Nature - USA (2020-01-02)

Nature | Vol 577 | 2 January 2020 | 71

correlation analysis^29 , SAT is a stronger control during break-up than
during freeze-up.
Applying this river ice model to future SAT data for the end of the
century (2080–2100) from the CESM climate model (under RCP 8.5)^30 ,
we found that, compared with a 2009–2029 reference period (chosen
to centre around the present year), monthly declines in global river
ice extent ranged from 9 to 66% (0.4–9.3 percentage points) (Fig.  3
shows the changes for the Northern Hemisphere). We found a simi-
lar pattern for RCP 4.5, with a smaller magnitude of change (globally
0.2–3.2 percentage points, corresponding to a 4–35% decline, Extended
Data Figs. 3, 4).
We divided the global landmass into zones defined by ice duration:
ice-free (duration < 5 days), intermittent (5 days ≤ duration < 15 days),
0.5–3 months, 3–6 months and >6 months (Fig. 4a). We found substan-
tial areal decline for regions with ice duration of >6 months and a gen-
eral shift of zones with shorter ice duration to higher latitudes. Across

−50 −25 025

0

25

50

75

100

0

25

50

75

100

30-day prior mean SAT (ºC)

River ice extent (%)

River ice extent (%)

1

10

100

1,000

10,000

Number of observations

Period

Break-up

Freeze-up

Mean bias RMSE

−20 −10 01020 −20 −10 01020

−20

0

20

40

60

80

30-day prior mean

SAT (ºC)

30-day prior mean

SAT (ºC)

Ice cover extent (%)

Model

0 ºC isotherm

Logistic

regression

a

b

Fig. 2 | Modelling river ice extent. a, Logistic regression model (lines)
constructed from the relationship between river ice extent and 30-day prior
mean SAT, with the period encompassing break-up (August–January) and
freeze-up (February–July) treated separately. b, Comparison of river ice models
by mean bias and RMSE.

–1.5 (–68%) –8.7 (–59%)

September October

–12.3 (–31%) –8 (–15%)

November December

–8 (–33%) –3.6 (–53%)

May June

–0.5 (–68%) –0.4 (–68%)

July August

–6.2 (–11%) –5.6 (–9%)

January February

–6.6 (–12%) –8.1 (–19%)

March April

–60 –50 –40 –30 –20 –10 0

River ice extent change (percentage points)

Fig. 3 | Modelled average monthly river ice difference between 2009–202 9

and 2080–2100 using CESM SAT output (RCP 8.5). The percentage point

change over Northern Hemisphere is shown in red, with the corresponding

percentage change in parentheses. White land areas denote a lack of Landsat-

observable rivers.