Journal of Sensors

Volume 2016 (2016), Article ID 2750862, 14 pages

http://dx.doi.org/10.1155/2016/2750862

## GNSS-R Delay-Doppler Map Simulation Based on the 2004 Sumatra-Andaman Tsunami Event

Faculty of Engineering and Applied Science, Memorial University, St. John’s, NL, Canada A1B 3X5

Received 20 March 2015; Revised 19 June 2015; Accepted 29 June 2015

Academic Editor: Jose C. Nieto-Borge

Copyright © 2016 Qingyun Yan and Weimin Huang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

A new method for simulating Global Navigation Satellite System-Reflectometry (GNSS-R) delay-Doppler maps (DDMs) of a tsunami-dominant sea surface is presented. In this method, the bistatic scattering Z-V model, the sea surface mean square slope model of Cox and Munk, and the tsunami-induced wind perturbation model are employed. The feasibility of the Cox and Munk model under a tsunami scenario is examined by comparing the Cox and Munk model based scattering coefficient with the Jason-1 measurement. A good consistency between these two results is obtained with a correlation coefficient of 0.93. After confirming the applicability of the Cox and Munk model for a tsunami-dominated sea, this study provides the simulations of the scattering coefficient distribution and the corresponding DDMs of a fixed region of interest before and during the tsunami. In the final analysis, by subtracting the simulation results that are free of tsunami from those with presence of tsunami, the tsunami-induced variations in scattering coefficients and DDMs can be clearly observed. As a result, the tsunami passage can be readily interpreted.

#### 1. Introduction

A tsunami is a special ocean event that manifests its characteristics in terms of high propagation speed in the deep sea and extremely high wave height nearshore. It has been widely recognized that tsunamis are one of the worst natural hazards. For example, the Sumatra-Andaman tsunami that occurred in 2004 claimed many lives and caused tremendous damage to several countries [1]. Therefore, tsunami detection is especially important.

The conventional buoy measurement is a costly and inefficient method to detect tsunamis due to its high expense and low coverage [1]. The satellite altimeter may provide some direct information about the tsunami such as sea surface height (SSH) and the radar backscattering coefficient. For example, Jason-1 satellite altimeter encountered the 2004 Sumatra-Andaman tsunami on its path 109 for cycle 129, thereby offering valuable data on tsunami measurement [2]. However, only a handful of definitive SSH changes due to a tsunami event have been measured out of more than 150 documented tsunami events since the launch of the TOPEX/Poseidon satellite altimeter in 1992 [3]. This is mainly because of the limited coverage of the satellite altimeter [2]. Recently, GNSS-R emerged as an efficient and accurate technique for ocean remote sensing due to its advantages in temporal and spatial coverage and immunity to weather effects [4]. Those benefits of the application of GNSS-R may provide a promising solution to tsunami remote sensing. Moreover, manifestations of a tsunami in the deep ocean have been investigated by a large amount of researchers, thereby laying a theoretical foundation for the GNSS-R-based deep sea tsunami detection. In 1996, tsunami-induced variations in sea surface roughness were first reported by Walker [5] and were given the name “tsunami shadow” based on observations of the darkened stripes along the tsunami front. Later, Godin [6] explained that the tsunami-induced changes in sea surface roughness are due to the tsunami-induced perturbations in sea surface wind speed. Based on these results, a theoretical model for the calculation of tsunami-induced sea surface wind velocity has been developed in [2].

In addition, recent research has made significant development on GNSS-R DDM-based sea surface wind remote sensing (e.g., [7–9]). These works have also contributed to the DDM simulation in this paper for a tsunami-dominated sea surface, which is based upon the tsunami-perturbed sea surface wind speed. There are a few reports (e.g., [1, 10, 11]) in the literature about the GNSS-R altimetry-based tsunami detection. However, there is no publication on tsunami detection from GNSS-R DDM, to the authors’ knowledge. In this paper, a process for simulating tsunami-dominant sea surface DDM is proposed. This method is based on the Zavorotny and Voronovich (Z-V) bistatic scattering model [12], the Cox and Munk sea surface mean square slope model [13], and the tsunami-induced wind speed perturbation model [2]. Followed by the introduction to this method, the feasibility of the Cox and Munk model [13] under a tsunami scenario is examined by comparing the simulated scattering coefficient with the Jason-1 measurement. After verifying its applicability, the tsunami DDM simulation can be achieved through inputting the background wind speed over the sea surface and the tsunami-induced sea surface change. In this work, the simulation results before and during a tsunami over a region of interest are presented. Through analysis, the passage of the tsunami over this region can be interpreted based on the observation of tsunami-induced variations in scattering coefficient and DDMs. This work may provide some new support for the GNSS-R DDM-based tsunami detection in the future.

The remainder of this paper is organized as follows. The procedures of tsunami-dominant sea surface DDM simulation are described in Section 2. The verification of the Cox and Munk model under a tsunami scenario followed by the simulation results is presented in Section 3. Conclusions are presented in Section 4.

#### 2. Model Implementation and Simulation Process

The Cox and Munk model [13] and the Z-V model [12] have already been successfully applied to the GNSS-R DDM-based sea surface wind sensing (e.g., [7, 14]). The Z-V model depicts the scattered GPS signal power as a function of time delay and Doppler frequency shift, the transmitter elevation angle, and the receiver height as well as the surface scattering coefficient (). The Cox and Munk model substantiates an empirical relationship between the wind speed at the height of 10 m above the sea surface () and the sea surface mean square slope (MSS). Consequently, the sea surface scattering coefficient is determined by MSS [7]. In summary, with knowledge of the corresponding DDM can be simulated by combining the Cox and Munk model and the Z-V model. With this in mind, the associated DDM simulation can be completed if the distribution of over a tsunami-dominant sea surface is available.

The Z-V model [12] can be described as follows: where is the time delay between the received signal and the local code replica, , when ; ; otherwise is the length of one code chip. Consider , is the coherent integration time, is the displacement vector of a surface point from the specular point (SP), is the antenna radiation pattern, and are the distances from a point on the ocean surface to the GNSS-R transmitter and receiver, represents the effective scattering surface area (glistening zone), and is the surface scattering coefficient.

With the exception of , the rest of the terms in (1) are usually known for a specific GNSS system and its geometry. Therefore, we mainly consider the scattering coefficient , which may be written as [7] where is the Fresnel reflection coefficient that depends on the local elevation angle, polarization, and the complex dielectric constant of sea water [7]; the scattering vector can be obtained with the locations of the transmitter, receiver, and corresponding surface point; is the ocean surface slope, denoted hereafter as . is the slope Probability Density Function (PDF) of the ocean surface gravity wave which is believed to be subject to Gaussian distribution with wind-dependent upwind variance and crosswind variance [15]. It is worth mentioning that tsunami waves are gravity waves. is expressed as [7]where is the angle between the up-down wind direction and the -axis. Subsequently, the clean sea surface mean square slope model of Cox and Munk [13] is introduced to link the wind speed and wind direction to the upwind and crosswind variances, as where

Following similar steps as presented in [7, 14], the DDMs can be readily simulated with the knowledge of , based on the Cox and Munk model [13] and the Z-V model [12] for a tsunami-free sea surface.

For a tsunami-dominant sea surface, the effective wind speed can be derived from the tsunami-induced wind speed perturbation model [2], that is, the so-called Godin model. This model was proposed based on the observation data of “tsunami shadow” from the October 4, 1994, Hokkaido tsunami [5]. The theoretical derivation of this model and its validation based on simulation were presented in [2]. Moreover, this model has been successfully applied in the simulation of radar backscattering strength over a tsunami region (e.g., [2, 3]). The tsunami-induced variations in radar backscattering strength estimated based on the Godin model were consistent with the Jason-1 measurement [2]. Thus, the Godin model is employed here to determine the effective wind speed during a tsunami period. This model shows that the effective wind speed during a tsunami event depends on tsunami parameters and differs from the background wind speed by a factor of [2], and where , , is the height of the background logarithmic boundary layer, is the sea surface height change due to tsunami, is the tsunami phase speed, where is the acceleration due to gravity, is the depth of sea, and where represents the roughness length and is tsunami period.

By employing these models, the tsunami DDMs can be simulated with different tsunami parameters and background wind speed.

#### 3. Simulation Results

In this section, feasibility of the Cox and Munk model under a tsunami scenario is tested first. Then, the parameters associated with tsunami DDM simulation are set. After that, the tsunami DDM simulation results are presented.

##### 3.1. Feasibility of the Cox and Munk Model under a Tsunami Scenario

The Jason-1 satellite altimeter encountered the tsunami on the morning of December 26, 2004 [2] (shown in Figure 1). It recorded radar backscattering coefficient and sea surface wind speed, thereby offering an opportunity to study the wind speed and during the tsunami event. Before exerting the tsunami DDM simulation, the feasibility of the Cox and Munk model under a tsunami event should be examined. By employing the Cox and Munk model, the of a tsunami-dominant sea surface can be simulated with the knowledge of over the corresponding region. Based on this, a comparison between the Jason-1 measured and the simulated can be made.