M. Gloor, O.L. Phillips, J. Lloyd, S.L. Lewis, Y. Malhi, T.R. Baker, G. Lopez-Gonzalez, J. Peacock

S. Almeida, E. Alvarez, A.C. Alves de Oliveira, I. Amaral, S. Andelman, L. Arroyo, G. Aymard, O. Banki, L. Blanc, D. Bonal, P. Brando, K.-J. Chao, J. Chave, N. Davila,

T. Edwin, J. Espejo, A. di Fiore, T. Feldpausch, A. Freitas, R. Herrera, N. Higuchi, E. Honorio, E. Jiménez, T. Killeen, W. Laurance, C. Mendoza, A. Montegudo,

H. Nascimento, D. Neill, D. Nepstad, P. Núñez Vargas, J. Olivier, M.C. Penuela, A. Peña Cruz, A. Prieto, N. Pitman, C. Quesada, R. Salamão, M. Schwarz, J. Stropp, A. F. Ramírez, H. Ramírez, A. Rudas, H. ter Steege, N. Silva, A. Torres, J. Terborgh,

A. R. Vásquez, G. van der Heijden

AcknowledgementsBruce Nelson, Laurens Poorter, Fernando Santo-Espirito, Aaron

Clauset, C.T. Shalizi

Does the disturbance hypothesis explain the biomassincrease in basin-wide Amazon forest plot data?

A simple data-based analysis

Outline

1. Introduction on large-scale forest census results2. Hypothesis why trends wrongly interpreted3. Rainfor and Blowdown data as basis for simulator4. Implications

Land biomass inventories

Forest census, Peru

Possibly large-scale response of tropical rainforests to a changing atmospheric environment and climate

Implications on: - global carbon budget and greenhouse warming - future feedbacks of forests on climate

Relevance

Positive Growth trends are artefact of1. ‘Slow in rapid out’ effect which biases results

2. Basin wide catastrophe responsible for observed growth trends

Hypothesis

a) Old-growth forest plots (RAINFOR network)

135 plots 226.2 ha 11.3 years /plot

Fairly good coverage of main axis of known aboveground biomass gains controls

b) Blow-down data from Bruce Nelson estimated from Landsat images (thanks again!)

The Data

€

dAGB

dt= g(AGB) −μ

AGB aboveground biomass

g stochastic function − from data

μ stochastic function − from data

The Model

LossesRAINFOR

€

p1yr(m) = λe−λm

probability of mass loss m per hectare and year

€

p2yr(m) = p1yr(m1)

mass lossduring year 1

1 2 3 p1yr(m− m1)

mass lossduring year 2

1 2 4 3 4 m1 <=m

∫ dm1

€

pnyr(m) =(λm)n−1

(n−1)!λe−λm

e.g. for ,

similarly for n year census interval€

p1yr(m) = λe−λm

€

p2yr(m) = (λm)λe−λm

€

p1yr(x) =α −1

xmin

x

xmin

⎛

⎝ ⎜

⎞

⎠ ⎟

−α

Blow-downs (Nelson et al. 1994)

Goldstein M. L., Morris S.A., Yen G. G. (2004) Problems with fitting to the power law distribution. Eur. Phys. J. B 41, 225-258. Clauset A., Shalizi C.T. Newman M.E.J (2007) Power law distri- butions in empirical data. [http://physics,data-an] arXiv:0706.1062v1

‘power law - fat tail’

=3.1 Maximum Likelihood Estimator (Ordinary Least Squares not appropriate method)

Bootstrapping: power law plausible distribution for Nelson blow down data

Mathematical nature of RAINFORmortality stats

€

p1yr(m)∝λe−λm , m < m0

m−2, m ≥ m0

⎧ ⎨ ⎩

Models for biomass losses

Mixed exponential - power law model

Pure exponential model

€

p1yr(m) = λe−λm

Model for biomass gains

€

g = N(μ,σ )

with μ = 5.2 / 6.1 t ha−1 yr−1,

σ =1.5 / 1.6 t ha−1 yr−1

SimulatorResults

Statistical significance of biomass gains

E Amazon W Amazon All Amazon

Exp. model 0.19 0.19 0.14Mixed model 0.41 0.41 0.30

€

(σ / N ) /μ

N number of censusesPooling of results from different census intervals: exploit that variance grows linearly with observation period-> permits to scale variances to one-year periods - then use common rule to combine independent estimates

Severity of disturbance and Return times

€

P(X ≥ m) = p(x)dx =m

∞

∫ 1− p(x)dx = 1− P(m)0

m

∫Probability of mass loss event with loss > m

where

€

P(m) ≡ p(x)dx0

m

∫

€

τ ≥1

P(X ≥ m)=

1

1− P(m)

Return time of such an event

Biomass loss associated with a given return time

€

m(τ ) = P−1(1−1

τ)

Percentile Return time Mortality loss (%) (yr) (t ha-1 yr-1) (%) (t ha-1 yr-1) (%) (W / E) (W / E) All Amazon

Exponential Model Mixed Model

95 20 12.5 / 13.6 5.0 / 3.6 12.8 3.499 100 19.1 / 20.9 7.6 / 5.5 25.4 6.799.9 1000 28.8 / 31.4 11.5 / 8.3 96.4 25.4

Severity of disturbance and Return times

Summary

Statistical power of RAINFOR network forest census data is sufficient to detect a positive above ground biomass signal; ‘Slow in - rapid out’ effect is covered by the network; Large-scale disturbances are just really, really rare

Highly likely there is indeed an Amazon wide forest response growth response to exterior forcing

Exciting !

Thank you for your Attention !

Thank you for your attention

€

var =1

nλ2

Observed and predicted decrease in variance with increasing census interval according to exponential model

n (yr): census interval

Summary of observed aboveground biomass gains’ significance base d on th eratiobetween modelled sample standard deviation σ an d observe d me anμ of biomassgains.

Obs Peri od E Amazon W Amazon All Amazon(yr) # censuses (σ/μ) #censuses (σ/μ) #censuses (σ/μ)

(0.5,1.5) 121 0.40 27 0.87 148 0.37(1.5,2.5) 80 0.35 21 0.67 101 0.31(2.5,3.5) 18 0.60 30 0.47 48 0.37(3.5,4.5) 24 0.45 35 0.38 59 0.39(4.5,5.5) 21 0.44 49 0.28 70 0.24…*A ll 303 0.19 178 0.19 481 0.14

* Gi ventha t variance grows linearl ywith observation period and assuming independence

of plot measurements we can scale variances to one ye ar periods and use ∑=iitot22 11σσ to

obtain the ratio σ/μ for plots from different observation period lengths.

Main axis of forest biomass gains controls

2006.70

2006.40

2006.10

2005.80

2005.50

2005.20

2004.90

2004.60

2004.30

2004.00

2003.70

2003.40

2003.10

2002.80

2002.50

2002.20

2001.90

2001.60

2001.30

2001.00

2000.70

2000.40

2000.10

1999.80

1999.50

1999.20

1998.90

1998.60

1998.30

1998.00

1997.70

1997.40

1997.10

1996.80

1996.50

1996.20

1995.90

1995.60

1995.30

1995.00

1994.70

1994.40

1994.10

1993.80

1993.50

1993.20

1992.90

1992.60

1992.30

1992.00

1991.70

1991.40

1991.10

1990.80

1990.50

1990.20

1989.90

1989.60

1989.30

1989.00

1988.70

1988.40

1988.10

1987.80

1987.50

1987.20

1986.90

1986.60

1986.30

1986.00

1985.70

1985.40

1985.10

1984.80

1984.50

1984.20

1983.90

1983.60

1983.30

1983.00

1982.70

1982.40

1982.10

1981.80

1981.50

1981.20

rounddecimal

4.00

3.00

2.00

1.00

0.00

-1.00

-2.00

95% CI netratechangeChambersdbh1

Courtesy Oliver Phillips

Thank you for your attention