moving t-test known as Cramer's test [Lawson et al., 1981] is applied to the annual rainfall data to measure the difference, in terms of moving t-statistic, tk, between the mean of each successive 10 year period and the mean of the entire 100 year period. For significance of Cramer's t-value at 5% level, the required t-value is ±1.96 or more [Mooley and Parthasarathy, 1984].

[23] For identifying the trend in the annual rainfall data, the linear least squares fitting method is used. The results obtained are further verified by using a powerful and nonparametric Mann-Kendall Statistics (S) [Gilbert, 1987].

[24] Further the Correlogram analysis [Parthasarathy and Dhar, 1975; Mooley and Parthasarathy, 1984] is performed on the annual rainfall data to find a cycle, if any, present in the rainfall data. The autocorrelation coefficients (ACC) of annual rainfall data for all India and its subregions have been worked out up to 45 lags (i.e., for lag less than N/2, where N is the number of years) because at large value of lag, much of the data is lost and the correlations for the lag > N/2 and lag > N/3 are rarely computed [Wilks, 1995]. The critical values of ACC for a given significance level say 95%, depends on whether the test is one-tailed or two-tailed. In the present study, a two-tailed test is applied (http://www.ltrr.arizona.edu/∼dmeko/notes_3.pdf ).

[25] In addition to this, the decadal spectra have been used to evaluate the changes, which take place in the rainfall pattern, on decadal basis. The red noise spectrum [Wilks, 1995] of each decadal spectrum is computed. The confidence limits associated with the red noise spectrum is calculated, assuming χ2 statistics with two degrees of freedom. The required χ2 values, for 90%, 95%, and 99% confidence levels, are 4.605, 5.991, and 9.210. Prior to perform the spectral analysis, the 5 day running mean of daily rainfall data of each year was performed, so that the high-frequency fluctuations may die out and more accurate periodicities can be obtained.

4. Results

[26] The statistical parameters of all India and its subregions annual rainfall for the analysis period (1901–2000) have been computed and tabulated in Table 1. The area average of the climatological mean rainfall over all India, southwest, southeast, central, and northwest regions are 3.47 mm/d, 4.05 mm/d, 2.41 mm/d, 3.38 mm/d, and 1.45 mm/d, respectively. The mean (standard deviation) annual rainfall for all India, southwest, southeast, central, and northwest regions are 1252.1 mm (110.3 mm), 1462.6 mm (185.8 mm), 869.6 mm (119.3 mm), 1218.8 mm (158.8 mm), and 522.05 mm (126.7 mm), respectively. This means that southwest/northwest is the heavy/low rainfall occurring region, whereas the central/southeast is the more moderate/less moderate rainfall occurring region. The coefficient of variation (COV), a statistical measure of how the individual data points vary about the mean value, for all India, southwest, southeast, central, and northwest regions are 8.81%, 12.7%, 13.7%, 13.03%, and 24.27%, respectively.

Table 1. Statistics of Annual Rainfall over the Period 1901–2000
RegionClimatological Mean Rainfall (mm/d)Mean Annual Rainfall (mm)Standard Deviation (mm)Coefficient of Variation (%)
All India3.471252.1110.38.81
Southwest4.051462.6185.812.7
Southeast2.41869.6119.313.7
Central3.381218.8158.813.03
Northwest1.45522.05126.724.27

[27] The annual mean anomaly of globally averaged monthly SSTs and its linear trend which was computed using the linear least squares fitting method is shown in Figure 3 with solid black and red lines, respectively. The annual mean of globally averaged monthly SSTs shows an increasing trend during the analysis period. This increasing trend is further verified by using Mann-Kendall Statistics. The positive values of Mann-Kendall statistics, S, is an indicator of an increasing trend. In addition to this, the normalized test statistic, Z, and statistical probability (1 − p) associated with S is also computed for quantifying the significance in the trend, as tabulated in global SST entries for confidence in trend and nature of trend in Table 2. The values given are at 95% level of significance. The value of Z is positive and the statistical probability is greater than the level of significance which indicates the “increasing trend” condition. This means that there is a significant increasing trend observed in global SST during the last century.

Figure 3.

Trend of annual mean anomaly of globally averaged monthly SSTs.

Table 2. Mann-Kendall Statistics (S)
RegionSZConfidence in Trend (1 − p)Nature of Trend
Global SST344210.2477100Increasing
All India5421.611289.1No Trend
Southwest4821.432585.7No Trend
Southeast5381.599288.9No Trend
Central−572−1.700590.6No Trend
Northwest3961.176480.03No Trend

[28] According to Intergovernmental Panel on Climate Change [2001] report that most of the global surface temperature increase has occurred in two periods, namely (1910–1945) and since 1976. Therefore, during the period of analysis (1901–2000), the periods (1910–1945) and (1976–2000) have been referred to as global warming periods and (1901–1909) and (1946–1975) have been referred to as nonglobal warming periods, which can be clearly recognizable from Figure 3.

[29] To address the issue raised in the present paper for assessing the effect of this increasing trend, which is generally referred to as global warming, on the annual rainfall trend of all India and its four important subregions, the statistical analysis is performed in sections 4.1 and 4.2.

4.1. Trend Analysis

[30] The Cramer's t-value moving curve and the 10 year moving average curve of annual rainfall data is analyzed for all India and its subregions separately which shows similar behavior as represented in Figures 4, 5, 6, 7, and 8.

Figure 4.

(a) The 10 year moving average curve and (b) the 10 year moving Cramer's t-value for all India.

Figure 5.

(a) The 10 year moving average curve and (b) the 10 year moving Cramer's t-value for southwest region.

Figure 6.

(a) The 10 year moving average curve and (b) the 10 year moving Cramer's t-value for southeast region.

Figure 7.

(a) The 10 year moving average curve and (b) the 10 year moving Cramer's t-value for central region.

Figure 8.

(a) The 10 year moving average curve and (b) the 10 year moving Cramer's t-value for northwest region.

[31] For annual rainfall of all India, 10 year moving average curve shows a gradual rise up to the year 1940, and afterward it decreases up to the year 1949. From the year 1949 onward it again rises and reaches its highest in the year 1955 and decreases afterward, followed by a slight increasing trend beyond 1965. The tk value is significant at 5% level during the six 10 year periods, 1901–1910 to 1906–1915, for which the mean annual rainfall of all India was the lowest. In addition to this, one highest average 10 year period, 1955–1964, is observed which is also significant at 5% level; during this one 10 year period, the mean annual rainfall of all India is highest.

[32] The 10 year moving average curve of annual rainfall data, for southwest region, initially shows a decrease that reaches to the lowest value in the year 1904, and afterward it rises up to year 1908. From 1908 onward it starts decreasing and again attains the lowest value in the year 1918, after which it shows a gradual rise and reaches the highest value in the year 1953, and afterward it again starts decreasing. From 1965 onward it shows a slight increasing trend up to 1974 followed by a decrease up to the year 1982, after which it again starts increasing. The tk value is significant at 5% level during the five 10 year periods, namely, 1902–1911 to 1904–1913 and 1917–1926 to 1918–1927. For these five 10 year periods the mean annual rainfall for the southwest region is lowest. In addition to this, the seven highest average periods are being observed from 1950–1959 to 1956–1965, which are significant at 5% level.

[33] For the southeast region, the 10 year moving average curve of annual rainfall decreases to the lowest value in the year 1904. From 1904 onward it increases up to the year 1913, after which it oscillates about the mean up to the year 1980. From 1980 onward it shows an increasing trend, attains the highest value in the year 1989, and remains constant from then onward. There are two lowest average 10 year periods, 1903–1912 and 1904–1913, and three highest average 10 year periods, 1989–1998 to 1991–2000, significant at 5% level, are observed for the southeast region.

[34] The 10 year moving average curve of annual rainfall for central region shows an increasing trend and reaches to the highest value in the year 1936. From then onward it starts decreasing and reaches to the lowest value in the year 1965 followed by a slight increase before it becomes constant. The tk value was significant at 5% level during the eight 10 year periods 1917–1926, 1929–1938 to 1931–1940, and 1933–1942 to 1936–1945; during these eight 10 year periods, the mean annual rainfall for central region is highest. In addition to this, one lowest average period 1965–1974, significant at 5% level, is also observed.

[35] The 10 year moving average curve for the northwest region reaches to the highest value in the year 1908, followed by a decrease up to 1911, and from then onward it oscillates about the mean value, as shown in Figure 8a. The tk value for the northwest region lies between ±1.96 (threshold value for the significance of Cramer's t-value at 5% level) throughout the analysis period. This indicates that during the analysis period, the annual rainfall of northwest region neither attains the highest (heavy rainfall) nor the lowest (deficient rainfall) value; that is, the northwest region received the normal rainfall throughout the analysis period.

[36] The variability analyzed thus show the presence of some increasing/decreasing trends during certain period of time for all India and its subregions. Now the question arises whether there is any increasing/decreasing trend present in annual rainfall data for all India and its subregions over the epoch of 100 years (1901–2000)? And if so, then is it significant or not?

[37] To address the same question, the linear trends were computed using the linear least squares fitting method, as shown with red lines in Figures 4a, 5a, 6a, 7a, and 8a. All India, southwest, southeast, and northwest show an increasing trend, whereas a decreasing trend is observed for the central region.

[38] In addition to this, Mann-Kendall Statistic is applied to the annual rainfall data for all India and its subregions to verify the increasing/decreasing trends obtained earlier by using the linear least squares fitting technique.

[39] The results of Mann-Kendall Statistic, S, normalized test statistic, Z, confidence in trend i.e., statistical probability (1 − p), and nature of trend computed for all India and its subregions for the analysis period (1901–2000) of annual rainfall data has been tabulated in Table 2. The positive values of Mann-Kendall statistics, S, for all India, southwest, southeast, and northwest regions is an indicator of an increasing trend, whereas the negative value of S for central region indicates the decreasing trend. The results obtained by using the Mann-Kendall Statistic are in agreement with the ones obtained by the linear least squares fitting technique.

[40] Now, to statistically quantify the significance of the trend, the normalized test statistic, Z, and statistical probability, (1 − p), associated with S is also computed and tabulated the confidence in trend and nature of trend columns of Table 2. The values given are at 95% level of significance. For all India, southwest, southeast, and northwest the value of Z is positive, whereas for the central region it is negative, and the statistical probability is less than the level of significance for all the regions, which indicates the “no trend” condition. This means that for all India and its subregions the annual rainfall shows the lack of trend or climate change signal but definitely contains the coherent multidecadal variability. This simply implies that there is no detectable effect of global warming on the annual rainfall trend during the last 10 decades.

[41] The salient features that could be extracted from Cramer's test statistics are the epochs of above- and below-normal rainfall observed for all India and its subregions (shown in Figure 4b, 5b, 6b, 7b, and 8b). The variability of epochs as obtained for all India and southwest regions appears to be small during recent decades (1970–2000) as compared to the earlier period. For the central region, the above- and below-normal epochs tend to last for approximately 4 decades. It shows multidecadal variability with an approximate periodicity of about 80–90 years. In addition to this, the variability during the earlier and the recent decades appears to be same for this region. Such epochs have been previously observed in case of ISMR for all India, the homogeneous Indian region and the west central Indian region by Goswami [2005] which were reported to last for about 3 decades. It was also reported that the eastern equatorial Pacific SST (Niño 3) also shows a similar interdecadal variability but is approximately out of phase with that of the summer monsoon rainfall. Kripalani and Kumar [2004] also observed such epochs for the northeast monsoon rainfall (NEMR) which tends to last for about a decade or two. This variability appears to be enhanced (suppressed) during the decades when the Indian Ocean dipole is active (inactive).

[42] In the present study, the observed interdecadal variability of annual rainfall for all India and its subregions may be attributed to the interdecadal variability of eastern equatorial Pacific SST (Niño 3) or Indian Ocean Dipole Mode.

[43] The ACC for all India and its subregions are shown in Figures 9a9e. The oscillatory nature of annual rainfall data series for all India and its subregions also conforms to that of Correlogram [Parthasarathy and Dhar, 1975; Mooley and Parthasarathy, 1984] as well. Although, the high ACC values for lags 2, 27, and 42 and low ACC values for lags 18, 36, and 41 were observed for all India, none of these values is significant at 95% level. The Correlogram of southwest region shows high ACC values for lags 1, 2, and 15 and low ACC values for lags 11, 25, 26, and 41, and out of these the values at lags 15 and 41 are only significant at 95% level. In the case of the southeast region, no significant ACC value is obtained. Besides this, the values are continuously negative from lag 7 to 11 for this region. The correlogram of the central region shows many high ACC values for lags 10, 17, 19, and 27 and low values for lags 18, 32, 40, and 43 where the ACC values at lags 17, 19, and 43 are significant at 95% level. The ACC values for the central region are continuously positive from lag 2 to 14, but are not significant. The correlogram for northwest region also contains many high (17, 33) and low (22, 32, 41, and 43) ACC values, out of which only the ACC value at lag 17 is 95% significant.

Figure 9.

Correlogram analysis for (a) all India, (b) southwest, (c) southeast, (d) central, and (e) northwest regions.

[44] In order to understand the possible ocean forcing mechanisms for decadal rainfall variability, the correlations of the decadally filtered rainfall indexes with SSTs were analyzed. The map of decadal correlation coefficient between summer monsoon rainfall for the southwest region and the Hadley SST (as shown in Figure 10b) shows the interdecadal Pacific oscillations (IPO) [Parker et al., 2007] and Atlantic multidecadal Oscillations (AMO) [Parker et al., 2007] like patterns.

Figure 10.

Maps of decadal correlation coefficients between summer monsoon rainfall and SSTs for (a) all India, (b) southwest, (c) southeast, (d) central, and (e) northwest regions.

[45] The large correlations in the North Atlantic are referred as AMO and such a link was proposed by Goswami et al. [2006], Zhang and Delworth [2006] and Li et al. [2008]. The physical mechanism responsible, outlined by Goswami et al. [2006], is that the AMO in its positive phase (that is the positive anomalies in the North Atlantic) increases the meridional tropospheric temperature gradient over the whole Northern Hemisphere, including Eurasia, and may cause the late withdrawal of Indian summer monsoon, which causes increase of the seasonal mean Indian monsoon rainfall. The large anticorrelations in the tropical and South Indian Ocean indicate that cooling in that region tends to increase the ISMR. The possible mechanisms of how this tropical SST pattern influences the decadal ISMR variability are discussed by Krishnamurthy and Goswami [2000]. In brief, it could be inferred that the cooling in the tropical Indian and Pacific oceans leads to low-level equatorial convergence in the Indian Ocean that influences the local Walker and Hadley circulation in such a way as to modulate precipitation over the Indian subcontinent by causing low-level divergence there. Recently, Kucharski et al. [2009] confirmed the proposed SST-Indian monsoon teleconnections using the model simulations.

[46] The maps of decadal correlation coefficients between summer monsoon (June-July-August-September (JJAS)) rainfall and SSTs (JJAS) for all India, southwest, southeast, central, and northwest regions are shown in Figures 10a10e. The correlation of decadal variability of summer monsoon rainfall and that of AMO is highly positive for all India, southwest, and central regions as shown Figures 10a10d, whereas the decadal correlation of summer monsoon rainfall and IPO is highly negative for southwest and northwest regions as shown in Figures 10b and 10e. The correlations of the decadal variability of AMO index and IPO index with decadal variability of rainfall indices for all India and its subregions are tabulated in Table 3. This signifies that AMO affects the rainfall of all India, southwest, and central regions on an interdecadal basis, since high correlations are found for these regions. This means that for all India, southwest, and central regions, the multidecadal wet period is in phase with the positive AMO phase (warm North Atlantic Ocean) and dry periods are in phase with negative AMO phase. This implies that the warm phase of AMO and cold phase of IPO cause the enhancement of the rainfall for the southwest region, as shown in Figure 11. On the other hand, in the case of all India and central regions only the warm phase of AMO plays a significant role in enhancing the rainfall in the respective regions. In addition to this, the southern Indian Ocean shows strong anticorrelation in SST and monsoon rainfall for the southwest region as shown in Figure 10b, indicating that cooling in that region tends to increase the rainfall over the southwest region.

Figure 11.

Decadal variability of rainfall over southwest region along with the decadal variability of AMO and IPO indices. The unit of AMO and IPO is °C, while that of decadal variability of rainfall is millimeters.

Table 3. Correlations of the Decadal Variability of AMO and IPO With Decadal Variability of the Rainfall for All India and Its Subregions
RegionAMOIPO
All India0.5028−0.1803
Southwest0.4689−0.5002
Southeast−0.1901−0.0036
Central0.4702−0.1853
Northwest0.1662−0.4389

[47] In the case of the central region, due to the dipole structure in the North Atlantic, there is AMO contribution to rainfall decadal variability. On the other hand, all the field is dominated by negative values, which is consistent with the effect that in the central region a downward trend is observed (though it is not significant at 95% as against 90% level of significance because of fewer data points) in rainfall and positive trend in global SST. Figures 12a and 12b show the decadal variability of AMO and IPO indices with rainfall indices for all India and its subregions.

Figure 12.

Decadal variability of rainfall indices for all India and its subregions with (a) AMO and (b) IPO indices. The unit of AMO and IPO is °C, while that of rainfall indices is millimeters.

4.2. Spectral Analysis

[48] As anticipated, the annual cycle and its multiples (semiannual, terannual, and quadannual), dominates the power spectra for all India and its subregions during the analysis period (1901–2000), due to which the high-frequency cycles are suppressed (figures not shown). Therefore, in order to see the relative strength of other cycles, the spectra are reconstructed after excluding the annual and its multiples for all India, southwest, southeast, central, and northwest regions as shown in Figures 13a13e. The red, pink, blue, and green lines depict the red noise spectra, 90%, 95%, and 99% confidence levels, respectively, for each power spectrum. The spectral peaks and not the troughs are of interest; therefore only the upper limits of the confidence interval, which corresponds to the confidence levels (one-sided limits of confidence intervals), are plotted [Weedon, 2003]. Spectral peaks, emerging above the confidence levels, attached to the estimated spectral background can be easily identified.

Figure 13.

Power spectra after excluding the annual, semiannual, terannual, and quadannual cycles, during the analysis period 1901–2000, for (a) all India, (b) southwest, (c) southeast, (d) central, and (e) northwest regions.

[49] The intraseasonal oscillations of ISMR are naturally occurring component of our coupled ocean-atmosphere system and represent a broadband spectrum with periods between 10 and 90 days but have two preferred oscillations [Krishnamurti and Bhalme, 1976; Krishnamurti and Ardanuy, 1980; Yasunari, 1980]: one is the Madden-Julian [Madden and Julian, 1971] and the other is quasibiweekly. The MJO, also known as the 30–60 day, 40–50 day, and tropical intraseasonal oscillation [Wang, 2006], is the dominant component of the intraseasonal variability in the tropical atmosphere which basically consists of large-scale coupled pattern in atmospheric circulation and deep convection, propagating eastward, slowly through the Indian and Pacific oceans, where the sea surface is warm. The other is the quasibiweekly periodicity, also known as 10–20 day oscillations, associated with the westward moving waves or synoptic-scale convective systems generated over the warm Bay of Bengal, propagating inland and contributing the substantial rain.

[50] It can be observed that the reconstructed spectra of all India and its subregions, shown in Figures 13a13e, contains the dominant as well as significant cycles, namely, 10–20 day, 20–30 day, 30–40 day, 40–50 day, and 50–80 day, which can be clearly distinct as enormous peaks in their respective spectra.

[51] In order to determine the dominance and significance of such peaks on decadal basis and its variability, if any, the decadal spectral analysis is also performed for all India and its subregions (figures not shown). The dominant peak lying between different periods for all India and its subregions along with their confidence level for all decades is tabulated in Tables 4, 5, 6, 7, and 8.

Table 4. Power Spectra in Each Decade of Rainfall Over all Indiaa
DecadePeriod
10–20 Day20–30 Day30–40 Day40–50 Day50–80 Day
  • a

    Entries without footnotes: 90% CL. HI, high intensity; CL, confidence level.

  • b

    Indicates 99% CL.

  • c

    Indicates 95% CL.

1901–191017.2b28.4b32.2b46.9c53.9c
1911–192019.9b27.3b34.1c40.6b-
1921–193017.9b21.4b36.1b43.572.2b
1931–194011.5b20.2b39.7b40.6c53.1c
1941–195017.5b29.1b31.7b43.572.2c
1951–196019.6b28.2b32.2b45.151.6
1961–197018.6b25.8b33.1b (HI)--
1971–198016.3b27.1b31.9b44b-
1981–199017.7b25.8b39.7b42.9c72.2
1991–200017.9b24.6b30.9b40.6b-
Table 5. Power Spectra in Each Decade of Rainfall Over Southwesta
DecadePeriod
10–20 Day20–30 Day30–40 Day40–50 Day50–80 Day
  • a

    HI, high intensity; CL, confidence level.

  • b

    Indicates 99% CL.

  • c

    Indicates 95% CL.

1901–191016.3b28b30.3b49.5b53.9b
1911–192018.5b23.4b30.8b44b51.6c
1921–193019.4b25.6b38.8b43.5b72.2c
1931–194018.7b27.3b35.7b47.5c62.2c
1941–195017.6b29.1b38.8b49.5b53.1c
1951–196015b26.4b32.8b45.7b61.2,c 52.3b
1961–197017.8b28.9b36.5b (HI)45.1b50.8c
1971–198019.3b27.8b39.2b44b50.1b
1981–199016.9b25.8b32.8b45.1b51.6b (HI)
1991–200015.6b25.2b (HI), 27.1b38.8b40.1b (HI)53.1c
Table 6. Power Spectra in Each Decade of Rainfall Over Southeasta
DecadePeriod
10–20 Day20–30 Day30–40 Day40–50 Day50–80 Day
  • a

    Entries without footnotes: 90% CL. HI, high intensity; CL, confidence level.

  • b

    Indicates 99% CL.

  • c

    Indicates 95% CL.

1901–191017.6b28b39.2,b 30.3b44c-
1911–192019.9,b 17b29.6,b 27.3,b 25.4b32.2b43b60.2
1921–193019.4b20.6b30.1b43c54.7c
1931–194019.6b29.3b35b42c54.7
1941–195019.4b29.1b34.7b49.5-
1951–196017.8b (HI)29.1b33.4b45.7b73.7
1961–197017.2b21.1b37.6b49.5b56.4
1971–198018.5b24.2b39.7b (HI)44.6c53.1c
1981–199015.3b24.4b39.7,b 36.1,b 33.1,b 30.1b41b51.6b
1991–200018.9b20.2b32.2b (HI)46.9c59.2, 50.8
Table 7. Power Spectra in Each Decade of Rainfall Over Centrala
DecadesPeriod
10–20 Day20–30 Day30–40 Day40–50 Day50–80 Day
  • a

    Entries without footnotes: 90% CL. HI, high intensity; CL, confidence level.

  • b

    Indicates 99% CL.

  • c

    Indicates 95% CL.

1901–191018b25.2b32.2b46.9b53.9b
1911–192019.7b27.8b34.4c44.654.7
1921–193018.8b21.4b35.4c43.5,c 40.6c-
1931–194015b23.9b39.7c44.6-
1941–195014.3b27.6b31.7b--
1951–196019.6b27.8b32.8b44.6-
1961–197017.4b29.8b (HI)33.1b40.6c50.8
1971–198018.6,b 13b22.7b33.1c44.6-
1981–199019.2b24.2b31.7b42-
1991–200018.7b22.8b33.4c40.1-
Table 8. Power Spectra in Each Decade of Rainfall Over Northwesta
DecadePeriod
10–20 Day20–30 Day30–40 Day40–50 Day50–80 Day
  • a

    Entries without footnotes: 90% CL. HI, high intensity; CL, confidence level.

  • b

    Indicates 99% CL.

  • c

    Indicates 95% CL.

1901–191017.6b26b37.2b46.9b53.9b
1911–192016b27.3b32.8b43.5-
1921–193018b26.2b32.8b45.1c51.6b
1931–194019.3b24.2b39.7b46.9b64.5,b 54.7b
1941–195017.3b23b30.3c47.5c64.5,c 54.7c
1951–196014.2b26.2b30.9c45.7c50.2c
1961–197019.6b28.7b33.1b46.9c63.3,c 53.9b
1971–198018.8b29.3,b 27.1b35,b 31.9b45.7c52.3
1981–199016.6b28.4,b 26.4,b 20.9b31.7b-63.3c
1991–200019.3b23.4b36.8b45.1,b 40.1b51.6

[52] As far as low-frequency components are considered, the power spectra of rainfall for all India as well as for its subregions in each decade does not exhibit much variation on decadal scale during the last 10 decades.

[53] The basic difference between the decadal power spectra of all India and its subregions, lies in the ratio of strength of annual and other cycles that represent intraseasonal oscillations. The dominant as well as the significant cycles lying between the periods 10–20 day, 20–30 day, 30–40 day, and 40–50 day are highly variable on interdecadal basis. The dominant cycle lying between 50 and 80 day is also highly variable on interdecadal basis for all India and its subregions, except the central region, in which the cycles lying between this period range is significant only for first (1901–1910), second (1911–1920), and seventh (1961–1970) decades.

[54] In contrast, the higher-frequency components i.e., the 80th or nearby harmonics corresponding to the cycle of 40–50 day (MJO), has been noticed for all the regions. But for southwest and southeast regions, the intensity of this cycle is very high, especially for southwest region, and is significant above 95% and 99% levels. For all India, the intensity of this cycle is very weak and not highly significant. But during the last 3 decades the intensity of the dominant cycles lying between this range has increased and is significant at 95% and 99% levels. For the central region also, this cycle is not highly significant as compared to the southwest and for the fifth (1941–1950) decade the significance of this cycle is not even 90%, whereas for the northwest region this cycle is 99% significant only for the first (1901–1910), fourth (1931–1940), and tenth (1991–2000) decade. Thus it can be concluded that, the 40–50 day oscillations is mainly associated with the southern Indian region, namely southwest and southeast.

[55] For each decade of all India, southwest, and southeast regions, the dominant cycle lying between 30 and 40 day periods is 99% significant, except for the second decade of all India. For some decades of southwest and southeast regions in which the MJO is much more prominent, the intensity of this 30–40 day cycle is even more than the 40–50 day cycle present in that decade. The 30–40 day oscillation has been found to be a gradually increasing factor on decadal scale during the last 4 decades of the southeast region. This cycle was also observed for the other two subregions. The dominant cycle and its significance for these two regions can be seen from the 30–40 day column of Tables 7 and 8.

[56] The dominant cycles lying between the 10–20 and 20–30 day are also 99% significant for each decadal spectrum of all India and its subregions. The intensity of 20–30 day cycle is quite high for the last decade (1991–2000) of southwest and central regions.

5. Conclusion

[57] In this paper we have explored the trend and spectral analysis of rainfall, over India, during 1901–2000. The gross features of rainfall variability are captured both by 10 year moving average and Cramer's t-value curves for all India and its subregions. The 10 year moving average of annual rainfall for all India as well as southwest, southeast, and central regions shows significant fluctuations attaining highest averages (heavy rainfall) and lowest averages (deficient rainfall). The all India has one highest/six lowest, southwest has seven highest/five lowest, southeast has three highest/two lowest, and central has eight highest/one lowest events recorded. However, for the northwest subregion, the mean annual rainfall neither attains highest average nor the lowest, signifying normal rainfall throughout the analysis period.

[58] No significant trend is discernable during the last 10 decades, when the linear least squares fitting method and Mann-Kendall statistic to identify the trend and the normalized test statistic and statistical probability to quantify the significance of the trend are applied on the annual rainfall data for all India and its subregions. The correlogram of all India and its subregions show that the annual rainfall data series is somewhat oscillatory in nature. Further, it shows the presence of a 15 year cycle for the southwest region and a 17 year cycle for the central and the northwest regions. The central region also contains a cycle of 19 years.

[59] To understand the variability physically, the correlation of decadal variability of ISMR with that of SSTs was computed, and it can be inferred that the warm phase of AMO and cold phase of IPO causes the enhancement of the rainfall for the southwest region, whereas in the case of all India and central regions, only the warm phase of AMO plays a significant role in enhancing the rainfall. The southern Indian Ocean shows strong anticorrelation in SST and monsoon rainfall for the southwest region, indicating that cooling in that region also tends to increase the rainfall over the southwest region. Due to the presence of dipole structure in North Atlantic for the central region, there is AMO contribution to rainfall decadal variability. On the other hand, the entire field is dominated by negative values which are consistent with the effect that in the central region, a downward trend is observed in rainfall and a positive trend in global SST. Thus the trend analysis in the present case also confirms the physical phenomenon on large-scale spatiotemporal SST variability.

[60] As far as low-frequency components are concerned, the power spectra in each decade for all India as well as for its subregions does not exhibit much variation on decadal scale during the last 10 decades, whereas the high-frequency cycles are highly variable on an interdecadal basis. The 40–50 day oscillations referred to as MJO are mainly concerned with southern India. The 30–40 day oscillations have been found to be a gradually increasing factor on decadal scale during the last 4 decades for the southeast region.

Acknowledgments

[61] We acknowledge our sincere thanks to National Center of Antarctic and Ocean Research, Goa, for the financial support. We are also heartily grateful to V. Krishnamurthy, T. Delsole, and Fred Kucharski for fruitful discussions in understanding the issues that helped us a lot in improving the manuscript. We also thank the anonymous reviewers for their useful comments, which improved our manuscript substantially.