A simple forest stand growth model,

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A simple forest stand growth model, and a test
for a mixed-species conifer forest on complex
terrain Remko A. Duursma John D.
Marshall Andrew P. Robinson Vienna, April 2004
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Introduction

• Long history of empirical forest growth models
  Long history of detailed process-based
  modelling
• Empirical models are probably site-specific,
  process models calibrated to site-specific data
• Transport process models to many new sites
  towards a simple closed carbon balance model
• Stand growth models
• Remote sensing
• Data requirement

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A simple hybrid 3PG?

• developed in an attempt to bridge the gap
  between conventional, mensuration-based growth
  and yield, and process-based carbon balance
  models (Landsberg et al 2003)
• 3PG is a simple process-based model requiring
  few parameter values and only readily available
  data as inputs (Landsberg et al 2003)
• Many highly simplified submodels are used in 3PG
• 3PG has often been driven by remote sensing data

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General structure 3PG C cycle
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Some problems with 3PG

• The stand is described with the mean tree only
  applicable to even-aged stands only
• Radiation-use efficiency and fertility rating,
  and usually various other parameters are
  subjectively fitted to match observed data
• Allocation routine does not work for longer-lived
  foliage (Landsberg et al 2003) litterfall is not
  replaced
• Is there only an empirical way to estimate
  RUEmax?

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This study

• Development of a simple carbon balance model that
  gives useful predictions of forest growth over a
  wide range of conditions
• Hierarchy of generalized submodels
• No fitting to observed data independent test
• Short term prediction of stemwood growth no test
  of stand dynamics
• Fit in 3PG framework
• Simplifications necessary to meet goals
• Allometric equations may prove robust?

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Overview

• Simple canopy photosynthesis model
• Allocation routine based on allometric ratios
• Parameterization for 35 plots in mixed-species
  conifer forest across complex terrain in
  North-Idaho

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4PG Canopy photosynthesis model (1)

• Multi-layer model 10 vertical layers
• Division into sunlit and shaded foliage in each
  layer
• Accounting for clumping of foliage (but assume
  random distribution of trees) (Kucharik et al
  1999 TreePhys 19695-706)
• Slope correction to extinction coefficients (Wang
  et al 2002 EcolMod)
• Integrate to daily total with
  Gaussian
  integration
• GPP estimated 5 times
  a day using
  modelled VPD,
  T and PAR diurnals

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4PG Canopy photosynthesis model (2)

• Leaf assimilation model
• Amax estimated from leaf nitrogen
• Global review for conifer species (Duursma et al
  in prep)
• Empirical VPD, T adjustments
• Seasonal cycle of photosynthetic capacity
  chlorophyll fluorescence study (Nippert,Duursma,Ma
  rshall in review)
• AmaxabNarea f(VPD) f(T1) f(T2)
• ? constant f(T1) f(T2)
• T1 kinetics, T2 low temperature damage

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Dry matter allocation (1)

• Root allocation we present no solution and
  assume an estimate is available a priori
• Allocation equations

Woody Foliage

• Goal find ?s to maintain allometric
  equations
• ?S 0, ?F 1 / leaf longevity

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Dry matter allocation (2)

• Goal maintain proportionality of diameter (D),
  dry matter pools of stem wood (SW), foliage (F),
  branches (BR) and bark (BA)

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Dry matter allocation (3)

• Foliage litterfall once a year, allocation once
  a year.
• Allocation to foliage last years lost foliage
  (litter) plus a term for the growth of the
  foliage pool
• where ? leaf longevity, WF total foliage mass (t
  ha-1)

• Allocation to woody drymatter is the leftover
  NPP

• And the new state of the woody pool

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Dry matter allocation (4)

• The new D after incrementing the woody pool is
  given by inverting the allometric equation (where
  ? stems ha-1)

• And the new state of the foliage pool is
  estimated as

• Allocation to foliage depends on new D, which
  depends on allocation to the woody pool solution
  by iteration

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Dry matter allocation (5)

• Use of the mean diameter in allometric equations
  causes potentially large bias

• Duursma and Robinson (2003) showed that

• For allocation purposes, the average diameter
  needs to be solved from WS at t1

• And we assume that the SD stays constant

Solution is obtained by iteration CV depends on
Dt1
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Dry matter allocation (6)

• Approximate with one effective allometric
  equation

• ltagt is estimated as the logarithmic mean of
  the as
• And ltbgt is then simply solved (calibrated),

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Dry matter allocation (7)

• WS,t1 includes stemwood, branches, bark, one
  allometric equation was used for aboveground dry
  matter
• Branches and bark estimated from separate
  allometric equations, substracted from woody pool

• Branch turnover a constant fraction of leaf
  litter

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Parameterization (1)

• Goal independently parameterize the model,
• Test against measured volume growth for a 10yr
  period
• Ignore mortality, regeneration, assume steady
  state for 10yrs
• Challenge few data available, very complex
  situation.
• No litterfall data, allometric equations
  generally for too short dbh range

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Parameterization (2)

• Measurements of
• Leaf area index (allometric and optically based)
• Specific leaf area, nitrogen concentration (and
  vertical gradients)
• Wood density, stand density, diameters, species
  composition
• Root allocation 40 of NPP
• Calibrated against Raich and Nadelhoffer (1989)
  empirical relationship with litterfall
• Species specific allometric equations, leaf
  longevity
• Assume parameters that are used in linear
  equations only can be averaged across the plot
• Use of mixed-effects models to estimate
  parameters per plot, using the random effects
  (BLUPs)

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Parameterization (3)

• MTCLIM for VPD, T, Solar radiation
• Using measured lapse rates for temperature
• Validated for 101 days on one site

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Priest River Experimental Forest
Pocewicz et al 2004 CJFR 34465

• Precipitation 800-900mm (mostly Oct-May)
• Altitude 700-1700m
• Steep slopes, much disturbance, old-growth and
  recent clearcuts, management, roadcuts
• High summer VPD, distinct drought season
• 10 common conifer species, Thuja plicata,
  Pseudotsuga menziesii, Tsuga heterophylla dominant

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Old-growth Thuja plicata, Tsuga heterophylla
Dense stands of 6-8 conifer species
High altitude Abies lasiocarpa, Picea engelmannii
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Model runs

• Constant Leaf area index for 10yr
• Either allometric estimate, or optically-based
  estimate
• Allocation routine
• Estimated for each plot using allometric
  equations, leaf longevity
• Or constant (averaged allocation estimates
  across all plots)
• Test annual wood volume increment

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Variable allocation allometric LAI Variable
allocation ceptometer LAI
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Leaf specific volume increment

• With optical LAI estimate, constant allocation

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Discussion soil water?

• Water balance could not be closed no estimates
  of soil water holding capacity, soil evaporation,
  understorey transpiration
• Some data for similar stands soil water content
  10 in the summer months (July, August,
  September), and 50 in May/June.
• Using Landsberg Warings soil water modifier
  (silt/clay)

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Discussion / Conclusions

• Allocation routine failed to improve estimates of
  stem growth importance of accurate allometric
  equations, litterfall data, and difficulty of
  species composition
• Allometric equations a problem for big trees
• Constant NPP/GPP? How much variation between
  stands?
• Species composition average parameters?
• Overall promising results but more data needed
  for improvement of predictions of this type of
  model
• Consideration in simpler situations

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Many thanks to Ben Miller, Ben Harlow, Jesse
Nippert, Chris Chambers for field
work McIntire-Stennis
Priest River Experimental Forest (USDA Forest
Service)