Currently a paradigm shift is made from global averaged to spatially variable
sea level change (SLC) projections. Traditionally, the contribution from ice
sheet mass loss to SLC is considered to be symmetrically distributed.
However, several assessments suggest that the probability distribution of
dynamical ice sheet mass loss is asymmetrically distributed towards higher
SLC values. Here we show how asymmetric probability distributions of
dynamical ice sheet mass loss impact the high-end uncertainties of regional
SLC projections across the globe. For this purpose we use distributions of
dynamical ice sheet mass loss presented by

Sea level change (SLC) will be one of the major impacts of climate change in
the 21st century

Local impact studies

There are several components that contribute to SLC: surface mass balance
changes of glaciers and ice sheets, global steric plus dynamic topography and
atmospheric pressure, groundwater depletion, glacial isostatic adjustment
(GIA) and dynamical ice sheet mass loss. Particularly the uncertainty of the
last component, dynamical ice sheet mass loss, is under debate

Higher percentiles of the probability distribution are used to study
uncertainties of SLC projections, in line with coastal safety assessments
that use a return-frequency-based approaches to determine safety levels

The main objective of this paper is to analyze the sensitivity of higher
percentile of regional SLC projections to asymmetric probability
distributions for dynamical ice sheet mass loss. This is done by comparing
the impacts of the probability distributions of

In order to make a comparison between symmetric and asymmetric contributions
of dynamical ice sheet mass loss to SLC all other components contributing to
SLC are kept the same for all simulations. Regional SLC fields of

Probability density functions (left column) and cumulative density functions (CDFs) (right column) for dynamical ice sheet mass loss of Greenland ice sheet (GIS), Antarctic ice sheet (AIS), West Antarctic ice sheet (WAIS) and East Antarctic ice sheet (EAIS). IPCC-AR5 does not have separate distributions for WAIS and EAIS. In the CDFs the dotted lines indicate the 90th, 95th and 97.5th percentiles.

Overview of the used data: which data are combined and in which
section the computations are discussed. Each box represents a distribution
for the global average; these global average data are converted to a regional
contribution using the fingerprints of

The normal, symmetric contributions for dynamical ice sheet mass loss are
based on the median and likely range from IPCC-AR5

Mass loss of an ice sheet does not result in a globally uniform rise in sea
level as a result of the gravitational effect, the added water mass will be
redistributed according to a geographical pattern, the so-called
fingerprint. Fingerprints of each ice sheet

The regional SLC fields of

Two aspects influence changes in the median between the PDFs constructed with
symmetric and asymmetric components. First of all, the medians of the
asymmetric projections for ice sheet mass loss are higher compared to the
symmetric IPCC distributions (Fig.

Finally it is important to note that we first assume that all components of
SLC are uncorrelated, and eventually a correlation between climate-driven
projections of SLC and ice dynamical contributions of SLC is also
investigated (Sect.

Future probability distributions of regional SLC are calculated by combining
the probability distributions of the different components that contribute to
sea level changes. For this analysis the SEAWISE model is developed.
Computations are done on a global grid, with a grid size of 1

The composed distribution

Example of the merging of several probability density functions
(PDFs), here depicted for Denmark Strait (Fig.

This combined SLC probability distribution can be combined with a third SLC
probability (e.g., Fig.

Total combined probability density of sea level change by 2090, for three locations
marked in panel

Appendix

For the regional projections,

Combining the SLC probability distribution for the symmetric ice sheet
contribution with the probability distribution for all other components to
SLC results in an area-averaged global median (50th percentile) SLC of

Median sea level rise projections by 2090; regional projections of

More important than the average shift in median is that both regional SLC
projections (with symmetric and asymmetric components) show large regional
variability. These spatial variations (Fig.

Changes in the tails of the probability distribution are much larger than the
shift in median, as indicated by the probability distribution for seven locations
(Fig.

At locations where the GIS contribution is near zero (e.g., New York Bight,
Fig.

Sea level change (SLC) projections for high-end percentiles and the change therein by
2090. Left column:

The spatial pattern of the (change in) the higher percentiles including the
asymmetric VW15 dynamical ice sheet contribution are shown in
Fig.

Sea level change (SLC) projections by 2090 for high-end percentiles corrected with
shift in local median. Left column:

As mentioned before, the globally average value increases by

Based on the IPCC-AR5

Left column:

To analyze the impact of different PDFs of dynamical ice mass loss on
regional SLC, we computed the 90th, 95th and 97th percentiles for projections
that include probability distributions for EAIS and WAIS following

The asymmetric probability distributions for the contribution of ice sheet
mass loss in this research are based on two projections of dynamical ice
sheet mass loss. One of these studies (VW15) is based on an expert judgment
data set. This approach has a number of limitations. Firstly, the
interpretation of the expert data can largely influence the shape of the tail
of the probability distribution

In Sect.

In coastal safety assessment higher percentiles are often used to calculate
return-frequency-based extremes. The uncertainty bands of these extreme
events are often used to project whether a specific event is changing
significantly under a future climate. The projections of high-end
uncertainties also have an uncertainty

The method presented here could also be used to analyze the effect of
(asymmetrical) uncertainties in other components that contribute to SLC such
as thermal expansion

Until recently, SLC studies focused on projections with symmetric uncertainty
ranges. Here, we have shown that the tail towards high values of SLC of the
probability distribution of dynamical ice sheet mass loss highly influences
the 90th, 95th and 97.5th percentiles of regional SLC. This shift of higher
percentiles has large regional variability due to local differences in the
contribution to SLC from dynamical ice sheet mass loss, related to the
distance to the ice sheets of Greenland and East and West Antarctica. Asymmetric
distributions of dynamical ice sheet mass loss can affect the median of SLC
projections, with a global average shift in median of 0.18 m for the
simulations with the asymmetric distributions of dynamical ice sheet mass
loss by

The 90th, 95th and 97.5th percentiles of regional SLC are strongly effected
by the analyzed asymmetric probability distribution. The difference between
the asymmetric input probability distributions of dynamical ice mass loss of

The data set is freely available at

In order to analyze the effect of dependent components that contribute to SLC,
Eq. (

If the distributions of the two combined components are fully correlated then
only the combination of

Therefore the fractional difference

Subsequently a correlation function

The generalized form of Eq. (

The numerical form of Eq. (

Contributions of dynamical ice sheets mass loss to sea level change
at three locations (depicted in Fig.

Sea level change (SLC) projections for high-end percentiles by 2090 with symmetric
IPCC-based distribution of dynamical ice sheet mass loss combined with the
regional SLC projection of

Sea level change (SLC) projections for high-end percentiles and the change therein by
2090 if asymmetric VW15 dynamical ice sheet mass loss is partly correlated
with climate-change-induced SLC changes. Left column:

Difference between the

RSWvdW conceived the study and designed the method with TJR. TJR developed the SEAWISE software. RCdW carried out the analysis and wrote the manuscript under guidance of RSWvdW. RCdW and TJR wrote the Methods section. ABAS, HdV and TE prepared the data for the different contributions to SLC. All authors contributed to editing the manuscript.

The authors declare that they have no conflict of interest.

Renske C. de Winter and Aimée B. A. Slangen acknowledge the ALW-NPP program of NWO. Thomas J. Reerink is funded by Netherlands Earth System Science Center. Edited by: Paolo Tarolli Reviewed by: two anonymous referees