12When is a trend meaningful? Insights to carbon cycle variability from an initial-condition large ensemble

34Gordon B. Bonan1, Clara Deser1, William R. Wieder1,2, Danica L. Lombardozzi3,1, and Flavio Lehner4,1,5

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6
7

1

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Institute of Arctic and Alpine Research, University of Colorado Boulder, Boulder, CO, USA

93Department of Ecosystem Science & Sustainability, Colorado State University, Fort Collins, CO, USA

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Department of Earth and Atmospheric Sciences, Cornell University, Ithaca, NY, USA

115Polar Bears International, Bozeman, MT, USA

Climate and Global Dynamics Laboratory, NSF National Center for Atmospheric Research, Boulder, CO,
USA

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Supplementary Information

14

This file contains Supplementary Tables 1–3 and Supplementary Figures 1–11

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19
20

Supplementary Table 1. Annual gross primary production (g C m–2 yr–1) for Harvard Forest. Data forUrbanski et al. (2007) (ref. 13) are for 28 October of the preceding year to 27 October of the nominalyear. Data for Finzi et al. (2020) (ref. 19) are for 1 November–31 October. Data for Munger (2022) (ref.
52) are the GPP_NT_VUT_REF product.
Year
1992
1993
1994
1995
1996
1997
1998
1999
20002001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012
2013
2014
2015
2016
2017
2018
2019
2020

21
22
23
24

Urbanski et al. (2007)
1180
1350
1230
1260
1330
1400
1210
1400
1450
1630
1520
1530
1710

Finzi et al. (2020)
1176
1354
1233
1260
1328
1401
1207
1405
1451
1629
1523
1525
1711
1387
1638
1636
1602
1791
2133
1885
1679
1496
1562
1605

Munger (2022)
1144.711304.131300.541288.33
1363.771408.80
1224.141341.121473.35
1627.031589.891498.36
1742.67
1430.29
1667.37
1599.17
1590.79
1886.52
1981.201713.37
1778.40
1498.92
1704.41
1900.64
1614.45
1436.06
1547.58
1520.98
1262.28

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26
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Supplementary Table 2. Annual gross primary production (g C m–2 yr–1) for Morgan-Monroe State
Forest. Data are the GPP_DT_VUT_REF product (ref. 53).
Year
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012
2013
2014
2015
2016
2017
2018
2019
2020

28
29

Novick and Phillips (2022)
1475.59
1558.251672.48
1792.80
1657.35
1628.47
1777.55
1670.40
1765.63
1706.371527.43
1689.311503.34
1482.62
1742.911728.411645.15
1824.30
1624.98
1768.49
1804.86
1630.84

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Supplementary Table 3. Annual gross primary production (g C m–2 yr–1) for Howland Forest (ref. 20).
Year
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2010
2011
2012
2013
2014
2015
2016
2017
2018
2019
2020

31
32

Hollinger et al. (2021)
1309.55
1371.291417.031395.441510.841534.201332.091228.881342.55
1286.681315.27
1236.06
1296.151373.66
1354.56
1357.47
1289.95
1158.15
1280.071270.82
1246.961317.60
1306.30
1267.00

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Supplementary Fig. 1. Trends in annual GPP for 1991–2020 in 18 randomly chosen ensemble
members. Stippling denotes statistical significance (n = 30 years; p ≤ 0.05).

404142434445464748495051525354

Supplementary Fig. 2. Histogram of annual GPP trends for 1991–2020 at four grid cells. Grid cells
correspond to the location of core terrestrial sites for four domains in the National EcologicalObservatory Network (NEON). See Fig. 1 for the location of the sites. Panels show (a) D16: PacificNorthwest, (b) D07: Appalachians & Cumberland Plateau, (c) D18: Tundra, and (d) D12: NorthernRockies sites. The left axis is the frequency distribution for the n = 50 ensemble members, and the blackline is the cumulative distribution (right axis). Yellow shading shows members with a statisticallysignificant trend (n = 30 years; p ≤ 0.05), and light blue shading shows non-significant trends. The mean
± standard deviation and the percentage of members with a non-significant (n.s.) trend are provided in
the upper left of each panel. Also shown is the 95% confidence interval (red circles) obtained as therange of trends (n = 48) after excluding the smallest and largest trends.

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Supplementary Fig. 3. 95% confidence interval in annual GPP trends for 1991–2020. Shown are the (a)low and (b) high values for the 95% confidence interval obtained directly from the 50-memberensemble. These are the trends after excluding the smallest and largest trends for each grid cell.

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Supplementary Fig. 4. 95% confidence interval in annual GPP trends for 1991–2020. In (a), the 95%
confidence interval is obtained directly from the 50-member ensemble. It is the range of trends (n = 48)
after excluding the smallest and largest trends for each grid cell. Panels (b–f) show the 95% confidence
interval obtained from the standard error of the regression trend. The confidence interval is 2 ∗ 2.048 ∗𝑠𝑏1 , where 𝑠𝑏1 is the standard error of the trend and 𝑡0.975,28 = 2.048 is the critical t-value for 𝑛 = 30
years of data. Shown are (b–d) three ensemble members chosen at random, (e) the ensemble member
in Fig. 1c, and (f) the ensemble member in Fig. 1d. Stippling shows where the trend is statisticallysignificant (n = 30 years; p ≤ 0.05) for the particular ensemble member.

74757677787980

Supplementary Fig. 5. 95% confidence interval in annual GPP trends for 1991–2020. In (a), the 95%
confidence interval is obtained directly from the 50-member ensemble. It is the range of trends (n = 48)
after excluding the smallest and largest trends for each grid cell. Panels (b–f) are as in SupplementaryFig. 4, but show the difference from (a).

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89909192
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Supplementary Fig. 6. 95% confidence interval in annual GPP trends for 1991–2020 at individual gridcells. The 95% confidence interval obtained from the standard error of the regression trend for each of
the 50 ensemble members is shown as a histogram. The confidence interval is 2 ∗ 2.048 ∗ 𝑠𝑏1 , where𝑠𝑏1 is the standard error of the trend and 𝑡0.975,28 = 2.048 is the critical t-value for 𝑛 = 30 years ofdata. The thick black line is the 95% confidence interval obtained directly from the 50-member
ensemble. It is the range of trends (n = 48) after excluding the smallest and largest trends for each gridcell. Confidence intervals are shown for the grid cells corresponding to NEON core terrestrial sites for (a)D01: Northeast, (b) D19: Taiga, (c) D02: Mid-Atlantic, and (d) D09: Northern Plains. These are the fourgrid cells in Fig. 2.

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Supplementary Fig. 6 (continued). (e) D16: Pacific Northwest. (f) D07: Appalachians & Cumberland
Plateau. (g) D18: Tundra. (h) D12: Northern Rockies. These are the four grid cells in Supplementary Fig.
2.

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Supplementary Fig. 7. Trends in annual mean surface air temperature (TSA) for 1991–2020. (a) Meantrend for the 50-member ensemble obtained from the ensemble mean time series. (b) Signal-to-noise
ratio defined as the ensemble mean trend (absolute value) divided by the standard deviation of trends
across the 50 members. Also shown are trends for two members with small (c) and large (d) continental
mean trends. Ensemble members 1301.013 and 1011.001 are the members at the 3rd (6th percentile)and the 47th (94th percentile) ranks, respectively, based on continental mean trends. Stippling denotes
statistical significance (n = 30 years; p ≤ 0.05) using the ensemble mean time series or the individual
ensemble member time series. Trends are multiplied by 30 to report the change in temperature overthe 30-year period.

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Supplementary Fig. 8. Trends in annual precipitation for 1991–2020. (a) Mean trend for the 50member ensemble obtained from the ensemble mean time series. (b) Signal-to-noise ratio defined as
the ensemble mean trend (absolute value) divided by the standard deviation of trends across the 50members. Also shown are trends for two members with small (c) and large (d) continental mean trends.
Ensemble members 1281.015 and 1231.018 are the members at the 3rd (6th percentile) and the 47th(94th percentile) ranks, respectively, based on continental mean trends. Stippling denotes statisticalsignificance (n = 30 years; p ≤ 0.05) using the ensemble mean time series or the individual ensemble
member time series. Trends are multiplied by 30 to report the change in precipitation over the 30-year
period.

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Supplementary Fig. 9. Box plots of annual GPP trends for 1991–2020. Trends are given for the full 50member large ensemble (LENS), the 10-member macro-initialization (Macro), and the four microinitializations with 10-members each (start years 1231, 1251, 1281, and 1301 of the preindustrial
control). Plotted are the mean ± one standard deviation, the minimum and maximum, the median, andthe mean. Trends are shown for the grid cells corresponding to NEON core terrestrial sites for (a) D01:Northeast, (b) D19: Taiga, (c) D02: Mid-Atlantic, and (d) D09: Northern Plains. These are the four gridcells in Fig. 2.

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Supplementary Fig. 9 (continued). (e) D16: Pacific Northwest. (f) D07: Appalachians & Cumberland
Plateau. (g) D18: Tundra. (h) D12: Northern Rockies. These are the four grid cells in Supplementary Fig.
2.

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Supplementary Fig. 10. Estimates of annual gross primary production (GPP) at the AmeriFlux US-Ha1(Harvard Forest) flux tower. Data are from Finzi et al. (2020) (ref. 19) for 1992–2015 and the AmeriFlux(Munger, 2022) database (ref. 52) for 1992–2020 using the GPP_NT_VUT_REF and GPP_DT_VUT_REF
products. The two products differ in nighttime (NT) and daytime (DT) partitioning of net ecosystem
exchange to obtain GPP. The GPP_NT_VUT_REF product compares favorably with the Finzi et al. data.

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Supplementary Fig. 11. Statistical distribution of annual GPP trends sampled in Monte Carlosimulations using the AmeriFlux US-Ha1 (Harvard Forest) observations. (a) The full 1992–2020
AmeriFlux time series (ref. 52). Shown is the linear regression (dashed line) with the estimated slope ±standard error. Open circles show the years 1992–2004, closed circles extend the dataset to 2015, andopen squares are the additional data to 2020. The inset panel shows the frequency distribution of theresiduals. (b) Distribution of trends obtained with Monte Carlo methods in which annual GPP for eachyear from 1992 to 2020 is calculated as a random deviate about the regression line drawn from thedistribution of residuals. The trend for the 29-year randomly sampled time series is estimated by linear
regression, and the procedure is repeated 100,000 times to obtain the statistical distribution of thetrend. The randomly sampled trends are normally distributed with a mean of 127.0 g C m–2 yr–1 per 10years and a standard deviation of 41.3.