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**The Cryosphere**
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**Brief communication**
01 Apr 2019

**Brief communication** | 01 Apr 2019

Brief communication: PICOP, a new ocean melt parameterization under ice shelves combining PICO and a plume model

- Department of Earth System Science, University of California, Irvine, CA 92697-3100, USA

- Department of Earth System Science, University of California, Irvine, CA 92697-3100, USA

**Correspondence**: Tyler Pelle (tpelle@uci.edu)

**Correspondence**: Tyler Pelle (tpelle@uci.edu)

Abstract

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Basal melting at the bottom of Antarctic ice shelves is a major control on
glacier dynamics, as it modulates the amount of buttressing that floating ice
shelves exert onto the ice streams feeding them. Three-dimensional ocean
circulation numerical models provide reliable estimates of basal melt rates
but remain too computationally expensive for century-scale projections. Ice
sheet modelers therefore routinely rely on simplified parameterizations based
on either ice shelf depth or more sophisticated box models. However, existing
parameterizations do not accurately resolve the complex spatial patterns of
sub-shelf melt rates that have been observed over Antarctica's ice shelves,
especially in the vicinity of the grounding line, where basal melting is one
of the primary drivers of grounding line migration. In this study, we couple
the Potsdam Ice-shelf Cavity mOdel (PICO, Reese et al., 2018) to a buoyant
plume melt rate parameterization (Lazeroms et al., 2018) to create PICOP, a
novel basal melt rate parameterization that is easy to implement in transient
ice sheet numerical models and produces a melt rate field that is in
excellent agreement with the spatial distribution and magnitude of
observations for several ocean basins. We test PICOP on the Amundsen Sea
sector of West Antarctica, Totten, and Moscow University ice shelves in East
Antarctica and the Filchner-Ronne Ice Shelf and compare the results to PICO.
We find that PICOP is able to reproduce inferred high melt rates beneath Pine
Island, Thwaites, and Totten glaciers (on the order of 100 m yr^{−1}) and
removes the “banding” pattern observed in melt rates produced by PICO over
the Filchner-Ronne Ice Shelf. PICOP resolves many of the issues contemporary
basal melt rate parameterizations face and is therefore a valuable tool for
those looking to make future projections of Antarctic glaciers.

How to cite

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How to cite.

Pelle, T., Morlighem, M., and Bondzio, J. H.: Brief communication: PICOP, a new ocean melt parameterization under ice shelves combining PICO and a plume model, The Cryosphere, 13, 1043–1049, https://doi.org/10.5194/tc-13-1043-2019, 2019.

1 Introduction

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Glaciers around the periphery of the Antarctic Ice Sheet (AIS) have undergone dynamic changes due to the spreading of warm modified Circumpolar Deep Water (mCDW) onto the continental shelf and, sometimes, into sub-ice shelf cavities (e.g., Jacobs et al., 2011; Pritchard et al., 2012). This process drives enhanced basal melting, which has the potential to reduce the buttressing effect that ice shelves exert on grounded ice upstream (e.g., Rignot and Jacobs, 2002). This spreading of mCDW is expected to increase along sectors of the periphery of the AIS due to the poleward intensification of the Southern Hemisphere westerly winds (Dinniman et al., 2012). As such, accurately parameterizing these basal melt rates is necessary in making future projections of the AIS due to the large computational cost of two way ice–ocean model coupling. Many early basal melt rate parameterizations (i.e., parameterizations based on the local heat flux at the ice–ocean interface, DeConto and Pollard, 2016; Beckmann and Goosse, 2003; or on basal slopes, Little et al., 2012) do not accurately capture the impact of ocean circulation within sub-shelf cavities, which is a key control of basal melting. Two of the most recently published melt parameterizations that resolve sub-shelf ocean circulation are the Potsdam Ice-shelf Cavity mOdel (PICO, Reese et al., 2018) and one based on the physics of buoyant meltwater plumes (plume model, Lazeroms et al., 2018). Although both parameterizations are novel in their own regards, melt rates calculated by PICO suffer from unrealistic “banding” as a product of its box model approach and remain too low near grounding lines. In addition, the plume model requires complete sub-shelf ocean temperature and salinity fields as inputs and has not been adapted to use in transient model runs. We overcome these limitations by combining both PICO and the plume model to form PICOP: we rely on PICO's box model to reconstruct the temperature and salinity fields beneath ice shelves based on far-field ocean properties and then use this reconstruction to drive the plume model, which calculates the basal melt rate field. In this brief communication, we describe the physics used to derive PICOP and compare melt rates produced by PICO and PICOP to observations by Rignot et al. (2013) in three basins of varying oceanic conditions and geometry.

2 Methods

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PICO is a two-dimensional sub-shelf melt rate parameterization that simulates
vertical overturning in sub-shelf cavities and is used here to produce
ambient ocean temperature and salinity fields (Reese et al., 2018). Inputs for
PICO are the basin-averaged ocean temperature *T* and salinity *S*, and
sub-shelf ocean circulation is driven by the *ice pump* mechanism
(Lewis and Perkin, 1986). Individual mesh elements or grid cells within the model
domain are assigned a box number based on their relative distance from both
the grounding line and ice front. In general, PICO solves for the transport
of heat and salt between boxes in contact with the base of the ice shelf,
starting at the grounding line and ending at the ice front (boxes
*B*_{k} for $k=\mathit{\{}\mathrm{1},\mathrm{\dots},n\mathit{\}}$, where *n* is typically less
than or equal to 5). After simplification and assuming steady-state
conditions, the balance of heat and salt in all boxes along the base of the
ice shelf can be written as

$$\begin{array}{ll}{\displaystyle}& {\displaystyle}q\left({T}_{k-\mathrm{1}}-{T}_{k}\right)-{A}_{k}\phantom{\rule{0.125em}{0ex}}{m}_{k}{\displaystyle \frac{{\mathit{\rho}}_{i}}{{\mathit{\rho}}_{w}}}{\displaystyle \frac{L}{{c}_{p}}}=\mathrm{0}\\ \text{(1)}& {\displaystyle}& {\displaystyle}q\left({S}_{k-\mathrm{1}}-{S}_{k}\right)-{A}_{k}\phantom{\rule{0.125em}{0ex}}{m}_{k}{S}_{k}=\mathrm{0}.\end{array}$$

Using a simplified formulation of the three-equation melt model by
Holland and Jenkins (1999), the transport equations can be solved for salinity *S*_{k}
and temperature *T*_{k} in box *B*_{k} and are dependent on the
local pressure *p*_{k}, the box area *A*_{k}, and the temperature *T*_{k−1} and
salinity *S*_{k−1} of the upstream box *B*_{k−1}. The strength of
the overturning circulation, *q*, is calculated once per time step in box
*B*_{1} from the density difference between the far-field and
grounding line water masses:

$$\begin{array}{}\text{(2)}& q=C({\mathit{\rho}}_{\mathrm{0}}-{\mathit{\rho}}_{\mathrm{1}}).\end{array}$$

Here, we do not use PICO's melt rate parameterization but only use the sub-shelf temperature and salinity fields to drive the plume model (Fig. 1). All constants and external parameters referenced in this paper are summarized in Table 1. For a full derivation of PICO, see Reese et al. (2018).

Reese et al. (2018)Reese et al. (2018)Fretwell et al. (2013)Fretwell et al. (2013)The plume model is a basal melt rate parameterization based on the theory of
buoyant meltwater plumes that travel upward along the base of the ice shelf
from the grounding line to the location where the plume loses buoyancy. The
two-dimensional formulation from Lazeroms et al. (2018) is adapted from the
one-dimensional plume model developed by Jenkins (1991) for a plume
traveling in direction *X* in an ocean with ambient temperature *T*_{a} and
salinity *S*_{a} (provided by PICO). We begin by defining the grounding line
depth, *z*_{gl}, over the entire ice shelf, as it is necessary to determine
where individual plumes originate in order to employ this parameterization.
As a first approximation, we solve an advection equation:

$$\begin{array}{}\text{(3)}& \left\{\begin{array}{ll}v\cdot \mathrm{\nabla}{z}_{\mathrm{gl}}+\mathit{\u03f5}\mathrm{\Delta}{z}_{\mathrm{gl}}=\mathrm{0}& \text{in}\mathrm{\Omega}\\ {z}_{\mathrm{gl}}={z}_{\mathrm{gl}\mathrm{0}}& \text{on}\mathrm{\Gamma}\end{array}\right.,\end{array}$$

where *z*_{gl0} is the grounding line height defined at the grounding line Γ, Ω is the
ice shelf, and as a first approximation, *v* is the modeled, depth-averaged ice velocity.
Note that *ϵ* is a small diffusion coefficient introduced to minimize noise and to provide numerical
stability. We attempted using other advection schemes, for example based on basal slopes, but the level
of noise made these approaches unpractical. As such, we make the assumption that the source of
individual meltwater plumes coincides with the direction of ice velocity. That is, for any given point
*x* on the base of an ice shelf, the grounding line height *z*_{gl}(*x*) (i.e., the depth at which the plume
originates) associated with that point can be found by following an ice flow line upstream of *x* to
Γ. Note that this does not
specify the path the plume takes from *z*_{gl}(*x*) to *x*. The path the plume traverses is a product of the ice shelf basal
slopes, which is acted on by changes in ice shelf thickness along the plume's trajectory. If
areas of ice convergence and divergence on a shelf are neglected, we generally expect for ice shelf
thickness to decrease as we move from the grounding line to the ice front. Since meltwater plumes are
driven by buoyancy, it is then reasonable to assume that for small ice shelves, the average trajectory of
a plume would be from the grounding line to the ice front. As such, using the ice velocity in the advection scheme to
approximate the depth at which the plume originates is not an unreasonable assumption as a first
approximation. For larger ice shelves, however, sub-shelf flow is affected by different mechanisms
that cannot be captured by a simplified parameterization, such as polynya variability.

In a second step, we correct *z*_{gl} such that, if *z*_{gl} is greater than
the height of the base of the ice shelf, *z*_{b}, then we set *z*_{gl}=*z*_{b}.
Compared to the algorithm used to determine *z*_{gl} in Lazeroms et al. (2018),
advecting grounding line heights is computationally more efficient for higher-resolution model runs because we do not have to search for multiple possible
plume sources at every point within a given ice shelf.

Now that *z*_{gl} is defined, we continue by computing both the characteristic freezing
point *T*_{f,gl} and the effective heat exchange coefficient Γ_{TS} as follows:

$$\begin{array}{ll}\text{(4)}& {\displaystyle}& {\displaystyle}{T}_{\mathrm{f},\mathrm{gl}}={\mathit{\lambda}}_{\mathrm{1}}{S}_{\mathrm{a}}+{\mathit{\lambda}}_{\mathrm{2}}+{\mathit{\lambda}}_{\mathrm{3}}{z}_{\mathrm{gl}}{\displaystyle}& {\displaystyle}{\mathrm{\Gamma}}_{TS}=\\ \text{(5)}& {\displaystyle}& {\displaystyle}\phantom{\rule{0.25em}{0ex}}\phantom{\rule{0.25em}{0ex}}\phantom{\rule{0.25em}{0ex}}\phantom{\rule{0.25em}{0ex}}{\mathrm{\Gamma}}_{T}\left({\mathit{\gamma}}_{\mathrm{1}}+{\mathit{\gamma}}_{\mathrm{2}}{\displaystyle \frac{{T}_{\mathrm{a}}-{T}_{\mathrm{f},\mathrm{gl}}}{{\mathit{\lambda}}_{\mathrm{3}}}}\times {\displaystyle \frac{{E}_{\mathrm{0}}\mathrm{sin}\mathit{\alpha}}{{C}_{\mathrm{d}}^{\mathrm{1}/\mathrm{2}}{\mathrm{\Gamma}}_{T{S}_{\mathrm{0}}}+{E}_{\mathrm{0}}\mathrm{sin}\mathit{\alpha}}}\right).\end{array}$$

A geometric scaling factor *g*(*α*) and length scale *l* are defined in order to give the
plume model the proper geometry dependence and scaling according to the distance traveled
along the plume path. The scaling factor and length scale are computed as follows:

$$\begin{array}{ll}{\displaystyle}& {\displaystyle}g\left(\mathit{\alpha}\right)={\left({\displaystyle \frac{\mathrm{sin}\mathit{\alpha}}{{C}_{\mathrm{d}}+{E}_{\mathrm{0}}\mathrm{sin}\mathit{\alpha}}}\right)}^{\mathrm{1}/\mathrm{2}}{\left({\displaystyle \frac{{E}_{\mathrm{0}}\mathrm{sin}\mathit{\alpha}}{{C}_{\mathrm{d}}^{\mathrm{1}/\mathrm{2}}{\mathrm{\Gamma}}_{TS}+{E}_{\mathrm{0}}\mathrm{sin}\mathit{\alpha}}}\right)}^{\mathrm{1}/\mathrm{2}}\\ \text{(6)}& {\displaystyle}& {\displaystyle}\phantom{\rule{0.25em}{0ex}}\phantom{\rule{0.25em}{0ex}}\phantom{\rule{0.25em}{0ex}}\phantom{\rule{0.25em}{0ex}}\left({\displaystyle \frac{{E}_{\mathrm{0}}\mathrm{sin}\mathit{\alpha}}{{C}_{\mathrm{d}}^{\mathrm{1}/\mathrm{2}}{\mathrm{\Gamma}}_{TS}+{E}_{\mathrm{0}}\mathrm{sin}\mathit{\alpha}}}\right),\text{(7)}& {\displaystyle}& {\displaystyle}l={\displaystyle \frac{{T}_{\mathrm{a}}-{T}_{\mathrm{f},\mathrm{gl}}}{{\mathit{\lambda}}_{\mathrm{3}}}}\times {\displaystyle \frac{{x}_{\mathrm{0}}{C}_{\mathrm{d}}^{\mathrm{1}/\mathrm{2}}{\mathrm{\Gamma}}_{TS}+{E}_{\mathrm{0}}\mathrm{sin}\mathit{\alpha}}{{x}_{\mathrm{0}}\left({C}_{\mathrm{d}}^{\mathrm{1}/\mathrm{2}}{\mathrm{\Gamma}}_{TS}+{E}_{\mathrm{0}}\mathrm{sin}\mathit{\alpha}\right)}}.\end{array}$$

The dimensionless scale factor *x*_{0} used in the second term of *l* defines
the transition point between melting and refreezing and is constant for all
model results. For a complete explanation of the individual terms that make
up these two factors, see Sect. 2.2 of Lazeroms et al. (2018).

The length scale is then used in the computation of the dimensionless coordinate, $\widehat{X}$:

$$\begin{array}{}\text{(8)}& \widehat{X}={\displaystyle \frac{{z}_{\mathrm{b}}-{z}_{\mathrm{gl}}}{l}}.\end{array}$$

Note that $\widehat{X}=\mathrm{0}$ corresponds to the
position of the grounding line and $\widehat{X}=\mathrm{0.56}$ is the aforementioned transition point, but
$\widehat{X}=\mathrm{1}$ does not necessarily correspond to the position of the calving front due to the
dependence of $\widehat{X}$ on *l*. In order to ensure valid values of $\widehat{X}$, we set a lower bound for
the ambient ocean temperature: ${T}_{\mathrm{a}}\ge {\mathit{\lambda}}_{\mathrm{1}}{S}_{\mathrm{a}}+{\mathit{\lambda}}_{\mathrm{2}}$. The melt rate $\dot{m}$ is then calculated as

$$\begin{array}{}\text{(9)}& \dot{m}=\widehat{M}\left(\widehat{X}\right)\times M,\end{array}$$

where $\widehat{M}\left(\widehat{X}\right)$ is a dimensionless melt curve defined in
Lazeroms et al. (2018) and *M* is defined as

$$\begin{array}{}\text{(10)}& M={M}_{\mathrm{0}}\times g\left(\mathit{\alpha}\right)\times {\left({T}_{\mathrm{a}}-{T}_{\mathrm{f}}\left({S}_{\mathrm{a}},{z}_{\mathrm{gl}}\right)\right)}^{\mathrm{2}}.\end{array}$$

For a full derivation of the buoyant plume model used in PICOP, see Lazeroms et al. (2018).

3 Results and discussion

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We evaluate PICOP using geometry from Bedmap2 (Fretwell et al., 2013) and far-field ocean temperature
and salinity values averaged at the depth of the continental shelf between 1975 and 2012 (Reese et al., 2018; Schmidtko et al., 2014). Here, we compare the modeled basal melt rates calculated by PICO and PICOP
to melt rates inferred from conservation of mass and satellite interferometry (Rignot et al., 2013),
which we refer to as “observations”. Additionally, we compare the modeled basal melt rate field of
select ice shelves to in situ observations and regional modeling studies.
We focus on three regions: the Amundsen Sea sector of the West
Antarctic Ice Sheet, the Totten and Moscow University ice shelves of the East Antarctic Ice Sheet,
and the Filchner-Ronne Ice Shelf (FRIS). Model inputs for these basins are 0.47 ^{∘}C and 34.73 psu,
−0.73^{∘} C and 34.73 psu, and −1.76 ^{∘}C and 34.82 psu, respectively.

The spatial distribution of melt rates produced by PICOP is in significantly
better agreement with observations compared to PICO, especially in the
vicinity of the grounding line where accurate melt rates are needed in order
to correctly capture the glacier's grounding line dynamics. In Fig. 2, we see that modeled melt rates produced by PICOP reach
approximately 100 and 70 m yr^{−1} near the grounding
line of Pine Island and Thwaites glaciers, respectively, compared to
approximately 20 m yr^{−1} by PICO. These high melt rates are a product
of the deeply entrenched bed that both Pine Island and Thwaites glaciers are
grounded to. These bed depths are advected with the modeled ice velocity when
*z*_{gl} is solved for, leading to high melt rates that better match
observations. Melt rates modeled by Dutrieux et al. (2013), constrained by high-resolution satellite and airborne observations of ice surface velocity and
elevation, show melt rates on the order of 100 m yr^{−1} near Pine
Island glacier's grounding line and 30 m yr^{−1} a short 20 km
downstream. This sharp gradient in the melt rate field was reproduced by
PICOP and will certainly have a major impact on the ice dynamics of this
glacier.

A similar situation occurs under Totten ice shelf; melt rates modeled by
PICOP reach a maximum of about 50 m yr^{−1}, while those from PICO
reach a maximum of approximately 20 m yr^{−1}. Simulated melt rates by
Gwyther et al. (2014) show a similar pattern of melt, with basal melt rates of
approximately 50 m yr^{−1} computed near the most upstream portion of
both Totten and Moscow University's grounding lines. Modeling these high melt
rates is especially important in this region of Totten's grounding line, as
complex grounding line retreat has been observed over the past 17 years and
has been found to be strongly sensitive to changes in ocean temperature
(Li et al., 2015). Over the FRIS, the inherent geometry dependence of PICOP
reduced the banding that modeled melt rates from PICO displayed. This is a
significant improvement because as can be seen in Fig. 2,
there is a very sharp gradient in the melt rate field computed by PICO over
the FRIS that would lead to unrealistic ice shelf dynamics in transient model
runs. PICOP produces a smooth transition from high to low melt rates that
better matches observations. Shelf-wide basal melt rate fields computed by
three-dimensional ocean–ice shelf coupled models
(e.g., Timmermann et al., 2012) show maximum melting (4.5–7 m yr^{−1})
near the deepest sectors of the grounding line of Ronne glacier, agreeing
well with PICOP. Site-specific observations (e.g., Jenkins et al., 2010)
show a decrease in basal melting to less than 1 m yr^{−1} near the
Korff ice rise, which is also reproduced by PICOP.

In all three basins, area-weighted mean melt rates calculated with PICOP show
better agreement with Rignot et al. (2013). The values reported in Fig. 2
corresponding to PICO differ from those used in Fig. 5 of Reese et al. (2018)
because we model these basins using a significantly higher mesh resolution
(minimum element size of 500 m, maximum of 10 km). By modeling Totten,
Pine Island, and Thwaites ice shelves with a coarse mesh, only two boxes were
defined for these smaller shelves in Reese et al. (2018), and thus a larger
proportion of the ice shelf was modeled as the grounding line box. Melt rates
computed in this box are the highest across the shelf because no heat has
been lost from the ocean water by the addition of cold meltwater, leading to
higher mean melt rates when compared to those displayed in Fig. 2. By using
a finer mesh to evaluate PICOP, we are able to capture the fine details of
the melt pattern, which are key in predicting the evolution of grounding line
dynamics, as well as maintain shelf-averaged melt rates that are in
relatively good agreement with observations. The mean melt rates for Pine
Island and Thwaites ice shelves are underestimated (10.25 and
11.60 m yr^{−1}, respectively), as calculated melt rates are too low
away from the vicinity of the grounding line. In addition, the mean melt rate
for Totten ice shelf is slightly overestimated (12.30 m yr^{−1}) when
modeled with PICOP due to the strong grounding line advection used to compute
*z*_{gl} in this region. Over the FRIS, PICOP models a shelf-mean melt rate
that is in better agreement with observations than PICO because PICOP
produces melt further downstream of the grounding line as a result of its
geometry dependence. In this sector of the ice shelf, PICO primarily computes
refreezing ($\dot{m}<\mathrm{0}$), which drives the mean melt rate down to
0.01 m yr^{−1}.

While PICOP resolves many of the issues displayed in contemporary sub-shelf
melt rate parameterizations, it is limited by the assumptions that were made
when both PICO and the plume model were originally derived (see
Reese et al., 2018; Lazeroms et al., 2018). In addition, when computing
*z*_{gl}, we assumed that the depth of the plume origin at any point
on an ice shelf could be found by following the flow of velocity upstream to
the grounding line. Although a good first approximation, we expect this
assumption to fail in zones of complex basal geometry (i.e., areas of
convergent and divergent ice flow) that would lead melt water plumes to
follow more convoluted paths. We also expect this assumption to fail in large
sub-shelf cavities, such as under the FRIS or Ross ice shelf, where plume
paths are influenced by processes not captured by this parameterization
(i.e., sea ice and polynya variability, the coriolis effect that produces a
clockwise sub-shelf ocean circulation, and tides). Finally, PICOP does not
model refreezing well in cold basins due to the lower limit imposed on the
ambient ocean temperature. The ocean temperature output from PICO in cold
basins (i.e., the FRIS and Ross ice shelves) falls below this lower bound,
especially in the vicinity of the ice front, where the coldest ocean
temperatures are modeled. As such, melt rates computed in the coldest
cavities might be overestimated and cannot be further improved unless this
constraint is relaxed, as discussed in Appendix A of Lazeroms et al. (2018).
This is exemplified in the modeled basal melt rates produced by PICOP in
Fig. 2. Observations show patches of refreezing under the
FRIS that are not resolved by PICOP as a result of this lower temperature
bound. Yet, PICOP remains an accurate and computationally efficient melt rate
parameterization that can be easily implemented into high-resolution,
transient ice sheet numerical models.

4 Conclusions

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Here, we presented a new basal melt rate parameterization that is a combination of both PICO and a plume model. By utilizing PICO to resolve the sub-shelf ocean circulation and produce ambient ocean temperature and salinity fields, we reduce model inputs to only basin-averaged values. Additionally, the geometry dependence of the plume model produces melt rates that show better agreement with observations in terms of both spatial distribution and magnitude than with PICO alone. Ocean-induced melting has been cited as a major driver of change for Antarctic glaciers, and over the coming century enhanced spreading of mCDW onto the continental shelf is expected as Southern Ocean conditions are projected to change (Dinniman et al., 2012). As such, the improvements to the spatial distribution and magnitude of modeled melt rates produced by PICOP, as well as the computational efficiency of this parameterization, offer a valuable tool to more accurately make future projections of Antarctic glaciers.

Code and data availability

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Code and data availability.

The basal melt rate fields produced by our model runs are available as the Supplement to this publication. ISSM is open source and freely available at http://issm.jpl.nasa.gov (last access: 20 March 2019).

Supplement

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Supplement.

The supplement related to this article is available online at: https://doi.org/10.5194/tc-13-1043-2019-supplement.

Author contributions

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Author contributions.

TP developed the idea of combining PICO and a plume model and implemented it into ISSM with help from MM and JHB. All authors participated in the writing of the paper.

Competing interests

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Competing interests.

The authors declare that they have no conflict of interest.

Acknowledgements

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Acknowledgements.

This work was performed at the University of California Irvine under a contract with the National Aeronautics and Space Administration, Cryospheric Sciences Program (no. NNX15AD55G).

Review statement

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Review statement.

This paper was edited by Olaf Eisen and reviewed by David Gwyther and Hartmut Hellmer.

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Short summary

How ocean-induced melt under floating ice shelves will change as ocean currents evolve remains a big uncertainty in projections of sea level rise. In this study, we combine two of the most recently developed melt models to form PICOP, which overcomes the limitations of past models and produces accurate ice shelf melt rates. We find that our model is easy to set up and computationally efficient, providing researchers an important tool to improve the accuracy of their future glacial projections.

How ocean-induced melt under floating ice shelves will change as ocean currents evolve remains a...

The Cryosphere

An interactive open-access journal of the European Geosciences Union