# Evaluating HF Coastal Radar Site Performance for Tsunami Warning

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Radar Current Velocity Mapping

#### 2.1. Antenna Size

^{®}, a commercially available HF radar, involves two crossed loops mounted inside a dome, see Figure 2, and a coaxially aligned vertical monopole or dipole element. Direction finding is based on the orthogonal patterns of the loops. Even when patterns are distorted, their measurement after installation allows accurate bearing estimates. See [18] for more detail.

#### 2.2. Signal Propagation

#### 2.3. Antenna Location vs. Propagation

## 3. Modeling Tsunami Flow

#### 3.1. Tsunami Features in the Near-Field

#### 3.2. Simple Models

#### 3.2.1. Modeling for Water with Near-Constant Depth

^{2}).

- The “hump” of water we choose is the positive-going half of a cosine wave.
- Vertical flow at the bottom where z = D is zero (the bottom boundary condition).

#### 3.2.2. Modeling for Slowly Changing Water-Depth

#### 3.3. Modeling Near-Field Tsunami When Depth Change is Sharp

#### 3.3.1. Hydrodynamic Equations

#### 3.3.2. Partial Differential Equation for Tsunami Wave Height

#### 3.3.3. PDE Solution Using MATLAB™

#### PDE Solution Domain

#### Boundary Conditions

#### Initial Conditions

#### Denormalization

#### Depiction of Outputs/Movies

## 4. Band-Representation of Simulated Tsunami Velocities and Heights

## 5. Evaluation of Radar Sites for Tsunami Detection Using Simulated Tsunami Velocities

#### 5.1. Site-Evaluation Method

_{Sim}).

_{Site}over the 5-h time period.

_{sim}are multiplied by a factor F and added to V

_{Site}to produce combined velocities V

_{comb}, which are analyzed to produce q-factors, using the tsunami detection algorithm. This is repeated for a range of increasing values of the factor F, representing increasing tsunami intensity. The minimum value of F (F

_{detect}) is sought that will lead to detection of the q-factor peak. Tsunami heights corresponding to the q-factor values F

_{detect}are then calculated. These define the minimum height of a tsunami that can be detected at that radar site.

#### 5.2. Application of the Site-Evaluation Method at BRNT

_{Site})

_{comb}were created by multiplying the simulated band-velocities by a factor F and adding them to the site velocities, which are then analyzed to give band velocities and q-factors. Each q-factor value obtained comes from analysis of four adjacent spectral sidebands. The factor F was increased to a value F

_{detect}which resulted in an acceptable detection of the q-factor peak, with a q-factor value greater than the limit of 400 set for BRNT. Figure 11 shows the resulting band velocities V

_{comb}and q-factors for the same 5-h time window shown in Figure 10.

## 6. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- McGehee, D.; McKinney, J. Tsunami detection and warning capability using nearshore submerged pressure transducers—case study of the 4 October 1994 Shikotan tsunami. In Proceedings of the 4th International Tsunami Symposium, IUGG, Boulder, CO, USA, 2–14 July 1995; pp. 133–144. [Google Scholar]
- Milburn, H.M.; Nakamura, A.I.; Gonzalez, F.J. Real-time tsunami reporting from deep ocean. In Proceedings of the OCEAN96 MTS/IEEE International Conference Fort Lauderdale, Fort Lauderdale, FL, USA, 23–26 September 1996; pp. 390–394. [Google Scholar]
- Mofjeld, H.; Titov, V.; Gonzalez, F.; Newman, J. Analytic Theory of Tsunami Wave Scattering in the Open Ocean with Application to the North Pacific. Available online: https://repository.library.noaa.gov/view/noaa/11006/noaa_11006_DS1.pdf (accessed on 27 September 2019).
- Gonzalez, F.J.; Milburn, H.M.; Bernard, E.N.; Newman, J.C. Deep-Ocean Assessment and Reporting of Tsunamis (DART): Brief Overview and Status Report. Available online: https://nctr.pmel.noaa.gov/Pdf/dart_report1998.pdf (accessed on 22 November 2019).
- Shimizu, K.; Nagai, T.; Lee, J.H.; Izumi, H.; Iwasaki, M.; Fujita, T. Development of real-time tsunami detection system using offshore water surface elevation data. In Proceedings of the Techno-Ocean 2006—19th JASNAOE Ocean Engineering Symposium, Kobe, Japan, 19 October 2006; p. 24. [Google Scholar]
- Beltrami, G.M. An ANN algorithm for automatic, real-time tsunami detection in deep-sea level measurements. Ocean Eng.
**2008**, 35, 572–587. [Google Scholar] [CrossRef] - Nagai, T.; Shimizu, K. Basic design of Japanese nationwide GPS buoy network with multi-purpose offshore observation system. J. Earthq. Tsunami
**2009**, 3, 113–119. [Google Scholar] [CrossRef] - Bressan, L.; Tinti, S. Detecting the 11 March 2011 Tohoku tsunami arrival on sea-level records in the Pacific Ocean: Application and performance of the Tsunami Early Detection Al10 gorithm (TEDA). Nat. Hazards Earth Syst. Sci.
**2012**, 12, 1583–1606. [Google Scholar] [CrossRef] - Di Risio, M.; Beltrami, G.M. Algorithms for automatic, real-time tsunami detection in wind-wave measurements: Using strategies and practical aspects. Procedia Eng.
**2014**, 70, 545–554. [Google Scholar] [CrossRef] - Cecioni, C.; Bellotti, G.; Romano, A.; Abdolali, A.; Sammarco, P.; Franco, L. Tsunami early warning system based on real-time measurements of hydro-acoustic waves. Procedia Eng.
**2014**, 70, 311–320. [Google Scholar] [CrossRef] - Chierici, F.; Embriaco, D.; Pignagnoli, L. A new real-time tsunami detection algorithm. J. Geophys. Res. Oceans
**2017**, 122, 636–652. [Google Scholar] [CrossRef] - Available online: https://en.wikipedia.org/wiki/2018_Sunda_Strait_tsunami (accessed on 27 September 2019).
- Lipa, B.; Parikh, H.; Barrick, D.; Roarty, H.; Glenn, S. High Frequency Radar Observations of the June 2013 US East Coast Meteotsunami. Nat. Hazards
**2013**. [Google Scholar] [CrossRef] - Barrick, D.E. A coastal radar system for tsunami warning. Remote Sens. Environ.
**1979**, 8, 353–358. [Google Scholar] [CrossRef] - Lipa, B.; Barrick, D.; Isaacson, J. Coastal Tsunami Warning with Deployed HF Radar Systems, Tsunami, Mohammad Mokhtari (Ed.), InTech. 2016. Available online: http://www.intechopen.com/books/tsunami/coastal-tsunami-warning-with-deployed-hf-radar-systems (accessed on 22 November 2019).
- Titov, V.; González, F. Implementation and Testing of the Method of Splitting Tsunami (MOST) Model; NOAA Tech. Memo. ERL PMEL-112 (PB98-122773); NOAA/Pacific Marine Environmental Laboratory: Seattle, WA, USA, 1997; p. 11.
- Barrick, D.E.; Evans, M.W.; Weber, B.L. Ocean Surface Currents Mapped by Radar. Science
**1977**, 198, 138–144. [Google Scholar] [CrossRef] [PubMed] - Lipa, B.J.; Barrick, D.E. Least-Squares Methods for the Extraction of Surface Currents from CODAR Crossed-Loop Data: Application at ARSLOE. IEEE J. Ocean. Eng.
**1983**, 8, 226–253. [Google Scholar] [CrossRef] - Available online: http://cordc.ucsd.edu/projects/mapping/maps/ (accessed on 22 November 2019).
- Kinsman, B. Wind Waves; Chapter 5; Prentice-Hall, Inc.: Englewood Cliffs, NJ, USA, 1965; 874p. [Google Scholar]
- Temam, R. Navier–Stokes Equations: Theory and Numerical Analysis; Elsevier Science Publishers: New York, NY, USA, 1984. [Google Scholar]
- The MathWorks, Inc. Partial Differential Equation Toolbox User’s Guide—MATLAB; Version 1.0.15; The MathWorks, Inc.: Natick, MA, USA, 2009; 317p. [Google Scholar]

**Figure 1.**Sketch of SeaSonde

^{®}radar operating at the coast, employing a single-mast transmit/receive antenna.

^{®}indicates a Registerd Trademark.

**Figure 2.**Photo of a HF surface-wave radars (HFSWR) SeaSonde radar operating at the coast employing a single-mast transmit/receive antenna. The half-dome contains the two crossed-loop receive antennas required for bearing angle measurement.

**Figure 3.**Geometry illustrating partial differential equations (PDE) solution off New Jersey, centered on Brant Beach (designated BRNT).

**Figure 4.**Map of simulated heights/velocities for Brant Beach, New Jersey. In this map, the height of the wave is shown by color (see the color bar at the right), while the arrows represent particle (orbital) velocity. The largest vectors correspond to currents of ~1.0 m/s.

**Figure 5.**BRNT simulated radial current velocities and the area-bands selected for the analysis which are 2 km wide and approximately parallel to the depth contours. The largest vectors correspond to currents of ~1.0 m/s.

**Figure 6.**Two-kilometer area-band velocity components V

_{Ref}calculated from the simulated radials plotted versus time in hours. Distance offshore: blue 4–6 km; red 6–8 km; black 8–10 km; green 10–12 km; (a)/(b) velocity components perpendicular/parallel to the area-band boundary.

**Figure 7.**Simulated velocities signaling the tsunami arrival. Area-band velocity components plotted versus time in hours: Distance offshore: blue 4–6 km; red 6–8 km; black 8–10 km; green 10–12 km; (

**a**) velocity components perpendicular to the area-band boundary (

**b**) velocity components parallel to the area-band boundary.

**Figure 8.**Radar observations of 13 June 2013 band-velocities averaged over 12 min, plotted versus time (hours UTC from 13 June 2013, 17:09 meteotsunami): red 4–6 km; black 6–8 km; green 8–10 km; blue 10–12 km; maroon 12–14 km; yellow 14–16 km; cyan 16–18 km.

**Figure 9.**Simulated tsunami heights averaged over area-bands. Distance offshore: blue 4–6 km; red 6–8 km; black 8–10 km; green 10–12 km.

**Figure 10.**Radial band velocities obtained every 2 min from measured BRNT radar cross spectra plotted vs. time (hours from May 30, 2019, 01:38 UTC) for bands: blue 2–4 km; red 4–6 km; black 6–8 km; green 8–10 km. (

**a**)Velocity components perpendicular to the band boundary. (

**b**) Velocity components are parallel to the band boundary.

**Figure 11.**Radial area-band velocities and q-factors from combined BRNT CSQs for F

_{detect}= 0.5, plotted vs. time (hours from 30 May 2019, 01:38 UTC): (

**a**) Velocity components perpendicular to the band boundary; blue 2–4 km; red 4–6 km; black 6–8 km; green 8–10 km; (

**b**) Velocity components parallel to the band boundary; blue 2–4 km; red 4–6 km; black 6–8 km; green 8–10 km; (

**c**) Perpendicular q-factors; blue 2–10 km; red 4–12 km; black 6–14 km; green 8–16 km. (

**d**) Parallel q-factors; blue 2–10 km; red 4–12 km; black 6–14 km; green 8–16 km.

**Figure 12.**Tsunami height required for detection plotted vs. date/time for bands: blue 2–4 km; red 4–6 km; black 6–8 km; green 8–10 km.

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Lipa, B.; Barrick, D.; Isaacson, J.
Evaluating HF Coastal Radar Site Performance for Tsunami Warning. *Remote Sens.* **2019**, *11*, 2773.
https://doi.org/10.3390/rs11232773

**AMA Style**

Lipa B, Barrick D, Isaacson J.
Evaluating HF Coastal Radar Site Performance for Tsunami Warning. *Remote Sensing*. 2019; 11(23):2773.
https://doi.org/10.3390/rs11232773

**Chicago/Turabian Style**

Lipa, Belinda, Donald Barrick, and James Isaacson.
2019. "Evaluating HF Coastal Radar Site Performance for Tsunami Warning" *Remote Sensing* 11, no. 23: 2773.
https://doi.org/10.3390/rs11232773