the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 14 Aug 2024
The demise of the world's largest piedmont glacier: a probabilistic forecast
Abstract. Sít' Tlein in Alaska's St. Elias Range (briefly known as Malaspina Glacier) is the world's largest piedmont glacier and has thinned considerably over 30 years of altimetry, yet it's low-elevation piedmont lobe has remained intact in contrast to the glaciers that once filled neighboring Icy and Disenchantment bays. In an effort to forecast changes to Síit' Tlein over decadal to centennial time scales, we take a data-constrained dynamical modelling approach, in which we constrain the parameters of a higher order model of ice flow – the bed elevation, basal traction, and surface mass balance – with a diverse but spatio-temporally sparse set of observations including satellite-derived time-varying velocity fields, radar-derived bed and surface elevation measurements, and in situ and remotely sensed observations of accumulation and ablation. Nonetheless, such data do not uniquely constrain model behavior, so we adopt an approximate Bayesian approach based on the Laplace approximation and facilitated by low-rank parametric representations to quantify uncertainty in the bed, traction, and mass balance fields alongside the induced uncertainty in model-based predictions of glacier change. We find that Sít' Tlein is considerably out of balance with contemporary (and presumably future) climate, and we expect its piedmont lobe to largely disappear over the coming 150 years. We forecast a total mass loss at Sít' Tlein of between 500 and 1000 km3 of ice, a range that represents not only uncertainty in model inputs, but also in future warming scenarios. The resulting retreat and subsequent replacement of glacier ice with a marine embayment or lake will yield a significant modification to the regional landscape and ecosystem.
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The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
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Journal article(s) based on this preprint
Interactive discussion
Status: closed
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RC1: 'Comment on egusphere-2024-2354', Anonymous Referee #1, 18 Oct 2024
- AC1: 'Reply on RC1', Douglas Brinkerhoff, 21 Dec 2024
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RC2: 'Comment on egusphere-2024-2354', Anonymous Referee #2, 24 Oct 2024
This is a review of the manuscript by Brinkerhoff et al. on "The demise of the world's largest piedmont glacier: a probabilistic forecast", submitted to The Cryosphere. This study is focused on Sit' Tlein, the world's largest piedmont glacier. It describes the methodological advances needed to estimate time-dependent glacier model parameters for Sit' Tlein over the historical period, and then to produce a probabilistic forecast of it's future evolution. During the historical period, a range of observations have been made which are used as the inputs to a Bayesian method which efficiently estimates the posterior distribution of model parameters which are then used in future forecast simulations.
This is an impressive study, and one which clearly brings together many years of work on observational and modeling techniques to produce efficient methods for Bayesian parameter estimation and probabalistic forecasting. This style of modeling is at the forefront of ice sheet modeling, and as such this study represents a valuable and important benchmark for the ice sheet modeling community, and how we "should" be doing things.
I have a number of technical questions about the methods that came up as I read through the manuscript. These are detailed below. First, I detail some of my broader concerns with the manuscript and its structure, and a few bigger choices.
1. Perhaps my biggest comment is that the shear length and density of this manuscript may be a barrier to more widespread engagement with this important work. The paper almost read as two papers to me: a methods paper and a modeling paper. While many of the individual methodological steps have been detailed in prior publications, sections 2 and 3 and parts of 4 (constituting about half the manuscript) put all these pieces together to describe what is effectively (for lack of a better descriptor) a data assimilation workflow for glacier modeling. While I think these details are very interesting, that may not be true of the entire audience for this paper, particularly with the eye-catching results that come out of this method. I think there are two options to address this issue: (1) the easiest thing to do would be to move the bulk of the methodological detail into the appendix and simply provide a high-level overview in a single short section in the main text, with heavy reference to the appendix, or (2) there could be a whole second paper just on the methods, appropriate for a journal like GMD or JAMES.
2. This study was incredibly meticulous in constructing a state-of-the-art method for accurate Bayesian parameter (and state) estimation for the hindcast period. It was then surprising that a few highly simplistic choices were made in configuring the forecast simulations that were only lightly justified or explored. There are two in particular that it would be useful to understand in more detail:
(a) SMB forcing - the "control" case is a reasonable end member, but I'm not sure what to make of the linear extrapolation. You show that while most of the piedmont lobe is effectively "committed" to future mass loss based on current climate, there is a large difference between the present and projected climate states (comparable or larger than posterior parametric uncertainty projected from hindcast). It thus bears more justification that this continued rate of SMB change is comparable to what is actually projected for this region. Polar temperatures are warming faster than the global average, and in some places accelerations are expected in the future. It would be nice to have maybe a high end-member based on some reasonable realistic projection of SMB changes in this region due to a high-end emissions scenario. As you indicates, its easy enough computationally to run a new set of simulations sampling the posterior, so it shouldn't be too challenging to do this.
(b) Basal traction - I like the attempt at representing the surge cycle by repeating the time-dependent basal traction estimate. However, I have no sense if this is actually important. I don't really see any evidence for periodicity in the forecast, so I wonder how much the basal traction variability really matters for the forecast. This is easy enough to test: simply do further forecasts where the basal traction is held constant to values at 2023, and perhaps another for values held constant to something around the late 1980's, since these clearly capture periods with very different velocities along the centerline.
3. I say this down below as well, but something I was wondering about throughout the first half of the manuscript is whether this method strictly constitutes a parameter estimation problem or whether direct state estimation occurs as well? It would be helpful to be explicit about exactly what things are being estimated and which aren't. Perhaps a list/table.
Minor comments:
L12: can you may this statement of "between 500 and 1000" more precise? What are the probabilistic bounds and what are the exact numbers? Perhaps just give the 95% credible range to be more specific.L22: The total area
L25: is thinning
L27: removed from the coast
L30: one point connected to piedmont
L53: it would be useful to be clear about whether this is strictly a parameter estimation problem, or a joint parameter and state esimation problem. It was a little unclear to me at this point in the paper
L94: equations;
L110: can you give a bit more justification of this 80% or SL water pressure configuration for effective pressure?
L140: perhaps add these convergence experiments to the supplement
L199: you talk about this simplification a bit more later, but is there a technical/computatoinal reason why you can't treat bed elevation the same as basal traction (i.e. in a time-dependent fasion) in the parameter estimation problem? Wouldn't this address the concern you bring up later about tidewater sedimentation?
L200: (not here, but I though of it here) would be useful to cite some of MacKie's papers on geostatiscal emulation of bed topography
L212: this implicitly makes an assumption about smoothness then? Perhaps state explicitly what that assumption is.
L236: Does this mean that only covariance with neighboring elements is preserved? Would this have grid-depedence issues?
L258: in Tober
L345: be more specific about which geometric observations
L420: this spinup procedure makes me curious why you didn't use historical observations directly in the estimation procedure? The error would be large, but you are implicity using them here, and you already have the framework to incorporate them directly
L425: is it possible hysteresis could be going on here? I think there needs to be a stronger argument here.
L440: offers complete coverage
L448: does interpolation induce correlation?
L490: explain why the log posterior is more convenient
L517: unconstrained or underconstrained?
L565: I think the equation reference here is incorrect
L632: that are associated
Figs 6-7: these should probably have different colormaps, and the Fig 6 colormap would be more intuitive if thinning was red and thickening was blue
Fig 9: it would be more intuitive if the points were colored by their corresponding cross section
L658: where faster flow
Figs 10-12: I think it would make more sense to plot these as change in thickness. For Fig 10, from 1915 and for Figs 11-12, from 2023.
Fig 13: I think the change in x-axis scale is a bit more confusing that illuminating, and I was looking for an explanation of the apparent acceleration until I read all the way through the caption. I would instead may the x-axis have a single time scale and then plot an inset in the lower left corner, which is empty anyway, with the zoomed in period up to 2060.
L697: another way to say this that might be more straightforward is that changes in the piedmont ablation zone are largely already commmited by climate change pre-2023 and changes in the accumulation zone are still largely dependent on future climate change.
L703: im not sure if you can say this is "significantly" greater as they are within +/-2 sigma
7.1.3 and 7.1.4 section titles: should say "surface mass balance"
L732/736: need more citations of these points presented as facts with little support
L762: it would help to cite Fig 13 here which shows this exact point.
L777: isn't it ithe case that this won't really effect the glacier when it is monotonically retreating? Since this modification to bed elevation only occurs in places not in contact with the ice base? Or is there something subtle about floating ice that I'm missing here? In any case, more explanation of how this affects the glacier in this particular case would be useful.
L791: are consistent
L795: changes alone cannot
L797: as in Brinkerhoff
7.3.1-7.3.4: I appreciate the thorough review of prior work here, but it isn't all really necessary for the discussion that comes after in 7.3.5. I would eliminate these section and fold in the reference to prior work into 7.3.5 only where they are referenced in comparison to your work.
L838: modelling
L893: is this on one processor? Would make more sense to use an actual computational unit, not just a "laptop" (also specifying the hardware).
L911: "This could constitute the largest removal of park lands in the history of the National Park System." This is a striking statement that should go in the abstract.
L920: the problem
Citation: https://doi.org/10.5194/egusphere-2024-2354-RC2 - AC1: 'Reply on RC1', Douglas Brinkerhoff, 21 Dec 2024
Interactive discussion
Status: closed
-
RC1: 'Comment on egusphere-2024-2354', Anonymous Referee #1, 18 Oct 2024
- AC1: 'Reply on RC1', Douglas Brinkerhoff, 21 Dec 2024
-
RC2: 'Comment on egusphere-2024-2354', Anonymous Referee #2, 24 Oct 2024
This is a review of the manuscript by Brinkerhoff et al. on "The demise of the world's largest piedmont glacier: a probabilistic forecast", submitted to The Cryosphere. This study is focused on Sit' Tlein, the world's largest piedmont glacier. It describes the methodological advances needed to estimate time-dependent glacier model parameters for Sit' Tlein over the historical period, and then to produce a probabilistic forecast of it's future evolution. During the historical period, a range of observations have been made which are used as the inputs to a Bayesian method which efficiently estimates the posterior distribution of model parameters which are then used in future forecast simulations.
This is an impressive study, and one which clearly brings together many years of work on observational and modeling techniques to produce efficient methods for Bayesian parameter estimation and probabalistic forecasting. This style of modeling is at the forefront of ice sheet modeling, and as such this study represents a valuable and important benchmark for the ice sheet modeling community, and how we "should" be doing things.
I have a number of technical questions about the methods that came up as I read through the manuscript. These are detailed below. First, I detail some of my broader concerns with the manuscript and its structure, and a few bigger choices.
1. Perhaps my biggest comment is that the shear length and density of this manuscript may be a barrier to more widespread engagement with this important work. The paper almost read as two papers to me: a methods paper and a modeling paper. While many of the individual methodological steps have been detailed in prior publications, sections 2 and 3 and parts of 4 (constituting about half the manuscript) put all these pieces together to describe what is effectively (for lack of a better descriptor) a data assimilation workflow for glacier modeling. While I think these details are very interesting, that may not be true of the entire audience for this paper, particularly with the eye-catching results that come out of this method. I think there are two options to address this issue: (1) the easiest thing to do would be to move the bulk of the methodological detail into the appendix and simply provide a high-level overview in a single short section in the main text, with heavy reference to the appendix, or (2) there could be a whole second paper just on the methods, appropriate for a journal like GMD or JAMES.
2. This study was incredibly meticulous in constructing a state-of-the-art method for accurate Bayesian parameter (and state) estimation for the hindcast period. It was then surprising that a few highly simplistic choices were made in configuring the forecast simulations that were only lightly justified or explored. There are two in particular that it would be useful to understand in more detail:
(a) SMB forcing - the "control" case is a reasonable end member, but I'm not sure what to make of the linear extrapolation. You show that while most of the piedmont lobe is effectively "committed" to future mass loss based on current climate, there is a large difference between the present and projected climate states (comparable or larger than posterior parametric uncertainty projected from hindcast). It thus bears more justification that this continued rate of SMB change is comparable to what is actually projected for this region. Polar temperatures are warming faster than the global average, and in some places accelerations are expected in the future. It would be nice to have maybe a high end-member based on some reasonable realistic projection of SMB changes in this region due to a high-end emissions scenario. As you indicates, its easy enough computationally to run a new set of simulations sampling the posterior, so it shouldn't be too challenging to do this.
(b) Basal traction - I like the attempt at representing the surge cycle by repeating the time-dependent basal traction estimate. However, I have no sense if this is actually important. I don't really see any evidence for periodicity in the forecast, so I wonder how much the basal traction variability really matters for the forecast. This is easy enough to test: simply do further forecasts where the basal traction is held constant to values at 2023, and perhaps another for values held constant to something around the late 1980's, since these clearly capture periods with very different velocities along the centerline.
3. I say this down below as well, but something I was wondering about throughout the first half of the manuscript is whether this method strictly constitutes a parameter estimation problem or whether direct state estimation occurs as well? It would be helpful to be explicit about exactly what things are being estimated and which aren't. Perhaps a list/table.
Minor comments:
L12: can you may this statement of "between 500 and 1000" more precise? What are the probabilistic bounds and what are the exact numbers? Perhaps just give the 95% credible range to be more specific.L22: The total area
L25: is thinning
L27: removed from the coast
L30: one point connected to piedmont
L53: it would be useful to be clear about whether this is strictly a parameter estimation problem, or a joint parameter and state esimation problem. It was a little unclear to me at this point in the paper
L94: equations;
L110: can you give a bit more justification of this 80% or SL water pressure configuration for effective pressure?
L140: perhaps add these convergence experiments to the supplement
L199: you talk about this simplification a bit more later, but is there a technical/computatoinal reason why you can't treat bed elevation the same as basal traction (i.e. in a time-dependent fasion) in the parameter estimation problem? Wouldn't this address the concern you bring up later about tidewater sedimentation?
L200: (not here, but I though of it here) would be useful to cite some of MacKie's papers on geostatiscal emulation of bed topography
L212: this implicitly makes an assumption about smoothness then? Perhaps state explicitly what that assumption is.
L236: Does this mean that only covariance with neighboring elements is preserved? Would this have grid-depedence issues?
L258: in Tober
L345: be more specific about which geometric observations
L420: this spinup procedure makes me curious why you didn't use historical observations directly in the estimation procedure? The error would be large, but you are implicity using them here, and you already have the framework to incorporate them directly
L425: is it possible hysteresis could be going on here? I think there needs to be a stronger argument here.
L440: offers complete coverage
L448: does interpolation induce correlation?
L490: explain why the log posterior is more convenient
L517: unconstrained or underconstrained?
L565: I think the equation reference here is incorrect
L632: that are associated
Figs 6-7: these should probably have different colormaps, and the Fig 6 colormap would be more intuitive if thinning was red and thickening was blue
Fig 9: it would be more intuitive if the points were colored by their corresponding cross section
L658: where faster flow
Figs 10-12: I think it would make more sense to plot these as change in thickness. For Fig 10, from 1915 and for Figs 11-12, from 2023.
Fig 13: I think the change in x-axis scale is a bit more confusing that illuminating, and I was looking for an explanation of the apparent acceleration until I read all the way through the caption. I would instead may the x-axis have a single time scale and then plot an inset in the lower left corner, which is empty anyway, with the zoomed in period up to 2060.
L697: another way to say this that might be more straightforward is that changes in the piedmont ablation zone are largely already commmited by climate change pre-2023 and changes in the accumulation zone are still largely dependent on future climate change.
L703: im not sure if you can say this is "significantly" greater as they are within +/-2 sigma
7.1.3 and 7.1.4 section titles: should say "surface mass balance"
L732/736: need more citations of these points presented as facts with little support
L762: it would help to cite Fig 13 here which shows this exact point.
L777: isn't it ithe case that this won't really effect the glacier when it is monotonically retreating? Since this modification to bed elevation only occurs in places not in contact with the ice base? Or is there something subtle about floating ice that I'm missing here? In any case, more explanation of how this affects the glacier in this particular case would be useful.
L791: are consistent
L795: changes alone cannot
L797: as in Brinkerhoff
7.3.1-7.3.4: I appreciate the thorough review of prior work here, but it isn't all really necessary for the discussion that comes after in 7.3.5. I would eliminate these section and fold in the reference to prior work into 7.3.5 only where they are referenced in comparison to your work.
L838: modelling
L893: is this on one processor? Would make more sense to use an actual computational unit, not just a "laptop" (also specifying the hardware).
L911: "This could constitute the largest removal of park lands in the history of the National Park System." This is a striking statement that should go in the abstract.
L920: the problem
Citation: https://doi.org/10.5194/egusphere-2024-2354-RC2 - AC1: 'Reply on RC1', Douglas Brinkerhoff, 21 Dec 2024
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Douglas Brinkerhoff
Brandon Tober
Michael Daniel
Victor Devaux-Chupin
Michael Christoffersen
John W. Holt
Christopher F. Larsen
Mark Fahnestock
Michael G. Loso
Kristin M. F. Timm
Russell Mitchell
Martin Truffer
The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
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