Numerical modeling of tide-surge interaction along Orissa coast of India

Transcription

1 Nat Hazards () 5:13 7 DOI 1.17/s ORIGINAL PAPER Numerical modeling of tide-surge interaction along Orissa coast of India Prakash C. Sinha Æ Indu Jain Æ Neetu Bhardwaj Æ Ambarukhana D. Rao Æ Shishir K. Dube Received: 19 December / Accepted: 5 August 7 / Published online: 1 November 7 Ó Springer Science+Business Media B.V. 7 Abstract The Orissa coast of India is one of the most vulnerable regions of extreme sea levels associated with severe tropical cyclones. There was extensive loss of life and property due to the October 1999 super cyclone, which devastated large part of the Orissa coast. The shallow nature of the head bay, presence of a large number of deltas formed by major rivers of Orissa such as Mahanadi and Dhamra, and high tidal range are responsible for storm surge flooding in the region. Specifically, rising and falling tidal phases influence the height, duration, and arrival time of peak surge along the coast. The objective of the present study is to evaluate the tide-surge interaction during the 1999 Orissa cyclone by using nonlinear vertically integrated numerical models. The pure tidal solution for the head bay region of the Bay of Bengal provides the initial condition for the fine resolution nested grid Orissa model. However, the feedback from the Orissa model does not affect the head bay model as the study provides a one-way interaction. Numerical experiments are performed to study the tide-surge interaction by considering various relative phases of the tidal waves with the surge-wave produced by 1999 Orissa cyclone. The comparison, although utilizing only the limited estimates of tidal data, appears adequate to assert that the principal features are reproduced correctly. Keywords Bay of Bengal Orissa coast Numerical model Tide-surge interaction P. C. Sinha I. Jain (&) N. Bhardwaj A. D. Rao Centre for Atmospheric Sciences, Indian Institute of Technology Delhi, Hauz Khas, New Delhi 111, India indu_jain@yahoo.com S. K. Dube Indian Institute of Technology, Kharagpur 713, West Bengal, India

2 1 Nat Hazards () 5: Introduction The surge generated by many tropical cyclones originating in the northern Indian Ocean has resulted in large scale flooding and destruction along the Indian coastline. In order to minimize the loss of life and property, storm surge models have been developed for many parts of the world and have long been used to provide routine flood warnings along the coastal regions in several countries. Flierl and Robinson (197) documented many cases where the occurrence of abnormally high sea-surface levels in the Bay of Bengal led to coastal flooding and inundation. The problem of storm surges in the Bay of Bengal was reviewed by Murty et al. (19). They concluded that, on the oceanographic scale, a major difficulty lies in the interaction of surge and tide, a thorough understanding of both being necessary for accurate forecasting of the magnitude and time of peak water level. The interaction effect between tide and surge in the Bay of Bengal was also studied by Johns and Ali (19), Johns et al. (195), and by Sinha et al. (199). However, the study of tidesurge interaction along the Orissa coast, in particular, has received little attention. While studying coastal flooding, Proudman (1955a, b; 1957) investigated theoretically the effects of interaction between tide and surge along an estuary. Later, Banks (197) showed that non-linear effects involving tide and surge could be of significance throughout the entire North Sea as well as the Thames River. Overland and Myers (197) investigated the tide and surge propagation in Cape Fear estuary. Rady et al. (199) studied tide-surge interaction in the Gulf of Suez. In their investigation, the surge is based on an analytical formulation for a rectangular water body having uniform depth. In another work, Flather (199) concluded that the timing of cyclone landfall and its coincidence with the high tide determine the area worst affected by flooding during 1991 Bangladesh cyclone. Earlier investigations studied the influence of cyclone characteristics and astronomical tide on the value of highest water levels along the head bay region of the Bay of Bengal. However, the influence of rising and falling tidal phase on the height, duration, and arrival time of peak surge along the Orissa coast has not been investigated so far. The objective of the present work is to evaluate the tide-surge interaction during the October 1999 Orissa cyclone, which devastated large part of the Orissa coast. Unfortunately, a continuous record of tide-gage measurements throughout the duration of the cyclonic event is not available. However, we are unlikely to have access to any better data describing an actual surge event. Therefore, the best we can do is to make the most effective use of the limited data that are available for the Orissa coast. The total water level at the coast due to an approaching cyclone comprises storm surge, astronomical tide, and wave setup. However, in the present article we have confined our attention to a study of the non-linear tide-surge interaction. The wind-generated waves are not considered here for surge height calculations. Orissa has a coastline of 59 km, which is important for not only having one of the major commercial seaports of the country, Paradip, but also for having long stretches of highly fertile and densely populated land. The coast has a combination of several deltas of varied size and shapes formed by major rivers of Orissa like Mahanadi and Dhamra. The tidal range in this area varies from. m during springs to.7 m during neaps (The Indian Tide Tables Part ). Along the Orissa coast, the tidal elevation above equilibrium level may be approximated by f ¼ f þ a cosfðpt=tþ ug ð1þ

3 Nat Hazards () 5: where f is the mean tide, T is the semidiurnal period, and a and u are the amplitude and phase of the tidal wave. In the present study, Eq. 1 consists of the amplitude and phase of the local M constituent, as only the M tide has been used in the computations. In our applications, we simulate the actual tide at Paradip on October 9, 1999 when part of the Orissa coast was also affected by a surge induced increase in the sea-surface level. According to Satapathy (1999), height of the tide inside the sea was about 3 m before the cyclone approached. As no actual tide-gage data during the event is available, an estimate is taken from the past available records. Accordingly, using the Admiralty tide table for 1995, the times and heights of high and low water at Paradip are deduced as given in Table 1. The average duration of each of the tidal cycles is about 1.3 h and is marginally less than the M period. The average difference between high and low water is approximately 1. m. Therefore, on October 9, 1999, the variation of the tidal elevation at Paradip may be approximately represented by Eq. 1 with a &.5 m and T = 1.3 h (Fig. 1). Due to the absence of tidal forcing in the storm surge models accurate warning cannot be given about the intensity and arrival time of the life threatening surges. Also, the relative phase of the surge and tide can affect the arrival time and the duration of the peak surge. Keeping this in view, a numerical model is developed to study the combined effect of tide and surge in the region to compute the peak surge, its time of occurrence and the duration for which this peak value will be sustained. We have considered two stair-step Table 1 Times of high and low water on October 9, 1995 at Paradip Time (I.S.T) Height above local datum level (m) h.w. (h) l.w. (h) h.w. (h) l.w. (h) Fig. 1 Map showing Orissa coast and analysis region of the model

4 1 Nat Hazards () 5:13 7 models that are combined into a unified computational scheme. The first model is a tidal model for the head bay region (referred to as model A) and the second one is a nested high-resolution storm surge model for the Orissa coast (referred to as model B). The analysis area for model A extends from 1 Nto3 N and 3.5 E to 9.5 E. Its southern open sea-boundary is parallel to latitude 1 N. For model B, the analysis area runs from 19 N to N and.9 E to.5 E with its southern open boundary located at latitude 19 N. Although the principal component is surge, the sea-surface elevation may either be decreased or increased with respect to surge value, depending on its phase with astronomical tide. However, the mutual interaction of tide and surge is nonlinear, and both processes must be considered simultaneously. Formulation The curvature of the earth s surface is neglected and all conditions are referred to a system of Cartesian coordinates. With the origin, O, located within the equilibrium level of the sea-surface and at the south-western extremity of model A, Ox points toward east, Oy toward north, and Oz is directed vertically upward. The displaced position of the seasurface is given by z = f (x, y, t) and the position of the sea floor by z =-h(x, y). The depth averaged equations of continuity and momentum used for the dynamical processes are given as (Heaps 199) ou ot þ u ou ov ot þ u ov ox þ v ou oy ox þ v ov oy of ot þ oðhuþ þ oðhvþ ¼ ox oy of fv ¼ g ox þ 1 s f x ku H q H ðu þ v Þ 1= of þ fu ¼ g oy þ 1 s f y kv H q H ðu þ v Þ 1= : Here, f denotes the Coriolis parameter, the pressure is taken as hydrostatic and the direct effect of astronomical tide generating forces is omitted. Also, the effects of barometric forcing terms are neglected. The bottom friction is parameterized in terms of a conventional quadratic law with the friction coefficient, k, taken as The density of water q is assumed uniform and H is the total depth (=f + h). The applied surface wind stress (F s, G s ) are given by ðf s ; G s Þ¼c d q a u a þ 1=ðua v a ; v a Þ ð5þ where, c d = is the surface drag coefficient, q a is the air density, and u a, v a are the x and y components of the surface wind. In contrast to model A, the western boundary of model B does not consist of a continuous vertical wall. Instead a onedimensional model similar to that used in Dube et al. () has been included to represent the Mahanadi River which joins the Bay near the Orissa coast. A -km length of the river is taken into consideration with no mass flux from its head. The breadth and mean depth are based on the data available from the Survey of India (SOI). The distance between computational elevation points is taken as 57 m and the time-step has been taken as 1 s. ðþ ð3þ ðþ

5 Nat Hazards () 5: Boundary conditions The boundary conditions along the coastline require that the normal component of the velocity be zero, i.e., 9 u ¼ at the meridional boundaries = v ¼ at the latitudinal boundaries ðþ ; f ¼ u ¼ v ¼ for t ¼ At the southern open sea-boundary of model A, we use a radiation boundary condition as applied by Johns et al. (191). This condition allows the outward propagation of internally generated response from the analysis region and communicates with the tides of the Bay of Bengal coming toward the Orissa coast. The condition has the form v þ g 1=f ¼ aðg=hþ 1= sin pt h T þ u at y ¼ ð7þ In Eq. 7, a and u denote, respectively, the prescribed amplitude and phase of the tidal wave and T is the period of the tidal constituent under consideration. If the tidal response entering the analysis region p at y = is in the form of a progressive wave with its g crest parallel to y =, then v ¼ ffiffi h f and Eq. 7 reduces to pt f ¼ a sin T þ u at y ¼ ðþ In this case a and u correspond to the amplitude and phase of the tidal elevation along y =. A consequence of applying (7) rather than () is that the values of neither f nor v are separately prescribed along the open-sea boundary of model A. Thus, during the solution process the boundary values of both f and v may correlatively adjust subject only to Eq. 7. Wind forcing module Two main forces, which generate storm surges on the sea surface, are surface wind stress and pressure gradient force. These act parallel and normal to the sea surface respectively and their relative importance depends on the water depth. In view of the strong associated winds, the forcing due to barometric changes is neglected. Thus, the surface wind field associated with a tropical cyclone is the primary requirement for modeling of storm surges. For this purpose, the wind field at the sea surface is derived by using a dynamic storm model (Jelesnianski and Taylor 1973). To obtain a dynamic wind profile, initially a stationary symmetric model wind profile is taken, and then correction is applied to approximate the asymmetry due to storm motion. The vector equation which rules the horizontal motion of wind flow near the sea surface in the area of storm is dv g dt ¼ 1 q a grad p þ f V g k þ F ð9þ where, k is the vertical unit vector, V g is the wind velocity, q a is the density of air, f is Coriolis parameter, p is the pressure of atmosphere, and F is the horizontal frictional force per unit mass.

6 1 Nat Hazards () 5:13 7 Assume that the pressure and the wind fields move forward without change at the velocity of storm. For a stationary symmetric storm, from Eq. 9 we get, at a distance r from the center of the cyclone (Myers and Malkin 191; Ueno 191) dp dr ¼ q av g K s sinu 1 dv g V g dr du ð1þ 1 dp q a dr cosu ¼ f V g þ V g r cosu V g dr sinu þ K nv >; g where, u(r) is the inflow angle of wind, that is, angle toward the storm center. K s and K n are empirically determined coefficients representing stress coefficients in the directions opposite and to the right of the wind, respectively. These stresses are given by the coefficient times the square of the wind speed. By eliminating pressure from Eq. 1, one can get du dr ¼ K su sinu fr K nv g r ð11þ where, u = V g r cos u. We can solve Eq. 11 numerically and get the distribution of u(r) or u(r). Then, integrating the first Eq. of 1, we can also get the distribution of p(r). For this we have to know first the wind profile which is given by Jelesnianski (197) as R m r V g ðrþ ¼V R ðr m þ r ð1þ Þ where, V R is the value of the maximum wind speed and R m is the distance from the center where the maximum wind speed appears. The value of R m is usually fixed from the synoptic map (here its value is taken as -km) while the value of V R is determined by solving the Eqs. 1 and 11 numerically. 9 >= 5 Numerical procedure Using a depth averaged model, the basic hydrodynamic Eqs. are solved by a finitedifference scheme similar to that used by Sinha and Mitra (19). The governing equations are solved numerically by considering a set of grid points defined by x ¼ x i ¼ði 1ÞDx i ¼ 1; ;...m ð13þ y ¼ y j ¼ðj 1ÞDy j ¼ 1; ;...::n where, Dx =b/(m-1) and Dy = L/(n-1) are the grid increments while m and n are the number of grid points in the x and y directions, respectively. The length and breadth of the analysis areas is taken as L and b. In model A we have chosen b = 11 km, L = 53. km, m = 331, n = 15 and as a result Dx and Dy are found to be 3.7 and 3.5 km, respectively. In model B, we have taken b = 399 km, L = km, m = 31, and n = 35, which gives Dx = Dy = 9 m. A sequence of time instants is defined by t ¼ t p ¼ p Dt p ¼ 1; ;... ð1þ Here, a conditionally stable semi-explicit finite-difference scheme is used to solve the governing equations on a staggered grid. The space derivatives in the momentum equations and the continuity equation are evaluated at the advanced time level. The

7 Nat Hazards () 5: Coriolis term in Eq. 3 is evaluated explicitly at the old time level, whereas in Eq. it is evaluated at the advanced time level by using the previously updated value of u. Leendertse (197) reported that the application of the above scheme for the Coriolis term gives satisfactory results. Finally, in both the momentum equations the bottom friction term is evaluated implicitly and forward differencing is used for the time stepping. The stability is conditional upon the time-step being limited by the space increments and the gravity wave speed. The general procedure followed in the numerical solution is to begin by generating the co-oscillating tide in model A by prescribing the temporal variation of the seasurface elevation along the southern open boundary. The pure tidal solution developed in model A then provides the initial dynamical conditions for the nested fine resolution model B. Firstl, model A is run for four tidal cycles to obtain steady tidal solutions. After that at each time-step the elevation computed by model A provides the boundary condition to model B. Although the model A could accommodate much larger timesteps, however, to avoid any complications in the computations for both the models we utilize the same time-step of 1 s, which is found to be consistent with computational stability. The procedure of the tide-surge interaction is similar to that applied in earlier studies of the North Sea (Banks 197) and the Bay of Bengal (Johns et al. 195). The bathymetry used in this study has been taken from the Naval Hydrographic Charts (Fig. ). An important feature of the scheme is that the response in model A is independent of the conditions for the model B. However, the response in model B depends on the tidal conditions generated in model A. We find that the results from model A are unrealistic in the region, where a river joins the bay. This is presumably due to the lack of representation of the river system as well as the coarser resolution of the model. These inadequacies are taken care of in the model B which gives a satisfactory result Balasore 1 Chandabali.5 MAHANADI R. Paradip Puri 19.5 Gopalpur Fig. Analysis region of model B and the isobaths of the model bathymetry (m)

8 Nat Hazards () 5:13 7 Results and discussion.1 Generation of tide and verification of the tidal model The paucity of data on surges generated along the Orissa coast of India is such that a direct verification of model B for surge prediction is difficult. However, we have used the limited coastal data available for the pure M tidal response in the head bay region for verification purposes. If a comparison of the computed and observed tidal response is satisfactory, one would feel justified in asserting that the dynamical processes are correctly represented in the model. If the values of a and u in Eq. 7 were known with precision along the open-sea boundary of model A, there would be no problem in integrating the model equations ahead in time subject to the prescribed forcing along y =. From the initial state of rest, the transient response would then be gradually dissipated by friction and also radiated out of the computational domain. Thereafter, an oscillatory response would remain in the Bay corresponding to the tidal constituent with period T. Unfortunately, precise values of a and u are not available. Therefore, we have had to resort to numerical experimentation and a series of tests to ascertain the values of the forcing parameters. We found that the interpolated value of a from the literature (Murty and Henry 193) and an arbitrarily chosen u =, are not noticeably inferior to other cases considered. Moreover, the computed tidal amplitude at Paradip and Chandabali are. and.9 m compared with the observed values of.5 and.97 m. Figure 3 depicts the isolines of the computed tidal amplitudes along the Orissa coast. At some of the coastal stations we have also inserted observationally determined values. The computed amplitudes generally correlate well with the observed one, especially at Paradip Gopalpur O R I S S A Paradip Puri Balasore Chandabali Fig. 3 The isolines of computed amplitudes (m) of M and S tides along the Orissa ccoast. The numbers along the coast refer to observed tidal amplitudes in meters

9 Nat Hazards () 5: and Chandabali. The discrepancies between computations and observations are generally of the order of 7%.. Tide-surge interaction along the Orissa coast Since the astronomical tide is a continuous process in the sea, the surges due to tropical storms always interact with the astronomical tide. So, the pure tidal oscillations provide the initial state of the sea for the tide-surge interaction phenomenon. In this section, we propose to determine the nature of the interaction between the tide and the surge during the period of abnormally high sea-surface levels encountered along the Orissa coast on October 9, A low-pressure system intensified and became a depression on 5 October 1999 morning and lay centered at 1.5 N, 9.5 _E off the coast of Andaman and Nicobar Islands. By UTC on October it had moved in the west-northwestward direction and intensified into a cyclone lying centered at 13. N and 95. E. Moving further ahead in the northwest direction, it became a severe cyclone at UTC on 7 October centered at 1.5 N, 91.5 H and later in the night, attained hurricane intensity and lay centered at 17. N, 9.5 E. On the night of October, the cyclone system intensified further and was classified as a Super Cyclone by the India Meteorological Department (IMD) with wind speeds exceeding km/h. The super cyclone hit the coast of Orissa at about UTC of 9 October, near Paradip. After crossing the coast, the system moved northwestward and remained stationary as a super cyclone for about h. To determine the overall sea-surface elevation due to combined tide and surge the next requirement is the initial sea-state condition. The only procedural requirement is that of adjusting the phase of the tidal solution computed in Section 5.1 so that the initially prescribed dynamical state corresponds to the actual tidal conditions at the model time t =. As per the report (Satapathy 1999), the high tides at Paradip on October occurred at 173 UTC. This is 11.5 h after the commencement of the wind stress forcing in the proposed model simulation. Accordingly, when t = 11.5 h in the model, it must be high tide at Paradip. The correct phase in the tidal solution derived in Section 5.1 to produce this condition may be arranged by specifying an appropriate non-zero value for u in Eq. 7, rather than zero. The semidiurnal component of the tidal response in the model is then given by f ¼ a 1 cosfðpt=tþþu u 1 þ bg ð15þ The value of u 1 at Paradip is -3.3 rad. High tide at Paradip must be at t = 11.5 h and hence Eq. 15 immediately leads to a value of u = -. rad. This value of u is used subsequently as the tidal component in phase with storm surge, during the tide-surge interaction experiments. To investigate the relative influences of the flooding and ebbing tidal phases on the height and arrival time of the maximum surge, an additional phase, b,is introduced, the value of b is when tide is in phase with surge. For numerical experimentation, its value vary in the range ±.5, ±.7 and ±1.5 as the time of surge leads/ lags the high tide by ±1 h,±3 h and ± h, respectively. Figure shows the surge contours during the event of October 1999 cyclone along the Orissa coast. The track of the cyclone and the relevant data are taken from IMD who estimated a lowest pressure of 9 hpa and a radius of maximum wind of km at landfall point near Paradip. These data were used in the model to carry out numerical

10 Nat Hazards () 5: O R I S S A Puri Balasore Chandabali Paradip 19.5 Gopalpur Fig. Peak surge contours (m) associated with October 1999 Orissa cyclone experimentation. The wind stress forcing for driving the model was computed by using the storm model of Jelesnianski and Taylor (1973). It may be noted that the computed peak surge value is 7.5 m at Paradip, which is situated at a distance of about 5 km toward the right of landfall point. However, the peak surge values at Chandabali and Balasore are 5. and. m, respectively. Though these stations are at a far distance from the landfall point, yet owing to the high tidal range the peak surge value is quite high. The extreme surge development in the region resulting in a high surge value of 7.5 m at Paradip may be attributed to the nearshore topography and orientation of the coastline with reference to the storm track (Dube et al. 19). Post-storm survey reports of IMD also show that the surge was more than 7 m in proximity to Paradip. The results of the simulation may be presented in several different ways, each illustrating a different aspect of the tide-surge interaction. From the point of view of the potential flooding risk, the important parameters are the maximum total elevation of the sea surface and the arrival time of the peak, predicted at the points along the coastline. From Fig. 5, it is observed that the value of peak surge at Balasore, Chandabali, Paradip, and Puri are., 5., 7.5, and 3.5 m, respectively. Here it is to be noted that due to interaction of astronomical tide there is an extra rise in sea level of.,.,.5, and.3 m, respectively, at these stations. An inference to be drawn here is that the maximum surge response appears to progress along the Orissa coast. On moving northeast from Puri, the time of occurrence of the peak elevation becomes progressively later, suggesting that the response has the form of a solitary wave propagating along the coast. It may be noted that the peak surge at Paradip, which witnessed the maximum water level, is mainly generated by cyclone and tide has little influence on the peak value. In this study of non-linear tide-surge interaction the main emphasis has been placed on the relative phases of the tide and the surge which has an important bearing on the occurrence of peak water level on the coast.

11 Nat Hazards () 5: (a) Surge Only Tide only Tide-surge interaction (b) Surge only Tide only Tide-Surge interaction S rg e ( m ) u S rg e ( m ) u 9 October October October October 1999 Landfall Time (c) Surge only Tide only Tide-Surge interaction (d) Surge only Tide only Tide-Surge interaction S rg e ( m ) u S rg e ( m ) u 9 October October October October 1999 Fig. 5 Computed variation of sea level with time at (a) Balasore, (b) Chandabali, (c) Paradip, and (d) Puri For this purpose numerical experiments have been carried out to examine the effect of relative phases of the tidal and surge waves by plotting the temporal variation of total water level at three coastal stations, namely, Paradip, Balasore, and Puri. As the maximum surge was reported at Paradip we have centered our discussion at Paradip, together with one station (Balasore) to the north of Paradip and the other (Puri) to its south. From Fig., it may be seen that at Paradip, which is near the landfall point, the difference between the arrival time of the actual peak surge and those generated for 1 and 3 h lag or lead are the same, that is, 1 and 3 h, respectively. A similar behavior is observed at Puri, a station to the south of the landfall point (Fig. ). But at Balasore, which is situated to the north of the landfall point, the difference between the arrival time of the peak surge and those generated for 1 and 3 h lead are and h, respectively (Fig. 7). However, for 1 and 3 h lag, the differences are about and h, respectively. In other words, the arrival time of the peak surge in the northern region is gradually delayed as the landfall time of cyclones lag or leads the arrival time of the local astronomical tidal peak near the landfall point.

12 Nat Hazards () 5:13 7 Surge leads tide by : Hr 1 Hr 3 Hrs Hrs Pure surge Surge lags behind tide by : Hr 1 Hr 3 Hrs Hrs Pure surge Surge (in meter) Surge (in meter) 9 October October October October 1999 Fig. Temporal variation of total water level for different relative phases of surge and the tide at Balasore (station to the north of the landfall point) At the places of low tide, the rate of progression of the surge wave is reduced as depth decreases, since the propagation speed of the long-wave depends on the square root of the total depth of water. At a depth of m (say, during high tidal peak) propagation speed is about 9 m s -1. If the depth is reduced from to 1 m during low tide, then the speed will reduce to about m s -1. To travel 15 km (distance between Paradip and Balasore) the tidal wave will take about 3 h during high tide and about.5 h during low tide. This theoretical calculation agrees with the numerical results when gradually shoaling depth is considered. Moreover, as bottom friction is inversely proportional to the depth, a tidal trough will increase the friction and retard the surge even further. Thus, the presence Surge leads tide by : Hr 1 Hr 3 Hrs Hrs Pure surge Surge lags behind tide by : Hr 1Hr 3 Hrs Hrs Pure surge Surge (in meter) Surge (in meter) 9 October October October October 1999 Fig. 7 Temporal variation of total water level for different relative phases of surge and the tide at Paradip (near the location of landfall point)

13 Surge (m) 3 1 Surge leads tides by Hr 1 Hr 3 Hrs Hrs Pure surge Surge (in meter) 3 1 Surge lags behind tide by : Hr 1 Hr 3 Hrs Hrs Pure surge October October 1999 l 9 October October 1999 Fig. Temporal variation of total water level for different relative phases of surge and the tide at Puri (station to the south of the landfall point) of a negative surge causes retardation of the tidal wave speed and a positive surge hastens the tide. Rossiter (191) showed analytically that a phase shift might also occur when the principal mode of interaction is caused by the tide. It is also observed from Figs. that the peak surge generated during a falling ebb tidal phase (when the cyclone s time of landfall lags behind the tidal peak) is longer in duration than sharper peak generated by a rising flood tidal phase (when the cyclone s time of landfall leads the tidal peak). This is because during the falling ebb phase the wind stress from a cyclone would produce low water level for longer stretches of the coast (and over a longer duration) than during the rising flood phase when the low water level soon changes to a tidal peak. The reduction of propagation velocity by the opposing tidal currents and increased bottom friction due to the current direction may also influence the surge duration. The present study also shows that a cyclone that makes landfall either during the rising tidal phase (i.e., before the arrival of the tidal peak) or during the falling tidal phase (i.e., after the arrival of the tidal peak) produces a lower peak value than that occurring at the time of tidal peak B a a s o r e P a a d i p P u i r r Nat Hazards () 5: Fig. 9 Arrival time of peak surge values (more than m) along the Orissa coast during rising and falling tidal phases T i m e ( i n h r s ) Ti de l a g cy cl one by Hr Ti de l a g cy cl one by 3 Hr Ti de l a g cy cl one by 1Hr Ti m e of l andfal l Ti de l e a d cy cl one by Hr Ti de l e a d cy cl one by 1 Hr Ti de l e a d cy cl one by 3 Hr Ti de l e a d cy cl one by Hr

14 Nat Hazards () 5:13 7 Figure 9 shows that the speed of propagation of surge wave (and hence the arrival time of peak surge) is more influenced by the tide toward the southern side than the northern side of the point of landfall. Johns et al. (195) and Yamashita (1993) have found that the height of the surge peak depends whether the local tide is above the mean sea level or below it. From the present study we find that, when tide-surge interaction is included, the cyclone that makes landfall before the arrival or after the arrival of local tidal peak produces relatively lower surge values. The behavior of surges is similar to that in the southern North Sea and the River Thames, where the pattern of interaction causes positive surge peaks to not to coincide with times of tidal high water, so that they are most likely to occur on the rising tide (Prandle and Wolf 197). Thus, the surge along the Orissa coast can be estimated for any tidal phase. 7 Conclusions Numerical models have been developed to study the tide-surge interaction along the Orissa coast of India. The models are non-linear and are able to simulate the general features of the interaction. The wind-generated waves, which can be significant in many cases, are not considered here for surge height calculation. The tide surge interaction along the Orissa coast shows the local tidal properties of progressive waves in general. The head bay model has been validated with the available tidal records. Numerical experiments are conducted with various relative phases of the local astronomical tide and that of the surge due to 1999 Orissa super cyclone. It is found that the peak surge can develop during any tidal phase, and the one that develops around the time of local peak tide travels faster than the surge that develops in any other tidal phase. Also, the cyclone that makes landfall h before or h after the tidal peak produces larger duration surge in comparison to other tidal phases. It is found that the arrival time of the peak surge in the northern region is gradually delayed as the landfall time of cyclones lag or leads the arrival time of the local astronomical tidal peak near the landfall point. The effect of the tidal phase on the duration of the tidal peak is more at Balasore, a place toward the north of the landfall point, than at Puri, which is to the south of the landfall point. However, the maximum surge height at Paradip is mainly generated by cyclonic winds and tide has little influence on the peak value. During this study it has become clear that further progress in the modeling of tide-surge interaction as well as pure surges in the Bay of Bengal is dependent upon a data acquisition program. Tidal data for the model generation of astronomical tides in the Bay are inadequate. The essential information required relates to both elevation and current data along the southern boundary of the Bay where it communicates with the northern Indian Ocean. Also, there is a need for continuous tide-gage recordings throughout the duration of the event at selected coastal stations along the Orissa coast most affected by the surge. Only then will there be sufficient data to effect a complete validation of the surge prediction. References Banks JE (197) A mathematical model of a river-shallow sea system used to investigate tide, surge and their interaction in the Thames-southern North Sea region. Phil Trans Roy Soc 75:57 9 Das PK, Sinha MC, Balasubhramanayam V (197) Storm surges in the Bay of Bengal. Quart J Roy Met Soc 1:37 9

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