Ocean Dynamics

, Volume 64, Issue 9, pp 1319–1332 | Cite as

Study on the relation of river morphology and tsunami propagation in rivers

  • Hitoshi Tanaka
  • Kosuke Kayane
  • Mohammad Bagus Adityawan
  • Min Roh
  • Mohammad Farid
Article
Part of the following topical collections:
  1. Topical Collection on the 7th International Conference on Coastal Dynamics in Arcachon, France 24-28 June 2013

Abstract

The relations of river morphology and tsunami propagation in rivers were studied at several rivers in the Tohoku region during The Great Chilean Tsunami of 2010 and The Great East Japan Tsunami of 2011. It was found that river mouth morphological features play an important role in the intrusion of low magnitude tsunamis in which the geological and geographical conditions are an important factor. Nevertheless, the effects of these features were not found in the case of an extreme tsunami wave. As the wave enters the river, the propagation depends on other factors. It was found that the intrusion distance correlates well to the riverbed slope. The measurements of water level and riverbed slope were analyzed to propose an empirical method for estimating the damping coefficient for the tsunami propagation in rivers based on the tsunami of 2011. The proposed empirical method was used to approximate the length of the tsunami intrusion into a river by assuming that the furthest distance is given for the ratio of local tsunami wave height to the tsunami wave height at the river entrance of 0.05 (5 %). The estimated intrusion length from the proposed method in this study shows a good comparison with measurement data.

Keywords

Tsunami Propagation River morphology Bed slope 

1 Introduction

Tsunami waves are one of the natural disaster events that may, depending on the magnitude, cause severe damages to coastal areas. A massive tsunami wave may affect and cause damage to a larger area since the wave may propagate further in land. Past tsunamis have shown the tremendous damage that a tsunami wave may cause to the coastal area. In the past decade, several major tsunami events were recorded globally. They are The Great Indian Ocean Tsunami of 2004, The Great Chilean Tsunami of 2010, and The Great East Japan Tsunami of 2011. In the last two events, the effect of both tsunami waves was felt in the northeast coast of Japan.

The Chilean Earthquake occurred on 27 February 2010 with a moment magnitude (Mw) of 8.8 causing tsunami waves that reached as far as Japan. The epicenter of the earthquake was 3 km off the Chilean Coast. Some areas in Chile suffered from the tsunami wave that reached up to 30 m, causing tremendous damage (Fritz et al. 2011). The tsunami wave traveled a great distance and reached the North East Japan coast at approximately 1 m in height. There were no significant damages to the coastal area in Japan. However, the tsunami wave intruded into some rivers and propagated the upstream. This phenomenon was efficiently recorded and reported by Tanaka et al. (2011).

The Great North East Japan Earthquake occurred on 11 March 2011 with a moment magnitude (Mw) of 9.0. The epicenter was approximately 70 km east of the North East Japan coast at an underwater depth of approximately 32 km. It generated a huge tsunami wave that was the biggest ever recorded in Japan. The wave hit the north east coast of Japan, affecting the Tohoku and Kanto districts, with devastating effects, which significantly changed the coastal morphology, especially in estuaries (Suppasri et al. 2012; Tanaka et al. 2012; Tappin et al. 2012). In Iwate, Japan, a tsunami height of approximately 40 m was recorded (Mori et al. 2012). As well, the generated tsunami wave and resulting debris were reported to travel as far as California in the USA.

In general, the river mouth is more vulnerable to a tsunami threat than the seashore. Additionally, the tsunami propagation in a river has higher celerity than the tsunami propagation over land. The tsunami intrusion in the river may maintain and propagate the wave energy further upstream (Adityawan et al. 2012a). Thus, tsunami intrusion in a river may cause damage to the infrastructure along the river and to the area far from the shoreline. Viana-Baptista et al. (2006) had simulated the tsunami propagation in the river at the Tagus estuary, Lisbon, and showed that the tsunami propagation in the river causes severe flooding in the upstream area, far from the shoreline. Yeh et al. (2011) conducted a similar study, in which a simulation of a hypothetical tsunami propagating in the Columbia River may travel as far as 173 km from the ocean. A detailed study by Tanaka et al. (2007) on Sri Lankan rivers, in the tsunami event of 2004, discovered that the tsunami intrusion along a small river that flowed inside a city had caused flooding and local damages, extending the impact of the tsunami to the upstream area. Thus, it is important to understand the effects of tsunami propagation along a river to take proper disaster prevention measures in case of a future tsunami.

The fundamental function of a river is to serve as drainage. A river collects and carries the excess water on land to the downstream end. An attempt to reduce the tsunami wave propagation in a river may cause conflict with this function. Therefore, tsunami disaster prevention in a river must be studied in detail. There have been various studies on the tsunami propagation process over land. However, there were only a few studies related to the tsunami propagation process in a river. Abe (1986) analyzed The Central Sea of Japan Earthquake of 1983 with respect to the propagation of the tsunami wave in five large rivers. He concluded that various factors, i.e., meandering, flow branching, and so on, may complicate the observed wave profiles. Tsuji et al. (1991) found that the tsunami height in a river might be amplified by a factor of 1.5, based on laboratory experiment and theoretical approach. Yasuda et al. (2010) showed that, in general, the propagation of the tsunami wave in the rivers did not reach the upstream area during The Great Indian Ocean Tsunami on 2004 in Sri Lanka. Their study stated that the tsunami propagation in the Japanese rivers might extend upstream due to the rivers-specific characteristics.

The river morphology and the scale of the tsunami affect the tsunamis propagation in a river. Therefore, an investigation that involves two or more rivers and two or more tsunami events is required in order to understand the tsunami propagation in a river. However, past studies were mostly based on a single tsunami event or a single river. This study covers several rivers in Miyagi Prefecture, Japan, as shown in Fig. 1. The river morphology and water level data, recorded during The Great Chilean Earthquake of 2010, and The Great East Japan Tsunami of 2011 were collected. In addition, field surveys were conducted after the 2011 tsunami to trace the tsunami wave height. The collected data were used to investigate the effects of the river morphology to the tsunami propagation in a river.
Fig. 1

Study area

2 Tsunami height and river morphology

2.1 Water level data

The measurement data of the water level in the rivers for The Great East Japan Tsunami of 2011 were acquired from the Ministry of Land, Infrastructure and Transport, Japan. In the latest tsunami event, most of the water level measurement devices were destroyed due to the massive force of the tsunami. Nevertheless, some of them were in good condition and continued to measure the water level during the tsunami. They are located in the Sunaoshi River, the Naruse River, and the Kitakami River (see Fig. 1). The stations measured the water level variation at 10 min intervals. The water level data in the Kitakami River were not used for further analysis due to the existence of a weir, which will be explained in detail at the end of this section. The water level data in the Sunaoshi River and the Naruse River were used for further analysis in this study.

The Great East Japan Earthquake of 2011 caused land subsidence in many places (Udo et al. 2012). The subsidence may cause uncertainty in the measurement of the water level and the tidal level in some places due to the possible vertical shifting of the measurement device. It may be difficult to estimate the tsunami height based on the normal water level. Therefore, for the 2011 tsunami, the wave height was defined as the water level difference from the first peak recorded to the water level drop prior to this peak without tidal correction.

An example of the recorded water level data is shown in Fig. 2. The figure shows the recorded water level data at three measurement stations along the Naruse River. They are Nobiru (at 0.5 km from the river mouth), Ono (at 4.18 km from the river mouth), and Kashimadai (at 8.99 km from the river mouth) as shown in Fig. 2a, b, and c, respectively. It is clearly shown that the effect of the tsunami at Kashimadai was still relatively strong. Based on the tsunami height definition as stated above, the tsunami wave height at Nobiru, Ono, and Kashimadai was approximately 6.2, 5.3, and 2.7 m, respectively. It is also noted that the 2011 tsunami caused the vertical shift of the water level in the river to the corresponding tidal level in Nobiru and Ono. This may correspond to the amount of subsidence at the measuring station (Yeh et al. 1995). However, the subsidence effect was not calculated in this study.
Fig. 2

Water level data at measurement stations along the Naruse River, tsunami of 2011, a Nobiru (0.50 km from the river mouth), b Ono (4.18 km from the river mouth), and c Kashimadai (8.99 km from the river mouth)

The 2011 tsunami traveled to the upstream part in most of the rivers. However, a weir existed in some of the rivers that may have reduced the tsunami propagation. A weir was located in the Kitakami River at approximately 17 km from the river mouth as shown in Fig. 3. This weir was not designed to sustain tsunami force from downstream. It suffered some damages as shown in Fig. 4. Nevertheless, the weir significantly reduced further tsunami intrusion in this river, even though the incoming wave near the river mouth was extremely violent as shown in a captured footage in Fig. 5.
Fig. 3

Weir at the Kitakami River

Fig. 4

Damages to the weir at the Kitakami River due to the tsunami of 2011. a vertical dislocation of the gate (95 cm), b leakage at the downstream of the gate

Fig. 5

Tsunami of 2011, the Kitakami River

The measurement stations along the Kitakami River show the effect of the weir on the tsunami propagation as shown in Fig. 6. The tsunami height is approximately 3.3 m at Fukuchi station (8.6 km from the river mouth). Here, the vertical shift of the water level data to the tidal level was also observed, suggesting the land subsidence occurrence in this station. The wave height decreased significantly in the upstream portion of the river due to the weir. The wave height at Wakiya-Jouryu station (25.8 km from the river mouth) and Tome (32 km from the river mouth) is approximately 0.5 and 0.3 m, respectively. The wave was still traveling up to Oizumi station (49 km from the river mouth). The wave height at this location was only approximately 0.1 m. Unfortunately, Fukuchi station is the only measurement station in the downstream area of the weir in Kitakami River. Thus, the measurement data in this river cannot be used to investigate the relation of riverbed slope to the tsunami intrusion distance in the later section.
Fig. 6

Water level data at measurement stations along the Kitakami River, Tsunami of 2011

2.2 Tsunami traces

The tsunami height along the rivers for the 2011 tsunami was also acquired from the field survey by the Ministry of Land, Infrastructure and Transport, Japan. The survey was conducted at five rivers. They are the Kitakami River, the Old Kitakami River, the Naruse River, the Natori River, and the Abukuma River. The maximum water level was estimated by measuring the level of the tsunami trace, which remained in the riverbank, based on Tokyo Peil (T.P.). An example of the maximum water level based on the tsunami trace survey for the Naruse River is shown in Fig. 7. For this type of data, the maximum tsunami height was defined based on the water level from the tsunami trace to the water level before the tsunami. The water level before the tsunami was estimated in the same way as in the previous section. However, the measurement stations were only available at certain distance from the river mouth. The water levels in these stations were interpolated based on the linear relation of the water level to the distance between stations. It was found that the estimated tsunami height, as given in this section, correlates well with the tsunami height in the previous section for approximately the same location (Fig. 7 (i and ii)). The water level data were measured every 10 min, therefore the maximum water level may not be recorded accurately.
Fig. 7

Tsunami height of 2011 (field survey/trace)

The tsunami height based on the survey for the Kitakami River and the Abukuma River is shown in Fig. 8a and b, respectively. As in the Kitakami River, there is a weir in the Abukuma River. The weir in the Abukuma River is located approximately 10 km upstream from the river mouth. As in Fig. 6, the field survey also shows that for both of the rivers, the wave height drops significantly in the upstream area of the weir. Here, the wave height drops by 3.3 and 3.9 m in the Kitakami River and the Abukuma River, respectively. Figure 8a and b box (i) also shows the effect of the weir to the tsunami propagation in the downstream area of the weir in the Kitakami River and the Abukuma River, respectively. It was found that the tsunami wave regained its height at approximately 3 km downstream of the weir in the Kitakami River and at approximately 3.4 km in the Abukuma River. This increase in wave height may reach up to 2 m in the Kitakami River and 2.2 m in the Abukuma River. It was concluded that this was caused by the wave reflection due to the weir. Therefore, the location where the wave reflection was observed (Fig. 8 box (i)) as well as the upstream portion of the weir was omitted from the analyses.
Fig. 8

The effect of weir on tsunami intrusion into the rivers, Tsunami of 2011. a the Kitakami River, b the Abukuma River

2.3 2010 water level data

The water level data in the rivers for The Great Chilean Tsunami of 2010 were acquired from the same source as in the 2011 tsunami. The water level for this event was recorded in three rivers. They are the Kitakami River, the Old Kitakami River, and the Naruse River. Examples of the data are given in Fig. 9a and b, which shows the water level variation at the Naruse River during the tsunami of 2010 at the Nobiru Station and the Ono Station, respectively. The tsunami crossed the Pacific Ocean before it reached Japan. Thus, the waveform had changed considerably by the time it reached the northeast coast of Japan. Therefore, the maximum wave height cannot be determined based on the first peak, as in the 2011 tsunami. The tsunami height for the tsunami of 2010 was determined by estimating the normal water and then calculating the maximum deviation from this estimated level. The normal water level is the astronomical tidal level for the station located near the river mouth. The normal water level for the station far from the river mouth is estimated by calculating the moving average with a window of 40 h. The tsunami height at the Nobiru and Ono station was approximately 0.8 and 0.4 m, respectively. It is also noted that in the case of the tsunami of 2010, the water level near the river mouth does not show vertical shift to the tidal level as shown in Fig. 9a. However, the same location on the 2011 tsunami shows the vertical shift of the water level to the tidal level. This further suggests that the vertical shift in the 2011 water level data occurred due to the land subsidence.
Fig. 9

Water level data at measurement stations along the Naruse River, Tsunami of 2010. a Nobiru (0.50 km from the river mouth), b Ono (4.18 km from the river mouth)

2.4 River mouth classification and the effect on tsunami reduction

The Japanese system for the river classification was used in this study. The rivers in Japan are divided into Class-A and Class-B based on their importance. A Class-A river is more important than a Class-B river since it has a larger catchment area. The national government is responsible for maintaining the Class-A rivers, and the prefectural government is responsible for maintain the Class-B rivers. Therefore, the Class-A rivers are usually larger. The river morphology data were obtained from the corresponding authorities of each river. The river mouth in this study is also categorized into two types based on the proposed classification by Tanaka et al. 2011. The first type of river mouth, type 1, either has non-constricted jetties at its river mouth or is located inside a harbor or rocky bay. The river mouth entrance has no buffer and, therefore, there is no significant reduction in the wave energy. On the other hand, a type 2 river mouth has constricted structure or sand spit formation at the entrance of the river mouth that acts as a buffer. This buffer helps to dissipate the wave energy due to wave breaking or shoaling effects. An example of a typical river mouth condition for each type is shown in Figs. 10 and 11.
Fig. 10

The Jo River Mouth, type 1

Fig. 11

The Abukuma River Mouth, type 2

There were only a limited number of measurement stations along the river for the 2010 tsunami as described in the previous section. However, the tsunami height in the river mouths was mostly measured and well documented during the 2010 tsunami in Japan (Tanaka et al. 2011; Adityawan et al. 2012b). The water level measurement data were obtained from river measuring stations near the river mouth. In the case of a mild tsunami incidence such as in the case of the tsunami in 2010, the river mouth morphology may have reduced the tsunami wave significantly. Figure 12 shows the river classification in relation to the tsunami wave height in the river for the tsunami event in 2010. In general, the wave height in Class-A rivers is lower than that found in Class-B rivers. The physical dimensions of Class-A rivers are larger than Class-B, naturally it has a larger river mouth and flow area, which reduces the wave height. It is also shown that the wave height in type 2 river mouths tends to be smaller than that in type 1. The tsunami energy is significantly reduced in type 2 river mouths as previously explained.
Fig. 12

Wave height and river classification, tsunami of 2010

In the case of a mega tsunami, like The Great East Japan tsunami 2011, there was no significant difference in the tsunami wave height entering the river caused by river mouth types or classification. The massive force of the tsunami severely eroded the protection buffer in type 2 rivers, as shown Fig. 13. Tanaka et al. (2014) has reported in detail on the sand bar erosion and recovery process in a type 2 river due to the 2011 tsunami. The river mouth morphology does not have any significant effects in reducing the wave height at the river entrance in the 2011 tsunami. Nevertheless, in both tsunami events, after the wave enters the river, the tsunami propagation in the river depends on the river morphology, i.e. riverbed slope, which will be further investigated in the following section.
Fig. 13

The Kitakami River Mouth (type 2), pre and post The Great East Japan Tsunami of 2011. a before the tsunami of 2011, b after the tsunami of 2011

3 The tsunami damping coefficient in the river

The following general exponential relation (Hunt 1952; Dalrymple 1992) gives the wave attenuation in a channel.
$$ H={H}_0{e}^{- kx} $$
(1)
where x is the propagation distance (m), H is the wave height (m), H0 corresponds to the incoming wave height at x = 0, and k is the damping coefficient (m-1). This relation was investigated in each river.
Figure 14a to f shows the tsunami height in relation to the propagation distance at six rivers during the 2011 tsunami based on the water level data as well as the field survey, accordingly. In addition, the water level data during the 2010 tsunami were also drawn where available. It was found that the data fit well with the exponential regression, based on the least-squares method.
Fig. 14

Tsunami damping in the rivers. a The Kitakami River, b The Old Kitakami River, c The Naruse River, d The Natori River, e The Abukuma River, f The Sunaoshi River

The value of the damping coefficient (k) was estimated for each data set and each tsunami event. In the case of the tsunami in 2011, the tsunami height based on survey and the water level data may yield slightly different values of k due to the reason stated in the previous section. The water level data were recorded at 10 min intervals, and it may not be short enough intervals to capture the exact tsunami height, which leads to the deviation from the survey data.

The damping coefficient in the Naruse River is found to be similar in both tsunami events as shown in Fig. 14c. It should be noted here that the Naruse River is mostly straight for approximately 11 km from the river mouth as shown in Fig. 15. The damping coefficient between the 2010 tsunami and the 2011 tsunami may vary depending on other river morphologies. The damping coefficient in the Kitakami River (Fig. 14a) and the Old Kitakami River (Fig. 14b) shows more range between the 2010 and 2011 tsunami. These two rivers in general are not as straight as the Naruse River (Fig. 15). The river meandering may have different effects on the damping coefficient in each tsunami. Furthermore, in the 2010 tsunami, the tsunami propagated along the main river channel. On the other hand, the 2011 tsunami propagation in the rivers on this area may have also propagated in the river flood plain, such as shown by Adityawan et al. (2012a). Therefore, the following discussion will focus on the 2011 tsunami.
Fig. 15

River meandering

4 Relation between the riverbed slope and the damping coefficient

The relation between the riverbed slope (S) and the damping coefficient (k) in the event of the 2011 tsunami was investigated. The riverbed slope was estimated by calculating the distance and the bed level difference between the farthest downstream and upstream measurement points, based on the 2011 tsunami. The data were provided by the Ministry of Land, Infrastructure and Transport, Japan.

The tsunami trace data has more points than the water level data. Thus, the k value obtained from the tsunami trace data was used for further analysis. However, there was no survey data for the Sunaoshi River, thus the k value in this river was estimated from the water level data.

Figure 16 shows that the damping coefficient in the river and the riverbed slope is closely related. It was found using the least squares method that they correspond well to the following exponential relation.
Fig. 16

Relation between riverbed slope and damping coefficient

$$ k=4.77\times {10}^{-5}{e}^{4.67\times {10}^3 S}\left({m}^{-1}\right) $$
(2)

5 Relation between the riverbed slope and the tsunami intrusion distance

The tsunami intrusion distance (xp) can be estimated based on Eq.(1), assuming that the propagation distance is defined at the location where the ratio of the wave height to the incoming wave height (H/H0) is 0.05. Substituting the obtained empirical Eq. (2) into Eq. (1) at xp gives the following relation.
$$ {x}_p=6.28\times {10}^4{e}^{-4.67\times {10}^3 S}(m) $$
(3)
Figure 17 shows the application of Eq. (3) for estimating the tsunami intrusion distance based on the riverbed slope. Here, Eq. (3) was also compared and verified with the actual tsunami intrusion distance in the rivers based on measurement from the tsunami event of 2011 in Japan. The intrusion distance for the rivers was not directly shown. The location of the intrusion distance was located between the two measurement stations (upper and lower). Therefore, both stations are shown and connected with a straight line. The exact intrusion distance is located within this line. In addition, the intrusion distance from the rivers in Banda Aceh, Indonesia, during The Indian Ocean Tsunami of 2004 obtained from the previous study (Adityawan et al. 2012b) was added.
Fig. 17

Relation between riverbed slope and tsunami propagation distance

6 Conclusions

This study investigated the relation of the river mouth morphology and the riverbed slope to the tsunami intrusion into the rivers. The study analyzed tsunami height based on the water level data as well as the tsunami trace survey for the rivers in Miyagi, Japan, based on The Great Chilean Tsunami of 2010 and The Great East Japan tsunami of 2011.

The effect of a weir to the tsunami propagation in a river was observed in the Kitakami River and the Abukuma River for the 2011 tsunami. In both rivers, the weir significantly reduced the tsunami wave height at the upstream part of the weir. However, the weir also caused wave reflection that increased the wave height at its downstream area. It was also reported that the weir suffered damage due to the tsunami since it was not designed to sustain its force coming from the downstream area. Thus, concerning future disaster prevention, it is recommended that a weir in a river that is located within the range of tsunami intrusion should be designed to sustain the force of a tsunami. In addition, the river weir may cause a significant water level increase in the downstream area due to the effect of the tsunami reflection. The affected river length may require further protection.

It was found that the river mouth morphological features have a significant effect on the wave height when entering the river. River mouth with a buffer, i.e. sand formation, at its entrance tends to reduce the wave energy higher than the river mouth with no buffer. Hence, the tsunami intrusion and wave height are smaller. However, the protective buffer has a high chance of being swept away in an extreme tsunami event, negating its effect. The tsunami propagation in the river itself will depend on the river morphologies.

The tsunami wave height decreases exponentially to the distance from the river mouth in the 2010 tsunami as well as in the 2011 tsunami. It was found that the damping coefficient is closely related to the riverbed slope. However, river meandering may have different affect on this parameter depending on the tsunami event. In addition, the 2010 tsunami flowed in the main channel and the 2011 tsunami flowed in the flood plain, which also affect the value of the damping coefficient in each tsunami event.

The relation was further utilized to propose a new method to estimate the tsunami intrusion distance based on the riverbed slope for the case of the 2011 tsunami. The estimated intrusion distance showed a good comparison to the measured value. The proposed method in this study can be used to estimate the required protection length of a river in relation to future mega tsunami prevention. However, it should be further verified with more combination of rivers and tsunami magnitude based on real case, numerical experiments, and with laboratory experiment.

Notes

Acknowledgements

The Ministry of Land, Infrastructure and Transport Tohoku district maintenance office and Miyagi Rivers Division provided the water level data and cross section in the rivers. The authors would like to thank the financial supports from Grant-in-Aid for Scientific Research from Japan Society for Promotion of Science (No. 2503364). This research was also funded by the Grant-in-Aid for Specific Research Project, International Research Institute of Disaster Science, Tohoku University, the Grant-in-Aid for Scientific Research from the River Environmental Fund (REF) in charge of the Foundation of River and Watershed Environmental Management (FOREM), and Assistance for Technological Development, Tohoku Construction Association.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Hitoshi Tanaka
    • 1
  • Kosuke Kayane
    • 1
  • Mohammad Bagus Adityawan
    • 2
    • 1
  • Min Roh
    • 1
  • Mohammad Farid
    • 2
  1. 1.Department of Civil EngineeringTohoku UniversitySendaiJapan
  2. 2.Water Resources Engineering Research GroupInstitut Teknologi BandungJawa BaratIndonesia

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