Reply on RC1

Question

1. How does the DNN model estimate flow conditions?

2. What topographical features are present in the Odaka district?

3. What is the basis of the DNN inverse model?

4. How is the DNN inverse model trained?

7. What were the maximum inundation distance and flow velocity predicted by the DNN inverse model for the 2011 Tohoku-oki tsunami deposits at Odaka?

Accepted Answer

The DNN model estimates flow conditions, such as flow velocity and depth, by analyzing data from the 2011 Tohoku-oki tsunami. It uses these parameters to calculate the Froude number (F r), which helps determine the type of prevailing flow, such as subcritical (F r < 1) or supercritical (F r > 1). This information is crucial for constructing preventive structural measures and mitigation strategies for tsunamis, particularly in the Minamisoma area. The study's findings, supported by field observations, provide a better understanding of tsunami inundation flow in Froude supercritical and subcritical conditions, which vary depending on the region and topographical settings. The research contributes to the limited number of studies that quantitatively address supercritical or subcritical conditions of tsunami inundation flows, highlighting the importance of the DNN model in estimating flow conditions and informing disaster preparedness efforts.

Accepted Answer

The topographical features of the Odaka district include a gentle slope of the coastal plain, beach ridges, marshes, lagoons, and sea dikes. The shoreline along Minamisoma is convex with alternating coastal bluffs and plains, and there are terrace-like seafloors with steeper ascending slopes near the coastline. Precise velocity measurement is absent in this area. Large variations in inundation heights along the coastal line were observed due to the complex coastal topography in Minamisoma City. The area experienced a co-seismic subsidence of 0.5-0.8m, causing a reduction in sea-wall heights. The inundation heights were measured by Sato et al. (2014) and the TETJSG at the Odaka region around the Joban coast. The topographic elevation for the TETJSG data sets was calculated using a 5 m mesh DEM (GSI) with various methods, and the values were used to calculate a measured flow depth from the measured inundation height. A post-tsunami survey was conducted along a transect in the area, collecting samples from 26 locations and measuring the thickness of the deposits at each site. Grain-size analysis was performed using settling tubes with the Stube application program, following specific cleaning and pretreatment procedures.

Accepted Answer

The DNN inverse model is based on the FITTNUSS forward model, which utilizes 1D shallow water equations. This model calculates the spatial variation of tsunami deposit thickness and grain-size distribution using input values such as maximum inundation distance, flow velocity, maximum flow depth, and sediment concentration. The model incorporates layer-averaged equations for fluid mass, momentum, and sediment mass conservation. It operates under the quasi-steady flow assumption, where tsunami run-up velocity remains constant, and inundation depth increases until reaching its maximum value at the seaward boundary. The model also considers the interaction of suspended sediment with bed sediment within the active layer, entrainment rate of basal sediment, bed friction, and sediment stratification. The grain-size distribution is discretized into six classes, and sedimentation is calculated using the Exner equation of bed sediment continuity. The model assumes sediment entrainment and deposition during the run-up phase and settling during the stagnant phase after inundation. The finite difference method is used for numerical solutions, and equations are detailed in Naruse and Abe (2017) and Mitra et al. (2020a).

Accepted Answer

The DNN inverse model is trained using an artificial neural network with five layers. It utilizes an artificial data set of depositional characteristics, such as thickness and grain-size distribution, produced by random and repetitive calculations of the forward model. The model undergoes validation using artificial test data sets. The workflow involves applying the inverse model to a sampling window around the proximal part of the volume per unit area distribution, considering potential errors in the distal part due to thinning of deposits and incomplete field measurements. The performance of the model is evaluated and compared with previous studies, ensuring its readiness for field application. The model is then applied to the field data set from the Odaka region to reconstruct the flow condition of the 2011 Tohoku-oki tsunami. The training process includes selecting a sampling window size, setting grid spacing, and subsampled data interpolation for accurate predictions and bias assessment.

Accepted Answer

The inverse model estimated approximately 0.4 m lower than the original values on average for maximum flow depth. This bias is similar to the 0.4 m and 0.5 m bias reported in Mitra et al. (2020b) and Mitra et al. (2020a) respectively. Correcting the model estimated values by adding this bias to the results, the reconstructed values were compared with field measurements. The mean bias and sample standard deviation for maximum flow depth were -0.5 m and 0.32 m, respectively. The bias and standard deviation for flow velocity were 0.2 m/s and 0.32 m/s, respectively. Sediment concentrations had a mean bias of approximately 0.01%.

Accepted Answer

The maximum inundation distance for tsunami deposits in the study area was observed to be 2,818 meters from the shoreline along the survey transect. Tsunami deposits were present from 183 to 2,563 meters from the shoreline. These deposits consisted primarily of sand-sized particles with an overlying mud layer. The mud layers ranged in thickness from 0.2 to 13.5 cm, while the overall sand thickness ranged from 0.5 to 22 cm. The spatial variation of grain-size distribution in the tsunami deposit was characterized by landward fining and thinning, with a thickness of 22 to 6 cm from the shoreline to around 1,600 meters. Beyond 1,600 meters, thinning of the deposits was observed, ranging from 2 to 0.5 meters to the maximum extent of the deposit at the landward side. The mean grain-size distribution in this region varies from 1.5 phi to 2.6 phi around the study area at Odaka. Sedimentary structures in the tsunami deposits were characterized by a single layer of a fining upward sequence with parallel lamination showing a prominent color variation.

Accepted Answer

The maximum inundation distance at Odaka was reconstructed to be 2,897 m with a mean subsampling bias of -16.9 m. The predicted flow velocity was 12.1 m/s. The estimation error for the maximum inundation distance was 91.1 m, and the estimation error for the flow velocity was 0.4 m/s. The jackknife error estimates for sediment concentration were all very small, ranging around 0.02-0.05%. The reconstructed flow conditions of the tsunami by the DNN inverse model were used to calculate the spatial distribution of the thickness and grain-size composition, and the measured distribution was compared with the calculated distribution. The value of the predicted maximum flow depth approximated the average of the measured flow depth around Tsunobeuchi, Murakami, and Tsukabara, where the variability of the measured values was extremely large around the surveyed field locations of the study area. The flow velocities of the 2011 Tohoku-oki tsunami run-up flow were measured 4.2 m/s on average, ranging from 1.9 m/s to 6.9 m/s from the aerial video records of the Sendai plain. The velocity measured from the survivors' videos of the December 26, 2004 Indian Ocean tsunami at Banda Aceh, Indonesia, was in the range of 2-5 m/s. No direct observations of the flow velocity were made in this study area; however, the velocity was comparable with the values reported near the study area. Sanuki et al. (2013) used video footage analysis around the mouth of the Kido river, which is located 30 km away from our field location but along the same coastline. They reported that the inundation flow was 14-11 m/s inside the river channel, whereas it was around 15-10 m/s in the coastal plain. Moreover, Sato et al. (2014) estimated that the overtopping flow on the seawall crown reached 11-17 m/s in velocity at the Idagawa area which is located approximately 3 km south of the study area, based on the Bernoulli's theorem. Hence, the reconstruction of the flow velocity by the DNN inverse model is said to be reasonable, suggesting that the exceptionally high flow velocity occurred in this area.

Accepted Answer

The Froude number (F r) is defined as F r = U/ gh, where U denotes the layer-averaged flow velocity, g is the gravitational acceleration, and h is the flow depth. It represents the ratio of inertia to gravity forces. In the context of tsunamis, the Froude number helps determine the type of inundation flow. A Froude number greater than 1 indicates a supercritical flow, characterized by high flow velocity and low flow depth, leading to rapid and unstable flow. On the other hand, a Froude number less than 1 indicates a subcritical flow, characterized by slow velocity or thick flow depth, resulting in stable and flat water surfaces. The study of the Odaka region's tsunami inundation flow revealed a Froude supercritical condition, suggesting a high flow velocity and local fluctuations in flow depth due to topographic complexities. This contrasts with the Sendai plain, where a subcritical flow was observed, indicating a more stable inundation flow.

Accepted Answer

The study reconstructed flow conditions such as maximum inundation distance, flow velocity, maximum flow depth, and sediment concentration around the Odaka district, Minamisoma, at the Joban coast. It incorporated flow-type characterization and highlighted the high flow velocity with shallow flow depth typical of supercritical flow type. Future research is needed to investigate the impact of supercritical inundation flow on coastal areas. Table 1 presents predicted results from the inverse model applied to the 2011 Tohoku-oki tsunami data obtained from Odaka, Joban coast, with standard error calculations using a 95% confidence interval.

Reply on RC1

Chat with Paper

AI Agents for this Paper

Most frequently asked questions

1. How does the DNN model estimate flow conditions?

2. What topographical features are present in the Odaka district?

3. What is the basis of the DNN inverse model?

4. How is the DNN inverse model trained?

5. What bias did the inverse model estimate for maximum flow depth?

6. What is the maximum inundation distance for tsunami deposits in the study area?

7. What were the maximum inundation distance and flow velocity predicted by the DNN inverse model for the 2011 Tohoku-oki tsunami deposits at Odaka?

8. What is the Froude number and how does it relate to the type of inundation flow in tsunamis?

9. What flow conditions were reconstructed in the 2011 Tohoku-oki tsunami study?

References

Survey of 2011 Tohoku earthquake tsunami inundation and run‐up

The mechanics of dunes and antidunes in erodible-bed channels

River-bed degradation with armoring

Damage from the Great East Japan Earthquake and Tsunami - A quick report

Challenges of anticipating the 2011 Tohoku earthquake and tsunami using coastal geology

Related Papers (5)

Numerical study on the effect of dissymmetry heating on flow instability of supercritical water in two parallel channels

Modern vision for critical flow in an egg-shaped section

A Froude-scaled model of a bedrock-alluvial channel reach: 1. Hydraulics

Unconfined expansion of supercritical water flow

Comment on egusphere-2023-369