QUANTIFICATION OF TSUNAMIS: A REVIEW
GERASSIMOS A. PAPADOPOULOS
National Observatory of
The efforts made since 1923 to quantify tsunami size in terms of either intensity or magnitude are critically reviewed. The existing 6-point intensity scales need a drastic revision and replacement by modern, detailed, 12-point scales in analogy to earthquake intensity scales. A new tsunami intensity scale proposed by Papadopoulos and Imamura  seems to meet these requirements. Among the existing tsunami magnitude scales even the most sophisticated ones need either better calibration of formulas based on more wave height data or significant improvement in the tsunami source energy calculation.
Efforts towards a quantification of tsunamis started about seventy-five years ago by the pioneering work of Sieberg [2, 3] who defined the first tsunami intensity scale. However, the tsunami quantification is still a puzzling aspect in the tsunami research since the several scales proposed to measure tsunami size often either are confusing as for the quantity they represent, that is intensity or magnitude, or lie under serious difficulty in their applicability. After several attempts made by many researchers to quantify tsunamis in terms of either intensity or magnitude it is extremely useful to reexamine critically not only the various definitions given but also their practical implementation. Particularly it is shown the general need for (1) to develop detailed, pure tsunami intensity scales, established on standard principles and on modern, well - elaborated criteria, and (2) to improve drastically calibration of magnitude scales.
2. Intensity and Magnitude Scales of Tsunami
The earthquake magnitude is an objective physical parameter that measures either energy radiated by, or moment released in, the earthquake source and does not reflect macroseismic effects. On the contrary, the earthquake intensity is a rather subjective estimate of the macroseismic effects. In every earthquake event only one magnitude or moment on a particular scale corresponds. However, every earthquake is characterized by different intensities in different locations of the affected area.
Okal  showed that source depth and focal geometry plays only a limited role in controlling the amplitude of the tsunami, and that more important are the effects of directivity due to rupture propagation along the fault and the possibility of enhanced tsunami excitation in material with weaker elastic properties, such as sedimentary layers. Therefore, a tsunami can be considered as a particular case of seismic wave and problems related to tsunami quantification could be approached in analogy to seismology.
Sieberg [2, 3] is very likely the first to present a 6-point tsunami intensity scale which, in analogy to earthquake intensity scales, was based not on the measurement or estimation of a physical parameter, e.g. the wave height, but it was established on the description of tsunami macroscopic effects, like damage etc. Ambraseys  published a modified version of Sieberg’s scale known as Sieberg-Ambraseys tsunami intensity scale. In the Japanese tsunami literature one may find a long tradition in the effort for tsunami quantification. Imamura [6, 7] introduced and Iida [8, 9] and Iida  developed further the concept of tsunami magnitude, m, defined as
m = log 2 H max (1)
Where H is the maximum tsunami wave height (in m) observed in the coast or measured in the tide gages. Practically, the so-called Imamura – Iida scale is a 6-point scale ranging from –1 to 4 giving the impression of a rather intensity than a magnitude scale. However, m does not estimate effects but it measures by definition H max that is a physical quantity. In this sense it may represent magnitude in a primitive way since it does not calibrate the wave height with the distance. In his attempt to improve the Imamura – Iida’s definition, Soloviev  proposed to define tsunami intensity, iS, by
iS = log 2 √2 ( H ) (2)
where H (in m) is the mean tsunami height in the coast. However, this is still a primitive magnitude scale since it is also based on the physical quantity H. Tsunami magnitude M t [12, 13, 14, 15] or m  was defined by the general form
M t = a log10 H + b log Δ + D (3)
where H =
maximum single (crest or trough) amplitude of tsunami waves (in m) measured by
tide gages, Δ is the distance (in km) from the earthquake epicenter
to the tide station along the shortest oceanic path (in km), and a, b, D are constants. Expression (3) is
similar to the
ML = 2 ( log10 E – 19) (4)
where E is the tsunami potential energy (in ergs). Definition of ML is in close analogy to the Kanamori’s  definition of moment magnitude
Mw = 2/3 (log10 M0 – 16.1) (5)
as well as to the mantle magnitude 
Mm = log M0 – 20
Where M0 is the seismic moment.
A particular scale measuring tsunami size is that proposed by Shuto  who considered it as an intensity scale:
i = log 2 H (6)
Where H is the local tsunami height (in m). Obviously by definition it is still a magnitude scale. However, in order to use it as an intensity scale for the tsunami damage description, Shuto  proposed to define H according to its possible impact. A 6-point classification of tsunami effects ranging from 0 to 5 is tabulated for the description of the expected damage or destruction as a function of H.
3. Possibilities and Limitations of the Tsunami Size Scales
All the tsunami magnitude scales that are based on measurements of tsunami wave heights at coastlines, from the primitive ones, like those of Imamura - Iida and Soloviev, to the more recent and more sophisticated scales of Abe and Hatori are very sensitive to local effects like coastal topography, near-shore bathymetry, refraction, diffraction and resonance. However, better calibration of formulas, based on more tide-gage and measured in the field wave heights, may drastically improve the applicability of such scales for the tsunami magnitude determination in the future.
TABLE 1. Time evolution of tsunami size scales proposed.
Type of Tsunami
Analogy to Earthquake Scales
Sieberg [2, 3]
primitive 6-point intensity scale
early intensity scales
improved 6-point intensity scale
improved intensity scales
developed 6-point intensity scale
developed intensity scales
Papadopoulos and Imamura 
new 12-point intensity scale
12-point intensity scale
Imamura –Iida (40’s, 50’s and 60’s)
primitive magnitude scale
local Richter magnitude
primitive magnitude scale
local Richter magnitude
Abe [12, 13, 14, 15]
Murty –Loomis 
moment – magnitude scale
On the other hand, the Murty-Loomis tsunami magnitude, which is directly based on the total tsunami energy, E, at the source, provides a wider magnitude range but is not easily applicable at the moment because of serious difficulties involved in the calculation of energy E . Better esimates of tsunami energy in the future certainly will result in the magnitude determination of a more and more increasing number of tsunamis. Table 1 summarizes a classification of the several tsunami size scales proposed and their analogy to earthquake size scales.
The tsunami intensity scale proposed by Sieberg [2, 3] and modified by Ambraseys  is a 6-point scale constructed in such a way that its divisions are not detailed enough and certainly do not incorporate the experience gained from the impact of large destructive tsunamis occurring in the last decades. Shuto’s  tsunami scale is by definition a magnitude scale because H is simply a physical parameter. On the other hand, its description of tsunami impact is a 6-point tsunami intensity scale, ranging from 0 to 5, the division of which, however, is a function of H. Therefore, the scale under discussion is a mixture of magnitude and intensity. Apparently, Shuto  tried rather to produce a predictive tool that describes expected tsunami impact as a function of H, than to create a new tsunami intensity scale describing tsunami effects independently from physical parameters that control the type and extent of the effects. The overall approach is a useful tool for the tsunami size quantification.
The lack of a pure tsunami intensity scale with a
detailed description of its divisions that incorporate recent experience from
large, catastrophic tsunamis of the Pacific Ocean, creates serious problems in
the standardization of the estimation of the tsunami effects, as well as in the
comparisons of the effects from site to site for a given tsunami and from case
to case for different tsunami events. Following the long seismological experience,
Papadopoulos and Imamura  proposed the establishment of a new tsunami
intensity scale based on the next principles: ( a ) independency from any
physical parameter ; ( b ) sensitivity,
that is incorporation of an adequate number of divisions (or points) in order
to describe even small differences in tsunami effects; (c) detailed description of each intensity division by taking
into account all possible tsunami impact on the human and natural environment,
the vulnerability of buildings and other engineered structures on the basis of
recent experiences gained from large, catastrophic tsunamis of the Pacific
Ocean. The new tsunami intensity scale incorporates twelve divisions and is
consistent with the several 12-point seismic intensity scales established and
extensively used in
The present review implies that the time evolution of the tsunami quantification follows the steps made for the earthquake quantification with a time shift of about 30 years. For a drastic improvement of the tsunami quantification some further, drastic developments are needed. In the field of tsunami intensity scaling, new, detailed and sensitive scales are needed with the intensity to be estimated independently from the wave heights or any other physical parameter observed. The intensity scale proposed recently by Papadopoulos and Imamura  seems to meet these requirements. As for the tsunami magnitude scales that are based on measurements of wave heights in tide-gages, there is a general need for better calibration of the formulas in use which strongly depends on the improvement of both the quality and quantity of instrumental data collected. Tsunami magnitude scales based on the energy at the source need improvement of the methods in use for the energy calculation that is improvement of our understanding of the tsunami generation mechanisms.
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of major earthquake tsunamis of the
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Appendix: A New Tsunami Intensity Scale
The new tsunami intensity scale proposed by Papadopoulos and Imamura 
incorporates twelve divisions and is consistent with the several 12-grade seismic
intensity scales established and extensively used in
I. Not felt
Not felt even under the most favourable circumstances.
No effect. No damage.
II. Scarcely felt
Felt by few people on board in small vessels. Not observed in the coast. No effect. No damage.
Felt by most people on board in small vessels. Observed by few people in the coast. No effect. No damage.
IV. Largely observed
Felt by all on board in small vessels and by few people on board in large vessels. Observed by most people in the coast. Few small vessels move slightly onshore. No damage.
Felt by all on board in large vessels and observed by all in the coast. Few people are frightened and run to higher ground.
Many small vessels move stronlgy onshore, few of them crash each other or overturn. Traces of sand layer are left behind in grounds of favourable conditions. Limited flooding of cultivated land.
Limited flooding of outdoors facilities (e.g. gardens) of near-shore structures.
VI. Slightly damaging
Many people are frightened and run to higher ground.
Most small vessels move violently onshore, or crash stronly each other, or overturn.
Damage and flooding in a few wooden structures. Most masonry buildings withstand.
Most people are frightened and try to run in higher ground.
Many small vessels damaged. Few large vessels oscillate violently. Objects of variable size and stability overturn and drift. Sand layer and accumulations of pebbles are left behind. Few aquaculture rafts washed away.
Many wooden structures damaged, few are demolished or washed away. Damage of grade 1 and flooding in a few masonry buildings.
VIII. Heavily damaging
All people escape to higher ground, a few are washed away.
Most of the small vessels are damaged, many are washed away. Few large vessels are moved ashore or crashed each other. Big objects are drifted away. Errosion and littering in the beach. Extensive flooding . Slight damage in tsunami control forest, stop drifts. Many aquaculture rafts washed away, few partially damaged.
Most wooden structures are washed away or demolished. Damage of grade 2 in a few masonry buildings. Most RC buildings sustain damage, in a few damage of grade 1 and flooding is observed.
Many people are washed away.
Most small vessels are destructed or washed away. Many large vessels are moved violently ashore, few are destructed. Extensive errosion and littering of the beach. Local ground subsidence. Partial destruction in tsunami control forest, stop drifts. Most aquaculture rafts washed away, many partially damaged.
Damage of grade 3 in many masonry buildings, few RC buildings suffer from damage grade 2.
X. Very destructive
General panic. Most people are washed away.
Most large vessels are moved violently ashore, many are destructed or collided with buildings. Small bolders from the sea bottom are moved inland. Cars overturned and drifted. Oil spill, fires start. Extensive ground subsidence.
Damage of grade 4 in many masonry buildings, few RC buildings suffer from damage grade 3. Artificial embankments collapse, port water breaks damaged.
XI . Devastating
Lifelines interrupted. Extensive fires. Water backwash drifts cars and other objects in the sea. Big bolders from the sea bottom are moved inland.
Damage of grade 5 in many masonry buildings. Few RC buildings suffer from damage grade 4, many suffer from damage grade 3.
XII. Completely devastating
Practically all masonry buildings demolished. Most RC buildings
suffer from at least damage grade 3.
Table 2. Possible correlation between the intensity domains, I, proposed here and the quantities H and i introduced in formula (5) by Shuto .
I-V <1.0 0
VI 2.0 1
VII-VIII 4.0 2
IX-X 8.0 3
XI 16.0 4
XII 32.0 5