Tides in the Mandovi and Zuari estuaries, , west coast of

D Sundar and SRShetye Physical Oceanography Division, National Institute of Oceanography, Dona Paula, Goa 403 004, India.

Mandovi and Zuari are two estuaries located in Goa, west coast of India. Variation of water level in the estuaries was monitored for a month at 13 locations using tide-poles during March–April 2003. Analysis of this data has provided for the first time, characteristics of how tidal constituents vary in the narrow and shallow estuaries, typical of those found along the west coast of India. At a distance of 45 km from the mouth the tidal range increased in both estuaries by approximately 20%. The tidal range at the upstream end of the two channels at the stations dropped sharply because of the increase in elevation of the channels.

1. Introduction located at Ganjem on the (figure 1). The gauge is located just beyond the distance up Located along the west coast of India are a num- to which variation in water level due to tides is ber of estuarine channels that connect the Arabian observed in the channel. The runoff recorded by Sea to the rivers that originate in the Western the gauge is typical of the runoff observed in the Ghats mountain range. The rise rivers located along the west coast. The runoff sharply from the coastline to an average height peaks during the most active phase of the Indian of about 1000 m. The runoff in the rivers is high summer monsoon, decreases rapidly after with- during June–September when the Indian summer drawal of the monsoon and remains negligible from monsoon is active. At this time winds along the about January till the onset of the next monsoon coast are approximately westerly and carry mois- which generally occurs during late May or early ture picked up during their passage over the north June. Indian Ocean, including the Arabian Sea. As a The flow in the estuarine channels is primarily result, the windward side of the Ghats receives tidal after withdrawal of the monsoon, and conti- high precipitation due to the topographic effect. nues to be so until onset of the next monsoon. In The rainfall along the central west coast of India is 1993, tide pole measurements were carried out at about 250 cm during June–September. 15 locations in the two estuaries for three days. The Mandovi and the Zuari are two estuaries The inferences derived from analysis of these data that are located along the west coast, in Goa were that the amplitude of the tide remains vir- (figure 1). Each of these two estuaries is about tually unchanged in the channels, and that phase 5 m deep. Their cross-sectional area decreases from propagates from mouth to head with an average mouth to head, and tides occur in the two estuaries speed of about 6 m/s (Shetye et al 1995). However, up to a distance of about 50 km (Shetye et al 1995). the time-series of the data collected then, being The increase in elevation of the estuarine channels only 3 days long, did not permit determination of prevents tides from propagating beyond this dis- characteristics of tidal constituents. tance. The runoff in the two estuaries is highly sea- During March–April 2003, tide pole measure- sonal, just as is the precipitation. This can be seen ments similar to those during 1993 were carried from figure 2 that gives runoff measured by a gauge out at 13 locations by recording the water level

Keywords. Harmonic analysis; tidal constituents; tide-pole; amplification; channel geometry.

J. Earth Syst. Sci. 114, No. 5, October 2005, pp. 493–503 © Printed in India. 493 494 D Sundar and S R Shetye

Figure 1. A map of the Mandovi and Zuari estuaries. The locations where water level observations were carried out are marked with a number in a circle. The name of the location is given at the bottom of the map. T indicates the location up to which variation in water level has been reported to occur. The depth contours are in m. once every fifteen minutes. In the present paper was requested to visually average the water level we report analysis of these data. The new time- for about a minute and then record the average series, being at least 30 days long, allows us to water level. It is, however, not clear what the carry out tidal analysis of 34 constituents. The error associated with such a measurement is. Below next section describes the data collected and the we make an estimate of the error involved in the method of analysis. The results are presented in estimation of amplitude and phase lag of each section 3. Section 4 provides a brief summary of the constituent. study. The distance of each of the 13 stations from the mouth, and start-and-end time of observation are given in table 1. The 15-minute data were 2. Data collection and analysis analyzed using TASK-2000 (Tidal Analysis Soft- ware Kit 2000) of the Permanent Service for Mean The 13 locations where tide pole measurements Sea Level, Proudman Oceanography Laboratory, were carried out during March–April 2003 are UK (Bell et al 1998) to determine tidal ampli- shown in figure 1. The zero of each tide-pole used tude and phase lag of 26 major constituents and 8 in the observations was referenced to a ‘local chart- related constituents. The analysis served as a tool datum’ for future reference. The tide pole readers for quality control too. Data points with large resi- worked in three shifts during a day. Each reader duals were examined to determine if the residuals Tides in the Mandovi and Zuari estuaries 495

propagation in the two main channels. Of the 13 stations where the observations were carried out, 6 were located in the Mandovi main channel, 5 in the Zuari main channel, and 2 in the Cumbar- jua Canal (figure 1). The quality controlled data at these 13 locations are shown in figure 3. Tidal analysis was carried out at only 11 stations. The water level variation at Ganjem and Sanguem was found to exhibit tidal effect only a part of the time. This is so because of the higher topographic eleva- tion of these stations. We have discussed this point in section 3.2. The data from these stations were not subjected to tidal analysis. Noting that the Mandovi–Zuari is the only estuarine system along the west coast of India where variation of amplitude and phase lag along the length of the estuarine channel is now known, we provide in tables 2 and 3 all the inferred tidal characteristics at the 11 locations. Of the Figure 2. Monthly-mean runoff (m3/s)atGanjeminthe 34 constituents whose amplitudes and phases were Mandovi river (for location see figure 1). The top (bottom) of determined, 5 constituents – M2,S2,N2,K1,and an error bar represents the maximum (minimum) discharge O1 – had amplitudes larger than 10 cm at the during a month. Climatological data (1980–97). Courtesy: Central Water Commission, New Delhi. mouth of the two estuaries. In the next section we discuss the behaviour of these constituents. In the rest of this section we make an estimate of the error associated with our determination of were due to errors in recording. If inferred to be so, amplitude and phase lag of the 34 constituents the suspect data were removed. All computations listed in tables 2 and 3. The procedure followed are referenced to the Indian Standard Time for this purpose is as follows: The amplitudes which leads the Greenwich Mean Time by 330 and phase lags given in tables 2 and 3 were minutes. computed from time-series with 15 minute separa- The main channels of the Mandovi and the tion between consecutive values. The amplitudes Zuari are connected by the Canal. Its and phase lags were recomputed using a time series cross-sectional area is, however, much too small to in which the time interval between two consecu- have a major impact on the characteristics of tidal tive values was two hours. As the original data are

Table 1. Distance of each of the 13 stations where the observations were carried out and the start-and-end time of the observations.

Distance from Station mouth (km) Start time End time Mandovi Verem 4.81 0000 hrs/10th March 2345 hrs/13th April Britona 8.86 0000 hrs/10th March 2345 hrs/13th April Akkada 20.31 0000 hrs/10th March 2345 hrs/13th April Volvoi 32.91 0000 hrs/10th March 2345 hrs/13th April Usgao 41.07 0000 hrs/10th March 2345 hrs/13th April Ganjem 49.83 0000 hrs/10th March 2345 hrs/13th April Zuari Dona Paula 0.00 0000 hrs/11th March 2345 hrs/13th April Cortalim 11.70 0000 hrs/10th March 2345 hrs/13th April Borim 21.02 0000 hrs/10th March 2345 hrs/13th April Sanvordem 45.22 0000 hrs/10th March 2345 hrs/13th April Sanguem 54.94 0000 hrs/11th March 2345 hrs/13th April from Dona Paula through Zuari Madkai 14.74 0000 hrs/10th March 2345 hrs/13th April Banastarim 24.61 0000 hrs/10th March 2345 hrs/13th April 496 D Sundar and S R Shetye

Figure 3. Observed sea level (cm) during the period of observation. The horizontal axis gives date and month. separated by 15 minutes, we get 8 independent standard deviation to be indicative of the error 2-hour time series. From these we get 8 values associated with our determination of amplitudes for amplitude and phase lag of each constituent and phase lag. Tables 4 and 5 give the values at a station. We then computed standard devia- obtained through this exercise at one station, tion of both amplitude and phase lag. We take the Akkada in the Mandovi (location 3 in figure 1). Tides in the Mandovi and Zuari estuaries 497 Cumbarjua 0.5705 1.4530 7.29163.7558 6.7107 1.00110.6627 4.0379 0.8044 0.6557 1.9180 1.7820 2.30001.15725.3350 4.0349 1.0909 0.6037 5.0293 0.5086 0.9923 0.9806 2.0113 0.3634 0.4596 1.5668 6.5520 5.0396 0.27900.48832.4405 0.2761 0.4832 2.2910 1.6128 2.7977 3.0707 2.5993 1.46531.83950.2897 1.9088 0.9406 0.5092 0.8368 1.0826 1.6173 1.3009 1.20150.44020.3685 1.1943 0.4353 0.6953 1.6505 0.8669 Madkai Banastarim 19.6141 18.4902 14.1031 14.3811 11.545634.8810 11.4235 34.5121 14.421057.6406 13.3986 55.7980 Zuari 1.4200 3.3896 1.46883.6251 3.6067 2.3742 4.7417 10.4019 7.23305.2581 7.14831.7379 6.53150.6169 6.4123 1.8909 3.7028 0.6746 4.1737 0.9846 5.4631 0.73761.6527 1.9506 0.7114 1.6418 2.10901.22315.6388 1.8569 1.1700 5.39381.4647 1.2800 5.9011 2.53111.2956 1.3560 1.9948 6.2513 1.4922 2.7667 1.61670.7767 2.4183 3.6605 0.7135 0.4238 4.9818 2.5750 0.8482 1.8638 3.6859 2.3511 5.14600.25980.4546 4.2798 0.28412.0291 0.49710.9390 0.3106 1.2337 0.54352.4107 2.9748 0.2995 2.4624 0.5242 2.3948 3.2009 1.3564 3.07631.8490 6.5673 0.8148 2.7086 1.93991.4783 3.17120.5231 1.8844 0.8182 1.5370 1.20531.7895 4.0068 1.2955 1.6668 1.4805 0.59350.9450 3.6295 0.5935 2.4239 2.1739 1.4654 0.5194 4.5593 0.6079 0.6142 1.9691 0.9933 0.51930.8014 0.3044 1.1674 0.6693 0.7638 1.1902 0.9139 16.9912 14.765410.747432.4694 13.9013 11.7531 35.5078 16.2402 12.8499 38.8214 12.3925 12.4265 37.4396 12.3444 15.857320.7309 13.9618 19.8300 21.6953 22.9826 54.0399 59.9542 63.8844 69.7756 Dona Paula Cortalim Borim Sanvordem . Mandovi 3.86670.8006 3.9718 0.7554 4.2544 0.8978 4.00921.9320 0.7999 3.9122 1.4386 1.1474 0.99173.0189 1.22331.0749 3.1784 1.9873 4.9554 1.0304 3.7990 4.7502 1.05760.7559 5.4268 4.8758 1.1614 0.56320.6492 6.4047 5.3542 1.2212 0.6335 1.5864 5.6298 0.4696 0.7383 1.2806 0.6528 1.7180 1.7017 0.9869 2.3047 1.9981 2.2832 5.79604.3692 6.3502 4.5059 6.93250.6378 4.8061 6.5066 0.64180.2686 5.0299 8.5160 0.6498 0.2702 4.8080 1.40721.6407 0.6761 0.27360.0780 1.3750 1.6557 0.6971 2.3931 0.2847 1.1833 1.4471 1.7157 2.4150 0.2935 3.6507 1.7244 1.9134 2.5026 4.6092 0.8233 2.1119 0.1199 2.7909 5.0406 0.7339 0.8459 3.0805 0.5157 0.3804 1.97020.2170 0.75350.5289 1.0762 2.3468 0.0397 0.1326 0.8120 2.2508 2.6092 0.4198 0.8368 0.6674 2.3297 0.8743 1.7633 1.8081 1.7067 2.5361 0.4700 0.4729 0.4788 0.4982 0.5136 0.3988 0.7077 1.3826 1.77660.2133 1.3981 0.1348 0.32780.16400.2228 0.3415 0.8060 0.9609 0.2950 0.7338 1.5734 1.2553 0.5249 0.6696 1.8862 2.4757 1.0133 0.8154 2.8575 1.2801 Verem Britona Akkada Volvoi Usgao 14.9116 14.784911.112033.5709 14.5834 11.1813 33.7804 14.3197 11.3199 34.1991 15.0861 11.7783 35.583912.3358 12.1439 36.6885 53.2327 12.4486 52.4094 12.899818.2183 55.3923 14.3861 17.4640 61.1507 15.8789 17.9257 63.6825 19.6847 20.6977 Amplitude (cm) of the tidal constituents at the 11 stations Table 2. Constit. MM OO1 MSF O1 PI1 P1 MU2 T2 S2 2SM2 MK3 SN4 MS4 MSN6 Q1 PHI1 J1 2N2 N2 M2 M3 MN4 M4 2MN6 K2 MO3 M6 2MS6 2SM6 M1 K1 PSI1 NU2 L2 498 D Sundar and S R Shetye Cumbarjua 81.15542.686 74.609 56.437 73.526 72.002 33.878 81.993 15.440 26.465 75.812 43.136 30.289 50.146 43.345 0.637 73.526 72.002 15.44015.440 26.465 26.465 73.526 72.002 73.52673.526 72.002 72.002 47.637 99.314 Madkai Banastarim 115.161 91.583 118.081 82.309 270.603 318.245 343.093 3.236 325.452 340.493 149.673277.105 116.918 306.023 321.333 306.208 228.363 295.895 193.924 210.151 334.240 355.833 144.060 148.469 298.568 322.417 312.832 349.503 247.722 291.547 153.167 204.297 298.568 322.417 298.568 322.417 Zuari . 3.921 136.841 198.032 244.340 marks is in table 5 97.58459.489 64.11355.65524.973 55.732 83.451 62.675 91.98367.726 78.458 54.975 52.154 66.167 63.174 61.577 62.934 140.184 70.087 78.365 30.960 97.302 90.027 89.249 23.564 13.57140.858 64.874 117.115 41.802 140.600 157.348 11.338 77.730 135.762 144.731 67.726 63.174 70.087 78.365 67.726 63.17467.72667.726 70.087 63.17465.870 63.174 78.365 70.087 155.675 70.087 141.197 78.365 78.365 192.215 69.198 166.952 179.735 225.894 359.737 3.110 22.095 48.896 242.441 284.022 327.921 44.350 138.421 40.387 29.098 32.253 274.202 267.853 311.854263.795 267.327 315.571 8.959 80.296 313.743 319.644 335.014 350.163 308.930 354.020 2.417 15.762 288.132 292.307335.463 318.000 251.625 339.378 288.256 276.407 251.599 258.679 352.705 91.652 359.737359.737 3.110200.715 3.110 22.095346.305 208.194 22.095 48.896 47.453 356.851 48.896 191.197 250.399 134.828 305.871 263.367 294.596 18.548 288.132 292.307288.132 318.000 292.307 339.378 318.000 339.378 ∗ Dona Paula Cortalim Borim Sanvordem Legend of Mandovi 59.81751.21157.990 66.967 54.789 71.966 71.59961.568 60.879 62.661 77.692 67.092 62.74456.678 87.009 83.746 75.001 67.152 84.065 92.405 77.568 104.115 83.265 106.993 154.074 54.141 91.561 158.405 201.016 259.898 93.168 84.506 85.333 80.715 70.841 63.150 36.318 45.676 49.488 64.667 25.171 72.298 284.806 199.220 237.212 25.959 6.022 50.616 86.870 102.193 61.568 67.092 75.001 77.568 83.265 61.568 67.092 75.001 77.568 83.265 61.56861.568 67.092 67.092 75.001 75.001 77.568 77.568 83.265 83.265 Verem Britona Akkada Volvoi Usgao 299.530 312.355318.239318.400 329.152 329.646 308.134358.172 336.316 345.560 310.170 11.117 345.170 353.312 308.044351.502 32.536 0.005 298.184 356.598 41.343 350.873 51.038 353.028301.019 351.267 292.527 5.050 44.078 67.567 342.181 349.031 359.897 5.155 354.315 113.743 122.276 160.307 165.684 202.507 110.857245.539 51.665 279.957 28.116278.840 326.938166.005 46.791 63.432 329.147 132.658 68.197 358.221 253.495 12.755 292.914 1.241 344.131 18.997 162.165 184.527 210.337 218.747 266.609 254.105 292.718353.656 335.286 325.455 23.630 23.451 45.042 57.875 96.931 358.172358.172 11.117 11.117 32.536 32.536 41.343 41.343 51.038 51.038 299.530 312.355299.530 329.152 312.355 336.316 329.152 345.170 336.316 345.170 Same as table 2 but for phase lag in degrees (referenced to IST). PI1 (K1) K2 (S2) T2 (S2) 2N2 (N2) NU2 (N2) P1 (K1) PHI1(K1) PSI1(K1) Table 3. Constit. MM ∗ ∗ N2 M3 Q1 L2 SN4 MS4 K1 S2 2SM2 ∗ MN4 2MN6 2MS6 ∗ ∗ MK3 M6 ∗ ∗ J1 M4 MO3 MSF OO1 O1 M1 ∗ MU2 MSN6 M2 Tides in the Mandovi and Zuari estuaries 499

Table 4. Estimation of error (cm) associated with the determination of amplitude (cm) at Akkada. From the original data at 15 min intervals, 8 data sets were derived by sub-sampling at 2-hour intervals. The column x000 contains the data from values at 0000 hr, 0200 hr, 0400 hr and so on. The column x015 contains the data from values at 0015 hr, 0215, 0415 and so on. Similar is the case for x030, x045, x100, x115, x130 and x145. The mean and standard deviation were calculated using these eight columns. The values in the column x are from ALL the original values from data at 15 min intervals.

Std. Constit. x000 x015 x030 x045 x100 x115 x130 x145 Mean dev. x

MM 6.88 7.03 6.99 6.89 6.89 6.94 6.90 6.94 6.93 0.052 6.93 MSF 4.79 4.94 4.82 4.75 4.83 4.85 4.75 4.73 4.81 0.065 4.81 Q1 4.20 4.21 4.29 4.35 4.33 4.18 4.24 4.25 4.26 0.058 4.25 O1 14.59 14.63 14.57 14.61 14.47 14.47 14.60 14.72 14.58 0.080 14.58 M1 0.87 0.91 0.89 0.84 0.93 0.93 0.91 0.91 0.90 0.028 0.90 PI1 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.001 0.65 P1 11.34 11.34 11.31 11.29 11.36 11.33 11.29 11.30 11.32 0.023 11.32 K1 34.25 34.26 34.16 34.12 34.31 34.24 34.12 34.12 34.20 0.070 34.20 PSI1 0.27 0.27 0.27 0.27 0.27 0.27 0.27 0.27 0.27 0.001 0.27 PHI1 0.48 0.48 0.48 0.48 0.48 0.48 0.48 0.48 0.48 0.001 0.48 J1 0.94 0.93 0.85 0.91 1.09 1.11 1.07 1.06 1.00 0.092 0.99 OO1 1.31 1.37 1.37 1.53 1.68 1.54 1.42 1.34 1.45 0.119 1.45 2N2 1.73 1.71 1.70 1.71 1.70 1.72 1.73 1.73 1.72 0.011 1.72 MU2 3.74 3.74 3.71 3.75 3.65 3.46 3.57 3.59 3.65 0.097 3.65 N2 12.98 12.83 12.79 12.86 12.81 12.91 13.03 12.99 12.90 0.086 12.90 NU2 2.52 2.49 2.48 2.49 2.48 2.50 2.53 2.52 2.50 0.017 2.50 M2 55.43 55.32 55.25 55.25 55.26 55.41 55.68 55.53 55.39 0.144 55.39 L2 3.73 3.87 3.96 3.79 3.89 3.78 3.72 3.67 3.80 0.090 3.80 T2 1.05 1.06 1.06 1.07 1.06 1.05 1.05 1.05 1.06 0.005 1.06 S2 17.86 17.96 17.96 18.10 17.98 17.85 17.86 17.84 17.93 0.084 17.93 K2 4.86 4.89 4.89 4.92 4.89 4.85 4.86 4.85 4.88 0.023 4.88 2SM2 1.55 1.52 1.31 0.99 1.26 1.49 1.55 1.50 1.39 0.183 1.38 MO3 1.81 2.04 2.04 2.00 2.02 2.02 1.96 1.87 1.97 0.079 1.97 M3 0.74 0.62 0.59 0.67 0.64 0.51 0.64 0.73 0.64 0.069 0.63 MK3 1.08 1.07 1.13 0.95 1.09 1.22 1.17 0.96 1.08 0.088 1.08 MN4 0.31 0.26 0.29 0.38 0.31 0.30 0.36 0.14 0.30 0.067 0.13 M4 1.37 1.29 1.26 1.19 1.17 1.26 1.30 1.42 1.28 0.079 1.28 SN4 0.25 0.27 0.39 0.56 0.63 0.64 0.41 0.29 0.43 0.151 0.42 MS4 0.86 0.62 0.69 0.56 0.53 0.58 0.74 0.80 0.67 0.111 0.67 2MN6 0.82 0.91 0.87 0.78 0.73 0.68 0.77 0.91 0.81 0.078 0.81 M6 1.10 1.01 1.00 0.89 0.90 0.94 1.07 1.08 1.00 0.075 0.99 MSN6 0.71 0.48 0.59 0.76 0.79 0.93 0.94 0.84 0.76 0.151 0.73 2MS6 1.45 1.41 1.40 1.21 1.11 1.13 1.21 1.14 1.26 0.130 1.26 2SM6 0.58 0.46 0.33 0.37 0.56 0.65 0.76 0.62 0.54 0.137 0.52

After examining the corresponding tables at all converging, narrow and shallow channel can be the stations, we concluded that for all constituents looked at as resulting from two waves: an inci- whose amplitude is greater than 3 cm, the upper dent shallow-water wave triggered by the tide at limit of the error bar of the values listed in tables 4 the mouth and a reflected shallow-water wave and 5 is ±0.5 cm for amplitude and ±5◦ for phase that gets generated as the incident wave prop- lag. agates through the channel. In some channels the contribution of the reflected wave can be 3. Results neglected (Friedrichs and Aubrey 1994). In gen- eral, however, both the waves need to be taken into 3.1 Distribution of amplitude and phase lag account. When they are, the variation of ampli- tude and phase difference along the channel is Variation of amplitude and phase lag with dis- a function of friction, geometry of the channel tance from mouth to head in an estuary with a (rate of convergence of the channel from mouth 500 D Sundar and S R Shetye

Table 5. Same as table 4 but for the phase lag in degrees (referenced to IST) at Akkada. The ‘star’ marked entries are related constituents which have not been computed independently, but computed in relation to the independent major constituents with larger amplitudes, given in brackets next to them. Hence is the same phase lag.

Std. Constit. x000 x015 x030 x045 x100 x115 x130 x145 mean dev. x

MM 85.9 86.4 85.6 86.2 85.1 84.6 83.6 85.4 85.3 0.84 85.3 MSF 359.5 359.4 359.5 359.9 358.4 359.9 1.8 0.9 359.9 0.95 359.9 Q1 72.7 72.4 71.0 69.8 70.7 71.3 72.5 72.5 71.6 1.00 71.6 O1 61.0 60.9 60.9 60.8 61.0 60.6 61.0 60.8 60.9 0.12 60.9 M1 61.0 58.8 59.9 64.5 62.1 66.9 65.7 62.3 62.6 2.66 62.7 ∗PI1 (K1) 74.8 74.7 74.7 75.1 75.3 75.3 75.1 75.0 75.0 0.24 75.0 ∗P1 (K1) 74.8 74.7 74.7 75.1 75.3 75.3 75.1 75.0 75.0 0.24 75.0 K1 74.8 74.7 74.7 75.1 75.3 75.3 75.1 75.0 75.0 0.24 75.0 ∗PSI1 (K1) 74.8 74.7 74.7 75.1 75.3 75.3 75.1 75.0 75.0 0.24 75.0 ∗PHI1 (K1) 74.8 74.7 74.7 75.1 75.3 75.3 75.1 75.0 75.0 0.24 75.0 J1 100.6 97.3 103.5 112.7 107.3 106.1 104.1 100.9 104.1 4.44 104.1 OO1 161.9 157.7 157.4 161.5 160.0 159.9 162.3 161.8 160.3 1.78 160.3 ∗2N2 (N2) 329.9 329.0 329.3 328.9 328.6 328.3 329.1 330.2 329.2 0.60 329.2 MU2 44.8 44.7 45.8 48.1 46.0 45.1 44.6 46.4 45.7 1.11 45.7 N2 329.9 329.0 329.3 328.9 328.6 328.3 329.1 330.2 329.2 0.60 329.2 ∗NU2 (N2) 329.9 329.0 329.3 328.9 328.6 328.3 329.1 330.2 329.2 0.60 329.2 M2 345.8 345.6 345.6 345.8 345.5 345.2 345.3 345.7 345.6 0.18 345.6 L2 308.7 311.0 311.8 309.3 311.8 311.9 308.2 308.4 310.2 1.53 310.2 ∗T2 (S2) 32.5 32.1 32.1 32.6 32.8 32.8 32.7 32.7 32.5 0.26 32.5 S2 32.5 32.1 32.1 32.6 32.8 32.8 32.7 32.7 32.5 0.26 32.5 ∗K2 (S2) 32.5 32.1 32.1 32.6 32.8 32.8 32.7 32.7 32.5 0.26 32.5 2SM2 219.4 218.9 214.7 208.0 203.8 199.2 202.4 215.0 210.2 7.36 210.3 MO3 32.2 26.4 26.2 25.7 25.2 27.3 31.0 32.1 28.2 2.78 28.1 M3 0.1 355.5 345.5 338.2 335.2 347.3 0.6 1.7 350.5 9.79 350.9 MK3 330.8 321.7 320.0 323.3 325.9 325.7 332.5 336.7 327.1 5.37 326.9 MN4 206.3 230.0 276.5 278.0 307.4 343.2 39.3 143.2 228.0 91.99 284.8 M4 163.0 157.4 157.9 157.1 155.2 154.0 159.3 162.3 158.3 2.96 158.4 SN4 336.1 350.6 0.2 349.1 354.6 8.3 21.8 353.9 356.8 12.80 358.2 MS4 251.6 252.7 254.8 272.9 253.9 246.6 245.1 254.9 254.1 7.90 253.5 2MN6 343.4 344.9 345.4 336.2 326.6 329.3 322.9 329.9 334.8 8.32 335.3 M6 7.0 14.2 7.1 5.0 4.1 359.1 359.6 2.9 4.9 4.51 5.1 MSN6 40.9 19.8 13.3 4.2 7.1 20.0 33.2 38.4 22.1 13.12 23.5 2MS6 47.6 50.2 51.8 58.6 55.9 46.6 51.7 46.1 51.1 4.16 50.6 2SM6 120.5 99.6 97.2 59.7 80.5 64.4 87.3 100.3 88.7 18.83 89.6

to head) and tendency of the two waves to set up not linear with respect to distance from the mouth. standing modes (Shetye 1999; Nayak and Shetye A linear variation would have been expected if 2003). the reflected wave was absent. Further studies are Figure 4 shows how amplitude and phase lag of needed to determine how the three processes – the most important tidal constituents (amplitude friction, geometric effect and co-oscillation of inci- greater than 10 cm at the mouth) grow from mouth dent and reflected wave – set up the variation seen to head before topographic effect comes into play. in figure 4. Before the topographic influence is felt, amplitude of M2 increased by about 20% in the Mandovi 3.2 Decay of tidal amplitude due to increase from mouth to head, and by about 30% in the in channel elevation Zuari. The increase in K1 was by about 10% in the Mandovi and 15% in the Zuari. Phase lag increased Each of the 7 panels in figure 5 gives a section from mouth to head for both diurnal and semi- of the channel topography and water level along diurnal constituents. However, this variation was a line drawn through the middle of the Mandovi Tides in the Mandovi and Zuari estuaries 501

Figure 4. Variation in amplitude (cm) and phase lag in degree (referenced to IST) of M2,S2,N2,K1 and O1 in the main channels of the Mandovi and Zuari estuaries. channel. Both the topography and the water level hence, understand how the increase in channel ele- are based on observations: the topography is the vation causes the tidal amplitude to drop at the same as that described in Shetye et al (1995), and upstream end in an estuarine channel. As seen the water surface depicted in the figure is based from figure 3, the magnitude of water level varia- on data collected during the 2003 observations. tion drops sharply from Usgao to Ganjem in the Two consecutive panels in the figure show how Mandovi and from Sanvordem to Sanguem in the the water level changed during a period of two Zuari. From figure 5 it is seen that the tide reaches hours during spring tide. The panels together cover Ganjem in the Mandovi only when the tide is high a typical 12-hour cycle during springs. The fig- enough to overcome the effect of increased channel ure helps to visualize how the water level along elevation. The impact of the tide is felt at Ganjem the channel changes during a tidal cycle. And in panels A, E, F, and G of the figure. In the rest 502 D Sundar and S R Shetye

Figure 5. Each of the 7 panels in the figure gives an instantaneous section of the channel topography and water level along a line drawn through the middle of the Mandovi channel. Two consecutive panels are separated by two hours during spring tide. The water level at the upstream end is controlled by dynamics of the river flow. of the panels no influence of the tide is seen at 4. Summary Ganjem and the water level is determined merely by whatever little runoff that exists in the river The Mandovi and the Zuari are typical of the channel. estuaries found along the west coast of India. The Tides in the Mandovi and Zuari estuaries 503 estuaries are fed at the upstream end by rivers that Acknowledgements originate on the slopes of the Western Ghats. In this paper we have described how the character- We are grateful to David Pugh and Philip Wood- istics of tidal constituents change from mouth to worth for reviewing the manuscript. Their com- head in these shallow (∼5 m deep), narrow (usually ments have been very useful. We thank Shri Arun less than few hundred meters wide, except near the Y Mahale and Shri S Akerkar, DTP for their help mouth) and converging channels. To our knowledge in drawing figures 1 and 5. This is NIO contribution this is the first time that such a description is 4018. available for the west coast estuaries. The exercise was carried out using tide-pole readers numbering about fifty. The present socio-economic conditions References in this part of the world still make it more eco- nomical to employ tide-pole readers rather than Bell C, Vassie J M and Woodworth P L 1998 POL/PSMSL self-reading tide-gauges. The estimated errors in Tidal Analysis Software Kit 2000 (TASK-2000), Perma- the computed values of tidal constituents are small nent Service for Mean Sea Level, UK, p. 21. enough to conclude that the spatial pattern of vari- Friedrichs C T and Aubrey D G 1994 Tidal propagation in 99 ation in tidal constituents is dependable. Hence the strongly convergent channels; J. Geophys. Res. C2, 3321–3336. method of measurement still remains attractive to Nayak R K and Shetye S R 2003 Tides in the Gulf of Khamb- gain insights into dynamics of the tide propagation hat, west coast of India; Estuarine, Coastal and Shelf Sci- in this estuary. ence 57 249–254. The results of this study show that both the Shetye S R 1999 Tides in the Gulf of Kutch, India; Conti- 19 diurnal and semi-diurnal tidal constituents amplify nental Shelf Research 1771–1782. Shetye S R, Gouveia A D, Singbal S Y, Naik C G, Sun- in the estuarine channels, the amplification being dar D, Michael G S and Nampoothiri G 1995 Propa- larger in the case of the semi-diurnal constituents. gation of tides in the Mandovi–Zuari estuarine network. It is expected that the observed amplitude results Proc. Indian Acad. Sci. (Earth Planet. Sci.) 104(4) from an incident and a reflected wave, both of 667–682. which get altered by channel geometry and friction. Unnikrishnan K, Shetye S R and Gouveia A D 1997 Tidal propagation in the Mandovi–Zuari estuar- Further research is needed to determine the contri- ine network, west coast of India: Impact of fresh bution of each wave to the observed amplitude and water influx; Estuarine, Coastal and Shelf Science 45 phase lag. 737–744.

MS received 11 June 2004; revised 9 May 2005; accepted 29 July 2005