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EARTH, ATMOSPHERIC, AND PLANETARY SCIENCES feedbacks. Thus, for our baseline ensemble of Thwaites Glacier, those periods of fast retreat. This spread between simulations our conservative estimate for the statistics of ocean-induced melt amounts to instantaneous differences of hundreds of kilometers variability is τF = 10 y and σM = 1.4 m/y. In reality, we also in the grounding-line position (Fig. 3D). Following this growth expect that Mmax varies in space, due to (for example) the Cori- of uncertainty during the centuries of most rapid retreat, the olis effect on ocean circulation in the subshelf cavity, which ensemble then contracts and skews in the opposite direction would quantitatively (but not necessarily qualitatively) affect as individual ensemble members achieve complete deglacia- our results. tion of Thwaites Glacier, due to the limited model domain Fig. 3A shows the evolution of the probability distribution used in our simulations. In simulations of the entire Antarc- of a 500-member ensemble of ISSM-simulated ice volume at tic Ice Sheet in which the marine ice sheet instability spreads Thwaites Glacier in response to decadal variability in subice shelf to other glaciers (5, 6), we would expect even faster amplifi- melt rate. All ensemble members initialized with the modern cation of uncertainty as multiple glaciers become involved in state of Thwaites Glacier eventually reach complete deglacia- deglaciation. tion (Fig. 3B), in agreement with previous studies (24, 25). The In Fig. 4, we compare Thwaites Glacier ensemble statis- rate of grounding-line migration (Fig. 3C) experiences significant tics, given a comparable amplitude (σM = 1.4 m/y) of vari- variability over the course of the retreat due to the stochas- ability in Mmax, but differing degrees of temporal persistence. tic ocean forcing and the presence of forward-sloping “speed As predicted by theory, ensemble spread (Fig. 4A) increases bumps” in the bed topography, both of which can slow the rate √with longer persistence in forcing variability (proportional to of retreat or even cause advance for short durations (28). Even τF ; SI Appendix). During the century of fastest retreat, mul- with the relatively conservative assumption that there is no vari- tidecadal ocean variability (yellow line; τF = 30 y) produces ability in surface mass balance and a small amplitude of subshelf skewed uncertainty that is nearly 50% of the total ice loss from melt variability (representing <2% of the time-averaged subshelf Thwaites glacier or ∼40 cm of uncertainty in projected sea- melt), the spread in the ensemble spans ∼20 cm of uncertainty level rise. Some studies have suggested that Antarctic glaciers in projected sea-level rise during periods of fast retreat (i.e., the may be subject to such multidecadal variability in forcing green probability distribution functions [PDFs] in Fig. 3A), with through low-frequency coupled modes of the ocean–atmosphere a probability distribution skewed in the direction of lower ice vol- system (26) or sporadic detachment of very large tabular ume (greater contribution to sea level). This uncertainty is over icebergs (29). 25% of the entire sea-level rise due to deglaciation of Thwaites Poorly constrained subice shelf properties [such as roughness Glacier and 50% of the median sea-level rise achieved during (30)] and the small scale of the turbulent ice–ocean boundary

Fig. 3. Evolution of a 500-member ensemble of ISSM simulations of Thwaites Glacier evolution over 500 y (where year 0 in model time is the modern glacier state) in response to decadal variability and constant average in maximum subice shelf melt rate. (A) Evolution of ensemble PDF over time, plotted every 25 y, with probability on the y axis and Thwaites Glacier ice volume (in cm sea-level equivalent [SLE]) on the x axis. (B) Black lines are simulated ice volume contained in Thwaites Glacier catchment in cm SLE for all ensemble members. (C) Black dots are evolving grounding-line migration rates for all ensemble members (based on the centroid of the 2D grounding line). (D) Snapshots (red, orange, and pink lines) of grounding-line positions at year 635 in model time, from 5th percentile, 50th percentile, and 95th percentile ice volume ensemble members.

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Euler–Maruyama the (Eq. model Model. minimal Minimal of Solution Numerical sea- Methods useful and Materials most the make depend who them. can stakeholders on those we for 2100 sophisticated beyond that Such projections level 34). ensure the (31, captures will quan- dynamics that methods sheet reduction uncertainty ice order for of model methods complexities and efficient 37) (32, need Antarctic tification possible will pro- Ice of Antarctic range we be complete entire futures, the can the capture fully to ensembles To extended Sheet. model sea- when rapid be future large expensive of can for hibitively However, scenarios scenarios ensembles rise. catastrophic possible (5, model potentially sea-level of that rise including range shown sea-level rise, a stud- have level future quantify ensemble We to to 35). in contribution used 34, seen sheet 32, ice been 6, total has of as glacier’s ies projections, each uncertainty sea-level of considerable to in uncertainty leading the potentially over evolution, integrates instability future also sheet ice glaciers instability. marine many rapid the of most contribution of of the sheet regardless Integrating periods ice the instability, during in uncertainty sheet broad growth we projection rapid ice that sufficiently experience of will such a involved, type dynamics, processes to any sheet ice that applies regarding expect study assumptions frame- this of cause that theoretical set to in shows the kind) developed Indeed, analysis any growth. work (of our uncertainty instability sheet, rapid rapid or more more ice (36) expect stabilize an should might we (6) that destabilize here mathemati- there considered further Although common not (22). a processes systems nonlinear are is unstable which of property uncertainty, cal of amplifiers are rvddb S rn L-751 t ... n S rn PLR-1643299 Grant NSF was and A.A.R.) support (to G.H.R.). Advanced Financial PLR-1735715 (to Center. NASA Grant NSF Research the by Ames through provided provided Program at were Computing Division work High-End Supercomputing Predic- this by NASA and supporting the supported Analysis resources by Modeling, was Computing and the H.S. Programs. Science by Dynamics. tion Cryospheric coordinated Climate NASA is from in which grants School Course, Research Dynamics of Climate Norwegian Insti- stages Advanced California Mini-Symposium, the early Cryosphere the and Laboratory the through Propulsion nucleated Technology–Jet during was of discussions tute collaboration helpful This project. to this contributed Mantelli E. constant held and ACKNOWLEDGMENTS. domain the of surface bal- the mass from time. at period in Surface applied 2010 to are persistence. 1979 (39) the long-term monthly over RACMO2 averaged the of temperatures SD of surface and the regardless ance that m/y, ensure 5 depth to always renormalized a and at month occurs every func- that simple rate a follows melt melt depth basal of shelf the tion facilitate Subice and simulations. load fixed ensemble computational held large reduce are to and catchment) simulation friction, Glacier the Thwaites basal throughout modern the temperature, a of (covering Ice basis is boundaries (38). the rigidity basin on assimilation ice inverted data are and using both law velocities our and viscous temperature, In linear ice step. resolu- of time a function 1-km 2-wk follows each friction at on basal catchment position simulations, Thwaites grounding-line the in and everywhere elevation, tion base and surface SMi nt-lmn otaepcaewihi sdt ov the solve to used is which package software finite-element a is ISSM = 0 /)drn niiil50ysi-ppro.A h end the At period. spin-up 500-y initial an during m/y) −0.006 https://github.com/aarobel/StochasticMISI. b(x M https://issm.jpl.nasa.gov/ (z ) = ) = −0.002x ,adpotdi i.2 r ovdnmrclyusing numerically solved are 2, Fig. in plotted and 1), M max .Hslf,W on .Ta,C ee,and Meyer, C. Tsai, V. Moon, W. Haseloff, M. − n steady-state and , M max (z z (t max max )bgn l oeue ornthese run to used code All begin. )) h nebesmltosuigthe using simulations ensemble The etrain in Perturbations . − h oe ovsfrievelocity, ice for solves model The . z ,where ), L NSLts Articles Latest PNAS = 5 m h e topog- bed The km. 250 M max M stemaximum the is max t = r varied are ,which 0, | M max f6 of 5 is

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