modelling climate and disturbance effects on net ecosystem productivity of temperate and boreal...

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Modelling Climate and Modelling Climate and Disturbance Effects on Disturbance Effects on Net Ecosystem Net Ecosystem Productivity of Productivity of Temperate and Boreal Temperate and Boreal Forests Forests Robert F. Grant* and colleagues in Robert F. Grant* and colleagues in the Fluxnet-Canada Research the Fluxnet-Canada Research Network Network * Department of Renewable Resources Department of Renewable Resources University of Alberta University of Alberta Edmonton, AB Edmonton, AB Canada Canada

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Page 1: Modelling Climate and Disturbance Effects on Net Ecosystem Productivity of Temperate and Boreal Forests Robert F. Grant* and colleagues in the Fluxnet-Canada

Modelling Climate and Modelling Climate and Disturbance Effects on Net Disturbance Effects on Net Ecosystem Productivity of Ecosystem Productivity of

Temperate and Boreal ForestsTemperate and Boreal Forests

Robert F. Grant* and colleagues in the Robert F. Grant* and colleagues in the Fluxnet-Canada Research NetworkFluxnet-Canada Research Network

**Department of Renewable ResourcesDepartment of Renewable ResourcesUniversity of AlbertaUniversity of Alberta

Edmonton, ABEdmonton, ABCanadaCanada

Page 2: Modelling Climate and Disturbance Effects on Net Ecosystem Productivity of Temperate and Boreal Forests Robert F. Grant* and colleagues in the Fluxnet-Canada

Fluxnet-Canada: Fluxnet-Canada: Influence of Influence of Climate and Climate and

Disturbance on Disturbance on Carbon Cycling Carbon Cycling

in Forest and in Forest and Peatland Peatland

EcosystemsEcosystems

Page 3: Modelling Climate and Disturbance Effects on Net Ecosystem Productivity of Temperate and Boreal Forests Robert F. Grant* and colleagues in the Fluxnet-Canada

Terrestrial Carbon Sink

1. It absorbs a significant amountof the anthropogenic carbon that is emitted to the atmosphere (e.g., 15 to 30%).

2. It is located in northern terrestrial ecosystems.

3. It has high inter-annual variability.

4. It provides a very valuable environmental service.

Page 4: Modelling Climate and Disturbance Effects on Net Ecosystem Productivity of Temperate and Boreal Forests Robert F. Grant* and colleagues in the Fluxnet-Canada

Canadian Forest SectorCanadian Forest Sector(forests and peatlands falling within (forests and peatlands falling within Canada’s forest biomass inventory)Canada’s forest biomass inventory)

Standing Biomass: ~ 15 Gt Standing Biomass: ~ 15 Gt

Soil and Peat: ~ 71 GtSoil and Peat: ~ 71 Gt

TotalTotal ~ 86 Gt ~ 86 Gt

Canada’s carbon stocks are nearly Canada’s carbon stocks are nearly

500500 times greater than Canada’s times greater than Canada’s anthropogenic emissions!!anthropogenic emissions!!

Canadian Anthropogenic C Emissions: ~ 0.18 Gt/yr

Page 5: Modelling Climate and Disturbance Effects on Net Ecosystem Productivity of Temperate and Boreal Forests Robert F. Grant* and colleagues in the Fluxnet-Canada

Canadian Forest SectorCanadian Forest SectorPhotosynthesis: Photosynthesis: ~ 2.8 Gt C / yr~ 2.8 Gt C / yr

Respiration and fires: Respiration and fires: ~ 2.8 Gt C / yr ~ 2.8 Gt C / yr

Natural flux is Natural flux is 1515 times greater than times greater than anthropogenic C emissions!!anthropogenic C emissions!!

Thus, ecosystem processes are a key Thus, ecosystem processes are a key part of the overall carbon problem.part of the overall carbon problem.

Page 6: Modelling Climate and Disturbance Effects on Net Ecosystem Productivity of Temperate and Boreal Forests Robert F. Grant* and colleagues in the Fluxnet-Canada

Any attempt to understand and Any attempt to understand and eventually manage Canada’s eventually manage Canada’s overall carbon emissions must overall carbon emissions must address the effects of …..address the effects of …..

Climate Climate - temperature, precipitation, CO- temperature, precipitation, CO22

Natural Disturbance Natural Disturbance - fire, pests- fire, pests

Land Use Activities Land Use Activities - logging, fertilization, vegetation control- logging, fertilization, vegetation control

Page 7: Modelling Climate and Disturbance Effects on Net Ecosystem Productivity of Temperate and Boreal Forests Robert F. Grant* and colleagues in the Fluxnet-Canada

A New National A New National Research Research Network: Network:

Fluxnet-CanadaFluxnet-Canada

Page 8: Modelling Climate and Disturbance Effects on Net Ecosystem Productivity of Temperate and Boreal Forests Robert F. Grant* and colleagues in the Fluxnet-Canada

The general objectives of the The general objectives of the network are:network are: (1) (1) To increase our understanding To increase our understanding

and our ability to model the and our ability to model the effects of climate, natural effects of climate, natural disturbances, and forest disturbances, and forest management on terrestrial C management on terrestrial C cycling processes in the forests cycling processes in the forests and peatlands of Canada. and peatlands of Canada.

Page 9: Modelling Climate and Disturbance Effects on Net Ecosystem Productivity of Temperate and Boreal Forests Robert F. Grant* and colleagues in the Fluxnet-Canada

(2) (2) To contribute insights, ideas, and To contribute insights, ideas, and well-documented archived data well-documented archived data sets to efforts aimed at sets to efforts aimed at understanding, constraining, and understanding, constraining, and quantifying regional, national and quantifying regional, national and global C cycles.global C cycles.

Page 10: Modelling Climate and Disturbance Effects on Net Ecosystem Productivity of Temperate and Boreal Forests Robert F. Grant* and colleagues in the Fluxnet-Canada

(3)(3) Make a major contribution to Make a major contribution to understanding Canada’s role in the understanding Canada’s role in the northern terrestrial carbon sink, northern terrestrial carbon sink, specifically:specifically:

(a) (a) What is Canada’s What is Canada’s contribution contribution to the northern to the northern terrestrial sink?terrestrial sink?(b) (b) How does it vary spatially How does it vary spatially and and temporally?temporally?(c) (c) What might influence it in What might influence it in the the future?future?(d) (d) What are the effects of land What are the effects of land

use management and use management and natural disturbance?natural disturbance?

Page 11: Modelling Climate and Disturbance Effects on Net Ecosystem Productivity of Temperate and Boreal Forests Robert F. Grant* and colleagues in the Fluxnet-Canada

(4) (4) To train graduate students and To train graduate students and postdoctoral researchers in postdoctoral researchers in terrestrial carbon cycle terrestrial carbon cycle science.science.

Page 12: Modelling Climate and Disturbance Effects on Net Ecosystem Productivity of Temperate and Boreal Forests Robert F. Grant* and colleagues in the Fluxnet-Canada

These objectives These objectives will be attained by will be attained by establishing, establishing, maintaining and maintaining and reinforcing an reinforcing an east-west transect east-west transect of carbon flux of carbon flux research stations research stations across the across the commercial forest commercial forest zone of Canada.zone of Canada.

Page 13: Modelling Climate and Disturbance Effects on Net Ecosystem Productivity of Temperate and Boreal Forests Robert F. Grant* and colleagues in the Fluxnet-Canada

Eddy covariance flux Eddy covariance flux towers will be used to towers will be used to measure ecosystem-measure ecosystem-level fluxes and these level fluxes and these will be combined with will be combined with studies of ecosystem studies of ecosystem components (e.g., components (e.g., soils, vegetation) so soils, vegetation) so that we can understand that we can understand the processes driving the processes driving the tower fluxes.the tower fluxes.

Page 14: Modelling Climate and Disturbance Effects on Net Ecosystem Productivity of Temperate and Boreal Forests Robert F. Grant* and colleagues in the Fluxnet-Canada
Page 15: Modelling Climate and Disturbance Effects on Net Ecosystem Productivity of Temperate and Boreal Forests Robert F. Grant* and colleagues in the Fluxnet-Canada

Fluxnet Canada

Page 16: Modelling Climate and Disturbance Effects on Net Ecosystem Productivity of Temperate and Boreal Forests Robert F. Grant* and colleagues in the Fluxnet-Canada

Combustion lossesCO2, CO, CH4

Decomposition

Successional vegetation to crown closure

DecompositionCWD, regeneration

Renewed mature forest stand

Page 17: Modelling Climate and Disturbance Effects on Net Ecosystem Productivity of Temperate and Boreal Forests Robert F. Grant* and colleagues in the Fluxnet-Canada

What can models contribute?What can models contribute? Policy decisions require information about changes in GHG Policy decisions require information about changes in GHG

exchange between diverse terrestrial ecosystems and the exchange between diverse terrestrial ecosystems and the atmosphere across at large temporal (years to centuries) atmosphere across at large temporal (years to centuries) and spatial (kmand spatial (km22 to continental) scales to continental) scales

These changes are determined by complex interactions These changes are determined by complex interactions among weather, soils and disturbance, both natural (fire, among weather, soils and disturbance, both natural (fire, pests) and human (tillage, planting, fertilizing, harvesting).pests) and human (tillage, planting, fertilizing, harvesting).

Research about how these changes are determined (e.g. Research about how these changes are determined (e.g. FCRN) takes place in only a few ecosystems at much FCRN) takes place in only a few ecosystems at much smaller temporal (seconds to seasons) and spatial (mm to smaller temporal (seconds to seasons) and spatial (mm to kmkm22) scales than those at which information is required) scales than those at which information is required

Modelling provides a way to use research conducted at Modelling provides a way to use research conducted at smaller scales to derive policy-relevant information at smaller scales to derive policy-relevant information at larger scaleslarger scales

Page 18: Modelling Climate and Disturbance Effects on Net Ecosystem Productivity of Temperate and Boreal Forests Robert F. Grant* and colleagues in the Fluxnet-Canada

Some Recent Examples of Policy-Some Recent Examples of Policy-Relevant Model ResultsRelevant Model Results

BIOME-BGC was used to estimate that average NEP and NBP BIOME-BGC was used to estimate that average NEP and NBP of a 8.2 Mha forested region of Oregon was 168 and 100 g C of a 8.2 Mha forested region of Oregon was 168 and 100 g C mm-2-2 y y-1 -1 (Law et al., 2004)(Law et al., 2004)

CBM-CFS2 was used to estimate that average NEP of a 97.6 CBM-CFS2 was used to estimate that average NEP of a 97.6 Mha forested region in northern Canada rose from 53 g C mMha forested region in northern Canada rose from 53 g C m -2-2 yy-1 -1 in 1920–24 to 75 g C min 1920–24 to 75 g C m-2-2 y y-1 -1 in 1960 and then declined to in 1960 and then declined to 26 g C m26 g C m-2-2 y y-1 -1 in 1991-95 (Li et al., 2003).in 1991-95 (Li et al., 2003).

CENTURY was used to estimate that average NEP of Chinese CENTURY was used to estimate that average NEP of Chinese boreal forests would rise from 64 g C mboreal forests would rise from 64 g C m -2-2 y y-1-1 with a harvest with a harvest cycle of 30 years to 102 g C mcycle of 30 years to 102 g C m -2-2 y y-1-1 with one of 100 years but with one of 100 years but decline to 88 g C mdecline to 88 g C m-2-2 y y-1-1 with one of 200 years (Jiang et al., with one of 200 years (Jiang et al., 2002)2002)

BIOME-BGC was used to estimate NEP from 100 to 300 g C BIOME-BGC was used to estimate NEP from 100 to 300 g C mm-2-2 y y-1-1 for 4 diverse coniferous forests in Europe, much of for 4 diverse coniferous forests in Europe, much of which was attributed to rising Cwhich was attributed to rising Caa and N depositions (Churkina and N depositions (Churkina et al., 2003). et al., 2003).

Page 19: Modelling Climate and Disturbance Effects on Net Ecosystem Productivity of Temperate and Boreal Forests Robert F. Grant* and colleagues in the Fluxnet-Canada

Stand-Scale ModellingStand-Scale Modelling

Page 20: Modelling Climate and Disturbance Effects on Net Ecosystem Productivity of Temperate and Boreal Forests Robert F. Grant* and colleagues in the Fluxnet-Canada

dominantdominantpopulationpopulation

subdominantsubdominantpopulationpopulation

residueresiduesoil surfacesoil surface

soil layersoil layerrootsroots

Rn,LE,HRn,LE,H

heatheat

Gases: OGases: O22, NH, NH33, ,

NN22O, NO, N22, CH, CH44

gasesgases

waterwater

waterwater N,PN,P

CC

Mass and energy transfer scheme in ecosys

NHNH44++,NO,NO33

--NN22

Page 21: Modelling Climate and Disturbance Effects on Net Ecosystem Productivity of Temperate and Boreal Forests Robert F. Grant* and colleagues in the Fluxnet-Canada

Example of Model Development: Example of Model Development: Modelling age effects on forest NEPModelling age effects on forest NEP Disturbances such as clearcutting affect forest NEP for

many decades afterwards. Regional forest NEP therefore depends upon times since

last major disturbance of all component stands. The effects of logging on forest C exchange have to be

assessed over long time periods. Although chronosequence research can substitute space

for time when assessing these effects, it also substitutes spatial for temporal variation.

Modelling can be used to assess forest age effects on NEP for use in regional estimates of NEP.

Page 22: Modelling Climate and Disturbance Effects on Net Ecosystem Productivity of Temperate and Boreal Forests Robert F. Grant* and colleagues in the Fluxnet-Canada

Model HypothesesModel Hypotheses

(1) Early regrowth after disturbance is controlled (1) Early regrowth after disturbance is controlled by mineralization-immobilization of N by fine and by mineralization-immobilization of N by fine and woody residue.woody residue.

(2) Later growth is constrained by declining (2) Later growth is constrained by declining hydraulic conductance and rising water potential hydraulic conductance and rising water potential gradients in taller trees.gradients in taller trees.

(3) Later growth is also constrained by rising (3) Later growth is also constrained by rising respiration requirements caused by accumulating respiration requirements caused by accumulating phytomassphytomass

Page 23: Modelling Climate and Disturbance Effects on Net Ecosystem Productivity of Temperate and Boreal Forests Robert F. Grant* and colleagues in the Fluxnet-Canada

Hypothesis (1): model C and N transformations of fine and Hypothesis (1): model C and N transformations of fine and coarse woody litter that control N uptake during regenerationcoarse woody litter that control N uptake during regeneration

NH4+

NO3-

Humus C:N ~ 15 Micr. Residue C:N~8 Humus C:N ~ 15 Micr. Residue C:N~8

DOC, DONDOC, DON

Microbial C:N ~ 8 Microbial C:N ~ 8

Surface litter

Non-woody litter C:N ~ 40 Woody litter C:N ~ 40

Microbial C:N ~ 8

Non-woody litter C:N ~ 40 Woody litter C:N ~ 40

NH4+

NO3-

Microbial C:N ~ 8

Humus C:N ~ 15 Micr. Residue C:N~8 Humus C:N ~ 15 Micr. Residue C:N~8

Soil litter

DOC, DON DOC, DON

Microbes compete with roots for mineral N

Root

Shoot

Page 24: Modelling Climate and Disturbance Effects on Net Ecosystem Productivity of Temperate and Boreal Forests Robert F. Grant* and colleagues in the Fluxnet-Canada

canopy layer 1

atmosphere

vapor pressureatm

vapor pressurecanopy

bo

un

dar

y

ccanopy layer n

r,n

r,2

r,1

s,n

s,2

s,1

soiln

soil2

soil1

radialn

radial2

radial1axia

l 3 axia

l 1

axia

l 2

cap

acit

ance

stomatalshaded,n

stomatalshaded,1

stomatalsunlit,n

stomatalsunlit,1

soil layer n

soil layer 2

soil layer 1

Rn LE HHypothesis (2): model axial conductance that affects c at which root water uptake+ capacitance= transpiration

Page 25: Modelling Climate and Disturbance Effects on Net Ecosystem Productivity of Temperate and Boreal Forests Robert F. Grant* and colleagues in the Fluxnet-Canada

Test of model hypothesesTest of model hypotheses

Mass and energy exchange were measured in Mass and energy exchange were measured in 2002 over a post-clearcut chronosequence of 2002 over a post-clearcut chronosequence of coastal Douglas fir stands originating in 2000 (3coastal Douglas fir stands originating in 2000 (3rdrd year), 1989 (14year), 1989 (14thth year) and 1949 (53 year) and 1949 (53rdrd year) by year) by UBC FCRN site.UBC FCRN site.

These data were used to test modelled mass and These data were used to test modelled mass and energy exchange during a 120-year run of energy exchange during a 120-year run of ecosysecosys, an ecosystem model developed at the U , an ecosystem model developed at the U of A as part of FCRN, under soil, weather and land of A as part of FCRN, under soil, weather and land

use conditions for the Douglas fir site.use conditions for the Douglas fir site.

Page 26: Modelling Climate and Disturbance Effects on Net Ecosystem Productivity of Temperate and Boreal Forests Robert F. Grant* and colleagues in the Fluxnet-Canada

CHRONOSEQUENCE OF 3 DOUGLAS-FIR STANDSVANCOUVER ISLAND

2000 1949Planted

30-35 3-8Height (m) 0.3

54-year-oldClearcut

14-year-old

Photos from Andy Black

Page 27: Modelling Climate and Disturbance Effects on Net Ecosystem Productivity of Temperate and Boreal Forests Robert F. Grant* and colleagues in the Fluxnet-Canada

Site and soil characteristics of the Campbell River site.

Site CharacteristicsLatitude : N 4952.137’Longitude : W 12520.120’Elevation: 300 mMean annual precipitation: 1461 mm/y*Mean annual temperature: 8.3 C*Dominant vegetation: 53 year old Douglas-fir (Pseudotsuga menziesii) with 17% red cedar (Thuja plicata Donn) and 3% western hemlock (Tsuga heterophylla (Raf.) Sarg.)Understory vegetation: sparse, mainly consisting of various mosses, ferns and herbaceous/ woody species such as salal, dull oregon grape, vanilla-leaf deerfoot.Mean basal area (1998) 71 m2 ha-1 (overstory) Fertilization: 20 g N m-2 as urea in 1994.

Soil Characteristics†Horizon L-H Ap/Ae Bf1 ---------------- Bf2/Bfc ---------------- CDepth to bottom (m)0.10.2 0.3 0.4 0.5 0.6 0.7 0.9Bulk Density (Mg m-3) 0.1 0.90 1.18 1.57 1.50 1.42 1.42 1.58Field Capacity (m3 m-3)0.241 0.203 0.203 0.203 0.203 0.203 0.203 0.203Wilting Point (m3 m-3) 0.117 0.068 0.068 0.068 0.068 0.068 0.068 0.068Ksat (mm h-1) 36 94 121 133 97 121 107 107Sand (g kg-1) - 692 809 880 898 838 883 875Silt (g kg-1) - 227 169 105 93 157 97 98Clay (g kg-1) - 81 23 15 9 6 20 26Coarse Fragments (m3 m-3) 0 0.267 0.267 0.353 0.35 0.353 0.356 0.356pH 5.2 5.45 5.45 5.92 5.92 5.92 5.0 6.87Organic C (g kg-1) 81 62.1 28.5 17.5 17.0 18.6 10.0 10.3Total N (g Mg-1) 1620 640 640 560 560 560 250 200Exch. P (g Mg-1) 16 15 15 11 11 11 17 20

†Keser and St. Pierre, 1973. Soils of Vancouver Island: A compendium. B.C. For Serv. Res. Note 56 – Hart soil

Page 28: Modelling Climate and Disturbance Effects on Net Ecosystem Productivity of Temperate and Boreal Forests Robert F. Grant* and colleagues in the Fluxnet-Canada

Model runs for coastal Douglas-fir Model runs for coastal Douglas-fir forestforest

EcosysEcosys was initialized with was initialized with • soil and topographic properties soil and topographic properties • above- and below-ground residues corresponding to those left after above- and below-ground residues corresponding to those left after

logging. logging. EcosysEcosys was then seeded with Douglas-fir and run for 65 years was then seeded with Douglas-fir and run for 65 years

• under repeated 6-year sequences (1998 – 2003) of weather data under repeated 6-year sequences (1998 – 2003) of weather data recorded at the 1949 site. recorded at the 1949 site.

After 70 years, a simulated logging was applied in mid-JanuaryAfter 70 years, a simulated logging was applied in mid-January• 0.1, 0.1 and 0.65 of foliar, non-foliar non-woody, and coarse woody 0.1, 0.1 and 0.65 of foliar, non-foliar non-woody, and coarse woody

above-ground phytomass respectively was removed. above-ground phytomass respectively was removed. The modelled site was then reseeded in mid-March with Douglas-fir The modelled site was then reseeded in mid-March with Douglas-fir

and deciduous bush to simulate competing pioneer populations. and deciduous bush to simulate competing pioneer populations. The reseeded site was then run for a further 200 years The reseeded site was then run for a further 200 years

• under repeated 7-year sequences (1998 – 2004) of weather data under repeated 7-year sequences (1998 – 2004) of weather data recorded at the 2000, 1988 and 1949 sites. recorded at the 2000, 1988 and 1949 sites.

Page 29: Modelling Climate and Disturbance Effects on Net Ecosystem Productivity of Temperate and Boreal Forests Robert F. Grant* and colleagues in the Fluxnet-Canada

How does CO2 and energy exchange respond to a warming event on Vancouver Island in July 2002?

199 200 201 202 203 204 205 206 207 208 2090

200

400

600

800

1000 radiation temperature

Ra

dia

tio

n (

W m-2

)

0

5

10

15

20

25

30

Air T

em

pe

ratu

re (

oC)

Page 30: Modelling Climate and Disturbance Effects on Net Ecosystem Productivity of Temperate and Boreal Forests Robert F. Grant* and colleagues in the Fluxnet-Canada

Greater sensitivity of gc to high D in older forest

Hydraulic limitations on gc of coastal Douglas fir during warming event on Vancouver Island in July 2002

199 200 201 202 203 204 205 206 207 208 209-20

-10

0

10

20

30 (c)

Fig. 6

(b)

CO 2

(mo

l m-2

s-1

)

Day of Year

0

2

4

6

8

10

12

(a)g c (

mm

s-1

)

-3.0

-2.5

-2.0

-1.5

-1.0

-0.5

0.0 c

(MP

a)

14 30 53 109

Declines in CO2 influxes begin earlier in older forest

Page 31: Modelling Climate and Disturbance Effects on Net Ecosystem Productivity of Temperate and Boreal Forests Robert F. Grant* and colleagues in the Fluxnet-Canada

Different sensitivities of Different sensitivities of ggcc to to DD with forest age affects with forest age affects

energy exchange (measurements from FCRN)energy exchange (measurements from FCRN)

2000

1989

1949

shift from LE to H with increasing age

199 200 201 202 203 204 205 206 207 208 209

-500

-400

-300

-200

-100

0

100

-500

-400

-300

-200

-100

0

100

-500

-400

-300

-200

-100

0

100

Fig. 3

(c)

(b)

(a)

LE H

Day of Year

En

erg

y F

lux (

W m

-2)

Page 32: Modelling Climate and Disturbance Effects on Net Ecosystem Productivity of Temperate and Boreal Forests Robert F. Grant* and colleagues in the Fluxnet-Canada

Different sensitivities of Different sensitivities of ggcc to to DD with forest age also affects with forest age also affects

COCO22 exchange (measurements from FCRN) exchange (measurements from FCRN)

2000

1989

1949

As forests age, nutrient constraints on CO2 fixation become less, but diurnal declines in CO2 influx begin earlier.

199 200 201 202 203 204 205 206 207 208 209-20

-10

0

10

20

30

-20

-10

0

10

20

30

-20

-10

0

10

20

30

Fig. 4

(c)

(b)

(a)C

O 2 F

lux (m

ol m

-2

s-1

)

DOY

Older forests change from a sink to a source of CO2 under high D

Page 33: Modelling Climate and Disturbance Effects on Net Ecosystem Productivity of Temperate and Boreal Forests Robert F. Grant* and colleagues in the Fluxnet-Canada

0 30 60 90 120 150 180 210 240 270 300 330 360-8

-4

0

4

8 (d) 1949

Day of Year

-8

-4

0

4

8 (c) 1989

Ne

t E

co

syste

m P

rod

uctivity (

g C

m-2 d

-1)

-8

-4

0

4

8 (b) 2000

05

1015202530

Fig. 5

(a)

Ma

x.

Te

mp

(o C

)

Greater variability in daily NEP with weather in older forests

Page 34: Modelling Climate and Disturbance Effects on Net Ecosystem Productivity of Temperate and Boreal Forests Robert F. Grant* and colleagues in the Fluxnet-Canada

NEP < 0 during first 15 years– nutrient constraints

NEP rises rapidly from 10 to 30 years– alleviation of nutrient constraints

NEP reaches maximum values between 30 and 50 years after clearcut

Then NEP declines gradually – hydraulic constraints

-800

-600

-400

-200

0

200

400 (a)

Fig. 8

source

sink

urea broadcast at 20 g N m-2

NE

P (

g C

m-2 y

-1)

0 20 40 60 80 100 120 140 160 180 2000

5

10

15

20

25

30

35

40

45 (b)

So

il o

r T

ree

C (

kg

C m

-2)

Years After Clearcut

above-ground forest growth function (average) growth function (high) soil

Time course of modelled wood growth followsthat estimated from wood inventory

Page 35: Modelling Climate and Disturbance Effects on Net Ecosystem Productivity of Temperate and Boreal Forests Robert F. Grant* and colleagues in the Fluxnet-Canada

Is long-term NEP greater in a 60 vs. 120 year harvest cycle?Is long-term NEP greater in a 60 vs. 120 year harvest cycle?

Gain in NEP of 120-year cycle during post-harvest periods in 60-year cycleLoss in NEP of 120-year cycle during later growth

Greater wood accumulation in 120-year cycle

0 60 120 180 24005

1015202530354045 (c)

Fig. 9

Wo

od

C (

kg

m-2 )

Years After First Clearcut

10

15

20

25

30

35 (b)

So

il C

(kg

m-2 )

-1400-800-600-400-200

0200400 (a)

NE

P (

g C

m-2 y

-1 )

60 year 120 year

Page 36: Modelling Climate and Disturbance Effects on Net Ecosystem Productivity of Temperate and Boreal Forests Robert F. Grant* and colleagues in the Fluxnet-Canada

Changes in C stocks of a coastal Douglas fir after Changes in C stocks of a coastal Douglas fir after four logging cycles of 60 years each or two logging four logging cycles of 60 years each or two logging

cycles of 120 years eachcycles of 120 years each

reduction in wood harvest removal

gain in soil C storage

C Stock 4 x 60 Years 2 x 120 Years------------g C m-2 ------------

Removalwood 53425 45592other 432 160

D Soil -2400 +5398DOC Export 447 447DIC Export 1252 1366Total NEP 53156 52963

Page 37: Modelling Climate and Disturbance Effects on Net Ecosystem Productivity of Temperate and Boreal Forests Robert F. Grant* and colleagues in the Fluxnet-Canada

Effects of drought and climate Effects of drought and climate change on NEP of boreal aspenchange on NEP of boreal aspen

Page 38: Modelling Climate and Disturbance Effects on Net Ecosystem Productivity of Temperate and Boreal Forests Robert F. Grant* and colleagues in the Fluxnet-Canada

Drought during 2001 – 2003 adversely Drought during 2001 – 2003 adversely affected productivity of this aspen forestaffected productivity of this aspen forest

Annual climate data at the Southern Old Aspen site during the period of flux measurement

Year Average Temp. Precipitation0C mm

1994 1.00 4771995 0.18 4201996 -1.06 4421997 2.66 4131998 3.31 5471999 2.89 4792000 1.26 4842001 2.96 2352002 0.69 2862003 1.83 2612004 0.77 741

drought

Page 39: Modelling Climate and Disturbance Effects on Net Ecosystem Productivity of Temperate and Boreal Forests Robert F. Grant* and colleagues in the Fluxnet-Canada

Model runs for boreal aspenModel runs for boreal aspen EcosysEcosys was initialized with was initialized with

• the site and soil properties given in Table 1 the site and soil properties given in Table 1 • the biological properties of aspen and hazelnut the biological properties of aspen and hazelnut

EcosysEcosys was then run for 3 disturbance cycles of 100 years was then run for 3 disturbance cycles of 100 years• each under repeated 11-year sequences of 1994 – 2004 each under repeated 11-year sequences of 1994 – 2004

meteorological data (shortwave radiation, air temperature, meteorological data (shortwave radiation, air temperature, relative humidity, wind speed and precipitation measured 10 m relative humidity, wind speed and precipitation measured 10 m above the canopy). above the canopy).

• concentrations of NHconcentrations of NH44++ and NO and NO33

-- in precipitation were set to 0.1 in precipitation were set to 0.1 and 0.4 g N mand 0.4 g N m-3-3 respectively respectively

• concentrations of COconcentrations of CO22 and NH and NH33 in the atmosphere were set at in the atmosphere were set at 370 and 0.0025 370 and 0.0025 mol molmol mol-1-1 respectively. respectively.

During each cycle, a stand-replacing fire was implemented During each cycle, a stand-replacing fire was implemented on 30 June of the first year on 30 June of the first year • all above-ground phytomass and 0.6 of the surface litter was all above-ground phytomass and 0.6 of the surface litter was

destroyed.destroyed. Results were compared with measured values during the Results were compared with measured values during the

8585thth – 87 – 87thth years of the model run under 2001 – 2003 years of the model run under 2001 – 2003 weather weather

Page 40: Modelling Climate and Disturbance Effects on Net Ecosystem Productivity of Temperate and Boreal Forests Robert F. Grant* and colleagues in the Fluxnet-Canada

Site and soil characteristics of the Southern Old Aspen Site.

Site CharacteristicsLatitude: 53.6 ° N Longitude: 106.2 ° WElevation: 600 mMean annual precipitation 484 mmMean annual temperature 1.5˚CDominant vegetation: aspen (Populus tremuloides) regenerated from fire in 1919Understory vegetation: hazelnut (Corylus cornuta)Mean basal area (1994) 33.5 m2 ha-1 (overstory)

Soil Characteristics†Horizon L F H Ae Bt Bmk Ck1 Ck2Depth to bottom (m)0.02 0.05 0.10 0.32 0.70 0.85 1.25 1.85Bulk Density (Mg m-3) 0.09 0.11 0.19 1.38 1.53 1.67 1.67 1.67Field Capacity (m3 m-3)0.45 0.45 0.40 0.24 0.23 0.19 0.18 0.21Wilting Point (m3 m-3) 0.10 0.10 0.10 0.10 0.13 0.11 0.10 0.13Sand (g kg-1) - - - 589 568 485 484 484Silt (g kg-1) - - - 293 187 280 276 276Clay (g kg-1) - - - 118 245 235 240 240Coarse Fragments (m3 m-3)0 0 0 0 0 0 0 0pH 6.4 6.5 6.6 6.6 6.5 6.8 8.5 8.5CEC (cmol(+) kg-1) 103 119 120 9.2 14 12 12 10Organic C (g kg-1) 430 415 313 6.2 3.4 2.0 3.4 3.4Total N (g Mg-1) 20199 21573 19522 521 317 286 200 200Total P (g Mg-1) 1442 1269 1220 212 304 459 448 448

† Anderson, D. 1998. BOREAS TE-01 Soils Data over the SSA Tower Sites in Raster Format, Available online at [http://www-eosdis.ornl.gov/] from the ORNL Distributed Active Archive Center, Oak Ridge National Laboratory, Oak Ridge, Tennessee, U.S.A.]

Page 41: Modelling Climate and Disturbance Effects on Net Ecosystem Productivity of Temperate and Boreal Forests Robert F. Grant* and colleagues in the Fluxnet-Canada

Soil water depletion occurred earlier as the Soil water depletion occurred earlier as the drought progresseddrought progressed

0.0

0.2

0.4

0.6

0.8

0.0

0.2

0.4

0.6

0.8

0 30 60 90 120 150 180 210 240 270 300 330 3600.0

0.2

0.4

0.6

0.8

Day of Year

Fig. 1

(c) 2003

(b) 2002

(a) 2001S

WC

(m3 m

-3)

TDR measurements 0 – 15 cm

Modelled water contents 0 – 15 cm

Page 42: Modelling Climate and Disturbance Effects on Net Ecosystem Productivity of Temperate and Boreal Forests Robert F. Grant* and colleagues in the Fluxnet-Canada

Forest water relations remained Forest water relations remained favourable during 2001favourable during 2001

c >= -2.0 MPa

high gc, but note midafternoon declines on some days

185 186 187 188 189 211 212 213 214 215 2160

2

4

6

8

10

12 (b)

Fig. 2

g c (

mm

h-1)

Day of Year

185 186 187 188 189 211 212 213 214 215 216-3.5

-3.0

-2.5

-2.0

-1.5

-1.0

-0.5

0.0 (a)

c (

MP

a)

Page 43: Modelling Climate and Disturbance Effects on Net Ecosystem Productivity of Temperate and Boreal Forests Robert F. Grant* and colleagues in the Fluxnet-Canada

LE effluxes and COLE effluxes and CO22 influxes were influxes were

rapid during 2001rapid during 2001

EC measurementsmodel values

LE > H

185 186 187 188 189 211 212 213 214 215 216-15-10-505

1015202530

185 186 187 188 189 211 212 213 214 215 216-500

-250

0

250

500

750

Fig. 2

(d)

CO

2 F

lux

(mo

l m-2 s

-1)

Day of Year

(c)

En

erg

y F

lux

(W m

-2)

Rn LE H

midafternoon declines during August

Page 44: Modelling Climate and Disturbance Effects on Net Ecosystem Productivity of Temperate and Boreal Forests Robert F. Grant* and colleagues in the Fluxnet-Canada

Forest water relations were adversely Forest water relations were adversely affected by drought later in 2002affected by drought later in 2002

c < -2.0 MPa, doesn’t recover overnight

large midafternoon declines in gc

193 194 195 196 197 211 212 213 214 215 2160

2

4

6

8

10

12 (b)

Fig. 3

g c (

mm

h-1)

Day of Year

193 194 195 196 197 211 212 213 214 215 216-3.5

-3.0

-2.5

-2.0

-1.5

-1.0

-0.5

0.0 (a)

c (

MP

a)

Page 45: Modelling Climate and Disturbance Effects on Net Ecosystem Productivity of Temperate and Boreal Forests Robert F. Grant* and colleagues in the Fluxnet-Canada

LE declined below H and COLE declined below H and CO22 influxes influxes

declined later in 2002declined later in 2002

LE < H

193 194 195 196 197 211 212 213 214 215 216-15-10-505

1015202530

193 194 195 196 197 211 212 213 214 215 216-500

-250

0

250

500

750

Fig. 3

(d)

CO

2 F

lux

(mo

l m-2 s

-1)

Day of Year

(c)

En

erg

y F

lux

(W m-2

)

Rn LE H

Page 46: Modelling Climate and Disturbance Effects on Net Ecosystem Productivity of Temperate and Boreal Forests Robert F. Grant* and colleagues in the Fluxnet-Canada

Forest water relations were adversely Forest water relations were adversely affected by drought during most of affected by drought during most of

20032003

c < -2.5 MPa

gc remains very low

181 182 183 184 185 211 212 213 214 215 2160

2

4

6

8

10

12 (b)

Fig. 4

g c (

mm

s-1)

Day of Year

181 182 183 184 185 211 212 213 214 215 216-3.5

-3.0

-2.5

-2.0

-1.5

-1.0

-0.5

0.0 (a)

c (

MP

a)

Page 47: Modelling Climate and Disturbance Effects on Net Ecosystem Productivity of Temperate and Boreal Forests Robert F. Grant* and colleagues in the Fluxnet-Canada

LE and COLE and CO22 influxes declined sharply in influxes declined sharply in

20032003

LE << H

188 189 190 191 192 211 212 213 214 215 216-15-10-505

1015202530

188 189 190 191 192 211 212 213 214 215 216-500

-250

0

250

500

750

Fig. 4

(d)

CO

2 F

lux

(m

ol m

-2 s

-1)

Day of Year

(c)

En

erg

y F

lux

(W m

-2)

Rn LE H

Page 48: Modelling Climate and Disturbance Effects on Net Ecosystem Productivity of Temperate and Boreal Forests Robert F. Grant* and colleagues in the Fluxnet-Canada

Soil COSoil CO22 effluxes are a major component of effluxes are a major component of

ecosystem COecosystem CO22 exchange exchange

dryingrainfall

183 184 185 186 187 220 221 222 223 224 225-10

-8

-6

-4

-2

0 (a) 2001

192 193 194 195 196 211 212 213 214 215 216-10

-8

-6

-4

-2

0

(c) 2003

(b) 2002

So

il C

O 2 F

lux (m

ol m-2

s-1)

188 189 190 191 192 211 212 213 214 215 216-10

-8

-6

-4

-2

0

Fig. 5 Day of Year

Page 49: Modelling Climate and Disturbance Effects on Net Ecosystem Productivity of Temperate and Boreal Forests Robert F. Grant* and colleagues in the Fluxnet-Canada

Daily NEP rose less and declined Daily NEP rose less and declined earlier as drought progressedearlier as drought progressed

0 30 60 90 120 150 180 210 240 270 300 330 360-6-4-202468

10 (c) 2003

Day of Year

-6-4-202468

10

Fig. 6

(b) 2002

Ne

t E

co

syste

m P

ro

du

ctivity (

g C

m-2 d

-1 )

-6-4-202468

10 (a) 2001

Page 50: Modelling Climate and Disturbance Effects on Net Ecosystem Productivity of Temperate and Boreal Forests Robert F. Grant* and colleagues in the Fluxnet-Canada

Annual carbon budgets at the Southern Old Aspen site modelled by ecosys (M) and estimated (E)† from EC flux and biometric measurements during three years of drought.

† from Barr et al. (2004)‡ all modelled autotrophic values are the sums of overstory (aspen) and understory (hazelnut) components.§ aspen and hazelnut respectively¥ from Griffis et al. (2004). Above-ground value for leaves and bole only

2001 2002 2003S E S E S E---------------------------------g C m-2 -----------------------------------

GPP 1791 1413‡,1615¥ 1287 1032‡ 1290 1057‡

Ra : above 613 353±51¥ 479 544 : below 308 452¥ 220 242 : total 921 805¥ 699 786NPP 870 810¥ 588 504Litter: above 254 211 208 :below 217 217 193 :exudation 147 127 100 : total 618 555 501 wood C 195 123 670 root C 48 -70 -40 reserve C 9 -42 25Rh 595 510¥ 509 481Soil resp’n 903 962±192¥ 726 723Eco. resp’n 1519 1046‡ 1205 888‡ 1267 954‡

1315±253¥

SOC 68 36 43 Soil CO2 -45 10 -23

NEP 275 320 82 125 23 91Peak LAI§ 3.7, 1.9 2.9, 2.3‡ 3.2, 1.8 2.1, 1.9‡ 3.1, 1.8 2.0, 2.1‡

NEP declined during drought

Page 51: Modelling Climate and Disturbance Effects on Net Ecosystem Productivity of Temperate and Boreal Forests Robert F. Grant* and colleagues in the Fluxnet-Canada

C is lost for several years after a fire, then C C is lost for several years after a fire, then C is gained during later regrowthis gained during later regrowth

net C loss for 10 – 15 years after fire

net C gain during later regrowth

net C gain calculated from EC measurements

-25 0 25 50 75 100 125 150 175 200 225-1200-1000-800-600-400-200

0200400

-25 0 25 50 75 100 125 150 175 200 22514

16

18

20

22

24

26

28 SOC wood C

Years Since Fire

SO

C (

kg

C m-2

)

0

2

4

6

8

10

12

14(b) Wo

od

C (k

g m -2)

(a)

NE

P (

g C

m-2 y

-1)

wood C growth compared with inventory data

NEP declines during drought

Page 52: Modelling Climate and Disturbance Effects on Net Ecosystem Productivity of Temperate and Boreal Forests Robert F. Grant* and colleagues in the Fluxnet-Canada

How would a longer 6-year droughts and climate How would a longer 6-year droughts and climate change affect these losses and gains of C?change affect these losses and gains of C?

-25 0 25 50 75 100 125 150 175 200 2250

5

10

15

20

25

Wo

od

C (

kg

m-2)

Year Since Fire

-25 0 25 50 75 100 125 150 175 200 225-1400-1200-1000-800-600-400-200

0200400600

NE

P (

g C

m-2 y

-1)

3-year drought, current climate 6-year drought, current climate 3-year drought, climate change 6-year drought, climate change

greater C losses during 6-year droughts

but greater C gains when rain is adequate

slower wood C growth under 6-year drought

faster wood C growth under climate change

Page 53: Modelling Climate and Disturbance Effects on Net Ecosystem Productivity of Temperate and Boreal Forests Robert F. Grant* and colleagues in the Fluxnet-Canada

Effect of Effect of Climate and Climate and Disturbance Disturbance on NEP of on NEP of

Boreal Boreal Jack Jack PinePine

Page 54: Modelling Climate and Disturbance Effects on Net Ecosystem Productivity of Temperate and Boreal Forests Robert F. Grant* and colleagues in the Fluxnet-Canada

Warming event over a boreal Warming event over a boreal coniferous stand in 2003coniferous stand in 2003

228 229 230 231 232 233 234 235 236 237 2380

2

4

6

8 VPD wind speed precipitation

Day of Year

D (

kP

a)

Win

d S

pee

d (

m s

-1)

0

1

2

3

4

5

Fig. 6

(b)

(a)

0

200

400

600

800 rad'n temp.

Radia

tio

n (

W m

-2)

0

5

10

15

20

25

30 Air T

em

p. (

oC)

Pre

cip

itatio

n (m

m h

-1)

Page 55: Modelling Climate and Disturbance Effects on Net Ecosystem Productivity of Temperate and Boreal Forests Robert F. Grant* and colleagues in the Fluxnet-Canada

228 229 230 231 232 233 234 235 236 237 238-600

-400

-200

0

200

400

600

-600

-400

-200

0

200

400

600

-600

-400

-200

0

200

400

600

Fig. 7

(c) SOJP

(b) HJP94

(a) HJP02

En

erg

y F

lux (

W m

-2)

Day of Year

Rn LE H

stomatal constraint to LE vs. H under high temperatures

Page 56: Modelling Climate and Disturbance Effects on Net Ecosystem Productivity of Temperate and Boreal Forests Robert F. Grant* and colleagues in the Fluxnet-Canada

High temperature reduces afternoon COHigh temperature reduces afternoon CO22 influxes influxes

and raises nighttime COand raises nighttime CO22 effluxes in conifers effluxes in conifers

228 229 230 231 232 233 234 235 236 237 238-10

-5

0

5

10

-10

-5

0

5

10

-10

-5

0

5

10

Fig. 9

(c) SOJP

(b)HJP94

(a) HJP02C

O 2 F

lux (m

ol m-2 s

-1)

Day of Year

Page 57: Modelling Climate and Disturbance Effects on Net Ecosystem Productivity of Temperate and Boreal Forests Robert F. Grant* and colleagues in the Fluxnet-Canada

Foliar N concentrations measured (M) and simulated (S) for boreal jack pine stands at different ages following clearcut. Foliar C in the model was converted to foliar DM at 0.45 g C g DM-1. 

Age (Date) N Concentration

  M S

  ----------mg N g DM-1 --------

2 (16 Sept. 2004)

  14.56

8 (4 Sept. 2002)

12.88 ± 0.29 10.48

10 (16 Sept. 2004)

15.11 ± 0.30 11.12

79 (4 Sept.2002)

8.96 ± 0.17 9.21

81 (16 Sept. 2004)

11.75 ± 0.11 9.34

Page 58: Modelling Climate and Disturbance Effects on Net Ecosystem Productivity of Temperate and Boreal Forests Robert F. Grant* and colleagues in the Fluxnet-Canada

C is lost for several years after clearcutting, C is lost for several years after clearcutting, then C is gained during later regrowththen C is gained during later regrowth

-400

-300

-200

-100

0

100

200

model

EC C stocks

(a)

NEP (

g C

m-2 y

-1)

0 50 100 150 200 250 3000

2

4

6

8

10 (b)

Fig. 10

So

il o

r W

oo

d C

(kg

C m-2

)

Years Since First Clearcut

wood C inventory wood C stocks wood C model SOC model

Page 59: Modelling Climate and Disturbance Effects on Net Ecosystem Productivity of Temperate and Boreal Forests Robert F. Grant* and colleagues in the Fluxnet-Canada

Climate change causes loss of coniferClimate change causes loss of conifer

0 50 100 150 200 250 300-400

-200

0

200

400 (c) ecosystem

NEP (

g C

m-2 y

-1)

Years Since First Clearcut

0

200

400

600

800 (b) bush

NPP (

g C

m-2 y

-1)

0

200

400

600

800

Fig. 11

current climate climate change

(a) jack pineNPP (

g C

m-2 y

-1)

and replacement by bushand replacement by bush

Page 60: Modelling Climate and Disturbance Effects on Net Ecosystem Productivity of Temperate and Boreal Forests Robert F. Grant* and colleagues in the Fluxnet-Canada

Climate change accelerates growth but Climate change accelerates growth but shortens life cycle of conifershortens life cycle of conifer

02468

101214 (a)

Wo

od

(kg

C m

-2)

current climate, N climate change, N current climate, 2N climate change, 2N

0 50 100 150 200 250 3005

6

7

8

9

10

Fig. 13

(b)

SO

C (

kg

C m-2)

Years Since First Clearcut

More rapid N More rapid N deposition deposition accelerates accelerates growthgrowth

Loss of conifer C under climate change Loss of conifer C under climate change partially offset by gain in SOC under bushpartially offset by gain in SOC under bush

Page 61: Modelling Climate and Disturbance Effects on Net Ecosystem Productivity of Temperate and Boreal Forests Robert F. Grant* and colleagues in the Fluxnet-Canada

Regional and Regional and National-Scale National-Scale

ModellingModelling

Page 62: Modelling Climate and Disturbance Effects on Net Ecosystem Productivity of Temperate and Boreal Forests Robert F. Grant* and colleagues in the Fluxnet-Canada

Non-disturbance Factors

TemperaturePrecipitationCO2 concentrationNitrogen deposition

HeterotrophicRespiration

Nitrogen mineralization and fixation

(9 pools)

AnnualNet Biome

Productivityy

DisturbanceFactors

Forest fireInsect-induced mortalityTimber harvest

HistoricalNPP Variation

Turnover Available Nutrient

Integrated Terrestrial Ecosystem Carbon Cycle Model

Ref.: Chen et al. (2003), Tellus

Page 63: Modelling Climate and Disturbance Effects on Net Ecosystem Productivity of Temperate and Boreal Forests Robert F. Grant* and colleagues in the Fluxnet-Canada

Chen et al. 2003, Tellus

Forest stand age is a key input to this model

Page 64: Modelling Climate and Disturbance Effects on Net Ecosystem Productivity of Temperate and Boreal Forests Robert F. Grant* and colleagues in the Fluxnet-Canada

InTEC output for net biome productivity

Page 65: Modelling Climate and Disturbance Effects on Net Ecosystem Productivity of Temperate and Boreal Forests Robert F. Grant* and colleagues in the Fluxnet-Canada

-150

-100

-50

0

50

100

150

200

250

300

1900 1920 1940 1960 1980 2000

Year

Net

Bio

me

Pro

du

ctiv

ity (T

g C

yr

-

1 )

All

Climate+Disturbance

CO2+Disturbance

N deposition+Disturbance

Disturbance

Canada’s NBP in InTEC depends on the factors Canada’s NBP in InTEC depends on the factors

affecting NBP that are considered in the modelaffecting NBP that are considered in the model

Due to climate, N and CO2

Ju and Chen, 2005, Hydrological Processes; Ju et al., 2005, Tellus

Page 66: Modelling Climate and Disturbance Effects on Net Ecosystem Productivity of Temperate and Boreal Forests Robert F. Grant* and colleagues in the Fluxnet-Canada

Global Scale Inverse Global Scale Inverse ModellingModelling

Page 67: Modelling Climate and Disturbance Effects on Net Ecosystem Productivity of Temperate and Boreal Forests Robert F. Grant* and colleagues in the Fluxnet-Canada

Recent Nested Global Inversion Results Recent Nested Global Inversion Results

USA: -0.89 ± 0.19 PgC/y (sink)

Canada: -0.063 ± 0.10 PgC/y (sink)

In PgC/yRed: sourceGreen: sink

Page 68: Modelling Climate and Disturbance Effects on Net Ecosystem Productivity of Temperate and Boreal Forests Robert F. Grant* and colleagues in the Fluxnet-Canada

Modelling in Fluxnet-Canada - Modelling in Fluxnet-Canada - Future DirectionsFuture Directions

Extend spatial scale of stand-level model (Extend spatial scale of stand-level model (ecosysecosys) ) to watersheds through 3-D landscape modelling to watersheds through 3-D landscape modelling (e.g. Grant, 2003). (e.g. Grant, 2003).

Compare stand-level and regional-level models Compare stand-level and regional-level models ((ecosysecosys and InTEC) at a common spatial scale. and InTEC) at a common spatial scale.

Use stand-level model at local scale and regional-Use stand-level model at local scale and regional-level model at regional and national scales to level model at regional and national scales to predict changes in ecosystem productivity under predict changes in ecosystem productivity under different climates and disturbancesdifferent climates and disturbances

Use stand-level and regional-level models to Use stand-level and regional-level models to constrain global inverse modelconstrain global inverse model