5.2.1. Filtering and Resonance
 Little is known about seismic attenuation in glacier ice, but we expect that high frequencies are rapidly attenuated. Perhaps this provides a reason for the lack of a high-frequency component in calving seismograms. Additionally, glacier ice may be acting as a high-pass filter such that low-frequency energy (<1 Hz) is filtered by the ice, and any low-frequency energy generated by calving cannot reach the seismometers. If ice has high seismic attenuation or a low seismic quality factor, Q, (as may be expected for fluid filled, faulted rock [Métaxian et al., 2003; Stein and Wysession, 2003]) it is possible that most energy below the 1–3 Hz passband is scattered or attenuated while traveling through the glacier. Although we cannot rule this explanation out, we feel it is unlikely, because some power spectra for observed calving events contain low-frequency energy. However, the energy from such events could have reached our sensors via a raypath through the ocean and bedrock, without propagating through the ice.
 Rather than acting as a filter, the glacier may respond to energy inputs from mechanical failure during calving by resonating at its fundamental frequency f:
Resonance frequency depends on the layer thickness, H, making this hypothesis testable using historical data. If path effects, including layer resonance, were significant, we would expect to have seen a shift in the fundamental resonance frequency due to changes in ice thickness in the near terminus region during the 25 years of retreat. Shear wave speeds, Vs, published by Deichmann et al.  of 2.0 km s−1, combined with water depth estimates taken from Brown et al.  and collected during our study, suggest that the fundamental resonance frequency at Columbia Glacier today would be lower (because the terminus is now located in deep water the thickness in a several km neighborhood has increased since the onset of retreat) than for historical events. Tidewater glaciers all exhibit similar cliff heights ranging between 40 and 70 m [Brown et al., 1982; O'Neel et al., 2003], which allows ice thickness to be estimated using measured water depths under the assumption of a flat bed in the near-terminus neighborhood. The thickness at Harvard Glacier was estimated at ∼110 m thickness by Brown et al. , and Wolf and Davies  present PSD with peaks at 1.65 Hz. Similarly, during the 1980s at Columbia Glacier (∼200 m thickness [Krimmel, 2001]), Qamar  estimated the dominant frequency component of calving events at 1–2 Hz. Our measurements, using broad band sensors, reveal a higher characteristic frequency today, in contrast to resonance theory predictions of a lower-frequency fundamental mode. Additionally, we found that seismograms recorded at ranges between 0.5 and 15 km from the terminus exhibit similar spectral characteristics, thus strongly suggesting the harmonic codas are not predominantly caused by resonance. Similar to our result, Qamar concluded that the source mechanism is more important in generating the harmonic coda of calving waveforms, not spectral characteristics of the glacier.
 A second interpretation of concentrated calving-generated energy in the 1–3 Hz frequency range attributes a common fault size to all events, which by this hypothesis are generated by processes similar to tectonic earthquakes. If the failure process for calving bears similarities to earthquake ruptures, where frequency content scales with rupture area, then large events should be characterized by broader band energy [Stein and Wysession, 2003]. Our results show uniform spectral composition regardless of size. This suggests that large calving events do not result from a single rupture; rather they result from a series of small ruptures, for which failure occurs after a critical (but small) rupture destabilizes a large, nearly detached block of ice. Note that since standard earthquake magnitude scales are logarithmic, calving event end-members may vary only slightly on an earthquake magnitude scale. Local magnitudes calculated for both small calving events and the largest observed range from ML = 1 to 2.5, which result in a corner frequencies for small earthquakes exceeding 10 Hz, significantly different than our observations.
 Following this interpretation, processes leading to calving may begin by weakening the ice at significant distances upstream of the terminus. Crevasse-style ruptures may weaken the ice so that the final release of an iceberg happens from a small-area fault slip. Swarms of high-frequency events (akin to expectations of crevassing events; Figure 2), may indicate fracture during calving. Impulses like this may occur during long-duration events as single events destabilize deeper blocks of ice and cause them to fail in rapid succession. This argument strengthens the notion that duration is a good initial proxy for event magnitude, and suggests we may be able to fully quantify the energy release by integrating the time domain signal coda during events. Additionally, seismically detected calving events (1–3 Hz) and fracturing events (10–20 Hz) exhibit a linear correlation (r = −0.52), which suggests that the two processes are not acting independently; rather there is an interaction between the two processes as ice moves toward the terminus and is eventually calved off.
 A third possible interpretation deviates from a tectonic-like source, and borrows from volcanoseismology theory. This idea does not eliminate our previous hypothesis, but rather provides a mechanism for some portion of calving events. Calving event seismograms can be described as monochromatic, and such seismic signals are uncommon in nature. However, earthquakes associated with some landslides and long-period (LP) volcanic events produce similar waveforms [McNutt, 1986; Varnes and Savage, 1996; Chouet, 1996]. LP volcanic waveforms are extremely similar to those generated by calving, being characterized by emergent onsets that contain an excitation phase of high-frequency energy followed by a monochromatic 1–5 Hz coda with no clear S wave arrival [e.g., Chouet, 1996]. The source for such events is still debated, but site and/or path effects (e.g., resonance or filtering) are generally ruled out due to detection of similar waveforms at multiple stations at various distances from the source [e.g., Chouet, 1996; Métaxian et al., 2003]. A leading theory developed by Aki et al.  attributes a source for LP events to slowly propagating waves in voids (cracks, conduits) within the solid medium caused by fluid pressure transients [see also St. Lawrence and Qamar, 1979; Chouet, 1996]. The nondestructive LP events attain their monochromatic form by resonating motion around constrictions or obstructions to magma flow in the voids and are very similar in space and time. LP volcanic events are much more repeatable than calving event signals (C. Rowe, personal communication, 2006), which suggests variations of the source model between the two processes. Clearly, calving is a destructive process, and this may explain the less repeatable waveforms. However, similar harmonic waveforms are generated by noncalving glaciers, although their relationship with the dynamics is unresolved [Métaxian et al., 2003; C. Larsen, personal communication, 2006]. In the glacier system, water would take the role of magma (and material properties can thus be better constrained), as the pressurized fluid aiding crack propagation. Fracturing may be initiated by hydraulic changes, producing high-frequency seismic energy, as described above. This hypothesis may be most intuitive to the large submarine events although harmonic waveforms are produced by all events.
 Each hypothesis has strengths and weaknesses supported by data and observations. The harmonic waveforms and observations of large floods suggests that, at least intermittently, subglacial hydraulics are actively involved in the process of iceberg calving. Repeat pulses of short-lived, high-frequency energy may indicate that pressurized water is enhancing crack propagation during prolonged events. The similar form of small subaerial events may stem from surface water generated by meteorological processes aiding in propagation of crevasse tips [Van der Veen, 1998]. This may indicate that the rupture areas are limited by maximum basal pressures such that repeated fracture propagation proceeds at small length scales until an iceberg is generated. This result suggests a percolation theory model may apply as suggested by Bahr  but where water causes stress buildups in the ice. In summary, our data indicate that a combination of hypotheses two and three are involved in calving.
5.2.2. External Forcings
 A favored conceptual model for calving relates failure to exceeding a floatation threshold [e.g., Meier and Post, 1987; Van der Veen, 1996; Vieli et al., 2001; O'Neel et al., 2003, 2005]. Most discussion focuses on seasonal to secular timescales, such that the terminus position is modulated by increasing water depth or the water depth-ice thickness ratio at the terminus. Some stochastic component likely governs the smallest, most frequent events, but we suggest that similar buoyancy arguments may govern the location and timing of large individual calving events, especially in response to rapid transients in water pressure. If water pressure transients are important for calving, we may expect some relationship between water storage and calving over daily to secular timescales.
 Minimum water pressure is bounded by sea level, but also modulated by the state of the subglacial hydraulic system and the ease of water throughput (e.g., bed slope). Physical conditions prohibit water storage measurements, but we can explore water input forcing by comparing the 1–3 Hz seismicity to meteorological data collected during the experiment in Valdez.
 We calculated PSDs for recorded temperature and precipitation data and found no direct evidence for simple forcing by either process when comparing 70 day time series. No clear evidence exists for either semidiurnal or diurnal periodicity, even given the robust data set for the statistical analysis. Although Warren et al.  and O'Neel et al.  found evidence for long-period tidal modulations of calving, we found no conclusive evidence for this. However, these periods require longer time series to be completely ruled out.
 As suggested by Warren et al. , O'Neel et al. , and our field observations, an internal, self-regulated forcing plays a role in calving flux variations. None of the physically motivated, external forcing processes appear to have a direct influence on calving, yet periodicities exist at ∼2, 3, 5 and 20 days. A possible explanation involves stretching and thinning of the terminus after major calving events before reattaining critical floatation levels for large-scale calving. During this time, only minor calving events occur, and from our data it appears that this time may be ∼20 days for Columbia Glacier. This may also indicate a characteristic life span for the subglacial hydraulic system near the terminus of a fast moving outlet glacier. The weak and multiple length forcings described here are expected, because hydraulic events including rains storms, heat waves, or rapid changes in hydraulic connectivity may disrupt the natural cycle.
5.2.3. Framework of Rapid Retreat
 Our data show a 15% increase in calving between seasonally defined summer 2004 and 2005, which is in agreement with observations and knowledge of the glacier geometry and subglacial topography [Mayo et al., 1979; O'Neel et al., 2005]. Between 2001 and 2005, the terminus was located in the gap between Kadin Peak and the Great Nunatak (Figure 1). Prior to 2001, a significant icefall was located in this constriction, and associated steep surface slopes provided buoyancy stability and served to slow retreat rates since the late 1990s [Krimmel, 2001]. The slowed retreat rates have been accompanied by strong laterally convergent, concave-up downstream terminus geometries, which suggest that lateral stresses provide terminus stability while upstream thinning continues. Thinning and upstream drawdown have continued or accelerated, reducing the glacier width by ∼50% and changing the icefall into a very flat, dynamically sensitive region of the glacier.
 During winter 2004 and 2005, and possibly before, large (∼0.5 × 0.5 km) embayments formed at the glacier terminus west margin. These excursions suggest that stability is being lost, and that retreat from the constriction is imminent. Most recent observations in September 2006 suggest that this has occurred. Higher rates of calving are likely in the near future, as retreat from the gap will increase the terminus width while remaining in deep (or deeper) water, sustaining large buoyancy forces near the terminus. This is especially true because initial retreat from the constriction will cause a nonlinear increase in terminus width as it enters the confluence of the West and Main Branches of the glacier. The width of the calving cliff will increase from approximately 2 km to 7–10 km with only ∼2 km of further retreat, and over a majority of this terminus, water depths will remain deep (∼500 m). No known major obstructions to retreat exist until the location where the bed rises above sea level (km 36) and the glacier surface is relatively flat up to this location. However, there are suggestions of basal bumps ∼4 km upstream from the terminus, which may retard the retreat rate. Thus we expect that upon retreat from the constriction, retreat rates will increase dramatically.