Geophysical Research Letters
Supporting Information for
Toward "optimal" integration of terrestrial biosphere models
Christopher R. Schwalm1,2†, Deborah N. Huntinzger2,3, Joshua B. Fisher4, Anna M. Michalak5,
Kevin Bowman4, Philippe Cias6, Robert Cook7, Bassil El-Masri8, Daniel Hayes7, Maoyi
Huang9, Akihiko Ito10, Atul Jain8, Anthony W. King7, Huimin Lei11, Junjie Liu4, Chaoqun Lu12,
Jiafu Mao7, Shushi Peng13, Benjamin Poulter14, Daniel Ricciuto7, Kevin Schaefer15, Xiaoying
Shi7, Bo Tao13, Hanqin Tian12,Weile Wang16, Yaxing Wei7, Jia Yang12, Ning Zeng17
[1] Center for Ecosystem Science and Society, Northern Arizona University, Flagstaff, AZ 86011, USA
[2] School of Earth Sciences and Environmental Sustainability, Northern Arizona University, Flagstaff, AZ 86011,
USA
[3] Department of Civil Engineering, Construction Management, and Environmental Engineering, Northern Arizona
University, Flagstaff, AZ 86011, USA
[4] Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Dr., Pasadena, CA 91109, USA
[5] Department of Global Ecology, Carnegie Institution for Science, Stanford, CA 94305, USA
[6] Laboratoire des Sciences du Climat et de l'Environnement, LSCE, 91191 Gif sur Yvette, France
[7] Environmental Sciences Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA
[8] Department of Atmospheric Sciences, University of Illinois, Urbana, IL 61801, USA
[9] Atmospheric Sciences and Global Change Division, Pacific Northwest National Laboratory, Richland, WA 99354,
USA
[10] National Institute for Environmental Studies, Tsukuba, Ibaraki 305-8506, Japan
[11] Department of Hydraulic Engineering, Tsinghua University, Beijing 100084, China
[12] International Center for Climate and Global Change Research and School of Forestry and Wildlife Sciences,
Auburn University, Auburn, AL 36849, USA
[13] Laboratoire des Sciences du Climat et de l'Environnement, LSCE, 91191 Gif sur Yvette, France
[14] Department of Ecology, Montana State University, Bozeman, MT 59717, USA
[15] National Snow and Ice Data Center, Boulder, CO 80309, USA
[16] Ames Research Center, National Aeronautics and Space Administration, Moffett Field, Mountain View, CA
94035, USA
[17] Department of Atmospheric and Oceanic Science, University of Maryland, College Park, MD 20742, USA
† Corresponding author: (Tel: +1-928-523-8413, Fax: +1-928-523-7423, christopher.schwalm@nau.edu)
Contents of this file
Figures S1 to S13
Table S1
Introduction
Supporting information contains a series of figures that show overall reliability by model (Figure
S1), skill for each reference factor for each model (Figures S2-S11), variants of optimal NEE
(Figure S12), and variability in model rankings (Figure S13). A tabular summary (including
equations and notes on derivation) of each reference factor is also provided (Table S1).
1
Figure S1. Model reliability. Each panel shows composite model reliability (𝑅̃𝑖 ) for a given model
by grid cell, computed from seven reference factors assuming equal importance, based on
FLUXNET-reconstructed GPP and IPCC Tier-1 vegetation biomass from 1982 to 2008.
2
Figure S2. Reliability factors and composite reliability (𝑅̃𝑖 ) for BIOME-BGC.
3
Figure S3. Reliability factors and composite reliability (𝑅̃𝑖 ) for CLM.
4
Figure S4. Reliability factors and composite reliability (𝑅̃𝑖 ) for CLM4VIC.
5
Figure S5. Reliability factors and composite reliability (𝑅̃𝑖 ) for DLEM.
6
Figure S6. Reliability factors and composite reliability (𝑅̃𝑖 ) for GTEC.
7
Figure S7. Reliability factors and composite reliability (𝑅̃𝑖 ) for ISAM.
8
Figure S8. Reliability factors and composite reliability (𝑅̃𝑖 ) for LPJ.
9
Figure S9. Reliability factors and composite reliability (𝑅̃𝑖 ) for ORCHIDEE-LSCE.
10
Figure S10. Reliability factors and composite reliability (𝑅̃𝑖 ) for VEGAS.
11
Figure S11. Reliability factors and composite reliability (𝑅̃𝑖 ) for VISIT.
12
Figure S12. Optimal NEE variants. Maps show differences between optimal and naïve NEE
based on a single reference factor. The default optimal case is shown in lower right for
comparison. Color map appears “washed out” when differences approach zero.
13
Figure S13. Variability in NEE model rank. Red squares show model rank based on equal
relative importance of all seven reference factors, the default optimal case. Grey color map
indicates proportion of bootstrap replicates exhibiting a given rank.
14
Reference
Reference
factors
Equation
Bias in mean GPP
𝑓𝐵,𝑖 =
𝜖𝑦
|𝑦̂ − 𝑦|
Bias in standard
deviation of GPP
𝑓𝜎,𝑖 =
𝜖𝜎
|𝜎̂ − 𝜎|
Convergence in
simulated GPP
𝑓𝐶,𝑖 =
𝜖𝑦
|𝑦̂ − 𝑦̃|
Bias in GPP trend
𝑓𝑇,𝑖 =
𝜖𝑇
|𝑚
̂ − 𝑚|
GPP
Correlation in GPP
𝑓𝜌,𝑖 = 𝜌
Variables
𝑦̂ simulated mean GPP
𝑦 reference mean GPP
𝜖𝑦 standard deviation (in time) of 𝑦
𝜎̂ simulated GPP standard deviation
𝜎 reference GPP standard deviation
𝜖𝜎 uncertainty in 𝜎 using block
bootstrapping
𝑦̂ simulated mean GPP
𝑦̃ median model GPP
𝜖𝑦 standard deviation of 𝑦
𝑚
̂ simulated GPP trend in time
𝑚 reference GPP trend in time
𝜖 𝑇 standard error of trend in 𝑚
𝜌 correlation between 𝑦̂ and 𝑦
𝑣̂ simulated biomass
Bias in biomass
𝑣 reference biomass
𝜖𝑣 uncertainty in 𝑣
Biomass
𝑣̂ simulated biomass
𝜖𝑣
Convergence in
𝑓𝛾,𝑖 =
𝑣̃ median biomass
|𝑣̂ − 𝑣̃|
simulated biomass
𝜖𝑣 uncertainty in 𝑣
Table S1. Reference factors. Reference factors are bound (0,1], i.e., 0 is excluded from the
range of possible values whereas unity is not, and computed by grid cell from 1982-2008. 𝜖𝜎 is
derived from the standard deviation across 1,000 block bootstrap reference product replicates
using a block size of 12 months. 𝜖𝑣 is based on 50% relative uncertainty [sensu Waggoner,
2009], i.e., is set to half the reference value. For GPP 𝑦̂ and 𝑦 reference raw data except for the
correlation factor where anomalies (mean seasonal cycle removed) are used. For 𝑓𝑇,𝑖 the
difference in trend is only used when simulated and reference trends show statistical
significance at 𝛼 = 0.05. Otherwise 𝑓𝑇,𝑖 is set to 10-10, an order of magnitude smaller than the
smallest 𝑓𝑇,𝑖 value with statistical significance. Similarly, 𝑓𝜌,𝑖 is linearly remapped to (0,1] using
the same offset. All other reference factors are naturally greater than zero. The offset applied to
𝑓𝑇,𝑖 and 𝑓𝜌,𝑖 prevents either from driving 𝑅𝑖 to zero. All reference factors (except 𝑓𝜌,𝑖 ) are
assigned a value of unity if the denominator is less than the corresponding 𝜖. Simulation values
for 𝑣̂ are given by the mean annual value from 1995 to 2005.
𝑓𝛽,𝑖 =
𝜖𝑣
|𝑣̂ − 𝑣|
References
Waggoner, P. E. (2009), Forest inventories. Discrepancies and uncertainties, Discussion Paper
RFF DP 09-29, Resources for the Future, Washington, D. C.
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