Attribution of global lake systems change to anthropogenic forcing

Abstract

Lake ecosystems are jeopardized by the impacts of climate change on ice seasonality and water temperatures. Yet historical simulations have not been used to formally attribute changes in lake ice and temperature to anthropogenic drivers. In addition, future projections of these properties are limited to individual lakes or global simulations from single lake models. Here we uncover the human imprint on lakes worldwide using hindcasts and projections from five lake models. Reanalysed trends in lake temperature and ice cover in recent decades are extremely unlikely to be explained by pre-industrial climate variability alone. Ice-cover trends in reanalysis are consistent with lake model simulations under historical conditions, providing attribution of lake changes to anthropogenic climate change. Moreover, lake temperature, ice thickness and duration scale robustly with global mean air temperature across future climate scenarios (+0.9 °C °Cair–1, –0.033 m °Cair–1 and –9.7 d °Cair–1, respectively). These impacts would profoundly alter the functioning of lake ecosystems and the services they provide.

Full text

Articles
https://doi.org/10.1038/s41561-021-00833-x
1Department of Hydrology and Hydraulic Engineering, Vrije Universiteit Brussel, Brussels, Belgium. 2ETH Zurich, Institute for Atmospheric and Climate
Science, Zurich, Switzerland. 3Pacific Northwest National Laboratory, Richland, WA, USA. 4Institute for Environmental Sciences, University of Geneva,
Geneva, Switzerland. 5Lomonosov Moscow State University, Moscow, Russia. 6Moscow Center for Fundamental and Applied Mathematics, Moscow,
Russia. 7Obukhov Institute for Atmospheric Physics, Russian Academy of Science, Moscow, Russia. 8Water Systems and Global Change Group, Wageningen
University & Research, Wageningen, the Netherlands. 9European Space Agency Climate Office, ECSAT, Harwell Campus, Didcot, UK. 10Research
Department, European Centre for Medium-Range Weather Forecasts (ECMWF), Reading, UK. 11Leibniz-Institute of Freshwater Ecology and Inland Fisheries,
Berlin, Germany. 12Potsdam Institute for Climate Impact Research, Potsdam, Germany. 13Department of Ecology and Genetics, Uppsala University, Uppsala,
Sweden. 14Catalan Institute for Water Research (ICRA), Girona, Spain. 15University of Girona, Girona, Spain. ✉e-mail: luke.grant@vub.be
Lakes provide ecosystem services to local communities1,2 and
modulate local climates3–7. The seasonality of lake ice cover and
lake temperatures are the foundations of the lake environment,
controlling many lake processes8,9. In recent decades, lake tempera-
tures have been rising, and seasonal ice cover has been declining
on regional10–12 and global scales13,14. Among other things, these
changes alter lake stratification15, impact lake ecosystem productiv-
ity16 and disturb fisheries17,18.
New historical simulations of lake ice cover and mixed-layer
temperature from the European Centre for Medium-Range Weather
Forecasts (ECMWF) Reanalysis v5 - Land (ERA5-Land) reanaly-
sis19—lake model simulations forced by the observation-assimilated
atmosphere of ERA5—provide a high-resolution outlook on lake
changes in recent decades (Fig. 1a–c and Supplementary Fig. 1).
From 1981–1990 until 2010–2019, these simulations reveal rapid
changes; 130,472 lake grid cells worldwide have experienced two
weeks of lake ice-cover loss, while on average lakes have lost nine
days of ice cover. Likewise, global-scale reanalysed lake mixed-layer
temperature shows substantial increases, with 64,382 lake grid cells
warming more than 1.5 °C and a global annual average increase of
0.4 °C (Fig. 2e).
While observed and reanalysed changes in lake ice cover and
lake temperatures are large, the possibility that they are due to natu-
ral climate variability has so far not been ruled out. They have also
not been attributed to anthropogenic drivers using formal statisti-
cal approaches. Formally, ‘detection’20,21 of climate change impacts
consists of showing that observed changes are inconsistent with
natural variability by comparing them with simulated variability
under human-free climate conditions. Upon successful detection,
anthropogenic greenhouse gas emissions are a plausible candidate
to explain ongoing changes in lakes, but this causal link must again
be formally established. Such ‘attribution’20,21 to anthropogenic
emissions is achieved by showing consistencies between observed
changes and response patterns derived from historical climate
impact simulations. Together, detection and attribution represent
a cornerstone of assessments by the Intergovernmental Panel on
Climate Change (IPCC)22,23.
Climate change detection and attribution
We investigate climate change detection and attribution in
ERA5-Land reanalysed lake variables using two complemen-
tary approaches and simulations with five global-scale lake mod-
els forced by four global climate models (GCMs)24 (Methods and
Supplementary Note 1.5). The first approach25–27 considers a dis-
tribution of rank correlations between the multimodel mean of
lake simulations forced by GCMs under historical climate forc-
ings (HIST) and a collection of individual pre-industrial control
(PIC) lake simulations. This distribution of correlations, assumed
to arise from pre-industrial climate variability, is compared with
the single correlation between HIST and the reanalysed time series
(ERA5L for reanalysis). Here, detection is inferred by rejecting
the null hypothesis that reanalysed trends are consistent with the
Attribution of global lake systems change to
anthropogenic forcing
Luke Grant 1 ✉ , Inne Vanderkelen 1, Lukas Gudmundsson 2, Zeli Tan 3, Marjorie Perroud4,
Victor M. Stepanenko 5,6, Andrey V. Debolskiy 5,6,7, Bram Droppers 8, Annette B. G. Janssen 8,
R. Iestyn Woolway 9, Margarita Choulga10, Gianpaolo Balsamo10, Georgiy Kirillin 11,
Jacob Schewe 12, Fang Zhao 12, Iliusi Vega del Valle 12, Malgorzata Golub 13, Don Pierson 13,
Rafael Marcé 14,15, Sonia I. Seneviratne 2 and Wim Thiery 1,2
Lake ecosystems are jeopardized by the impacts of climate change on ice seasonality and water temperatures. Yet historical
simulations have not been used to formally attribute changes in lake ice and temperature to anthropogenic drivers. In addi-
tion, future projections of these properties are limited to individual lakes or global simulations from single lake models. Here
we uncover the human imprint on lakes worldwide using hindcasts and projections from five lake models. Reanalysed trends
in lake temperature and ice cover in recent decades are extremely unlikely to be explained by pre-industrial climate variability
alone. Ice-cover trends in reanalysis are consistent with lake model simulations under historical conditions, providing attribu-
tion of lake changes to anthropogenic climate change. Moreover, lake temperature, ice thickness and duration scale robustly
with global mean air temperature across future climate scenarios (+0.9 °C °Cair–1, –0.033 m °Cair–1 and –9.7 d °Cair–1 , respectively).
These impacts would profoundly alter the functioning of lake ecosystems and the services they provide.
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Articles Nature GeoscieNce
distribution of correlations representative of pre-industrial climate
variability (correlation-based approach28; Fig. 2a–d). The second
approach employs regularized optimal fingerprinting (ROF)20,29. In
this method, the slope parameters (henceforth referred to as scaling
factors) that scale HIST to fit ERA5L in a total least squares (TLS)
regression communicate detection when they are significantly dif-
ferent from 0 (that is, when the 95% confidence intervals of the scal-
ing factors exclude 0). Attribution is achieved when scaling factors
additionally overlap with unity (Methods).
Strict attribution to anthropogenic emissions requires both
all-forcings historical and natural historical response patterns (includ-
ing, for example, solar and volcanic influences but without anthropo-
genic emissions). Through rigorous statistics, the relative disparities
or likeness of these experiments to a reference observed trend can
confirm attribution. Our experimental framework does not include
a natural historical climate scenario. This limits formal attribution to
all combined historical forcings (Methods). However, in light of the
dominant role of anthropogenic emissions relative to natural forc-
ings in historical climate change30, we argue that any attribution in
this framework entails the imprint of human influence. In addition,
out of necessity for a comprehensive spatial and temporal representa-
tion of lake trends, we substitute the use of observed records for lake
ice cover and temperatures with observation-validated reanalysis in
ERA5L (Supplementary Note 1.1).
For lake water temperature at 2 m depth (hereafter, lake temper-
ature), the correlation-based approach shows a strong distinction
between the correlation of ERA5L and HIST on the one hand and
the distribution of correlation coefficients of PIC and HIST on the
other hand (Fig. 2a). This implies that lake temperature reanalysis
simulations for the recent past lie outside the typical variability of
pre-industrial climate conditions and therefore cannot be explained
by pre-industrial climate variability (99% confidence level). For ice
onset, break-up and duration, correlations between ERA5L and
HIST anomalies are again substantially larger than PIC versus HIST
correlations (Fig. 2b–d) and significant (at confidence levels of 95%,
95% and 99%, respectively). This supports the detection of a climate
change signal in lake temperature and all three lake ice indices.
Scaling factor confidence intervals for lake temperature and
all three ice indices are significantly different from 0, confirming
the detection of a climate change imprint in all four variables (Fig.
2e–h). For ice onset, break-up and duration, the HIST time series
closely resembles ERA5L, and scaling factors overlap with unity
(Fig. 2g–h), providing strong evidence to attribute changes in these
variables to external forcings. Lake temperature changes cannot be
likewise attributed, as the scaling factor interval for this variable
remains below unity. On the whole, this formal statistical evidence
confirms that external forcings—and by extension, anthropo-
genic emissions—can explain reanalysed changes in lake ice onset,
break-up and duration.
Future climate projections
Only a few recent studies13,15,31 project end-of-century changes
in lake temperature and ice cover over large areas under multiple
GCM forcings and representative concentration pathways (RCPs),
thereby accounting for uncertainties related to meteorological forc-
ing and climate scenario. However, these studies so far disregard
both lake model uncertainty and transient lake response to green-
house gas forcing. Having demonstrated the foregone imprint of
climate change on lakes, we project lake temperature and ice con-
ditions across pre-industrial to future periods (1661–2099) under
RCPs 2.6, 6.0 and 8.5 (Methods).
By the end of the century, annual mean lake tempera-
tures increase and ice cover decreases unanimously under the
high-emission scenario RCP 8.5 (Fig. 3a–e). Lakes warm the most
(+4–5 °C by 2070–2099 relative to 1971–2000) in southern temper-
ate latitudes in North America and in temperate latitudes across
Eurasia (Fig. 3a and Supplementary Figs. 2–7). In many boreal
zones, the June–July–August lake temperature warming exceeds
global mean surface air temperature warming by a factor of 1.5–2.0
(Fig. 3b), indicating a high climate sensitivity for these lakes asso-
ciated with the polar amplification of atmospheric warming32 and
local amplification due to decreased ice cover and local stratifica-
tion. These spatial sensitivity patterns are consistent across RCPs
for lake temperature (Supplementary Figs. 8–10), ice thickness
(Supplementary Figs. 11–13) and ice-cover indices (Supplementary
Figs. 14-–16). Ice duration decreases by 28–80 days (5th to 95th
percentile), with the largest reductions occurring in coastal regions
and Scandinavia (>45 days, Fig. 3e). Ice duration projections are
a b c
135° E
45° E30° N
40° N
50° N
60° N
70° N
30° N
40° N
50° N
60° N
70° N
30° N
40° N
50° N
60° N
70° N
45° W
45° W
45° W 45° E
∆ reanalysed ice index (days)
Earlier date (panels a,b) or shorter duration (panel c)Later date (panels a,b) or longer duration (panel c)
45° E
≤ –30 –25 –20 –15 –10 –5 0 5 10 15 20 30≤ 25
135° E
135° E
135° W 135° W 135° W
Fig. 1 | Reanalysed historical lake ice changes. a–c, Changes (Δ) in ice onset (a), ice break-up (b) and ice duration (c) in 40 years across baseline (1981–
1990) and recent (2010–2019) periods as obtained from ERA5-Land.
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2.0
HIST, ERA5L
HIST
HIST
HIST ERA5L PIC
201020001990
201020001990
201020001990
201020001990
0
1
2
0
1
2
HIST
0
1
2
HIST
0
1
2
PIC, HIST
a e
fb
c g
hd
Spearman (rank) correlation coefficient Year
99%
95%
1.0
0
0.5
1.0
0
2.0
1.0
0
2.0
1.0
0
2.0
–0.8 –0.4 0.4 0.80
–0.8 –0.4 0.4 0.8
–12
–10
–8
–6
–6
–4
–4
–2
–2
0
0
0
2
2
2
4
4
5
3
1
–1
6
0
–0.8 –0.4 0.4 0.80
–0.8 –0.4 0.4 0.80
1.0
0
Water temperature density (–)
Water temperature anomaly (°C)
Ice onset density (–)
Ice onset anomaly (days)
Ice break-up density (–)
Ice break-up anomaly (days)
Ice duration density (–)
Ice duration anomaly (days)
Fig. 2 | Detection and attribution of the human imprint on lake variables. a–d, Empirical distribution of correlation coefficients between PIC and HIST for
lake temperature (a), ice onset (b), ice break-up (c) and ice duration (d). Red lines show the correlation coefficient between HIST and ERA5L. Vertical blue
lines mark the 95% and 99% cumulative probability of an assumed normal distribution for the sample of PIC–HIST coefficients. e–h, Global multimodel
mean time series and spread (ensemble standard deviation) for PIC and HIST forced response patterns and ERA5L smoothed by a 5 yr running mean for
lake temperature (e), ice onset (f), ice break-up (g) and ice duration (h). Results of single-factor ROF output on HIST are displayed in insets. Scaling factor
confidence intervals denote their 2.5–97.5% uncertainty range and infer detection when excluding the 0 line. Attribution is achieved when confidence
intervals additionally include unity.
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driven mostly by changes in the timing of ice break-up, which hap-
pens consistently earlier in the year by the end of the century and
agrees with the seasonality of ice thickness losses (Fig. 3c–e and
Supplementary Figs. 17–22).
In all future scenarios, global mean lake temperatures increase
while ice thickness and ice duration decrease (Fig. 4). Multimodel
mean projections under RCPs 2.6, 6.0 and 8.5 diverge by 2050 at
the latest, with only RCP 2.6 showing an end-of-century stabiliza-
tion (Fig. 4a–c). Global mean projections show high inter-model
consistency for all variables, except for ice thickness computed by
Community Land Model version 4.5 (Supplementary Figs. 23–25).
By 2100, the scenario spread exceeds the uncertainty originating
from the lake models, GCMs and natural variability, underscoring
the value of mitigation for avoiding severe lake system changes.
Across all future climate scenarios, multimodel mean lake tem-
perature, ice thickness and ice cover scale robustly with air tempera-
ture at the global mean level (Fig. 4d–f). Projected global-average
mean annual scalings with global mean air temperature for lake
temperature, ice duration and ice thickness are +0.9 °C °Cair–1,
–9.7 d °Cair–1 and –0.033 m °Cair–1, respectively. RCP 8.5 projections
indicate end-of-century global mean anomalies of +4.0 °C for lake
temperature, –0.17 m for ice thickness and a 46-day decrease in
ice duration relative to pre-industrial conditions. Compared with
changes at the global scale, zonal mean annual projections reveal
that impacts for lake ice scale the strongest with global mean air
temperature anomalies in boreal latitudes (Supplementary Fig.
38b,c). By contrast, annual lake temperature scaling in the tropics
exceeds its global mean rate of change (Supplementary Fig. 38g).
Patterns of change
Our projections reveal coastal–inland gradients in ice duration
projections around northern European and Scandinavian coasts
and far eastern and western North America that agree with previ-
ous studies33. Large decreases in ice thickness projected in spring
months relative to fall months (Supplementary Figs. 17–19) agree
with observed changes in lake ice cover around the Northern
Hemisphere11,34,35. This is also consistent with the dominant contri-
bution of earlier ice break-up dates to ice duration changes relative
to delayed ice onset (Supplementary Figs. 14–16 and 20–22), which
has been ascribed to a stronger climate change impact on the spring
90° N
60° N
30° N
30° S
60° S 135° W
≤ –5
≤ –90 –75 –60
Earlier date (panels a,b) or shorter duration (panel c) Later date (panels a,b) or longer duration (panel c)
–45 –30 –15 0 15 30 45 60 75 90 ≤
–4 –3
Colder
135° W 135° E
45° E
45° W 30° N
40° N
50° N
60° N
70° N
135° W 135° E
45° E
45° W 30° N
40° N
50° N
60° N
70° N
135° W 135° E
45° E
45° W 30° N
40° N
50° N
60° N
70° N
Warmer Low sensitivity High sensitivity
–2 –1 0 1 2 3 4 5 ≤
90° W 45° W
∆ lake temperature (°C)
45° E 90° E 135° E0° 135° W
≤ 00.25 0.5 0.75 1 1.25 1.5 1.75 2 ≤
90° W 45° W
∆ lake temperature/∆ global mean air temperature (°C/°C)
∆ ice index (days)
45° E 90° E 135° E0°
0°
a
c d e
b
Fig. 3 | End-of-century change in lake temperature and ice onset, break-up and duration according to RCP8.5. a, Multimodel mean change in annual
lake temperatures at 2 m depth. b, The mean June–July–August lake temperature change at 2 m depth divided by the change in same-year, global-average,
annual mean surface air temperature. c–e, Changes in ice onset, break-up and duration, respectively. All results compare end-of-century (2070–2099) with
present-day (1971–2000) conditions.
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return of the 0 °C isotherm than on its fall timing36. At the global
mean level, our lake temperature and ice-cover projections for 2100
(Supplementary Figs. 23 and 25) agree with RCP 2.6 and 6.0 projec-
tions from a single lake model study over a smaller set of lakes15.
Suitability of ERA5-Land
Challenges to global-scale lake modelling arise from parameter
value selection, the spatio-temporal coverage and quality of ref-
erence products, and the selection of adequate impact variables.
While anchored to reality through the step-wise bias correction
of their boundary conditions19 (Methods), the lake variables of
ERA5-Land are diagnostics and not subject to direct assimilation
with remote sensing or in situ data. Importantly, when compared
with in situ and satellite-observed lake changes, ERA5-Land lake
simulations perform satisfactorily in representing the global-scale
time-series characteristics required as a substitute reference product
to lake surface temperature and ice-cover detection and attribution
(Supplementary Note 1.1 and Supplementary Figs. 29–36). In addi-
tion, ERA5-Land is the only available lake product with sufficient
spatial and temporal extent necessary for detection and attribution
purposes. In light of this validation, the notable warm bias that exists
between ERA5L and HIST lake temperatures (Fig. 2e) could result
5
Pre-industrial control Historical RCP 2.6
5
4
3
2
1
0
–1
0.1
0
–0.1
–0.2
–0.3
–0.4
10
0
–10
–20
–30
–40
–50
–60 012
Global warming since pre-industrial time (°C)
3 4 5
0 1 2 3 4 5
0 1
2050, 2090
2050,
2090
2030
2030
1980
1980
2000
2000
2020
2020
2030
2030
2030
2050
2050
2050
2050
2090
2090
2090
2090
2 3 4 5
RCP 6.0 RCP 8.5 Range
4
3
2
1
Lake temperature anomaly (°C)
Ice thickness anomaly (m)
Ice duration anomaly (days)
0
–1
0.1
0
–0.1
–0.2
–0.3
–0.4
10
0
–10
–20
–30
–40
–50
–60
1950 2000 2050 2100
1950 2000 2050 2100
1950 2000
Year
2050 2100
2030
2050, 2090
2030
1980
2000
2030 2050
2050
2090
2090
2030
a
b
c
d
e
f
2020
Fig. 4 | Anomalies for lake temperature, ice thickness and ice cover. a–c, Multimodel mean anomaly time series of global annual mean lake temperatures
(a), ice thickness (b) and ice-cover duration (c). Uncertainty bands in a, b and c represent ±1 standard deviation in lake model ensemble projections. d–f,
The same lake variable anomalies are scaled against global-average annual mean air temperature anomalies, with uncertainty bands representing the full
range of scaled projections. The dashed line in d represents a 1:1 scale.
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from differences in the HIST lake model depth fields, forcing and
water-clarity parameterization (Supplementary Note 1.3). Despite
this shortcoming and substantial mean biases for some models and
variables (Supplementary Figs. 26–28 and Supplementary Note 1.2),
the inter-model agreement both at the global scale (Supplementary
Figs. 23–25) and with respect to latitudinal, coastal and seasonal
characteristics (Supplementary Figs. 2–22) adds confidence to the
quality of our projections. Future attribution studies may, however,
benefit from the ongoing development of global-scale, multidecadal
lake temperature and ice-cover datasets based on remote sens-
ing37. As reference datasets and lake models are updated in the near
future, optimal fingerprinting techniques may provide even more
robust evidence of detection and attribution.
In summary, we showed increases in lake temperature and
decreases in ice cover with strong inter-model consistency using an
ensemble of five global-scale lake models. With detections achieved
at the 95% confidence level, we demonstrate that reanalysed his-
torical changes in lakes worldwide are extremely unlikely38 to have
occurred due to pre-industrial climate variability alone. Further,
we attribute changes in all three ice-cover indices to anthropo-
genic emissions. Our ensemble framework encompasses climate
model, lake model, natural variability and scenario uncertainties,
which bolsters our projections and reduces sampling uncertainties
in detecting and attributing the anthropogenic signal in historical
lake variable changes. These projected changes could have manifold
consequences for lake thermal regimes, lake ecological processes
and provision of lake ecosystem services. The clear dependency
of our projections on the radiative forcing scenario and the strong
arguments we make for reanalysed changes being both unexplain-
able by pre-industrial climate variability alone and consistent with
anthropogenic forcings underline the benefit of stabilizing lake
systems through major societal adjustments towards mitigating cli-
mate change.
Online content
Any methods, additional references, Nature Research report-
ing summaries, source data, extended data, supplementary infor-
mation, acknowledgements, peer review information; details of
author contributions and competing interests; and statements of
data and code availability are available at https://doi.org/10.1038/
s41561-021-00833-x.
Received: 19 August 2020; Accepted: 31 August 2021;
Published: xx xx xxxx
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Articles
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Methods
Inter-Sectoral Impact Model Intercomparison Project. We perform global-scale
simulations with ve lake models as a part of phase 2b of the Inter-Sectoral
Impact Model Intercomparison Project (ISIMIP2b). All simulations adhere to the
lake sector protocol24, which determines simulated periods and scenarios, lake
model forcing datasets, the spatial and temporal resolutions of model outputs
and lake locations and depths. Pre-industrial control simulations (1661–2099)
assume a pre-industrial climate without anthropogenic greenhouse gas forcing39.
Historical simulations (1861–2005) use a historical climate, whereas future
projections (2006–2099) consider RCPs 2.6, 6.0 and 8.5. Four GCMs contributing
to phase 5 of the Coupled Model Intercomparison Project (CMIP5)—
GFDL-ESM2M, HadGEM2-ES, IPSL-CM5A-LR and MIROC5—are used as
input to the lake models aer bias adjustment to the EWEMBI reference dataset,
which is compiled from ERA-Interim reanalysis data adjusted by WATCH forcing
methodology, eartH2Observe forcing data and NASA/GEWEX Surface Radiation
Budget data39,40.
The lake models contributing to this study are the Community Land Model
version 4.541 (CLM4.5), the Arctic Lake Biogeochemistry Model42 (ALBM),
SIMSTRAT-UoG43, VIC-lake44 and LAKE45. All lake models operate globally
at 0.5° × 0.5° horizontal resolution. The lake models simulate daily vertical
temperature profiles per grid cell based on the mean depth and summed surface
area of all lakes within that cell. Presence and grid-scale fractions of lakes within
each 0.5° grid cell are given by the Global Lake Database (GLDB)46–48, which is
aggregated from the original 30 arcsec to the 0.5° × 0.5° grid. GLDB also provides
average lake depth per grid cell for all models except CLM4.5. In CLM4.5, every
grid cell has a constant lake depth at 50 m. Individual model characteristics are
provided in Supplementary Table 1.
ERA5-Land. We use ERA5-Land reanalysis lake ice depth and mixed-layer
temperature datasets as reference for lake model evaluation and climate change
detection and attribution19. The ERA5-Land product delivers lake variables at
0.1° horizontal and hourly temporal resolution computed by the Freshwater Lake
model (FLake). ERA5-Land is a land-only re-run of ERA5 with a finer resolution
for improved application as reference product for land-based energy and water-flux
studies. The ERA5-Land lake reanalysis uses lower atmospheric forcing from the
ERA5 reanalysis as boundary conditions and is therefore forced by observations
through their assimilation in the atmosphere of ERA5. Lake model computations
are embedded as a tile in the Tiled ECMWF Scheme for Surface Exchanges over
Land incorporating land surface hydrology49. Here, lake variables are computed in
each grid cell where inland water bodies cover at least 1% of the surface area of the
cell. At the time of analysis, this dataset spans 1981 to 2019 (inclusive).
Using an ERA5-Land derived ice-cover duration series, we apply selection
criteria on our projection maps for lake ice variables (Figs. 1 and 3 and
Supplementary Figures) based on the first two decades of the series (1981–1999) to
avoid presenting results for lakes with erratic or ephemeral ice cover. This baseline
is chosen because it contains the reference period in Fig. 1 (1981–1990) and it
overlaps with the ‘present-day’ period (1971–2000) used in results for Fig. 3 and
projections in the Supplementary Information. Moreover, using two decades for
the following criteria better accounts for inter-annual variability than does using
a single decade (1981–1990). Our criteria involve selecting pixels from the native
ERA5L ice-cover series where ice occurs for at least 20 days in 10 years of 1981–
1999. This effectively limits our consideration of changes in ice cover to regions
with more consistent ice according to our reference product.
Data processing. Post-processing of model ice thickness outputs was performed
to attain homogenized ice onset, break-up and duration values. Ice-cover indices
were calculated with hydrological years, defined as year-long periods that contain
ice onset or break-up dates for lakes in the Northern Hemisphere. For ice onset
calculations, we select the October to September hydrological year and convert
each pixel value with ice cover to the day of the year of its time step. After this, we
added 365 to periods between 1 January and 30 September so that the days of the
year monotonically increase during one hydrological year. A temporal minimum
was calculated across this adjusted 1 October (year t) to 30 September (year t + 1
series). This was performed for all available October to September hydrological
years in the series, resulting in annual maps of ice start dates. The same process
with a temporal maximum calculation across its September to August hydrological
year was done for ice break-up calculations, resulting in maps of annual ice end
dates. Ice duration is computed as the sum of all ‘ice-on’ days across the October
to September hydrological year. We analyse lake temperature at 2 m depth to
enable comparison with ERA5-Land mixed-layer temperatures and to avoid an
overly strong dependence on surface air temperature, which can be expected
from lake surface temperature analyses. Global mean calculations on ice thickness
datasets include all pixels without ice cover. Reanalysis data are coarsened to the
0.5° × 0.5° ISIMIP grid. Before calculating spatial means, all datasets are masked
for overlapping pixels between lake model simulations and reanalysis data. For all
scaling plots, we use global mean air temperature anomalies to scale lake variable
impacts to communicate results in the context of the IPCC trajectories and
internationally agreed climate targets such as the Paris Agreement to limit global
warming to well below 2 °C (ref. 39).
Detection and attribution. We generate all-forcings response patterns (HIST) by
concatenating each ISIMIP lake model’s historical time series (1861–2005) with
the RCP 8.5 (2006–2099) future simulations to sample forced response patterns for
the same period as the ERA5L (1981–2019). Here, only the RCP 8.5 anomalies are
used for the 2006–2019 period to avoid the artificial consistencies among HIST
patterns that would occur if all future scenarios were added to the ensemble, which
would replicate 1981–2005 anomalies. Next, global annual means are computed
from these series, yielding a total of 40 HIST realizations (8 per lake model). For
a forced response pattern without human influence (PIC), all available ISIMIP
pre-industrial control simulations are concatenated for each lake model and cut
into non-overlapping global mean ‘chunks’ matching the time span of ERA5L.
This ideally provides 44 (11 × 4) chunks of pre-industrial climate-variability-driven
simulations per lake model if pre-industrial control simulations span 1661–2099
for each GCM forcing. Reanalysis reference products and response patterns are
then computed as anomalies through temporal centring (each series’ temporal
mean is subtracted) and applied to two detection and attribution approaches: a
correlation-based view on detection and ROF to confirm detection and attribution.
The correlation approach (Fig. 2a–d) uses all available HIST and PIC
anomalies without smoothing. For each lake variable, Spearman (rank) correlation
coefficients are calculated between the global annual mean of all available
historical simulations (HIST) and every available global annual mean PIC chunk.
These correlation coefficients comprise the empirical distributions in Figure 2. A
correlation coefficient is then computed between ERA5L and the mean of the HIST
ensemble, plotted as a red vertical line. A normal distribution using the mean and
standard deviation of PIC–HIST correlations is assumed for reporting the 95%
and 99% confidence levels for comparison with ERA5L–HIST correlation. We use
the Spearman correlation coefficient because of its resistance to outliers; however,
results are consistent with a Pearson correlation.
We use ROF with a TLS regression to compute scaling factors that fit annual,
multimodel mean HIST anomalies to ERA5L at the global mean level (Fig. 2e–h)
for one lake variable at a time. This follows a generalized linear regression model
of the form:
y
=
X
∗
β
+
ε
X=X∗+ν
where y is a vector of n observations (ERA5-Land lake reanalysis; ERA5L),
X is a matrix of m columns of multimodel mean simulated response patterns
containing noise ν (ISIMIP simulations; HIST), β is a vector of scaling factors and
ε is the regression residual, representing the internal variability in y. We take a
single-factor approach; the regression is fit for one response pattern generated with
all external forcings (HIST) instead of regressing y onto a linear combination of
response patterns to separate external forcings. The latter approach is often some
collection of additive response patterns to natural and anthropogenic forcings
(such as NAT representing volcanoes and aerosols, ANT for anthropogenic
emissions and LU for land cover change). Therefore, in this study, X contains
only one column or response pattern (m = 1) in each lake variable’s analysis. The
outcome of the analysis is therefore the single slope parameter of the regression,
β and its confidence interval. If β does not overlap with 0, ROF communicates
detection, revealing that an aspect of lake systems—the lake variable of interest—
is statistically different from its natural or pre-industrial state. In addition, if β
overlaps with 1, ROF attributes the changes in a given lake variable to all external
forcings, revealing that a lake variable’s trend can be explained by historical climate
forcings dominated by anthropogenic climate change.
In a TLS framework, the regression is computed to minimize residuals
perpendicular to the best fit line21. This addresses uncertainty in X, underlining the
assumption in the TLS approach to optimal fingerprinting that model simulated
response patterns are not perfectly known. In other words, TLS contends with
the presence of noise in the observed X, represented by ν, which affects the true
deterministic X*. Therefore, TLS is a strong choice for small-ensemble study
cases with greater sampling uncertainty. This contrasts the ordinary least squares
approach, which fits a regression by minimizing vertical residuals, thereby only
accounting for noise in y and assuming that the response patterns in X are perfectly
known (as residuals are not accounted for along the x-axis). The TLS regression is
achieved through a singular value decomposition (SVD) on [y, X].
Before the TLS fit, y and X are converted to 5 yr block means, temporally
centred (by subtracting their mean) and pre-whitened. Pre-whitening to achieve
unit noise is the ‘optimization’ of signals in ROF. This is done with a regularized
covariance matrix,

C1
, which represents internal variability in our lake variables.

C1
is derived from one of two covariance estimates, C1 and C2, computed from
non-overlapping, equal-sized samples (chunks) of all available PIC series. As we
use a model-derived estimate of noise to pre-whiten y, its compatibility with the
noise in y is later validated second-hand by a residual consistency test (RCT).
Key to ROF, regularization involves conforming

C1
to equal λC1 + ρI. Here, I is
the identity matrix, and λ and ρ are coefficients whose estimators are provided by
Ledoit and Wolf50. This avoids underestimating the lowest eigenvalues of

C1
29. C2 is
used for calculating the confidence intervals on scaling factors and performing the
RCT. Final computations of scaling factors, their confidence intervals and RCTs are
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Articles Nature GeoscieNce
taken as the median of 1,000 realizations of ROF through shuffling the PIC chunks
from which C1 and C2 are computed51.
The RCT validates the residuals in the TLS regression against the assumed
internal variability estimated using PIC chunks29. Here, C2 and X are used in
Monte Carlo simulations to bootstrap 1,000 samples of virtual reference series,
fingerprints and covariance matrices assuming a perfect fit with β = 1. The
smallest squared singular value (or eigenvalue, λ) of the SVD in the original TLS
fit—representing the residuals in the regression—is then corrected and used as a
test statistic against 1,000 virtual eigenvalues (λvirt,i = 1,...1000) and their kernel density
estimates (λ is tested against 1,000 virtual, empirical distributions). The RCT is
passed if λ is consistent with these distributions, which is considered true if the
average position of λ in the virtual distributions yields a P value greater than 0.10
(Supplementary Note 1.4).
Future projections. We calculate all maps as signals across 1971–2000 and
2070–2099 mean baseline and future periods. For scaling, each signal map is
first divided by the change in global mean air temperature for the same period
before calculating ensemble means. For each GCM–Lake model combination,
we compute global mean anomalies relative to the global temporal average of the
pre-industrial control simulation (Fig. 4). Global mean air temperature series from
GCMs are treated the same. In Fig. 4d–f, series are smoothed with a 21 yr running
mean to reduce natural variability effects.
Data availability
The ISIMIP2b lake sector simulations presented in this study are available through
the Earth System Grid Federation (ESGF, https://esgf-data.dkrz.de/). The ERA5-Land
lake data used in this study are developed by the European Centre for Medium-Range
Weather Forecasts (ECMWF) and are available through the Copernicus Climate
Change Service’s Climate Data Store (CDS, https://cds.climate.copernicus.eu/
cdsapp#!/search?type=dataset). The Global La ke Temp erature Collaboration Dataset
lake surface temperatures used for evaluating ERA5-Land can be found here: https://
portal.edirepository.org/nis/mapbrowse?packageid=knb-lter-ntl.10001.3. ESA CCI
lake products can be found here: https://catalogue.ceda.ac.uk/uuid/3c324bb4ee394d
0d876fe2e1db217378. The Global Lake and River Ice Phenology Database is available
at https://nsidc.org/data/lake_river_ice/.
Code availability
All code used to generate these analyses are available through the GitHub
repository of the Department of Hydrology and Hydraulic Engineering at VUB
(https://github.com/VUB-HYDR/2021_Grant_etal).
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Acknowledgements
We are grateful to the Potsdam Institute for Climate Impact Research (PIK) for initiating
and coordinating the ISIMIP initiative, with special thanks to M. Büchner for his
oversight of ISIMIP data publishing, and to the modelling centres for making their
impact simulations publicly available through ESGF. We acknowledge the European
Centre for Medium-Range Weather Forecasts (ECMWF) and the Copernicus Climate
Change Service for their provision of publicly available ERA5-Land lake data; this paper
contains modified Copernicus Climate Change Information [2021]. Furthermore,
L.Grant is funded by European Copernicus Climate Change Service (C3S) implemented
by the European Centre for Medium-Range Weather Forecasts (ECMWF) under the
service contract Independent Assessment on ECVs led by National Research council
of Italy (CNR) with the funding number ECMWF/Copernicus/2017/C3S_511_CNR.
We owe many thanks to F. Fröb and A. Winkler for sharing their regularized optimal
fingerprinting python code and to M. Schmid for the helpful discussions. We also
thank the National Center for Atmospheric Research (NCAR) for maintaining CLM
and making the source code publicly available. I.V. is a research fellow at the Research
Foundation Flanders (FWO) (FWOTM920). W.T. acknowledges the Uniscientia
Foundation and the ETH Zurich Foundation for their support to this research. Z.T. is
supported by the US DOE’s Earth System Modeling programme through the Energy
Exascale Earth System Model (E3SM) project. The computational resources and services
used in this work were provided by the VSC (Flemish Supercomputer Center), funded
by the Research Foundation Flanders (FWO) and the Flemish Government, department
EWI. R.M. participated through the project WATExR of the JPI Climate ERA4CS
Program and acknowledges funding from the CERCA programme of the Generalitat
de Catalunya. V.M.S. and A.V.D. used the HPC facilities of Lomonosov Moscow
State University (‘Lomonosov-2’ supercomputer) and were supported by the Russian
Ministry of Science and Higher Education, agreement no. 075-152019-1621. A.B.G.J
acknowledges the Talent Programme Veni of the Netherlands Organisation for Scientific
Research (NWO) (VI.Veni.194.002).
Author contributions
L. Grant, I.V. and W.T. designed the study. L. Grant wrote the manuscript with support
from all authors and performed all analyses under the supervision of I.V. and W.T. L.
Gudmundsson provided guidance on the detection analysis. Z.T., M.P., V.M.S., A.V.D.,
B.D., A.B.G.J., S.I.S. and W.T. conducted the global lake model simulations. J.S., F.Z.,
M.G., D.P., R.M. and W.T. coordinated the ISIMIP lake sector activities. M.C. and G.B.
helped validate ERA5-Land reanalysis data as reference products. I.V.d.V. provided
oversight for data publishing. L. Grant and I.V. performed additional analyses in
response to referee comments and together composed the referee response letter with the
help of all authors.
Competing interests
The authors declare no competing interests.
Additional information
Supplementary information The online version contains supplementary material
available at https://doi.org/10.1038/s41561-021-00833-x.
Correspondence and requests for materials should be addressed to Luke Grant.
Peer review information Nature Geoscience thanks Peter Stott, Matthew Hipsey and
the other, anonymous, reviewer(s) for their contribution to the peer review of this work.
Primary Handling Editor: Thomas Richardson.
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