both for vertical oscillations and horizontal velocities measured every 30 seconds for 13 days.
The pdf does not show the horizontal displacements. Do you have a nice graph of that posted somewhere else? It's not made explicit from the PNAS paper what should be expected or indeed if the two data sets synergize being from different years.
First off, station GZ-00 of 2015 needs to be located graphically relative to the PNAS fringes and subglacial channels.
"The observed full range of vertical glacier displacements diminishes from almost 2 m about 26 km seaward of the grounding zone (GZ+26) to 0.6 m in the grounding zone (GZ-00) to nil (within the uncertainty) at GZ-20, about 20 km landward of the grounding zone." - pdf
"The reduced vertical and increased horizontal (not shown) tidal oscillations at GZ-00 reflect
active flexing of the glacier."- pdf
In view of the Ciracì paper distinguishing between grounding zone migration and tidal flexure, which is the pdf referring to?
It seems that Fig.4 could be re-drawn for GZ-00 providing elevation with respect to that of the fixed underlying bedrock of the grounding line, rather than mean sea level.
"Note here that grounding zone refers to the zone of migration of the grounding line during the tidal cycle. It should not be confused with the zone of tidal flexing of an ice shelf, previously called a grounding zone (17, 18), but more appropriately named the
tidal flexure zone. - pnas
We find that the grounding line migrates at tidal frequencies over a kilometer-wide (2 to 6 km) grounding zone, which is one order of magnitude larger than expected for grounding lines on a rigid bed." - pnas
It seems nil vertical displacement at GZ-20 is unfortunate as it does not allow much of a flexure decay function to be determined, ie GZ-5 might also be nil but not GZ-3. GZ-00 was somewhere else back then as it moved 3800 m inland in the last four years.
Sometimes fourier analysis can pull a signal out when there seems to be just instrument noise -- here we know the tidal driving frequency, phase and relative vertical weighting in advance, plus the averaging outcome might receive internal validation from discernable major and minor high tide peaks.
In terms of horizontal motion, Petermann Glacier is sliding forward at about 1180 m per year which is 3 m per 24 hr tidal cycle or 12 cm/hr (5 inches/hr).
Presumably this forward velocity is strictly uniform only in the average. Seasonally, melt water in subglacial channels may briefly reduce friction at the grounding line, peaking variably in early August in high melt years.
On a daily tidal scale, horizontal motion may proceed in the form of lurches coordinated with the reduction in friction as the tide lifts the grounding zone 0.6 m (less farther back depending on flexure). The GPS deployed in 2015 can easily resolve this:
"Our final glacier speed estimate originates from three dual frequency geodetic GPS receivers that provide centimeter accuracy at 30-second intervals; however, we only have time series for the 13 day numbers 223-236 that the instruments were deployed during 11-23 August 2015." - pdf
"For the 13 days of measurements, we find the glacier moving a total of 26 m 20 km landward of the grounding line, 44 m at the grounding line, and 43 m at the site seaward for speeds of 732, 1,235 and 1,208 ± 1 m yr–1, with maximum speed at the grounding line." - pdf
"As the glacier lifts and migrates, the water can rush in for over a mile, thinning the ice by as much a 250 feet (76 m) a year in some places. You have this constant flushing of seawater going many kilometers below the glacier and melting the ice,” said Eric Rignot in a WaPo interview.
What determines how far the seawater rushes in with the tide - and how would this change after another major caving? The shelf itself is already floating in approximate hydrodynamic equilibrium but ice upstream of the (retreating) grounding line must be lifted.