Ocean & Shoreline Management U (1988) 195-209
A Study of Seasonal Longshore Transport Direction Through Grain-Size Trends: An Example from the Quilon Coast, Kerala, India T. N. Prakash & M. Prithviraj Marine Sciences Division, Centre for Earth Science Studies, PO Box 7250, Trivandrum 695031, India (Received 15 January 1988; accepted 3 May 1988) ABSTRACT The longshore transport direction in relation to the pre-monsoon, monsoon and post-monsoon seasons was studied, utilising the textural parameters of the foreshore sediments along a 41 km stretch of the Paravur-Purakkad coast in Kerala. The seasonal grain-size variation and sediment budget along the coast was also examined. This coast was divided into two sectors viz., southern and northern, based on the variation in the sediment type and a change in the orientation of the coastline. The sediment transport direction deduced from both statistical methods and field measurements are in agreement for the southern sector, signifying the availability of sediment for transport; in contrast, in the northern sector, no correlation was found except during the premonsoon season. The reason given for the obscured direction of sediment transport is the possible removal and transportation of the beach sand to the near-shore shelf during the monsoon and postmonsoon seasons, and also mining activities. The deposition of winnowed material from the southern sector, on to the beaches of the northern sector may be responsible for the northerly-oriented current during the pre-monsoon season.
1 INTRODUCTION The littoral zone is the most dynamic environment of the coast, and one in which constant mobility of sediment is observed. T h e m o v e m e n t of 195 Ocean & Shoreline Management 0951-8312/88/$03.50 © 1988 Elsevier Science Publishers Ltd, England. Printed in Northern Ireland
196
T. N. Prakash, M. Prithviraj
material in this zone, depends mainly on three factors: the nature of the material available for transport, i.e. size and density; orientation and other geomorphic features of the coast; 1 and the angle of wave approach. 2 Littoral transport plays a major role in the development of certain shore features like spits and bars, and in causing considerable coastal erosion and accretion. 3 A proper understanding of the seasonal littoral transport trend is important for the efficient management and development of the coast. The direction of sediment movement is obtained by the use of artificially introduced 4-8 or naturally occurring radioactive materials in the sediments. 9 Heavy minerals were also used as indicators but were found to be unsatisfactory. 1° Empirical equation, 11 wave refraction studies 12'~3 and recognition of progressive changes in grain size distribution in a series of sequential deposits 14-~7 have also been used to indicate sediment transport direction. Apart from these methods, the deployment of drift bottles in the surf zone, in order to measure the littoral current velocity, has been found to be fairly successful. 18'19 The present study involves comparing the seasonal variation in the littoral transport trends, as observed by the drift bottle method, calculated sediment transport trends, 2° and the seasonal grain-size variations and sediment budget along the coast.
2 A R E A OF I N V E S T I G A T I O N The N W - S E oriented Quilon coast (Fig. 1), extending between Paravur and Purakkad, is about 41 km long. Varied coastal geomorphic features including lagoons, a barrier beach system, cliffed beaches, open beaches and pocket beaches are seen along this coast. Three lagoons are prominent: Paravur in the south, Asthamudi in the central sector and Kayamkulam in the north. Asthamudi, fed by the Kallada river, is the largest lagoon of the three, and opens into the Arabian Sea at Neendakara. A prominent rocky headland located immediately south of Neendakara (between CES stations 88-94) separates the coast into two main sectors; northern and southern. Previous studies of the foreshore sediments 2L22 have indicated a significant variation between the textural characteristics of the southern and northern sectors. The sediments of these sectors also vary in their composition. This conspicuous variation in textural and compositional characteristics (Fig. 1) may be due to differences in their source. 23
197
Seasonal longshore transport direction on the Quilon coast 76° 40'
30'
,,3\~.
L~2~
\
~\
-.o
\~
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INOIEX MAP
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t
I
I
I
I
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e PARVUR
\ ~._r~
Fig. 1. Map showingthe location of profile stations and the bathymetry. Hence, for the present study, the two sectors have been treated independently. The northern sector, which is characterised by the barrier beach system, is rich in placer mineral deposits, including ilmenite, rutile, zircon, monazite, garnet, and sillimanite. This area is being mined at Chavara, by Indian Rare Earths Company Limited.
1-37 1.94 1.45 1-64 0-49 1.16 1.15 0-65 0.83 0.54 0.75 1-84 1.44 2.87 2-98 2.49 2.21 2.11 2.74
Mean
0-76 0-60 0.87 0-79 1.00 0.76 0-89 0.90 0.88 0.69 0.70 1-26 0.81 0-45 0.41 0-46 0.94 0-74 0.50
Sorting 0-17 0.18 -0-03 -0.30 0-32 -0-10 0.03 -0.02 -0-25 -0-78 -0-61 -0-86 -0.39 - 1-54 -0-89 1-06 -1-67 -1.21 -0-04
Skewness 74 77-75 79 80 81 82 83 84 85 86 88* 97 99 100 101 107 109 111 112 113
Station No. 1-38 1-40 0.91 1-42 1.32 1-01 1-05 1.36 1.03 1-14 0.37 2-58 2-57 2.05 2-09 2.24 2.62 2-08 2.76 2-31
Mean 0-53 0.71 0-96 0-89 0.98 1-00 0.82 1.02 0-85 0.72 0-73 0.54 0.64 0.90 0.95 0.57 0.48 0.65 0.47 0-46
Sorting
Post-monsoon
-0.12 -0.11 -0.03 -0.21 -0-35 0-07 -0.01 -0-54 -0-08 0.06 -0-58 -1-15 -0.66 -0.93 -0.96 -1-06 -0.19 -0-86 -0.95 0-22
Skewness
* Stations not considered for the present Study as they are in the vicinity of the promontory.
74 77-75 79 80 82 83 84 85 86 87* 88* 95* 97.6 100 101 107 109 110 113
Station No.
Monsoon
77-75 79 80 81 82 83 84 85 86 87* 88* 92* 95* 97.6 99 100 101 107 109 112 113 114 115
Station No.
TABLE 1 Grain Size Data from the Quiion Coast in the Three Principal Seasons
1-18 1.58 1.92 1-67 1-59 1.45 1.42 1.59 1.56 1.27 1.22 1.32 2-87 2.85 2.25 2-85 2.92 2.30 2-54 2.47 2.29 2-06 2.19
Mean
0.80 0-77 0-75 0.69 0-93 0.65 0.72 0-69 0-63 0.79 0-46 1-51 1.45 0-44 0-88 0.90 1.86 0-83 0.67 0.54 0-66 0-73 0-57
Sorting
Pre-monsoon
0.57 0-24 -0.05 0-29 0-96 -0.09 -0-06 0-00 -0.20 -0-16 0-65 0.05 -1.56 -0-01 - 1.05 -1.00 -1-97 -0.51 -0-09 -0.58 -0.61 -0-70 -0.20
Skewness
199
Seasonal longshore transport direction on the Quilon coast
3 M E T H O D S OF STUDY As a part of a Coastal Zone Management Programme being carried out by the Centre for Earth Science Studies, monthly beach profiling was undertaken at one kilometre intervals (CES 74-114), for a period of one year (between March 1980 and March 1981). From such data, the sand budget for the three principal seasons was calculated. Simultaneously, the longshore current direction and velocity was measured at each station by deploying a suitably buoyant drift bottle in the surf zone, while foreshore sediment samples were collected from the uppermost 5 cm of beach material at the low-, mid- and high-water line. 24 For the present study, only the mid-water line samples of August (monsoon), October (post-monsoon) and March (pre-monsoon) have been considered. Stations CES 87-95 were not considered as they lie within the vicinity of the rocky promontory. In the laboratory, the samples were washed, dried and sieved at ½tp intervals in a Rotap Sieve Shaker. The data was used for the computation of moment grain-size parameters (Table 1) and used in the longshore transport studies.
4 S E A S O N A L V A R I A T I O N IN G R A I N - S I Z E P A R A M E T E R S Table 2 and Fig. 2 reveal the seasonal variation in average grain-size parameters of the foreshore sediments taken from both coastal sectors. In the southern sector, a significant fining of sediments was observed from the monsoon (Mz--1.18tp) through the pre-monsoon season TABLE 2
Average Grain-Size Parameters in the Southern and Northern Sectors Southern sector (stations 74-86) Textural parameters
Monsoon
Northern sector (stations 97-115)
Postmonsoon
Premonsoon
Sediment category
Monsoon
Postmonsoon
Premonsoon
Sediment category
Mean (~p)
1.18
1.20
1.55
Medium sand
2.40
2.34
2.47
Fine sand
Sorting
0.82
0-83
0.73
Moderately well sorted to moderately sorted
0.61
0-64
0.80
Well sorted to moderately well sorted
-0.18(+0-07)
-0.10(+0-36)
-0-96
-0.80
-0.67
Skewness (SK)
-0.18(+0-18)
Negatively skewed
More negatively skewed
T. N. Prakash, M. Prithuiraj
200
NORTHERN SECTOR
SOUTHERN SECTOR
3
z
Z
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:E
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0.5
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'
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MON
POST
PRE
~v
~
(--) VE
SKEWNESS
-~
('~') VE
SKEWNESS
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POST
PRE
Fig. 2. Figure showing the average and range of grain-size parameters, of the southern and northern sectors.
(Mz = 1"554). The sorting of the sediments was slightly less developed during post-monsoon (0-834) in comparison to the monsoon season (0.824); but in the pre-monsoon season, they became better sorted (0.734). The majority of stations, excepting two or three, indicated a negative skew. The negative skewness values increased from the
Seasonal longshore transport direction on the Quilon coast
201
monsoon period (-0.14), and became more negatively skewed in the post-monsoon (-0-18) season. Furthermore, during the pre-monsoon season, there was a significant reduction in the value of skewness (-0.10), indicating a tendency to normalise the grain-size distribution. During the monsoon season, the sediments of the northern sector exhibited an average mean size value of 2-40q0 with better sorting (0.61) and a high negative skew (-0.96). In the post-monsoon season, a slight increase in mean size value (2-349) with poorer sorting index (0.64) and a decrease in the negative skew (-0.80) was noticed. Furthermore, during the pre-monsoon season of the subsequent year, a slight decrease in the mean grain size (2-47~), very poor sorting (0.80%), and a decrease in the negative skewness value (-0.67) was observed.
5 SAND V O L U M E C H A N G E S The beach profile data collected during the study period, when examined for sand volume changes, suggests a net loss of 0.18 x 10 6 m 3 of sand for the entire coast. The data in Table 3 shows an accretion trend in the southern sector, and an erosion trend in the northern sector. The accretional zones indicated a net gain of 0.194 x 10 6 m 3 of sand (Table 4) during the monsoon and post-monsoon period, in spite of a net loss during the pre-monsoon season. Significant loss at CES 87 and 88, and an appreciable loss at CES 84, was found during the pre-monsoon season. However, along the northern sector, significant sand loss was observed in all of the three seasons, with the highest losses occurring in the monsoon (183 000 m3), moderate losses occurring during the post-monsoon (154 000 m3), but considerably less sand loss occurring in the pre-monsoon season (37 000 m3). It is interesting to note a smooth bathymetric contour (10 m) in the southern sector, which is suggestive of the reworking of near-shore sands by waves. 25
6 L O N G S H O R E T R A N S P O R T STUDIES 6.1 Drift bottle method The longshore or littoral transport depends mainly on the angle of wave approach and on the near-shore topography. In general, a seasonal reversal in the longshore currents has been observed along the Kerala coast, with breaker angle between 160 ° and 170° during the monsoon period, and between 5° and 10° during the post- and pre-monsoon s e a s o n s . 26
T. N. Prakash, M. Prithviraj
202
TABLE 3 Comparative V o l u m e C h a n g e s b e t w e e n the Stations
CES
Pre-raonsoon
Monsoon
Post-monsoon
reference points
Cut (m 3)
Fill (m 3)
Cut (m 3)
Fill (m 3)
Cut (m 3)
Fill (m 3)
74 75.77 79 80 81 82 84 85 86 87 88 95 97.6 98
1 000 6 000 4000 7 000 80000 4 000 38000 -11000 16000 14 000 --20 000
52 000 8 000 6000 30 000 5000 3 000 -20 000 -10000
16 000 28 000 30000 12 000 15000 -5000 -1000 --
-15 000 14000 40 000 8000 28 000 11000 9 000 -15000
--7000 18 000 4000 38 000 6000 -2000 3000
22 000 24 000 26000 32 000 68000 32 000 24000 16 000 1000 8000 1 000 7000 ---
99
--
I00
1000
I01
24 000
--
2 000
--
1 000
4000 3 000 -11000
--23 000 10000
24000 32 000 --
2000
6000
2000
--
5000
--
--
7 000 --
5 000
20 000
--
-12 000 19 000 22000
--
102
1000
2000
4000
--
4000
103
--
5 000
5 000
--
4 000
--
104
1000
--
2000
--
2000
--
106 107 108 109
4000 18 000
--
--
25000 3 000 17 000 7 000
--
9000
---
--
10 000
7000 3 000 18 000 --
--
38 000 19 000 28 000 13000
10000 3 000 --
6 000 ---
Ii0
--
16000
111
--
11000
6000
--
5000
112
9000
--
8000
--
--
113
17000
--
37000
--
35000
--
114
14000
--
12000
13000
--
1000
5000
Note: The March profile is taken as a reference for calculating cut-and-fill; sand loss or gain in terms of m 3 w e r e carried out by taking the product of the area measured in the profile using a distance of influence of I km (500 m up-coast and 500 m down-coast from the profile line). Field measurements o f l o n g s h o r e c u r r e n t s ( F i g . 3) i n t h e s o u t h e r n sector indicate northerly-directed currents with velocities ranging from 1 0 c m / s t o 50 c m / s d u r i n g t h e p r e - a n d p o s t - m o n s o o n s e a s o n s . D u r i n g t h e m o n s o o n , i n t h e s a m e s e c t o r , a c h a n g e in t h e d i r e c t i o n o f l o n g s h o r e currents from north to south, with a velocity range of 10-60 cm/s, was observed. In the northern sector, the direction of the longshore
Seasonal longshore transport direction on the Quilon coast
203
TABLE 4 Seasonal Volume Chances in the Southern and Northern Sectors Sectors
Pre-monsoon
Monsoon
Cut
Fill
Cut
Fill
Cut
Fill
(m 3)
(m 3)
(m 3)
(m 3)
(m 3)
(m 3)
Southern (Accreting)
145000 102000
Northern (Eroding)
105 000
55000 110000
68 000 225 000
Total change
Post-monsoon
(1 x 106 m 3)
7000 189000
42 000 174 000
0-194
20 000
Fill
0-374 Cut
currents was found to remain northwards throughout the year, with a velocity range of 1-50 cm/s. 6.2 Statistical methods The transport directions deduced 26 from the Z-scores 27 of the southern and northern sectors are represented in Fig. 4 and Table 5 respectively. For the southern sector, during the monsoon season, the study revealed a strong southerly transport trend (0-05 significance level) of lower energy regime (case B). This trend was found to continue during
45
35' "I-
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0 z I`5
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CES POINTS
83
B5
87'l
95
99
I01
103
105
108
I10
II2
114
I0
~20
~ PRE M O N S O O N
0 " f~ 3 0 -
o
~
MONSOON
o
POST MONSOON
40 50 6O
1~.3.
Seasonal longshore current pattern along the Quilon coast (Drift bottle
method).
204
T. N. Prakash, M. Prithviraj 76 ° 4 0 '
76 ° 30'
9° 5'
9°
\
LLg L12 111
\
,o9
~.
9_0_ °
9~ O0
'"
Io0
8°
r 8° 55'
55' 95 I
8°
8°
50'
,50
CASE'S'
8°
/%
MONSOON
CASE'S'-- - - ~
POST-- MONSOON
CASE B....
PRE - - MONSOON
~-~
CASE C ....... ~
1
PRE - - MONSOON
8°
45'
~ x 7 6 ° 301
45
76 ° 4 0 '
Fig. 4. Seasonal longshore current pattern along the Quilon coast (by grain-size trends). the post-monsoon season, but at a very low significant level. During the pre-monsoon season of the following year, a change in the direction of transport trend from south to north, in the lower energy regime, was noticed; this, again, was of a very low significant level. In the northern sector, no significant transport trend was observed
Seasonal longshore transport direction on the Quilon coast TABLE
205
5
Summary of a Number of Pairs on the Quilon Coast Samples Producing Transport Trends Southern sector stations (74-86)
Northern Sector stations (97-115)
North
North
South
South
CaseB
F B -
N = 36 x= 6 Z= 0.38
N = 36 x = 11 Z= 1.65
N = 21 x= 3 Z= 0-16
N = 21 x= 4 Z= 0.60
CaseC
C B +
N = 36 x= 1 Z=-0.89
N = 36 x= 2 Z=-0-64
N = 21 x= 2 Z=-0.27
N = 21 x= 1 Z=-0-70
F B -
N = 45 x= 5 Z=-0.13
N = 45 x = 12 Z= 1-29
N = 36 x= 5 Z= 0.13
N = 36 x= 1 Z=-0-88
C B +
N= x= Z=
N = 45 x= 7 Z= 0-28
N= x= Z=
N= x= Z=
F B -
N = 36 x = 10 Z= 1.40
N= x= Z=
N = 45 x= 1 Z=-0.94
N = 45 x= 1 Z=-0-94
C B +
N = 36 x= 2 Z=-0.63
N = 36 xZ-
N = 45 x = 15 Z= 1-90
N = 45 x= 4 Z=-0.33
Monsoon
CaseB Post-monsoon CaseC
CaseB
45 8 0.48
36 3 0.38
36 5 0-13
36 1 0.88
Pre-monsoon CaseC
Z = 1.645 = 0.05 level of significance Z = 2-33 - 0.01 level of significance N = Total number of possible unidirectional pairs. x = Observed number of pairs representing a particular case in one of the opposing directions.
during the monsoon and post-monsoon seasons, but a strong northerly transport trend (0-05 significance level) of higher energy regime (case C) was noticed during the pre-monsoon season.
7 DISCUSSION One of the likely reasons parameters of the foreshore
for the seasonal variation in grain-size s e d i m e n t s in t h e s o u t h e r n s e c t o r m a y b e
206
T. N. Prakash, M. Prithviraj
the winnowing of finer grains by monsoonal wave action and their subsequent return in the succeeding seasons. This process leads to the coarsening of the foreshore sediments with a moderate sorting index during the monsoon season. In the post-monsoon season, with the reversal in the trend of longshore current direction, increased sedimentation on the foreshore might be one reason for poorer sorting and reduction in the mean grain-size of the sediments. In the pre-monsoon season, the littoral processes would have attained equilibrium and thus, during this period of time, there would be a tendency to normalise the grain-size distribution, leading to a considerable reduction in the mean grain-size and an increased degree of sorting of the sediments. The sand volume changes also support this suggestion (Tables 3 and 4). In the northern sector, it is evident from the sand volume changes, that during the monsoon and post-monsoon seasons, most of the heaviest and lightest minerals are being winnowed by waves, thus increasing both the sorting index and the mean grain-size of the foreshore sediments. However, in the subsequent season, lighter minerals of a coarser nature (winnowed from the southern sector) may add to the deposition on certain beaches of the northern sector. This considerably reduces the sorting index, with a slight increase in the skewness value from - 0 . 9 6 in the monsoon period to -0.67 in the pre-monsoon. The sediment transport directions deduced from the Z-scores and field measurements are comparable for the southern sector. However, for the northern sector, the results obtained from these two study approaches do not corroborate. The field observations indicate that there is a northerly transport direction in each of the three seasons, while the calculated transport directions do not suggest any significant transport trend for the monsoon and the post-monsoon seasons and signify a northerly trend for the pre-monsoon season. The reasons for the obscured preferred direction of sediment transport may be the extensive removal of sand by mining (Fig. 1) and/or transportation of material by littoral processes to near-shore parts of the shelf during the first two seasons. This may be leading to a paucity of sediment available for littoral transportation. This is also evident from the previous study, 22 which indicated an extensive loss of sand in the monsoon and post-monsoon seasons. A significant transport trend is observed during the pre-monsoon season, which may be due to the progressive deposition of the winnowed material from the southern sector, onto the foreshore zone of the northern sector, because of the northerly directed littoral currents during this season.
Seasonal longshore transport direction on the Quilon coast
207
8 CONCLUSION This study provides a fairly comprehensive picture of the seasonal longshore transport direction along the Quilon coast, shown by both grain-size trends and the use of the drift bottle method; one that has not been available hitherto. It is clear that the beaches of the southern sector are more stable than those in the northern sector. The mining of black sand within the barrier beach complex, and sand transportation to the near-shore parts of the shelf as a result of monsoonal wave conditions on the northern sector beaches may strongly influence the sand budget in a negative manner. Additional data will need to be collected over several more years in order to be able to forecast beach stability, and to understand the variations in the seasonal longshore transport trend. Good progress has been made towards these goals. ACKNOWLEDGEMENTS The authors would like to thank the Director, Centre for Earth Science Studies, for providing research facilities. Thanks are due to Shri P. Aby Verghese for the collection of samples and beach profile data during his involvement (1980-1982) in the Marine Sciences Division of the Coastal Zone Management Programme (Project No. 2--Monitoring of Planimetric Changes of Beaches of Kerala). We also wish to thank the scientists and staff of MSD for a variety of assistance during the preparation of the paper. REFERENCES 1. Swift, D. J. P., Coastal Sedimentation. In Marine sediment transport and environmental management eds Stanley, D. J. & Swift, D. J. P. John Wiley and Sons, New York, 1976, pp. 255-310. 2. King, C. A. M., Beaches and coasts. Edward Arnold, London, 1972, pp. 559. 3. King, C. A. M., Introduction to Marine Geology and Geomorphology. English Language Book Society and Edward Arnold, London, 1974, pp. 309. 4. Galvin, C. J. Jr., A selected bibliography and review of the theory and use of tracers in sediment transport studies, 1, US Army, Corps of Engineers, Coastal Engineering Research Centre, Washington, 1964. 5. Brunn, P., Use of tracers in coastal engineering. Shore and Beach, 34 (1966) 13-17.
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6. Duane, D. B. & Judge, C. W., Radioisotopic sand tracer study, Point conception, California, MP 2-69, U.S. Army, Corps of Engineers, Coastal Engineering Research Centre, Washington, 1969. 7. Ray, I., Mallik, T. K. & Venkatesh, K. V., Fluorescent tracer studies in Calicut and Baypore area, Kerala--A preliminary appraisal. Indian Minerals, 29 (1975) 42-6. 8. Machado T. & Baba, M., Movement of beach sand in Vizhinjam bay, West coast of India. Ind. Jour. Mar. Sci., 13 (4) (1984) 144-6. 9. Kamel, A. M. & Johnson, J. W., Tracing coastal sediment movement by naturally radioactive minerals. Proc. of the Eighth Coastal Engineering Conference, ASCE, 1962, p. 324. 10. Judge, C. W., Heavy minerals in beach and stream sediments as indicators of shore processes between Monterey and Los Angeles, California, TM-33, US Army, Corps of Engineers, Coastal Engineering Research Centre, Washington, 1970. 11. Longuet-Higgins, M. S., Longshore currents generated by obliquely incident sea waves, 1, J. Geophy. Res., 75 (33) (1970) 6788-801. 12. Reddy, M. P. M. & Varadachari, V. V. R., Sediment movement in relation to the wave refraction along the west coast of India. Proc. Ind. Geophy. Union, 10 (1973) 169-82. 13. Kurian, N. P., Baba, M. & Shahul Hameed, T. S., Prediction of nearshore wave heights using a refraction programme. Coastal Engineering, 9 (1985) 347-56. 14. Krumbein, W. C., Size frequency distributions of sediments and the normal phi curve. J. Sed. Petrol., 8 (1938) 84-90. 15. Stapor, F. W. & Tanner, W. F., Hydrodynamic implications of beach, beach ridge and dune grain size studies. J. Sed. Petrol., 45 (1975) 926-31. 16. McCave, I. N., Grain size trends and transport along beaches: Example from Eastern England. Mar. Geol., 28 (1978) M43-M51. 17. Haner, B. E., Santa Ana river: An example of a sandy/braided flood plain system showing sediment source area imprintation and selective sediment modification. Sed. Geol., 38 (1984) 247-61. 18. DeWall, A. E., Littoral environment observations and beach changes along the southeast Florida coast, Technical paper TP 77-10, US Army, Corps of Engineers, Coastal Engineering Research Centre, Oct. 1977. 19. Samsuddin, M. & Suchindan, G. K., Beach erosion and accretion in relation to seasonal longshore current variation in the northern Kerala coast. India., J. Coastal. Res., 3 (1987) 55-62. 20. McLaren, P. & Bowels, D., The effects of sediment transport on grain size distributions, J. Sed. Petrol., 55 (1985) 457-70. 21. Prakash, T. N., Mallik, T. K. & Aby Verghese, P., Differentiation of accreted and eroded beach by grain size trends---study in Quilon district of Kerala, West coast of India. Ind. J. Mar. Sci., 13 (1984) 202-4. 22. Prakash, T. N. & Aby Verghese, P., Seasonal beach changes along Quilon district coast, Kerala. J. Geol. Soc. Ind., 29 (1987) 390-8. 23. McKinney, T. F. & Friedman, G. M., Continental shelf sediments of Long Island, New York. J. Sed. Petrol., 411 (1970) 213-48. 24. Aby Verghese, P., Beach monitoring in Quilon district, Kerala during 1980-81, Tech. Rep. 39, Centre for Earth Science Studies, Trivandrum, 1984.
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25. Dietz, R. S., Wave base, marine profile of equilibrium, and wave-built terraces: A critical appraisal. Geol. Soc. Am. Bull., 74 (1963) 971-90. 26. Narayanaswamy, G., Udayavarma, P. & Paylee, A. Wave climate of Trivandrum (Kerala), Mahasagar--Bull. Nat. Inst. Oceanography, 12 (1979) 127-33. 27. Spiegel, M. R., Theory and problems of statistics: Schaumm's outline series. McGraw-Hill, New York, 1961, pp. 359.