A novel observational technique to map surface ocean currents at high spatial resolution in narrow regions is developed. Low-altitude remote sensing using a digital camera suspended from a vessel-towed balloon is used to track trajectories of floating buoys deployed on the ocean. Surface-current velocities are thereafter computed by sequentially moving buoy locations on photo images converted into ground (Cartesian) coordinates. Field experiments were conducted in July and August 2013 using a balloon towed by a research vessel on the Seto Inland Sea. The image-derived currents were compared with those derived from buoy locations recorded by GPS receivers attached to each floating buoy. It was found that surface currents computed using GPS data contain unrealistic values arising from stochastic fluctuations in those data. However, the image-derived currents reproduced well convergent flows and a cyclonic eddy that accumulated foam and marine debris, as actually observed during the surveys. This performance is attributed to the fact that the image processing acts as a filter to remove erroneous buoy locations in computing surface currents. The estimated error was 4.1 cm s−1, sufficiently small to measure snapshots of surface coastal currents with magnitudes greater than several tens of centimeters per second.
Difficulty in coastal oceanographic studies mainly stems from the fact that conventional observation methods are inadequate to uncover coastal features such as internal waves and oceanic fronts, because these are strongly variable in both time and space. For instance, consider tidal front formation in coastal waters between thermally stratified and tidally mixed regions during summer. Although frontal locations are predicted well by the Simpson and Hunter (1974) parameter, tidal fronts are unstable in time because of rapidly growing frontal eddies along these dynamically unstable oceanic fronts. Such frontal eddies are critical in transporting nutrients from the mixed region to the subsurface layer in stratified regions; see the numerical modeling studies of Fukuda et al. (2006) and Sun and Isobe (2006). However, it is difficult to confirm the accuracy of these model products because hydrographic and current measurements of spatial (temporal) scale less than 1 km (a couple of days) are required to resolve coastal processes, and in situ coastal measurements with such fine spatiotemporal resolution have not been well established.
In contrast with satellite observations that are frequently unsuitable for coastal measurements because of coarse spatial (>1 km) and temporal resolutions as well as shading by clouds, aerial photography by aircraft (or helicopters) flying beneath the clouds has been a powerful tool to map oceanic features at fine resolution in coastal waters. In fact, these “low altitude” aerial photography methods have been adopted to observe various oceanic features such as wind waves (e.g., Dugan et al. 2001), oceanic fronts (visualized by debris, foam, whitecaps, and phytoplankton; e.g., Garvine 1974; Chelton et al. 2006; Ryan et al. 2014), sea ice (e.g., Tschudi et al. 2001; Perovich et al. 2002; Lu et al. 2010; Renner et al. 2013), and sea grass conditions (e.g., Robbins 1997; Kendrick et al. 2000; Moore et al. 2000; Lathrop et al. 2006, 2014).
However, aerial photography of surface currents is still an immature observational technique in coastal waters compared with open oceans, where satellite altimetry indirectly provides surface currents under the assumption of geostrophy. In the 1970s, Assaf et al. (1971) observed surface circulation based on aerial photographs of dye distributions, founding small-scale Langmuir cells within a several-hundred-meter square. However, this was a qualitative observation of the surface circulation, because it is difficult to map current vectors from dye distributions. To investigate the behavior of jellyfish patchiness in a bay, Magome et al. (2007) used aerial photographs of drifters deployed around the patchiness to compare jellyfish behavior with ambient currents. They examined the drifters once per hour from a Cessna plane within an area of 300 m × 300 m. Although the objective of their study was not to map surface currents, the present study is motivated by their photography, in which drifter locations were traced on images after georeferencing (shown later in section 2a). However, in addition to the substantial expense of aircraft use, we still encountered difficulties in measuring surface coastal currents using aerial photography. This is because aircraft, which cannot loiter above targets for a long period, are unlikely to take sequential aerial photographs with sufficiently fine temporal resolution for coastal currents that can vary even over a few minutes or hours. Moreover, it is difficult to find a relationship between aerial-derived photos and oceanic interior conditions, unless we conduct ship observations concurrently with that photography.
Like the airborne observations mentioned above, high-frequency (HF) radar that is a powerful alternative tool for remote sensing of coastal surface currents has a disadvantage. For instance, very high-frequency (VHF) radar (Haza et al. 2010) can cover a tens-of-kilometers square with a spatial resolution of a few hundred meters. However, both HF and VHF radars have a problem with immobility, so it is difficult to choose the most suitable observation site for radar observations. Current measurements in coastal waters are frequently required simultaneously with observations of physical (e.g., oceanic fronts), chemical (e.g., nutrient transport), and biological (e.g., jellyfish patchiness in Magome et al. 2007) phenomena. Thus, a critical factor in the design of current measurements is mobility to trace the aforementioned phenomena with fine spatiotemporal resolution.
To overcome the three disadvantages of the aforementioned observations (coarse resolution, asynchrony between aerial photography and ship observations, and immobility), we established a novel observational method to measure surface currents in coastal waters. Our study proposes a combination of aerial photography from a vessel-towed balloon equipped with a digital camera (balloon photography) and buoy-tracking experiments to map surface currents around coastal fronts and/or streaks. In this application, surface currents are computed based on trajectories of floating buoys with GPS receivers (GPS buoy). GPS buoys are a conventional technique familiar to oceanographers for measuring surface currents, although erroneous GPS data intermittently giving erroneous locations sometimes prevent accurate computation of the currents. However, we used GPS data from only several selected buoys, not for measuring surface currents but for processing the balloon photos (explained later as “projective transformation”; Magome et al. 2007). A novel aspect of the present study is that surface currents were computed using buoy trajectories overlaid on processed images. Those surface currents were computed in two ways for comparison. One way was determined conventionally, using trajectories from GPS data on all buoys, and the other was based on balloon photography with the projective transformation.
a. Aerial photography system for mapping surface currents
Surface-current velocities around a coastal front or streak were computed using balloon photography with the facilities below. In this aerial photography experiment, we used a digital camera (GR II, provided by Ricoh Imaging Company, Ltd., without a polarizer lens that takes an image of 3648 × 2736 pixels) suspended from a balloon of 5.5-m length, filled with helium gas. This “Sky Catcher” system was developed by MHI Ship and Ocean Engineering Co., Ltd. (Fig. 1a). The balloon was towed with a thin rope from a research vessel like a kite (see Kako et al. 2012 for details). A digital camera was attached inside a control box suspended at the bottom of the balloon. A researcher released the shutter and adjusted camera angles manually and remotely in both horizontal and vertical directions on the vessel. Aerial photographs of the sea surface were taken by the researcher who sought photo opportunities by watching an onboard color monitor. The GPS buoys were made from a thin polystyrene foam board (45 cm × 60 cm × 0.3 cm) painted red, yellow, green, and white, which are all readily detectable at the sea surface by eye (Fig. 1b). Each drifter had a polystyrene foam board with a 210-g weight acting as a drogue (45 cm × 30 cm × 0.5 cm) connected by a 15-cm-long tether, made of 1-cm-diameter polyethylene rope. The thin boards with drogue were designed to move beneath the sea surface in the absence of the projected area pushed directly by winds, and thus the GPS buoys were carried mostly by surface ocean currents. Nonetheless, our drogue was smaller than those designed for conventional coastal experiments, such as the U.S. Coastal Ocean Dynamics Experiment (Davis 1985). Therefore, the buoy trajectories are potentially subject to the action of wind. However, our field experiments were during calm days for safe operation of the balloon, which was vulnerable to strong winds. The wind speed had to be <1000 cm s−1 over the course of the operation. In fact, during our experiment, calm wind conditions have been recorded by the Yashima Observatory in Japan [Fig. 2; located at 61.4-m height from the sea surface; data were downloaded from JODC (2013)]. Each buoy had a single GPS receiver (six GPS-CS3K models from Sony Marketing Inc., and 18 M-241 wireless GPS loggers furnished by Holux Technology Inc.) on the board to record its location.
Aerial photographs are generally taken at oblique angles to the horizontal plane. Therefore, we had to convert images into ground (Cartesian) coordinates via geometric correction or georeferencing to determine the actual configuration and horizontal scale of coastal oceanic features. Thus, the projective transformation method developed by Magome et al. (2007) and Kako et al. (2012) was used for the georeferencing. Twenty-four GPS buoys were deployed around a coastal front and streak as markers required for the projective transformation of the aerial photographs [see the appendix or Kako et al. (2012) for the detailed procedure]. The location data of 5 of 24 GPS buoys with “correct” locations (shown next) were chosen as reference points for the projective transformation of each photograph.
These correct GPS data were selected through trial and error as explained below. GPS data from the five buoys that gave the smallest differences were regarded as correct. First, we arbitrarily determined the “origin point” outside the photos’ domain. Second, the projective transformation was conducted using five GPS buoys chosen arbitrarily on each photograph. Third, distances between the origin point and those buoys were computed in two ways, using either GPS data or locations on the processed image. Fourth, through trial and error, the projective transformation was repeated using various combinations of the five buoys until the differences in distances determined in the two ways all became <10 m. GPS data with difference >10 m were regarded as erroneous.
Surface currents were thereafter calculated by the remaining 19 buoy trajectories determined from their locations on the images following the projective transformation. For comparison, surface currents were again calculated using GPS data of these 19 buoys, which were regarded as Lagrangian drifters. The above-mentioned two sets of GPS buoy locations every 60 s provide both current velocities based on balloon photography and GPS data. The advantage of the balloon photography over the GPS data for mapping surface currents is that we can select several GPS buoys (5 in this case) for which location errors are minimal, and the locations of the remaining buoys (19 in this case) on the processed images yield trajectories (hence, surface-current velocities) as accurate as the above-selected GPS buoys.
b. Calibration of GPS receivers
We evaluated data fluctuations caused by the GPS receivers (calibration) before the field experiments mentioned in the next subsection. This is because these fluctuations can be regarded as measurement error of surface currents, regardless of the dataset (GPS data or images) used for computing the current velocities. In general, GPS receiver accuracy depends on product quality, the surroundings of the receivers, and weather (Han et al. 2001; Takano et al. 2011).
To evaluate the potential error of the GPS data, we set all 24 receivers at a fixed point on the ground and recorded anomalous distances fluctuating around the fixed point. The recorded distance-divided-by-time interval provides “erroneous velocities” that may be included in the surface-current velocities obtained from the actual ocean. A 3-s interval was chosen for recording, but the location data were subsampled every 60 s, similar to the interval used in the field experiments. Balloon photography in the actual ocean was done over the ocean, free of surrounding obstructions. This photography was done on clear-sky days, because the digital camera and control box were not waterproof. To be consistent with actual balloon photography, the GPS receivers were calibrated on a clear day in a broad athletic field free of obstructions. These environmental conditions are consistent with those present during our aerial photography experiment done over the open ocean on clear-sky days (the digital camera and control box were not waterproof). Twenty-four GPS receivers were set at the center of this field over the entire day to record their locations. The erroneous velocities were calculated using data from all 24 receivers.
c. Field experiment
To examine the capability of the balloon photography in mapping surface currents at fine resolution, field experiments were performed at Iyo Nada in the Seto Inland Sea of Japan (Fig. 2a), using the Research Vessel Isana of Ehime University. There were two experiments, on 25 July (enlarged in Fig. 2b) and 20 August (Fig. 2c) 2013. These observations were made under calm and clear weather conditions at spring tides. First, prior to the balloon photography, an oceanic front and streak were selected for the experiments by visually seeking convergence of marine debris and/or foam on the vessel (dots in Figs. 2b and 2c, determined by the balloon photography). Second, 10 stations across the debris/foam line were established at an interval of ~100 m to conduct conductivity–temperature–depth (CTD) sensor casts (see dots in Fig. 2a and colored squares indicating sea surface temperature in Figs. 2b and 2c). These CTD casts were made to confirm ocean hydrographic structures. Third, immediately after the CTD observations, 24 GPS buoys were deployed around the debris/foam lines at an interval ~10 m (shown by small open circles in Figs. 2b and 2c). As mentioned above, these GPS buoys were used not only for Lagrangian drifters to compute surface-current velocities by their trajectories, but also for markers to apply the projective transformation. Fourth, aerial photographs of the sea surface with GPS buoys were taken subsequently during 1124–1136 Japan standard time (JST; UTC + 9 h) 25 July and 1248–1254 JST 20 August. The balloon remained at ~200 m altitude throughout the experiments, providing images with an area of 100 m × 100 m. In total, 198 (83) photographs in the July (August) experiments were taken at about 3–4-s intervals by the researcher, who adjusted the camera angle manually on the vessel.
Figures 2b and 2c show that the debris/foam lines observed by the balloon photography (small dots in those figures) were near stations 5 and 6 on 25 July and stations 7 and 8 on 20 August, respectively. The CTD casts were initiated immediately after finding the debris/foam lines, and the period for completing the casts was relatively short (~30 min). Thus, we assumed approximately that the debris/foam lines found before the CTD casts were observed during the balloon photography period. However, the CTD stations were south of the debris/foam lines at distances < 1 km (Figs. 2b and 2c), because of the intense and complex surface currents in the observation areas.
d. Gridding surface currents
Current velocities along the trajectories of the GPS buoys were then gridded to depict a surface-current field. We adopted a method with a weighting function described in Kutsuwada (1998), who constructed a dataset of surface wind speed and wind stress fields. Although his weighting function depends on both space and time, our function depends only on space because of the very short duration of each experiment (<10 min). We calculated the velocities at each grid cell Vi,j (i and j denote grid locations in the zonal and meridional directions, respectively) with grid size 20 m in both zonal and meridional directions, as follows:
where υk (k = 1, 2, . . . , N) represents velocities along a GPS buoy trajectory and wk denotes the weighting function at the observation point. Term N observation points were chosen within the radius of influence (R = 100 m in the present study), beyond which velocity data were not used for the grid. The weighting function was computed using distances between the center of each grid cell (Xi, Yj) and data point (Xk, Yk) in ground coordinates, as follows:
This gridding was applied to both data observed by GPS receivers and buoy trajectories on images after the projective transformation.
a. Calibration of GPS receivers
GPS locations of all receivers were recorded every 60 s. Their locations and hence velocities clearly fluctuated around the mean location of those receivers, despite their being fixed in time on the ground (Fig. 3a). In this experiment, the mean location was regarded as the true one, under the assumption that the fluctuations were random over time. Figure 3a shows strong clustering around the mean location (i.e., the origin); 80% (99%) of the data were within a distance < 10 m (20 m) from that location. Dividing two consecutive locations by the time interval (60 s) gave an error estimate that could be included in the current velocities.
If the GPS data were perfectly correct, then the velocities computed from the fixed receivers would always be zero. However, this was not the case in the above-mentioned experiment. The maximum error measured by the GPS sensor was 28 m (47 cm s−1, computed using both zonal and meridional distances in Fig. 3a), which is considered typical for the sensors. Erroneous velocities are on average 10 cm s−1 with a standard deviation of 7 cm s−1. It is believed that the current velocities computed using GPS buoy trajectories were contaminated because of these errors.
As mentioned above, however, erroneous GPS data were not selected for processing images from balloon photography, because they were recognized as outliers of the 10-m criterion described in section 2a. Next, for evaluating the error in the computed velocities, GPS location data that exceeded thrice the standard deviation from the mean location (i.e., outliers) were also eliminated. The maximum (mean) error of the current speed was thereby reduced to 2.0 (0.4) cm s−1 (Fig. 3b), below which the current velocities computed by the balloon photography are unreliable. The standard deviation of the current speed ascertained using the GPS data was ±1.3 cm s−1. We believe that 2.0 cm s−1 is the unavoidable maximum error that may be contained in the current field stemming from the balloon photography, even if we use five selected buoys to determine the correct locations of projective transformation.
b. CTD observations
Temperature cross sections were constructed along two observation lines (Fig. 4) because, in the absence of major river mouths, water density (not shown) strongly depended on water temperature in the study area. The surface layer (top 20- and 50-m layers in July and August, respectively) is magnified in the figure because the water temperature was nearly homogeneous in the deep layers. Although these transects lie along the 10 stations marked by inverted triangles, the stations did not form a straight line.
The temperature cross sections mentioned above ably demonstrate how surface convergence of debris/foam occurs (dots in Figs. 2b and 2c). We first address the temperature transect in July. The debris/foam line detected by balloon photography was unfortunately separate from the CTD transect, probably because of surface currents during the observation. Hence, it is difficult to correlate observed hydrographic structure with the surface convergence. Nevertheless, the temperature cross section (Fig. 4a) shows a remarkable undulation of the pycnocline at 5-m depth. In general, this undulating interface develops alternating convergent and divergent surface flows above the pycnocline. It is well known that this flow pattern accumulates floating objects along convergence bands (e.g., Pingree and Mardell 1985). In fact, the debris/foam line observed in July was between stations 5 and 6 (Fig. 4a; see also Fig. 2b), consistent with a classic internal-wave structure, such as in Simpson and Sharples (2012) (cf. our Fig. 4 with their Fig. 4.8). Floating objects accumulated perpendicular to the survey line (Fig. 2b), along which we could observe the internal wave (Fig. 4). The survey line was ~500 m south of the debris/foam line (Fig. 2b), and thus it is likely that the internal wave generating the debris/foam line in July had a horizontal scale of at least 500 m.
In the August observation, we recognized an oceanic front between well-stratified waters from stations 1 to 7 and a cold dome from station 7 to an area probably beyond station 10 (Fig. 4b). Cold domes are familiar hydrographic structures in the Seto Inland Sea (Chang et al. 2009). Hill (1996) constructed a quasigeostrophic spindown model to examine the dynamics of a cold dome in the Irish Sea. Hill’s model demonstrated that a cyclonic (anticyclonic) circulation in the upper (lower) layer develops during spindown of cold domes, because of vortex stretching (shrinking) in the upper (lower) layer. Alternatively, a cyclonic vortex was initially forced by geographic features such as an island or headland, and a cold dome structure was subsequently generated through geostrophic adjustment. In either case, floating debris/foam observed near the cold dome (stations 7 and 8 in Fig. 2c) might have been trapped within the vortex around the dome.
c. Mapping of surface currents
We initially applied projective transformation to photographs from the balloon to convert buoy trajectories to surface currents in Cartesian coordinates. Photographs at 1139 JST 25 July (Fig. 5a) and 1251 JST 20 August (Fig. 5b) are examples of these aerial photographs. In Figs. 5a and 5b, white and brown objects form accumulated debris/foam lines along the oceanic front and streak. In addition, various colored GPS buoys (red arrows) were confirmed on these images. Using the projective transformation, the photographs were rotated in both the horizontal and vertical directions to Cartesian coordinate planes (Figs. 5c and 5d).
We next show GPS buoy trajectories computed using locations from both processed images (Figs. 6a and 6c) and GPS data (Figs. 6b and 5d) on each observation day. After the projective transformation, we traced pixels located at the center of the GPS buoys in Cartesian coordinates by calculating the distance from the origin point. Of the 198 photographs 10 (8 of 83) at time intervals of 1–2 min were used to calculate buoy trajectories in July (August). These photographs were chosen so that the buoys were widely dispersed over the survey domain for surface-current map coverage of broad areas, and for successful completion of the projective transformation using the five selected buoys. The time interval (60–120 s) was sufficiently short to resolve the current field [O(100) cm s−1, typical in these coastal waters] over the survey domain (~500 m), because the buoy displacement [O(100) cm s−1 × 60–120 s = 60–120 m] is smaller than the investigated area. In addition, that interval was sufficiently long to remove GPS data fluctuations shorter than 1 min. Trajectories extending upward on the images from almost all deployment locations suggest that northward or northeastward currents were dominant in July (Figs. 6a and 6b). Analogously, observed currents in August were largely directed southward or southwestward, because of trajectories extending downward in Figs. 6c and 6d. Note that deployment locations on image-derived trajectories (Figs. 6a and 6c) do not necessarily coincide with those of GPS-derived trajectories (Figs. 6b and 6d). This difference arises from the different start times of the trajectory construction. The GPS-derived trajectories started tracking at 1124 JST (1248 JST) in the July (August) experiment, whereas the image-derived trajectories began 40 s (16 s) later. This was because photographs were taken after deploying GPS buoys (we could determine GPS-derived trajectories immediately after deployment), and because we had to wait until those buoys were widely dispersed in the target domains to conduct the projective transformation successfully.
Compared with the image-derived trajectories, GPS-derived trajectories of each buoy appeared incoherent in both July and August (Figs. 6b and 6d). Nonetheless, northeastward (Figs. 6b) and southwestward (Figs. 6d) currents indeed prevailed as with the image-derived trajectories on maps processed by the projective transformation. However, zigzag movements, implausible in reality, were evidenced (Figs. 6b and 6d).
The aforementioned trajectories were converted to current velocities on each 10-m grid with the procedure described in subsection 2d (Fig. 7). Overall, the surface-current map derived from images appears more reasonable than that derived from GPS data. In the July experiment (Figs. 7a and 7b), current speeds were drastically different between the image-derived (Fig. 7a) and GPS-derived (Fig. 7b) maps, although their directions were both northward. For example, the current speed in the image-derived field ranges from 40 to 140 cm s−1, whereas that in the GPS-derived field exceeds 200 cm s−1 at the southern extremity. Overestimation of current speed was also found in the August experiment (Figs. 7c and 7d). Overall, the area with current speed faster than 200 cm s−1 is broader in the GPS-derived field (Fig. 7d) than in the image-derived one (Fig. 7c). The predominant tidal constituent in the Seto Inland Sea is the M2 with a current speed of O(100) cm s−1 (Guo et al. 2004; Valle-Levinson and Guo 2009). Therefore, the image-derived current velocities are consistent with the typical tidal current velocities in this region.
The barotropic mode of tidal currents was likely to be homogeneously distributed in the relatively narrow study area (several hundred meters square), because that area is distant from islands, headlands, and shallow shoals (Fig. 2a). We therefore attempted to “detide” by removing the spatial average current velocity, because tidal currents are unlikely to generate the fine current structure that was our focus. Figure 8 shows residual current vectors using spatial anomalies of both zonal and meridional components. The image-derived field in July (Fig. 8a) is considered reasonable because current vectors are directed toward the debris/foam line, and the accumulation of the floating debris and foam occurred because of these convergent flows. However, strong current regions, which were unnaturally isolated from the surrounding moderate-current field, remained at the southern extremity of the GPS-derived current field in July (Fig. 8b). In addition, the current direction was inconsistent with the occurrence of the debris/foam line. Both observation and the numerical model (Yanagi et al. 1995; Chang et al. 2009) have showed that residual currents with the speed of O(10) cm s−1 appear in the Seto Inland Sea. Likewise, the image-derived current velocities obtained in the present study have the same order of magnitude as this typical value.
The observed current field in August (Figs. 8c and 8d) also shows the advantage of the image-derived map over the GPS-derived one. The image-derived current field clearly depicts a cyclonic (counterclockwise) eddy with debris/foam patchiness trapped at its center (Fig. 8c). It also seems reasonable that the current speed increases outward from the eddy center. However, the GPS-derived field (Fig. 8d) shows sporadic strong current patchiness, and random current directions are inconsistent with the occurrence of the debris/foam patchiness. These sporadic strong current regions are not artifacts from the interpolation method because buoy trajectories (hence, measured current velocities) distribute mostly over the areas (see Fig. 6 with Figs. 7 and 8).
a. Advantage of image-derived current mapping
In this section, we discuss the reason for the more reasonable image-derived currents relative to GPS-derived ones. The GPS-derived buoy trajectories (Figs. 6b and d) appear to include unrealistic values from both July and August observations. For instance, some buoys “leapfrogged” unnaturally over distances greater than 200 m during 1 min. These unnatural movements are effectively demonstrated by depicting the time series of each buoy location from the origin after the projective transformation (Fig. 9). Figures 9a and 9b (Figs. 9c and 9d) show temporal variations of image-derived and GPS-derived buoy locations in the July (August) experiments. The image-derived locations (Figs. 9a and 9c) changed monotonically in time relative to those derived by GPS data (Figs. 9b and 9d). The remarkable difference between image- and GPS-derived locations is emphasized by comparing trajectories computed using the projective transformation with those using GPS data (red, blue, and green lines in Fig. 9). The zigzag motion in the GPS-derived time series (Figs. 9b and 9d) almost disappears in the image-derived time series (Figs. 9a and 9b). The sporadic patchiness of strong current in the GPS-derived maps (Figs. 8b and 8d) is believed to result from the leapfrogging motion within the time series data of GPS-derived locations.
The advantage of the image-derived current estimates originates from the removal of erroneous fluctuations in GPS data by choosing five accurate buoy locations for the projective transformation (section 2a). The accuracy of all buoy trajectories (hence, current speed) on the images after this transformation is therefore the same as that of the accurate buoy locations, so the image processing acts as a filter to remove erroneous data from observed current data.
b. Error estimation
Given the above, stochastic fluctuations are nonetheless included in GPS data even if the receivers are fixed on the ground (section 3a). However, the error estimate for current speeds is <2.0 cm s−1 (0.4 cm s−1 on average in Fig. 3b), which is negligibly small in the current maps of Figs. 8a and 8c. In addition to the fluctuations within GPS data, erroneous estimates occur during the projective transformation to obtain image-derived currents. Hence, we calculated the differences between GPS-derived current velocities of the five buoys selected for the projective transformation (section 2a; regarded as “pseudotrue” data) and image-derived velocities of the same five buoys. The maximum velocity difference, mean difference, and root-mean-square error (RMSE) in Fig. 3c were estimated at 8.6, 3.4, and ±4.3 cm s−1, respectively. It is believed that part of this RMSE resulted from the propagation of stochastic fluctuations of GPS data (section 3a), with a standard deviation of ±1.3 cm s−1. Thus, the error caused by the projective transformation is estimated at 4.1 cm s−1 (=). It is therefore anticipated that the error (4.3 cm s−1) caused by both stochastic fluctuations and projective transformation is negligibly small compared with the current velocities in the processed image (Figs. 8a and 8c), which have magnitudes greater than several tens of centimeters per second. In addition, the maximum velocity difference (8.6 cm s−1), mean difference (3.4 cm s−1), and RMSE (4.3 cm s−1) were all significantly smaller than the maximum error (47 cm s−1), mean error (10 cm s−1), and standard deviation (7.0 cm s−1) that may be present in the GPS-derived current velocities (section 3a).
We established a novel observational technique to map current vectors in narrow regions, by combining a buoy-tracking experiment and balloon photography. Aerial photographs from a balloon towed by a research vessel were rotated to images in Cartesian coordinates for georeferencing, using five GPS data on each image. Two field experiments were conducted in summer 2013 around debris/foam lines, to examine the ability of balloon photography to accurately measure surface currents. In these experiments, the image-derived currents were compared with those from GPS data of floating buoys. The former currents were found more reasonable than the GPS-derived currents, which were disturbed by stochastic fluctuations of GPS data. The image-derived currents reasonably reproduced convergent flows, and a cyclonic eddy that accumulated foam and marine debris actually observed during the surveys. The estimated error was 4.3 cm s−1, which is sufficiently small for measuring snapshots of surface coastal currents with speed greater than several tens of centimeters per second (Figs. 8a and 8c).
There are three advantages to measuring surface currents by balloon photography. The first is high resolution, owing to the low-altitude remote sensing that can accurately determine buoy trajectories on aerial images. The second advantage, over observations of HF radars fixed at particular sites, is significant balloon mobility for measurement. This mobility is facilitated by research vessels towing the balloons. We sought a foam/debris line (i.e., oceanic front) in the present application. It is therefore anticipated that balloon photography will be capable of capturing surface-current fields in waters within a narrow region. The third advantage is that balloon photography can be readily combined with other oceanographic surveys. Herein, the combination of balloon photography and hydrographic surveys showed that convergent flows associated with debris/foam lines (Fig. 8a) occurred because of an internal wave (Fig. 4a), and that debris and foam were trapped at the center of a cyclonic eddy (Fig. 8b) associated with a cold dome (Fig. 4b). The aforesaid combination can furnish novel information with respect to finescale ocean dynamics, as mentioned above. Also, this success gives us confidence in using the method to observe various small-scale coastal processes relevant to current fields (e.g., jellyfish patchiness and nutrient transport across oceanic fronts).
A limitation of this procedure is the relatively short period of the surveys. For instance, strong convergent flows accumulate GPS buoys toward oceanic fronts, and so the accuracy of the projective transformation declines drastically because the buoys are unlikely to give reference points dispersed widely across a domain. To overcome this limitation, we must establish an efficient image processing method free of reference points (five GPS buoys in the present case), possibly measuring the oblique angle to the ground coordinate with a sensor on the camera. The other limitation is that the aerial-tracking information is obtained only within areas covered by the buoys (see blank areas in Figs. 7 and 8), unless the number of buoys is sufficiently large to cover target domains.
Part of this work was supported by JSPS KAKENHI Grant 2561041 and a Sasakawa Scientific Research Grant from the Japan Science Society. The comments of the peer reviewers were very valuable in improving the manuscript.
The projective transformation was used to convert aerial photographs into images in ground coordinates. According to Magome et al. (2007) and Kako et al. (2012), the conversion from the photographic coordinate (x, y) on images to the ground coordinate (X, Y) is represented as follows:
where X and Y are measured from an origin point arbitrarily determined using GPS data, and bi and ci (i = 1, 2, …, 5) denote coefficients to be solved as outlined below. The 10 coefficients for b and c can be reduced to 8 using a simple mathematical operation (Magome et al. 2007; Kako et al. 2012), and they were determined by a least squares method using buoy GPS data (providing X and Y) and the locations of those buoys on the photograph (x and y). In the present study, five GPS data (10 values in the x and y directions) on each photograph were used to solve the abovementioned equations.