Estimated Speed of Aves Ridge Solitons Packets by Analysis of Sequential Images from the Moderate Resolution Imaging Spectroradiometer (MODIS)

Estimated Speed of Aves Ridge Solitons Packets by Analysis of Sequential Images from the Moderate Resolution Imaging Spectroradiometer (MODIS) By Edwin Alfonso-Sosa, Ph. D. September 24, 2012 Recently, 250-m resolution MODIS images acquired by the Earth Observing System Terra and Aqua Satellites during sunglint conditions allowed us to survey high-frequency nonlinear internal solitary wave occurrences on a near-global scale (Christopher Jackson, 2007). It is possible to detect internal solitons packets leaving the generation area during fortuitous conditions: minimum cloud cover, near-specular reflectance pattern of sunlight off the ocean surface (sunglint) and strong oceanic stratification. On a few days of September 2012 all these favorable conditions concurred allowing us to track the movement of solitons packets across the Caribbean Sea. Some of the packets traveled 540 km from Aves Ridge toward Puerto Rico, exciting coastal seiches as was hypothesized by Chapman and Giese (1990). Others traveled toward Curacao and the Netherland Antilles. Two sets of sequential images were analyzed. The first set covers SEP 01-04 2012 (YD 245-YD 248) and the second set covers SEP 17-20 2012 (YD 261-YD 264). September is the peak month of the hurricane season, but luckily most of the tracks were far from the Caribbean Sea and the cloud cover was notably reduced. The first MODIS image shows four solitons packets west from Aves Ridge, they are named: Lopez245, Hollander245, Harris and the farthest is Forel. The suffix corresponds to the image yearday. For example, Lopez246 is the same soliton packet, but one day later. The traveled distance was measured by georefencing the images in Google Earth and using the application called ruler. Distance traveled measurements were calculated using only the lead soliton of each packet. We obtained 87 km for Lopez246. The time of each image comes from the metadata file. Time interval between successive images is 78300 seconds. Dividing travel distance by time interval we obtained a soliton speed of 1.11 m/s. Table 1 displays the calculated lead soliton celerity for Lopez and Hollander packets. A simple visual inspection of the sequential images shows an evolution within the wave packets. The solitons separation distance (SS) increases the wave packet width (WPW). The ratio of these two physical parameters, SS/WPW, follows a logarithmic curve for the Harris Packet (Figure 1). If we plot this ratio against the waves source distance we get a useful linear trend (Figure 2). Plotting the linear trends for each wave packet (of the first set) against the lead soliton distance allowed us to get a clear picture of packet evolution, as they move away from the source. The trend lines slope have a tendency to reduce their values as the packets move away from Aves Ridge (Figure 3). Plotting the slopes of the trend lines (Table 2) against the lead soliton distance from Aves Ridge shows a logarithmic decrease in the slope value, as we move away from the source (Figure 4). This evidence supports that the spreading of the solitons occurred just after passing over the Aves Ridge. The origin point for our distance measurements was selected at the southern tip of the prominent crest, the origin coordinates were: 14°03’ 12” N, 63°36’ 35” W. There are several MODIS images of internal solitary waves about 10-20 km east of this location moving west toward our origin position, these images show one or two solitary waves but not packets (see last MODIS image of this paper). These waves could be a lee wave before been released or a solitary wave generated at other ridge crest about 100 km East. Just after the solitary waves passed over the Aves Ridge the soliton packets appeared. It is interesting to note that the horizontal scale of soliton packet separation is of the order of 100 km. The second set of images shows packet Apel moving SW (237°) toward Curacao and the Netherland Antilles and packet Chapman moving NW (294°) toward Puerto Rico and the Dominican Republic. From the image analysis we obtained a speed of 0.81 m/s for the lead soliton of packet Apel. The lead soliton speed of packet Chapman ranged between 1.22 m/s and 1.75 m/s (Table 3). The estimated time of arrival (ETA) of the soliton packet to Puerto Rico is shown on Table 4. The true arrival time was mark as the start of large seiche oscillations (> 0.4 feet) in the tidal record of Magueyes Island (Figure 5). Our ETA’s were offset by 11 hours from the true arrival time (Table 5). One day later, a second package arrived and excited more large amplitude oscillations. Assuming an average package separation distance of 92.5 km, it is possible to estimate a speed of 0.97 m/s. In conclusion, our analysis of the second set of MODIS images revealed that soliton packages speeds ranged between 1.22 to 1.75 m/s, equivalent to a travel time of 3.6 to 5.1 days to reach Isla Magueyes, Puerto Rico. Top: Modis Image: LesserAntilles.2012245.aqua.721.250m (01/SEP/2012 17:30 UTC) Bottom: Modis Image: LesserAntilles.2012246.terra.721.250m (02/SEP/2012 15:15 UTC). Morell Susanto Lopez248 Modis Image: LesserAntilles_2012248_terra_721_250m (04/SEP/2012 15:00 UTC). Table1. Traveled distance and soliton celerity based on multiple image analysis. Wave packet name Lopez246 Hollander246 Lopez248 Time Lead Traveled Interval soliton between distance separation (km) Images (km) (s) 87 70 134.6 7 9 11 78300 78300 171900 Lead soliton celerity (m/s) 1.11 0.89 0.78 Figure 1. Ratio between Soliton Separation (SS) and Wave Packet Width (WPW) for each soliton in the packet. Figure 2. Ratio SS/WPW for each soliton versus distance from source. Figure 3. Ratio SS/WPW for eight soliton packets on three different days. The trend lines slope have a tendency to reduce their values as the packets move away from the source. Table2. Trend line slope and R-squared for each soliton packet. Wave Packet Name Lead soliton distance from source Lopez245 Lopez246 Hollander245 Susanto Hollander246 Harris Lopez248 Forel 22.9 99.29 122.78 166.29 189.57 228.26 243.6 265.38 Slope 0.0229 0.0091 0.0065 0.0033 0.0042 0.0024 0.0016 0.0027 R-Squared 1 0.98 0.9863 0.7617 0.9463 0.9384 0.9317 0.8714 Figure 4. Logaritmic decrease in the slope. Top: MODIS image: LesserAntilles.2012261.aqua.721.250m. 17-SEP 2012 17:30 UTC. Bottom: MODIS image: LesserAntilles.2012262.terra.721.250m. 18-SEP-2012 15:10 UTC. Top: MODIS image: LesserAntilles.2012262.terra.721.250m. 18-SEP-2012 15:10 UTC. Bottom: MODIS image: LesserAntilles_2012263_aqua_250m. 19-SEP-2012 17:20 UTC. MODIS image: LesserAntilles.2012264.terra.250m. 20-SEP-2012 15:00 UTC. Table3. Traveled distance and soliton celerity based on multiple image analysis. The suffix in the wave packet name represents the yearday of the image. Wave packet name Traveled distance (km) Apel261 Apel262 Chapman262 Chapman263 Chapman264 62.96 114.68 136.55 Lead soliton separation (km) Distance from Aves Ridge (km) 7 9.84 6.24 4.14 1.69 174 236.96 116.26 230.94 367.49 Time Interval between Images (s) Soliton Celerity (m/s) 78000 0.81 94200 78000 1.22 1.75 Table4. Estimated Time of Arrival (ETA) based on soliton celerity versus the true arrival time of the first wave packet. Wave Packet Name Distance to Run (km) Travel Time (d) Chapman263 309.1 2.94 Chapman264 172.5 1.14 Estimated Time of Arrival (ETA) 9/22/12 15:51 9/21/12 18:22 Arrival of First Packet 9/22/12 5:12 9/22/12 5:12 Arrival minus ETA (h) -10.7 10.8 Figure5. Water Level at Magueyes Island shows large amplitude coastal seiches excited by the arrival of two soliton packets. First excitation was observed on 20120922 05:12 GMT and the second on 20120923 07:36 GMT. Table5. Estimated soliton celerity based on the time interval between the arrivals of two soliton packets responsible for the seiche excitation. Time Interval between Packets (d) Time Interval between Packets (s) Average Distance between Packets (km) Soliton Celerity (m/s) 1.1 95040 92.5 0.973 MODIS image: LesserAntilles.2010091.terra.721.250m. April 1, 2010 14:55 UTC References Alfonso-Sosa, E., 2011. ¿Dónde están los solitones? : mecanismo necesario para explicar los seiches costeros en la Isla Magueyes. Reprint 12851, Marine Science Collection, UPR-RUM General Library. 11 pp. Christopher Jackson, 2007. Internal wave detection using the Moderate Resolution Imaging Spectroradiometer (MODIS). JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 112, C11012, doi:10.1029/2007JC004220. Giese, G.S., Chapman, D.C., Black, P.G., Fornshell, J.A., 1990. Causation of large-amplitude coastal seiches on the Caribbean coast of Puerto Rico. Journal of Physical Oceanography 20, 1449-1458