Global Change Biology
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Supplementary Information for “Application of the metabolic scaling theory
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and water-energy balance equation to model large-scale patterns of maximum
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forest canopy height”
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Sungho Choi1*, Christopher P. Kempes2, Taejin Park1, Sangram Ganguly3, Weile Wang4,
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Liang Xu5, Saikat Basu6, Jennifer L. Dungan7, Marc Simard8, Sassan S. Saatchi8, Shilong Piao9,
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Xiliang Ni10, Yuli Shi11, Chunxiang Cao10, Ramakrishna R. Nemani12, Yuri Knyazikhin1,
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Ranga B. Myneni1
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Department of Earth and Environment, Boston University, Boston, MA 02215, USA
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Control and Dynamical Systems, California Institute of Technology, Pasadena, CA 91125, USA
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/ The Santa Fe Institute, Santa Fe, NM 87501, USA
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Field, CA 94035, USA
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NASA Ames Research Center, Moffett Field, CA 94035, USA
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90095, USA
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Department of Computer Science, Louisiana State University, Baton Rouge, LA 70803, USA
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Earth Science Division, NASA Ames Research Center, Moffett Field, CA 94035, USA
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Science, Peking University, Beijing 100871, China
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Chinese Academy of Sciences, Beijing 100101, China
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Nanjing 210044, China
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94035, USA
Bay Area Environmental Research Institute (BAERI) / NASA Ames Research Center, Moffett
Department of Science and Environmental Policy, California State University at Monterey Bay /
Institute of the Environment and Sustainability, University of California, Los Angeles, CA
Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA 91109, USA
College of Urban and Environmental Sciences and Sino-French Institute for Earth System
State Key Laboratory of Remote Sensing Sciences, Institute of Remote Sensing Applications,
School of Remote Sensing, Nanjing University of Information Science and Technology,
NASA Advanced Supercomputing Division, NASA Ames Research Center, Moffett Field, CA
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*
Corresponding author: Sungho Choi ([email protected])
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LIST OF SUPPORTING INFORMATION
S0. ACRONYMS, SYMBOLS AND ABBREVIATIONS USED IN THIS STUDY
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S0.1. Main manuscript
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S0.2. Supplementary Information
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S1. ASRL MODEL FRAMEWORK
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S1.1. Tree branching architecture
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S1.2. Basal metabolic flow rate (Q0)
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S1.3. Potential (available) inflow rate (Qp)
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S1.4. Evaporative flow rate (Qe)
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S1.5. Implementation of large-scale disturbance history
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S1.6. Parametric adjustments and physical meanings
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S2. REFERENCES
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S3. SUPPORTING TABLES
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Table S1. Ecoregion codes and full names over the CONUS
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Table S2. FLUXNET data used for the evaluation of the ASRL model framework
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S4. SUPPORTING FIGURE
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Figure S1. Spatial distribution of independent reference datasets
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Figure S2. Inter-comparisons between reference and model predicted heights
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Figure S3. Adjusted ASRL parameters
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Figure S4. Comparisons between FIA- and GLAS-derived ASRL parameters
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S5. SAMPLE CODE FOR ASRL MODEL (MATLAB)
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S0. ACRONYMS, SYMBOLS AND ABBREVIATIONS USED IN THIS STUDY
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S0.1 Main manuscript
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99th
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a, b and c: Curvature parameters for the Chapman-Richards growth curve
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aL: Effective tree area (Unit: m2)
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ASRL: Allometric Scaling and Resource Limitations
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Atree: Effective tree area (Unit: m2)
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B: Plant metabolic rate (respiration, photosynthesis or xylem flow)
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CA: Catchment area (Unit: km2)
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CA0: Normalization catchment area at a flat hilltop (Unit: km2)
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CV: Coefficient of variations
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Eflux: Evaporative molar flux (Evapotranspiration flux) (Unit: Mmol m–2 month–1)
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FIA: Forest Inventory and Analysis
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G: Soil heat flux (Unit: W m–2)
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GEDI: Global Ecosystem Dynamics Investigation Lidar
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GLAS: Geoscience Laser Altimeter System
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Group A (○): Pacific Northwest/California forest corridors and Rocky Mountain forests
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Group B (□): Intermountain, Southwest semi-desert, Nevada-Utah, Colorado, Arizona-New
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hASRL: 99th Percentile of the ASRL modeled height (Unit: m)
Mexico, and Great Plain Dry Steppe forests
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Group C (△): North Woods (Laurentian forests), Midwest, and Northeastern Appalachian forests
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Group D (▽): Southeast and Outer Coastal Plain forests
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H: Sensible heat flux (Unit: W m–2)
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h: Tree height (Unit: m)
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hASRL: ASRL modeled maximum forest canopy height (Unit: m)
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hc: Contemporary forest height (Unit: m)
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hcro: Tree crown height (Unit: m)
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hf: Field-measured height (Unit: m)
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hGLAS: 90th percentile of the Geoscience Laser Altimeter System (GLAS) heights (Unit: m)
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hLVIS: 90th percentile of the Laser Vegetation Imaging Sensor (LVIS) heights (Unit: m)
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hmax: Maximum potential forest canopy height (ASRL initial prediction) (Unit: m)
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ICESat-2: Ice, Cloud, and land Elevation Satellite-2
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Iwater: Accessible water supply
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L: Thermal radiation flux (Unit: W m–2)
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LVIS: Laser Vegetation Imaging Sensor
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M: Plant mass
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MAE: Mean Absolute Error
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m
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MODIS: Moderate Resolution Imaging Spectroradiometer
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MST: Metabolic Scaling Theory
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NACP: North American Carbon Program
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NCEP/NCAR: National Centers for Environmental Prediction/National Center for Atmospheric
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hASRL: Average of the ASRL modeled height (Unit: m)
Research
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P: Precipitation (Unit: mm month–1)
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PET: Potential evapotranspiration (Unit: mm month–1)
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Pinc: Long-term monthly incoming precipitation (Unit: mm)
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PM: Penman-Monteith
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Q0: Basal metabolic flow rate (Xylem flow rate) (Unit: L year–1)
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Qe: Evaporative flow rate (Unit: L year–1)
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Qp: Potential water inflow rate (Unit: L year–1)
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Rabs: Absorbed solar radiation (Unit: W m–2)
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rroot: Radial root extent (Unit: m)
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rstem: Tree stem radius (Unit: m)
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sleaf: Area of single leaf (Unit: m2)
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slp: Terrain slope (Unit: °)
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slp0: Normalization terrain slope at a flat hilltop (Unit: °)
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tc: Forest age information (Unit: year)
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tf: Field-measured forest age (Unit: year)
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USGS: US Geological Survey
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USFS: US Forest Service
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AM: Alpine Meadow
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OW: Open Woodland
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SD: Semi-Desert
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V: Plant volume
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vwater: Molar volume of water (Unit: m3 mol–1)
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β1: Normalization constant for the basal metabolism (Unit: L day–1 m–η1)
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γ: Water absorption efficiency
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η1: Normalization exponent for the basal metabolism
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θ: Metabolic scaling exponent (theoretical value = 3/4)
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λ : Latent heat of evaporation (Unit: J mol–1)
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λEflux: Latent heat flux (W m–2)
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ρ: Plant tissue density
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σwater: Water absorptance
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ϕ : Exponent for the tree height and stem radius allometry (theoretical value = 2/3)
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Ψ: Topographic index
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S0.2 Supplementary Information
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#
aL: Theoretical effective tree area (Unit: m2)
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#
hcro: Theoretical tree crown height (Unit: m)
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#
LAI: Theoretical Leaf Area Index (Unit: m2 m–2)
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#
rcro: Theoretical crown radius (Unit: m)
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V: Theoretical crown volume (Unit: m3)
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#
β3: Theoretical crown ratio (= 0.79)
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#
τcro: Theoretical crown transmittance of light
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a, b and c: Curvature parameters for the Chapman-Richards growth curve
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adj-best
sleaf: Adjusted area of single leaf (Unit: m2)
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adj-best
γ: Adjusted water absorption efficiency
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adj-best
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adj
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aL: Effective tree area (Unit: m2)
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ASRL: Allometric Scaling and Resource Limitations
β1: Adjusted normalization constant for the basal metabolism (Unit: L day–1 m–η1)
Nleaf: Adjusted number of leaves
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astm: Area of a stoma (Unit: m2)
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B: Plant metabolic rate (respiration, photosynthesis or xylem flow)
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cp: Specific heat of air (unit: J mol–1 °K–1)
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csoil: Soil heat flux constant (unit: MJ m–2 day–1 °C–1)
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dh: Displacement height (Unit: m)
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dleaf: Volumetric leaf density (Unit: number m3)
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dstm: Leaf stomatal density (Unit: number m–2)
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Dvpr: Vapor diffusivity (Unit: m2 s–1)
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ea: Actual vapor pressure (unit: kPa)
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ED: Ecosystem Demography Model
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Eflux: Evaporative molar flux (Evapotranspiration flux) (Unit: Mmol m–2 month–1)
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Fcro: Crown shape factor
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FIA: Forest Inventory and Analysis
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FLUX-ID: FLUXNET site IDs
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G: Soil heat flux (Unit: W m–2 or MJ m–2 day–1)
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gBv: boundary layer vapor conductance (Unit: Mmol m–2 day–1)
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gdyn: aerodynamic conductance (Unit: Mmol m–2 day–1)
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gHa: Heat conductance (unit: Mmol m–2 day–1)
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GLAS: Geoscience Laser Altimeter System
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gr: Radiative conductance (unit: Mmol m–2 day–1)
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Group A (○): Pacific Northwest/California forest corridors and Rocky Mountain forests
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Group B (□): Intermountain, Southwest semi-desert, Nevada-Utah, Colorado, Arizona-New
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Mexico, and Great Plain Dry Steppe forests
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Group C (△): North Woods (Laurentian forests), Midwest, and Northeastern Appalachian forests
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Group D (▽): Southeast and Outer Coastal Plain forests
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GRP: Regional groups
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gstm: stomatal vapor conductance for a leaf (unit: Mmol m–2 day–1)
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gSv: Total stomatal vapor conductance (unit: Mmol m–2 day–1)
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gv: Vapor conductance (unit: Mmol m–2 day–1)
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H: Sensible heat flux (Unit: W m–2 or MJ m–2 day–1)
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h: Tree height (Unit: m)
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hc: Contemporary forest height (Unit: m)
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hcro: Tree crown height (Unit: m)
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hmax: Maximum potential forest canopy height (ASRL initial prediction) (Unit: m)
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hobs : Observed forest height (Unit: m)
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inv
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J: Cost function solved by the constrained non-linear multivariable optimization
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k: von Karman constant
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Ks: Extinction coefficient of the spherical leaf angle distribution
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L: Thermal radiation flux (Unit: W m–2 or MJ m–2 day–1)
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LAI: Leaf Area Index (Unit: m2 m–2)
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Lgen: Total number of leaves generation
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LM3-PPA: Land Model 3-Perfect Plasticity Approximation Model
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LMA: Leaf Mass per unit of leaf Area
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lN: Terminal branch length (Unit: m)
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Lstm: Pore perimeter of a cylinder stoma (Unit: m)
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LVIS: Laser Vegetation Imaging Sensor
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M: Plant mass
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mo–1
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mo+1
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Mroot: Root mass (Unit: kg)
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Mstem: Stem mass (Unit: kg)
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N: Number of branch generations
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n: Number of daughter branches
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NACP: North American Carbon Program
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Nleaf: Number of leaves
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pa: Air pressure (Unit: kPa)
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PFT: Plant Functional Type
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Pinc: Long-term monthly incoming precipitation (Unit: mm)
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PM: Penman-Monteith
kB: Inverse von Karman-Stanton number
Tair: Air temperature of preceding month (unit: °C)
Tair: Air temperature of following month (unit: °C)
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Pr: Pradtl number for air
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Q0: Basal metabolic flow rate (Xylem flow rate) (Unit: L year–1)
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Qe: Evaporative flow rate (Unit: L year–1)
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Qp: Potential water inflow rate (Unit: L year–1)
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Rabs: Absorbed solar radiation (Unit: W m–2 or MJ m–2 day–1)
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rcro: Crown radius (Unit: m)
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rN: Terminal branch radius (Unit: m)
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Rnet~abs: Net absorbed shortwave radiation (Unit: W m–2 or MJ m–2 day–1)
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Rnet~lw: Net absorbed longwave radiation (Unit: W m–2 or MJ m–2 day–1)
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rroot: Radial root extent (Unit: m)
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Rso: Clear-sky solar radiation (Unit: W m–2 or MJ m–2 day–1)
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rstem: Tree stem radius (Unit: m)
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Rsw~abs: Absorbed shortwave radiation (Unit: W m–2 or MJ m–2 day–1)
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Rsw~inc: Total incident solar radiation (Unit: W m–2 or MJ m–2 day–1)
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Sc: Schmidt number for water vapor
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sleaf: Area of single leaf (Unit: m2)
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SZA: Solar Zenith Angle (Unit: °)
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Tair: Air temperature (unit: °C)
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Tair: Air temperature (unit: °K)
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tc: Forest age information (Unit: year)
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Tcro: crown temperature (unit: °C)
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Tcro: crown temperature (unit: °K)
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u*: Friction velocity with surface obstacles
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u200: Wind speed at 200 meters height (Unit: m s–1)
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uz: Wind speed at measurement height z (= 10 m) (Unit: m s–1)
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V: Crown volume (Unit: m3)
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vwater: Molar volume of water (Unit: m3 mol–1)
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zh: roughness height for heat transfer (Unit: m)
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zl: roughness length for forests (Unit: m)
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zm: Roughness length for open flat terrain (Unit: m)
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zstm: Depth of a stoma (Unit: m)
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αcro: Crown reflectance
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αleaf: Mean reflectivity of a leaf
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αsoil: Soil reflectance
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αsoil*: Deep soil reflectance
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β1: Normalization constant for the basal metabolism (Unit: L day–1 m–η1)
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β2: Isometric coefficient for relationship between stem and root mass
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β3: Crown ratio (relationship between height and crown height)
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Δ: Derivative of saturation vapor pressure (unit: kPa °C–1)
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εcro: Leaf emissivity
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η1: Normalization exponent for the basal metabolism
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λ: Latent heat of evaporation (unit: J mol–1)
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λEflux: Latent heat flux (Unit: W m–2 or MJ m–2 day–1)
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μwater: Molar mass of water (Unit: kg mol–1)
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ρair: Molar density of air (Unit: mol m–3)
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ρwater: Density of water (Unit: kg m–3)
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σ: Stefan-Boltzmann constant (Unit: MJ m–2 day–1 °K–4)
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σcro: Crown absorptance
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ϕ : Exponent for the tree height and stem radius allometry (theoretical value = 2/3)
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ψ: Plant senescence ratio
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Ψ: Topographic index
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ψmax: Maximal senescence ratio
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S1. ASRL MODEL FRAMEWORK
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* Sample code for the ASRL model (Matlab) is also provided (asrl_height_unopt_sample.m).
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S1.1. Tree branching architecture
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Tree geometry is considered using a fractal branching architecture (West et al., 1997). The model
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describes a tree of height h with a terminal branch radius of rN (≈ 4×10–4 m) and terminal length
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of lN (≈ 4×10–2 m) after N branching generations. Each branch generation results in n (= 2)
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daughter branches, in which case h can be expressed as (West et al., 1997; 1999):
𝑛𝑁(𝜙/2) 𝑙𝑁
ℎ ≈
1 − 𝑛−𝜙/2
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(S1)
where ϕ is the regional-specific allometric relationship between h and stem radius rstem: h  rstemϕ.
We can calculate the number of branch generations as N = (2/ϕ) ln [(1 – n–ϕ/2)h/lN] / ln n, and the
total number of leaves generated as nN, given overall tree size and the theoretical branching
architecture.
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S1.2. Basal metabolic flow rate (Q0)
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The basal metabolic flow rate Q0 (unit: L year–1) represents the minimum required, life-sustaining
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water circulation. The tree-size dependent Q0 is expressed as:
12 months
𝑄0 = ∑
𝛽1 ℎ𝜂1
(S2)
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where 1 and η1 are the normalization constant and exponent for the metabolism, respectively. The
theoretical value of η1 (= 3) was replaced with the regional-specific 2/ϕ.
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The parameter 1 also varies across study regions and forest plant functional types, and their
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initial values (= 0.0177 L day–1 m–η1 on average from data) are iteratively adjusted to minimize
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the modeling errors. The dashed curve of Fig. 2 in the main text is derived from a natural
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logarithm equation:
ln 𝑄0 = 𝜂1 ln ℎ + ln ∑ 𝛽1
(S3)
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S1.3. Potential (available) inflow rate (Qp)
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The potential inflow rate Qp (unit: L year–1) is determined by water absorptance and accessible
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local water supply. Mechanical stability for trees predicts an isometric relationship between stem
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and root mass (Niklas & Spatz, 2004; Niklas, 2007): Mroot ≈ β2Mstem (β2 ≈ 0.423 from data). The
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metabolic scaling theory for plant B  rstem2  h2/ϕ  Mθ  Mϕ/(2+ϕ) allows for mass-to-length
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inter-conversion: Mstem  h2/(θϕ)  h(2+ϕ)/ϕ and Mroot  rroot2/(θϕ)  rroot(2+ϕ)/ϕ. Thus, the radial root
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extent is given by: rroot = β2ϕ/(2+ϕ)h. We used hemispheric root surface area accessible to local
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water supply: 2πrroot2. The tree-size dependent Qp with local water availability is expressed as:
12 months
2
𝛾(2𝜋𝑟root
)𝛹𝑃inc = ∑
𝑄𝑝 = ∑
12 months
𝜙/(2+𝜙)
𝛾2𝜋(𝛽2
2
ℎ) 𝛹𝑃inc
(S4)
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where γ is the absorption efficiency related to local soil/terrain properties, and its initial value (= 0.5)
is also adjusted during the parametric optimization. The normalized topographic index Ψ accounts
for both terrain slope and surface water flow direction and accumulation. Pinc is an input geospatial
predictor representing the long-term monthly incoming precipitation rate (unit: m month–1).
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Note that the model estimates annual potential inflow rate (unit: L year–1). The dash-dot curve of
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Fig. 2 in the main text is derived from a natural logarithm equation:
2𝜙/(2+𝜙)
ln 𝑄𝑝 = 2 ln ℎ + ln ∑ 𝛾2𝜋𝛽2
𝛹𝑃inc
(S5)
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S1.4. Evaporative flow rate (Qe)
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The evaporative flow rate Qe (unit: L year–1) is a good proxy for the metabolic energy use. The
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effective tree area aL (unit: m2) is derived from the branching architecture and crown plasticity
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(Purves et al., 2007) with possible plant interaction and self-competition for light. The Penman-
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Monteith (PM) theory (Monteith & Unsworth, 2013) estimates monthly evaporative molar flux
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Eflux (unit: Mmol m–2 month–1). The tree-size dependent Qe incorporates geospatial predictors
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such as altitude and long-term monthly solar radiation, air temperature, vapor pressure and wind
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speed and can be expressed as:
12 months
𝑄𝑒 = 𝑎L 𝑣water ∑
𝐸flux
(S6)
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where the molar volume of water vwater is derived from the molar mass of water μwater (= 1.8×10–2 kg
mol–1) and the density of water ρwater (= 103 kg m–3). The model accumulates the monthly mean
evaporative flow rate over the growing-degree months (unit: L year–1).
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The dashed curve of Fig. 2 in the main text is derived from the Qe. Because both aL and Eflux
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scale with the h, it is difficult to rewrite the Qe in a natural logarithm form, opposed to the Q0 and
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the Qp. Hence, detailed information on the tree-crown geometry and the PM equation is delivered
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in the following sections.
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S1.4.1. Tree crown geometry
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The crown height hcro has an isometric relationship with h (Enquist et al., 2009; Kempes et al.,
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2011): hcro ≈ β3h. The theoretical crown ratio #β3 = 1 – n–1/3 (≈ 0.79) is generally greater than the
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measured β3 in actual forests where open habitat is not common. Trees typically compete for light
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and this changes their crown geometry. This crown-rise (β3 ≤ #β3) is likely due to crown plasticity.
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Our model assumes that the crown-rise should be accompanied by shrinking crown radius rcro for
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the mechanical stability of spheroidal tree-crown shape. Self-pruning of branches (or leaves)
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explains the disparity between the actual h to hcro relationships and those predicted by the theory.
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The model supposes a large tree at the h with the theoretical crown height #hcro.
#
ℎcro = #𝛽3 ℎ
(S7)
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For the simplicity of the model, we retained for each region the uniform crown shape factor Fcro =
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2rcro/hcro during the self-pruning process. Then, we obtain the theoretical crown radius #rcro from
#
𝑟cro = #ℎcro 𝐹cro /2
(S8)
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The tree branching architecture provides the total number of leaves generated Lgen = nN. We can
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use the theoretical crown volume #Vcro and the Lgen to derive the volumetric leaf density dleaf.
#
𝑉cro = (4/3) 𝜋 #𝑟cro
2 #
3
ℎcro /2 = 𝜋𝐹cro 2 #ℎcro /6
𝑑leaf = 𝐿gen / #𝑉cro = 𝑛𝑁 / #𝑉cro
(S9a)
(S9b)
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Then, the number of leaves Nleaf is calculated from the regional dleaf and the crown volume Vcro =
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(4/3) πrcro2hcro/2. The value of Nleaf does not exceed Lgen: Nleaf ≤ Lgen. Because the self-pruning
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rate is dependent on tree size (Mäkinen & Colin, 1999), we further located the regional-specific
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plant senescence ratio ψ, which is proportional to the probability of light interception by the tree
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crown. We can calculate theoretical total leaf area and Leaf Area Index (LAI) as
#
#
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𝑎L = 𝑠leaf 𝐿gen
(S10a)
2
LAI = #𝑎L / (𝜋 #𝑟cro )
(S10b)
where #aL is the theoretical effective tree area with the area of single leaf sleaf ≈ 0.0010 m2 (initial
value from data). The sleaf is iteratively adjusted during the model optimization. The theoretical leaf
area index #LAI can be calculated using the #aL and the #rcro.
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Based on Beer’s law, we can estimate the theoretical crown transmittance of light #τcro with the
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mean reflectivity of a leaf αleaf = 0.5 (full spectrum) and the extinction coefficient of the spherical
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leaf angle distribution Ks = 0.5sec(SZA) = 0.5 (where the Solar Zenith Angle (SZA) = 0°).
#
𝜏cro = 𝑒𝑥𝑝(−√𝛼leaf 𝐾𝑠 #LAI)
(S11)
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The maximal senescence rate ψmax is applied to trees with the least transmittance: ψmax = (Lgen –
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Nleaf) / Lgen. The estimated ψ value is used to calculate the adjusted number of leaves
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ψLgen.
𝜓 = 1 − (1 − 𝜓max )/(1 − #𝜏cro )
adj
Nleaf =
(S12)
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S1.4.2. Penman-Monteith equation
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The total Eflux is derived from the PM equation:
𝑅abs − 𝐿 − 𝐺 − 𝐻 − 𝜆𝐸flux = 0
(S13)
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350
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where Rabs is the absorbed solar radiation (shortwave and longwave, unit: MJ m–2 day–1), L is the
thermal radiation loss (unit: MJ m–2 day–1), G is the soil heat flux (unit: MJ m–2 day–1), H is the
sensible heat loss (unit: MJ m–2 day–1) and λEflux is the latent heat loss (unit: MJ m–2 day–1).
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The absorbed shortwave radiation Rsw~abs is obtained from the crown absorptance σcro and the
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total incident solar radiation Rsw~inc (input data, normal to ground, unit: MJ m–2 day–1).
𝑅sw~abs = 𝜎cro 𝑅sw~inc
(S14)
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adj
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Here, the crown geometry (aL and LAI using
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Ks, τcro, crown reflectance αcro, soil reflectance αsoil and deep soil reflectance αsoil*) determine the
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σcro. We first calculate the adjusted total leaf area, LAI, and crown transmittance using the similar
359
equation S10–S11 above:
𝑎L = 𝑠leaf
adj
Nleaf and rcro) and the radiation coefficients (αleaf,
𝑁leaf
2
(S15a)
LAI = 𝑎L / (𝜋 𝑟cro )
(S15b)
𝜏cro = 𝑒𝑥𝑝(−√𝛼leaf 𝐾𝑠 LAI)
(S15c)
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Then, the crown reflection coefficient αcro can be derived from Eq. S15 based on an assumption
362
that canopy is not dense and the effect of the soil is significant (Monteith & Unsworth, 2013).
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∗
𝛼soil
− 𝛼soil
𝑒𝑥𝑝(−2√𝛼leaf 𝐾𝑠 LAI)
∗
𝛼soil 𝛼soil − 1
=
∗
𝛼𝑠𝑜𝑖𝑙
− 𝛼𝑠𝑜𝑖𝑙
∗
1 + 𝛼soil
𝑒𝑥𝑝(−2√𝛼leaf 𝐾𝑠 LAI)
∗
𝛼soil 𝛼soil − 1
∗
𝛼soil
+
𝛼cro
363
364
365
(S16)
where the αsoil = 0.3 (full spectrum) and the αsoil* = 0.11 (full spectrum).
Finally, the crown absorptance σcro can be approximated as:
𝜎cro = 1 − 𝛼cro − (1 − 𝛼soil )𝜏cro
(S17)
366
367
The monthly G is estimated from the input air temperature (unit: °C) of preceding month mo–1Tair
368
and following month mo+1Tair and the soil heat flux constant csoil = 0.07 (unit: MJ m–2 day–1 °C–1)
369
as (Allen et al., 1998):
𝐺 = 𝑐soil ( mo−1𝑇air + mo+1𝑇air )
(S18)
370
371
The L is obtained from the linearization of the PM given the crown temperature Tcro (unit: °K) as:
4
𝐿 = 𝜖cro 𝜎T4cro ≈ 𝜖cro 𝜎𝐓air
+ 𝑐𝑝 𝑔𝑟 (𝐓cro − 𝐓air )
(S19)
= 𝑔2 + 𝑔1 (𝐓cro − 𝐓air )
372
373
374
375
376
377
378
where the emissivity εcro = 0.95 (leaf) and the Stefan-Boltzmann constant σ = 4.9×10–9 MJ m–2 day–
1
°K–4. The air temperature Tair (unit: °K), the specific heat of air cp = 29.3 (unit: J mol–1 °K–1) and
the radiative conductance gr = 4εcroσTair3/cp are used to estimate the thermal radiative energy loss.
The g2 term in the L will be combined with the Rsw~abs to achieve the net absorbed solar radiation
Rnet~abs.
The H is obtained from the difference between the Tcro and the Tair as:
𝐻 = 𝑐𝑝 𝑔Ha (𝐓cro − 𝐓air )
(S20)
= 𝑗1 (𝐓cro − 𝐓air )
379
where gHa is the heat conductance (unit: Mmol m–2 day–1) explained in SI Section S1.4.3.
380
381
The λEflux is obtained from the linearization of the PM equation using the crown temperature Tcro
382
(unit: °C) and the air temperature Tair (unit: °C) as:
𝜆𝐸flux = 𝜆𝑔𝑣 (𝑒𝑠 (𝑇cro ) − 𝑒𝑎 )/𝑝𝑎 ≈ 𝜆𝑔𝑣 (∆/𝑝𝑎 )(𝐓cro − 𝐓air ) + 𝜆𝑔𝑣 (𝑒𝑠 (𝑇air ) − 𝑒𝑎 )/𝑝𝑎
(S21)
= 𝑓1 (𝐓cro − 𝐓air ) + 𝑓2
383
384
where λ is the latent heat of evaporation (unit: J mol–1). The vapor conductance gv is derived from
aerodynamic, boundary layer and leaf stomatal conductance values (unit: Mmol m–2 day–1) (see SI
-14-
385
386
387
388
389
390
Section S1.4.3). The actual vapor pressure ea (unit: kPa) is an input geospatial predictor. The input
altitude data are used to estimate the air pressure pa (unit: kPa) (Allen et al., 1998). The saturation
vapor pressure es (unit: kPa) is a function of temperature T (unit: °C): es(T) = b1exp[b2T / (b3 + T)]
(where b1 = 0.61 kPa, b2 = 17.5 and b3 = 240.97 °C). We obtain the derivative of saturation vapor
pressure Δ (unit: kPa °C–1) = b1b2b3exp[b2T / (b3 + T)] / (b3 + T)2.
391
To estimate the λEflux, we rearrange the Rsw~abs, G, L and H in the PM equation by eliminating the
392
temperature difference term (Tcro – Tair) because it is difficult to obtain the Tcro from data. The
393
λEflux is expressed as:
𝜆𝐸flux = 𝑓1
394
395
396
397
398
399
𝑅net~abs − 𝐺 − 𝑓2
+ 𝑓2
𝑓1 + 𝑔1 + 𝑗1
(S22)
where the Rnet~abs = σcroRsw~inc – Rnet~lw. Because the input solar radiation accounts only for the
shortwave incident radiation, we should further incorporate the L (longwave radiation) to estimate
the net absorbed solar energy Rnet~abs (shortwave and longwave). We implemented the g2, the clearsky radiation Rso (based on the Sun-Earth geometry, unit: MJ m–2 day–1) and the ea to retrieve the
net longwave radiation Rnet~lw = g2 (0.34 – 0.14ea1/2) × (1.35Rsw~inc / Rso – 0.35) (Allen et al., 1998).
400
S1.4.3. Conductances (gHa and gv)
401
First, we can calculate the friction velocity with surface obstacles using the input wind speed data
402
(Gerosa et al., 2012):
𝑢200 = 𝑢𝑧 ln(200⁄𝑧𝑚 )/ln(𝑧⁄𝑧𝑚 )
(S23a)
𝑢∗ = 𝑘𝑢200 /ln((200 − 𝑑ℎ )⁄𝑧𝑙 )
(S23b)
403
404
405
406
407
408
409
where uz (unit: m s–1) is the wind speed at measurement height z (= 10 m), u200 is the wind speed at
200 m height and u* is the friction velocity with surface obstacles. The roughness length for open
flat terrain zm = 0.03 m, the von Karman constant k = 0.41, the displacement height dh = (2/3) h (unit:
m), the roughness length for forests zl = (1/10) h (unit: m) and the roughness height for heat transfer
zh = zl / exp(invkB) where the inverse von Karman-Stanton number invkB = 2. The molar density of air
ρair (unit: mol m–3) is derived from the Tair and the air pressure pa (unit: kPa, Boyle-Charles’ law).
410
Then, gHa (unit: Mmol m–2 day–1) and the aerodynamic conductance gdyn (unit: Mmol m–2 day–1)
411
can be estimated from the h and the friction velocity u* following
𝑔Ha = 𝑔dyn = 𝑘𝑢∗ 𝜌air /ln((200 − 𝑑ℎ )⁄𝑧ℎ )
(S24)
412
413
414
where the molar density of air ρair (unit: mol m–3) is derived from the Tair and the pa (Boyle-Charles’
law).
415
The boundary layer vapor conductance gBv (unit: Mmol m–2 day–1) also incorporates h and u* as
416
(Gerosa et al., 2012):
-15-
𝑔Bv = 𝑘𝑢∗ 𝜌air / inv𝑘𝐵 /(𝑆𝑐/𝑃𝑟)2/3
417
418
(S25)
where Sc is the Schmidt number for water vapor and Pr is the Pradtl number for air.
419
Lastly, the total stomatal vapor conductance gSv (unit: Mmol m–2 day–1) is estimated as (Gerosa et
420
al., 2012):
𝑔stm = 𝑑stm 𝜌air 𝐷vpr / (
𝑔Sv = 𝑔stm
421
422
423
424
425
426
𝑧stm
𝜋
+
)
𝑎stm 2𝐿stm
adj
𝑁leaf
(S26a)
(S26a)
where the stomatal vapor conductance for a leaf gstm is derived from the leaf stomatal density dstm =
101×106 m–2, the depth of a stoma zstm = 10×10–6 m, the area of a stoma astm = 459×10–12 m2
(Kempes et al., 2011), the pore perimeter of a cylinder stoma Lstm = 2π(astm/π)1/2 and the vapor
diffusivity Dvpr (unit: m2 s–1). Combining all conductance terms (gdyn, gBv and gSv), we can obtain the
final vapor conductance gv = 1 / (1/gdyn + 1/gBv + 1/gSv).
427
S1.5. Implementation of large-scale disturbance history
428
The preliminary ASRL model treated all forests as being at their maximum growth state and thus
429
carried overestimations in forests with recent disturbance. However, forest structure is clearly
430
related to stand ages (Obrien et al., 1995; Shugart et al. 2010). Indirect and non-physical solution,
431
which implemented lidar altimetry information and adjusted model parameters to reduce overall
432
errors (Shi et al., 2013), did not suffice. The updated model still retains the initial prediction of
433
maximum potential h, but alternatively traces the h-age trajectory of regional forests based on a
434
generalized growth equation, Chapman-Richards’ curve (Richards, 1959; Chapman, 1961): hc =
435
hmax[1 – exp(–atc)]1/b. In this function, the contemporary height hc is estimated from the upper
436
asymptote hmax, which is the maximum potential h that the model initially generates using the
437
local metabolic/geometry parameters and geospatial predictors. Large-scale disturbance history
438
data feeds age information tc into the model. The curvature parameters a and b regulate inflection
439
point, growth rate and maturation age (0.3 ≤ b ≤ 1.0 and 0 < a for the h-age trajectory (Garcia
440
1983)).
441
442
S1.6. Parametric adjustments and physical meanings
443
Each flow rate is determined by one free, but meaningful parameter (β1 for the Q0, γ for the Qp
444
and area of single leaf sleaf for the Qe). The modeled h is sensitive to all three variables, which are
445
simultaneously, and iteratively, adjusted to minimize the overall difference between the
-16-
446
predictions and input in-situ observations for each sub-region. We allocate β1 to the second-level
447
factor embracing the intra-/inter-species deviation while the η1 is treated as the first-order cue
448
affecting the xylem water fluidity. The natural logarithm Q0 curve (Fig. 2) is transformed by both
449
the β1 and η1 that determine y-intercept and slope, respectively.
450
451
The parameters γ and sleaf have more apparent controls during the parametric adjustment. The
452
local soil and terrain properties are reflected in γ showing how well a tree converts accessible
453
water supply into the Qp. A combination of γ, tree size, and local water availability attributes to y-
454
intercept of the natural logarithm Qp curve (Fig. 2). Similarly, aL is a product of the sleaf and
455
number of leaves Nleaf, and thus, sleaf alters the Eflux and its expansion to the whole-plant Qe. Both
456
y-intercept and slope of the natural logarithm Qe curve (Fig. 2) couple with the sleaf. The updated
457
model uses a cost function J solved by the constrained non-linear multivariable optimization
458
(MathWorks, 2014) as:
J(β1, γ, sleaf) = ∑{[hobs – hc(β1, γ, sleaf)]2}
459
(S27)
460
461
462
463
464
465
466
467
468
where the cost function J has initial ASRL parameters (β1 = 0.010 L day–1 m–η1, γ = 0.5 and sleaf =
0.0010 m2, Enquist et al., 1998; Kempes et al., 2011). In-situ observed height hobs and the modeled
hc are compared in the J. For each sub-region, we minimize the J by calibrating all three parameters
within ranges (0.005 < β1 < 0.020, 0.01 < γ < 1.00 and 0.0001 < sleaf < 0.0100). β1 range was derived
from Enquist et al., 1998 (based on 95% confidence intervals of scaling exponent for stem radius to
xylem transport) while sleaf range was achieved from the TRY Database (WWW1: www.try-db.org).
The model finally replaces each hc with the hASRL that uses the best-adjusted regional parameters as:
hASRL(adj-bestβ1, adj-best γ, adj-best sleaf).
469
It should be noted that many widely used models have a variety of parameters that are adjusted to
470
local environments or plant functional types (PFTs). A type of strategies in the model
471
optimization is matching model outputs with actual observations and finding best parameter
472
values that minimize local errors. General circulation models in climate change science make
473
numerous assumptions with bulk parameters, and they are individually palatable and adjustable
474
in real-world applications. Ecosystem models require summarizing the rich detail of ecology and
475
evolution, and those details are replaced with bulk parameters when applied to real-world
476
patterns or problems.
477
478
For instance, a bulk quantity, LMA (leaf mass per unit of leaf area), used in the LM3-PPA model
479
(Land Model 3-Perfect Plasticity Approximation) cannot be simply derived from basic principles.
-17-
480
The LM3-PPA model digests PFT-specific constants. Weng et al. (2015) tuned several model
481
parameters to yield realistic predictions. In addition, a remarkable improvement in the Ecosystem
482
Demography (ED) model performance was reported in Medvigy et al. (2009). This was
483
associated with significant changes in a number of parameters away from their initial, literature-
484
prescribed values when the ED was applied at Harvard forests.
485
486
The original ASRL model also used the bulk quantities of β1, γ, and sleaf. It is a way to summarize
487
entire study region with single parameter values. Kempes et al. (2011) already tested sensitivity
488
of bulk parameters and showed the potential for the parametric adjustments. The bulk parameters
489
allow the flexibility in process-based models. We believe that this is an advantage of the ASRL
490
model because the results of the parametric adjustments provide a set of testable values for future
491
studies, and these values will have true biophysical meanings given realistic model predictions
492
for different study regions and time.
493
494
We made a simple analysis to show physical meanings of those ASRL parameters. For instance,
495
the adjusted sleaf of broadleaf were larger than of needleleaf. This implies that the demand for
496
water (Qe) is higher in broadleaf forests than in conifer forests (Figs. S3a,b). It should be noted
497
that the ED model also showed similar water demand patterns for hardwoods and coniferous
498
given different specific leaf area (Medvigy et al., 2009). The adjusted γ were highest at ~100 mm
499
of monthly mean precipitation for growing season. Southeast and Northwest forests have
500
relatively low γ that explains large amount of annual runoff. Intermediate γ in the US Southwest
501
implies relatively low water use efficiency compared to the US Northeast. The γ showed a typical
502
mono-modal curve against the growing season mean temperature, which indicates less
503
photosynthetic activities or water use efficiency in cold or hot environments (Figs. S3c–e). Lastly,
504
the β1 showed mono-modal relationships with precipitation and temperature (Figs. S3f–h). These
505
patterns can be explained by less xylem water fluidity in cold, hot, or dry regions due to less
506
photosynthetic activities (Lambers et al., 2008).
507
508
We spatially compared the adjusted parameters derived from Forest Inventory and Analysis (FIA)
509
and Geoscience Laser Altimeter System (GLAS) case studies (Fig. S4). Comparison pairs are
510
valid when (i) 10 or more pixels are available for each group and (ii) absolute relative difference
-18-
511
of predicted heights from two case studies, |(hcase_fia – hcase glas)|/hcase
512
adjusted sleaf (R2 = 0.82) and γ (R2 = 0.95) displayed statistically significant agreement. The
513
adjusted β1 explained 96% of variation in the comparison pairs (p < 0.001). Those sleaf and γ pairs
514
are mainly related to the ASRL water-limited environment (see Fig. 2a in the main text) where
515
the maximum forest growth is determined by the water resource availability (~87% of US
516
forests). Rocky and Northeastern Appalachian forests (23% of pixels) were associated with the
517
energy-limited maximum growth and with β1 (Fig. S4d). Deviations between FIA- and GLAS-
518
derived ASRL parameters were mainly obtained from Pacific Northwest and California forest
519
(symbol ○) where spatial mismatches between FIA and GLAs data might introduce significant
520
deviations.
fia,
is less than 20%. The
521
522
We believe that the physical meanings of the parameters are sufficiently addressed in (i) their
523
spatial distribution, (ii) relationships to forest functional type, growing season precipitation and
524
temperature, and (iii) inter-comparisons of the ASRL parameters between FIA and GLAS case
525
studies.
-19-
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
S2. REFERENCES
Allen, R.G., Pereira, L.S., Raes, D. & Smith, M. (1998) Crop evapotranspiration: Guidelines for
computing crop water requirements. In: FAO Irrigation and Drainage Paper 56. pp. 1–15,
Rome, Italy, Food and Agriculture Organization (FAO) of the United Nations.
Chapman, D.G. (1961) Statistical problems in dynamics of exploited fisheries populations. In:
Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability,
Volume 4: Contributions to Biology and Problems of Medicine. pp. 153–168, Berkeley, CA,
USA, University of California Press.
Enquist, B.J., Brown, J.H. & West, G.B. (1998) Allometric scaling of plant energetics and
population density. Nature, 395, 163-165.
Enquist, B.J., West, G.B. & Brown, J.H. (2009) Extensions and evaluations of a general
quantitative theory of forest structure and dynamics. Proceedings of the National Academy
of Sciences of the United States of America, 106, 7046–7051.
Garcia, O. (1983) A stochastic differential equation model for the height growth of forest stands.
Biometrics, 39, 1059–1072.
Gerosa, G.A., Mereu, S., Finco, A. & Marzuoli, R. (2012) Stomatal conductance modeling to
estimate the evapotranspiration of natural and agricultural ecosystems. In:
Evapotranspiration - Remote Sensing and Modeling, (ed Irmak, A.), pp. 403–420, InTech,
Rijeka, Croatia.
Kempes, C.P., West, G.B., Crowell, K. & Girvan, M. (2011) Predicting maximum tree heights
and other traits from allometric scaling and resource limitations. Plos One, 6,
DOI:10.1371/journal.pone.0020551.
Mäkinen, H. & Colin, F. (1999) Predicting the number, death, and self-pruning of branches in
Scots pine. Canadian Journal of Forest Research, 29, 1225–1236.
Mathworks (2014) Statistics and Machine Learning Toolbox User’s Guide. pp. 9:1–9:187, Natick,
MA, USA, The Mathworks Inc.
Medvigy, D., Wofsy, S.C., Munger, J.W., Hollinger, D.Y. & Moorcroft, P.R. (2009) Mechanistic
scaling of ecosystem function and dynamics in space and time: Ecosystem Demography
model version 2. Journal of Geophysical Research-Biogeosciences, 114,
DOI:10.1029/2008jg000812.
Monteith, J. & Unsworth, M. (2013) Principles of Environmental Physics: Plants, Animals, and
the Atmosphere, Fourth Edition, pp. 217–247, Academic Press, Oxford, UK.
Niklas, K.J. (2007) Maximum plant height and the biophysical factors that limit it. Tree
Physiology, 27, 433–440.
Niklas, K.J. & Spatz, H.C. (2004) Growth and hydraulic (not mechanical) constraints govern the
scaling of tree height and mass. Proceedings of the National Academy of Sciences of the
United States of America, 101, 15661–15663.
Obrien, S.T., Hubbell, S.P., Spiro, P., Condit, R. & Foster, R.B. (1995) Diameter, height, crown,
and age relationships in 8 Neotropical tree species. Ecology, 76, 1926–1939.
-20-
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
Purves, D.W., Lichstein, J.W. & Pacala, S.W. (2007) Crown plasticity and competition for
canopy space: A new spatially implicit model parameterized for 250 North American tree
species. Plos One, 2, DOI:10.1371/journal.pone.0000870.
Richards, F.J. (1959) A flexible growth function for empirical use. Journal of Experimental
Botany, 10, 290–301.
Shi, Y., Choi, S., Ni, X., Ganguly, S., Zhang, G., Duong, H., Lefsky, M., Simard, M., Saatchi, S.,
Lee, S., Ni-Meister, W., Piao, S., Cao, C., Nemani, R. & Myneni, R. (2013) Allometric
scaling and resource limitations model of tree heights: Part 1. Model optimization and
testing over continental USA. Remote Sensing, 5, 284–306.
Shugart, H.H., Saatchi, S. & Hall, F.G. (2010) Importance of structure and its measurement in
quantifying function of forest ecosystems. Journal of Geophysical ResearchBiogeosciences, 115, DOI:10.1029/2009jg000993.
Simard, M., Pinto, N., Fisher, J.B. & Baccini, A. (2011) Mapping forest canopy height globally
with spaceborne lidar. Journal of Geophysical Research-Biogeosciences, 116,
DOI:10.1029/2011jg001708.
Weng, E.S., Malyshev, S., Lichstein, J.W., Farrior, C.E., Dybzinski, R., Zhang, T., Shevliakova,
E. & Pacala, S.W. (2015) Scaling from individual trees to forests in an Earth system modeling
framework using a mathematically tractable model of height-structured competition.
Biogeosciences, 12, 2655-2694.
West, G.B., Brown, J.H. & Enquist, B.J. (1997) A general model for the origin of allometric
scaling laws in biology. Science, 276, 122–126.
West, G.B., Brown, J.H. & Enquist, B.J. (1999) A general model for the structure and allometry
of plant vascular systems. Nature, 400, 664–667
WWW1: TRY Database - Quantifying and scaling global plant trait diversity, Available on-line
[http://www.try-db.org], Data accessed: 2015/05/15.
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590
S3. SUPPORTING TABLES (S1–S2)
591
592
593
594
Table S1. Ecoregions over the contiguous United States. The US Forest Service (USFS)’s 36
eco-province codes and full names are provided. Information on the FIA tree samples and ASRL
forest pixels (1-km2 grids) for each ecoregion is also given.
595
596
597
598
599
samples: d)MODIS pixels:
code
n (%)
km2 (%)
242
Pacific Lowland Mixed Forest
5551 (0.3)
20985 (0.6)
M242
Cascade Mixed Forest, Coniferous Forest & e)AM
72525 (3.6)
210581 (6.0)
M261
Sierran Steppe, Mixed Forest, Coniferous Forest & AM
69518 (3.4)
158896 (4.6)
261
California Coastal Chaparral Forest & Shrub
2219 (0.1)
3564 (0.1)
262
California Dry Steppe
145 (0.0)
- (0.0)
A
263
California Coastal Steppe, Mixed Forest & Redwood Forest
7210 (0.4)
15167 (0.4)
M262
California Coastal Range f)OW, Shrub, Coniferous Forest & AM
2813 (0.1)
4435 (0.1)
M331
Southern Rocky Mountain Steppe, OW, Coniferous Forest & AM
59398 (2.9)
223242 (6.4)
M332
Middle Rocky Mountain Steppe, Coniferous Forest & AM
54635 (2.7)
188134 (5.4)
M333
Northern Rocky Mountain Forest, Steppe, Coniferous Forest & AM
41121 (2.0)
146596 (4.2)
313
Colorado Plateau g)SD
18657 (0.9)
74199 (2.1)
M313
Arizona-New Mexico Mountains SD, OW, Coniferous Forest & AM
9376 (0.5)
62189 (1.8)
315
Southwest Plateau, Plains Dry Steppe & Shrub
19545 (1.0)
24297 (0.7)
321
Chihuahuan SD
4996 (0.2)
- (0.0)
322
American SD & Desert
2072 (0.1)
- (0.0)
B
331
Great Plains & Palouse Dry Steppe
8600 (0.4)
12733 (0.4)
332
Great Plains Steppe
4384 (0.2)
1688 (0.0)
341
Intermountain SD & Desert
16208 (0.8)
18001 (0.5)
M341
Nevada-Utah Mountains SD, Coniferous Forest & AM
17832 (0.9)
63354 (1.8)
342
Intermountain SD
5096 (0.3)
12018 (0.3)
M334
Black Hills Coniferous Forest
4549 (0.2)
11797 (0.3)
M223
Ozark Broadleaf Forest & Meadow
9416 (0.5)
19795 (0.6)
231
Southeastern Mixed Forest
259947 (12.9)
456561 (13.1)
M231
Ouachita Mixed Forest & Meadow
12242 (0.6)
32693 (0.9)
C
232
Outer Coastal Plain Mixed Forest
290380 (14.4)
408829 (11.7)
234
Lower Mississippi Riverine Forest
13920 (0.7)
21685 (0.6)
255
Prairie Parkland (Subtropical)
15553 (0.8)
45407 (1.3)
411
Everglades
2773 (0.1)
2933 (0.1)
211
Northeastern Mixed Forest
92760 (4.6)
168704 (4.8)
M211
Adirondack-New England Mixed Forest, Coniferous Forest & AM
85737 (4.3)
152217 (4.4)
212
Laurentian Mixed Forest
391946 (19.4)
291336 (8.4)
221
Eastern Broadleaf Forest
102251 (5.1)
220796 (6.3)
D
M221
Central Appalachian Broadleaf Forest, Coniferous Forest & Meadow
88314 (4.4)
195357 (5.6)
222
Midwest Broadleaf Forest
89806 (4.5)
37809 (1.1)
223
Central Interior Broadleaf Forest
108496 (5.4)
167110 (4.8)
251
Prairie Parkland (Temperate)
26071 (1.3)
12474 (0.4)
Total
2016062 (100)
3485582 (100)
a)Group A–D: Ecoregions aggregated into four groups in this present study (Spatial distribution is depicted in Fig. 3e);
b)USFS code: Eco-province class codes assigned by the USFS (code “M” refers to mountainous ecoregions);
c)FIA tree samples: FIA data spanning years from 2003 to 2007 (live and (co-)dominant trees only);
d)MODIS pixels: MODIS Landcover for the year 2005 (1 km2 grids; forest only);
e)AM: Alpine Meadow; f)OW: Open Woodland and g)SD: Semi-Desert.
a)Group
b)USFS
c)FIA
Full name
-22-
600
601
Table S2. FLUXNET data used for the evaluation of the ASRL model framework in this study.
Spatial distribution is depicted in Fig. 3e.
a)
GRP
A
B
C
602
603
604
b)
FLUX-ID
US-Blo
US-CPk
US-GLE
US-MRf
US-Me1
US-Me2
US-Me3
US-Me5
US-Me6
US-NR1
US-Vcm
US-Vcp
US-Wrc
Latitude
38.90
41.07
41.36
44.65
44.58
44.45
44.32
44.44
44.32
40.03
35.89
35.86
45.82
Longitude
–120.63
–106.12
–106.24
–123.55
–121.50
–121.56
–121.61
–121.57
–121.60
–105.55
–106.53
–106.60
–121.95
PI name
Goldstein, A
Ewers, B & Pendall, E
Massman, B
Law, B
Law, B
Law, B
Law, B
Law, B
Law, B
Blanken, P
Litvak, M
Litvak, M
Bible, K & Wharton, S
US-Blk
US-Fmf
US-Fuf
US-Fwf
US-FR2
US-Mpj
US-Wjs
US-FR3
US-Bar
US-CaV
US-ChR
US-GMF
US-Ha1
US-Ha2
US-Ho1
US-Ho2
US-Ho3
US-KFS
US-Kon
44.16
35.14
35.09
35.45
29.95
34.44
34.43
29.94
44.06
39.06
35.93
41.97
42.54
42.54
45.20
45.21
45.21
39.06
39.08
–103.65
–111.73
–111.76
–111.77
–98.00
–106.24
–105.86
–97.99
–71.29
–79.42
–84.33
–73.23
–72.17
–72.18
–68.74
–68.75
–68.73
–95.19
–96.56
Meyers, T
Dore, S & Kolb, T
Dore, S & Kolb, T
Dore, S & Kolb, T
Litvak, M
Litvak, M
Litvak, M
Heilman, J
Richardson, A
Meyers, T
Meyers, T
Lee, X
Munger, W
Hadley, J & Munger, W
Hollinger, D
Hollinger, D
Hollinger, D
Brunsell, N
Brunsell, N
GRP
a)GRP:
C
D
FLUX-ID
US-Los
US-MMS
US-MOz
US-NMj
US-Oho
US-PFa
US-Syv
US-UMB
US-UMd
US-WBW
US-WCr
US-Wi0
US-Wi1
US-Wi2
Us-Wi3
US-Wi4
US-Wi5
US-Wi6
US-Wi7
US-Wi8
US-Wi9
US-Ced
US-Dix
US-Slt
US-Dk1
US-Dk2
US-Dk3
US-Goo
US-KS1
US-KS2
US-NC1
US-NC2
US-Skr
US-SP1
US-SP2
US-SP3
Latitude
46.08
39.32
38.74
46.65
41.55
45.95
46.24
45.56
45.56
35.96
45.81
46.62
46.73
46.69
46.63
46.74
46.65
46.62
46.65
46.72
46.62
39.84
39.97
39.91
35.97
35.97
35.98
34.25
28.46
28.61
35.81
35.80
25.36
29.74
29.76
29.75
Longitude
–89.98
–86.41
–92.20
–88.52
–83.84
–90.27
–89.35
–84.71
–84.70
–84.29
–90.08
–91.08
–91.23
–91.15
–91.10
–91.17
–91.09
–91.30
–91.07
–91.25
–91.08
–74.38
–74.43
–74.60
–79.09
–79.10
–79.09
–89.87
–80.67
–80.67
–76.71
–76.67
–81.08
–82.22
–82.24
–82.16
PI name
Desai, A
Novick, K & Phillips, R
Gu, L
Chen, J
Chen, J
Desai, A & Davis, KJ
Desai, A & Davis, KJ
Gough, C & Curtis, P
Gough, C & Curtis, P
Meyers, T
Desai, A & Davis, KJ
Chen, J
Chen, J
Chen, J
Chen, J
Chen, J
Chen, J
Chen, J
Chen, J
Chen, J
Chen, J
Clark, K
Clark, K
Clark, K
Oishi, C et al.
Oishi, C et al.
Oishi, C et al.
Meyers, T
Drake, B
Drake, B
Noormets, A
Noormets, A
Barr, JG & Fuentes, J
Martin, T
Martin, T
Martin, T
Four regional Groups A–D;
FLUXNET site IDs;
Shaded rows represent where the ASRL model framework could not explain the calculated FLUXNET evaporative flow rate Qe.
b)FLUX-ID:
-23-
605
S4. SUPPORTING FIGURE
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607
608
609
Figure S1. Spatial distribution of independent reference datasets. The Forest Inventory and
Analysis (FIA; black symbol ×) and the North American Carbon Program (NACP; black symbols
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○ and △) are field measurements. The Laser Vegetation Imaging Sensor (LVIS; blue scatters) and
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612
613
614
the Geoscience Laser Altimeter System (GLAS; red scatters) are airborne and spaceborne lidar
altimetry data, respectively. An existing global forest height product (Simard et al., 2011) based
on a machine learning algorithm (Random Forest) covers all the forest pixels (green) in this study.
All reference data are spatially independent from each other (no overlaps within 10 km radius).
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(b)
100
Predicted height − Improved ASRL (m)
Predicted height − Kempes et al. 2011 (m)
(a)
R2=0.10 (p<0.01)
MAE = 12.2 m
80
60
40
20
0
0
20
40
60
80
Reference height (m)
100
100
R2=0.56 (p<0.001)
MAE = 7.1 m
80
60
40
20
0
0
20
40
60
80
Reference height (m)
100
615
616
617
618
619
Figure S2. Inter-comparisons between reference (FIA) and model predicted heights. (a) Data
from Kempes et al. (2011). (b) Data from the improved ASRL model. The updated model
outperformed the original work at individual pixel level. Mean absolute errors (MAE) decreased
from 16.8 m to 7.1 m while R2 increased from 0.10 to 0.56. Underestimations in the original
work were associated with needleleaf forests in Pacific Northwest and California where the initial
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sleaf generated excessive water demand (symbol ○). Overestimations in the original work were
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related to Northeastern Appalachian (symbol △) where forests are not mature yet. The errors in
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the original work have been significantly reduced after incorporating disturbance histories and
parametric adjustments into the new ASRL model framework.
-25-
(a)
(b)
x 10
−3
Area of single leaf (m2)
10
8
6
4
2
0
EN
EB
DN
DB
Forest functional types
MX
(c)
(d)
0.8
0.6
0.4
0.2
0
0
0.6
0.4
0.2
0
12
14
16
18
Growing season monthly mean temperature (degC)
20
(g)
Norm. constant for basal metabolism
0.008
0.006
0.004
0.002
0
0
(h)
0.01
0.01
Norm. constant for basal metabolism
0.8
50
100
150
200
Growing season monthly mean precipitation (mm)
(f)
624
625
626
627
628
629
630
631
632
633
634
(e)
1
Water absorption efficiency
Water absorption efficiency
1
50
100
150
200
Growing season monthly mean precipitation (mm)
0.008
0.006
0.004
0.002
0
12
14
16
18
Growing season monthly mean temperature (degC)
20
Figure S3. Area of single leaf (sleaf), water absorption efficiency (γ), and normalization constant
for basal metabolism (β1) used in the model after parametric adjustments using GLAS data. (a)
Five forest functional types (EN: evergreen needleleaf, EB: evergreen broadleaf, DN: deciduous
needleleaf, DB: deciduous broadleaf, and MX: mixed forests) were implemented to group the sleaf.
Upper, middle (red line), and lower box edges show the 75%, 50%, and 25% percentile of data.
(b) Spatial distribution of sleaf over the US Mainland. (c) Relationship of γ to growing season
monthly precipitation. (d) Relationships of γ to growing season monthly mean temperature.
Symbol represents mean γ for each group with one standard deviation (e) Spatial distribution of γ.
(f) Relationships of β1 to growing season precipitation. (g) Relationships of β1 to growing season
temperature. Symbol represents mean β1 for each group with one standard deviation. (h) Spatial
distribution of β1.
-26-
(a)
(b)
1
100
R2=0.82 (p < 0.001)
0.001
10
5
1
0.0001
0.001
Area of single leaf (using FIA)
0.8
50
0.6
0.4
5
0.2
1
0
0
0.01
(c)
10
Number of pixels (*1000)
Water absorption efficiency (using GLAS)
R =0.95 (p < 0.001)
50
0.0001
100
2
Number of pixels (*1000)
Area of single leaf (using GLAS)
0.01
0.2
0.4
0.6
0.8
Water absorption efficiency (using FIA)
1
(d)
100
2
R =0.96 (p < 0.001)
50
0.015
0.01
10
5
Number of pixels (*1000)
Norma. constant for basal metabolism (using GLAS)
0.02
0.005
1
0
0
0.005
0.01
0.015
0.02
Norma. constant for basal metabolism (using FIA)
635
636
637
Figure S4. Comparisons between FIA- and GLAS-derived parameters. (a) adjusted sleaf, (b)
adjusted γ, (c) adjusted β1. Valid pairs should include 10 or more 1-km2 pixels. The absolute
relative difference between two case studies, |(hcase_fia – hcase glas)|/hcase fia, should be less than 20%.
638
Symbols correspond to four regional Groups A–D. Groups A: ○ (Pacific Northwest, California
639
and Rocky Mountain), B: □ (Intermountain, Southwest semi-desert and Great Plain Steppe), C:
640
△ (North Wood and Northeastern Appalachian), D: ▽ (Southeast and Outer Coastal Plain).
641
642
643
644
645
646
Color of each scatter presents number of pixels associated with the segments. (d) Distribution of
ASRL environments related to water or energy-driven maximum growth given bulk quantities of
sleaf, γ, and β1. In the US Mainland, water resource availability determines maximum tree growths
in 87% of US forests while Rocky and Northeastern Appalachian (23% of pixels) were predicted
as the ASRL energy-limited environment. See fig. 2 in main text for the definition of water- and
energy-driven maximum forest growths.
-27-
647
S5. SAMPLE CODE FOR ASRL MODEL (MATLAB)
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654
655
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658
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662
663
664
665
666
667
668
669
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671
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673
674
675
676
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681
682
683
684
685
686
A matlab code for ASRL model is provided in a separated file (“asrl_height_unopt_sample.m”).
ASRL INPUT DATA COMPOSITION
A. [Raster Data: 0.008333 Deg. (~1 km) Spatial Resolution]
./input/
~ dem.nc: altitude (in meter)
~ lc.nc: IGBP landcover (1=EN;2=EB;3=DN;4=DB;5=MX)
~prcp.nc: long-term mean (1981-2005: DAYMET) monthly total precipitation (in mm)
~srad.nc: long‐ term mean monthly shortwave solar radiation (in w/m2 with a scale factor
of 0.1 [real data=value*0.1])
~tmax.nc: long‐ term mean monthly maximum air temperature (in deg. C with a scale
factor of 0.01)
~ tmin.nc: long‐ term mean monthly minimum air temperature (in deg. C with a scale
factor of 0.01)
~ vp.nc: long‐ term mean monthly vapor pressure (in Pa)
~ wnd.nc: long‐ term mean (1981-2010 NCEP/NCAR) monthly wind speed (in m/s with a
scale factor of 0.01)
./input/ecoregion/
~ ecor_prov.nc: USFS eco‐ region at the province level
./input/forest_age/
~ fage.nc: Forest stand ages from Pan et al. 2011
./input/fia/
~ fia_hmax_training.nc: FIA 90th percentile field‐ measured tree heights for each pixel
B. [Vector or Parameter Data]
./input/param/
~ prmt.mat: initial ASRL parameters (beta = 3; gamma = 0.5; s_leaf = 0.0010)
~ init_fit_tree.mat: initial tree allometries (US Mainland) for stem radius (r)-to-tree
height (h), h-to-crown height (hcro), h-to-crown radius (rcro).
~ ecor_fit_tree.mat: ecoregional tree allometries
./input/ecoregion/
~ prov_code.mat: USFS province identification code
./input/fia/
~ fia_ageh.mat: FIA tree height and stand age data
ASRL MODEL CODE (MATLAB) AND RUN
A. [ASRL Model Source Code]
./
~ asrl_height_unopt_sample.m
-28-
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690
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692
693
694
695
696
B. [ASRL Model Run]
>> asrl_height_unopt_sample;
C. [ASRL Model Results]
./results/ASRL_hmax_unopt.nc: ASRL predicted maximum potential heights
./results/ASRL_height_unopt.nc: ASRL predicted contemporary forest heights
./results/prmt_unopt.mat: ASRL parameters used in the model run
./results/Qflows_unopt.mat: ASRL Q0, Qp, Qe flows for each pixel
./results/WE_unopt.mat: ASRL water(value=2)/energy(value=3) limited environment
code for each pixel. [1] = model failed.
-29-