Assessment of Circulation Indices Affecting Indian Summer Monsoon Rainfall, in Addition to ENSO and Equinoo

  • Aakash Kumar Singhania
  • Ganesh D. Kale
  • Abhik Jyoti Borthakur
Original Paper

Abstract

Indian summer monsoon rainfall (ISMR) is a crucial factor affecting the economy of the country. Prediction of ISMR is crucial for formulating strategies of agriculture and its planning and for better management of water resources of the country. Thus, in the present study, significant lagged circulation indices affecting rainfall of months of ISMR are determined by application of linear correlation, removal of multi-collinearity present among significant lagged circulation indices, and formulation of monthly composite index (MCI). Four models are formed for assessment of hydro-climatic teleconnections between rainfall of months of ISMR and different lagged circulation indices, each having model development phase and testing phase. Four models are having model development phase periods 1950–1999, 1950–1994, 1950–1989, and 1950–1984. The MCIs derived for the different months of ISMR for all four models are used for prediction of rainfall for the period of 2000–2014, which is a common testing period for all the four models. From the study, it is observed that significant lagged circulation indices used in development of MCIs for rainfall of each month of ISMR are changing with respect to time periods, having some common indices and some uncommon indices. Also, in the present study, circulation indices in addition to El Niño-Southern Oscillation (ENSO) and Equatorial Indian Ocean Oscillation (Equinoo) which are affecting rainfall of each month of ISMR significantly are determined for better prediction of ISMR.

Keywords

Hydro-climatic teleconnection Circulation indices Removal of multi-collinearity Monthly composite index 

Introduction

The rainfall occurring over India in four months of monsoon season (June–September) is so crucial for the economy of the country that the effect of reduction in summer monsoon rainfall by 19% in 2002 resulted in loss of billions of dollars for India. Thus, ISMR prediction remains a crucial issue [2]. In the water resources management field, rainfall values of month are more crucial than the total rainfall of the complete monsoon period for reservoir operations, planning operations of cropping, distribution of water to various users, etc. [9]. Thus, in the present study, rainfall of each month of ISMR is considered in the analysis.

Though authentic prediction of hydrologic variates is challenging scientifically, it is needed for devising and planning of strategies of agriculture and for improved management of country’s water resources [8]. Hydrologic variates are connected significantly with the circulations in the atmosphere. Such connection can be modeled in two ways: (1) simulations performed by general circulation models (GCMs) and (2) assessment of statistical relationship present among the hydrologic variates and oceanic/atmospheric variates from various parts of the globe. Such connection is called as “hydro-climatic teleconnection” [8].

Simulations performed by GCMs show a significant climate change impact on water resources and hydrology. However, GCM skill significantly decreases (1) from hemispheric or continental spatial scale to scale of local subgrid, (2) from free troposhperic variates to surface variates, and (3) from climate-linked variates like humidity, wind, temperature, pressure etc. to runoff, precipitation, soil moisture, etc. The later variates are more significant for the regime of hydrology [8].

Statistical downscaling and dynamic downscaling of outputs of GCM to regional scale are used in macroscale hydrologic modeling. “Downscaling” means computation of spatially disseminated gridded data at greater resolution through its lower resolution. The basic assumption of statistical invariance in the case of statistical downscaling technique is arguable while dynamic downscaling admits regional climate models (RCMs) which are unable to fit with hydrologic system scale. So, another method to analyze effect of atmospheric circulation on hydrologic variates at basin scale, is to inquire about hydro-climatic teleconnection present among them [8]. The assessment of the hydro-climatic teleconnection between rainfall variation in space, time, and various large-scale circulations present in the atmosphere is very crucial for the socio-economic welfare of a country [9].

Many researchers have studied teleconnections between rainfall (other than rainfall occurring over various spatial scales in India or rainfall of India) and large-scale circulation indices. Karumuri et al. [5] studied the effect of Indian Ocean Dipole (IOD) on winter rainfall of Australia for the duration 1979–1997. They observed that IOD has significant negative partial correlation with Australia rainfall over southern and western regions, causing reduction in the rainfall over the influenced areas of Australia.

Marcella and Eltahir [11] assessed association between monthly and annual rainfall of Kuwait with North Atlantic Oscillation (NAO) and they found significant correlation between them. They also assessed association between Southern Oscillation Index (SOI) and Kuwait annual rainfall and they found significant negative correlation between them. Ionita [4] studied the relationship between East Atlantic/Western Russia (EAWR) pattern and rainfall variability over the Europe, from late spring to mid-winter by using rotated principal component analysis for the time period of 1950–2012. They found that EAWR has significant impact on variability of climate over the Europe from late spring to mid-winter.

Rasanen et al. [18] performed temporal and spatial analysis of effect of ENSO on hydroclimate. The study was divided into two parts: (1) Mainland Southeast Asia (MSEA) seasonal precipitation analysis over the period 1980–2013, (2) proxy Palmer Drought Severity Index (PDSI) analysis for the season March to May for two places located in MSEA over the period 1650–2004. The study provided better understanding of seasonal development of anomalies of precipitation during ENSO events. The impacts of ENSO were observed to be most concordant and seen over the greatest areal extents during the months of March to May while ENSO events decay. The study found that, over a longer time period, ENSO has influenced March to May hydroclimate of the region over most of the years of analysis  period and that over half of the analysis period shown a significant increment in hydro-climatic variability because of ENSO.

Taibi et al. [20] analyzed relationship between the annual, monthly, and daily rainfall data of Northern Algeria with the four circulation indices as follows: NAO, ENSO, Mediterranean Oscillation (MO), and Western Mediterranean Oscillation (WeMO) for the period 1940–2010 by using correlation and the Kendall correlation coefficient. Study revealed that, relationships between variation in rainfall and indices of general atmospheric circulations for extreme and interannual event variability are reasonably impacted by the ENSO and MO. Significant correlations are found between the SOI and yearly rainfall in the northwestern region of study area, which is probably associated with the rainfall decrement in this region. In Northern Algeria, seasonal rainfall was found to be influenced by MO and NAO. Wei et al. [21] analyzed relationship between extreme precipitation indices and three circulation indices namely East Asian Summer Monsoon (EASM), Pacific Decadal Oscillation (PDO), and SOI for the period 1960–2014 by using correlation analysis. The study found that, alteration in extreme precipitation may be afflicted by PDO, EASM, and ENSO.

Some researchers have found out teleconnection between the rainfall of basin or state (located in India) and climatic indices. Kashid et al. [6] studied the association between individual grid point’s weekly rainfall and lagged weekly Equinoo and ENSO indices, highest correlated grid point’s rainfall at instant preceding time step, grid point rainfall at instant preceding time step, and Outgoing Longwave Radiation (OLR) of preceding time step over the upper Mahanadi River basin by using correlation and Kendall’s Tau. Predicted rainfall is farther utilized in genetic programming model for prediction of streamflows.

Sankaran and Reddy [19] investigated relationship between summer monsoon rainfall of Kerela state with four climatic oscillations, which are Atlantic Multidecadal Oscillation (AMO), ENSO, Quasi-Biennial Oscillation (QBO), and Equinoo, by using time-dependent intrinsic correlation (TDIC) with multivariate empirical mode decomposition (MEMD) in multiple time scales. They found that nature and strength of relationship between different climatic indices and summer monsoon rainfall varies with time scales. Yin et al. [22] assessed hydro-climatic teleconnections present between annual and seasonal precipitation and climatic indices of Indian summer monsoon (ISM), IOD, ENSO, and NAO in Beas River basin over the period 1982 to 2010. They found that association between ISM and monsoon precipitation was not significant, while association between ENSO and precipitation in winter season was less significant as compared to that of in monsoon season. Also, association of winter/monsoon precipitation with IOD was not evident as in the case of ENSO. They also found that, NAO and ENSO have played crucial roles in the alterations of winter and monsoon precipitation.

Maity and Nagesh Kumar [10] studied the effect of sea surface temperature (SST) on Indian subdivisional monthly rainfall by using time series similarity search approach over the time period 1901–1990. Both temporal and spatial effects were investigated in the study. The Euclidean distance was used as a measure of assessing similarity between two time series. Also, relative importance of ocean-land temperature contrast (OLTC), land surface temperature (LST), and SST and their alteration from season to season and from subdivision to subdivision was studied. They found that, there was not much similarity between rainfall series and LST and they also found relatively higher effect of OLTC in early monsoon and pre-monsoon periods. They also observed that SST played a more significant role during post-monsoon and late monsoon periods.

Affecting global centers of agricultural production and population, variation in the monsoon of India subsists as a fluctuation of climate and is having enormous socio-economic significance [1]. Gadgil et al. [2] studied the association of ISMR anomalies with the averages of Equinoo and ENSO index computed over the months of June to September. They found significant correlation of ISMR with Equatorial Zonal Wind (EQWIN) index as well as with ENSO. Maity and Nagesh Kumar [9] assessed hydro-climatic teleconnection present between MCI of ENSO and Equinoo with monthly ISMR by using correlation. They found significant association between MCI and monthly ISMR. Also, they have observed that, 25% of the variability in monsoon monthly rainfall of all India (ALLIN) can be described by the MCI as compared to 11% by ENSO information only and 4% by Equinoo only.

Maity and Nagesh Kumar [7] used Copula-based approach to identify dependence among ISMR and combined index of Equinoo and ENSO. They found correlation of 0.81, between predicted and observed rainfall for the months of summer monsoon. None of the above studies on teleconnection between ISMR and climatic indices used more than two climate indices. Also, effect of different time periods of analysis on teleconnection between rainfall of months of ISMR and climatic indices had not been studied by any of the aforementioned studies.

Thus, in the present study, teleconnection between rainfall of months of ISMR and eleven climatic indices (with each index having four lags) is assessed by formulation of four models to determine the significant lagged circulation indices affecting rainfall of different months of ISMR, in addition to ENSO and Equinoo, which is not performed by any aforementioned study. Also, effect of different time periods of analysis on teleconnection between rainfall of months of ISMR and climatic indices has been studied by formulation of four different models having model development phase periods as 1950–1999, 1950–1994, 1950–1989, and 1950–1984. Thus, in the present study, effect of different time periods of analysis on teleconnection between rainfall of months of ISMR and climatic indices is studied, which is not performed by any aforementioned study. Identification of common significant lagged circulation indices obtained from four different models and affecting rainfall of each month of ISMR, in addition to ENSO and Equinoo will enhance the predictability of rainfall of each month of ISMR few months ahead.

Data

Monthly ISMR Data

The monthly rainfall data of ALLIN is obtained from the website of Indian Institute of Tropical Meteorology (IITM), Pune, India (ftp://www.tropmet.res.in/pub/data/rain/iitm-regionrf.txt). There are total 306 uniformly spreaded rain gauge stations over 30 meteorological subdivisions having areal extent of about 2,880,000 sq.km., which covers 90% of total areal extent of India. The subdivisional monthly rainfall data is prepared by using area of district as weight for every rain gauge station in given subdivision. Similarly, regional and ALLIN monthly rainfall data is prepared by using weight for each subdivision, lying in given region or all India (ftp://www.tropmet.res.in/pub/data/rain/Readme.pdf). The data used in the study is part of “IITM Indian regional/subdivisional Monthly Rainfall data set (IITM-IMR)” [12, 13, 14, 15, 16, 17]. The total time period of extracted data of monthly ISMR used in the present study is 1950 to 2014. The monthly data of ISMR is converted into monthly anomaly data and the procedure for preparing monthly anomaly data is given in Maity et al. [8].

Data of Circulation Indices

The circulation indices which are considered in the present study are NAO, PDO, EAWR, ENSO index, Arctic oscillation (AO), East Atlantic (EA), East Pacific/North Pacific (EPNP), EQWIN which is index of Equinoo, Pacific/North American Oscillations (PNA), Scandinavia (SCAND), and West Pacific (WP).

The data of aforesaid indices (except EWQIN) is obtained from National Oceanic and Atmospheric Administration (NOAA) website; web links for source of data of each index (except EQWIN) are given in Table 1. Raw data required for preparation of EQWIN index data is also given in Table 1. The description of Equinoo, preparation of index of Equinoo (EQWIN), and procedure of preparation of anomaly data are given in Maity et al. [8]. Anomaly data of monthly ISMR and circulation indices is used in the model development and testing phases.

Methodology

The teleconnections between rainfall of each month of ISMR and eleven circulation indices are assessed in the present study by formulating four different models. Thus, four models are formulated and each model is segmented into model development and testing phases. The time periods of model development phase for four different models are 1950–1999, 1950–1994, 1950–1989, and 1950–1984 while common time period for testing phase for all four models is 2000–2014. Extensive reductions have been observed in continental diurnal temperature range (DTR) since 1950s, which concurred with increment in cloud amounts [3]. Thus, in the present study, the starting year of model development phase in all four models is considered as 1950.

Maity and Nagesh Kumar [10] used 35 years sliding window for evaluation of various coefficients of MCI equations and they found that coefficients are nearly stable with very small variation. So, in the present study, duration of all models is either 35 years or more. In the model development phase, correlation between the lagged circulation indices (one to four lags for each circulation index) and rainfall of each month of ISMR is assessed along with its significance and then lagged circulation indices having significant correlation with ISMR are determined. Multi-collinearity present among selected significant lagged circulation indices corresponding to each month of ISMR is assessed by using correlation. If multi-collinearity is present among selected significant lagged circulation indices, then it is removed by keeping those significant lagged circulation indices having higher correlation with corresponding target output, i.e., given monthly rainfall of ISMR. Then, significant lagged circulation indices obtained after removal of multi-collinearity are used in the formulation of MCI by using multivariate linear regression for rainfall of each month of ISMR. The potential of developed MCIs for predicting monthly rainfall of ISMR is assessed by computing correlation between predicted and observed rainfall in testing phase. The aforesaid procedure of model development and testing is followed for all four models.

Results

Model 1

Model Development Phase (1950–1999)

Selection of Statistically Significant Lagged Circulation Indices

Significant lagged circulation indices are selected based on correlation at 5% significance level, present between each lagged index (eleven indices with four lags for each index) and rainfall of each month of ISMR. The significant lagged circulation indices selected for monthly rainfall of June, July, August, and September are shown in Figs. 1, 2, 3, and 4 respectively. Figures 1, 2, 3, and 4 are showing bar plots of correlation coefficients between the lagged circulation indices and rainfall of months of June to September respectively. Unfilled bars in Figs. 1, 2, 3, and 4 are showing lagged circulation indices having statistically significant correlation with corresponding monthly rainfall. These statistically significant lagged circulation indices, selected for each month of ISMR are presented in Table 2 and they are assessed further for presence of multi-collinearity among them.
Fig. 1

Correlation coefficients of lagged circulation indices with rainfall of June month for model 1

Fig. 2

Correlation coefficients of lagged circulation indices with rainfall of July month for model 1

Fig. 3

Correlation coefficients of lagged circulation indices with rainfall of August month for model 1

Fig. 4

Correlation coefficients of lagged circulation indices with rainfall of September month for model 1

Table 2

Significant lagged circulation indices selected for each month of ISMR for the time period (1950–1999)

Month

Significant lagged circulation indices

June

EQWINMarch

EAWRMarch

July

EQWINJune

EPNPJune

EPNPMarch

EAMarch

August

EPNPJuly

September

EAWRAugust

ENSOJuly

ENSOJune

ENSOAugust

EPNPAugust

EPNPJuly

Formulation of MCI for Each Month of ISMR

Multi-collinearity is found between significant lagged circulation indices, selected for rainfall of months of July and September. The multi-collinearity present in these lagged circulation indices is removed. After removing multi-collinearity, MCI for each month of rainfall of ISMR is formulated by using multivariate linear regression model and all formulated MCIs  are shown in Table 3. Significant correlations observed between MCIs, developed for the months June, July, August, and September and their corresponding monthly rainfall are 0.41, 0.53, 0.29, and 0.69 respectively.
Table 3

MCI formulated for each month of ISMR and it's correlation with corresponding month rainfall for model 1

Month

MCI

Correlation coefficients*

June

RainJune = − 0.28*EQWINMarch − 0.21*EAWRMarch

0.41

July

RainJuly = 0.15*EPNPJune − 0.21*EPNPMarch + 0.29*EAMarch

0.53

August

RainAugust = − 0.24*EPNPJuly

0.29

September

RainSeptember = − 0.71*ENSOAugust − 0.30*EPNPAugust − 0.15*EPNPJuly

0.69

*The correlation coefficient is significant at 5% significance level

Testing Phase (2000–2014)

Regression relationships developed in terms of MCIs are shown in Table 3 (for model 1) and these are used for prediction of corresponding rainfall over the testing period (2000–2014). The correlation is assessed between the predicted rainfall of each month of ISMR (for model 1) and corresponding observed rainfall for the period 2000–2014, and values of corresponding correlation coefficients are shown in Table 4.
Table 4

Correlation between predicted rainfall of each month of ISMR with corresponding observed rainfall for the time period 2000–2014

Month

June

July

August

September

Correlation coefficient

0.37

0.19

0.21

0.43

Model 2

Model Development Phase (1950–1994)

Selection of Statistically Significant Lagged Circulation Indices

Significant lagged circulation indices are selected based on assessment of correlation at 5% significance level, present between each lagged circulation index (eleven indices with four lags for each index) and rainfall of each month of ISMR. These statistically significant lagged circulation indices chosen for each month of ISMR are shown in Table 5 (no significant lagged circulation indices are found in rainfall of August month) and these are assessed further for presence of multi-collinearity between them.
Table 5

Significant lagged circulation indices selected for each month of ISMR for time period (1950–1994)

Month

Significant lagged circulation indices

June

EQWINMarch

EAWRMarch

EPNPMay

July

EQWINJune

ENSOJune

WPJune

EAMarch

September

EAWRAugust

ENSOJuly

ENSOJune

ENSOAugust

EPNPAugust

EPNPJuly

Formulation of MCI for Each Month of ISMR

Multi-collinearity is observed between significant lagged circulation indices, selected for monthly rainfall of June and September. The multi-collinearity present in these lagged circulation indices is removed. After removing multi-collinearity, MCI for each month of rainfall of ISMR is formulated and all formulated MCIs are shown in Table 6. Significant correlations found between MCIs, developed for the months June, July, and September and their corresponding monthly rainfall are 0.48, 0.73, and 0.71 respectively, while significant correlation is not found between lagged circulation indices and observed rainfall for the month of August.
Table 6

MCI formulated for each month of ISMR and it's correlation with corresponding month rainfall for model 2

Month

MCI

Correlation coefficients*

June

RainJune = − 0.23*EQWINMarch − 0.17*EAWRMarch − 0.28*EPNPMarch

0.48

July

RainJuly = − 0.19*WPJune + 0.47*EQWINJune − 0.25*ENSOJune + 0.40*EAMarch

0.73

September

RainSeptember = − 0.80*ENSOAugust − 0.31*EPNPAugust − 0.31*EPNPJuly

0.71

*The correlation coefficient is significant at 5% significance level

Testing Phase (2000–2014)

Regression relationships developed in terms of MCIs are shown in Table 6 (for model 2) and these are used for prediction of corresponding rainfall over the testing period (2000–2014). The correlation is evaluated between the predicted rainfall of each month of ISMR (for model 2) and corresponding observed rainfall for the period 2000–2014, and values of corresponding correlation coefficients are shown in Table 7.
Table 7

Correlation between predicted rainfall of each month of ISMR with corresponding observed rainfall for the time period 2000–2014

Month

June

July

September

Correlation coefficients

0.17

0.30

0.42

Model 3

Model Development Phase (1950–1989)

Selection of Statistically Significant Lagged Circulation Indices

Significant lagged circulation indices are selected based on assessment of correlation at 5% significance level, present between each lagged index (eleven indices with four lags for each index) and rainfall of each month of ISMR. These statistically significant lagged circulation indices, selected for each month of ISMR are shown in Table 8 and these are assessed further for presence of multi-collinearity among them.
Table 8

Significant circulation indices selected for each month of ISMR for time period (1950–1989)

Month

Significant lagged circulation indices

June

NAOApril

EPNPMay

AOApril

July

WPJune

WPApril

EQWINJune

EPNPJune

EAMarch

ENSOJune

August

EPNPJuly

EAWRMay

EAJune

September

EQWINJuly

EPNPAugust

EPNPJuly

EAWRAugust

ENSOAugust

ENSOJuly

ENSOJune

Formulation of MCI for Each Month of ISMR

Multi-collinearity is observed between significant lagged circulation indices, selected for rainfall of each month of ISMR. The multi-collinearity present in these significant lagged circulation indices is removed. After removing multi-collinearity, MCI for each month of rainfall of ISMR is formulated and all formulated MCIs are shown in Table 9. Significant correlations found between MCIs, developed for the months June, July, August, and September and their corresponding monthly rainfall are 0.50, 0.75, 0.27, and 0.74 respectively.
Table 9

MCI formulated for each month of ISMR and it's correlation with corresponding month rainfall for model 3

Month

MCI

Correlation coefficients*

June

RainJune = − 0.35*NAOApril − 0.34*EPNPMay

0.50

July

RainJuly = − 0.20*WPJune + 0.90*WPApril + 0.46*EQWINJune + 0.15*EPNPJune + 0.35*EAMarch

0.75

August

RainAugust = − 0.22*EPNPJuly

0.27

September

RainSeptember = 0.25*EQWINJuly − 0.29*EPNPAugust − 0.11*EPNPJuly − 0.78*ENSOAugust

0.74

*The correlation coefficient is significant at 5% significance level

Testing Phase (2000–2014)

Regression relationships developed in terms of MCIs are shown in Table 9 (for model 3) and these are used for prediction of corresponding rainfall over the testing period (2000–2014). The correlation is found between the predicted rainfall of each month of ISMR (for model 3) and corresponding observed rainfall for the period 2000–2014, and values of corresponding correlation coefficients are shown in Table 10.
Table 10

Correlation between predicted rainfall of each month of ISMR with corresponding observed rainfall for the time period 2000–2014

Month

June

July

August

September

Correlation coefficients

0.20

0.064

0.21

0.49

Model 4

Model Development Phase (1950–1984)

Selection of Statistically Significant Lagged Circulation Indices

Significant lagged circulation indices are selected based on assessment of correlation at 5% significance level, present between each lagged index (eleven indices with four lags for each index) and rainfall of each month of ISMR. These statistically significant lagged circulation indices chosen for each month of ISMR are shown in Table 11 and these are assessed further for presence of multi-collinearity between them.
Table 11

Significant lagged circulation indices selected for each month of ISMR for time period (1950–1984)

Month

Significant lagged circulation indices

June

PNAApril

NAOApril

EPNPMay

EAMay

AOApril

July

EPNPJune

EAMarch

August

EPNPJuly

September

EPNPAugust

EPNPJuly

EAWRAugust

ENSOAugust

ENSOJuly

ENSOJune

Formulation of MCI for Each Month of ISMR

Multi-collinearity is observed between significant lagged circulation indices selected for monthly rainfall of June and September. The multi-collinearity present in these lagged indices is removed. After removing multi-collinearity, MCI for each month of rainfall of ISMR is formulated and all formulated MCIs are shown in Table 12. Significant correlations found between MCIs developed for the months June, July, August, and September and their corresponding monthly rainfall are 0.63, 0.57, 0.35, and 0.71 respectively.
Table 12

MCI formulated for each month of ISMR and it's correlation with corresponding month rainfall for model 4

Month

MCI

Correlation coefficients*

June

RainJune = 0.27*PNAApril − 0.36*NAOApril − 0.27*EPNPMay − 0.30*EAMay

0.63

July

RainJuly = 0.17*EPNPJune + 0.35*EAMarch

0.57

August

RainAugust = − 0.28*EPNPJuly

0.35

September

RainSeptember = − 0.34*EPNPAugust − 0.12*EPNPJuly − 0.79*ENSOAugust

0.71

*The correlation coefficient is significant at 5% significance level

Testing Phase (2000–2014)

Regression relationships developed in terms of MCIs are shown in Table 12 (for model 4) and these are used for prediction of corresponding rainfall over the testing period (2000–2014). The correlation is found between the predicted rainfall of each month of ISMR (for model 4) and corresponding observed rainfall for the duration 2000–2014, and values of corresponding correlation coefficients are shown in Table 13.
Table 13

Correlation between predicted rainfall of each month of ISMR with corresponding observed rainfall for the time period 2000–2014

Month

June

July

August

September

Correlation coefficients

− 0.01

0.06

0.21

0.42

The average of significant correlation coefficients of four models corresponding to correlation between MCI developed for rainfall of each month of ISMR and corresponding observed rainfall for four different model development phase periods (1950–1999, 1950–1994, 1950–1989, and 1950–1984) are shown in Table 14.
Table 14

The  average of significant correlation coefficients of four models corresponding to correlation between MCI developed for rainfall of each month of ISMR and corresponding observed rainfall

Month

* Average of significant correlation coefficients

June

0.51

July

0.65

August

0.30

September

0.71

* The correlation coefficients of each month corresponding to four models are significant at 5% significance level

From Table 14, it can be observed that averages of significant correlation coefficients are more than 0.6 for the monthly rainfall of July and September which shows good predictability of MCIs developed for these months.

Average of correlation coefficients of four models corresponding to correlation between predicted and observed rainfall for each month of ISMR assessed over the common testing period (2000–2014) are shown in Table 15.
Table 15

Average of correlation coefficients of four models corresponding to correlation between predicted and observed rainfall for each month of ISMR evaluated over the common testing period (2000–2014)

Month

Average correlation coefficient

June

0.19

July

0.15

August

0.21

September

0.44

From Table 15, it can be observed that predictability of rainfall for September month is highest followed by rainfall of August, June, and July months.

The significant lagged circulation indices selected for formation of MCI, after removing multi-collinearity, for rainfall of each month of ISMR for all four models are shown in Table 16. In Table 16, common significant lagged circulation indices (common among two models or more than two models) are shown in italic and uncommon significant lagged circulation indices are shown in normal font.
Table 16

Significant lagged circulation indices selected for formation of MCI, after removing multi-collinearity, for rainfall of each month of IMSR for all four models

Model No. →

Month of ISMR ↓

Model 1

Model 2

Model 3

Model 4

June

EQWINMarch

EAWR March

EPNP May

EAWR March

NAO April

EPNP May

PNAApril

NAO April

EPNP May

EAMay

July

EPNP June

EPNPMarch

EA March

WP June

EQWIN June

EA March

ENSOJune

WP June

WPApril

EQWIN June

EPNP June

EA March

EPNP June

EA March

August

EPNP July

 

EPNP July

EPNP July

September

EPNP August

EPNP July

ENSO August

EPNP August

EPNP July

ENSO August

EQWINJuly

EPNP August

EPNP July

ENSO August

EPNP August

EPNP July

ENSO August

From Table 16, it can be observed that significant lagged circulation indices used in development of MCI for rainfall of June, July, and September (except August) months of ISMR are changing with respect to time periods, having some common indices and some uncommon indices. Common significant lagged circulation indices (common significant lagged circulation indices among atleast two models) affecting June month rainfall are EPNPMay, EAWRMarch, and NAOApril while uncommon significant lagged circulation indices are EQWINMarch, PNAApril, and EAMay. Common significant lagged circulation indices affecting July month rainfall are EAMarch, EPNPJune,WPJune, and EQWINJune while uncommon significant lagged circulation indices are EPNPMarch, ENSOJune, and WPApril. Common significant lagged circulation index among all four models affecting July month rainfall is EAMarch.

Common significant lagged circulation index affecting August month rainfall is EPNPJuly. There is no uncommon significant lagged circulation index affecting August month rainfall. Thus, EPNPJuly is solely important and significant lagged circulation index affecting the August month rainfall as observed in the present analysis. Similarly, common significant lagged circulation indices affecting September month rainfall are EPNPAugust, EPNPJuly, and ENSOAugust while uncommon significant lagged circulation index affecting September month rainfall is EQWINJuly. Common significant lagged circulation indices among all four models affecting September month rainfall are EPNPAugust, EPNPJuly, and ENSOAugust. Sankaran and Reddy [19] have also found that robustness and nature of relationship between summer monsoon rainfall and oscillations of climate, change with time periods, and temporal scales. In the present study, too, it has been found that hydro-climatic teleconnection between rainfall of June, July, and September months of ISMR and lagged circulation indices is changing with respect to model development phase periods which is similar to that of observed by Sankaran and Reddy [19].

Common significant circulation indices affecting rainfall of different months of ISMR except ENSO and Equinoo (considered if significant and common) are EPNP, EAWR, and NAO for June month; EA, EPNP, and WP for July month and EPNP for August and September months. Identification of significant lagged circulation indices in addition to ENSO and Equinoo affecting rainfall of different months of ISMR is one of the contributions of the present study. Common and uncommon significant lagged circulation index/indices affecting rainfall of each month of ISMR (after removing multi-collinearity) can be used as predictor(s) for prediction of corresponding month rainfall few months ahead. Addition of significant circulation index/indices, in addition to ENSO and Equinoo (considered if significant and common), may enhance the predictability of rainfall for months of ISMR.

Conclusions

In this study, hydro-climatic teleconnection between the rainfall of each month of ISMR and significant lagged circulation indices, in addition to ESNO and Equinoo is established, after removing multi-collinearity, if present. Effect of different time periods on the selection of significant lagged circulation indices is also studied by formulation of four models having different model development phase periods (1950–1999, 1950–1994, 1950–1989, and 1950–1984) along with common time period of testing phase (2000–2014) for all four models.

In the present study, it has been found that hydro-climatic teleconnection between rainfall of June, July, and September months of ISMR and significant lagged circulation indices (after removing multi-collinearity, if present) is changing with respect to model development phase periods which is similar to that of observed by Sankaran and Reddy [19]. Common and uncommon significant lagged circulation index/indices affecting rainfall of each month of ISMR can be used as predictor(s) for prediction of corresponding month rainfall few months ahead. Addition of significant lagged circulation index/indices, in addition to ENSO and Equinoo (considered if significant and common), may enhance the predictability of rainfall for months of ISMR.

Notes

Compliance with Ethical Standards

Conflict of Interest

The paper has used data and information from various sources which are properly acknowledged in the references and text. The paper has no conflict of interest with any published sources as per the knowledge of the authors.

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Copyright information

© Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  • Aakash Kumar Singhania
    • 1
  • Ganesh D. Kale
    • 1
  • Abhik Jyoti Borthakur
    • 1
  1. 1.Civil Engineering DepartmentSV NITSuratIndia

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