Classification of summer monsoon rainfall patterns over India

INTERNATIONAL JOURNAL OF CLIMATOLOGY, VOL. 12,269-280 (1992) 551.577.32: 551.585.3(540)

CLASSIFICATION OF SUMMER MONSOON RAINFALL PATTERNS OVER INDIA

ASHWINI KULKARNI, R. H. KRIPALANI AND S . V. SINGH

Indian Institute of Tropical Meteorology, Pune-4l1008, India

Received 28 February 1991 Revised 6 September 1991

ABSTRACT

Seasonal (June through September) percentage departure from normal rainfall patterns over India have been classified by objective methods utilizing data for a 120-year period (1871-1990). The methods used are the map-to-map correlation method and the k-means clustering method. Empirical orthogonal functions (EOFs) are also presented.

It is seen that 75 per cent of the charts can be cIassified into six distinct types by the map-to-map method. Six distinct types also are obtained by the k-means method. The first four dominant EOFs explain 52 per cent of the variance.

Intercorrelations and contingency tables among the types obtained by these methods and visual examination suggests that the dominant patterns are similar, irrespective of the method used. It is also seen that the monsoon rainfall for the country as a whole and the spatial patterns may have no relationship. Even during normal monsoon years, the spatial patterns may be different.

The advantages and disadvantages of the methods used are discussed.

KEY WORDS Classification Rainfall patterns

1. INTRODUCTION

Pattern recognition methods have been used to characterize the joint spatio-temporal behaviour of meteorological fields. These procedures identify the recurring spatial configurations, or type patterns and thus characterize the climate and climate variability. In meteorology, the objective classification methods commonly used are:

(i) map-to-map (MM) correlation (Lund, 1963) (ii) k-means (KM) clustering method (Kruizinga, 1979)

This analysis is an empirical study of a small selection of many possible clustering methods (Everitt, 1980). Though empirical orthogonal functions (EOFs) (Kutzbach, 1967) are not designed specifically to find clusters, we have presented the unrotated and rotated EOFs as well.

There are two problems of interest here. What are the spatial patterns of precipitation over India? What causes them? This paper addresses only the first. Hence in the present study the principal features of the spatial distribution of seasonal percentage departure from normal rainfall patterns as realized during the 120- year period (1871-1990) are examined with the help of the above methods. This study is directed to serve two main purposes. The first is to show that there exist certain dominant modes of variability in monsoon rainfall and that the above methods are able to identify these modes. Secondly we wish to show that, the all-India monsoon rainfall (MR) and the spatial distribution may have no relationship. Even during normal MR the patterns may be different.

In section 2 we describe the rainfall data used. The methods are briefly described in section 3. The results of these methods are presented and compared in section 4. Finally in section 5 we compare the advantages and disadvantages of the two methods and enumerate the main conclusions.

0899-841 8/92/030269-12$06.00 0 1992 by the Royal Meteorological Society

270 A. KULKARNI ET AL.

2. DATA

Monthly rainfall data for 306 stations spread over the country for the months June through September 1871-1984 were obtained in a processed form from B. Parthasarathy, who received the original data from the India Meteorological Department. The quality and the details of the rainfall data are given in Parthasarathy et al. (1987; henceforth to be referred to as P). Instead of using the meteorological subdivisions, which have irregular shape and size, we have used uniform blocks of 2.5" latitude by 2.5" longitude (Figure 1). Hence from these monthly data of 306 stations, seasonal averages for 51 blocks (Figure 1) were prepared. The number of stations in a block varies from 3 to 12. However, the number of stations for any block is fixed throughout the data period (1871-1984). The percentage departures from normal were prepared for each of the 51 blocks. For classification purposes, only seasonal percentage departures from normal for these 5 1 blocks are utilized. The MR is taken from P. This data set also is prepared from the above station data. Data for the meteorological subdivisions for the years 1985-1989 have been collected from Mausam and for 1990 from the Weekly Weather Report of the India Meteorological Department (1986, 1987, 1988, 1989, 1990a, b). From this, data for the 51 blocks have been estimated by interpolation. For classification purposes we have used the data for the 114-year period (1871-1984) since it is from the same source.

3. METHODS

3.1. The M M method

Step 1. Consider a series of n (here 114) consecutive maps that show the spatial distribution of some variable, X, based on observations at m (here 51) locations. The correlation coefficient ri , between the m values for map i and corresponding m values for map j is used as a measure of similarity between two maps.

Step 2. The correlations between each pair of map patterns are arranged as the elements of the n by n matrix R, with (i, j)th element riTi.

Step 3. The matrix R is then searched, row by row, to find that map pattern which is highly correlated with a maximum number of others. Here we must define what is meant by a 'high' correlation. In practice, a

Figure 1. Map showing the location of 51 blocks. The topmost block is not used

INDIAN SUMMER MONSOON RAINFALL 27 1

threshold value of the correlation coefficient, r, is selected from experience, and any value equal to or above it is classified as a ‘high’ correlation.

Step 4. If row i of the correlation matrix has the greatest number of high correlations, map pattern i and all map patterns having correlation >rl with map pattern i, are identified as type 1 patterns. Type 1 patterns are removed from the data and the process is repeated to find successive type patterns.

3.2. The KM method

In this method a class is represented by the mean of all patterns belonging to that class. Step I . Establish the number k of classes. Choose, at random, k patterns from the complete data set and

assign one to each class. At this stage the mean pattern of every class is equal to its respective chosen pattern. Step 2. Assign each pattern of the complete data set to the class whose mean is nearest according to the

distance measure d i , j given by rn d . , .= C ( x i - x j ) 2

i, j = 1 L J

This is the usual Euclidean distance between two m-dimensional vectors. Step 3. Compute new mean patterns for each class. Step 4 . Repeat step 2 and note whether there are any patterns that change class. If so, then repeat steps 3

and 4. The above-described procedure converges quickly.

3.3. EOF technique

The procedure for determining these functions is available in numerous papers (e.g. Kutzbach, 1967). It consists of two basic steps.

Step 1. From the n maps each having m points, prepare a symmetrical correlation/covariance matrix of order m by m.

Step 2. Determine the eigenvalues and the eigenvectors from this symmetrical matrix. The spatial distribution of the elements of the eigenvectors gives the desired empirical functions and the eigenvalues are the measures of the variance explained by each function.

To determine the eigenvalues and eigenvectors we have used the software package of the Numerical Algorithm Group (UK) Fortran Library installed on the Norsk-Data 560 Computer system at the Indian Institute of Tropical Meteorology.

4. RESULTS

4.1. Classijication b.y the M M method

Though this method of classification is objective some subjectivity is involved in deciding the threshold correlation coefficient (rJ. Lund (1963) pointed out that a high value of rt leads to fewer maps being included in each type, a greater similarity between types, and a greater number of cases not included in any type, whereas the use of lower rl includes too many charts in the first few types and sufficiently distinct types cannot be classified. Keeping this in view, and the fact that seasonal patterns are removed, we have selected a value of 0.35 for rl, which is significant for a sample of 51.

With this method, 75 per cent of the charts could be classified into six distinct types. Here only the first six types are retained since the frequency of the seventh type was five and it had significant correlation with the first type. Four of these five could be classified in the first type. The frequency of the remaining classes was less than three. Instead of retaining the single year representations as typical types, the best three correlated (having spatial similarity) with each single representation are averaged to obtain smooth types. The years considered for averaging are shown in Table I.

The most dominant type, type A in Figure 2, is associated with negative departures (NDs) over the entire country, except the north-eastern parts. Negative departures of the order of - 80 per cent are observed over

Tabl

e I.

Freq

uenc

ies (

FQ) f

or th

e ty

pes o

btai

ned

by th

e M

M an

d K

M m

etho

ds. T

he av

erag

e MR

asso

ciat

ed w

ith 3

repr

esen

tativ

e yea

rs (A

3) as

wel

l as a

ll ye

ars (

AL)

in

a t

ype

are

also

sho

wn

MM

met

hod

Type

Y

ears

A

3 F

Q

AL

Type

A

1899

19

11

1918

67

0 23

76

3 K

B

1893

19

17

1976

93

7 16

92

9 L

C

1881

18

84

1894

91

9 15

91

0 M

D

18

88

1923

19

48

834

14

856

N

E 19

03

1910

19

66

843

13

866

0

F

1913

19

27

1941

78

7 5

796

P

KM

met

hod

p

x

A3

FQ

A

L 2

1911

19

18

1939

72

3 20

76

9 - 2 P

Yea

rs

h

Y

1886

19

03

1949

87

7 19

86

4 18

88

1904

19

22

809

17

822

b

1884

19

26

1959

92

3 15

90

4 P

19

08

1917

19

76

918

15

92 1

1882

19

07

1946

85

9 6

844

INDIAN SUMMER MONSOON RAINFALL 273

2 0'

I 0'

20'

10.

Figure 2. The six typical types obtained by the MM method

the north-western parts of the country. The magnitude of the positive departures (PDs) over the north-eastern parts is less. It is of interest to note that all the 3 years considered for averaging of this type were drought years. The average MR for the 3 years is 670 mm, the normal value being 852 mm (P). The average MR for the 23 years falling in type A is 763 mm, confirming that this type is associated with severe droughts over the country, in particular over the north-western parts.

Type B shows PDs over north-western and south-eastern parts of the country, the PDs over north-western parts being very high. It shows NDs along the west coast. The average MR based on 3 years is 937 mm and for all the years falling in this type (16) is 929 mm, suggesting that this pattern could be associated with above normal MR. All the 3 years considered for obtaining type B had severe floods over north-western parts of India (P).

Except over north-eastern and south-western parts, type C shows PDs, with highest values centred around 22.OoN,69PE. The average MR for 3 years being 919 mm and for all years (15) 910 mm. Two of the three years considered for obtaining type C had severe floods over northern parts of India. This pattern also could be associated with normal or above normal MR.

The intensity of departures in type D is much less than the previous three types. Type D shows NDs over the north-western and south-eastern parts. It also shows PDs centred around 25-0'",81.OGE and southern parts of west coast. Average MR for 3 years is 834 mm and for all years (14) is 856 mm. Only one of the three years had severe droughts over Gujarat and Saurashtra and Kutch (P). This is the area showing NDs of -40 per cent in type D. This type could be associated with normal MR.

Type E has PDs over south-eastern parts and NDs practically throughout the country. The average MR for 3 years being 843 mm and for all (13) being 866 mm. None of the 3 years considered for obtaining Type E had floods or droughts. Hence, this pattern also could be associated with normal MR.

Type F has PDs centred around 23.0°N,71.0"E and 22.0"N,89.0°E and NDs over rest of the country. The MR here being 787 mm (3 years) and 796 mm for all (5) years in this type. The average MR suggests that this type could be associated with below normal MR.

To investigate whether the patterns have changed over time, the analysis was carried out on the first 57 years (1871-1927) and the last 57 years (1928-1984) separately. It was found that the first four patterns that emerged were similar. The fifth varied slightly and the frequency in the sixth type was very much less (< 3), suggesting that the dominant patterns have not changed over time.


We have computed correlations based on 5 1 values of each type (as shown in Figure 2) and corresponding 51 values of remaining types. Table I1 shows these correlations among the types obtained by this method. Except types A and D none of the other types are positively significantly correlated (>0.35), suggesting that distinct types are obtained by this method. Also, we find that extreme events, i.e. drought/flood over a region, have been brought out.

Instead of the correlation coefficient, a more meaningful measure for comparison would be an analysis of between and within group variance. We have computed the F ratio, i.e. the ratio of between group variance and within group variance. Figure 3 shows the spatial distribution of the F ratio when all the six MM types are considered. The significant F value with appropriate degrees of freedom is 3.25. Figure 3 shows clearly that except for some parts over north-eastern India and a small portion over south-western India, the values are highly significant.

4.2. ClussiJcution by the KM method

Since this method could be sensitive to the charts initially selected, several experiments were performed with different classes (6,8, 10) and different sets of randomly selected charts. We found that the first four dominant types were similar. When the number of classes (k) were more than six, we found that the frequencies in class 7 and beyond were less than five. Hence the results presented here are for k = 6. We had to repeat steps 2 to 4 of this method 13 times for convergence so that none of the charts changed its type.

'1'0 make this method comparable to the previous method, here we have averaged also the three best correlated maps with each of the initial typical patterns. The years considered for averaging are shown in Table 1.

70. 00" soo 70' 00' 90'

30'

20-

10.

Figure 3. The spatial distribution of the F ratio for the MM and KM method

Table 11. Correlations among the types obtained by the MM and KM methods. For correlations between types obtained through the MM method (Le. Types A through to F) see upper triangle and for types obtained through the KM method (i.e. Types K through to P) see lower triangle. Actual correlation

=table value x lo-'

A B C D E F

K - 48 - 46 41 - 08 10 A L - 23 26 - 33 04 - 05 B M 59 - 50 - 40 - 19 05 C N - 64 - 1 3 - 44 - 42 - 43 D 0 - 62 - 10 - 36 3Q - 05 E P - 15 - 39 - 08 27 06 F

K L M N 0 P


As can be seen from Figure 4, type K is similar to type A, and shows NDs over the entire country, except the north-eastern parts. Type L is similar to type E, showing PDs over the south-east of the peninsula and the area centred around 22.O0N,69,0"E. Negative departures are observed over the rest of the country. Type M is similar to type D, showing NDs running from north-western to south-eastern parts of the country and PDs over the remaining parts. Type N is similar to type C showing PDs over central'and north-western parts. Type 0 is similar to type B with maximum PDs over north-western India. Type P shows PDs over southern parts of the west coast. The magnitude of departures is very much less over the remaining parts. The average MR associated with these types also is shown in Table I.

From Table 11, showing the correlations among types obtained by this method, it is seen that except for type K and M (correlation=0.59) none of the others show positive significant correlation between each other, suggesting distinct patterns.

Figure 3 shows the spatial distribution of the F ratio for the KM method when all the six types are considered. Here again a similar pattern is observed. Thus it is seen that by this method also distinct types are obtained. In the next section we shall compare the types obtained by the MM and KM method in detail.

Table I11 shows the type assigned to each year (1871-1990) by the above two methods. It shows also the MR for each year. If a particular year shows significant correlation with more than one type, the year is assigned to the type with which it is maximally correlated. Among these two methods, the method with stronger correlation also is shown (column MX).

4.3. Interrelationship among the types obtained by the M M and KM methods

To investigate the interrelationships between the typical types obtained by these methods we have computed the correlation coefficient (CC) as shown in Table IV. These CCs are computed using 5 1 values of a type obtained by one method and corresponding 51 values of a type obtained by the second method.

It is seen that A and K have a CC of 0.96, B and 0 have a CC of 095, C and N have a CC 0.77, D and M have a CC of 0.80, and E and L have a CC of 0.77. Types F and P show no significant relationship. Also, type D shows a significant CC (0.43) with K and type A with M (0.60).

Thus we can conclude that the MM and KM methods are able to bring out similar dominant modes.

I 1 ' ' I ' I I " " ' 1

Figure 4. The six typical types obtained by the KM method


Table 111. Type assigned to each year (YR) by the MM and KM method. It also shows the MR for each year. Among the two methods, with which

a year has maximum (MX) correlation is also shown

Table IV. Intercorrelations among the types obtained by the MM (A-F) and KM (K-P) methods. Actual correlation= table value x lo-’

K L M N 0 P

A 96 - 16 60 - 67 - 60 - 26 B - 53 - 48 - 39 23 95 - 62 C - 48 - 17 - 30 77 27 - 19 D 43 - 52 80 - 46 - 27 43 E -11 77 - 45 - 18 23 - 22 F 13 - 12 - 13 28 - 15 28

It would be more useful to have a contingency table showing the number of years common to each group in each method. In other words, for each year classified as A, what were they classified as in the KM method. This will give a much clearer indication of whether these methods were picking out the same groups or not.

From Table V it is seen that 20 out of 23 type As can be classified as type K, 14 out of 16 type Bs can be classified as type 0 , 1 3 out of 15 type Cs can be classified as type N, 11 out of 14 type Ds can be classified as type M, and finally all 12 type Es can be classified as type L. Thus from this we can conclude that the first five dominant types picked by the MM and KM methods are similar.


4.4. Relationship between spatial patterns and M R

In this section we wish to show that there can be a wide difference between the MR associated with a particular type. Secondly we wish to show that though the MR may be normal, the spatial pattern may be different. Tabie VI is an extract of Table 111, showing the minimum and maximum MR associated with each type.

From the Table VI it is clear that there can be wide range in MR values within a type. From Table 111 it is seen that the years 1881 (MR=860, type C), 1903 (858, E), 1924 (862, D), 1927 (849, F), 1940 (850, U), 1963 (855, A), and 1976 (855, B) have normal MR, however, the patterns vary from A through F, and could even be unclassified. Similar conclusions are drawn with KM method also.

4.5. Empirical orthogonal functions

This method can use either a covariance or a correlation matrix. Empirical orthogonal functions of seasonal monsoon rainfall over India have been determined by several workers (e.g. Bedi and Bindra, 1980; Prasad and Singh, 1988). However, we have computed them from the same data of 114 years.

By the test of Overland and Preisendorfer (1982) only the first two EOFs are significant. However, since the variance explained by the third and fourth EOFs are substantial we are presenting the first four EOFs.

The variance explained (VE) by the first four functions together is 52 per cent (shown in Figure 5). The first EOF (VE = 25 per cent) shows loadings of the same sign (negative) over the entire country except the north- eastern part, suggesting that there is simultaneous variation over the entire country and that the north-eastern part behaves in the opposite phase. The second EOF (VE = 11.6 per cent) shows a dipole type structure with positive loadings centred around 23.0°N,82.5"E and negative loadings of the same intensity centred around 1 6.0"N,77.OoE. This pattern suggests that the rainfall departures north and south of 20.0"N latitude behave in

Table V. Contingency table showing the number of years common to each groups in two methods (U = unclassified, C =column, R = row)

K L M N 0 P U R total

A 20 3 23 B 14 2 16 C 13 2 15 D 1 11 2 14 E 12 12 F 1 2 3 6 U 7 2 1 1 3 20 34 C total 21 19 16 15 15 5 29 120

Table V1. Minimum and maximum MR and the corresponding year for the types obtained by the M M and K M methods

Minimum Maximum Minimum Maximum MM K M type Year MR Year MR type Year MR Year MR

A 1877 604 1938 908 K 1877 604 1938 908 B 1976 855 1917 1003 L 1965 707 1988 999 c 1937 843 1961 1017 M 1972 653 1942 958 D 1982 735 1942 958 N 1912 804 1961 1017 E 1965 707 1988 999 0 1873 754 1917 1003 F 1941 729 1927 849 P 1907 776 1882 90 1

1946


70. 80' 90'

30'

20.

to'

" " " I REOF-4

Figure 5. The first four dominant EOFs. The top panel shows the unrotated EOFs, while the lower panel shows the rotated EOFs (REOF). Figures in parentheses are the variances explained

opposite phases. The third EOF (VE=8.3 per cent) shows high negative loadings along the foothills of the Himalayas and also negative loadings over the south-eastern part of the peninsula. This type of rainfall feature is associated with the 'breaks' in the monsoon. The fourth EOF (VE= 6.6 per cent) shows positive loadings over the northern and southern parts and negative loadings over the western and eastern parts. These EOFs compare well with the EOFs published by Bedi and Bindra (1980) and Prasad and Singh (1988).

A major problem with EOF analysis is that the unrotated EOFs have a tendency to always produce a predictable sequence of patterns (Buell, 1979). Richman (1986) suggested that the EOFs should be rotated since the unrotated functions exhibit four characteristics that hamper their utility to isolate individual modes of variation. The four characteristics being domain shape dependence, subdomain instability, sampling problems and inaccurate portrayal of the physical relationships. Keeping the above in view we have rotated the first four EOFs. These rotated EOFs (REOFs) are also shown in Figure 5.

On rotation we find that the spatial pattern of EOF 1 remains the same. The area of negative loadings in EOF 2 has reduced in REOF 2. The major features of EOF 3 are retained in REOF 3. The area of maximum loadings (south-western) in EOF 4 is retained in REOF 4. Thus even after the rotation, we find that the major features remain unchanged, suggesting that the patterns are stable.

As in the case of the MM and KM methods, we can assign to each map, types that have been obtained through EOFs. This can be done by computing component scores for each map obtained by summing the products of the grid-point values and the eigenvectors for each function. Then each map can be assigned to a type dependent on its highest score. A major objection to this approach is that the components are unrealistic (Key and Crane, 1986), hence we have not presented them in Table 111.

5. DISCUSSION AND CONCLUSIONS

This study has shown that modern computerized statistical methods can construct classification systems which can perform just as well as the classical, mostly subjective, classification systems. These methods not only identify the major recurring types but also extract the major common component in less frequent types.

In this section we discuss the advantages and the disadvantages of each method.


As stated already, in the MM technique the value of the threshold correlation coefficient r, may influence the selection of the typical types. Our experience has shown that slight variation in rt will not change the most dominant modes obtained. In this method a certain number of charts remain unclassified. Also the type patterns may be well correlated with each other in a positive sense. Correlation coefficients measure only the pattern similarity and not the magnitude. The majority of the observed seasonal rainfall departure patterns can be compared with each type pattern and a type can be assigned to it (see Table 111).

In the KM method the initial selection of the number of classes and the initial selection of the patterns assigned to each class may play some role. However, our analysis has shown that the most dominant types remain unchanged.

The patterns obtained through the EOF technique are orthogonal (uncorrelated) with each other, while natural modes of atmospheric behaviour are not necessarily uncorrelated. Hence there is no guarantee that the EOFs represent the actual patterns of rainfall departures. Each observed seasonal rainfall departure pattern can be represented by some linear combination of the EOFs.

Map-pattern correlation typing appears to have distinct advantages over EOF analysis when used for the description of climate characteristics as opposed to predictive purposes.

Using the 120 years data, we have computed also correlation coefficients between one map and another (varying from a lag of 1 year to a lag of 20 years). The correlations are very poor suggesting that the present year’s pattern cannot be used to forecast the subsequent year’s spatial pattern.

From the above, the following broad conclusions can be drawn.

(i) It is seen that 75 per cent of the seasonal departure patterns can be classified into six distinct types. (ii) The dominant patterns brought out by the MM and KM methods are similar.

(iii) The range of MR associated with each type may be quite large. (iv) Though the all-India monsoon rainfall may be normal, the spatial patterns may be quite different for

these years. This poses a major challenge in forecasting the rainfall anomalies on smaller spatial scales.

ACKNOWLEDGEMENTS

Thanks are due to Shri D. R. Sikka, Director, Indian Institute of Tropical Meteorology and Dr S. S. Singh, Head, Forecasting Research Division for guidance and facilities provided. Thanks are also due to Shri N. Singh for reviewing an initial draft of the paper and to the anonymous referees for their valuable sug- gestions.

REFERENCES

Bedi, H. S. and Bindra, M. M. S. 1980. ‘Principal components of monsoon rainfall’, Tellus, 32, 296-298. Buell, C. E. 1979. ‘On the physical interpretation of Empirical Orthogonal Functions’, Sixth Conference on Probability and Statistics in

Everitt, B. 1980. Cluster Analysis, Heinemann, 136 pp. India Meteorological Department 1986. ‘Statement showing subdivisional means of rainfall in each month and during the season as a

India Meteorological Department 1987. ‘Statement showing subdivisional means of rainfall in each month and during the season

India Meteorological Department 1988. ‘Statement showing subdivisional means of rainfall in each month and during the season as a

India Meteorological Department 1989. ‘Statement showing subdivisional means of rainfall in each month and during the season as a

India Meteorological Department 1990a. Statement showing ‘Subdivisional means of rainfall in each month and during the season as a

India Meteorological Department 1990b. Weekly Weather Report for the week ending on 3rd Ocfobrr 1990, India Meteorological

Key, J. and Crane, R. G. 1986. ‘A comparison of synoptic classification schemes based on objective procedures’, J . Climatol., 6,375-388. Kruizinga, S. 1979. ‘Objective classification of daily 500 mb patterns’, Sixth Conference on Probability and Statistics in Atmospheric

Kutzbach, J. E. 1967. ‘Empirical eigenvectors of sea-level pressure, surface temperature and precipitation complexes over North

Lund, 1. A. 1963. ‘Map-pattern classification by statistical methods’, J . App l . Meteorol., 2, 56-65.

Atmospheric Sciences, American Met. SOC., Boston, Massachettus, pp. 112-1 13.

whole (June-Sept. 1985)’, Mausam, 37,416.

as a whole (June-Sept. 1986)’, Mausam, 38, 372.

whole (June-Sept. 1987)’, Mausam, 39, 326.



Department, New Delhi.

Sciences, American Met. SOC., Boston, Massachettus, pp. 126-129.

America’, J . Appl. Meteorol., 6, 79 1-802.


Overland, J. E. and Preisendorfer, R. W. 1982. ‘A significance test for principal components applied to a cyclone climatology’, Mon. Wea.

Parthasarathy, B., Sontakke, N. A,, Munot, A. A. and Kothawale, D. R. 1987. ‘Droughts/floods in summer monsoon season over different

Prasad, K. D. and Singh, S. V. 1988. ‘Large scale features of the Indian summer monsoon rainfall and their association with some oceanic

Richman, M. B. 1986. ‘Rotation of principal components’, J . Climatof., 6, 293-335.

Reo., 110, 1-4.

meteorological subdivisions of India for the period 1871-1984: J . Climatol., 7, 57-70.

and atmospheric variables’, Adu. Amos. Sci., 5, 499-512.

Documents

Classification of summer monsoon rainfall patterns over India