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Geophysical Research Letters RESEARCH LETTER 10.1002/2015GL064610 Key Points: • We have developed a 3-D tsunami-ionosphere coupling model WP-GITM • WP-GITM combines an analytical model and a fully physics-based ionospheric model • WP-GITM reproduces traveling ionospheric signatures of a real tsunami

Correspondence to: X. Meng, [email protected]

Citation: Meng, X., A. Komjathy, O. P. Verkhoglyadova, Y.-M. Yang, Y. Deng, and A. J. Mannucci (2015), A new physics-based modeling approach for tsunami-ionosphere coupling, Geophys. Res. Lett., 42, 4736–4744, doi:10.1002/2015GL064610.

A new physics-based modeling approach for tsunami-ionosphere coupling X. Meng1 , A. Komjathy1,2 , O. P. Verkhoglyadova1 , Y.-M. Yang1 , Y. Deng3 , and A. J. Mannucci1 1 Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California, USA, 2 Department of Geodesy and Geomatics Engineering, University of New Brunswick, Fredericton, New Brunswick, Canada, 3 Department of Physics, University of Texas at Arlington, Arlington, Texas, USA

Abstract Tsunamis can generate gravity waves propagating upward through the atmosphere, inducing total electron content (TEC) disturbances in the ionosphere. To capture this process, we have implemented tsunami-generated gravity waves into the Global Ionosphere-Thermosphere Model (GITM) to construct a three-dimensional physics-based model WP (Wave Perturbation)-GITM. WP-GITM takes tsunami wave properties, including the wave height, wave period, wavelength, and propagation direction, as inputs and time-dependently characterizes the responses of the upper atmosphere between 100 km and 600 km altitudes. We apply WP-GITM to simulate the ionosphere above the West Coast of the United States around the time when the tsunami associated with the March 2011 Tohuku-Oki earthquke arrived. The simulated TEC perturbations agree with Global Positioning System observations reasonably well. For the first time, a fully self-consistent and physics-based model has reproduced the GPS-observed traveling ionospheric signatures of an actual tsunami event.

1. Introduction Received 18 MAY 2015 Accepted 11 JUN 2015 Accepted article online 12 JUN 2015 Published online 30 JUN 2015

The original idea that tsunami-induced atmospheric gravity waves could be detected in the ionosphere [Hines, 1972] has been supported by observational evidence since the last decade, as reported by Artru et al. [2005a], Liu et al. [2006], Rolland et al. [2010], and Garcia et al. [2014], to name a few. The details of the physical processes are still being actively studied, yet an overall picture has become clear. Tsunamis displace the neutral atmosphere just above the ocean surface, generating atmospheric gravity waves. These waves propagate upward through the atmosphere. As the background neutral density drops with height, the wave amplitudes increase to conserve energy. At ionospheric heights the neutral disturbances cause perturbations of ions and electrons. The ionospheric perturbations manifest themselves in the total electron content (TEC) measurements via the time delay in transionospheric radio signals [Garner et al., 2008]. According to Hines’ speculation in 1972, ionosphere monitoring might provide potential early warnings of tsunamis, which are otherwise almost undetectable before they approach coastlines due to their small amplitudes and large horizontal extents in the open ocean. Thus, the subject of tsunami-ionosphere coupling has been appealing to researchers ever since. Of all the research efforts on tsunami-related ionospheric signatures, modeling has played an important role in interpreting observations and reproducing tsunami-gravity wave-ionosphere interactions. The earliest modeling work can be traced back to a two-dimensional (2-D) analytical model developed by Peltier and Hines [1976]. Their result corroborates the growth of the gravity wave amplitude with height. Later, Peltier and Hines’s model was adopted by Artru et al. [2005a, 2005b] to confirm the observed time of a gravity wave propagating from the ocean surface to the ionosphere. More advanced models, including three-dimensional (3-D) time-dependent numerical models [Occhipinti et al., 2006, 2008, 2011; Mai and Kiang, 2009] and a spectral full-wave model [Hickey et al., 2009], have been developed and applied to simulate ionospheric perturbations caused by tsunamis. All models mentioned above significantly contribute to the understanding of tsunami-ionosphere coupling. However, these models either rely on an empirical atmospheric and ionospheric background that lacks self-consistent coupling between neutrals and ions or neglect some physical processes (for example, chemical reactions, heat conduction, and radiative cooling) and space weather effects in the upper atmosphere, which limits the modeling ability to represent reality.

©2015. American Geophysical Union. All Rights Reserved.

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To overcome the limitations of previous models and better capture the upper atmospheric dynamics affected by tsunami-driven gravity waves, we have developed WP-GITM (Wave Perturbation-Global TSUNAMI-IONOSPHERE MODEL

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Ionosphere-Thermosphere Model), a 3-D tsunami-ionosphere coupling model, by implementing tsunami-induced gravity waves into the first-principles model of the ionosphere and thermosphere, GITM [Ridley et al., 2006]. The inputs of WP-GITM include tsunami characteristics: the tsunami wave height, wave period, wavelength, and propagation direction; along with the standard inputs for GITM: solar wind conditions, interplanetary magnetic field (IMF) conditions, and others. The output of WP-GITM is given by the GITM solution: the upper atmospheric state between 100 km and 600 km altitudes. For validation, we apply WP-GITM to simulate the upper atmosphere over the United States (U.S.) West Coast during the tsunami event caused by the March 2011 Tohoku-Oki earthquake. The simulated TEC perturbations are then compared against the TEC perturbations derived from Global Positioning System (GPS) observations. The following content of the paper is divided into three parts. Section 2 describes WP-GITM. Section 3 presents the simulation of a real event and model-data comparisons. Section 4 concludes the paper and proposes future work.

2. Model Description WP-GITM is a 3-D time-dependent numerical model solving for the global or regional upper atmospheric responses to tsunami-driven gravity waves. The model is a self-consistent combination of a fully physics-based model between altitudes of 100 km and 600 km and an analytical model linking tsunamis at the sea level to atmospheric perturbations at 100 km altitude. 2.1. Between 100 km and 600 km Altitudes The core of WP-GITM, extending from 100 km altitude to around 600 km altitude, is represented by GITM. GITM is governed by the continuity, momentum, and energy equations. It includes five major neutral species (O(3 P), O2 , N2 , N(4 S), and NO), five minor neutral species, and nine ions and electrons. Different neutral species are assumed to share the same horizontal velocity and temperature. The primitive variables for neutrals are the total mass density, velocity, and temperature, as well as the number density and vertical velocity of individual major species. GITM considers solar extreme ultraviolet heating, auroral particle precipitation, chemical reactions, ion-neutral and neutral-neutral collisions, viscosity, heat conduction, radiative cooling, high-latitude ionospheric electric field, and geomagnetic field for a comprehensive description of physical processes in the ionosphere and thermosphere. The governing equations of GITM are well documented [Ridley et al., 2006]. One important aspect of these equations is that they allow nonhydrostatic solutions; i.e., the pressure gradient in the vertical direction is not necessarily balanced by the gravity, which enables GITM to better describe gravity wave propagation than models restricted to hydrostatic equilibrium [Deng et al., 2008; Deng and Ridley, 2014]. The computational grid of GITM is based on geographic longitude, latitude, and altitude. In the longitudinal and latitudinal directions, a simulation domain can cover either the entire globe or a localized region of interest, and the grid resolution is flexible. For a specific simulation case, we adjust the horizontal grid size according to the horizontal wavelength of the gravity wave to achieve sufficient accuracy with affordable computational cost. In the vertical direction, the grid size is set to 30% of the scale height, which depends on the atmospheric condition at the initial time of a simulation and changes with altitude. The temporal resolution is on the order of seconds and dynamically changes in simulations. The initial and lower boundary conditions of GITM are acquired from empirical atmospheric models MSIS (Mass Spectrometer and Incoherent Scatter) [Hedin, 1991] and HWM (Horizontal Wind Model) [Drob et al., 2008]. The upper boundary acts as an open boundary, as do the horizontal boundaries in a spatially localized simulation. The boundary conditions are supplied in two layers of ghost cells. For example, at the lower boundary, two horizontal layers of grid cells just below 100 km are populated with values for the total neutral mass density, number densities of major neutral species, and the neutral temperature from MSIS and the horizontal neutral velocity from HWM at corresponding altitudes, as well as the vertical neutral velocities that are assumed to be zero. In the presence of tsunami-driven gravity waves, perturbations are added to the lower boundary condition (section 2.2). The geomagnetic field, auroral precipitation, and high-latitude electric field are provided by the Apex field [Richmond, 1995], the Fuller-Rowell and Evans model [Fuller-Rowell and Evans, 1987], and the Weimer 2005 model [Weimer, 2005a, 2005b], respectively. The inputs of GITM are the solar wind and IMF conditions, solar irradiance, and hemispheric power indices (a proxy for auroral particle precipitation). MENG ET AL.

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2.2. Coupling Between the Ocean Surface and 100 km Altitude To bridge the gap between the ocean surface and the lower boundary of GITM, we have developed a model that provides an analytical relation between the neutral atmospheric perturbations in the lower boundary ghost cells of GITM and the tsunami characteristics input to WP-GITM. We start from the fundamental equations of fluid dynamics, make a number of assumptions, derive the dispersion and polarization relations for gravity waves [Fritts and Alexander, 2003; Vadas and Fritts, 2005, 2009; Vadas and Nicolls, 2012], and finally connect tsunami waves to atmospheric perturbations. We will omit the detailed derivation but would like to state our assumptions. 1. The model applies a Cartesian coordinate system, with the x , y, and z axes pointing eastward, northward, and upward, respectively; z = 0 is at the surface of the Earth. 2. The atmosphere state is represented by the neutral density, velocity, and temperature, i.e., 𝜌, ux , uy , uz , and T . The background state only varies with height and satisfies 𝜌 = 𝜌0km exp(−z∕H), dux ∕dz ≪ 𝜔, duy ∕dz ≪ 𝜔, uz = 0, and T = constant, where H is the scale height and 𝜔 is the gravity wave frequency. 3. The wavelength and 𝜔 are constant; i.e., the wave is linear. 4. The wave amplitude does not change horizontally, but it may change vertically. 5. The rotational frequency of the Earth ΩEarth 0 and thus imposes an upper limit for 𝜔. Together with our assumption 5, 𝜔 is restricted to √ √ K2 + K2 √ x y ΩEarth ≪ 𝜔 < N√ + Kx ux + Ky uy (9) Kx2 + Ky2 + 4H1 2 Therefore, our analytical model is valid only for tsunamis with wave frequencies satisfying (9), implemented as a constraint.

3. Simulation of the 2011 Tohoku-Oki Event As the first validation and application of WP-GITM, we simulate the ionospheric perturbations over the U.S. West Coast induced by the Tohoku-Oki earthquake-caused tsunami. The U.S. West Coast is selected for two reasons. First, it is far away from the epicenter so the ionospheric signatures are primarily caused by the tsunami. Second, its dense GPS network provides excellent data that cover a broad region for model validation. The simulation domain is a 3-D box that extends from 132∘ W to 108∘ W in longitude, from 30∘ N to 50∘ N in latitude, and from 100 km to 600 km vertically. The horizontal grid resolution is 0.2∘ in both longitude and latitude, while the vertical grid size increases from 1.6 km to 15.5 km with increasing altitude. The horizontal grid size is determined such that the tsunami wavelength (see next paragraph) is covered by multiple computational cells. The two ghost cell layers for the GITM lower boundary are centered at 96.7 km and 98.3 km altitudes. This simulation takes solar wind and IMF conditions from the OMNI data, solar irradiance spectra from the Flare Irradiance Spectral Model [Chamberlin et al., 2008], and a constant hemispheric power of 10 GW (a typical value during geomagnetic quiet time) as inputs, apart from the tsunami properties. The simulation time starts at 14:45 UT and ends at 20:45 UT. The time step varies around 3.5 s during the simulation. We obtain the open ocean tsunami characteristics from the MOST (Method of Splitting Tsunami) model [Titov and Gonzalez, 1997] simulated tsunami waves of the Tohoku-Oki event. For simplicity, we only consider the leading tsunami wave and trailing waves with wave heights ≥8 cm and represent them by single periods of sine or cosine waves, as shown in Figure 1 (top row) for two different snapshots. Waves A, B, and C have the same wave period (20 min), wavelength (150 km), and propagation direction (9∘ south of east). The amplitudes of waves A, B, and C are 8 cm, 10 cm, and 9 cm, respectively. The waves move with a constant speed of 125 m/s and come to a stop at the coastline. The resulting neutral atmospheric perturbations at the lower boundary of GITM are shown in Figure 1 (bottom row). Only the total neutral mass density and vertical neutral wind perturbations are displayed, though other quantities are also perturbed following equations (4)–(7). According to our assumptions stated in section 2.2, the gravity waves propagate with the same horizontal speed as MENG ET AL.


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Figure 1. The tsunami waves at (top left) 14:58 UT result in the (bottom left) total neutral mass density perturbations and (bottom right) vertical neutral wind perturbations at 98.3 km altitude at 16:35 UT in the simulation. (top right) The input tsunami waves at 16:35 UT.

the tsunami waves at the sea level; therefore, the neutral atmospheric perturbations at 16:35 UT (Figure 1, bottom row), though induced by the tsunami waves at an earlier time 14:58 UT (Figure 1, top left), are at the same location as the tsunami waves at 16:35 UT (Figure 1, top right). For comparison, we also perform a simulation without tsunami waves. The difference between the two simulations give the atmospheric and ionospheric disturbances due to the tsunami itself. Figure 2 shows the total neutral mass density and electron number density perturbations in a latitudinal slice (45∘ N) at 16:35 UT. The neutral density perturbation clearly shows the upward propagating gravity waves driven by the tsunami waves A and C. Furthermore, the neutral and electron density perturbations induced by wave C are stronger than those induced by wave A. This could be due to the larger amplitude of wave C than wave A and different local atmospheric states in the vicinities of wave C and wave A. Wave B, very close to wave A in location, induces similar but stronger atmospheric perturbations compared to wave A (not shown here), since wave B has a larger amplitude. The neutral and electron density perturbations show different vertical variations. The magnitude of the neutral density perturbation does not always increase with altitude, which indicates wave attenuation in the ionosphere. The magnitude of the electron density perturbation changes with altitude nonmonotonically. Since the perturbation is transferred from neutrals to electrons through their momenta and chemistry, the vertical distribution of the electron density perturbation depends on several factors, including the neutral, ion and electron temperatures, the neutral wind, the neutral density, and the background electron density, all varying with altitude, as well as the electric field and the geomagnetic field. Figure 3 displays four snapshots of simulated TEC perturbations taken at different times. At 15:35 UT, the TEC perturbation is entirely due to waves A and B, as wave C has not entered the simulation region yet. The distribution of the TEC perturbation follows the propagation direction of the tsunami waves. At 16:35 UT, two groups of TEC perturbations appear nearby the horizontal locations where the lower boundary neutral atmospheric perturbations are imposed and where the tsunami waves are (Figures 1, bottom left and 1, top right). This suggests that the horizontal speed of the TEC perturbations is around the speed of the tsunami that causes them. Note that the TEC perturbations are induced by the tsunami at an earlier time instead of MENG ET AL.


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Figure 2. Simulated total neutral mass density and electron number density perturbations in percentage in the longitude-altitude plane at 45∘ N and at 16:35 UT.

the present time, since the gravity waves propagate obliquely upward. At 17:05 UT and 17:35 UT, the TEC perturbations continue to propagate toward the same direction. To validate the simulation, we select 16 ionospheric pierce points (IPPs) from a number of ground receivers and GPS satellites. An IPP is defined as the intersection between the line of sight from a moving satellite to a receiver and a thin shell representing the ionosphere. The thin shell is located near the mean altitude of the electron density peak. These IPPs are chosen such that their trajectories well cover the west coastal region. We use a wavelet-based technique to detect and extract the coherent structures of TEC perturbations along the IPP trajectories from the GPS measurement [Yang et al., 2012]. The simulated TEC perturbations along the IPP trajectories are directly extracted from the simulation. For identification purpose, we number the trajectories from 1 to 16. The comparisons between simulated and measured TEC perturbations are shown in Figure 4. Each panel corresponds to one IPP track. Tracks 1 and 2 are from satellite PRN15 and located farthest inland. The GPS measurements show TEC perturbations of magnitudes approaching 0.4 or even 0.6 TECU (total electron content unit, 1 TECU = 1016 el m−2 ) after 17:00 UT. The simulated TEC perturbations are similar in magnitude, but appear earlier than the measurement. These simulated TEC perturbations are due to leading waves A and B, as the ionospheric perturbations induced by wave C have not arrived in this area yet. The simulation thus confirms that a significant part of the measured TEC perturbations after 17:00 UT are caused by the leading tsunami wave. This also demonstrates that tsunami-induced ionospheric signatures continue to travel after the tsunami stops at the coastline, for more than 600 km farther inland. IPP tracks 3 and 4 are from PRN18, and large portions of the tracks are nearly parallel to the perturbation wave fronts. Hence, the tsunami-induced TEC signatures are not distinctive in both the measurements and simulation. On the contrary, IPP tracks 5 to 13, from PRN21, are almost perpendicular to the perturbation wave fronts. Thus, the TEC signatures, when present, are clear and pronounced. Such TEC signatures are seen in the measurements of tracks 5–7 and 11–13, which are approximately reproduced by the simulation. We find that these TEC MENG ET AL.


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Figure 3. Simulated TEC perturbations over the map at 15:35 UT, 16:35 UT, 17:05 UT, and 17:35 UT. The color contours show the magnitude of the TEC perturbations in TECU (total electron content unit, 1 TECU = 1016 el m−2 ). The black curves represent the trajectories of 16 ionospheric pierce points (IPPs). The red asterisks mark the locations of IPPs at the given time.

perturbations are induced by the tsunami wave C upon examining the IPP positions in Figure 3. The arrival times of the simulated TEC perturbations, marked by the red dashed lines, are close to the arrival times from the measurements, marked by the black dashed lines. The magnitudes of the simulated TEC perturbations also agree with the measured ones for tracks 5, 6, 12, and 13. Along track 9, both the measurement and simulation show little TEC variations. Along track 10, the simulation overestimates the TEC perturbations. Track 10 is very similar and close to track 12. The simulated TEC perturbations along these two tracks are almost identical, while the measured TEC perturbations seem very different. This implies that the ionospheric perturbations vary significantly in this region, which is not captured by the simulation. For track 8, the simulated TEC perturbations, arrived half an hour earlier than the measurement, are induced by the leading waves A and B, which indicates that the actual ionospheric disturbances caused by the leading tsunami wave travel inland slower than the simulation suggests. The last three IPP tracks, 14–16 refer to PRN22. Tracks 14 and 15 intersect the wave C-perturbed area where the simulation produces large TEC perturbations, while track 16 is located at the edge of the perturbed area where smaller TEC variations are produced. The simulation generally agrees with the measurements for these three tracks, yet greatly overestimates the magnitude for track 14. Possible reasons for model-data disagreement include limitations of the analytical model, the simplification of the input tsunami waves, and uncertainties in GPS-derived TEC perturbations. First, the analytical model neglects the vertical profiles of the neutral temperature and wind and simply takes the averages between 0 km and 100 km altitudes. Our experiment (not shown here) indicates that this assumption may affect the wave amplitude and phase through the inaccurately represented H and Kz , respectively. Second, our input tsunami waves A, B, and C are sine (cosine) waves with the same frequency and wavelength, while the real tsunami is better represented by a wave packet composed of waves with various frequencies and wavelengths. This could lead to different perturbation waveforms from the simulation and measurement, such as for tracks 5–7 and 11–13. The input tsunami waves move with a constant speed, while in reality a tsunami wave slows down as it approaches the coastline, which causes the ionospheric perturbations to slow down as well. This can cause the arrival time error for track 8. The magnitude of the actual tsunami also varies with location in a finer way than our input waves, which could explain the overestimation or underestimation of TEC perturbations MENG ET AL.


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Figure 4. Simulated (blue) and GPS-derived (black) TEC perturbations in TECU along the 16 IPP trajectories. The names of the GPS satellite (in PRN code) and ground receiver for each IPP track are given on each panel. The black and red dashed lines mark the arrival times of tsunami-induced TEC perturbations in the measurement and simulation, respectively.

for some IPP tracks, such as 10, 11, and 14. Finally, it is also worthwhile to note that the accuracy of GPS-derived TEC perturbations is limited by the estimation technique used [Yang et al., 2012].

4. Conclusions We have successfully developed and implemented a 3-D time-dependent numerical model WP-GITM that simulates tsunami-caused upper atmospheric disturbances. The model is constructed from a 3-D analytical model and the 3-D physics-based model GITM. The analytical model dynamically provides neutral atmospheric perturbations to lower boundary conditions for GITM, which computes the resulting upper atmospheric dynamics. WP-GITM performs reasonably well in simulating the ionospheric perturbations over the U.S. West Coast caused by the tsunami following the 2011 Tohoku-Oki earthquake. Comparing to other models of similar purposes, WP-GITM may be considered more advanced in its completely physics-based description of the ionosphere and thermosphere, including but not limiting to, a rich variety of physical processes and self-consistent neutral-ion coupling. MENG ET AL.


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WP-GITM has limitations and could be potentially improved. For example, the embedded analytical model assumes an ideal and isothermal atmosphere, which might not adequately describe the atmosphere below 100 km altitude. As a next step we will consider a stratified atmosphere based on the neutral density, wind, and temperature profiles from empirical atmospheric models. In addition, the Cartesian coordinate system adopted by the analytical model is not optimal for a large simulation region when the surface curvature of the Earth is not negligible; the input tsunami waves for the simulation presented in this paper are greatly simplified compared to actual tsunami waves. We will study the impacts of these limitations and refine the model and simulations accordingly. We also plan to include acoustic waves in the analytical model to account for ionospheric signatures due to earthquakes and volcanic eruptions. Acknowledgments Portions of this work were done at the Jet Propulsion Laboratory, California Institute of Technology, under contract with NASA. Funding for the research came from NASA’s Science Mission Directorate in Washington (ROSES NNH10ZDA001N-GEOIM and NNH07ZDA001N-ESI). The authors would like to acknowledge Aaron Ridley at the University of Michigan for beneficial discussions during the model development. The authors also thank J. H. King, N. Papatashvilli at AdnetSystems, NASA GSFC, and CDAWeb for providing the OMNI data (http://cdaweb.gsfc.nasa.gov/istp\_public/). GPS measurements used for this research were obtained from stations in the Plate Boundary Observation network. The computational resources were provided by the JPL high-performance computing. The Editor thanks two anonymous reviewers for their assistance in evaluating this paper.

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