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Understanding climate-driven impacts on the multivariate global wind-wave climate is paramount to effective offshore/coastal climate adaptation planning. However, the use of single-method ensembles and variations arising from different methodologies has resulted in unquantified uncertainty amongst existing global wave climate projections. Here, assessing the first coherent, community-driven, multi-method ensemble of global wave climate projections, we demonstrate widespread ocean regions with robust changes in annual mean significant wave height and mean wave period of 5–15% and shifts in mean wave direction of 5–15°, under a high-emission scenario. Approximately 50% of the world’s coastline is at risk from wave climate change, with ~40% revealing robust changes in at least two variables. Furthermore, we find that uncertainty in current projections is dominated by climate model-driven uncertainty, and that single-method modelling studies are unable to capture up to ~50% of the total associated uncertainty.
Hierarchical clustering of annual H¯s\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\bar{\boldsymbol{H}}}_{\boldsymbol{s}}$$\end{document} for the present-day climate (1979–2004) a, Cluster tree diagram (dendrogram) resulting from Euclidean distance-based Ward’s minimum variance clustering (Methods) using global pairwise annual H¯s\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\bar H_{\rm{s}}$$\end{document} (Methods). The vertical axis represents the distance or dissimilarity between clusters (and cluster members), presented as log-scale for clarity. On the horizontal axis, the members are labelled by GCM and WMM (coloured accordingly). The multi-model ensemble mean from each WMM is also included, with its respective colour. Full multi-member ensemble averages (weighted ensemble mean by WMM, ENSEMBLE-WM and uniformly weighted ensemble mean, ENSEMBLE) are coloured blue (Methods). Grey shading denotes five well-defined key clusters. b, Within each dashed line section, maps showing the mean of each cluster in terms of absolute value (top row) and relative percentage difference to the satellite database (bottom row) are shown for annual H¯s\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\bar H_{\rm{s}}$$\end{document} (Methods). The numbers at the bottom left of each panel represent the number of cluster members used to calculate the cluster mean.
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Articles
https://doi.org/10.1038/s41558-019-0542-5
1School of Built Environment and Engineering, Griffith University, Southport, Queensland, Australia. 2Commonwealth Scientific and Industrial Research
Organisation Oceans and Atmosphere, Hobart, Tasmania, Australia. 3US Geological Survey, Pacific Coastal and Marine Science Center, Santa Cruz, CA,
USA. 4Environment and Climate Change Canada, Climate Research Division, Toronto, Ontario, Canada. 5IHE-Delft, Department of Water Science and
Engineering, Delft, the Netherlands. 6Instituto Dom Luiz, Faculty of Sciences of the University of Lisbon, Lisbon, Portugal. 7Department of Infrastructure
Engineering, University of Melbourne, Parkville, Victoria, Australia. 8National Oceanographic Centre, Liverpool, UK. 9Environmental Hydraulics Institute
(IHCantabria), Universidad de Cantabria, Santander, Spain. 10European Commission, Joint Research Centre, Ispra, Italy. 11Disaster Prevention Research
Institute, Kyoto University, Kyoto, Japan. 12Climate and Ecosystems Science Division, Lawrence Berkeley National Laboratory, Berkeley, CA, USA.
13Norwegian Meteorological Institute, Bergen, Norway. 14Geophysical Institute, University of Bergen, Bergen, Norway. 15Helmholtz-Zentrum Geesthacht
Centre for Materials and Coastal Research, Geesthacht, Germany. 16Institute of Oceanography, Center for Earth System Research and Sustainability,
Universität Hamburg, Hamburg, Germany. 17Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, CA, USA. 18Graduate
School of Advanced Integrated Studies in Human Survivability/Hakubi Center for Advanced Research, Kyoto University, Kyoto, Japan. 19Department of
Ocean and Resources Engineering, University of Hawai’i at Mānoa, Honolulu, HI, USA. *e-mail: joao.morimnascimento@griffithuni.edu.au
Wind-waves are dominant contributors to coastal sea-level
dynamics1,2 and shoreline stability35, and can be major
disruptors of coastal population6, marine ecosystems7
and offshore/coastal infrastructures. Future changes to the mul-
tivariate global wind-wave climate (significant wave height (
Hs
),
mean wave period (
Tm
) and mean wave direction (
θm
)) result from
a combination of meteorologically driven changes in ocean sur-
face wind fields6,8 and morphologically driven changes nearshore
(combined effects of changes in sea level9, tides and reef structures10
with long-term changes in beach morphology11). These changes
might potentially exacerbate12,13, or even exceed in some coastal
regions1,1416, impacts of future projected sea-level rise. The impacts
could be further exacerbated when considering directional changes
in wave propagation (
θm
), which is a major driver of coastal stabil-
ity at all time-scales5,9,13,17. Establishing robust projections of global
wave characteristics (by identifying and assessing regions with lack
of climate signal and/or intermember agreement) (see Methods)18,
and quantifying the uncertainties introduced by the complex mod-
elling processes used for that purpose, is paramount to preventing
potentially costly maladaptation19,20. A problem, however, arises
from the wide range of wind-wave methodologies used to derive
wave characteristics from surface winds or pressure fields, which
increases the poorly understood uncertainty in existing projec-
tions2123. Consequently, the United Nations IPCC Fifth Assessment
Report (AR5)24 assigned low confidence to wave projections (with
medium confidence for Southern Ocean
Hs
increase), owing to the
limited number of available model simulations and the uncertainty
surrounding Global Climate Model (GCM) down-scaled surface
winds.
Since then, a new generation of global wind-wave projec-
tion studies has been completed by several international model-
ling groups2534 using atmospheric forcing fields obtained from
the Coupled Model Intercomparison Project Phase 5 (CMIP5)
GCM simulations. While each of these independent studies has
considered aspects of the uncertainty related to their own specific
climate-modelling process, they treated the uncertainty space very
differently (such as emission scenarios and/or GCMs). Furthermore,
no studies have quantified the uncertainty introduced by their own
particular wind-wave modelling method (WMM) to develop global
wind-wave fields. This uncertainty stems from different configura-
tions of statistical approaches (including transfer functions, training
datasets and predictor corrections) and/or dynamical wind-wave
Robustness and uncertainties in global
multivariate wind-wave climate projections
Joao Morim 1,2,3*, Mark Hemer 2, Xiaolan L. Wang4, Nick Cartwright 1, Claire Trenham 2,
Alvaro Semedo5,6, Ian Young 7, Lucy Bricheno8, Paula Camus 9, Mercè Casas-Prat 4, Li Erikson3,
Lorenzo Mentaschi 10, Nobuhito Mori11, Tomoya Shimura11, Ben Timmermans12, Ole Aarnes13,
Øyvind Breivik13,14, Arno Behrens15, Mikhail Dobrynin 16, Melisa Menendez9, Joanna Staneva15,
Michael Wehner 17, Judith Wolf8, Bahareh Kamranzad 18, Adrean Webb 11, Justin Stopa 19 and
Fernando Andutta1
Understanding climate-driven impacts on the multivariate global wind-wave climate is paramount to effective offshore/coastal
climate adaptation planning. However, the use of single-method ensembles and variations arising from different methodolo-
gies has resulted in unquantified uncertainty amongst existing global wave climate projections. Here, assessing the first coher-
ent, community-driven, multi-method ensemble of global wave climate projections, we demonstrate widespread ocean regions
with robust changes in annual mean significant wave height and mean wave period of 5–15% and shifts in mean wave
direction of 5–15°, under a high-emission scenario. Approximately 50% of the world’s coastline is at risk from wave climate
change, with ~40% revealing robust changes in at least two variables. Furthermore, we find that uncertainty in current projec-
tions is dominated by climate model-driven uncertainty, and that single-method modelling studies are unable to capture up to
~50% of the total associated uncertainty.
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Articles NAtUre ClimAte CHANge
models (including source-term parameterizations, sea-ice fields
and numerical resolution) (Supplementary Table 1).
Consequently, these studies present contrasting projected
changes in wind-wave characteristics (in terms of magnitude and/
or signal) across the world’s oceans21. Such limitations may poten-
tially have hampered broad-scale assessments of future coastal risk
and vulnerability1,22. These assessments have either used future
Hs
changes derived from a very limited number of GCM-forced global
wind-wave simulations surrounded by low confidence35,36, or have
neglected any future wave changes37,38 on the basis of the unavail-
ability of robust global data39 and the high uncertainty among exist-
ing studies40.
Here, we seek to minimize such limitations by perform-
ing a unique analysis of a coordinated, multi-method ensemble
of future global wave climate scenarios derived from ten inde-
pendent state-of-the-art studies2534, which have been under-
taken within a pre-designed, community-driven framework41,42.
Combined, these studies yield a large ensemble of 148 members
of global wave climate projections from which we identify robust,
projected, meteorologically driven changes in
Hs
,
Tm
and
θm
at
the global scale. Furthermore, this multi-method ensemble of
wave projections enables us to quantify (and compare) all three
dominant sources of uncertainty (emission scenarios, GCMs and
WWMs), which has not been previously attempted owing to lack
of multi-method ensembles.
Two33,34 of the ten contributing studies employ different statisti-
cal approaches to derive global wave projections exploiting relation-
ships between GCM-simulated sea-level pressure fields and wave
parameters. The remaining contributions2532 use different configu-
rations of dynamical approaches, in which GCM-simulated, high-
temporal resolution near-surface winds are used directly to drive
a global wind-wave model. Consult Supplementary Information
(Section 1.1 and Supplementary Table 1) for details on each contri-
bution and respective acronyms.
All contributing studies2534 have provided assessments of the
performance of their GCM-forced wave simulations to represent
the historical wave climate on an independent basis. Here, we com-
pare the model-skill of each ensemble member against the most
recent, and complete, calibrated dataset of satellite altimeter
Hs
measurements of
Hs
(ref. 43). In addition, we compare the model-
skill against the well-validated44 ERA-Interim45 (ERAI) multivariate
(
Hs
,
Tm
,
θm
) wave reanalysis for the present-day time-slice (1979–
2004) as a common reference dataset. Details of the two databases
are described in Methods. We present our model-skill comparisons
using Taylor diagrams46 at both the global and regional scale, pro-
viding spatial correlation, normalized standard deviation (NSD)
as well as centred-root-mean-square-difference (CRMSD) within
a single diagram. To further support our model-skill analysis, we
provide global pairwise comparisons maps of the mean and vari-
ability biases for a subset with common forcing GCM–WMM
(Supplementary Table 3, Section 5).
Overall, both dynamical and statistically based simulations
exhibit good agreement relative to satellite measurements and
ERAI. CRMSD values in annual/seasonal
Hs
are generally <0.5 m,
with NSD values <0.5 m and spatial correlation values >0.9 at
global and regional scales, regardless of the reference dataset used
here (Supplementary Figs. 1–4, 6–8). The agreement in annual
mean 99th percentile significant wave height (
Hs
99
) is relatively sim-
ilar to that seen for
Hs
. However, we find relatively less model-skill
in representing annual
Hs
99
at the regional scale, particularly across
the South Atlantic/Pacific and Southern Indian Ocean, with NSD
values up to ~1 m (Supplementary Fig. 5). The bias values in annual
Hs
and
Hs
99
relative to satellite data are usually below ~10–15% and
~15–17.5% over the global ocean, respectively (Supplementary Figs.
12–13). The ensemble mean of each study exhibits biases of less
than ~5% in annual
Hs
anywhere, respectively. Comparison against
the ERAI data in terms of annual/seasonal
Tm
and
θm
exhibits good
agreement, with CRMSD values <0.5 s and 0.75°, respectively, and
spatial correlation values >0.9 (Supplementary Figs. 6–8) at both
the global and regional scale (Supplementary Fig. 9). Further dis-
cussion on the model-skill at seasonal, regional and interannual
scales is provided in Supplementary Information (Sections 3 and 5).
Cluster analysis of
Hs
by member (Methods) over the present-
day time-slice delineates groups of ensemble members defined by
wave-modelling methodology, rather than by GCM-forcing (Fig.
1). These results, supported by Supplementary Fig. 12, show that
WMM strongly dominates the variance in this community ensem-
ble of historical wave simulations (which includes all GCM-forced
simulated wave data available to date). Within each WMM cluster,
we note close association of members with similar GCM-forcing
(that is, GCMs with shared dynamical cores).
Figure 1 shows two well-defined, statistically derived clusters
(1 and 5) explained by differences in the training datasets, transfer
functions and/or predictor corrections, and three dynamically based
clusters (2–4) arising from differences in dynamical wave model-
ling configurations (for example, model source-term parameteriza-
tions). Note that clusters 1 (IHC) and 5 (ECCC(s)) share common
characteristics, in which their members have very high similarity
as a consequence of their statistical calibrations and predictor cor-
rections33,47. This is also evident in our model-skill comparison
(Supplementary Figs. 1–3,12). Consult Supplementary Information
(Section 4) for details on the distinctive qualities of each cluster and
for discussion on within-cluster similarities.
Projected future changes in the climatological mean wave fields
over the globe by the end of the twenty-first century (2081–2100)
are assessed for two representative concentration pathways (RCPs):
a medium (RCP4.5) and a high-emission scenario (RCP8.5).
RCP4.5 and RCP8.5 exhibit very similar spatial patterns of pro-
jected changes for all wave parameters, but the latter shows relatively
larger changes (Fig. 2). Signals of projected changes in annual mean
wave parameters (
Hs
,
Tm
and
θm
) show robust change (Methods)
over ~36, 44 and 32% of the global ocean, respectively (under
RCP8.5; Supplementary Table 2).
A robust projected decrease in annual
Hs
is seen across the
North Atlantic Ocean and portions of the northern Pacific Ocean
of up to ~10% under RCP8.5, expanding further across the east-
ern Indian and southern Atlantic Oceans in austral summer. This is
consistent with the relatively uniform decrease in projected surface
wind speeds over the boreal extra-tropical storm belt48, partially
driven by a strongly reduced meridional temperature gradient due
to polar amplification of climate change49. The areas of robust pro-
jected increase are limited to the Southern Ocean and the tropical
eastern Pacific—in line with the intensification and poleward shift
of the austral westerly storm belt50 and increasing Southern Ocean
swell propagation into tropical areas23, respectively. In the austral
winter, regions of robust projected increase expand further across
the tropics. These findings are overall qualitatively consistent with
the Coordinated Ocean Wave Climate Project (COWCLIP) CMIP3
multi-model ensemble23, and other relevant literature21.
Storm significant wave height,
Hs
99
, shows annual/seasonal
characteristics of change similar to
Hs
although the fraction of
global ocean showing robust changes is much smaller (Fig. 2 and
Supplementary Table 2), highlighting the high uncertainty in
extreme wave climate projections. Although we present projected
changes in extreme
Hs
99
, we draw attention to the ongoing chal-
lenge of resolving storm wave conditions generated by intense
tropical/extra-tropical storms in wave simulations forced directly
with atmospheric surface fields (~1–2°) from CMIP5 GCMs. High-
resolution studies33,34 have highlighted the importance of increased
wind-forcing resolution (~0.25°) to adequately capture storm wave
climate in tropical cyclone-affected areas, and of the sensitivity of
projected changes to resolution.
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The extended influence of the increasing propagation of swells
from the Southern Ocean region to the tropics is shown by the
robust projected increase in
Tm
(~44% of the global ocean) and the
projected shift in
θm
over ~32% of the global ocean (clockwise over
the tropical Pacific and tropical Atlantic, anticlockwise elsewhere).
Consult Supplementary Figs. 21 and 22 for further discussion on
projected future seasonal changes. The results described are mecha-
nistically linked to well-documented, large-scale atmospheric wind
circulation changes48,49 and modes of natural climate variability23.
Beyond evaluating the robustness of the projected changes (Fig.
2), we assess the importance of changes relative to the magnitude
of present-day interannual variability (see Supplementary Fig. 20).
For RCP4.5, and we speculate the same for lower pathways51, most
robust projected changes in wave parameters fall within the range
of present natural variability (<100%). Under the high-emission
RCP8.5, however, nearly all robust changes exceed the simulated
present-day interannual variability (in some regions by >150%).
Figure 3 identifies robust projected changes in offshore mul-
tivariate wave conditions (
Hs
,
Tm
and
θm
) in the vicinity of the
world’s coastlines (Methods), which are considered dominant
physical drivers of coastal change5,6,13,52 and have served as a proxy
for broad-scale assessments of coastal risk and vulnerability26,35,36,53.
We find that ~50% of the world’s coasts (excluding sea-ice areas
and enclosed basins) exhibit robust projected changes in the adja-
cent offshore wave climate in at least one variable (
Hs
,
Tm
or
θm
).
Whilst there are regions where robust projections are limited to a
single variable (for example,
θm
changes off the southern and east-
ern coasts of Africa), there are several coastal sections (~40% of the
global coastline) where robust changes in offshore
Hs
,
Tm
and/or
θm
coincide (for example, New Zealand, southern Australia and the
western coasts of Central and South America). This is also the case
for the highly populated North American Atlantic coast (a well-
documented hotspot of accelerated sea-level rise54, where we find
a robust decrease in
Hs
and
Tm
). Future projected changes in
θm
(a
key driver of sustained coastal erosion55) are robust in the vicinity of
21% of the world’s coastlines, with magnitudes ranging ~±17°. We
exclude sea-ice-affected regions from our analysis. However, these
areas must be acknowledged as future locations of potentially high
wave climate change, owing to altered wind and fetch conditions
with changing sea-ice extent29,56.
Our community ensemble of global wave climate projections
has a range of uncertainty stemming from several different sources
(RCPs, GCMs and WMMs) that have remained largely unquanti-
fied in previous, stand-alone studies. We applied Ward’s analysis
of variation (ANOVA)-based clustering (Methods) to a designed
subset of projection scenarios (Supplementary Table 3) span-
ning two RCP emissions scenarios, ten GCM models and eight
WMMs, providing an overall analysis of similarity amongst the
projected changes (Fig. 4). We find that projected relative changes
in
Hs
largely cluster by GCM-forcing (that is, atmospheric forcing
from which the wave field originates). There are only a few cases
where RCP/WMM-related uncertainties dominate the dissimilar-
ity between projections (for example, MIROC5, BCC-CSM1.1 and
CNRM-CM5-forced members). See Supplementary Information
(Section 6.3) for further discussion on the distinctive qualities of
each cluster.
0
1.25
2.5
Dissimilarity (Ward’s linkage)
MIROC5-CSIRO
MRI-CGCM3-CSIRO
ACCESS1.0-CSIRO
HadGEM2-ES-CSIRO
BCC-CSM1.1-CSIRO
GFDL-CM3-CSIRO
ENSEMBLE-CSIRO
INM-CM4-CSIRO
CNRM-CM5-CSIRO
EC-EARTH-IHE-DELFT
EC-EARTH-ECCC (d)
ENSEMBLE-ECCC (d)
INM-CM4-ECCC (d)
BCC-CSM1.1-ECCC (d)
GFDL-ESM2M-ECCC (d)
MIROC5-ECCC (d)
ACCESS1.0-ECCC (s)
HadGEM2-ES-ECCC (s)
BCC-CSM1.1-ECCC (s)
MRI-CGCM3-ECCC (s)
MPI-ESM-LR-ECCC (s)
ENSEMBLE-ECCC (s)
MPI-ESM-MR-ECCC (s)
CSIRO-Mk3.6-ECCC (s)
GFDL-ESM2M-ECCC (s)
NorESM1-M-ECCC (s)
CCSM4-ECCC (s)
CNRM-CM5-ECCC (s)
EC-EARTH-ECCC (s)
IPSL-CM5A-LR-ECCC (s)
BCC-CSM1.1(m)-ECCC (s)
CanESM2-ECCC (s)
FGOALS-s2-ECCC (s)
INM-CM4-ECCC (s)
MIROC5-ECCC (s)
MIROC-ESM-ECCC (s)
MIROC-ESM-CHEM-ECCC (s)
ENSEMBLE
ENSEMBLE-WM
MIROC-ESM-IHC
MIROC-ESM-CHEM-IHC
FGOALS-g2-IHC
ACCESS1.0-IHC
HadGEM2-CC-IHC
HadGEM2-ES-IHC
BNU-ESM-IHC
CanESM2-IHC
CNRM-CM5-IHC
GFDL-CM3-IHC
GFDL-ESM2G-IHC
GFDL-ESM2M-IHC
ENSEMBLE-IHC
BCC-CSM1.1-IHC
BCC-CSM1.1(m)-IHC
CMCC-CM-IHC
CMCC-CMS-IHC
MPI-ESM-LR-IHC
MPI-ESM-MR-IHC
CCSM4-IHC
CESM1 (BGC)-IHC
NorESM1-M-IHC
CESM1 (CAM5)-IHC
CSIRO-Mk3.6-IHC
MIROC5-IHC
ACCESS1.3-IHC
MRI-CGCM3-IHC
IPSL-CM5B-LR-IHC
INM-CM4-IHC
IPSL-CM5A-LR-IHC
IPSL-CM5A-MR-IHC
EC-EARTH-JRC
ACCESS1.0-JRC
ENSEMBLE-JRC
ACCESS1.3-JRC
MRI-AGCM-KU
CESM1 (CAM5)-LBNL
EC-EARTH-NOC
ENSEMBLE-USGS
INM-CM4-USGS
BCC-CSM1.1-USGS
GFDL-ESM2M-USGS
MIROC5-USGS
(m) (%)
H
s
n = 33 n = 17 n = 3 n = 7 n = 21 0
1
2
3
4
5
Cluster 1
n = 33 n = 17 n = 3 n = 7 n = 21 –35
–17.5
0
17.5
35
Cluster 2 Cluster 3 Cluster 4 Cluster 5
Cluster 2 Cluster 3 Cluster 4
a
b
Cluster 5
Cluster 1
H
s
Fig. 1 | Hierarchical clustering of annual
HHss
for the present-day climate (1979–2004). a, Cluster tree diagram (dendrogram) resulting from Euclidean
distance-based Ward’s minimum variance clustering (Methods) using global pairwise annual
Hs
(Methods). The vertical axis represents the distance or
dissimilarity between clusters (and cluster members), presented as log-scale for clarity. On the horizontal axis, the members are labelled by GCM and
WMM (coloured accordingly). The multi-model ensemble mean from each WMM is also included, with its respective colour. Full multi-member ensemble
averages (weighted ensemble mean by WMM, ENSEMBLE-WM and uniformly weighted ensemble mean, ENSEMBLE) are coloured blue (Methods). Grey
shading denotes five well-defined key clusters. b, Within each dashed line section, maps showing the mean of each cluster in terms of absolute value (top
row) and relative percentage difference to the satellite database (bottom row) are shown for annual
Hs
(Methods). The numbers at the bottom left of each
panel represent the number of cluster members used to calculate the cluster mean.
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To further quantify the dominant drivers of uncertainty among
these global wave climate projections and their relative contribu-
tion to the total projection uncertainty, we applied a three-factor,
ANOVA-based variance decomposition to three opportunity
subsets (Table 4) containing all three sources of uncertainty. See
Methods for a description of the selection of the subsets used and
the ANOVA methodology. The findings show that no single source
of uncertainty is negligible, and that the full projection uncertainty
is not solely attributable to the different sources of uncertainty but is
also dependent on their interactions. For all subsets available (Fig. 5
and Supplementary Figs. 27 and 28) we find a dominating influence
of GCM uncertainty across most of the global ocean, accounting for
~30% to >50% of the total uncertainty associated with projected
future changes in climatological mean
Hs
. These results are consis-
tent with our cluster analysis (Fig. 4).
Scenario-driven uncertainty dominates over the North
Atlantic, western North Pacific and Southern Ocean (~40% to
>50% full uncertainty), but is exceeded by other uncertainty con-
tributors elsewhere. Choice of WMMs is a significant contribu-
tor to full uncertainty, particularly across the tropics/subtropics
(~25–50%), and the interactions between uncertainty sources
account for ~20–30% of total uncertainty across most of the
world’s oceans (dominated by GCM–WMM interactions; Fig. 5e).
These findings show that all three sources of uncertainty must
be adequately sampled to capture the full uncertainty in the pro-
jected change signal. They also demonstrate that previous studies
relying on a single methodology have not captured up to ~40–
50% of total uncertainty space (that is, the sum of all fractions
related to WMM).
Our global-scale study does not resolve the uncertainty in projec-
tions of wave fields introduced with atmospheric down-scaling tech-
niques. Although the regional down-scaling step has been widely used
in wave climate projection studies, and is a topic of intensive research57,
the various down-scaling techniques introduce an addit ional source of
RCP8.5 (2081–2100)
–10
0
10
–10
0
10
–5
0
5
–10
0
10
RCP4.5 (2081–2100)Historical (1979–2004)
Hs (m)
Hs (%) Hs (%) Tm (%) θm (°)
θm (° N) DJF Hs (m)JJA Hs (m)
Tm (s)
0
1
2
3
4
5
0
2
4
6
8
10
4
6
8
10
12
0
120
240
359
b ca
Hs (m)
99
Fig. 2 | Simulated wave climatological mean fields for the present day (1979–2004) and projected changes in climatological wave values for the period
2081–2100 under RCP4.5 and RCP8.5. a, Weighted multi-member mean of the 1979–2004 mean of annual mean significant wave height,
Hs
(December–
February (DJF) and June–August (JJA)).
Hs
within dashed box with same colour bar as for annual
Hs
; 99th percentile significant wave height,
Hs
99
; mean
wave period,
; mean wave direction,
θm
. b,c, Weighted multi-member mean of projected changes in the climatological mean of the respective wave
parameter for the period 2081–2100 relative to the period 1979–2004 under RCP4.5 (b) and RCP8.5 (c). Changes are expressed as percentage of present-
day climatological values. Changes in
θm
(clockwise) are absolute changes, with vector direction denoting
θm
for the present-day climatological mean field.
Hatching indicates areas of robust change (Methods). Seasonal changes for each wave parameter are provided in Supplementary Figs. 21 and 22.
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>
17
5
4
3
2
–1
0
1
2
3
4
5
<17
θ
m (° clockwise)
60° N
30° N
30° S
60° S 60° E
H
s
and
T
m
(10.7%)
H
s
(4.1%)
T
m
(10.7%)
H
s
and
T
m
(
~
0%)
H
s
and
T
m
(3.4%)
H
s
and
T
m
(
~
0%)
H
s
(1.5%)
T
m
(5.3%)
120° E 180° 120° W 60° W
Fig. 3 | Robust projected changes in offshore
HHss
,
TTmm
and
mm
θ
for 2080–2100 (under RCP8.5) in the vicinity of the world’s coastlines. Sections exhibiting
robust weighted multi-member mean changes under RCP8.5 are coloured according to the qualitative colour bar (bottom), which also shows the
percentage of affected coastline where changes are robust (Methods) for each wave characteristic(s). Regions exhibiting a simultaneous robust
increase in offshore
Hs
and robust decrease in offshore
(or vice versa) are extremely limited. Vectors represent robust projected changes in offshore
θm
, with their angle degrees north, representing wave direction over the historical time-slice (1979–2004) and their colour representing the magnitude
of future changes (according to the quantitative colour bar, right-hand side). The percentage of affected ice-free coastline with robust changes in
offshore
θm
is estimated at ~21% (Supplementary Table 2). Coastlines lacking a black outline represent sea-ice areas and enclosed seas, excluded from
the analysis (Methods).
a
b
0
1.75
3.5
Dissimilarity (Ward’s linkage)
MIROC5-CSIRO-RCP4.5
MIROC5-USGS-RCP4.5
MIROC5-IHC-RCP4.5
MIROC5-ECCC (s)-RCP4.5
MIROC5-USGS-RCP8.5
MIROC5-CSIRO-RCP8.5
MIROC5-ECCC (d)-RCP8.5
MIROC5-ECCC (s)-RCP8.5
MIROC5-IHC-RCP8.5
HadGEM2-ES-CSIRO-RCP4.5
HadGEM2-ES-IHC-RCP4.5
HadGEM2-ES-ECCC (s)-RCP4.5
HadGEM2-ES-CSIRO-RCP8.5
HadGEM2-ES-ECCC (s)-RCP8.5
ACCESS1.0-CSIRO-RCP4.5
ACCESS1.0-JCR-RCP4.5
ACCESS1.0-IHC-RCP4.5
ACCESS1.0-ECCC (s)-RCP4.5
ACCESS1.0-JCR-RCP8.5
ACCESS1.0-CSIRO-RCP8.5
ACCESS1.0-IHC-RCP8.5
ACCESS1.0-ECCC (s)-RCP8.5
ENSEMBLE-ECCC (s)-RCP4.5
ENSEMBLE-USGS-RCP4.5
ENSEMBLE-CSIRO-RCP4.5
ENSEMBLE-WMCOWCLIP-RCP4.5
ENSEMBLE-WFCOWCLIP-RCP4.5
ENSEMBLE-COWCLIP-RCP4.5
ENSEMBLE-IHC-RCP4.5
ENSEMBLE-JCR-RCP4.5
ENSEMBLE-CSIRO-RCP8.5
ENSEMBLE-JCR-RCP8.5
ENSEMBLE-ECCC (s)-RCP8.5
ENSEMBLE-IHC-RCP8.5
ENSEMBLE-COWCLIP-RCP8.5
ENSEMBLE-WFCOWCLIP-RCP8.5
ENSEMBLE-WMCOWCLIP-RCP8.5
ENSEMBLE-ECCC (d)-RCP8.5
ENSEMBLE-USGS-RCP8.5
CSIRO-Mk3.6-IHC-RCP4.5
CSIRO-Mk3.6-ECCC (s)-RCP4.5
CSIRO-Mk3.6-IHC-RCP8.5
CSIRO-Mk3.6-ECCC (s)-RCP8.5
BCC-CSM1.1-ECCC (s)-RCP4.5
BCC-CSM1.1-IHC-RCP4.5
BCC-CSM1.1-USGS-RCP4.5
BCC-CSM1.1-CSIRO-RCP4.5
BCC-CSM1.1-ECCC (s)-RCP8.5
BCC-CSM1.1-CSIRO-RCP8.5
BCC-CSM1.1-ECCC (d)-RCP8.5
BCC-CSM1.1-USGS-RCP8.5
BCC-CSM1.1-IHC-RCP8.5
EC-EARTH-NOC-RCP4.5
EC-EARTH-JCR-RCP4.5
EC-EARTH-ECCC (s)-RCP4.5
EC-EARTH-JCR-RCP8.5
EC-EARTH-ECCC (d)-RCP8.5
EC-EARTH-EC-RCP8.5
EC-EARTH-NOC-RCP8.5
EC-EARTH-ECCC (s)-RCP8.5
CNRM-CM5-IHC-RCP4.5
CNRM-CM5-CSIRO-RCP4.5
CNRM-CM5-ECCC (s)-RCP4.5
CNRM-CM5-IHC-RCP8.5
CNRM-CM5-CSIRO-RCP8.5
CNRM-CM5-ECCC (s)-RCP8.5
MRI-CGCM3-IHC-RCP4.5
MRI-CGCM3-CSIRO-RCP4.5
MRI-CGCM3-ECCC (s)-RCP4.5
MRI-CGCM3-IHC-RCP8.5
MRI-CGCM3-CSIRO-RCP8.5
MRI-CGCM3-ECCC (s)-RCP8.5
INM-CM4-USGS-RCP4.5
INM-CM4-CSIRO-RCP4.5
INM-CM4-IHC-RCP4.5
INM-CM4-ECCC (s)-RCP4.5
INM-CM4-ECCC (s)-RCP8.5
INM-CM4-IHC-RCP8.5
INM-CM4-ECCC (d)-RCP8.5
INM-CM4-CSIRO-RCP8.5
INM-CM4-USGS-RCP8.5
GFDL-ESM2M-ECCC (s)-RCP4.5
GFDL-ESM2M-IHC-RCP4.5
GFDL-ESM2M-USGS-RCP4.5
GFDL-ESM2M-USGS-RCP8.5
GFDL-ESM2M-ECCC (d)-RCP8.5
GFDL-ESM2M-IHC-RCP8.5
GFDL-ESM2M-ECCC (s)-RCP8.5
Cluster 5
n = 6 –10
–5
0
5
10
Cluster 4
n = 31
Cluster 3
n = 37
Cluster 2
n = 11
Cluster 1
(m)
Hs
n = 3
Cluster 2Cluster 1 Cluster 3 Cluster 4 Cluster 5
Fig. 4 | Hierarchical clustering of projected relative changes in annual
HHss
(2081–2100 relative to 1979–2004). a, Cluster tree diagram resulting from
Euclidean distance-based Ward’s minimum variance clustering using global pairwise projected annual
Hs
(Methods). The vertical axis represents the
distance or dissimilarity between clusters (and cluster members), presented in log-scale for clarity. On the horizontal axis, members are labelled by GCM-
forcing, WMM and RCP scenario (RCP4.5 simulations are italicized), respectively, and coloured by GCM, accordingly. The multi-model ensemble mean
from each study group is also included. Full multi-member ensemble averages (weighted ensemble mean weighted by WMM, ENSEMBLE-WM, uniformly
weighted ensemble mean, ENSEMBLE and ensemble mean weighted by forcing, ENSEMBLE-WF) are coloured blue (Methods). Grey shading denotes five
well-defined key clusters. b, Within each dashed line section, maps showing the mean of each cluster’s projected relative change in annual
Hs
(m) are
shown (Methods). The numbers at the bottom left of each panel represent cluster members used to calculate the cluster mean.
NATURE CLIMATE CHANGE | www.nature.com/natureclimatechange
Articles NAtUre ClimAte CHANge
uncertainty that (at present) is not possible to sample at the global-
ocean scale.
Our CMIP5-based coordinated ensemble of wave climate pro-
jections samples over RCP, GCM and WMMs, thus allowing a
much improved sampling of the uncertainty space relative to the
COWCLIP CMIP3-based ensemble of opportunity23, or to any pre-
vious study to date21. In addition to resolving the largely unquanti-
fied contribution of all three dominant sources of uncertainty, this
study attests to the importance of considering conceptually distinct
wind-wave methodologies. We note that some of the uncertainty
seen amongst dynamical simulations in terms of
Hs
biases could
potentially be reduced by further model calibration58,59 and improved
wind-wave model physics (for example, removal of dependence on
spectral model approximations, such as for nonlinear wave–wave
interactions60 and model limiters for spectral propagation veloci-
ties, applied to improve computational efficiency and accuracy61,62).
While, at present, it is not possible to isolate these components,
we advocate that future dynamical wave studies attempt to reduce
the overall
Hs
historical bias. Regarding model-skill, wind-forcing
correction could lead to improved wave model simulations59. The
results also stress the need for better understanding of the differ-
ences in the various global wave reanalyses and hindcasts (used to
develop historical trends of wave climate change1,63).
Our results provide a new perspective on the robustness of
multivariate global-scale wave projections, building far beyond
the restricted range of future wave climate scenarios published in
individual studies to date. These coordinated ensemble projec-
tions show that signals of wave climate change will not exceed the
magnitude of the natural climate variability if the goal of the Paris
Agreement target (2 °C) is kept. Under a high-emission scenario
(RCP8.5), ~48% of the world’s coast is at risk of wave climate change
owing to changes in offshore forcing
Hs
,
Tm
and/or
θm
(with ~40%
exhibiting robust changes in at least two of these wave variables).
The magnitude of future projected changes found for any of these
wave variables (~5–15%) is capable of inducing significant changes
in coastal wave-driven processes and their associated hazards52.
Broad-scale assessments of coastal impacts of climate change
are now beginning to include changes in wave climate1,35,36,53; how-
ever, these studies are yet to consider directional shifts in wave
propagation, which have been shown to be a dominant driver of
shoreline stability5,13. Whilst our results have far-reaching implica-
tions from many perspectives, they address only meteorologically
driven changes in wind-wave characteristics, which have been the
predominant focus of wind-wave climate projection studies to
date. Some localized-scale studies suggest that the morphologi-
cally driven component of wave climate change might lead to a
greater change in coastal zones than these meteorologically driven
changes11. Concentrated community effort is now required to
quantify morphologically driven wave climate change as a con-
tributor to global coastal water-level changes, as we look towards
improved coastal vulnerability assessments from the climate com-
munity64.
Online content
Any methods, additional references, Nature Research reporting
summaries, source data, statements of code and data availability and
associated accession codes are available at https://doi.org/10.1038/
s41558-019-0542-5.
Received: 16 November 2018; Accepted: 2 July 2019;
Published: xx xx xxxx
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Acknowledgements
This study represents Task 3 of the second phase of COWCLIP (https://cowclip.org/), an
international collaborative working group endorsed by the Joint Technical Commission for
Oceanography and Marine Meteorology, a partnership between the World Meteorological
Organization) and the Intergovernmental Oceanographic Commission of UNESCO. We
acknowledge the different climate-modelling groups, the Program for Climate Model
Diagnosis and Intercomparison and the World Climate Research Program’s Working
Group on Coupled Modelling. We acknowledge ECMWF for availability of ERAI data,
and Australia’s Integrated Marine Observing System for altimeter wind/wave data, used
for model validation. J.M., M.H. and C.T. acknowledge the support of the Australian
Government National Environmental Science Program Earth Systems and Climate
Change Hub. B.T. and M.W. acknowledge the support of the Regional and Global Climate
Modeling Program of the US Department of Energy, Office of Science, Off ice of Biological
and Environmental Research, through contrac t No. DE-AC02–05CH11231, and the
National Energy Research Supercomputing Center of the LBNL. I.Y. acknowledges ongoing
support from the Australian Research Council through grant No. DP160100738, and to the
Integrated Marine Observing System. N.M., T.S., A.B. and B.K. acknowledge the support
of the TOUGOU Program by MEXT, Japan, JSPS-Kakenhi Program. L.E. acknowledges
the support of the US Geological Survey Coastal and Marine Hazards/Resources Program.
Ø.B. and O.A. acknowledge the support of the Research Council of Norway through the
ExWaMar project through grant No. 256466. We thank all contributors to the COWCLIP
project, including C. Appendini (National Autonomous University of Mexico, Mexico), F.
Ardhuin (Ifremer, France), N. Groll (Helmholtz-Zentrum Geesthacht Zentrum, Germany),
S. Gallagher (Met Éireann, Ireland), S. Gulev (Moscow State University, Russia) and W.
Perrie (Bedford Institute of Oceanography, Canada).
Author contributions
All authors (except C.T., N.C., M.W., B.T. and F.A.) had input into experimental design
via workshops. J.M. led the analysis of ensemble, algorithm development for data analysis
and writing of the manuscript. M.H. co-led and conceived the experiment, supervised
analysis, provided CSIRO ensemble data and co-wrote the manuscript. X.L.W. co-led
and conceived the experiment, developed community codes, provided ECCC ensemble
data and contributed to analysis and writing of the manuscript. N.C. supervised analysis
and contributed to writing the manuscript. C.T. provided CSIRO ensemble data,
coordinated data and contributed to writing the manuscript. I.Y. provided satellite data
and contributed to analysis and writing the manuscript. A.S. provided IHE ensemble
data and contributed to analysis and writing the manuscript. N.M. and T.S. provided KU
ensemble data and contributed to writing the manuscript. L.E. provided USGS ensemble
data and contributed to writing the manuscript. O.A. and Ø.B. contributed ERAI
statistics. M.D., A.B. and J. Staneva contributed IHE ensemble data. L.M. contributed
Joint Research Centre ensemble data and developed community codes. M.C.-P.
contributed ECCC ensemble data and contributed to writing the manuscript. P.C. and
M.M. contributed IHC ensemble data and contributed to writing the manuscript. B.T.
and M.W. contributed LBNL ensemble data and contributed to writing the manuscript.
L.B. and J.W. contributed NOC ensemble data. A.W. and B.K. had input via workshops.
J. Stopa contributed to analysis and writing the manuscript. F.A. assisted with figure
development.
Additional information
Supplementary information is available for this paper at https://doi.org/10.1038/
s41558-019-0542-5.
Reprints and permissions information is available at www.nature.com/reprints.
Correspondence and requests for materials should be addressed to J.M.
Peer review information: Nature Climate Change thanks Gonéri Le Cozannet and the
other, anonymous, reviewer(s) for their contribution to the peer review of this work.
Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in
published maps and institutional affiliations.
© The Author(s), under exclusive licence to Springer Nature Limited 2019
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Articles
NAtUre ClimAte CHANge
Methods
Data contribution. We use a community-derived ensemble compiled from ten
CMIP5-based global wind-wave climate projection studies2534, completed under a
pre-designed framework41,42. Annual and seasonal means of signicant wave height
(
Hs
), mean wave period (
Tm
), mean wave direction (
θm
) as well as tenth/ninety-
ninth percentiles of annual/seasonal
Hs
, were obtained from the ten individual
studies. Consult Supplementary Information for a detailed description of the
datasets considered and framework.
Our analysis assesses projected relative changes between the representative
current (1979–2004) and future (2081–2100) time-slices. These time periods align
with the CMIP5 GCM archives of high-temporal resolution atmospheric fields
used to develop wind-wave projections, and correspond to the common period
across nine of the ten contributing datasets (see Supplementary Information,
Section 1.1 and Supplementary Table 1). Contributed datasets are considered
under two different greenhouse-gas RCPs—RCP4.5 and RCP8.5—describing,
respectively, medium-stabilizing and high-radiative forcing scenarios reaching
+4.5 W m–2 and +8.5 W m–2 (relative to pre-industrial (1850) conditions). Sea-ice
regions were excluded from the analysis, to support intercomparison between the
different contributions.
Skill of GCM-forced wave climate simulations. As previously mentioned,
all contributing studies2534 provided assessments of the skill of their GCM-
forced global wind-wave simulations to represent the historical wave climate
on an independent basis. Here we use two historical wave datasets (a recently
compiled dataset of altimeter measurement records and a well-known global wave
reanalysis) exclusively as a common point of reference for our model ensemble
intercomparison. The two datasets are briefly described below.
Historical satellite altimeter measurements. We compare the GCM-forced
wave simulations to the most recent (and complete) database43 of satellite
Hs
measurements. This database combines 13 radar altimeters that have been
calibrated extensively against the National Oceanographic Data Center buoy data,
and cross-validated against an independent compiled buoy dataset supplied by the
European Centre for Medium-Range Weather Forecasts (ECMWF)43,65. The dataset
contains
Hs
on a 2°-grid resolution (at global scale) over a period of 33 years
(1985–2018). After control analysis, we found only partial data for the period
1985–1989 (for which only GEOSAT data are available) and no data for 1991,
which limits the data to 1992–2018, providing a common time-slice duration for
comparison of 26 years.
In the comparison of GCM-forced global wave simulations with altimeter
measurements, the time-slice mismatch is ignored66. Since GCM atmospheric
forcing (and the spectral wave models) were not subject to any data assimilation,
they are considered as being representative of the historical wave climate regardless
of the time period66. Note that GCM simulations (and their natural internal climate
variability and its associated large-scale modes) are not in temporal phase with the
satellite database. We assume that any differences between GCMs and altimeter
measurements are attributable to model and observation biases and not to the non-
stationarity of the wind-wave climate23.
To allow for intercomparison, the wave parameters obtained from each of the
contributions2534 were collocated onto the satellite-database global grid, preserving
the original data. Taylor diagrams46 were used to compare the skill of the GCM-
forced wave simulations to represent the present
Hs
climate at both the global and
regional scale (Supplementary Figs. 1–3 and 4,5, respectively). We clarify that our
Taylor diagrams present a spatial pattern correlation of a temporal average (and not
a spatio-temporal correlation). In addition to Taylor diagrams, we present global
pairwise comparisons maps of the mean and variability
Hs
biases for a subset from
the full ensemble with common GCM–WMM (Supplementary Table 3), allowing
us to identify the spatial variation of the biases (Supplementary Figs. 12,13 and
16,17, respectively).
ERAI wave reanalysis. In addition to the univariate satellite data45, we compare
model-skill over the current wave climate (1979–2004) by comparing the present-
day GCM-forced global wave simulations to wind-wave parameters obtained from
the observationally constrained ECMWF ERAI45 global wave reanalysis. ERAI
is a consistent spatially and temporally complete dataset45 that has been widely
used1,25,67 and extensively validated44, being considered appropriate for multi-year
analysis and modelling of long-term processes44. The ERAI database provides
6-h values of
Hs
,
Tm
and
θm
on a 1° global resolution, allowing us to compare all
wave variables of interest at the global scale. The ERAI is therefore used as a well-
known reference database, allowing us to compare all contributing simulations
under the same reference. We note that, despite its relatively good model-skill
against buoy and altimetry measurements44, ERAI still exhibits some biases in the
Hs
upper percentiles (ninety-fifth and above), where it underestimates altimetry
measurements of
Hs
by ~10–15%44.
The original 6-h multivariate ERAI dataset was used to calculate a standard
set of statistics as performed for the contributing studies2534 (see Supplementary
Information, Section 2). To allow for intercomparison, the surface wave parameters
derived from each of the contributing studies2534 were bilinearly interpolated onto
the ERAI grid. Taylor diagrams46 were adopted as a representation of the skill of the
GCM-forced wave simulations to reproduce the present multivariate wave climate
(
Hs
,
Tm
and
θm
) at both the global and regional scale (Supplementary Figs. 6–8 and
9, respectively). The global pairwise comparison maps of mean and variability bias
using the ERAI dataset are presented in Supplementary Figs. 14,15 and 18,19).
Cluster methodology. We applied an agglomerative-hierarchical clustering
analysis, with the similarity criterion defined by Ward’s ANOVA-based minimum
variance algorithm68. The clustering method was used without imposing any
restrictions on the number and size, or apriori assumptions, of clusters. Initial
cluster distances were derived using a multi-dimensional approach where the
pairwise Euclidean distance (D) amongst ensemble members is calculated at every
grid location rather than spatially averaged, thereby clustering members with high
similarity in terms of spatial pattern and magnitude:
=−
=
Dxx() (1
)
ijkk
w
ik jk,, 1,,
2
where
xik,
and
xjk,
are the magnitudes of the relative projected change in the annual
mean significant wave height from GCMs i and j, respectively, at grid point k, with
w equal to the number of ocean grid points. Note that, for the clustering of present-
day wave simulations, we have used absolute values rather than relative changes.
The usage of annual
Hs
as our clustering variable is based on the fact that
Hs
is the
only parameter available from all the contributions and that our main objective is
to analyse the total community ensemble of wave simulations. Note that statistical
method-derived members33,34 from ECCC(s) and IHC did not provide wave period
and/or directions (Supplementary Table 1). We also carried out a multivariate
clustering based on annual
Hs
,
Tm
and
θm
(not shown) using our dynamical subset
of simulations, which showed results qualitatively similar to the
Hs
-based clustering
in both the present-day simulations and projected relative changes. Further
description of the clustering method application to the present-day climate and the
projected relative changes is provided below.
Application to present-day simulations. Annual
Hs
from each GCM-forced global
wave simulation over the present-day time-slice (1979–2004) was used in the
clustering method (equation (1)). We included all existing ensemble models as
well as the mean of each individual contributing study ensemble, a uniformly
weighted ensemble mean (that is, attributing equal weight to individual members)
and an ensemble mean weighted by WMM. The latter consisted of reducing the
full ensemble to n members with each single member representing the mean from
a specific WMM (when suitable). For example, the 30-model IHC ensemble was
reduced to one member, representing its ensemble mean. The relative differences
(%) between the average of all members within each main cluster and the satellite
data were calculated separately for each parameter, simply to highlight the key
qualities of each cluster (Fig. 1 and Supplementary Fig. 10). The relative difference
was also calculated using ERAI (Supplementary Fig. 11). Note that the clustering
analysis (Fig. 1) is fully independent from the comparison with the satellite or the
ERAI datasets as described above.
We applied the clustering analysis to annual and seasonal
Hs
values combined,
and the results are consistent with those obtained using annual mean values. We
also applied the clustering procedure to the other wave parameters (individually)
and obtained consistent findings. In all cases, the present-day simulations are
strongly dependent on the WMM adopted by each study group to develop future
wave fields, as shown in Fig. 1.
Application to projected future changes. To identify and resolve similarities in the
projected future change, the clustering procedure (equation (1)) was applied to the
projected relative changes in annual
Hs
between the present-day (1979–2004) and
future (2081–2100) time-slices, as estimated by each of the GCM-forced global
wave simulations:
Δ=
H
HH
H(2
)
jk jk jk
jk
,,
Future
,
Presentday
,
Presentday
where
ΔHjk,
is the projected change by GCM j at each grid node k.
To resolve the relative importance of the three different sources of uncertainty
(that is, RCP scenarios, GCMs and WMMs), we use a subset from the full
community ensemble where each member shares common GCM-forcing with at
least two other members obtained from different WMMs (see Supplementary Table
2). In the clustering of projected relative changes (equation (1)), we also included
the mean of each study contribution, the uniformly weighted ensemble mean
(see above), the ensemble mean weighted by GCM (see below) and the ensemble
mean weighted by WMM (for each RCP). Five key clusters were identified based
on the clustering results as an indication of ensemble members with considerable
dissimilarity in the projected change values. The mean of all members within each
main cluster (when available) was calculated for each wave parameter (Fig. 1 and
Supplementary Fig. 25), providing a robust indication of spatial and magnitude
dissimilarities over the global ocean.
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For completeness, we also applied cluster analysis to the entire community
ensemble of global wind-wave projections, yielding consistent dissimilarities and
respective associations between all available wave simulations (albeit less clear
owing to the large size of the ensemble) (Supplementary Fig. 26).
ANOVA methodology. Approach and selection of subsets. Uncertainty in the
projected future wave climate changes (2081–2100 relative to 1979–2004) within
our community-based, multi-member ensemble arises from three dierent sources:
choice of RCPs, GCMs and WMMs. e latter refers to the dierent statistical
and dynamical wave modelling approaches used to simulate global wind-wave
elds (representing dierent congurations of statistical methods such as transfer
functions, training datasets and/or predictor corrections, and/or dynamical wave
models including the source-term packages, sea-ice forcing and numerical model
resolution). In contrast with other climatic variables (for example, temperature or
precipitation), dynamically derived ensembles of wave projections are typically
available only for 20-year periods, constrained by the availability GCM-simulated
atmospheric surface winds with suciently high temporal resolution21,42
(Supplementary Table 2). is constrains the testing of projection uncertainty
against the natural (temporal) variability.
Hence, we decompose the total ensemble uncertainty in the projected changes
in the long-term (20-year) mean of annual/seasonal
Hs
into contributions from the
different sources of uncertainty (RCPs, GCMs and WMMs) and the interactions
among them. The fraction of uncertainty attributable to each source (at each
grid node) is determined using a three-factor ANOVA69-based variance partition
method (see below). The method was applied separately to three opportunity
subsets obtained from the full ensemble, with each subset containing all three
sources of uncertainty (Supplementary Table 3). No other subsets with the same
number of factors exist in this community ensemble. Note that the forcing GCMs
within subsets 2 and 3 represent a broad cross-section of the CMIP5 ensemble49,
particularly that with availability of high-temporal resolution surface wind fields,
in terms of model components70 and various GCM characteristics such as spatial
resolution70.
Subsampling scheme. The ANOVA-based variance decomposition using different
sample sizes of variance sources results in biased variance estimators71 (Fig. 4 and
Supplementary Figs. 27–29). To reduce such biases in estimates of variance for
quantification of the uncertainty contribution, we complemented the ANOVA-
based variance decomposition with a subsampling methodology previously
proposed71. In each subsampling iteration i, we selected two each from n climate
models and m wave models, representing a total of
C C
nm
22
subsamples, with n and
m denoting the number of GCMs and WMMs within each subset, respectively. For
each subsample iteration i, we end up with two GCMs, two RCPs and two WWM
approaches, which we used for variance decomposition as described below.
Three-factor ANOVA model-based variance decomposition. Letting
Yjkl
i
be our
response variable, representing the projected change in
Hs
from the jth GCM, kth
RCP and lth WMM, we define our three-factor ANOVA-based partition model71
without replication following refs. 71,72:
μαβγ αβ αγ βγ δ=+++++++Y() () ()
(3
)
jkl
ii
jik
ilijk
ijl
ikl
ijkl
i
where
μi
is the grand-mean projected change of subsample i. The terms
αji
,
βk
i
and
γli
represent the variance arising solely from factors GCMs, WMMs and RCPs
(respectively), with j, k and l denoting samples of the different factors (j = 1,2,
k = 1,2 and l = 1,2) for each subset of simulations by a combination of two GCMs
and two WMMs for two RCPs. The terms
αβ( )jk
i
,
αγ( ) jl
i
and
βγ( )kl
i
represent the
interactions between the specified pair of factors (that is, two-factor interaction
terms). The term
δjkl
i
represents the variance arising from the three-factor
interactions
αβγ( )jkl
i
and internal variability. Note that here the natural internal
variability is negligible, as we are analysing differences between two climatological
mean values—that is, involving very little temporal variance. Because there are no
replications for estimating internal variability, we cannot—and did not—test the
statistical significance of variance arising solely from each factor against the natural
variability, and thus did not require any assumptions for the residuals of model.
The results derived from each subsample i are the unbiased estimates of fraction of
the total uncertainty attributable to each source71,73, with the variance fraction
η2
for
each factor derived as
η=α
=
I
1
SS
SS (4
)
i
I
GCM
2
1
T
i
i
η=β
=
I
1
SS
SS (5
)
i
I
WMM
2
1
T
i
i
η=γ
=
I
1
SS
SS (6
)
i
I
RCP
2
1
T
i
i
η=αγ
=
I
1
SS
SS (7
)
i
I
GCMWMM
2
1
T
i
i
η=αγ
=
I
1
SS
SST (8
)
i
I
i
GCMRCP
2
1
i
η=βγ
=
I
1
SS
SS (9
)
i
I
RCPWMM
2
1
T
i
i
η=δ
−−
=
I
1
SS
SS (
10)
i
I
RCPGCM WMM
2
1
T
i
i
where SS represents sums of squares in each respective factor sample and total.
Values of 0 and 1 for the variance fraction
ηx
2
correspond to 0 and 100% contribution
of factor x to the total ensemble variance (uncertainty), respectively. The average
variance fractions are presented in Fig. 5 for each factor and for the sum of all the
interaction terms, to compare the relative magnitude of each source of uncertainty.
An assessment of the significance of the projected changes relative to the magnitude
of natural internal variability is provided in Supplementary Fig. 20, based on one
realization available for each member (Supplementary Table 1).
Analysis of projected change. Projected changes in all wave variables (except
θm
)
between the present and future time-slices were calculated as percentage changes,
for each member (from each contribution), directly forced by GCM-simulated
surface wind or pressure fields. The Lawrence Berkeley National Laboratory
(LBNL)31 and Kyoto University32 data were derived using down-scaled forcing via
high-resolution atmospheric models driven by particular sea surface temperature
conditions (Supplementary Information, Section 1.1), and therefore were not
included in this analysis.
Projected changes in
θm
were calculated as absolute values and are shown
as clockwise (anticlockwise) rotation in degrees relative to the present-day
climate mean. Projected changes were calculated under RCP4.5/8.5. A weighted
multi-member ensemble mean of projected changes was then calculated. Fifty
statistical wave projections are available from IHC and ECCC(s) combined (for
both scenarios), whilst the dynamical projections consist of 23 (RCP4.5) and 25
(RCP8.5) projected change scenarios, as per Supplementary Table 1. Because the
projected relative change is strongly dependent on GCM-forcing (atmospheric
wind or pressure fields from which the wave field originates) (Figs. 4,5), a weighted
multi-member ensemble mean was calculated by applying a weighting factor to
each member:
Δ
=
∑×
=
=
x
W
W
()
() (
11)
ki
n
ik ik
i
n
ik
1,,
1,
where
Δik,
is the projected change for a given wave parameter k by the ensemble
member i, and Wi is the weighting factor for ensemble member i for that same
parameter (determined as the number of ensemble members with that same forcing
GCM amongst all members, n). For all wave parameters, the global map of mean
projected change was derived as the n-member ensemble weighted mean difference
between projected and present wave climate fields from equation (11).
Robustness measure. We use a methodology18 identified by the IPCC AR5 WG1
(ref. 74) as being a suitable, effective method to identify regions of robustness. In
contrast to other criteria, this robustness criterion18 does not ignore the existence
of internal climate variability and clearly identifies regions with a lack of member
agreement and/or lack of climate signal (by assessing the level of consensus on the
significance of change as well as the signal of change)18,75.
We assessed the significance of change projected by each of the ensemble
members individually, with a two-tailed Welch’s t-test that allows for different
variances between present and future time-slices. The test was conducted at the
5% significance level. To define areas of robust projected changes, we first
identified areas (grid points) where 50% or more of the ensemble members
projected a significant change. Within these areas, we further identified those
areas where 90% or more of the ensemble members exhibiting a significant change
agreed on the sign of the projected changes—these are the areas of robust changes
projected by the ensemble, and are hatched in Fig. 2. Note that we employed a
higher threshold (90%) than the default 80%18,75 for members’ agreement on the
sign of the projected changes. The key conclusions are similar when other IPCC-
referenced methods were used to measure robustness74.
As a complement to the robustness criteria18, we further confirmed that,
within all regions with robust projected changes, the ensemble mean of projected
changes is statistically significantly different from zero (that is, it stands out of the
intermember variability) according to the result of a one-sample Student’s t-test at
the 5% significance level.
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Articles
NAtUre ClimAte CHANge
Percentage of coastline with robust changes in offshore forcing wave conditions.
In this analysis, we consider all the available offshore deepwater (200 m) grid
points, distributed along the global coast every ~100 km. The coast is taken from the
Global Self-consistent Hierarchical High-resolution Geography database76. We limit
our analysis to offshore changes, owing to the limited ability of the CMIP5 GCMs to
adequately capture fetch-limited, near-coastal wind fields and land–sea interactions
(for example, orographic and katabatic effects) given their coarse spatial resolution.
Nevertheless, we note that our GCM-forced wave simulations exhibit good
agreement against near-coast buoys30,53, even within semi-enclosed seas (for
example, the Mediterranean)53 and under extreme wave conditions77. The model-
skill reported for near-coast buoys is comparable to that against offshore buoys and
to high-resolution coastal wave hindcasts78. Sections of coast without available wave
model outputs were not considered, including sea-ice and enclosed seas.
Data availability
The data that support the findings of this study are available from the
corresponding author on request, or via the COWCLIP data access portal at https://
cowclip.org/data-access/.
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Articles
https://doi.org/10.1038/s41558-019-0542-5
Robustness and uncertainties in global
multivariate wind-wave climate projections
Joao Morim 1,2,3*, Mark Hemer 2, Xiaolan L. Wang4, Nick Cartwright 1, Claire Trenham 2,
Alvaro Semedo5,6, Ian Young 7, Lucy Bricheno8, Paula Camus 9, Mercè Casas-Prat 4, Li Erikson3,
Lorenzo Mentaschi 10, Nobuhito Mori11, Tomoya Shimura11, Ben Timmermans12, Ole Aarnes13,
Øyvind Breivik13,14, Arno Behrens15, Mikhail Dobrynin 16, Melisa Menendez9, Joanna Staneva15,
Michael Wehner 17, Judith Wolf8, Bahareh Kamranzad 18, Adrean Webb 11, Justin Stopa 19 and
Fernando Andutta1
1School of Built Environment and Engineering, Griffith University, Southport, Queensland, Australia. 2Commonwealth Scientific and Industrial Research
Organisation Oceans and Atmosphere, Hobart, Tasmania, Australia. 3US Geological Survey, Pacific Coastal and Marine Science Center, Santa Cruz, CA,
USA. 4Environment and Climate Change Canada, Climate Research Division, Toronto, Ontario, Canada. 5IHE-Delft, Department of Water Science and
Engineering, Delft, the Netherlands. 6Instituto Dom Luiz, Faculty of Sciences of the University of Lisbon, Lisbon, Portugal. 7Department of Infrastructure
Engineering, University of Melbourne, Parkville, Victoria, Australia. 8National Oceanographic Centre, Liverpool, UK. 9Environmental Hydraulics Institute
(IHCantabria), Universidad de Cantabria, Santander, Spain. 10European Commission, Joint Research Centre, Ispra, Italy. 11Disaster Prevention Research
Institute, Kyoto University, Kyoto, Japan. 12Climate and Ecosystems Science Division, Lawrence Berkeley National Laboratory, Berkeley, CA, USA.
13Norwegian Meteorological Institute, Bergen, Norway. 14Geophysical Institute, University of Bergen, Bergen, Norway. 15Helmholtz-Zentrum Geesthacht
Centre for Materials and Coastal Research, Geesthacht, Germany. 16Institute of Oceanography, Center for Earth System Research and Sustainability,
Universität Hamburg, Hamburg, Germany. 17Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, CA, USA. 18Graduate
School of Advanced Integrated Studies in Human Survivability/Hakubi Center for Advanced Research, Kyoto University, Kyoto, Japan. 19Department of
Ocean and Resources Engineering, University of Hawai’i at Mānoa, Honolulu, HI, USA. *e-mail: joao.morimnascimento@griffithuni.edu.au
SUPPLEMENTARY INFORMATION
In the format provided by the authors and unedited.
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Robustness and uncertainties in global multivariate wind-wave
climate projections
Joao Morim*,1,2,3, Mark Hemer2, Xiaolan L. Wang4, Nick Cartwright1, Claire Trenham2, Alvaro
Semedo5,6, Ian Young7, Lucy Bricheno8, Paula Camus9, Mercè Casas-Prat4, Li Erikson3, Lorenzo
Mentaschi10, Nobuhito Mori11, Tomoya Shimura11, Ben Timmermans12, Ole Aarnes13, Øyvind
Breivik13,14, Arno Behrens15, Mikhail Dobrynin16, Melisa Menendez9, Joanna Staneva15, Michael
Wehner17, Judith Wolf8, Bahareh Kamranzad18, Adrean Webb11, Justin Stopa19, Fernando Andutta1.
1School of Built Environment and Engineering, Griffith University, Southport, Queensland, Australia.
2Commonwealth Scientific and Industrial Research Organisation (CSIRO) Oceans and Atmosphere,
Hobart, Tasmania, Australia.
3US Geological Survey (USGS), Pacific Coastal and Marine Science Center, Santa Cruz, CA, USA.
4Environment and Climate Change Canada, Climate Research Division, Toronto, Ontario, Canada.
5IHE-Delft, Department of Water Science and Engineering, Delft, The Netherlands.
6Instituto Dom Luiz, Faculty of Sciences of the University of Lisbon, Lisbon, Portugal.
7Department of Infrastructure Engineering, University of Melbourne, Parkville, Victoria, Australia.
8National Oceanographic Centre, Liverpool, United Kingdom.
9Environmental Hydraulics Institute (IHCantabria), Universidad de Cantabria, Santander, Spain.
10European Commission, Joint Research Centre (JRC), Ispra, Italy
11Disaster Prevention Research Institute, Kyoto University, Kyoto, Japan.
12Climate and Ecosystems Science Division, Lawrence Berkeley National Laboratory (LBNL),
Berkeley, California, USA.
13Norwegian Meteorological Institute, Bergen, Norway.
14Geophysical Institute, University of Bergen, Bergen, Norway.
15Helmholtz-Zentrum Geesthacht Centre for Materials and Coastal Research, Geesthacht, Germany.
16Institute of Oceanography, Center for Earth System Research and Sustainability (CEN), Universität
Hamburg, Hamburg, Germany.
17Computational Research Division, Lawrence Berkeley National Laboratory (LBNL), Berkeley,
California, USA.
18Graduate School of Advanced Integrated Studies in Human Survivability/Hakubi Center for
Advanced Research, Kyoto University, Japan.
19Department of Ocean and Resources Engineering, University of Hawaiʻi at Mānoa, Honolulu, Hawaii,
USA.
*Corresponding author address:
Eng. Joao Morim
School of Built Environment and Engineering (G39), +61424467749, Griffith University,
Gold Coast, Southport 4222 QLD, Australia; Email: joao.morimnascimento@griffithuni.edu.au
Supplementary Information
1. Contributing datasets
2. Description of framework
3. Analysis of model skill
3.1 Taylor diagrams
3.1.1 Seasonal analysis
3.1.2 Regional analysis
4. Cluster analysis of present-day simulations
4.1 Distinctive characteristics of each cluster
5. Global pairwise comparison of data sets
5.1 Mean bias
5.1 Variability bias
6. Analysis of projected changes
6.1 Seasonal analysis
6.2 Global pairwise comparison of data sets
6.3 Cluster analysis of future relative changes
7. Supplementary References
1. Contributing datasets
The ten contributing studies and respective wave data sets are described in detail elsewhere25-34. Here,
we provide only a brief overview of each study and summarize their key characteristic in Supplementary
Table S1.
1.1 CSIRO: Hemer M., and Trenham C. (2016)25
Hemer and Trenham25 (hereafter CSIRO) presented global wave climate projections derived using a
dynamical wave approach. Surface wind fields at 3-hourly temporal resolution and sea-ice area fraction
at monthly frequency from 8 CMIP5 GCMs were used to force a 1° spatial resolution global WW3SM1
model under RCP4.5 and RCP8.5 scenarios for 3 time-slice periods: 1979 to 2005 representing current
climate, 2026-2045 representing mid-century conditions and 2080-2100 representing the end of century
climate conditions. Further details are given in Supplementary Table S1.
1.2 JRC: Mentaschi et al. (2017)26
Mentaschi et al.26 (hereafter JRC) presented an ensemble of global wind-wave climate projections by
forcing the WW3 model with 3-hourly wind forcing (no sea-ice concentration) from six CMIP5 GCMs.
Wave simulations were carried out at 1.5° spatial resolution between 1970 and 2100 under RCP4.5 and
RCP8.5. Further details are provided in Supplementary Table S1. Our analysis included their ensemble
members from three CMIP5 GCMs (ACCESS1.0, ACCESS1.3 and EC-EARTH).
1.3 USGS: Li et al. (2017)27
Li et al.27 (hereafter USGS) used 3-hourly winds (no sea-ice concentration) simulated by four CMIP5
GCMs to generate an ensemble of wave conditions for a recent historical time-period (1976-2005) and
projections for the middle and end of the 21st century under 2 forcing scenarios (RCP 4.5 and RCP 8.5).
The wave fields were simulated by the wave model WW3, applied globally at 1 × 1.25° grid resolution
with a nested grid across the Eastern North Pacific at 0.25° resolution. In this analysis, we use the results
obtained at global-scale. Further details are given in Supplementary Table S1.
1.4 NOC: Bricheno L., and Wolf J. (2017)28
Bricheno and Wolf28 (hereafter NOC) developed projections of coastal wave impacts under high-end
climate change (RCP4.5 and RCP8.5) scenarios using surface wind forcing from EC-EARTH and daily
sea-ice concentration to drive a WW3 wave model at global and regional-scale. The global wave climate
projections used 3-hourly surface winds as forcing and were carried out at ~0.7 × 0.5° from 1970-2100
using 1970-2004 as present climate. In this analysis, we use the global-scale simulations. Further details
are given in Supplementary Table S1.
1.5 ECCC (d): Casas-Prat M., Wang L., and Swart N. (2018)29
Casas-Prat et al.29 (hereafter ECCC d) presented global dynamical wave projections at 1° (refined to
0.5° nearshore) under scenario RCP8.5. These simulations were derived using WW3 model forced with
3-hourly surface wind fields and daily sea-ice concentrations from 5 CMIP5 GCMs, using 1979 to 2005
as present-day climate and 2081-2100 as representative of future climate. Further details are given in
Supplementary Table S1.
1.6 IHE-DELFT: Semedo et al. (2018)30
Semedo et al.30 (hereafter IHE-Delft) used a 7-member ensemble of dynamical global wave climate
projections. The ensemble was generated by forcing the wave model WAM at 1° resolution with surface
wind fields and sea-ice concentration from 7 different EC-EARTH realizations for RCP8.5. The period
of 1979-2005 was used as present climate and 2006-2100 as representative of future climate. The seven
EC-Earth runs were obtained from the larger CMIP5 EC-Earth ensemble. Here, we use the results from
ensemble member 1 (realization r1i1p1) for consistency. Further details are provided in Supplementary
Table S1.
1.7 LBNL: Timmermans et al. (2017)31
Timmermans et al.31 (hereafter LBNL) used monthly sea-ice concentration and 3-hourly surface wind
fields from the Community Atmospheric Model (CAM5), the atmospheric component of the NCAR
Community Earth System Model (forced by observed sea surface temperatures) at different horizontal
resolutions (~1.0° and 0.25°) to drive a high-resolution 0.25° global WW3 wave model under present
day conditions (1960-2012 and 1995-2005, respectively). Four simulations were performed using the
high-resolution wind forcing fields (~0.25°), each initialized with a different microscopically perturbed
atmospheric state. The simulation of future conditions were generated using the 0.25° CAM5 forcing
under RCP8.5 for 2081-2100 using observed SST + 2° C, where year 2081 corresponds with 1981. For
consistency, we only use the results obtained with 0.25° resolution forcing for the present-day and future
time-slice. The four-member ensemble mean is used to represent the present-day conditions. There is a
discrepancy of ten years in the LBNL data relative to the other study contributions within the present
time-slice (1995-2005 as opposed to 1979-2004). To support comparison, we assume that differences
for the present-day climate are attributable to model errors, and are not from the non-stationarity of the
wave climate system. Further details are given in Supplementary Table S1.
1.8 KU: Shimura T., Mori N., and Hemer M. (2016)32
Shimura et al.32 (hereafter KU) developed an ensemble of global wave climate projections produced
with WW3 wave model forced by 6-hourly surface winds (and monthly sea-ice data) at 0.6° horizontal
resolution from the high-resolution atmospheric GCM MRI-AGCM3.2H, at 0.5625° spatial resolution.
The forcing of the MRI-AGCM were 4 future SST conditions derived from CMIP5 GCMs under the
RCP8.5 scenario. The current-day climate was taken as 1979-2005 and the future climate as 2079-2100.
Further details are given in Supplementary Table S1.
1.9 IHC: Camus et al. (2017)33
Camus et al.33 (hereafter IHC) conducted a global multi-model wave climate projections at 1° spatial
resolution based on a semi-supervised, weather-type statistical downscaling approach using 30 CMIP5
GCM daily SLP fields (predictor) and a reference wave hindcast, GOW2SM2, as predictand observations.
In this study, the global ocean was divided in 11 sub-areas with a common SLP predictor. A regression-
guided clustering (using linear regression and k-mean clustering) was performed at each wave grid point
of GOW2SM2, allowing the estimation of the mean value of "# and $
% for each weather type (WT). The
global wave climate projections were estimated from the future probability of WTs and the mean value
of the wave variables associated with each WT at each wave grid node. The CFSR and GOW2SM2 data
from 1970-2015 were used in the training of the statistical relationship by comparing the estimations of
the monthly wave parameters calculated using the statistical approach and from the time series of the
GOW2SM2. In order to diminish climate model biases, the model SLP simulations were adjusted such
that they have the same climatological mean and standard deviation as the CFSR SLP data set (used as
proxy for observations over the period 1975-2005). The present conditions were taken between 1975-
2005 and the future climate between 2070-2100 (under scenarios RCP4.5 and RCP8.5). We used 29 of
their statistical members.
1.10 ECCC (s): Wang X., Feng Y., and Swail, R. (2014)34
Wang et al.34 (hereafter ECCC s) provided statistically-based projections of wave climate for RCP4.5
and RCP8.5 using a multi-variate regression model with lagged dependent variable to represent a SLP-
"# relationship. The global ocean was divided in 11 subregions with common SLP predictor. The ERAI
data was used to calibrate the statistical relationship between predictand "# and its SLP-based predictor.
In order to diminish climate model biases, the model SLP simulations were adjusted such that they have
the same climatological mean and standard deviation as the ERA-Interim SLP data used as proxy for
observations over the period 19812000. Time series of 6-hourly SLP-based predictors obtained from
20 CMIP5 GCMs were provided to the trained statistical model to predict 6-hourly "# over a 150-year
period from 1950-2100. The periods 1980-1999 and 2080-2100 were used to represent current-day and
future conditions, respectively.
2. Description of framework
The contributing studies were conducted under a community pre-established framework developed to
support intercomparison studies and quantification with a coverage of sampling space which cannot be
obtained with individual studies. This also removes confounding uncertainties among studies owing to
differences in time-slices and/or wave parameters used to characterize future changes. The datasets ("#,
$
% and &% when available) provided by each of the contributing groups were compiled and processed
with the standard set of wave statistics41,42. A total of 7 wave statistics (average, 10th, 50th, 90th, 95th and
99th percentiles, and annual maximum) were obtained from the "# and $
% sub-daily input data provided
by each contribution when available and two circular statistics were determined from the &% sub-daily
data sets (circular mean and circular standard deviation). In this analysis, we used annual and seasonal
mean "#, $
% and &%, and 10th and 99th percentiles of annual/seasonal "#. The 99th percentile "# is used
as an indicator of the size of the largest storm waves (largest 1%). USGS provided gridded time-series
of monthly mean "# values which were converted to annual/seasonal means (Supplementary Table S2).
3. Analysis of model skill
3.1.1 Seasonal analysis
The skill of each ensemble member from each contributing study to represent the annual mean climate
of the different wave parameters is shown in Fig. S1 (against the altimeter database) and Fig. S6 (against
ERAI) using Taylor Diagrams. Here, we compare the skill of the wave simulations to represent seasonal
variability (for simplicity, December-February DJF and June-August, JJA). The skill of the simulations
to represent the seasonal-mean climate (Fig. S2-S3) of the different wave parameters is generally similar
to that seen for the annual-mean climate (Fig. S1). In terms of "%, all the IHC statistical members show
relatively less ability to represent $
% than "#, systematically underestimating the ERAI data (Fig. S7-
S8). This is consistent with the relatively poorer skill of the IHC33 statistical members to represent mean
wave periods33, and the fact that the underlying statistical relationship developed is based on a different
wave database (GOW2SM2 as opposed to the ERAI). In terms of &%, ensemble members exhibit CRMSE
values between 0.25-0.75 and SC values of 0.8-0.9, regardless of the season considered.
3.1.2 Regional analysis
The model-skill comparison comprising all ensemble members from each contributing study is shown
in Fig. S1. Here, we assess model-skill to represent the annual mean wave climate of 8 sub-domains of
the global ocean defined on the basis that the wind-wave climate system has similar qualitative features
within each particular region34.
Comparison against the satellite database shows that model-skill is variable across regions exhibiting
less skill at regional-scale (Figs. S4-S5) than at global-scale in terms of both "# and "#
'' (Fig. S1). The
CRMSD and NSD values in annual "# reach ~0.75 m and ~0.5 m respectively across the North Pacific
and Tropical Atlantic Oceans, while the remaining regions show skill metrics more similar to those seen
at the global-scale. The spatial correlation is usually above 0.9 regardless of the region. In terms of "#
'',
the CRMSD and NSD values in annual "# are generally under 0.75 and 0.5, however, in the Southern
Australia and Southern Indian Ocean the CRMSD and NSD values range from 0.25 to ~1 m.
In terms of $
%, the CRMSD values are generally 0.25-0.5 s (regardless of region considered), except
across the Southern Indian and Pacific Oceans, with several members showing values up to ~0.75 s. SC
and CRMSD values for &% exhibit a similar degree of agreement as for $
% and "# over the tropics and
the South Indian and Pacific Oceans. A poorer spatial agreement between the simulations and the ERAI
is found over the North Pacific and Atlantic Ocean, with SC values between approximately 0.6-0.9 and
CRMSD values between 0.5-1° (Fig. S9).
4. Cluster analysis of present-day simulations
Fig. 1 shows five main cluster associated with the wave-modelling methodology (WMM) used (rather
than GCM forcing). For example, we see that the IHC-INM-CM4-forced member is clustered with the
IHC-members rather than clustered with the other INM-CM4-forced wave simulations from ECCC (s),
ECCC(d) and CSIRO. The same is seen for all other members of IHC and ECCC(s). These findings are
expected, as the GCM-simulated SLP (predictor) used in the IHC and ECCC(s) statistical methods have
been calibrated and corrected (Section 1.9-1.10).
However this feature is not limited to the statistical simulations. Fig. 1 shows that the CSIRO ensemble
members first cluster amongst themselves (cluster 4), before clustering with members obtained through
a different wave method. For example, the CSIRO-ACCESS1.0-forced simulation is clustered with the
CSIRO-members rather than clustered to the ACCESS1.0-forced simulations from ECCC(s), ECCC(d)
and JRC. The same is seen for CSIRO-BCC-CSM1.1, CSIRO-INM-CM4 and CSIRO-HadGEM2-ES.
Cluster 2 comprises simulations from different dynamical study groups using WW3 with ST2 and ST4
source-term physics (except the IHE-DELFT-WAM simulation and the CSIRO-MIROC5 and CSIRO-
MRI-CGCM3 members for reasons explained below - Section 4.1). We find the ECCC (d) and USGS-
BCC-CSM1.1 are not clustered with other BCC-CSM1.1-forced members from the ECCC (s) and IHC.
The same applies to the GFDL-ESM2M- and MIROC5-driven members (cluster 3). This as explained
above (1st paragraph) is largely explained by the correction of the forcing fields applied in the statistical
WMM. We note, however, that the GCM-forcing dominates the variance between the USGS and ECCC
(d) dynamical methods (which are highly similar) (Fig. S12).
At a lower level of dissimilarity, we see that within each cluster associated with a specific WMM, we
find a clusterization of members based on the interdependency of their forcing GCMs (i.e. the similarity
of their dynamical cores). In other words, within each cluster, members forced by GCMs with a similar
dynamical core (sharing atmospheric and/or ocean components) cluster together - before grouping with
members forced by GCMs with different model components. For example, we see that within cluster 1
and 5, all the members forced by the different versions of the MIROC models cluster together (because
these models share identical dynamical cores). The same is seen for other climate models with the same
GCM lineage (similar model genealogy) such as the MPI (cluster 1 and 5), BCC and/or GFDL’s models
(cluster 1). In cluster 4, we see that the ACCESS1.0 and HadGEM2-ES-forced simulations are the most
similar because of the similarity between the ACCESS1.0 and HadGEM2-ES surface wind fields (they
are the same atmospheric model). This is consistent with the description of model componentsSM3.
4.1 Distinctive characteristics of each cluster
Cluster 1 is comprised of IHC29 members exhibiting a negative bias (up to ~15%) in annual "# relative
to satellite measurements over the tropics and a positive bias (up to ~15.0%) elsewhere (Fig. 1). In terms
of "#
'', small negative bias are seen everywhere except across the high latitudes (Fig. S10). This cluster
has the smallest within-cluster variance (highest similarity among models), which is consistent with our
previous model-skill analysis (Fig. 1). As previously discussed (section 3.1.1), the IHC members show
a lack of ability to represent swell periods, with all 30-members systematically underestimating annual
$
% as evidenced by the relatively large negative bias observed globally (~25-30%) relative to the ERAI
(Fig. S11). We attribute this bias to differences between the GOW2SM2 and the ERAI datasets, the nature
of the statistical methodology, and differences in the definition of the mean wave period $
%.
Cluster 2 is composed by dynamically-derived members from ECCC(d), USGS, NOC, IHE-Delft and
JRC obtained using WW3 with ST2 or ST4 model source-term packages (Supplementary Table S2) for
all simulations except for the IHE-DELFT which uses the WAM model. This is consistent with previous
research showing that ST2 and ST4 physics package lead to relatively similar "# fieldsSM4. We attribute
the positive bias (<~15%) relative to the satellite data in annual "# fields (globally) to the overestimation
of swell-energy propagation from the southern and northern storm generation tracks intrinsic to the ST2
and ST4 source-term packagesSM4.
Cluster 3 is a high-energy dynamical cluster which also includes the high-resolution KU member. The
MIROC5-driven simulations from the USGS and ECCC (d) are also included in this cluster (as opposed
to cluster 2). We attribute this to the overprediction of swell energy propagation intrinsic to the ST2/ST4
physicsSM4 and the highly-energetic forcing characteristics of the MIROC5 GCM24,25. Cluster 4 consists
of the CSIRO-dynamical models derived using WW3 model with ST3 BAJ physics, and shows negative
biases in annual "# and ("#
'' (Fig. S10) across most of the global ocean21 of less than ~15% respectively.
This is reflected in terms of absolute values in Fig. 1. The relatively large disparity relative to cluster 2,
is consistent with the ST3 (BJA) source-term package (WAM Cycle 4+ physics) relying on a different
formulation for wind-generation and dissipation due to the whitecappingSM5. Note that CSIRO-MIROC
and CSIRO-MRIC-GCM3-forced members fall within cluster 2 as opposed to cluster 3, because of the
highly energetic wind forcing of these models26,27 partly offsetting the characteristics of the WW3 ST3
(BAJ) package (used by CSIRO).
The 5th cluster consists of the ECCC (s) ensemble34 (and alike cluster 1) is characterized by relatively
small within-cluster variance (high similarity amongst members) due to the standardized predictor used
in statistical downscaled variables where the bias of all the GCM-based forcing is corrected in terms of
mean and standard deviation. This cluster exhibits negative bias in "# (<10%) across most of the ocean
(except in the eastern Pacific positive bias) and "#
'' (<~25%) relative to the altimeter dataset (Fig. S10).
The relatively small annual "# bias across most of the global ocean when comparing against the ERAI,
translates the high-similarity between this ensemble and the ERAI dataset (Section 1.10).
5. Global pair-wise comparison of bias
The number of ensemble members used in this study is relatively large (see Supplementary Table S1).
To support our model-skill and cluster analysis, and more explicitly demonstrate dissimilarities between
datasets, we quantify differences within a reduced subset of ‘coherent’ simulations where each member
from a given contribution shares common forcing with at least two other contributions (methodologies).
Annual and seasonal mean percent differences relative to the Satellite and ERAI datasets were derived
for each single member (and wave parameter) over the representative present time-slice, allowing pair-
wise comparisons of the patterns of agreement/disagreement amongst the different members. The mean
and variability (measure as the standard deviation across n-members) within each study ensemble and
within each ensemble with common forcing was estimated. For simplicity, we only present results for
"# fields, as a comprehensive analysis including all other wave parameters has been already provided
using Taylor Diagrams.
5.1 Mean bias
Although dissimilarities between all pairs of members are overall comparable in terms of magnitude
(Supplementary Fig. S12-S13), different spatial patterns of differences are present. Consistent with the
cluster analysis performed (Fig 1), model-skill is strongly dependent on the methodology used by each
group to develop their wave-climate fields. For example, the CSIRO members exhibit less energetic "#
fields relative to USGS and ECCC (d) members (Fig. 1), due to the differences between ST3 (BJA) and
ST2/ST4 physics packages, respectively (Supplementary Table S1). The USGS and ECCC (d) members
exhibit relatively similar "# fields, showing that the inclusion of sea-ice forcing (out of sea-ice regions)
and differences in the parameterizations ST2 and ST4 have relatively small effect on the simulated wave
climate as previously shown via cluster analysis (Fig.1). This is further supported by the relatively good
agreement between the EC-EARTH dynamical members from the JRC, NOC and ECCC (d). Note that
statistical members exhibit very little variability, owing to their statistical calibration/corrections of the
predictor (SLP). The characteristics described above are seen, regardless of the reference database used
for comparison (i.e. Satellite database and ERAI). These results are reflected in the cluster analysis (Fig.
1) presented in the main manuscript.
5.2 Variability bias
As part of our skill analysis we compare model ability to represent inter-annual variations. A thorough
comparison of model skill to represent seasonal variability has been previously presented (section 3.2.1)
by comparing seasonal-derived values for all wave parameters between the models and the satellite data
Here, we compared the skill of the simulations to represent year-to-year variations, using the variability
bias derived from the time-series of annual mean "# and "#
''. The inter-annual variability bias is defined
as the ratio of the GCM simulated variance to the variance calculated from the satellite data26 (Fig. S16-
S17).
The magnitude of interannual variance in the dynamically-derived ensemble members, whilst strongly
variable, is of the same order of magnitude as the variance observed in the satellite and ERAI databases
The statistically-based members however, exhibit an inter-annual variance up to an order of magnitude
smaller than seen in the satellite and reanalysis, which is consistent with the COWCLIP CMIP3-derived
multi-model ensemble23. The magnitude of the inter-annual variance in "#
'' is likewise strongly variable
globally. The statistical members show a tendency to underestimate inter-annual variability in "#
'' (see
Supplementary Fig. S17) as seen for "#.
6. Analysis of projected change
6.1 Seasonal analysis
Future 21st century projected changes in seasonal mean wave-climate (for simplicity June-August JJA
and December-February DJF) are examined under the emission pathways RCP4.5 and RCP8.5. We find
that changes in the weighted multi-model mean for RCP4.5 and RCP8.5 exhibit identical spatial patterns
for all wave parameters but with relatively larger changes projected under RCP8.5 (Supplementary Fig.
S21-S22). Consistent with Fig. 2, ocean areas with robust projected changes under RCP4.5 are relatively
limited. Nonetheless, we find robust projected decreases in DJF "# fields (~5-10%) under RCP8.5 over
the North and South Atlantic and the western Indian Ocean (accounting for ~10-16% of the global ocean
area; see Supplementary Table S2). Regions of robust projected increases in DJF "# fields are extremely
limited. In terms of $
%, robust projected increases are found in the Eastern and South Pacific and in the
tropical Indian Ocean of up to 5% (~20% of the global ocean area). Regions of robust decrease comprise
the western Pacific Ocean and the Atlantic Europe (12.5% of the global ocean area). A robust clockwise
shift in DJF &% (~5-10°) is observed in the western Indian Ocean and the Atlantic Europe, accompanied
by robust anticlockwise directional shifts in the Southern Ocean.
In terms of projected changes in JJA-mean wave climate, we find projected increase in "# fields (~5-
10%) and $
% (~5%) over much of the global ocean (under RCP8.5) but regions of robustness are limited
to the Southern Ocean. Areas of robust projected decrease in "# fields are limited to the North Atlantic
Ocean and are not as extensive as for annual changes (Supplementary Table S2). Future changes in JJA
&% show robust anticlockwise rotation of wave direction (exceeding -10°) in the southern Pacific Ocean
and a robust clockwise rotation in the northern Pacific Ocean and northern/central Atlantic Ocean.
6.2 Global pairwise comparison of data sets
Supplementary Fig. S13-S14 show global pairwise comparison of projected future mean and extreme
"# fields under RCP8.5 within the coherent subset (Supplementary Table S3). It is seen that differences
between members are largely dependent on GCM-forcing (origin of the surface winds used to generate
the global wave fields). Consistent with our cluster analysis (Fig.4), differences in wind-wave modelling
approach are seen, particularly between statistical and dynamical-derived members with the same GCM
forcing (extending to other members not considered in this subset). For each GCM forcing, we observe
differences in magnitude and spatial pattern which are attributable to the different configurations of the
dynamical/statistical wave models. The influence of the wind-wave modelling method varies according
to the forcing GCM underlining the influence of the importance of the interactions between the different
sources of uncertainty as resolved by the ANOVA (Fig. 5, Methods).
6.3 Cluster analysis of future relative changes
Five well defined cluster are shown in Fig. 4. Cluster 1 to 4 exhibit common spatial patterns of change
characterized by different magnitudes (magnitude of change) and generally dominated by GCM forcing.
Cluster 5 is an anomaly cluster comprised of ECCC (s) projections and shows very different features of
change (spatial pattern and magnitude), and highlights the strong influence of the statistical downscaling
method34 on projected annual "# fields!across the global ocean - particularly when using specific GCM
forcing (MRI-CGCM3, EC-EARTH, and CNRM-CM5). These features are in line with Supplementary
Fig. S23. The results derived for all wave parameters are presented in Supplementary Fig. S25.
Cluster 1 is comprised of MIROC5-forced dynamical projections under RCP8.5, and show a relatively
large projected increase in annual "# fields (10th percentile, mean and 99th percentile) and $
% over the
Southern Ocean and eastern Pacific (~5-10%) and a large projected decrease in the North Atlantic and
Pacific Ocean (~5-10%). Cluster 2 is comprised of HadGEM2-ES and ACCESS1.0-driven projections,
and shows a similar spatial pattern of change to cluster 1 - but with smaller projected changes in annual
"# fields and $
%, except in the North Atlantic. In terms of directional changes, cluster 2 exhibits smaller
changes compared to cluster 1, particularly across the tropics and subtropics.
Cluster 3 is composed of both statistical and dynamical-based wave projections derived using CNRM-
CM5 CSIRO-Mk3.6, MRI-CGCM3 and BCC-CESM1.1 forcing (under RCP4.5 and RCP8.5 depending
on GCM). Cluster 3 exhibits relatively smaller changes in annual "# fields across the global ocean (up
to ~2%), with differences among projected change signals in "# explicitly shown in Supplementary Fig.
S23-S24. Cluster 4 exhibits a similar pattern of change as cluster 3, but with relatively larger magnitudes
of change across the global ocean. This cluster comprises statistical and dynamical projections obtained
from BCC-CESM1.1 (RCP8.5), EC-EARTH, MIROC5 and GFDL-ESM2M-derived forcing. Cluster 4
also comprises four statistical wave projections (2 derived from ACCESS1.0 forcing and 2 derived from
HadGEM2-ES forcing) which did not cluster with their corresponding dynamical projections (included
in cluster 2) highlighting the influence of statistical vs dynamical modelling method. These features are
consistent with Supplementary Fig. S23.
Supplementary Table S1 - Summary of the contributions to the intercomparison analysis. The emission scenarios (RCP pathways) and time-slices (representative of present and future
climate) used by each group to derive wave-climate projections is shown. The wave climate ensemble members provided by each contributing group are coloured. The methodology used
by each group to derive their wave-climate projections is detailed along with the set of wave statistics provided by each contribution.
Research centre/
Institution
Commonwealth
Scientific and
Industrial
Research
Organisation
(CSIRO)21
Joint
Research
Centre
(JRC)22
United
States
Geological
Survey
(USGS)23
National
Oceanography
Centre
(NOC)24
Environment
and Climate
Change
Canada
(ECCC)25
IHE Institute
for Water
Education
(IHE-
DELFT)26
Lawrence
Berkeley
National
Laboratory
(LBNL)27
Kyoto
University
(KU)28
Environmental
Hydraulics
Institute
(IHC)29
Environment
and Climate
Change
Canada
(ECCC)30
Country
Australia
UE
US
UK
Canada
Netherlands
US
Japan
Spain
Canada
Emission scenario
RCP4.5/8.5
RCP4.5/8.5
RCP4.5/8.5
RCP4.5/8.5
RCP8.5
RCP8.5
RCP8.5
RCP8.5
RCP4.5/8.5
RCP4.5/8.5
Historical simulation
1979-2005
1979-2005
1976-2005
1970-2004
1979-2005
1979-2005
1995-2005
1979-2004
1979-2005
1950-2005
Future simulation
2080-2100
2010-2100
2081-2100
2005-2100
2081-2100
2006-2100
2081-2100
2079-2100
2010-2100
2006-2100
CMIP5 GCM(s) forcing used
ACCESS1.0
ACCESS1.3
BCC-CESM1.1
BCC-CESM1.1(m)
BNU-ESM
CanESM2
CESM1 (BGC)
CESM1 (CAM5)
CCSM4
r6i1p1a
CMCC-CM
CMCC-CMS
CNRM-CM5
CSIRO-Mk3.6
EC-EARTH
r8i1p1a
r12i1p1a
r2i1p1a
r2i1p1a
FGOALS-s2
FGOALS-g2
GFDL-CM3
GFDL-ESM2G
GFDL-ESM2M
HadGEM2-CC
HadGEM2-ES
INMCM4
IPSL-CM5A-LR
IPSL-CM5A-MR
IPSL-CM5B-LR
MIROC-ESM
MIROC-ESM-CHEM
MIROC5
MPI-ESM-LR
MPI-ESM-MR
MRI-CGCM3
NorESM1-M
CMIP5-based/observed SST forcing used
CAM5-AGCM (SSTb +2°)
MRI-AGCM-SST0c
amodel run number as per CMIP5 syntax (r for realization, i for initialisation and p for physics, followed by integer). All other runs used ensemble member r1i1p1.
bobserved SST obtained from the HadISST1-based data setSM6 were used to force the atmospheric model CAM5.
cSST0 to SST3 correspond to four different SST future change patterns derived from CMIP5 GCM models to force the atmospheric model MRI-AGCM32.
ddefinition of each source-term package is extensively described in Tolman et al.SM1.
esimulations include !
" and/or !
#
fcorresponds to the second order mean wave period.
gonly provided monthly means of $%.
MRI-AGCM-SST1c
MRI-AGCM-SST2c
MRI-AGCM-SST3c
Number of GCM(s)
8
6
4
1
5
1
1
4
29
20
Atmospheric downscaling
Atmospheric downscaling
No
No
No
No
No
No
CAM5
MRI-AGCM
No
No
Wind-wave modelling configuration (WMM)
Wind-wave modelling method
Dynamical
Dynamical
Dynamical
Dynamical
Dynamical
Dynamical
Dynamical
Dynamical
Statistical
Statistical
Statistical/Spectral wave model
WW3
WW3
WW3
WW3
WW3
WAM4.5
WW3
WW3
Weather type
Regression
Surface/SLP forcing
3-hourly
3-hourly
3-hourly
3-hourly
3-hourly
3-hourly
3-hourly
6-hourly
Daily SLP
6-hourly SLP
Atmospheric correction
-
-
-
-
-
-
-
-
SLP
SLP
Source-term packaged
ST3 (BJA)
ST4
ST2
ST4
ST4
ST3
ST4
ST4
-
-
Calibration
Default
Default
Default
Default
Default
Default
Default
Default
-
-
Sea-Ice forcing
Monthly
No
No
Daily
Daily
Daily
Monthly
Monthly
-
-
Spatial resolution (°)
1 × 1
1.5 × 1.5
1.25 × 1
~0.7 × 0.5
1 × 1
1 × 1
0.25 × 0.25
~0.56 × 0.56
1 × 1
1 × 1
Spectral partition
29f × 24d
25f × 24d
25f × 24d
30f × 36d
29f × 24d
32f × 24d
32f × 36d
29f × 36d
-
-
Bathymetry data
ETOPO
ETOPO
DBDB2
GEBCO
DBDB2
ETOPO
ETOPO
ETOPO
-
-
Set of wave statistics provided
COWCLIP statistics
All
All
$%
g
All $%
e
All except !
&
e
All
All
All
$% and !
&
f
All $%
Supplementary Table S2 - Percentage of the world’s coastline (ocean) with offshore deepwater projected robust changes (Methods, Section 5) under high-
emission scenario RCP8.5. Length of coastline measured along ocean ice-free regions and excluding enclosed seas (Methods, Section 6).
RCP8.5
Annual
DJF
JJA
Wave
parameters
Percentage of coast
(ocean) with robust
projected increase
Percentage of coast
(ocean) with robust
projected decrease
Percentage of coast
(ocean) with robust
projected increase
Percentage of coast
(ocean) with robust
projected decrease
Percentage of coast
(ocean) with robust
projected increase
Percentage of coast
(ocean) with robust
projected decrease
$%
4.9 (15.1)
14.8 (20.6)
2.5 (6.3)
10.3 (18.1)
2.5 (9.6)
1.9 (5.4)
$%
'(
5.4 (10.9)
6.5 (21.0)
0.6 (4.0)
4.0 (12.4)
7.2 (10.6)
0.9 (7.6)
$%
))
3.0 (7.3)
2.2 (1.9)
0.6 (0.9)
0.5 (1.1)
2.2 (3.7)
1.1 (2.3)
!
&
8.7 (24.9)
21.4 (18.9)
11.1 (26.2)
20.4 (12.7)
2.8 (9.4)
1.1 (0.4)
*&
10.2 (12.8)
9.9 (19.4)
4.6 (3.9)
2.6 (4.9)
5.0 (8.2)
8.6 (8.8)
See Methods (Section 6) for definition of robustness. Increase (decrease) in wave direction (*&) corresponds to clockwise (anticlockwise) rotation.
Supplementary Table S