Uncertainty in Tsunami Sediment Transport Modeling

Transcription

1 Paper: Uncertainty in Tsunami Sediment Transport Modeling Bruce Jaffe,, Kazuhisa Goto, Daisuke Sugawara, Guy Gelfenbaum, and SeanPaul La Selle US Geological Survey Pacific Coastal and Marine Science Center 2885 Mission Street, Santa Cruz, CA, 95060, USA Corresponding author, International Research Institute of Disaster Science, Tohoku University, Sendai, Japan Museum of Natural and Environmental History, Shizuoka, Japan [Received May 5, 2016; accepted July 30, 2016] Erosion and deposition from tsunamis record information about tsunami hydrodynamics and size that can be interpreted to improve tsunami hazard assessment. We explore sources and methods for quantifying uncertainty in tsunami sediment transport modeling. Uncertainty varies with tsunami, study site, available input data, sediment grain size, and model. Although uncertainty has the potential to be large, published case studies indicate that both forward and inverse tsunami sediment transport models perform well enough to be useful for deciphering tsunami characteristics, including size, from deposits. New techniques for quantifying uncertainty, such as Ensemble Kalman Filtering inversion, and more rigorous reporting of uncertainties will advance the science of tsunami sediment transport modeling. Uncertainty may be decreased with additional laboratory studies that increase our understanding of the semi-empirical parameters and physics of tsunami sediment transport, standardized benchmark tests to assess model performance, and development of hybrid modeling approaches to exploit the strengths of forward and inverse models. Keywords: tsunami sediment transport, modeling, uncertainty, sedimentary deposits 1. Introduction To accurately assess future hazard posed by tsunamis, it is advantageous to understand past tsunami events. Tsunami deposits provide a means to quantify past tsunami events in that they record the flow conditions that form them. Recent research has made inroads into unlocking the hydraulic information contained in deposits for both modern [1 6] and paleo [7, 8] tsunamis. Much of this research focuses on development and application of numerical models for tsunami sediment transport to infer tsunami inundation, height and flow speed (see Sugwawara et al. [5] for a summary of current understanding of tsunami sediment transport). To use results from tsunami sediment transport modeling in tsunami hazard assessment, it is prudent to evaluate the uncertainty of model results. The goal of this paper is to improve understanding and assessment of uncertainty in tsunami sediment transport modeling. There is no single answer to what tsunami sediment transport modeling uncertainty is- it is tsunami dependent, site dependent, data dependent, grain size dependent, and model dependent. We explore the causes of uncertainty, give examples of its magnitude from published studies, and identify ways in which uncertainty can be reduced. After presenting a brief summary of published tsunami sediment transport models, we provide a framework for characterizing sources of uncertainty in these models. Key uncertainties are discussed for transport of sand and boulder by tsunamis. Future directions that may lead to a decrease in tsunami sediment transport model uncertainty, including laboratory studies, more sophisticated uncertainty analysis, and a hybrid approach to modeling is then discussed. Our conclusion is that, although tsunami sediment transport modeling results contain uncertainty, case studies for both forward and inverse models have shown that modeling provides useful information on tsunami inundation and hydrodynamics that can improve assessment of tsunami hazard. 2. Summary of Tsunami Sediment Transport Models Modeling of tsunami sediment transport has been an evolving and maturing science since the early 1960s (e.g., [9]). The number of publications on tsunami sediment transport has grown rapidly in the past ten years. The majority of published tsunami sediment transport models are for sand-sized particles, perhaps because there are more published reports on tsunami sand deposits than tsunami boulder deposits (a Scopus search on 14 March 2016 showed 1951 articles for sand versus 792 articles for boulders). Below is a brief summary of published tsunami sand and boulder transport models. Additional details on these models can be found in Sugawara et al. [5]. Some of these models (e.g., Delft3D and XBeach) have the capability of including multiple grain sizes, including mud. To Journal of Disaster Research Vol.11 No.4,

2 Jaffe, B. et al. Fig. 1. Schematic of forward and inverse modeling of tsunamis. Tsunami deposits can provide additional constraints on tsunami characteristics (e.g., flow speeds) beyond information conveyed by water alone (water levels, inundation distance, runup). Modified from Satake [78]. date, there are no published modeling studies addressing tsunami transport of mud and the resulting deposit. Tsunami hydrodynamic and sediment transport models can be classified into two modeling approaches: (1) forward, and (2) inverse (Fig. 1, Table 1). Forward models propagate tsunami waves from region of seafloor displacement (e.g., [10 11]) or may specify water level and/or tsunami velocity time series at the seaward boundary of the model domain (e.g., [12]). As the waves propagate toward land semi-empirical formulae are applied to calculate erosion, transport, and deposition of sediment. Inverse models use features of the observed tsunami deposit and auxiliary information (e.g., flow depth) to solve for tsunami characteristics, which may then be related to tsunami generation. For simulating tsunami sediment transport at a transect or sub-regional scale (e.g., [10, 12]), forward models solve the Nonlinear Shallow Water Wave equations (NLSWE) to produce time series of tsunami flow heights (tsunami depth added to the elevation of the bathymetry/topography) and velocities throughout the model domain and for the time period of interest (Table 1). These hydrodynamic outputs are used to calculated sediment transport and the resulting erosion and deposition. Modeled tsunami deposit characteristics include thickness and, for some models, horizontal and vertical grading (e.g., [13, 14]). Forward models can be 3D [12, 15 18], 2D vertical [4, 12, 16], or 2D horizontal [14, 17 23]. Forward tsunami sand transport models use formulae and coefficients originally developed for fluvial and coastal environments (Table 2). Most forward models use separate formulations for bedload and suspended load transport; although, Li et al [14, 22] use a total load approach. Bedload transport rates are a function of either the Shield s parameter, which is the ratio of the bottom shear stress to submerged weight, or the normalized excess bottom shear stress (i.e., the bottom shear stress greater than the critical shear stress normalized by the critical shear stress). The most commonly used formulations are by [24-26]. The Takahashi et al. [19] bedload transport formula, which includes empirical parameters derived from flume experiments, is also used (Table 1). Suspended load formulations used in tsunami sediment transport forward models are based either on vertical diffusion from turbulent mixing and a reference concentration near the bed [25] or a balance between the pick-up rate and settling rate, which is the product of the concentration and settling velocity. The settling velocity for sand is calculated in tsunami sand models using a variety of formulae (Table 2), which are grounded in laboratory experiments and force balance theory. Similar to hydrodynamic quantities, sand transport is solved for the entire domain and for all times of the simulation. Erosion and deposition are calculated from spatial gradients in transport and from exchanges between the bed and water column. Forward tsunami boulder transport models calculate forces from modeled flow speeds and compare to stabilizing forces based on boulder size, shape, and density to determine whether boulders move [5]. There are currently two published forward tsunami boulder transport models, both of which use the NLSWE for solving hydrodynamics [27, 28]. Both models use the approach of force balance with boulder transport occurring when lift, inertia and drag acting on moment arms overcome friction and submerged weight. Forward boulder transport models calculate not only the initiation of boulder transport but also the distance that boulders move. Inverse models for boulder transport [29 31] start with boulder dimensions and boulder density and calculate the flow speed and corresponding tsunami wave height necessary to move the boulder. Published inverse models for tsunami sand transport are either 1D line models using a series of deposits along a shore-normal (flow-parallel) transect [6, 32] or point models that calculate tsunami characteristics based on the deposit at a single location [1 3, 33] (Table 1). Tsunami characteristics are calculated from onshore tsunami deposits, and for some models, topography and bathymetry. The concepts applied in inverse tsunami sand transport 648 Journal of Disaster Research Vol.11 No.4, 2016

3 Model Type Hydrodynamic model Delft3D forward Delft3D Table 1. Summary of published tsunami sand transport models. Dimension 2D/3D (hydrostatic) XBeach forward COMCOT 2DH Ontowirjo et al. (2012) forward COMCOT 2DH C-HYDRO3D forward C-HYDRO3D STM Advectionsettling Particle settling Settling column TsuSedMod forward TUNAMI-N2 and others 3D (hydrostatic) 2DH inverse point inverse inverse inverse depth-averaged velocity, >runup than backwash point 1D point Tsunami characteristics estimated tsunami water level and velocity time series tsunami water level and velocity time series tsunami water level and velocity time series tsunami water level and velocity time series tsunami water level and velocity time series average flow speed from shore to deposit water depth in basin, runup elevation runup elevation, inundation distance maximum tsunami flow speed Deposit characteristics estimated Case studies* References thickness, horizontal and vertical grading thickness, horizontal and vertical grading thickness thickness thickness Vertical grading Fagafue Bay, Am. Samoa: 2009 Kuala Meurisi, Sumatra: 2004 Lhok Nga, Sumatra: 2004 Lhok Nga, Sumatra: 2004 Kirinda, Sri Lanka: 2004 Sendai, Japan: 2011 Kesen-numa, Japan: 2011 Lhok Nga, Sumatra: 2004 Kirinda, Sri Lanka: 2004 Taylor Bay, Newfoundland: 1929 Adipala, Java: 2006 Montrose, Scotland: ~8,000bp Taylor Bay, Newfoundland: 1929 Fullerton, Scotland: ~8,000bp Arop, Papua New Guinea: 1998 Satitoa, Samoa: 2009 Sendai, Japan: 2011 Cannon Beach, Oregon: 1700 Boca del Rio, Peru: ~200BC, 25 Gelfenbaum et al. [12] Apotsos et al. [16-18] Li et al. [14] Ontowirjo et al. [23] Kihara & Matsuyama [15] Takahashi et al. [19, 20] Yoshii et al. [21] Gusman et al. [4] Sugawara et al., [10] Moore et al. [1] Smith et al. [33] Soulsby et al. [32] Jaffe & Gelfenbaum [2] Jaffe et al. [3] runup elevation, nonlinear inundation distance, TSUFLIND inverse shallow water depth-average flow Vertical and Ranganathapuram 1D equations speed, flow depth, horizontal grading India: 2004 Tang & Weiss [6] representative wave amplitude Additional case studies for TsuSedMod not included in the table are: Kelapa & Bunton, Java: 2006 (Spiske et al. [68]); St. James Beach, India: 2004 (Spiske et al. [68]); Ranganathapuram, India: 2004 (Bahlburg and Weiss [66]); Ban Bang Sak, Thailand: 1400, 2004 (Brill et al. [69]); Puerto Casma, Peru: 1650 (Spiske et al. [70]) models are simple and vary with the model. Moore et al. [1] use advection-settling of larger particles found in an inland deposit to calculate the average flow speed from the shore to the deposit by equating the fall time of a particle to its transport time. Smith et al. [33] use the finest particles in a deposit to constrain the period of the tsunami wave and the runup elevation. Soulsby et al. [32] solve for runup elevation and inundation distance using deposits along a shore-normal transect assuming that sediment is entrained at the shoreline, and suspended uniformly throughout a water column that clears as the tsunami moves inland. Jaffe and Gelfenbaum [2] and Jaffe et al. [3] calculate tsunami flow speed from the portion of the tsunami deposit formed by sediment falling out from suspension using the concepts of suspended sediment capacity and turbulent diffusion of sediment in a Rouse profile. Tang and Weiss [6] in their TSUFLIND model combine the concepts and formulations from Moore et al. [1], Jaffe and Gelfenbaum [2], and Soulsby [32] with shallow water equations to calculate runup elevation, inundation distance, representative offshore wave amplitude, depth-averaged flow speed, and flow depth using a series of tsunami deposits along a shore-normal transect. Grain Journal of Disaster Research Vol.11 No.4,

4 Jaffe, B. et al. Table 2. Selected inputs and formulations for tsunami sand transport models presented in Table 1. Inputs Formulations Model Type Sediment Delft3D XBeach Ontowirjo et al. (2012) C-HYDRO3D STM Advectionsettling forward forward forward forward forward inverse Particle settling inverse Settling column inverse TsuSedMod TSUFLIND inverse inverse sand, mixed grain sizes sand, mixed grain sizes sand, one grain size sand, one grain size sand, one grain size settling velocity of a larger (D84 or D100) particle in deposit settling velocity of slowest settling particle in the deposit bulk distribution of grain size/settling velocities of deposit at multiple locations thickness and bulk distribution of grain size/settling velocities of suspension-graded interval in deposit at one location bulk distribution of grain size/settling velocities of deposit at multiple locations Bottom roughness Other Bedload Bathymetry and topography; may use water levels, velocities or a combination at boundaries Bathymetry and topography; may use water levels, velocities or a combination at boundaries Bathymetry and topography; may use water levels, velocities or a combination at boundaries Bathymetry and topography; may use water levels, velocities or a combination at boundaries Bathymetry and topography; may use velocity or velocity/water level maximum at shore, distance particle traveled [26, 38] [38] Soulsby [72] Ribberink [73] [24] Ashida & Michiue [72] Takahashi et al. [74] Suspended load [48, 71] [38] Soulsby [72] [25] [25] Takahashi et al. [75] Yoshi et al. [21] pond depth fractional thickness of grainsize components fractional thickness of grainsize components Madsen et al. [37] Madsen et al. [37] Settling velocity [38] [38] [25] Soulsby [72] Dietrich [76] Dietrich [76] Soulsby [72] Soulsby [70] Ferguson and Church [77] size distributions from a series of vertical intervals, or layers, of the deposits provide multiple constraints on the vertical flux of sediment from suspension, which are used to calculate shear velocity and flow depth. Inverse models for tsunami transport of sand use similar formulations as forward models for suspended load (Table 2). None of the published inverse tsunami transport models consider bedload transport. Both forward and inverse tsunami sediment transport models have been applied in a number of case studies (Table 1). In total, we found publications reporting results using 10 different tsunami sediment transport models to investigate both modern and paleo- tsunamis. The 10 models were equally divided into forward (5) and inverse (5) approaches. A primary goal of the case studies of modern tsunamis, which included the 1998 Papua New Guinea, 2004 Indian Ocean, 2006 West Java, 2009 South Pacific, and 2011 Tohoku-oki tsunamis, was to test the models skill by comparing predicted and observed deposition and erosion. Another goal, especially for the applications to historical or paleo- tsunamis was to determine the size (flow speed and depth) of the tsunamis, or the location of seafloor slip. Applying standard sediment transport formulations and parameters, forward model predictions, in general, reproduced observations of deposit thickness, grain size trends, and inundation distance of sediment. Inverse models, though more difficult to test, accurately reproduced flow characteristics, although some models had to be calibrated to achieve a good fit. 650 Journal of Disaster Research Vol.11 No.4, 2016

5 Table 3. Sources and types of uncertainties in tsunami sediment transport modeling with examples. Aleatory uncertainty, which is also referred to as stochastic uncertainty, variability or irreducible uncertainty, derives from the natural randomness in a process. Epistemic uncertainty, which is also referred to as reducible uncertainty or ignorance uncertainty, can be reduced or theoretically eliminated by increased understanding of the system. See Section 3 for more details. Sources of Uncertainty Type of Uncertainty Forward model examples Inputs Formulations Parameters Model Completeness Model Integration Aleatory Epistemic Epistemic Epistemic Epistemic Incomplete knowledge of inputs such as bed grain size, bathymetry, topography, water level and/or velocity time series at boundaries, bottom roughness when spatially varying and specified Imperfect formulations of hydrodynamics and sediment transport, choice of grid sizes Choice of resuspension coefficient and bottom roughness when a single value, or one value for onshore and one value for offshore is specified Not including key processes and physics in hydrodynamic and tsunami sediment transport models, for example density stratification and bore dynamics Incomplete integration and interaction between hydrodynamic and sediment transport components, for example the effect of high sediment concentrations on hydrodynamics Inverse model examples Incomplete knowledge of deposit grain size and/or thickness, and, for more complex models, topography and bathymetry Imperfect formulations of hydrodynamics and sediment transport Choice of resuspension coefficient, bottom roughness when a single value is specified Not including key processes and physics in hydrodynamic and tsunami sediment transport models, such as bed armoring Incomplete integration and interaction between hydrodynamic and sediment transport components 3. Sources of Uncertainties in Tsunami Sediment Transport Modeling Numerous papers address uncertainty in modeling physical phenomena (e.g., review by Roy and Oberkampf [34]). A common approach is to classify uncertainties into two types, aleatory and epistemic. Aleatory uncertainty (also referred to as stochastic uncertainty, variability or irreducible uncertainty) derives from the natural randomness in a process and is typically characterized by probability distributions [34]. Epistemic uncertainty, which Roy and Oberkamf [34] also refer to as reducible uncertainty or ignorance uncertainty, can be reduced or theoretically eliminated by increased understanding of the system. Oberkampf and Roy [35] point out that uncertainty in model results is caused by numerical approximation errors and model form, which results from all assumptions, conceptualizations, abstractions, and mathematical formulations on which the model relies such as ignored physics or physics in the model. Here we follow the conceptual framework of Roy and Oberkampf [34] of identifying aleatory and epistemic uncertainty and organize sources of uncertainty in tsunami sediment transport modeling into five general categories. Uncertainties arise from: (1) inputs, (2) formulations, (3) parameters, (4) model completeness, and (5) and model integration. Below and in Table 3 are examples of sources of uncertainty in tsunami sediment transport modeling and classification of the uncertainty as either aleatory or epistemic. More detailed information is given in Section 4, which addresses uncertainties in tsunami sediment transport modeling specific to the grain size of the particles transported. Although some published tsunami sediment transport models [10] are coupled with seafloor displacement models that generate initial water level displacements and associated velocities that propagate throughout the model domain, here we do not assess the uncertainty in modeling the generation of tsunamis Inputs Inputs, and associated uncertainties, differ for forward and inverse tsunami sediment transport models. Incomplete knowledge of the inputs to forward models such as bed grain size, bathymetry, topography, and water level and/or velocity time series at boundaries will create uncertainty in results. Bottom roughness can be considered either a model input, as is the case when it is specified as a spatially varying quantity [10, 14], or as a model parameter when a single value, or one value for onshore and one value for offshore bottom roughness are used (e.g., [18]). Uncertainty in inputs is aleatory in that for a given set of inputs, the uncertainty cannot be reduced. However, there is the potential to decrease uncertainty with more complete or more accurate inputs. For example, more accurate specifications of conditions (e.g., bed grain size, bathymetry, and topography) for forward models tend to decrease model uncertainty. Incomplete knowledge of inputs to inverse models, such as tsunami deposit grain size and/or thickness for the more simple models and bottom roughness variation Journal of Disaster Research Vol.11 No.4,

6 Jaffe, B. et al. and topography for the more complex models, also results in aleatory uncertainty. As with forward models, uncertainty can be reduced by improved inputs. For example, increased sampling accuracy may reduce uncertainty in model results. Although the uncertainty for a given set of inputs is not reducible, it can be evaluated. Sensitivity analyses where input values are varied are useful for assessing the potential uncertainty associated with inputs for both forward and inverse models Formulations Imperfect formulations for hydrodynamics (e.g., turbulence) and sediment transport lead to uncertainty in model results. For forward models, choice of grid sizes, for example too large a grid size necessitated by limited computing capacity, and numerical schemes used to solve equations may also lead to uncertainty. Uncertainty associated with imperfect model formulations is epistemic and can be reduced with increased knowledge of tsunami sediment transport physics Parameters Tsunami sediment transport models typically include semi-empirical parameters that must be specified. Specification of parameters introduces an uncertainty that is epistemic, which can be reduced with increased knowledge of the tsunami sediment transport. An example of a parameter in tsunami sediment transport formulations is the resuspension coefficient [36, 37] used for suspended sediment transport. Bottom roughness, when a single value, or one value for onshore and one value for offshore, is classified here as a parameter. Sensitivity analyses are useful for assessing the potential uncertainty associated with parameter specifications Model Completeness Models are, by necessity, simplifications of complex natural processes. Uncertainty may be introduced because not all of the processes are included in models. This is an epistemic uncertainty, which can be reduced by increased knowledge of the physics of tsunami sediment transport. If key processes and physics are not included in a tsunami sediment transport model, predictions can contain significant error. A model of tsunami sediment transport is never 100% complete, but can still be useful if the processes that are not included do not significantly change the sediment transport for a particular application. With improved understanding of the physics of tsunami sediment transport, models will become more complete, results will be more certain, and there is the potential for simpler models without extraneous physics that do not significantly affect sediment transport Model Integration For models that have multiple components, such as a hydrodynamic component that is influenced by sediment transport component that may result in high sediment concentrations in the water column, how the components interact, or are integrated, can lead to uncertainty. This is an epistemic uncertainty that can be reduced with increased knowledge. 4. Key Uncertainties in Tsunami Sediment Transport Modeling Because tsunami sediment transport modeling approaches differ with particle size, we discuss the key uncertainties in sand and boulder modeling separately. Four of the five uncertainty categories from above are addressed for tsunami transport of sand and boulders. Model integration is not addressed because, to the authors knowledge, there have been no attempts to quantify the effects of model integration on uncertainty for tsunami sediment transport Uncertainties in Tsunami Transport of Sand Inputs For forward models, specification of the initial bed grain size can have a large effect on predicted sediment transport and resulting tsunami erosion and deposition. Offshore grain size often is more poorly known than onshore grain size and grain size from offshore bed samples collected after a tsunami may not reflect the grain size present before the tsunami. An additional complication is that beach and offshore grain size may change seasonally. The uncertainty due to sediment grain size can be reduced if the choice of initial bed grain size is constrained by the grain size of the sediment found in the tsunami deposit. Few studies report the sensitivity of forward model results to initial bed grain size. An exception is a study by Apotsos et al. [13] that explored the effect of varying initial bed sediment grain size using a single grain size from 100 to 1000 µm on an idealized two-segment linear profile with a 1/100 offshore slope and a flatter 1/800 onshore slope based on an actual profile at Kuala Muerisi, Sumatra that was inundated by the 2004 Indian Ocean tsunami [12]. Apotsos et al. [13] found that a decrease in the grain size from 1000 to 100 µm increases the inland extent of the deposit by a factor of approximately 3, and the total volume by a factor of approximately 4, and correspondingly the thickness of the deposit because smaller sediments settle out of the water column more slowly allowing sediment to be transported inland in greater amounts and over longer distances. However, this range of effects is not likely as great in a real-world application because choice of the initial bed sediment grain size is informed by the observed grain size of the deposit. Because the [38] settling velocity formula is nonlinear with a larger effect for a decrease in grain size than for a similar increase the greater distance traveled by the smaller grains is enhanced. Smaller sediments may also travel farther inland when hindered settling in higher concentrations reduces the settling velocity (see hindered settling in section 4.1.4, Model completeness). 652 Journal of Disaster Research Vol.11 No.4, 2016

7 Similar to forward models, studies exploring the effect of grain size on inverse tsunami sediment transport model results are rare. Jaffe and Gelfenbaum [2] report the effect of grain size for a single grain size tsunami deposit. For a 10-cm thick deposit formed in 5 m flow depth, a 10% change in grain size of 0.15 mm results in a 5% change in estimated mean flow speed. Because the natural variation in grain size of source sediment can be large, grain size of the deposit can be the most significant factor in determining tsunami flow speed. A deposit of a particular thickness, with a particle density of 2.65 gm/cm 3,composed of coarse sand (d = 0.5 mm) would be created by a flow speed 2 to 3 times greater than a deposit composed of very-fine sand (d = mm). Specification of grain size is not as large an issue, in general, in inverse models as it is with forward models because grain size of the deposit, a known quantity, is the needed input, not the pre-tsunami bed grain size. However, uncertainty is introduced if grain size is measured by a method other than directly measuring the settling velocity, such as laser diffraction, optical methods, or sieving. This occurs because particle shape and density, which affect the conversion from grain size measured with these methods, is not know exactly. Although it hasn t been done to date, assessment of the sensitivity to inaccuracies in the conversion of grain size to settling velocity on model results for inverse models is possible. Such a sensitivity analysis could be used to quantify the contribution of conversion to settling velocity on uncertainty. The choice of the particle size to use for input to the advection-settling inverse model [1] affects the model outputs, the flow depth at the shoreline and the average tsunami flow speed from the shoreline to the location where the particle is deposited. Choices used in previous studies range from the 84 th to 95 th percentile of the grain size distribution. A possible reason for not using the largest particle found in the deposit is the concern that it was deposited by bedload processes rather than transported in suspension. The effect of using a larger particle size as model input is an increase in estimated tsunami flow depth and average flow speed. This occurs because the faster settling velocity decreases the times for settling from the top of the water column and for inland transport, which are equated in this model. The uncertainty in this inverse model can be determined by a sensitivity analysis using a range of input grain sizes. Another input to inverse sediment transport models that can create uncertainty in results is deposit thickness. Starting with an inaccurate tsunami deposit thickness because of measurement error creates less uncertainty in results than inaccurate specification of grain size. Jaffe and Gelfenbaum [2] report that for a deposit with 0.15 mm sand that was formed in a 5 m deep flow, a 1 cm (10%) difference in thickness of a 10 cm thick deposit results in a 3% difference in tsunami flow speed. Thinner deposits (2 cm) changed by 1 cm result in an 18% decrease (thinner) or 11% increase (thicker) in calculated tsunami flow speed. The reduced uncertainty in inverse model results relative to forward models derives from the sediment transport formulations. For example, for the inverse problem, the tsunami flow speed, the output, is a function of the measured grain size and thickness of the deposit raised to a power less than one so errors in these inputs do not have a large effect on calculated flow speeds. In the forward problem, the tsunami deposit composition, thickness, and distribution, which are the typical outputs, are a function of tsunami flow speed raised to a power greater than one and of the initial bed grain size so inputs such as grain size may have a large effect on the tsunami deposit formed. Another source of uncertainty in inputs is the specification of the bed thickness. Forward tsunami sediment transport models typically assume that deposit thickness is not limited by the quantity of sediment that can be eroded (i.e., the bed thicknesses are set to be larger than the potential erosion depths). Apotsos et al. [18] modeled a sediment-limited situation in a small embayment on the north coast of American Samoa. They were only able to reproduce the observed thicknesses of the deposits formed by the 2009 tsunami when specifying bed thicknesses that limited the source of sediment available to be eroded and transport onshore. Bathymetry and topography will affect how the tsunami flow velocity and height evolves moving onshore. Again, since this a non-reducible uncertainty (i.e., the input data is the limiting factor), uncertainty from errors in bathymetry and topography cannot be decreased without additional data and is difficult to assess because such errors are often not well known, especially for paleotsunamis. Additional geologic studies that constrain the location of the paleo-shoreline and of geomorphic features such as beach ridges can reduce uncertainty. It is also possible to run models on end members of the envelope of possible bathymetry/topography that includes excursions equal to the potential error (e.g., measured or estimated elevation +/ error) and assess the effect on model results Formulations Formulations used in tsunami sediment transport models are listed in Table 2. Evaluation of the uncertainty associated with the choice of formulas is difficult because comparisons between modeled and observed output (tsunami deposits, flow speeds, runup elevation, inundation distance, and flow depth for forward models; flow speeds, runup elevation, inundation distance, and flow depth for inverse models) are affected by inputs as well. Li and Huang [39] compared six different formulations for tsunami sand transport against measured bed changes observed in laboratory experiments and in the field after the 2004 tsunami. The formulations tested were Bagnold [40], Engelund and Hansen [41], Bijker [42], Ackers and White [43], Yang [44], and [24, 25]. Of the above formulations, only the ones by [24, 25] are used in published tsunami sediment transport models (Table 2). Li and Huang [38] found that all formulations failed to produce results in field conditions as good as in laboratory conditions and that the formula- Journal of Disaster Research Vol.11 No.4,

8 Jaffe, B. et al. Fig. 2. Comparison of observed (circles, triangles) and modeled (lines) vertical variation in grain size distributions in paleotsunami deposit from the 1700 Cascadia event at Cannon Beach, Oregon [7] and modern tsunami deposit from the 2011 Tohoku-oki event [3]. The paleotsunami deposit is from 62 to 63.5 cm below the surface. The suspension-graded interval in the modern deposit is from 2 to 4 cm below the surface. The top of the deposit, or for the modern deposit the top of the suspension-graded interval, is finer than the base of the deposit/interval in both the observed and modeled grain size distributions supporting deposit formation from settling from suspension. Observed and modeled distributions are nearly identical- symbols and lines nearly overlie each other. Both deposits reconstructed by the TsuSedMod inverse tsunami sediment transport model [3]. tions [24, 25] yielded relatively reliable results in both laboratory and field conditions. The Bagnold [40] formulation could also give reasonable results. The formulation for sediment suspension in TsuSed- Mod [2] can be evaluated by comparing the portion of the observed deposit attributed to formation from sediment falling out of suspension and model reconstruction of that portion of the deposit (Fig. 2). Two cases, a paleotsunami deposit from the 1700 Cascadia event at Cannon Beach, Oregon [7] and a modern tsunami deposit from the 2011 Tohoku-oki event [3] are evaluated. The top of the deposit, or for the modern deposit the top of the suspension-graded interval, is finer than the base of the deposit/interval in both the observed and modeled grain size distributions and the distributions are nearly identical supporting deposit formation from settling from suspension and the choice of formulations used in TsuSedMod. Tang and Weiss [6] also conclude that the suspended sediment formulations in TSUFLIND are supported by a favorable comparison between observed and modeled vertical variations in grain size distributions. TSUFLIND reproduces observed grain size distributions within 5% for tsunami deposits created by the 2004 tsunami at Ranganathapuram, India. Evaluation of the uncertainty introduced by the formulation of bedload transport is challenging. The empirical coefficients in bedload formulations used in tsunami sediment transport models are based on laboratory experiments for unidirectional flow or short-period oscillatory flow that is significantly weaker than that of moderate or large tsunamis. An unresolved question is whether these coefficients are valid for the stronger flows of tsunamis. The importance of accurately predicting bedload transport depends on the size of the tsunami and the grain size of the sediment available for transport. For large tsunamis and medium sand, Apotsos et al. [13] found that model predictions for the total amount of sediment transported by bedload was at least an order of magnitude less than for suspended load. However, for smaller tsunami and coarser particles, the importance of bed load relative to suspended load increases Parameters Few published reports directly address the effect of varying parameters on model results. Jaffe and Gelfenbaum [2] explored sensitivity of the TsuSedMod inverse tsunami sediment transport model to specifications of the resuspension coefficient and bottom roughness. Jaffe and Gelfenbaum [2] found that, for an idealized tsunami deposit composed of a single grain size, an increase in the resuspension coefficient from 10 4 to 10 3 decreases the tsunami flow speed by 44%, while a decrease in the resuspension coefficient from 10 4 to 10 5 increases the tsunami flow speed by 120%. This asymmetric behavior is related to the smaller resuspension coefficient lowering the amount of suspended sediment in the water column, which then requires a much greater shear velocity, and a corresponding greater tsunami flow speed, to increase both the amount in and mixing of the suspended sediment in the water column to match the portion of deposit formed from this sediment falling to the bed. They also found that calculated flow speeds are affected by the choice of bottom roughness. Increasing (decreasing) bottom roughness, as parameterized by z 0,byanorderof magnitude decreases (increases) average flow speed by 25%. The effects of varying bottom roughness in inverse modeling of the deposits of the 2011 Tohoku-oki tsunami on the Sendai coastal plain were explored by Jaffe et al. [3]. Bottom roughness in that study is parameterized by Manning s n. An increase (decrease) in Manning s n by 0.01 from a base value of 0.03 decreased (increased) calculated tsunami flow speed by as much as 31% (up to 90%) (Fig. 3a). The effects of varying bottom roughness for forward modeling at Sedanka Island, Alaska [11] did not have as large an effect on tsunami flow speed. An increase in Manning s n by 0.01 from a base value of 0.03 decreased calculated tsunami flow speed by as much as 12%, while decreasing Manning s n by increase flow speed up to 19% (Fig. 3b). Apotsos et al. [13] found that decreasing the offshore bottom roughness increased offshore flow velocities that erode and transport greater amounts of sediment and increase onshore deposition. In an idealized simulation a 654 Journal of Disaster Research Vol.11 No.4, 2016

9 Fig. 3. (a) Sensitivity of depth-averaged speed from TsuSedMod inverse model to bottom roughness parameter Manning s n at Sendai, Japan. See Jaffe et al. [3] for a description of the model and the study site. (b) Sensitivity of depth-averaged speed from Delft3D forward model to bottom roughness parameter Manning s n at Sedanka, Alaska. See Witter et al. [11] for a description of the hydrodynamic model and the study site. 50% decrease in the offshore roughness doubled the onshore deposit. Changes in the onshore roughness do not significantly affect the volume of sediment deposited onshore, but will partially dictate the lateral distribution of the deposit Model Completeness It is difficult to determine whether tsunami sand transport models are complete because either an incomplete model or a complete model that has imperfect inputs, formulations, parameters, and model integration could cause model results to differ from observations. One way of assessing model completeness is to develop a model with many processes and then evaluate whether all processes are needed to accurately model tsunami sand transport. Apotsos et al. [17] used this approach to evaluate the effect of including or omitting two processes that are not in many published tsunami sand transport models, sedimentinduced density stratification and hindered settling. Suspended sediment-induced density stratification occurs when large amounts of sediment are suspended in the water column, displacing less dense water. Because the source of suspended sediment is the bed, a stably stratified water column is created as the near-bed high suspendedsediment concentration is denser than the surface waters with lower suspended-sediment concentrations. Near-bed turbulence and the mixing of sediment into the upper water column are inhibited by the stable density stratification [45, 46]. To resolve this process, a numerical model must be three-dimensional (3D) or two-dimensional vertical and include a turbulence closure model. There are some 3D models (e.g. Delft3D and C-HYDRO3D), but, to date, Delft3D is the only model that resolves the density stratification during tsunami sediment transport. Apotsos et al. [17] found that neglecting suspendedsediment-induced density stratification for tsunamis increases the quantity and modifies the vertical profile of the suspended sediment in the inundating wave resulting in a thicker onshore deposit. They found that much of the extra sediment deposited onshore when sedimentinduced density stratification is neglected is suspended offshore by the backwash, where suspended-sedimentinduced density stratification would have the largest effect. Suspended-sediment-induced density stratification also affects the vertical profile of the horizontal flow velocity by preventing the faster moving surface water from mixing down into the lower water column [45]. In the time just after the backwash collides with the onrush of the next wave (i.e., when water column sediment concentrations are large) the vertical profile of the horizontal velocity differs significantly from that predicted under clear water conditions. Neglecting the difference in vertical velocity profile would obviously affect suspended sediment transport. Apotsos et al. [17] found that after the tsunami has inundated a few hundred meters onshore that suspended sediment concentrations have decreased and the effect on the flow is less important. Depth-averaged tsunami sand transport models can limit the maximum suspended sediment concentration to compensate for not including suspended-sedimentinduced density stratification. Gusman et al. [4] and Sugawara et al. [10] limited the depth-averaged suspended sediment volume concentration to 1% and 2%, respectively. Sugawara et al. [10] showed that the choice of the limiting concentration is an additional source of uncertainty. Hindered settling occurs when suspended-sediment concentrations are large enough that the upward flowing wakes around settling particles reduces the settling velocity of a particle compared to its clear fluid settling velocity. When suspended-sediment concentrations reach 20% a particle s settling velocity can be reduced by up to 40%, and higher concentrations may reduce the settling velocity by more than 90% [47, 48]. Apotsos et al. [17] found that the settling velocity can be reduced by more than 90% offshore of the shoreline during the strongest backwash of a tsunami if suspended-sediment concentrations are high. Settling velocities are less affected where concentrations are lower onshore of the shoreline and in the offshore seaward of the extent of the backwash. Typically, settling velocities are reduced more near the bed than in the up- Journal of Disaster Research Vol.11 No.4,

10 Jaffe, B. et al. per water column. Apotsos et al. [17] found that neglecting the effects of hindered settling reduces the amount of sediment suspended in the water column during inundation resulting in more sediment settling out offshore and a thinner deposit near the shoreline. The inland extent of the deposit is not changed significantly if hindered settling is neglected because sediment settling from the upper water column, where suspended sediment concentrations are typically smaller and hindered settling is not strong, controls how far particles travel inland. Poorly constrained interactions between vegetation and sediment transport can also lead to uncertainty in tsunami sediment transport modeling. Vegetation is typically implicitly included in tsunami sediment transport models through a higher bottom roughness that results in decreased tsunami flow speeds, which have the potential to alter the amount and distribution of sediment eroded and deposited. Gelfenbaum et al. [12] explicitly modeled the impact of a coastal forest on the sediment transport and resulting coastal morphological change during tsunami inundation. The forest was parameterized by rigid cylinders, and the diameter and density of the cylinders varied in their numerical experiments. Increasing plant density increased deposition within the forest and decreased deposition landward of the forest relative to the no-forest base case. Vegetation was found to play a role in the tsunami deposits from the 2010 Chile tsunami. Local thickening of tsunami deposits was observed in densely vegetated grassy fields compared to adjacent non-vegetated fields [49]. This effect may not occur often since tsunami flows typically are strong enough to erode the vegetation or lay the plants over. This phenomena is not included in any published tsunami sediment transport models and thicknesses of modeled to observed deposits in such areas would likely differ because they do not include pertinent processes, such as a reduction in turbulence, involved with deposit thickening in grassy areas. None of the published inverse tsunami sediment transport models for sand include bedload. It may be possible to develop an inverse model that exploits information contained in tsunami deposits from bedload deposition. A challenge for implementing such a model would be identification of the portion of the deposit created by bedload transport Uncertainties in Tsunami Transport of Boulders Inputs A key source of uncertainty in tsunami boulder transport derives from incomplete knowledge of the accuracy of the specification of inputs such as the size, shape, density and porosity of boulders. Accurate specification of these inputs will reduce uncertainty. Techniques such as terrestrial laser scanning to measure boulder size and shape [50] and Archimedean and optical 3D-profilometry measurements to determine boulder density [51] can produce highly accurate input data. When it is not practical to apply these techniques, assessment of errors in the inputs and propagation of the measurement errors through the boulder tsunami transport model allows assessment of uncertainty. One input parameter that is difficult or impossible to know is the pre-tsunami orientation of the boulder, i.e., the direction of the longest horizontal axis, relative to the tsunami flow. Boulder orientation relative to the flow can have a large effect on transport [27]. Treating the pretsunami orientation as a variable and running the boulder tsunami transport model for a spectrum of orientations will give a range of possible results that can be evaluated and used in an appropriate way according to application (e.g. tsunami hazard assessment) Formulations Depending on the size and density of the boulders, the clasts may be transported as bedload or suspended load. The uncertainty in the mode of transport of boulders may affect model results. The dominant transport mode for boulders in existing models is bedload, which includes sliding, rolling, and saltating. This choice of transport mode may be justified, as Goff et al. [51] found tsunamis transporting boulders in suspension is unlikely. Field evidence, such as whether the boulder is oriented with its original top surface towards the bed or whether there are marks on the surface indicating collision during rolling or saltating, may help to constrain the transport mode Parameters The choice of parameter values, such as the drag coefficient, lift coefficient, friction coefficient, coefficient of mass, may have a large effect on model results [5]. An example of this is the choice of the drag coefficient, which is a key to both forward and inverse models because drag force is the largest force acting on the boulder. Despite its importance, there is not general agreement on the correct value and researchers use values ranging from 1.05 to 2.0 (e.g., [27, 30, 53]). Complicating matters is that the Reynolds number of tsunamis in nature is very high, on the order of 10 7, which is not reproduced in laboratory experiments that are used to estimate the drag coefficient [27]. Therefore, without rigorous determination of each parameter when specifically reproducing tsunamilike currents with a very high Reynolds number, it should be understood that both the forward and inverse models have more or less uncertainty. Buckley et al. [31] quantified the uncertainty in modeling tsunami transport of boulders by allowing parameters to vary over the range of values reported in the literature. Such an approach is suggested when using boulders to quantify the size of paleotsunamis Model Completeness Four areas that existing models do not address, but may be important, are the roles of sediment-enhanced fluid density, collision of boulders during transport, tsunami wave shape, and large roughness elements in tsunami 656 Journal of Disaster Research Vol.11 No.4, 2016

11 transport of boulders. Kain et al. [54] argued that water alone might not be able to initiate the transport of boulders in some cases, but that including the increase in fluid density from suspended sediment in the water column may allow boulders to move. Kain et al. [54] advocate for inclusion of the effect of increasing fluid density from finer sediment in the water and suggest that eventually models for tsunami boulder transport use a Bingham flow approach. Existing forward models do not consider collision of boulders during transport. Such collisions may be an important factor limiting the distance that boulders can be transported. There is evidence of boulder collision from laboratory experiments [27, 56] and field observations [55]. Flow accelerations may be important for initiation of transport and sustained transport of boulders by tsunamis. Weiss and Diplas [57] conclude that including time variation, instead of just average or maximum values of flow characteristics, is an important consideration for accurate modeling of initiation of boulder transport. Existing models that employ the NLSWE also may not accurately reproduce the shapes and associated flow accelerations of tsunamis in nature. Although computationally intensive, exploration of tsunami boulder transport using more sophisticated models that accurately reproduce tsunami wave shapes and flow accelerations may prove useful for assessing the uncertainty from these factors in the representations of the existing models. Weiss [58] conducted numerical experiments exploring the effect of large bed roughness elements on the transport of boulders. This was motivated by field observations of roughness possibly inhibiting moving of boulders during the 2006 Kurile tsunami [59]. He found that when the bed roughness length scales were on the order of 10% of the boulder heights those boulders were not able to move, even by fast moving flows such as occur in a tsunami. In settings with karst weathering, such as occurs on limestone platforms of tropical islands, roughness scales large enough to inhibit transport of boulders by tsunamis may be present. 5. Decreasing Tsunami Sediment Transport Uncertainty 5.1. Laboratory Experiments Apotsos et al. [16] point out that laboratory experiments of tsunami sediment transport are difficult because of the limited size of most laboratory facilities and the fact that sediment becomes cohesive at small grain sizes. Additionally, waves used in laboratory studies are typically solitary waves, which may not be appropriate because the flow velocities and accelerations induced are likely to be different than those induced by long tsunami waves. Even with such difficulties, laboratory experiments may be useful for increasing our understanding of the physics of tsunami sediment transport, which may decrease uncertainty in model results. Two recent studies, one by Yamaguchi and Sekiguchi [60] and the other by Johnson et al. [61] are worthy of note. Yamaguchi and Sekiguchi [60] investigated the effects of tsunami magnitude and terrestrial topography on the sedimentary processes and the distribution of tsunami deposits in flume experiments. They found that depression in topography where water ponded affected the inland extent of tsunami deposits, with deeper pools decreasing inland transport of sediment and creating a gap between the deposit extent and the inundation of water. An additional finding was that complexities in topography obscured relationships between the local deposit thickness and tsunami magnitude (size) and that a clearer relationship existed between tsunami deposit volume and tsunami magnitude (size). Johnson et al. [61] conducted flume experiments to evaluate the inverse tsunami sediment transport model of Moore et al. [1], in which average tsunami flow speeds and flow depths are calculated from advection of the largest particles found in the tsunami deposit. Johnson et al. [60] found that the model was able to predict time-averaged flow depths within a factor of 2and time-averaged tsunami flow speeds within a factor of 1.5. The model performed very well with source grain size distributions that were finer and performed more poorly for bimodal distributions. Modeled and observed flow speed/depths were more similar when variation in grain size distributions from the more downstream end of the flume where sediment was transported fully in suspension Benchmark Tests Benchmark tests are commonly used to evaluate new tsunami hydrodynamic models, however standardized benchmark tests for tsunami sediment transport models do not exist. There is a need to develop benchmark tests using laboratory data and field observations for evaluating models. Apotsos et al. [16] point out that development of laboratory-scale benchmarks is challenging because benchmarks must include the effects of bedload transport, sediment suspension, advection, and settling on the appropriate time and length scales. As indicated in the previous section, the size of laboratory facilities and scaling issues such as sediment becoming cohesive at small grain sizes limit the design of laboratory experiments. Benchmarks using field data collected after modern tsunamis can also be problematic because initial conditions may not be well known and values for parameters such as bottom roughness may be poorly constrained. Even with the difficulties, the potential advantages of such benchmarks are worth pursuing. A tsunami deposits workshop in 2007 using preliminary benchmark tests concluded that there is a need for standardized benchmarks for tsunami erosion, sediment transport, and deposition [62] Rigorous Evaluation of Uncertainty For tsunami sediment transport modeling to advance and be used appropriately in tsunami hazard assessment Journal of Disaster Research Vol.11 No.4,

12 Jaffe, B. et al. the reporting of uncertainty in model results is a necessity. However, only a small percentage of the published papers report modeling uncertainties explicitly. The tsunami research community may benefit from the experience of the climate change community. Moss and Schneider [63] present guidance for evaluating uncertainty for the Third Assessment Report of the Intergovernmental Panel on Climate Change in the form of three questions, 1. Are the most important factors of uncertainties, and uncertainties that are likely to affect the conclusion identified for each of the major findings...? 2. Are ranges and distributions in the literature, including sources of information on the key causes of uncertainty documented? 3. Given the nature of the uncertainties and the state of science and the purpose of determining the appropriate level of precision: (i) Is the state of science such that only qualitative estimates are possible?... This guidance is applicable to reporting uncertainty in tsunami sediment transport modeling. A new approach to quantifying uncertainty for inverse tsunami sediment transport modeling that uses Ensemble Kalman Filtering (EnKF) is being developed by Wang et al. [64] and Tang et al. [65]. The TSUFLIND model [6] is used as a forward model that solves for the unknown quantities, shear velocity and flow depth, by using the EnKF inversion technique. This is done by combining distributions of possible shear velocities and flow depths with observations of the vertical flux of suspended sediment calculated from the grain size distributions of a series of layers in the tsunami deposit. The model assumes settling from a vertical distribution of suspended sediment according to Madsen et al. [37]. The EnKF technique narrows the range of possible shear velocities and flow depths in successive runs of the TSUFLIND model using revised sediment flux observations. The end result is a robust, narrow range of possible values of shear velocities and flow depths and uncertainty estimates based on the vertical variation in grain size distributions of layers in the tsunami deposit. An interesting result of the application of this technique, which can guide sampling of tsunami deposits, is that there is an optimum number of layers to reduce uncertainty. The TsuFlind-EnKF inversion model produced reasonable estimates and inland trends of Froude number and flow depth for deposits from the 2004 Indian Ocean tsunami near Ranganathapuram, India (description of deposits and field area originally presented in Bahlburg and Weiss [66]). Inversion modeling using EnKF is a promising method for quantifying and reducing uncertainty in tsunami sediment transport modeling. This method should be applied to deposits created at other locations and by other tsunamis to test whether it is generally applicable Development of Hybrid Models Hybrid models represent a new approach that combines forward and inverse tsunami sediment transport models (Fig. 4). Both models are constrained by observations of tsunami deposits and auxiliary data. Typically the initial modeling is forward, followed by an evaluation of model Fig. 4. Interactions between forward and inverse tsunami sediment transport models in a hybrid modeling approach. Both models are constrained by observations of tsunami deposits and auxiliary data. Typically the initial modeling is forward, followed by an evaluation of model outputs such as time series of water levels and flow velocities to determine if and where the inverse model can be applied. Outputs from the inverse model, such as tsunami flow speed, inundation distance, runup elevation, and flow depth, are then used to inform the forward model to improve the match between model and observations. Although depicted as a continuous loop, the hybrid model can be stopped when observations are matched to an acceptable level. outputs such as time series of water levels and flow velocities to determine if and where the inverse model can be applied (see Sugawara et al. [67] for an example of using a forward tsunami sediment transport model to evaluate whether the assumptions of the TsuSedMod of Jaffe et al. [2] are met). Outputs from the inverse model, such as tsunami flow speed, inundation distance, runup elevation, and flow depth, are then used to inform the forward model to improve the match between model and observations. Although depicted as a continuous loop, the hybrid model loop should be stopped when observations are matched to an acceptable level. A hybrid approach to tsunami sediment transport modeling holds the promise of quantifying and reducing uncertainty by: (1) comparison of forward and inverse model results, (2) using forward modeling, which outputs time series of velocities and water levels for every location in the domain and for every time during the model run, to identify if there are locations and times at which the assumptions of the inverse tsunami sediment transport models are met, and (3) using output from the inverse models to inform forward models. The hybrid modeling approach also has the advantage of selectively incorporating the most-certain parts of the forward and inverse modeling approaches and omitting the weakest parts. 6. Concluding Remarks Although tsunami sediment transport modeling results contain uncertainty, case studies for both forward and inverse models have shown that such modeling provides useful information on tsunami inundation and hydrodynamics that can improve assessment of tsunami hazard. It is imperative in any tsunami sediment transport study 658 Journal of Disaster Research Vol.11 No.4, 2016

13 to explicitly quantify uncertainty as much as possible, including the use of sensitivity analysis. Tsunami science will advance more rapidly with the advent of new techniques for quantifying uncertainty, such as Ensemble Kalman Filtering inversion, and more rigorous reporting of uncertainties. There are several future directions that may reduce uncertainty in tsunami sediment transport modeling: (1) laboratory studies that improve our assessment of the semi-empirical parameters and physics of tsunami sediment transport, (2) standardized benchmark tests to assess model performance, and (3) development of hybrid modeling approaches to exploit the strengths of forward and inverse models and de-emphasize their weaknesses. As uncertainty in tsunami sediment transport modeling is reduced, and as the ability to quantify uncertainty increases, the geologic record of tsunamis will become more valuable in the assessment of tsunami hazard. Acknowledgements Part of this study was financially supported by International Research Institute of Disaster Science, Tohoku University (Tokutei Project). BJ, GG, and SL were funded by the USGS Coastal and Marine Geology Program. This manuscript was significantly improved by comments and suggestions offered by Guto Schettini and two anonymous reviewers. Frances Griswold assisted in preparation of figures. BJ would also like to thank Jeff List for helpful discussions on the framework for addressing model uncertainty. References: [1] A. L. Moore, B. G. McAdoo, and A. Ruffman, Landward fining from multiple sources in a sand sheet deposited by the 1929 Grand Banks tsunami, Newfoundland, Sedimentary Geology, Vol.200, pp , 2007, j.sedgeo [2] B. E. Jaffe and G. Gelfenbaum, A simple model for calculating tsunami flow speed from tsunami deposits, Sedimentary Geology 200, pp , 2007, j.sedgeo [3] B. E. Jaffe, K. Goto, D. Sugawara, B. Richmond, S. Fujino, and Y. 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15 [78] K. Satake, Real-time inversion of tsunami waveforms, presented at Japan Meteorological Agency meeting held in Tokyo on 11 March 2011, Retrieved from /svd/eqev/data/study-panel/tsunami/benkyokai7/sankou siryou.pdf [accessed March 21, 2016] Name: Daisuke Sugawara Affiliation: Associate Professor, Museum of Natural and Environmental History Name: Bruce Jaffe Affiliation: Oceanographer, U.S. Geological Survey Address: 2885 Mission St., Santa Cruz, CA 95060, USA Brief Career: U.S. Geological Survey, Pacific Coastal and Marine Science Center Selected Publications: Flow speed estimated by inverse modeling of sandy tsunami deposits: results from the 11 March 2011 tsunami on the coastal plain near the Sendai Airport, Honshu, Japan, Sedimentary Geology, Vol.282, pp , Anthropogenic Influence on Sedimentation and Intertidal Mudflat Change in San Pablo Bay, California: 1856 to 1983, Estuarine Coastal and Shelf Science, Vol.73, No.(1-2), pp , Using nonlinear forecasting to determine the magnitude and phasing of time-varying sediment suspension in the surf zone, J. of Geophysical Research, Vol.101, No.C6, pp. 14,283-24, 296, Academic Societies & Scientific Organizations: American Geophysical Union (AGU) Name: Kazuhisa Goto Affiliation: International Research Institute of Disaster Science, Tohoku University Address: Aoba E303, Aramaki, Aoba-ku, Sendai , Japan Brief Career: Disaster Control Research Center, Tohoku University Planetary Exploration Research Center, Chiba Institute of Technology International Research Institute of Disaster Science, Tohoku University Selected Publications: K. Goto, K. Ikehara, J. Goff, C. Chague-Goff, and B. Jaffe, The 2011 Tohoku-oki tsunami 3 years on, Marine Geology, Vol.358, pp. 2-11, Academic Societies & Scientific Organizations: Geological Society of Japan (GSJ) Sedimentological Society of Japan (SSJ) Asia Oceania Geosciences Society (AOGS) Address: 5762 Ohya, Suruga-ku, Shizuoka City , Shizuoka, Japan Brief Career: Museum of Natural and Environmental History, Shizuoka Selected Publications: Sediment transport due to the 2011 Tohoku-oki tsunami at Sendai: Results from numerical modeling, Marine Geology, Vol.358, pp , Academic Societies & Scientific Organizations: American Geophysical Union (AGU) Geological Society of Japan (GSJ) Japan Geoscience Union (JGU) Name: Guy Gelfenbaum Affiliation: Oceanographer, U.S. Geological Survey Address: 2885 Mission St., Santa Cruz, CA 95060, USA Brief Career: Oceanographer, U. S. Geological Survey, Center for Coastal Geology and Regional Marine Studies, St. Petersburg, FL 1998-present Oceanographer, U.S. Geological Survey, Pacific Coastal and Marine Science Center, Menlo Park and Santa Cruz, CA Selected Publications: G. Gelfenbaum, A. W. Stevens, A. Miller, J. A. Warrick, A. S. Ogston, and E. Eidam, Large-scale dam removal on the Elwha River, Washington, USA, Coastal Geomorphic Change, Geomorphology, 2015, doi: /j.geomorph Academic Societies & Scientific Organizations: American Geophysical Union (AGU) Name: SeanPaul La Selle Affiliation: Geologist, U.S. Geological Survey Address: 2885 Mission St., Santa Cruz, CA Brief Career: U.S. Geological Survey, Pacific Coastal and Marine Science Center Selected Publications: Unusually large tsunamis frequent a currently creeping part of the Aleutian megathrust, Geophysical Research Letters, No.42, pp , Academic Societies & Scientific Organizations: American Geophysical Union (AGU) Journal of Disaster Research Vol.11 No.4,