1. Tsunami heights off southeast Indian coast from run-up measurements
JAYA KUMAR SEELAM
National Institute of Oceanography,
Goa, India
(Currently at The University of Queensland, St Lucia, Brisbane, Australia)
SAMIKSHA VOLVAIKER
National Institute of Oceanography,
Goa, India
Introduction
The Indian Ocean Tsunami on 26th December 2004 had a devastating effect on the southeast coast of India. Inundation limits and run-up heights were estimated from the post-tsunami surveys by various organizations along this coast. From the survey carried out by National Institute of Oceanography, Goa, the maximum run-up height was measured at Periyakalapet was 6.54 m above mean sea level. An indirect method of obtaining tsunami height from the run-up heights is attempted in this work. The measured data on the run-up heights, beach slopes, beach grain size (Jaya Kumar et al 2005; ) and estimated seabed slope are used as inputs to the various run-up formulae available in the literature.
(c) Gedik et al (2005) used the equation stating the relation between the run-up height and the wave height for non-armored beach is given by,
(C)
where, Gsp is specific gravity of sand, cot b is dimensionless slope angle, D is dimensionless diameter of sand and R/d is dimensionless parameters of run-up height
(d) The International Tsunami Information Centre of the UNESCO cites the estimation of tsunami magnitude from the maximum runup height as,
H = log2R (D)
where, H = Tsunami magnitude and R = Maximum runup height.
Figure 1. Location map and study region
Periyakalapet
Results & Discussion
Based on the above derived equations, measured run-up heights and other parameters from the field and hydrographic charts, estimated tsunami heights for different regions along the study region and for 50 m offshore depth indicate that the heights vary proportional to the run-up heights. Tsunami heights using equation C provides the least estimates due to presence of additional grain size parameter apart from bed slopes. Whereas from equation D, which has no other parameter except run-up height, the estimates are the largest. As the run-up heights are influenced primarily by the tsunami heights apart from the nearbed slope and the roughness of the region, the estimated tsunami heights based on run-up heights would be used cautiously. In the absence of reliable measured information on the tsunami heights, these results provide an immediate estimate of the tsunami heights considering the tsunami primarily as a solitary wave.
Methodology
Earlier studies (e.g., Gedik et al-2005, Hall and Watts-1953 and Synolakis-1987) reliably estimated run-up heights for given wave height on different beach surfaces (smooth or plane) and beach types (armored or non-armored) and walls (vertical or inclined) as well as islands.
The present work considered these run-up equations to estimate tsunami wave height from available run-up heights. The equations derived from the three works are presented here:
(a) Hall and Watts has used an empirical formula for solitary wave run-up on an impermeable slope with =45° is given by,
(A)
where, R is wave run-up height, d is water depth, and H is wave height.
(b) Synolakis obtained the following simple power law for the predicting solitary wave run-up on a smooth plane beach:
(B)
where,  is the inclination angle of the plane beach.
Figure 2.  Measured run-up heights onshore and estimated tsunami heights at 50 m depth
Acknowledgements
Authors thank the Director, National Institute of Oceanography, Goa, for the facilities provided and all the members of the NIO post-tsunami survey team who had been instrumental in collecting the field data.
References
Gedik et al., Ocean Engg. 32, (2005).
Hall and Watts, Tech Memo 33, USACE-Beach Erosion Board (1953).
Jaya Kumar S et al., Curr. Sci., 2005, 88 (11), 10 June 2005,
Synolakis, C. E., J Fluid Mechanics, 185, (1987)
UNESCO website: