Large calving events at Greenland's largest outlet glaciers are associated with glacial earthquakes and near-instantaneous increases in glacier flow speed. At some glaciers and ice streams, flow is also modulated in a regular way by ocean tidal forcing at the terminus. At Helheim Glacier, analysis of geodetic data shows decimeter-level periodic position variations in response to tidal forcing. However, we also observe transient increases of more than 100% in the glacier's responsiveness to such tidal forcing following glacial-earthquake calving events. The timing and amplitude of the changes correlate strongly with the step-like increases in glacier speed and longitudinal strain rate associated with glacial earthquakes. The enhanced response to the ocean tides may be explained by a temporary disruption of the subglacial drainage system and a concomitant reduction of the friction at the ice-bedrock interface, and suggests a new means by which geodetic data may be used to infer glacier properties.
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 Fast-flowing glaciers in Alaska have also shown speed variations related to ocean tides [e.g., Meier and Post, 1987], but little is known about tidal effects on the flow of outlet glaciers in Greenland. Previous workers observed tidal modulation of flow speed on a floating section of Kangerdlugssuaq Glacier [Hamilton et al., 2006; Davis et al., 2007], and the lower part of Jakobshavn Isbrae [Echelmeyer et al., 1991], but characterization of the glacier response has been limited by sparse data. Here, we use a large dataset of geodetic observations to characterize rapid changes in outlet-glacier response to tidal forcing associated with calving events and glacial earthquakes.
2. Data and Methods
 During the boreal summer seasons of 2007 and 2008, we acquired continuous Global Positioning System (GPS) measurements at sampling intervals of 1–5 s at several locations on Helheim Glacier (Figure 1a), and at three nearby locations on bedrock, for a period of ∼2 months [Nettles et al., 2008]. We estimate the time-dependent position of the GPS sites on the surface of the glacier relative to the static antennas on bedrock at 15-s intervals using the TRACK software package [Chen, 1998], as described by Nettles et al. .
 During part of the observing period, we also operated a water-pressure gauge ∼35 km from the glacier terminus to obtain a record of ocean tides. To extend the tide record to the full GPS observing period, we use the AOTIM-5 model [Padman and Erofeeva, 2004] to compute the ocean-tide height at an open-ocean location near the mouth of the glacial fjord (Figure 1a). The predicted tide agrees well with observed water heights during periods when measurements are available. The measured tide in the fjord is in phase (within 3 minutes) with the predicted tide, and their amplitudes agree at the cm-level.
 We estimate the response of the glacier to the ocean tide by performing a least-squares fit to the geodetic position estimates using a model that includes a mean glacier flow velocity, a mean acceleration when warranted, and an admittance parameter relating the ocean tide height to deviations in glacier displacement from the mean flow. The admittance parameter is thus the ratio between the amplitude of the tidal response of the glacier and the amplitude of the ocean tide. We also estimate a delay between the ocean tide and the response of the glacier by performing a χ2 grid search at 5-minute time steps. We compare the fits achieved using a constant-speed and a constant-acceleration model with an F-test at 95% confidence, and we also evaluate a constant-speed model that does not include a tidal signal, enabling us to assess the significance of the tidal signal and the acceleration for a given day and site. We analyze each day independently, and also perform fits to shorter time periods bounded by glacial earthquakes [Nettles et al., 2008]. We consider data from ice sites located up to ∼12 km behind the calving front (Figure 1a), where the amplitude of the tidal variations decays to ∼1 cm.
 During summer 2007, Helheim Glacier flowed at a mean speed of ∼25 m/day near the calving front, and at ∼12 m/day at locations ∼25 km upglacier, as reported by Nettles et al. . In summer 2008, glacier flow was slower (the site located closest to the calving front flowed at a mean speed of ∼20 m/day) and less variable. The largest variations in flow speed — step-like increases in glacier velocity that are coherent throughout the GPS network — are associated with glacial earthquakes [Nettles et al., 2008]. These changes in flow velocity decrease with distance upglacier, resulting in an increase in longitudinal strain rate.
 The along-flow motion of Helheim Glacier varies such that the glacier position is advanced at low tide and retarded at high tide (Figure 2) with respect to mean flow. We interpret this out-of-phase response of the glacier to tidal forcing as resulting from stress fluctuations on the terminus caused by variations in hydrostatic pressure associated with the ocean tides [e.g., Anandakrishnan and Alley, 1997]. We observe variations in the time delay of the response of 0–4 hrs, but the accuracy of the time-delay estimates does not allow the identification of any propagation of the tidal signal along the glacier. For all days studied, the tidal admittance parameters show an exponential decay with distance from the calving front, consistent with observations and model results of previous workers [Anandakrishnan and Alley, 1997]. Results from several representative days are shown in Figure 1b. During the time periods considered here, we observe no significant tidal signal in the vertical or cross-flow directions, indicating that the glacier tongue was grounded at the times and locations (very near the calving front) that we examine.
 Typically, tidal admittance amplitudes vary little from day to day. However, following glacial earthquakes the tidal admittance increases suddenly by a factor of as much as ∼2.5 (Figure 2). During the two seasons, six large glacial earthquakes occurred [Nettles et al., 2008], clustered in three different time periods: two in summer 2007 and one in summer 2008. The example shown here (Figures 1–3a), from 2007 and encompassing three earthquakes, is associated with the largest increase in velocity and largest increase in tidal response. The other events, occurring for different positions of the calving front in the fjord, show consistent behavior (Figure 3b).
 An immediate increase in tidal response following the earthquakes is clear from visual inspection of the signal in Figure 2b. Following the two glacial earthquakes on day 190, the admittance of the tidal signal increased by a factor of ∼2.5, coincident with an increase in velocity of ∼2 m/d. The first of the earthquakes shown in Figure 2b, on day 189, is associated with smaller changes in tidal response and flow speed. Like the change in flow velocity [Nettles et al., 2008], the change in tidal admittance decreases with distance upglacier (Figure 1).
 The enhanced tidal response lasts for one to two days after the glacial earthquake. The decrease in tidal response is temporally linked to a deceleration of the glacier (Figure 3a). However, unlike the tidal response, the glacier velocity typically recovers only partially. Both the magnitude of the change in tidal response following a glacial earthquake and its subsequent decrease correlate with changes in flow speed observed at those times (Figure 3b). Other variations in tidal response during the summer are small compared with changes associated with glacial earthquakes. As expected, the ocean-tide record varies smoothly and continuously throughout the period of increased tidal response (Figure 2a), with the exception of small tsunamis caused by the calving process [Nettles et al., 2008] that attenuate well before the tidal response recovers.
4. Discussion and Conclusions
 Our results indicate a temporal relationship between the glacier's enhanced response to tidal forcing and the flow acceleration and increased longitudinal strain rates that follow glacial-earthquake calving. Although the tidal stress is applied at the glacier terminus, the change in sensitivity to tidal forcing is observed at least 12 km upglacier after a glacial-earthquake calving event, indicating a coupling of flow characteristics over at least this distance. The loss of ice itself is unlikely to be the cause of the increased tidal response: while sustained flow-speed increases can be attributed to a long-term loss of ice at the glacier terminus, the rapid recovery of admittance amplitudes to pre-event values demonstrates that the change in distance to the calving front is not the primary control on the temporal variation in glacier tidal response. The recovery also occurs before the glacier front has readvanced significantly in the fjord, since the rate of advance is limited by the speed of glacier flow. A temporary decrease in resistance at the glacier bed would, however, enable the glacier to respond with higher amplitude to the tides.
 Following large calving events associated with glacial earthquakes, the glacier experiences an increase in surface velocity and strain rate. Since fast-moving outlet glaciers flow mainly by basal sliding, we expect a change in strain rate at the glacier surface to lead to a similar change at the glacier base. This change in strain rate may disrupt the subglacial hydrologic system, reducing the volume of water that can be accommodated in subglacial channels and increasing basal water pressure, further lubricating the ice-bedrock interface and enabling the glacier to enhance its response to the tides. Such reorganization of the basal hydrological system has been shown to act as a mechanism for glacier surges [e.g., Kamb et al., 1985].
 At Helheim, the disruption of the hydrological system is expected to be temporary, with more efficient drainage re-established as strain rate is reduced. Furthermore, this effect would cause a temporary additional acceleration, above the longer-term speedup caused by the loss of resisting forces at the terminus, that would recover at the same time as the tidal response.
 Alternatively, the nonlinear rheology of the ice may provide a mechanism for enhanced response to tidal forcing as velocity and strain rate increase.
 Our analysis demonstrates that large calving events rapidly change the response of Greenland's outlet glaciers to steady forcings, such as the ocean tide, in addition to inducing both temporary and persistent changes in the glaciers' flow regime, and highlights the need for understanding the mechanisms that induce such responses.
 This work was supported by the Spanish Ministry of Science and Innovation (MICINN), the Gary Comer Science and Education Foundation, the U.S. National Science Foundation, the Danish Commission for Scientific Research in Greenland (KVUG), the Geological Survey of Denmark and Greenland (GEUS), Geocenter Copenhagen, the Danish National Space Center, and NASA. JdJ acknowledges a CSIC pre-doctoral fellowship. GPS equipment and technical support were provided by UNAVCO, Inc. We thank S. Anandakrishnan and an anonymous reviewer, whose comments helped improve the manuscript.