Brief communication: A roadmap towards credible projections of ice sheet contribution to sea-level

. Accurately projecting mass loss from ice sheets is of critical societal importance. However, despite recent improvements in ice sheet models, our analysis of a recent effort to project Greenland’s (cid:58)(cid:58)(cid:58) ice (cid:58)(cid:58)(cid:58)(cid:58)(cid:58) sheet contribution to future sea-level suggests that few models reproduce historical mass loss accurately, and that they appear much too conﬁdent in the spread of predicted outcomes. The inability of models to reproduce historical observations raises concerns about the models’ skill at projecting 5 mass loss. Here we suggest that (cid:58)(cid:58)(cid:58)(cid:58)(cid:58)(cid:58)(cid:58)(cid:58)(cid:58)(cid:58) uncertainties (cid:58)(cid:58)(cid:58) in the future sea level contribution from Greenland (cid:58)(cid:58) and (cid:58)(cid:58)(cid:58)(cid:58)(cid:58)(cid:58)(cid:58)(cid:58)(cid:58) Antarctica (cid:58) may well be signiﬁcantly higher than reported in that study. We propose a roadmap to enable a more realistic accounting of uncertainties associated with such forecasts, and a formal process by which observations of mass change (cid:58)(cid:58)(cid:58)(cid:58)(cid:58) should be used to reﬁne projections of mass change. Finally, we note that tremendous government consensus (cid:58) and to guide future efforts, we recast the problem of ice sheet simulation through a probabilistic lens in characterization distributions, and assess how our two conditions above relate to this viewpoint. We then sketch a path forward for robustly characterizing the potential ice sheet contribution to sea level over the coming century.


Quantifying uncertainties
For the practical problem of predicting the ice sheets' contribution to sea level, we find it useful to adopt a probabilistic framework. In that framework, we seek to establish a credibility bound (say 90%)for predictions, and to determine the range : , 90 between which sea level contribution will fall with that pre-supposed probability. Such an interval can readily be constructed from a probability density function (PDF) for the cryosphere's contribution to global sea level :: by ::::::::: computing :::::::: quantiles, and thus this is the function that experiments aiming to quantify sea level contribution must correctly characterize. We write this predictive distribution as

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While interpretation of P (∆z|F) is straightforward, its accurate construction is a grand scientific challenge. The standard approach involves running computer programs that approximately solve mathematical equations describing our best understanding of ice sheet physics. In the best case, when all facets of a physical system are known (including initial and boundary conditions), the equations describing those systems are complete and deterministic, and the mechanism of solution is perfect, then uncertainty in the distribution collapses and : . :: In ::: this :::::::: idealized :::::::: situation :::: there :: is :: no ::::::::: predictive ::::::::: uncertainty :: in : sea level con-105 tribution, ::: and P (∆z|F) , can be characterized with a single model run. In practice, several types of uncertainties complicate the issue and introduce bias and variance in the predictions. In the following, we discuss these different categories of uncertainty as they pertain to the problem of sea level contribution.
Similar to model uncertainty, initial state uncertainty I affects the distribution over sea level contribution as

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where I is an initial state.
Details vary from model to model, but generally include initial conditions for the conservation of mass (ice thickness and extent), momentum (basal stress distribution), and energy (temperature or enthalpy).

Parametric uncertainty
Due to computational and conceptual constraints, there are limits to the level of detail at which processes can be simulated can be decomposed as where f represents a specific realization of a random forcing, and P (f |F) is its probability distribution under scenario F.

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Due to the relatively slow response time of the cryosphere to such forcings, aleatoric uncertainty often contributes little variance to predictions in sea level contribution over practical time scales of decades to centuries. However, in circumstances where these forcings may interact with a critical glaciological instability like the Marine Ice Sheet Instability (Mercer, 1978), aleatoric uncertainty has the tendency of producing 'fat tails', effectively biasing ice sheet evolution towards more extreme mass loss scenarios (Robel et al., 2019). While only a few studies have characterized the distribution over ice sheet responses 165 to aleatoric uncertainty :::::::::::::::::::::: (e.g. Hoffman et al., 2019), and its influence is not precisely known, Monte Carlo simulation can be used to understand the effects of this kind of uncertainty when multiple realizations of forcings are available.
3 Assessing the ISMIP6 ensemble through the probabilistic lens The response of an ice sheet to a given forcing F may be estimated with Earth System Models directly. At present, however, Earth System Models with built-in interactive ice sheets remain in their infancy (Vizcaino, 2014) and are not yet able to 170 ::::::::: adequately resolve ice sheet processes such as grounding line migration at the necessary resolution, requiring intermediate steps.
A common approach, pursued by , involves general circulations models to calculate how the global climate responds to a given forcing F, regional climate models to downscale the global climate response to the ice sheet scale, and process models and parameterizations (e.g., surface energy balance models, calving models or frontal ablation models) to interface with ice sheet models.

A biased sample over models
The implicit hypothesis made when accounting for model error using an ensemble approach is that each model is an independent sample from P (M), where the mode of P (M) is the true data generating process (i.e. reality). However, the models 215 included in the ensemble are not likely to be independent: they share many critical features like numerical methods, parameterizations, and a joint disregard ::::::: omission :: of : for potentially important physical processes that have not yet been discovered.
We emphatically note that this is not a methodological criticism: it is a challenge that exists generally in science, with analogous situations arising in climate modelling (Qian et al., 2016). We note also that such biases may also arise from incorrectly specified prior distributions over parameters and forcings. Nonetheless, the challenge remains real, as does its potential effect 220 on the accuracy :::::::: credibility : and uncertainty of sea level rise projections. As shown in Figure 1, ensemble predictions relative to contemporary observations of mass loss are strongly biased relative to present observations. While ::: the accurate reproduction of observed mass change was not a goal of , :: the : credible projection of future mass change was . There : a ::::: stated :::: goal. :::::::: However, ::::: there is no reason to believe that the ensemble : a ::::::::: prediction ::: that :: is :::::: biased :::: now does not remain biased in its future predictions.
All ice sheet models already perform this calibration for certain subsets of available observations, e.g. by calibration of basal traction or other parameters to yield observed surface velocity or ice geometry within observational uncertainty. In essence, we 260 argue that the existing calibration for parametric uncertainty be moved out from under the purview of individual models , and become an explicit step in the assessment of ice model ensembles.
National Science Foundation allocated $123M to research funded by its Office of Polar Programs (National Science Foundation, 2021)
It is unconscionable that the only scientific basis for sea level contribution from the ice sheets stems from an essentially volunteer effort. Given the lack of investment, it is small wonder that ice sheet mass change validation deviates so severely from 310 observations (Fig. 1). We urgently need more reliable assessments of the :: In :::: order :: to :::::: assess potential impacts of sea level rise, which includes a deliberate effort at quantifying ::: we ::::::: urgently :::: need :: to ::: be :::: able :: to :::::::::: deliberately ::::::: quantify : and then systematically reducing ::::: reduce : uncertainties. Ice sheet modeling, like climate modeling before it, developed from efforts to address basic science questions. However, despite major advances in the capabilities of ice sheet models and expanding appreciation for the importance of their projections, the funding model of modest grants to address basic science and accomplish incremental this financial support has contributed to a suite of models that now convincingly reproduce observed climate variability (Jones et al., 2013). It is time to similarly bring ice sheet modeling, ::::: both ::::::::: standalone ::: and ::::::::: embedded :: in ::::: Earth ::::::: System ::::::: Models, : to an operational level and support it with the funding the problem deserves.

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The ambitious characterization of uncertainties and ensemble conditioning we propose requires a massive international and inter-agency effort in both model development and improved observational capabilities. Similar to the manner by which American researchers conducting field work in Antarctica benefited in 2019 from $292M of investment in professional facilities, and operational and logistical support (National Science Foundation, 2021), we :: We : call for professional support for the largely computational sea level projection effort. These resources, in the form of dedicated developers and high performance comput-325 ing time, will free up scientists to continue basic science, while the global community receives the applied science (i.e., reliable sea level projections) it needs.