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Ice sheet mass loss is typically provided only for grounded ice, because changes in floating ice are more difficult to measure and contribute minimally to sea level rise. However, total ice sheet mass change (net freshwater volume flow rate across ice sheet boundaries) including floating ice is a better metric of ice sheet health and is a necessary input to research domains beyond sea level rise such as physical, chemical, biological, or ecological oceanography, among other fields.
Here we present total mass flows for both the Greenlandic and Antarctic ice sheets from 2010 through 2019. In addition to total mass flow, we provide all constituent terms (for example, components that combine to provide surface mass balance (SMB), not just the final SMB) and gross not net values (for example, gross frontal retreat and gross frontal advance, not just net retreat). We present results both in tabular form and using Sankey diagrams that show relationships between processes and increased information density over traditional tables.
In addition to the floating component, constituent terms provide a better metric of ice sheet health. For example, SMB can remain the same between two years, but have different inputs and outputs. Gross values lead to significantly larger estimates of some properties. For example, net frontal retreat of ice shelves in Antarctica is ~200 Gt yr-1, but we report double that amount or 400 Gt yr-1 of frontal retreat offset by 195 Gt yr-1 of frontal advance.
Ice mass loss in Greenland is 330 Gt yr-1 which is ~30 % larger than the 255 Gt yr-1 grounded ice mass loss estimates that neglect terminus retreat, frontal retreat, and sub-shelf melting. Ice mass loss in Antarctica is 450 Gt yr-1 which is ~240 % larger than the 190 Gt yr-1 grounded ice mass loss estimates that neglect ice shelves. Total freshwater volume flow rate from Greenland is ~1000 Gt yr-1 or ~3x mass loss (~4x grounded mass loss), and from Antarctica is ~3125 Gt yr-1, or ~7x mass loss (~17x grounded mass loss).
The flow of mass into, within, and out of ice sheets has global impacts including sea-level change, so Greenland and Antarctica’s net mass balance have been the focus of a great deal of recent scientific research (citet:ipcc_AR6_ch9,otosaka_2023,mankoff_2021,rignot_2019, and many others). The mass loss from the grounded portion of the Greenlandic and Antarctic ice sheets contributes to sea level rise (SLR), and can be captured by a single value or time series per ice sheet. Reporting a single value is beneficial because it simplifies interpretation and comparison. However, ice sheets are complex systems and while their contribution to sea level rise is important, focusing on their SLR contribution alone neither provides a holistic view nor captures the general health and state of the ice sheet. As one example, an ice sheet that increases output via discharge or submarine melting by X % but has that offset by an equal increase in snowfall would report no net mass change or SLR contribution, but has entered a different state when viewing constituent terms. Few studies consider all mass transport pathways and their relative magnitudes and uncertainties - this is typically limited to review papers, which may not focus on quantitative assessment of each process.
Net mass flow or mass balance is typically analyzed using one or a combination of four methods.
The gravimetric method is observation-based and excels at measuring the grounded ice contribution to sea level rise, but cannot observe changes in floating ice, nor distinguish processes that contribute to changes of the grounded ice. Spatial resolution is O(100) km and temporal resolution is monthly (e.g., citet:groh_2019).
The volumetric method is also observation-based, has spatial resolution of O(10) km and temporal resolution is monthly (c.f citet:khan_2022_alt,simonsen_2021). It can be used over floating ice, and this is the primary method for observing ice shelf thinning from which sub-shelf melt is inferred (e.g., citet:greene_2022,davison_2023). However, the volumetric method cannot be used to distinguish between surface and grounded basal processes and only reports total thinning \citep[c.f.,][]{karlsson_2021}.
The third observation-based method is relatively new and uses global navigation satellite system (GNSS) stations to measure bedrock uplift around Greenland citep:barletta_2024, from which ice sheet mass changes are estimated, or discharge from individual glaciers citep:hansen_2021. This method has spatial resolution of O(100) km and temporal resolution is daily.
Finally, the input-output (IO) method is a hybrid of regional climate models (RCM) and observation based (velocity, thickness). It is typically reported at low spatial resolution - at most individual glacier basin, but in theory can be applied at the resolution of the RCMs. Temporal resolution is ~10 days or whenever a new velocity map is generated, but given the relative stability of the ice discharge (10 day resolution) to the SMB (daily), the IO method can provide some estimate of daily mass balance citet:mankoff_2021. The IO method is the only one that captures all of the processes contributing to changes of grounded ice and provides gross values and constituent terms.
Here we use a combination of the IO method over grounded ice, the altimetry method over ice shelves, and other individual remote sensing estimates of ice shelf and glacier front advance and retreat.
Sankey diagrams are graphical representations of flow or movement of any property (e.g., mass, energy, money, etc.). An early and famous use was Charles Minard’s Map of Napoleon’s Russian Campaign of 1812 (c.f., citet:kraak_2021) that combines the magnitude of active soldiers overlaid on a geographical map. The method was later refined, popularized, and eventually named after Captain Matthew Henry Phineas Riall Sankey who used it to show, among other things, the energy efficiency of a steam engine.
A similar display to the diagrams presented here by \citet[][Figure 2]{cogley_2011} shows glacier processes overlaid an a glacier schematic and here we build on that work by adding magnitude of processes and making the graphics proportional to magnitudes.
Appendix A has details on the software used to generate these Sankey diagrams.
Sankey diagrams are generally intuitive, but the following section may still be helpful in interpreting the diagrams shown here.
The widths of all lines are all proportional to each other both within and among Figures \ref{fig:gl}, \ref{fig:aq}, and \ref{fig:aq_regions} (Appendix B) but not Fig. \ref{fig:aq_complex} (Appendix C).
Sankey diagrams balance all inputs and outputs, which introduces a complication for the use case here due to the mass imbalance. Traditionally, when a Sankey diagram has a loss term, it is an output. For example, all engines have energy inputs greater than outputs, the ratio between the two is a measure of efficiency, and the energy lost between input and output is displayed as an additional output.
In the Sankey diagrams here with net mass loss, outputs are greater than inputs, so mass loss must then be a balancing input representing drawdown of the historical ice mass or retreat of the ice sheet boundary. In the Sankey diagrams with net mass gain, inputs are larger than outputs, so mass gain is a balancing output representing ice build-up or boundary expansion.
Finally, the Sankey diagrams shown here are simplistic representations of mass flow across the three ice sheet boundaries (atmospheric, subglacial, and oceanic). We combine all inputs and outputs, not distinguishing between inputs over grounded ice vs. inputs over ice shelves, or other display options. However, alternate displays are possible, and a more complex display is shown in Appendix C which separates inputs and outputs by region (grounded, floating) in Antarctica.
We use the common terms from citet:cogley_2011 with a clarifying points.
For marine terminating glaciers without ice shelves, calving fronts and grounding lines are the same, and in this case we use the term `front’ as in `calving front’ or `frontal advance’. We only use `grounding line’ to refer to ice/ocean/bed interface underneath ice shelves.
Sublimation from surface mass balance is often a net term that includes condensation, deposition, evaporation, and true sublimation. Here, sublimation is only the solid to gas process. We define condensation as the process that converts gas to liquid, deposition as gas to solid, evaporation as liquid to gas, and sublimation as solid to gas.
This work does not explicitly report submarine melt, the sum of all melt that occurs underwater, but instead we use and report constituent terms when available. Frontal melt is from vertical faces at the calving edge of Greenlandic glaciers. There are no estimates of frontal melt at the calving edge of Antarctic ice shelves or non-shelf calving regions, but mass flow across this boundary is then included in the calving estimates. Sub-shelf melt is from horizontal surfaces under ice shelves in Greenland and Antarctica.
We do not use the term `basal melting’ because it does not distinguish between grounded or floating ice. Ice shelf basal melt is `sub-shelf melt’, and grounded ice basal melt is `grounded basal melting’.
We generally avoid the term `flux’ which is by definition mass or volume flow rate per unit area. Because we do not report results per unit area, we use `mass flow rate’ [Gt yr-1] which is equal to `volume flow rate’ [km^3 yr-1].
We also sometimes report process and sometimes product. In many cases products and process are the same (e.g., `snowfall’ process and the `snowfall’ data product from the RCM). An example where one product rather than process is presented is the `frontal retreat’ data product which is a combination of the calving and frontal melting processes. An examples where processes rather than product is presented is the Greenland ice discharge product which is not shown because discharge is measured a few km upstream of the grounding line. Instead, we show the downstream calving and frontal melting processes.
Below we detail the source of each mass flow term. We begin with the outputs as these are generally of broader interest, followed by the inputs. We then describe how net mass loss or gain are computed. Finally, we address other methods such as regional separation, temporal alignment, and rounding.
We use constituent terms (i.e., gross not net) of surface mass balance from the Modèle Atmosphérique Régional (MAR) RCM for both Greenland citep:fettweis_2020 and Antarctica citep:agosta_2013 (XAVIER, WHAT REF SHOULD I USE?). Sublimation is solid that converts directly to gas without melting. Evaporation is liquid that converts directly to gas. Runoff is meltwater that does not refreeze and instead leaves the model.
In Greenland, we use ice discharge across flux gates ~5 km upstream from the grounding lines citep:mankoff_2021. That discharge term at the flux gates is known to overestimate discharge across the downstream grounding line because it neglects SMB losses between the flux gate and grounding line. These losses are estimated at ~17 Gt yr-1 by citet:kochtitzky_2023 who uses flux gates closer to the grounding line than the citet:mankoff_2020_solid flux gates. To account for this increased melt due to more distant flux gates we increase the citet:kochtitzky_2023 estimates to 20 Gt yr-1 and reduce discharge by this amount. Peripheral glaciers are not included in the citet:mankoff_2020_solid product, but are added through estimates from citet:bollen_2023.
Greenlandic discharge from the flux gates is split into either calving or submarine melting at the grounding line. This split is highly uncertain and minimally studied, but citet:rignot_2010 estimate that 20 - 80 % of the summer ice-front is directly melted by the ocean for the three glaciers they studied. From this, we split the discharge 50 % between calving and submarine melt.
In Antarctica, calving includes grounded ice that leaves the ice sheet directly into the ocean (not an input to an ice shelf; citet:rignot_2019) and ice shelf calving from citet:greene_2022.
Both Greenlandic and Antarctic ice shelf calving and frontal melt assume steady state. See frontal advance and frontal retreat for the non steady state component.
Sub-shelf melting in Greenland comes from citet:wang_2024, and in Antarctica comes from citet:paolo_2023.
The frontal retreat products for Greenland citep:kochtitzky_2023 and Antarctica citep:greene_2022 are one part of the non steady state component of calving and frontal melt processes (the other part being frontal advance). Here we report the product (frontal retreat) not the processes (calving, frontal melt). Frontal retreat is presumably split between submarine melt and calving processes ~50/50 in Greenland citep:rignot_2010 with high uncertainty, and is likely to be primarily calving in Antarctica.
Grounding line retreat, by definition here only occurring under ice shelves, has no complete published estimates in the dimensions needed here, mass or length\textsuperscript{3} and time (e.g., (Gt or km3) yr-1), and are typically reported in dimensions of length and time (e.g., m yr-1).
In Greenland, there is no known assessment of ice shelf grounding line retreat in the dimensions needed here. We use published values of Petermann glacier grounding line retreat (units m) from citet:millan_2022, ice velocity from citet:millan_2022, ice thickness from citet:ciraci_2023, and ice density of 917 kg m3 to calculate grounding line retreat in units of Gt yr-1. We estimate ~1.5 Gt yr-1.
Grounding line retreat is reported in Antarctica for Pine Island, Thwaites, Crosson, and Dotson ice shelves at 45 Gt yr-1 citep:davison_2023. We use this value for Antarctica and West Antarctica, 1 Gt yr-1 for East Antarctica and the Peninsula. This value is wrong, but with no additional information we use it as placeholder until such time as there is a better estimate of this value.
Grounded basal melting citep:karlsson_2021 comes from geothermal heat flux, frictional heat from sliding, and in Greenland, viscous dissipation of surface runoff routed to the bed citep:mankoff_2017_VHD. Antarctic basal melting citep:van-liefferinge_2013 excludes surface runoff.
Frontal advance is the counter part to frontal retreat and comes from citet:greene_2022 in Antarctica. There is no frontal advance in Greenland provided by citet:kochtitzky_2023. Advance (plus retreat) provide the non steady state component of calving in Antarctica, and calving plus frontal melting in Greenland.
These SMB inputs come from the MAR model. A more complex Sankey diagram would show some rainfall leaving directly as runoff or evaporation, as not all rainfall turns to snow. We neglect this level of detail here for simplicity.
Sub-shelf freeze-on from citet:wang_2024 in Greenland and citet:paolo_2023 in Antarctica is the opposite of sub-shelf melting. We note there is no analogous frontal freeze-on opposite frontal melt.
We calculate net freshwater mass flow not simply as the sum of all outputs, but using net not gross for some terms, when one considers the physical processes involved. For example, in Antarctica gross sub-shelf melting is 1375 Gt yr-1, but sub-shelf freeze-on of 366 Gt yr-1 should be subtracted from this value (Table \ref{tab:aq}). Freshwater for sub-shelf freeze-on must be supplied either from either grounded basal melting (meaning that freshwater term water does not reach the open ocean) or extracted from ocean water that flows under the shelf, temporarily increasing the salinity of sub-shelf water.
This treatment of freshwater volume flow rate is because we are focusing on freshwater or salinity, and salt as a tracer is assumed to be rejected during freezing of ocean water, or if fresh grounded basal meltwater is frozen, then that water does not leave the system. In these cases, a unit freeze-then-melt has no impact on the net tracer value. The process is assumed to be conservative (i.e., no external change).
We warn that other use cases should carefully consider assumptions of tracer treatment, for example, if a tracer is not conserved during a freeze-then-melt cycle. By providing constituent and gross terms, we hope this data set is still useful for these scenario.
Similarly, when considering total freshwater export (salinity), gross frontal retreat and gross frontal advance should be combined to net frontal change.
We calculate change as the sum of all outputs minus inputs. In the Sankey diagrams, when outputs are larger than inputs and there is mass loss, mass loss is an input representing drawdown of the historical ice mass or contraction of the ice area. When outputs are less than inputs and there is mass gain, which only occurs in East Antarctica, mass gain is an output representing build-up of ice mass or expansion of the ice area.
In Antarctica, we use the MEaSUREs Antarctic Boundaries for IPY 2007-2009 from Satellite Radar, Version 2 (NSIDC product 0709; citet:mouginot_2017,rignot_2013) to separate Antarctica into East, West, and Peninsula. Discharge from Antarctic islands is reported once for all islands by citet:rignot_2019. In order to separate island discharge by region, we find the area of all islands per region, and divide the discharge proportional to area. This implicitly assumes that discharge from each island scales linearly with the area of each island.
Most values come from time series that we limit to 2010 through 2019, or are provided for that time span. Some values cover different periods, and in these cases we use the closest time span to 2010 through 2019 (Tables \ref{tab:gl} and \ref{tab:aq}.).
Values in most tables and all figures are rounded to the nearest 5, with the exception of values less than 2.5 and greater than 0 which are rounded up to 5. In Table \ref{tab:aq} we round to 1, with the exception of values less than 0.5 and greater than 0 which are rounded to 1.
All mass flow terms, values for each term, time span of each value, and reference publication are shown in Tables \ref{tab:gl} and \ref{tab:aq} and Sankey diagrams. Net freshwater mass flow rates are shown in Table \ref{tab:results_fw} and net mass loss by region and grounded vs marine are shown in Table \ref{tab:results_mc}.
\begin{figure*} \centering{\includegraphics[width=0.85\textwidth]{gl_baseline.pdf}} \caption{Sankey mass flow diagram for Greenland. All widths are proportional within and between images. Gray is ice, blue is liquid, and yellow is gaseous phase. Inputs (left, arrow tail) are balanced by outputs (right, arrow head). Because Sankey diagrams balance all inputs and outputs, mass losses require a `mass loss’ input (red) to balance the larger outputs. Mass loss inputs are additional flow through the system, the source being historical ice not represented by the other inputs.} \label{fig:gl} \end{figure*}
\begin{figure*} \centering{\includegraphics[width=0.85\textwidth]{aq_All.pdf}} \caption{Sankey mass flow diagrams for Antarctica. See Fig. \ref{fig:gl} for legend and details.} \label{fig:aq} \end{figure*}
Net freshwater export to the ocean (mass loss terms excluding sublimation and evaporation) is 1000 Gt yr-1 for Greenland and 3125 Gt yr-1 for Antarctica (Table \ref{tab:results_fw}, also reporting values in Sverdrup or 1E6 m^3 s-1).
| Region | Gt yr-1 | Sv |
|---|---|---|
| Greenland | 1000 | 0.032 |
| Antarctica | 3125 | 0.099 |
| Antarctica East | 1165 | 0.037 |
| Antarctica West | 1425 | 0.045 |
| Antarctic Peninsula | 535 | 0.017 |
Mass change for the 2010 through 2019 period is net mass loss for Greenland, West Antarctica, the Antarctic Peninsula, and Antarctica as a whole, but net mass gain in East Antarctica (Table \ref{tab:results_mc}).
Greenland lost 255 Gt yr-1 from grounded ice and an additional 75 Gt yr-1 (30 %) from floating ice.
Antarctica lost 190 Gt yr-1 from grounded ice and an additional 260 Gt yr-1 (~2.4x) from floating ice. The grounded ice mass loss is partitioned with 250 Gt yr-1 lost from West Antarctica and 20 Gt yr-1 lost from the Peninsula offset by 80 Gt yr-1 gained in East Antarctica. Marine losses are partitioned with 275 Gt yr-1 lost from West Antarctica and 175 Gt yr-1 lost from the Peninsula offset by 190 Gt yr-1 gained in East Antarctica.
| Region | Grounded | Marine | Total |
|---|---|---|---|
| Greenland | -255 | -75 | -330 |
| Antarctica | -190 | -260 | -450 |
| East | 80 | 190 | 270 |
| West | -250 | -275 | -525 |
| Peninsula | -20 | -175 | -195 |
\label{sec:limits}
These figures and tables neglect some mass flow processes (some of which are included in \citet[][Figure 2]{cogley_2011}, and simplify others.
Neglected processes include grounded ice basal freeze-on (c.f., citet:bell_2014). Basal melting estimates currently assume all melt leaves the ice sheet and is therefore mass loss. That seems unlikely, given both observations of freeze-on citep:bell_2014 and that some melt, especially from the geothermal term (c.f., citet:karlsson_2021) occurs under thick ice far inland and far from active subglacial conduits. That is, there should be a second `refreezing’ loop at the bottom of the Sankey diagrams to represent basal refreezing.
Sub-aqueous frontal melt is excluded in Antarctica, because it is usually excluded in the literature that focus on ice shelf basal melt or calving. This term is implicitly included in the calving estimates. This process remains unquantified on ice-sheet wide scales.
Subaerial frontal melt and sublimation of the vertical face above the water line \cite[][Figure 2]{cogley_2011} is not explicitly treated but is included in other terms.
Grounding line retreat in both Greenland and Antarctica is largely unquantified in the units needed to include it here, as discussed in the methods.
We neglect avalanche on and off ice sheets - these likely matter more for mountain glaciers.
Snow drift on and off is also excluded. There is likely little snow drift onto either ice sheet, but drifting off may be of similar magnitude to some of the other smaller terms shown here. Some drift off may be implicitly included in the sublimation term (TODO: Xavier?).
There are a variety of simplifications. For example, rainfall input does not all turn to ice as depicted by the arrows in these diagrams. Some enters as part of the refreezing loop, and some remains liquid and leaves as runoff or evaporation. Similarly, the evaporation output could pull from the refreezing loop (in the liquid phase, depicted by the blue color) and also directly from rainfall as stated above. Although some path details are simplified, the magnitudes are still as reported in the input products.
The value of some terms presented here are a function of the temporal resolution of the upstream product that is an input to this work. For example, in Greenland we report 50 Gt yr-1 frontal retreat and 0 Gt yr-1 frontal advance using decade-scale reporting from citet:kochtitzky_2023. However, it is likely that this is a net term despite the majority of this work reporting gross terms, and that at some point during the decade there was some glacier advance.
Given a theoretical reference front location for calving and frontal melt, \(X\) Gt of frontal retreat may actually be \(X + Y\) Gt frontal retreat offset by \(Y\) Gt frontal advance that occurred at a temporal resolution below the observations. This does not matter for total freshwater volume flow rate, which should be calculate using net frontal change, not gross frontal retreat. Sub-shelf freeze-on and sub-shelf melting share some similar temporal resolution dependent issues, and a decision to use net or gross is dependent on the use case.
Sankey diagrams do not typically include a display of uncertainty, although it is possible to add a visual indicator to the graphic citep:vosough_2019. We do not include a display of uncertainty in the graphics, but do in the tabular display (Tables \ref{tab:gl} and \ref{tab:aq}). Uncertainty values come from the upstream published products that are inputs to this work.
NEED HELP FROM XAVIER ON THIS PARAGRAPH: The most common uncertainty value of 15 % comes from the MAR RCM, but the RCM uncertainty is derived from net SMB, not the individual constituent terms. If the 15 % SMB uncertainty is applied to each term as done here and then summed to SMB using traditional mathematical uncertainty propagation of independent variables (a physically incorrect assumption), SMB is 235 Gt yr-1 and uncertainty is 122 Gt yr-1 or ~50 %. This is due to the large snowfall and runoff relative to other terms. The sum of seven equal terms with 15 % uncertainty treated independently, is 5.6 %.
Discharge uncertainty in Greenland is reasonably well constrained at ~10 % by citet:mankoff_2020_solid and other similar products.
The division of discharge when it is divided into submarine melt and calving is highly uncertainty. citet:rignot_2010 reports “We conclude from this comparison that 20–80% of the summer ice-front fluxes are directly melted by the ocean” with the remainder coming from calving. From this, we split discharge 50/50 between frontal melt and calving (see Methods), and assign an uncertainty of 30 %. However, in this case, the two terms are not independent. They are highly dependent, constrained by the upstream discharge with 10 % uncertainty. It is only the separation and form or phase (solid or liquid) that is highly uncertain.
Discharge and discharge uncertainty in Antarctica is challenging to quantify. At the low end, citet:rignot_2019 reports uncertainty of ~5 % on the discharge term. This seems unlikely for several reasons, including that discharge uncertainty in Greenland is more than 5 % and bed topography is better constrained there, or that citet:rignot_2019 calculates discharge using a corrective scaling factor ranging from 0.62 to 4.57 and rely on 5 separate methods (that are applied in isolation, not constraining each other).
At the high end, citet:davison_2023 report a discharge (from grounded ice to ice shelves) increase of 1770 ± 870 Gt which is ~50 %, but Antarctic-summed steady state discharge uncertainty is 429 Gt yr-1 on an observed 1839 Gt yr-1 which is ~25 %.
Oceanographic models often use ice sheet freshwater export as a forcing, but it can be challenging for those model developers to find appropriate inputs in part because some models are coupled to ice sheet models, or global climate models with ice sheets, that contain some but not all processes. Ocean models and modelers then need to understand what processes are and are not included in the ice sheet outputs, and for the processes that are included, they may need to determine the anomalies and then add that to the ocean model \citep[c.f.,][]{schmidt_2023}.
The smaller terms shown here are commonly excluded because they are small, but ocean modelers who work with anomalies should be careful of excluding these small terms. These smaller terms are also often less likely to be included in the ice component driving or coupled to the ocean model. They should be include in the ocean model, however, because they can match the magnitude of the anomaly, especially if several of the smaller terms are combined.
We recommend the community report constituent terms and gross not net values. If needed, it is relatively straightforward to include a net combined term. There are numerous advantages.
More information is better. The potential benefits for future researchers to address currently-unknown research questions or undefined needs is likely to outweigh the costs of increased complexity, time, storage, and access.
Sea level rise research often focuses on how and why, not only how much. However even the IO method that provides process level detail is usually estimated with a single SMB value rather than constituent terms as shown here, and may miss important information. For example, if net SMB remains constant over time, but snowfall and runoff both increase, this indicates a different ice sheet state, and this information should not be removed through reporting of net values.
Finally, although we argue for gross not net and inclusion of constituent terms in general when sharing outputs, we caution that any users should consider if this is the correct treatment for inputs. For any given term - basal melt and freeze-on being a likely candidate for freshwater studies - it may be more correct to use net not gross.
In this work we report total ice sheet mass change for both Greenland and Antarctica for the 2010 through 2019 period, reporting not just grounded ice mass loss, but also changes in floating ice. We have provided all available constituent terms and gross not net values. This detailed information provides a better picture of ice sheet health than focusing only on mass loss or only on grounded ice.
We have also displayed these constituent terms and net values using Sankey diagrams which provides an information-dense display showing a) the relationships between terms and processes, b) quantitative display of the magnitude of each term, and c) visual comparisons between different ice sheets or sub-regions of ice sheets, as the magnitude of the graphic uses the same proportion between all images.
\bibliography{library} \bibliographystyle{igs}
| Initials | Data | Graphics | Wrote | Edited | Discussed |
|---|---|---|---|---|---|
| KDM | 1 | 1 | 1 | 1 | 1 |
See https://drive.google.com/drive/folders/1g9vXuQofIL5MgtrtQ2zzlLiu69j1kTvJ?usp=sharing
No authors have any conflict of interest with the work presented here.
We thank Damien Ringeisen for conversations in the development of this work.
We thank citep:sankey for the \LaTeX TikZ Sankey package, and citet:cogley_2011 for a reference graphic. Analysis was aided by the software packages Pandas (citet:pandas_team), Xarray (citet:xarray), and GRASS GIS (citet:GRASS), among other tools.
\appendix
\label{appendix:sankey}
There are several software packages that support creating Sankey diagrams with various levels of complexity and control. The three applications we found, in order from easiest and most limited to most complex and feature-full are the Mermaid diagram tool, Plotly (which can be used from Python, R, or other popular languages), Matplotlib, and finally \LaTeX.
The simplest Mermaid option is produced with only a CSV file of the format ‘in,out,value’. Neither order nor closure (balance) is important, and a user has limited control over layout and color, although a user can edit things later manually if generating SVG format. We used Mermaid to generate the Sankey diagram in Appendix C, and the source for this diagram can be found in the supplemental source at http://doi.org/10.5281/zenodo.14624614 file mermaid.org. Mermaid diagrams in Markdown files on GitHub render directly in the browser from the data (no saved image file).
The main Sankey diagrams shown here are generated using a \LaTeX\enspace template that uses the TikZ Sankey package citep:sankey. We use a script that inserts CSV tables into the template. This architecture makes it trivial to generate similar diagrams for other time periods (e.g., a Sankey diagram per year), differences between time periods, other regions (for example, on diagram per glacier basin), etc.
Figure \ref{fig:aq_regions} shows Figure \ref{fig:aq} split by East, West, and Peninsula regions
\label{appendix:aq_regions}
\begin{figure*} \centering{\includegraphics[width=0.85\textwidth]{aq_E.pdf}} \centering{\includegraphics[width=0.85\textwidth]{aq_W.pdf}} \centering{\includegraphics[width=0.85\textwidth]{aq_P.pdf}} \caption{Sankey mass flow diagrams for Antarctica regions. East (top), West (middle), and Peninsula (bottom). All widths are proportional within and between images. In East Antarctica mass gain is an output at the bottom that balances the diagram, because without it, there are more flows into the system than out of it.\label{fig:aq_regions}} \end{figure*}
\label{appendix:sankey_alternate}
The main Sankey diagrams shown here (Figs. \ref{fig:gl} and \ref{fig:aq}) are simplistic representations of mass flow across the three ice sheet boundaries (atmospheric, subglacial, and oceanic). We combine all inputs and outputs, not distinguishing between inputs over grounded ice vs. inputs over ice shelves, or other display options. However, alternate displays are possible. Fig. \ref{fig:aq_complex} is an example of a more complex display, and separates inputs and outputs by region (grounded, floating) in Antarctica.
This display choice clearly separates grounded and floating ice, but makes it challenging to see, for example, net SMB terms which are readily available in Figs. \ref{fig:gl}, \ref{fig:aq}, and \ref{fig:aq_regions}. Even more involved displays with more branches (and possibly crossed paths) could all relevant terms in isolation and in combination.
\begin{figure*} \centering{\includegraphics[width=0.95\textwidth]{mermaid_AQ_gray.png}} \caption{Sankey mass flow diagrams for Antarctica split by grounded vs. floating ice. Upper and lower figure should be merged at black line, where mass flow output from grounded ice is mass flow input to ice shelves.\label{fig:aq_complex}} \end{figure*}
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((eq format 'ascii) (format "%s" desc))
)))
(setq-local org-latex-title-command "")(langtool-check) (langtool-correct-buffer) (langtool-check-done)
Export as ASCII, then,
(setq org-ascii-text-width 80)
(org-ascii-export-to-ascii)OLD=A380_ce66c80.tex
NEW=A380.tex
latexdiff --disable-citation-markup --append-safecmd="textcite,autocite" --config="PICTUREENV=(?:picture|DIFnomarkup|tabular)[\w\d*@]*" $OLD $NEW > diff.tex
# NOTE: Stil requires some manual editing of diff.tex, particularly
# when \DIFDEL and \DIFADD are inside CITE commands.
# latexmk diff.tex