2.1. Drift

Camera clocks drift and the drift can be substantial: daily subsecond to second drift can accumulate to multi-minute offsets within a few months. Clock drift varies between cameras of the same make and model, and drift, otherwise highly linear, is especially sensitive to changes in temperature, expected of any circuit-integrated oscillator (Reference Sundaresan, Allan and AyaziSundaresan and others, 2006).

Table 1 lists mean clock drift and temperature for a variety of cameras and treatments. The Nikon D200 (#1) and Canon 40D digital single lens reflex (DSLR) cameras were kept in a heated indoor space and compared repeatedly against Universal Time Coordinated (UTC) over 31 and 76 days, respectively. The weighted least-squares linear fits confirm that, at near-constant temperature, clock drift is indistinguishable from linear over month timescales (Fig. 1). In contrast, the drift rates of the Nikon D300S and Nikon D200 (#2), deployed year-round at Columbia Glacier, Alaska, vary by a factor of four between summer and winter. Although drift rates are specific to the individual camera, the pro-level Canon 5D Mark II and Nikon D2X are the best performers by a wide margin, suggesting that some camera models may benefit from substantially superior clock hardware and design.

Table 1.

Mean drift and air temperatures for a variety of cameras and treatments. Drift rates are for the individual camera and may not be representative of the camera model. Mean temperatures for the time-lapse deployments at Columbia Glacier were calculated from monthly averages reported for nearby Valdez, Alaska (http://www.wrcc.dri.edu/cgi-bin/cliMONtavt.pl?ak9685

Fig. 1.

Weighted least-squares linear fit of UTC–camera offset measurements for a Nikon D200 and a Canon 40D, evaluated using the NIST Web Clock (introduced in Section 3) following the methods of Section 4. Both cameras were kept indoors and held at near-constant temperature. The error bars are the sum of the subsecond resolution of the camera and the reported uncertainty of the NIST Web Clock at each offset measurement.

2.2. Resolution

Digital cameras record image-capture times following the Exchangeable image file format (Exif) standard (http://www.exif.org/Exif2-2.PDF). The DateTimeOriginal tag contains the year, month, day, hour, minute and second of original data generation. Subsecond decimals, if reported, are written to the SubSecTimeOriginal tag. While no unifying standard exists for videos, capture start times can typically be found within equivalent video file tags or as Exif in accompanying image thumbnails. Whether and at what resolution a camera records subsecond decimals is of foremost concern to subsecond applications.

A survey of the camera, camcorder and camera phone models of 17 leading manufacturers, using photo-sharing and camera-review websites, found only a handful of Nikon DSLR, Canon DSLR, Kodak EasyShare compact and Nokia phone cameras implementing the SubSecTimeOriginal tag (see supplementary material at www.igsoc.org/hyperlink/12j126/12j126Sect2.2.pdf). Furthermore, most of the cameras that do report subsecond information do so in a manner inconsistent with expectation. Figure 2 compares frequency distributions of the SubSecTimeOriginal tag (a value ranging from 0 to 99 × 10⁻² s) for all capable Nikon and Canon DSLR camera models, compiled from thousands of user-submitted photographs on the photo-sharing website Flickr (www.flickr.com). All Nikon (Fig. 2a–e) models record subsecond time with an effective resolution coarser than the expected 10⁻² s, whether by clipping (Fig. 2a), rounding (Fig. 2b–d) or subtly favoring values at discrete intervals (Fig. 2e). For most Canon (Fig. 2f–h) models, the SubSecTimeOriginal tag serves only to distinguish between images taken in rapid succession and otherwise strongly favors 0 (Fig. 2f) or 3 (Fig. 2g). Only the Canon 5D Mark II and Canon 500D approximate a uniform distribution (Fig. 2h) – the ideal behavior we would expect.

Fig. 2.

Frequency distributions of the SubSecTimeOriginal tag (a value ranging from 0 to 99 × 10⁻² s) for all capable Nikon and Canon DSLR camera models. Each panel is representative of a subset of the 40 cameras surveyed: (a) Nikon D1, D1X and D1H – shown for 1190 photographs by 35 Nikon D1X Flickr users; (b) Nikon D5000 and D3000 – shown for 871 photographs by 118 D3000 users; (c) Nikon D70 and D70s – shown for 839 photographs by 54 D70s users; (d) Nikon D100, D40, D40x, D50, D60, D80, D7000, D5100 and D3100 – shown for 925 photographs by 71 D3100 users; (e) Nikon D2X, D2Xs, D2H, D2Hs, D3, D3S, D300, D300S, D200 and D700 – shown as an average of all ten cameras with 7790 photographs by 458 Flickr users; (f) Canon 1 D Mark III, 1 Ds Mark III, 1 D Mark IV, 7D, 40D, 50D, 60D, 550D, 600D and 1100D – shown for 827 photographs by 128 60D users; (g) Canon 450D and 1000D – shown for 586 photographs by 82 1000D users; (h) Canon 5D Mark II and 500D – shown for 1476 photographs by 155 5D Mark II users.

2.3. Precision

Although a camera may report subsecond decimals with high resolution, the true precision of the image times may be much less. Figure 3 compares the clocks of a Nikon D2X and Canon 5D Mark II against UTC over a 40 min sample period. Although the SubSecTimeOriginal tag of the Canon 5D Mark II has a resolution approaching 0.01 s (Fig. 2h), the finest of any model evaluated in Section 2.2, the timestamps reported by the camera deviated from UTC by as much as 0.8 s. The Nikon D2X timestamps, in contrast, had a precision on par with the model’s ∼0.08 s resolution (Fig. 2e).

Fig. 3.

Clocks of a Nikon D2X and a Canon 5D Mark II evaluated against UTC, calculated from rapid sequences of images taken of a 0.01 s resolution Unix computer clock synchronized to Network Time Protocol (NTP) servers (introduced in Section 3) following the methods of Section 4. The 95% confidence intervals represent the deviation of measurements in each sample set, which would include the subsecond resolution of the camera, the 0.017 s (60 Hz) refresh rate of the computer monitor and the reported NTP accuracy (7–14 ms).

The sources of such errors are unknown. Camera manufacturers are reluctant to disclose engineering details, considering them trade secrets (personal communication from Canon Professional Services, 2010, 2011; personal communication from Nikon Support, 2010, 2011). Given the potential for substantial precision loss, the consistency of reported capture times should be evaluated for any camera considered for time-critical applications.

4.1. Subsecond: both camera and reference

In the simplest case, both T _c and T _r include subsecond components and Eqn (1) yields a subsecond resolution measurement of the offset between the camera and reference clocks. However, subsecond offset can be estimated even when one or both of the devices report only second rollovers. In these cases, a multi-second sequence of images is taken of the reference clock at the camera’s maximum frame-rate. First, a shutter speed faster than the target frame-rate needs to be used. To avoid buffer overrun in writing to memory, which can lead to slowing frame-rates in still image sequences and dropped frames in videos (and subsequently to a loss in the precision of the offset measurement), low-resolution output and fast memory cards are recommended for these procedures. The following subsections describe how to analyze the resulting image sequence to calculate a subsecond offset and an error estimate. Although we simply read the reference time off the photographs, a character-recognition algorithm could be developed to automate the procedure.

4.2. Subsecond: either camera or reference

In the case of a 1 s resolution reference clock and subsecond resolution camera clock, calculating the offset at each image yields a repeating pattern, such as the example from a Nikon D200 in Table 2. As a result of the stepwise nature of the reference clock sequence, the offset will reach a local maximum a_i at the frame preceding each second rollover and a local minimum b_i at the frame following each second rollover. Since the true second rollover occurs at a time between each [a_i , b_i ] pair, it follows that the offset can be no more than the smallest b_i and no less than the largest a_i minus 1 s, i.e.

For the sequence in Table 2, in which the true offset is constrained to the overlapping [a_i –1, b_i ] intervals [0.26 s, 0.51 s], [0.34 s, 0.50 s] and [0.32 s, 0.49 s], max (a_i ) − 1 = 0.34 s and min (b_i ) = 0.49 s, yielding the interval intersection 0.34 s ≤ offset ≤ 0.49 s, or more explicitly offset = 0.415 ± 0.075 s. In the case of only one-second rollover in the sequence, the range of the offset is equal to the time between the single [a–1, b] pair, by definition the frame-rate of the camera between those two images. Sampling a greater number of second rollovers drives the range of the offset estimate towards zero by increasing the probability that max (a_i ) −1 ≈ min (b_i ). If we assume a uniform probability distribution function over the full range (that is, we assume the camera is being triggered randomly and we ignore any sampling bias due to the camera’s regular frame-rate), the 95% confidence interval (CI) for the example above is ±0.073 s. In the reverse scenario, that of a subsecond resolution reference clock and 1 s resolution camera clock, the offset T _c – T _r reaches a local maximum a_i at the frame following each second rollover and a local minimum b_i at the frame preceding each second rollover. In this case the true offset can be no less than the largest a_i and no more than the smallest b_i plus 1 s, i.e.

Although ignored here for clarity, in practice the precision of both clocks is nonzero and needs to be added to the error estimate. This is made especially clear in cases when max (a_i ) −1 > min (b_i ).

Table 2.

Sequence of the second component of a subsecond resolution camera clock (T _c), 1 s resolution reference clock (T _r) and resulting offset (T _c – T _r) from photographs of the NIST Web Clock taken with a Nikon D200. Second rollovers by the reference clock are indicated by thin lines. Markers a_i and b_i are described in Section 4.2. In this case, the true camera offset is 0.415 ± 0.073 s (95% CI)

4.3. Subsecond: neither camera nor reference

In the case that both the camera and reference lack subsecond reporting, a more careful analysis is needed. Each time either the camera or reference clock rolls forward one second, the offset alternates between two consecutive values (e.g. −1 and 0, 2 and 3), yielding a periodic binary integer sequence. By stripping subseconds from the offset sequence in Table 2, the following integer sequence results: 0 1 1 | 0 0 0 1 1 | 0 0 0 1 1 | 0, where | denotes a second rollover by the (trailing) reference clock. In this example, the repeating five-frame pattern indicates that the camera fired at ∼5 frames s⁻¹, or 1 frame every 0.2 s, a result that agrees well with the average spacing between subsecond camera times in Table 2 (0.205 s) and the advertised ‘5 frames per second’ of the Nikon D200. Since the pattern is consistent over two full cycles, or ten frames, the apparent mean frame-rate f over that period could not differ from this estimate by >10%, i.e. f = 0.2 ± 0.02 s. The use of ‘apparent’ must be stressed because besides variations in the frame-rate of the camera, errors in the second rollover timing of both the reference and camera clocks can alter the sequence. In practice, since errors by both clocks may mask one another, the combined precision of the two clocks should be used instead if known to be coarser. Since the camera clock led the reference clock by 1 s for two frames each cycle (n = 2), the offset can be no smaller than (n−1)f (the camera clock advanced immediately before the first image in the cycle was taken, and the reference clock advanced immediately after the second or nth image was taken) and no larger than (n + 1)f (the camera clock advanced immediately after the first image in the cycle was taken, and the reference advanced immediately before the third or nth + 1 image was taken). This scenario for n = 2 is depicted in Figure 6. The (fully bounded) offset can be expressed more generally as

where min(o_i ) is the smallest or most negative of the offset measurements o_i , n is the average number of consecutive o_i larger than min(o_i ) within a full cycle in the sequence, f is the mean frame-rate and df is the uncertainty in f.

Unlike in Section 4.2, where we assumed a uniform distribution over the range of the offset, the probability distribution determined by this method is that of an upright isosceles triangle (Fig. 6c). The likelihood of a given offset decreases linearly with distance from the mean (where the cumulative range of compatible pairs of camera and reference rollovers is maximized), until it approaches zero probability a distance (f + df) from the mean (where the range of compatible camera and reference rollovers narrows to zero). Given this probability distribution, the 95% confidence interval is given by

In our example, where min (o_i ) = 0, n = 2, f = 0.2 and df = 0.02, this yields offset = 0.40 ± 0.17 s, which agrees with the result derived in Section 4.2, 0.415 ± 0.073 s.

Fig. 6.

Schematic illustrating the bounds on the possible range of the offset for the case in which both camera and reference lack subsecond resolution (drawn for the sequence in Table 2, in which the camera leads the reference for two frames). Thin vertical bars represent photographs in a sequence, numbers above and below the bars are the seconds reported by the camera and reference in those images, and thick vertical bars represent possible times of second rollovers for each device. The probability (c) of a particular offset is zero at the minimum (a), which can only be achieved if the camera rollover occurs as late as possible and the reference rollover occurs as early as possible, increases linearly to the mean offset (which can be achieved by the most combinations of camera and reference rollover times), then declines linearly to zero at the maximum (b), which can only be achieved if the camera rollover occurs as early as possible and the reference rollover as late as possible.

5.1. Accurate geotagging for DEM creation

Leading image-based approaches to three-dimensional (3-D) modeling (reviewed by Reference Hartley and ZissermanHartley and Zisserman, 2004) are now capable of performing automated scene reconstruction on even the largest and most poorly documented image collections: for instance, rebuilding Rome from thousands (Reference Agarwal, Snavely, Simon, Seitz and SzeliskiAgarwal and others, 2009) to millions (Reference Frahm, Daniilidis, Maragos and ParagiosFrahm and others, 2010) of street-level photographs. This accomplishment hinges on flexible structure-from-motion (SfM) algorithms which can triangulate from overlapping images taken from multiple perspectives (‘motion’) both the relative camera geometry and 3-D scene (‘structure’) that gave rise to the images. Therefore, although conventional ground control can be (and are best) used to scale and orient the resulting model to absolute coordinates (e.g. Reference Dowling, Read and GallantDowling and others, 2009; Reference Ployon, Jaillet, Barge, Jaillet, Ployon and VilleminPloyon and others, 2011), surveyed camera positions are theoretically sufficient – a significant advantage for measurement programs where fixed bedrock control is unavailable due to topographical or logistical constraints.

On 25 May 2010, airborne vertical stereo photographs (0.40m ground resolution) were acquired over Columbia Glacier, positioned and oriented using previously surveyed ground control, and processed to a 2 m accuracy digital elevation model (referred to as conventional DEM). Same-day oblique imagery was acquired with a Nikon D2X from the window of a second small aircraft flying the path shown in Figure 7 at a mean distance of 1.4 km above the glacier surface. A DeLorme PN-40 handheld GPS logged a position every second, equivalent to 32 m nominal point spacing at the average flight speed of 114 km h⁻¹. At such velocities, time-interpolating accurate camera positions from the tracklog requires subsecond calibration of the camera clock. The tracklog is believed to be tightly coupled to the internal rather than displayed time of the GPS device (the information required to confirm this assumption is not available from the manufacturer at this time) and therefore calibration to UTC was performed. At the onset of the 1 hour photograph acquisition period, we captured a sequence of images of the GPS which later revealed that the camera lagged behind the GPS clock display by 2.485 ± 0.054 s (95% CI). Following our return from the field, we compared the GPS display to a NTP-synchronized computer clock with millisecond accuracy and found that in 151 second rollovers over 2 months the GPS display lagged behind UTC by 0.173 ± 0.095 s (95% CI). A correction of +2.658 ± 0.109 s (95% CI) thus should provide the best agreement with the GPS tracklog. Camera clock drift was ignored due to the short photograph acquisition period and the small nominal drift of the Nikon D2X used (Table 1; −0.044 ± 0.004 s d⁻¹).

Fig. 7.

Map of the GPS tracklog and time-interpolated image-capture positions from the aerial photographic survey of Columbia Glacier, Alaska, conducted on 25 May 2010. The final DEM generated from the SfM model (dark hillshade) is overlaid on a regional 2007 Satellite Pour l’Observation de la Terre (SPOT) satellite DEM (http://www.alaskamapped.org/). UTM coordinates (zone 6) reference the World Geodetic System 1984 (WGS84) ellipsoidal elevation.

The photographs from our aerial survey were first processed with the open-source SfM package Bundler (http://phototour.cs.washington.edu/bundler/) to simultaneously calculate a sparse, relatively oriented point cloud (964 075 points) and corresponding camera positions, orientations and lens calibration parameters. To test the time calibration estimate, absolute camera positions for all 383 images were linearly time-interpolated from the GPS tracklog for a range of camera time corrections. The SfMcomputed and GPS-interpolated camera positions were then used to calculate a least-squares seven-parameter (Helmert) transformation (Reference ChallisChallis, 1995) for orienting and scaling the SfM model. The root-mean-square (rms) 3-D distance between the transformed model camera positions and time-interpolated GPS camera positions reaches a minimum (13.09 m) at +2.69 s within the expected range of the camera time correction (Fig. 8, bold line). In this case, precise knowledge of the camera–UTC offset markedly improves the agreement of the GPS positions with the relative camera geometry computed by SfM.

Fig. 8.

The rms 3-D distance between the transformed SfM camera positions and time-interpolated GPS camera positions (bold line), rms elevation error (m) between the conventional DEM and transformed SfM point cloud (thin line) and 95% CI of the predicted time correction (two vertical lines).

The rms elevation error between the conventional DEM and transformed SfM point cloud exhibits an equivalent but lower amplitude relationship to the camera time correction (Fig. 8, thin line). Since elevation differences depend on local slope, they offer a less sensitive confidence measure (e.g. an XY error in the transformation would result in no vertical error wherever the ground is flat, in error contours wherever the ground is sloped, and in randomly distributed error spikes over glacier crevasses). To better reflect the accuracy over the glacier surface, poorly constrained SfM points in the glacier forebay (occupied by ice melange) and on the peaks above 600 m (13% of total points) were discarded. Furthermore, the SfM elevations were corrected for a systematic −8.02 m bias (determined from bedrock regions of known elevation) likely associated with the single-frequency handheld GPS. The rms elevation error between the conventional DEM and transformed SfM point cloud reaches its minimum of 6.10 m at + 2.69 s, providing a second independent assessment of the camera time correction. The errors are nearly equally distributed (mean −0.77 m) and could be due largely to differences in crevasse depth penetration resulting from the varying viewing angles of the oblique images or the smoothing algorithms used by Inpho Match-T in computing the conventional DEM.

Automated software packages, both commercial and open-source, are becoming available (e.g. Agisoft Photoscan: http://www.agisoft.ru/products/; VisualSFM: http://homes.cs.washington.edu/∼ccwu/vsfm/), increasing the accessibility of the SfM method. Adoption of SfM technology and application of camera time calibration methods has enabled us to produce DEMs of comparable accuracy to conventional vertical photogrammetry using only oblique photographs and a consumer-grade tracklog of camera position.

5.2. Icequake source mechanisms

Since iceberg calving was first identified as a source of seismic energy (Reference QamarQamar, 1988), glaciologists have been attempting to identify the specific sources of that energy. These studies have largely been motivated by attempts to learn about and predict calving (i.e. develop ‘calving laws’) or to remotely monitor calving fluxes for mass-balance and dynamical studies of tidewater glaciers. Various portions of the calving process have been proposed as the sources of calving seismicity, including hydrofracture and resonating water-filled cracks (Reference O’Neel and PfefferO’Neel and Pfeffer, 2007), basal slip (e.g. Reference Wolf and DaviesWolf and Davies, 1986) and the rotation and terminus push-off of large icebergs (Reference Amundson, Truffer, Lüthi, Fahnestock, West and MotykaAmundson and others, 2008; Reference Tsai, Rice and FahnestockTsai and others, 2008).

In the present case study, we use the camera time calibrations developed in Section 4.3 to synchronize video of iceberg-calving events with seismograms, allowing us to draw correspondences between the directly observable calving process and the seismic record. Our efforts to constrain the seismic source of calving took place at Yahtse Glacier, an advancing tidewater glacier on the Gulf of Alaska (60.15° N, 141.38° W). Video was recorded with a Canon EOS 7D at 29.97 frames s⁻¹. We tested two commercially available standards for absolute timing by placing them together within the video: a wall clock synchronized to radio signal WWVB (Radio Shack, model 63-247) and a handheld GPS (Garmin eTrex Vista HCx). In 13 comparisons of 3–5 s each, we found that the radio clock lagged the GPS display by 0.56 ± 0.57 s. Following our return from the field, we compared the GPS to a NTP-synchronized computer clock with millisecond accuracy. In 14 measurements over 2 months, we found that the GPS lagged behind UTC by 0.01 ± 0.44 s. We therefore selected the GPS unit as our time standard and used it to synchronize each of our video clips to UTC. We conservatively assume that our video is accurate to within 1 s.

Figure 9 presents a sequence of video frames from a typical calving event with contemporaneous seismic data (the full video is available as supplementary material at www.igsoc.org/hyperlink/12j126/12j126Fig9.mov). At a distance of 1.8 km from the calving event, the digitizer of the broadband seismometer is connected to a GPS antenna and is synchronized to UTC at the time of recording. On the same amplitude scale, we present two passbands of vertical channel data, 1–5 and 5–50 Hz. Waveforms were filtered using a four-pole Butterworth filter that does not artificially offset the waveform timing, and the timing of the seismogram was adjusted to account for the travel time from the source to the receiver. We assumed a velocity of 1.9 km s⁻¹, the velocity measured for the peak amplitude as it moves through a local network of seismometers.

Fig. 9.

Example calving event with synchronized video stills and filtered seismograms. In the first two frames, the top of the major detached block is outlined with a dashed line. Ice associated with the calving event is observed to begin falling at UTC 2010:09:07 22:13:50.3 (t = 0). Two passbands of seismic waveform from the vertical channel of a nearby seismometer are scaled relative to each other; the maximum unfiltered seismic amplitude is 18.3 μm s⁻¹ at 10.0 s. Seismograms have been corrected by +0.95 s for seismic wave travel time. Video of this calving event, synchronized with the seismogram, is available as supplementary material at www.igsoc.org/hyperlink/12j126/12j126Fig9.mov

These methods reveal that, in this case, the largest-amplitude seismic signals are at relatively low frequencies (<5 Hz) and best associated not with ice fracture but with the splash of water seen erupting from sea level at ∼9 s after the calving event initiates. This result, and those from similar videos, indicates that calving seismicity is greatly influenced by calving style (i.e. submarine or subaerial calving) and how far from its neutrally buoyant position an iceberg is released (Reference Bartholomaus, Larsen, O’Neel and WestBartholomaus and others, 2012). Seismic methods are best suited to monitor iceberg-calving rates when the calving process is energetic, as is the case for subaerial events and submarine events released at great depths. Shallowly released submarine calving events, including some of the largest events at Yahtse Glacier, generate only gentle splashes and thus only weak seismic waves.

Owing to the 15–20 s duration of this and many other calving events at Yahtse Glacier, we have been able to correlate the visual record of calving to the seismic record with an accuracy of ∼1 s. In the absence of clock synchronization, there would be no rigorous method for relating the mechanical calving sequence to seismic signals, hampering further analysis of calving icequakes. If care were taken to better calibrate the timing of the video sequences, more might be learned about the connections between high-frequency seismicity and ice fracturing, particularly at the initiation of the calving event (0 ≤ t ≤ 6 s in this example). However, the 0.5 s dominant period of this seismogram and uncertainties pertaining to the wave travel time would still hinder some attempts at higher-accuracy analyses.