Research Article  Open Access
GNSSR DelayDoppler Map Simulation Based on the 2004 SumatraAndaman Tsunami Event
Abstract
A new method for simulating Global Navigation Satellite SystemReflectometry (GNSSR) delayDoppler maps (DDMs) of a tsunamidominant sea surface is presented. In this method, the bistatic scattering ZV model, the sea surface mean square slope model of Cox and Munk, and the tsunamiinduced 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 Jason1 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 tsunamidominated 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 tsunamiinduced 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 SumatraAndaman 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, Jason1 satellite altimeter encountered the 2004 SumatraAndaman 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, GNSSR 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 GNSSR 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 GNSSRbased deep sea tsunami detection. In 1996, tsunamiinduced 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 tsunamiinduced changes in sea surface roughness are due to the tsunamiinduced perturbations in sea surface wind speed. Based on these results, a theoretical model for the calculation of tsunamiinduced sea surface wind velocity has been developed in [2].
In addition, recent research has made significant development on GNSSR DDMbased sea surface wind remote sensing (e.g., [7–9]). These works have also contributed to the DDM simulation in this paper for a tsunamidominated sea surface, which is based upon the tsunamiperturbed sea surface wind speed. There are a few reports (e.g., [1, 10, 11]) in the literature about the GNSSR altimetrybased tsunami detection. However, there is no publication on tsunami detection from GNSSR DDM, to the authors’ knowledge. In this paper, a process for simulating tsunamidominant sea surface DDM is proposed. This method is based on the Zavorotny and Voronovich (ZV) bistatic scattering model [12], the Cox and Munk sea surface mean square slope model [13], and the tsunamiinduced 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 Jason1 measurement. After verifying its applicability, the tsunami DDM simulation can be achieved through inputting the background wind speed over the sea surface and the tsunamiinduced 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 tsunamiinduced variations in scattering coefficient and DDMs. This work may provide some new support for the GNSSR DDMbased tsunami detection in the future.
The remainder of this paper is organized as follows. The procedures of tsunamidominant 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 ZV model [12] have already been successfully applied to the GNSSR DDMbased sea surface wind sensing (e.g., [7, 14]). The ZV 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 ZV model. With this in mind, the associated DDM simulation can be completed if the distribution of over a tsunamidominant sea surface is available.
The ZV 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 GNSSR 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 winddependent 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 updown 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 ZV model [12] for a tsunamifree sea surface.
For a tsunamidominant sea surface, the effective wind speed can be derived from the tsunamiinduced wind speed perturbation model [2], that is, the socalled 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 tsunamiinduced variations in radar backscattering strength estimated based on the Godin model were consistent with the Jason1 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 Jason1 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 tsunamidominant sea surface can be simulated with the knowledge of over the corresponding region. Based on this, a comparison between the Jason1 measured and the simulated can be made.
Figure 2(a) illustrates the Jason1 measured sea surface wind speeds (solid line) over the range of (6.00°S, 83.60°E) to (4.99°N, 87.54°E) with the presence of the tsunami leading wave front. For the simulation, some assumptions are made below:(1)The GNSSR transmitter, receiver, and the SP are set on the same line that is also perpendicular to the sea surface.(2)The SP follows the Jason1 ground track.(3)The Jason1 measured is uniform along tsunami wave front.
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The first assumption is required to simulate the Jason1 backscattering scenario. The second assumes that the GNSSR system and Jason1 monitored this region at the same time. The last one aims at forming a twodimensional wind speed distribution over the glistening zone.
The size of GNSSR glistening zone is about 200 km by 200 km. Through inputting the wind speeds that are interpolated using the Jason1 measured over sea surface, the scattering coefficient can therefore be simulated. Here, only the at SP which follows the Jason1 ground track is recorded and compared with the Jason1 measurements. Figure 2(b) shows the measured by Jason1 and the simulated by the Cox and Munk model. A good consistency between the measured and the simulated can be observed with a correlation coefficient of 0.93. In Figure 2(b), the simulated scattering coefficients for GNSSR seem to be slightly overestimated compared to the measurement by Jason1. This is mainly due to the difference in the operating frequencies of GNSSR (1.5 GHz, i.e., Lband) and Jason1 (5.4 GHz, i.e., Cband). The average difference of the scattering coefficient is about 1.33 dB and this is consistent with the analysis in [16], where the difference of between L and Cband measurements is found to be about 2 dB. Therefore, the feasibility of the Cox and Munk model on the tsunami DDM simulation is confirmed.
3.2. Simulation Scenario Parameters
Based on the analysis above, it can be concluded that the of a tsunamidominant sea surface can be simulated via the Cox and Munk model [13]. Thus, the tsunami DDMs can be simulated through the ZV model [12], the Cox and Munk model [13], and the tsunamiinduced wind speed perturbation model [2] with reliability.
Here, to facilitate the simulation, the typical empirical values are adopted in alignment with those in [2]; that is, min, m, and m. If the SSH change due to tsunami and the background wind speed are known, the effective wind speed over a tsunami surface can therefore be determined by implementing the tsunamiinduced wind speed perturbation model [2].
The SSH measured by Jason1 on cycle 109 during the tsunami event is subtracted by the average SSH observed over the exactly same ground track on cycles 108 and 110, and the difference is regarded as tsunamiinduced SSH change (shown in Figure 2(c)). This process is in accord with [17]. Besides, it has been reported in [17] that the tsunamiinduced SSH change over the range from (5.00°S, 83.96°E) to (1.00°N, 86.12°E) can be well fitted by a sine wave with a wavelength of 580 km and an amplitude of 60 cm, as shown by a dash line in Figure 2(c). Alternatively, the sine model is treated as another form of input for reference. In addition, is assumed to distribute uniformly along the contours of the tsunami leading wave front, which are concentric circles with a center at the epicenter (3.4°N, 94.2°E).
The over the region under investigation measured by QuikSCAT on its orbit 28744 is considered to be the background wind speed. The data was recorded around 45 min before the earthquake appeared, which means this measurement is totally free of the tsunami influence. Therefore, it is reasonable to use the QuikSCAT measurement as the background . The effective is calculated using only the QuikSCAT measurement over the Jason1 ground track and is shown in Figure 2(a). Difference between the modelled and measured wind speeds can be seen in Figure 2(a). This is because the modelled wind speed significantly relies on the background wind speed (i.e., before the appearance of tsunami). The only available background wind speed data of the region under investigation, immediately before the tsunami, was measured by QuikSCAT. However, the data was collected 45 min before the earthquake happened. Moreover, Jason1 flew over the same region 115 min after the earthquake appeared. Thus, a time gap of 160 min exists between the measured and the modelled wind speeds. As we know, wind speed may change significantly after two hours. This may explain the difference between the modelled and measured wind speeds.
The parameters mentioned above are tabulated in Table 1. In terms of GNSSR simulation scenario, the parameters are kept the same as those in [18], also shown in Table 1.

In order to manifest a unique influence of the tsunami on GNSSR sea surface remote sensing in this work, a continuous detection over a fixed region is assumed. To achieve this, both the transmitter and the receiver are set fixed over time. In this fashion, the variations caused by the geometry change of GNSSR system will be eliminated as well, which allows a more direct observation of tsunami effect. The region of our interest is set around (6.0081°S, 83.6019°E) with a size of 200 km by 200 km. The first simulation result was conducted for 02:55:22 UT. The study region at this time was tsunamifree. Therefore, this first simulation result is considered as the initial baseline for the following results. Meanwhile, the SSH change in Figure 2(c) is regarded as initial distribution. The initial simulation only depends on the background over this region measured by QuikSCAT. However, within a few minutes, this region experienced a tsunami passage. The tsunamiinduced wind speed perturbation model must be employed with the tsunami entering into this region. The effective will be calculated based on this model with the knowledge of background and .
As we have assumed m, the tsunami propagation speed can thus be approximated by 200 m/s. Meanwhile, the initial distribution of over space is known. For this reason, the over this region at each moment can be easily deduced according to the distance and tsunami propagation speed. Then, the effective at different time can also be determined.
3.3. Results
The spatial distribution of tsunamiinduced SSH change based on a sine wave model is shown in Figure 3.
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Figure 4 displays the simulated by adopting the fitted sine wave model as input . The time gaps between the initial detection in Figure 4(a) and those from Figures 4(b) to 4(f) are 9.17 min, 22.92 min, 36.67 min, 50.42 min, and 64.17 min, respectively. Figure 5 shows the simulated DDMs corresponding to the scattering coefficient maps in Figure 4. In order to manifest the tsunamiinduced variations in and DDMs, the simulation results with tsunami are subtracted by the initial result that contains no tsunami; that is, subplots (b)–(f) in both Figures 4 and 5 are subtracted by the corresponding subplot (a). The resultant scattering coefficient and DDM differences are displayed in Figures 6 and 7, respectively. Although the overall shapes in each subplot of Figure 4 or Figure 5 are similar, variations still can be observed. From Figure 6, the variations caused by the tsunami are found to be about dB. This result is consistent with the analysis in [2].
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Intuitively, an increase in will lead to a reduction in factor according to (6). On the other hand, a decrease in will contribute to an increase in . On the whole, the variations in are coincident with the changes of . Therefore, the passage of the tsunami can be identified from Figure 6: (a) the leading front appears first; (b) then comes the crest; (c) the transition region between the crest and the trough approaches later; (d) after that, the trough emerges; and (e) finally, the tsunami wave propagates out of this region with only a small portion of the tail remaining. The variations in are approximately proportional to the tsunamiinduced SSH changes. The tsunamiinduced variations in DDMs can be observed in Figure 7.
The spatial distribution of tsunamiinduced SSH change based on Jason1 measurements is shown in Figure 8. Since the variations due to tsunami are not so obvious in simulated scattering coefficient maps and DDMs, only the differences between the results with and without tsunami are displayed in Figures 910. Due to the nonidealsine distribution of measured , these simulation results differ slightly from those based on fitted sine wave input . However, with a close observation of Figure 9, the variations in are also consistent with the distribution of measured .
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4. Conclusion
In this work, a process is proposed to simulate the DDM of a tsunamidominant sea surface. The ZV model, the Cox and Munk model, and the tsunamiinduced wind speed perturbation model are employed in this method. The feasibility of Cox and Munk model under the tsunami scenario is confirmed (a correlation coefficient of 0.93 between the simulated and measured is observed). After verifying the applicability of the Cox and Munk model for a tsunamidominated sea, and DDMs are simulated with two different tsunamiinduced SSH change inputs, that is, Jason1 measurement and fitted sine wave model. The variations caused by the tsunami are found to be about dB, which is consistent with the result in [2]. Finally, by studying the tsunamiinduced variations in , the passage of tsunami can be identified. In the future, tsunami parameters may be retrieved from the simulated DDMs of tsunamidominant sea surface. It is also necessary to further validate the proposed method using collected GNSSR data and corresponding measured background and effective wind speed dataset during a tsunami event. However, this study is not possible today as the available data for this research is limited. This may become possible with the launch of new spaceborne GNSSR missions, for example, TechDemoSat1 and Cyclone GNSS (CYGNSS) [19].
Conflict of Interests
The authors declare that there is no conflict of interests regarding the publication of this paper.
Acknowledgments
This work was supported by the Natural Sciences and Engineering Research Council of Canada Discovery Grant (NSERC 4023132012) to Dr. Weimin Huang. The authors would like to thank C. Arbour for her editorial help on this paper.
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Copyright
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.