Climate and the Amazonian Carbon Balance

Abstract

Amazonia is an important part of the global climate system and its rainforests host a large ‘labile’ carbon pool which may possibly feedback on climate on rather short timescales. Since the 1980s, the mean temperature in Amazonia has steadily increased and the hydrological cycle has intensified with the number of strong droughts, e.g. in 2005 and 2010, and severe floods increasing and, on average, wet season precipitation rising. The main determinants of the carbon balance of the vegetation have been a multi-decadal natural forest carbon sink and carbon loss caused by deforestation, and these two processes compensate each other approximately. Deforestation in the Brazilian Amazon, covering the largest fraction of the Basin, has encouragingly decreased over the last decade. Most recent droughts (2005, 2010) have, however, indicated a weakening of the forest sink, possibly indicating a longer term change as a result of ongoing changes in climate.

Appendix: Formalisation of Book Keeping Approach to Estimate Carbon Fluxes Caused by Deforestation Based on Data of Area Deforested and Simple Models of Woody Debris Decomposition and Vegetation Re-establishment

1.1 Carbon Release to the Atmosphere After Deforestation

Starting from Eq. (6.2) describing carbon release of woody debris after deforestation and using an annual time step Δt = 1 we obtain

$$ C\left({t}_{\mathrm{def}}+\Delta t,{t}_{\mathrm{def}}\right)=\left(1-\lambda \right)C\left(t,{t}_{\mathrm{def}}\right),C\left(t,{t}_{\mathrm{def}}\right)={\left(1-\lambda \right)}^{t-{t}_{\mathrm{def}}}C\left({t}_{\mathrm{def}},{t}_{\mathrm{def}}\right) $$

(6.9)

where C(t _def,t _def) is the originally left over woody debris carbon not immediately released at the time t _def of deforestation and C(t,t _def) the remaining not yet decomposed woody debris carbon. The flux to the atmosphere at time t caused by decomposition of leftover debris caused by deforestation at time t _def in the past is

$$ \begin{array}{l}{F}_{\mathrm{ld}\to \mathrm{at}}^{\mathrm{res}}\left(t,{t}_{\mathrm{def}}\right)=-\Big(\left(C\left(t+\Delta t,{t}_{\mathrm{def}}\right)-C\left(t,{t}_{\mathrm{def}}\right)\right)=\dots =\\ {}={\lambda}_{\mathrm{res}}{\left(1-{\lambda}_{\mathrm{res}}\right)}^{t-{t}_{\mathrm{def}}-1}C\left({t}_{\mathrm{def}},{t}_{\mathrm{def}}\right).\end{array} $$

(6.10)

The total flux to the atmosphere at time t due to deforestation in the past is then given by the sum of all contributions from the beginning of deforestation around 1970 until today or

$$ \begin{array}{ll}{F}_{\mathrm{ld}\to \mathrm{at}}^{\mathrm{res},\mathrm{tot}}(t)=& \underset{\begin{array}{l}\mathrm{carbon}\;\mathrm{immediately}\;\mathrm{released}\;\mathrm{during}\\ {}\mathrm{deforestation}\;\mathrm{in}\;\mathrm{y}\mathrm{ear}\;t\end{array}}{\underbrace{\alpha \cdot {r}_{C:M}\cdot {B}_{\mathrm{res}}\cdot \Delta A(t)}}\hfill \\ {}& +\underset{\mathrm{carbon}\;\mathrm{released}\;\mathrm{in}\;\mathrm{y}\mathrm{ear}\;t\;\mathrm{b}\mathrm{y}\;\mathrm{decomposing}\;\mathrm{leftover}\;\mathrm{debris}\;\mathrm{from}\;\mathrm{deforestation}\;\mathrm{in}\;\mathrm{previous}\;\mathrm{y}\mathrm{ear}\mathrm{s}}{\underbrace{\lambda_{\mathrm{res}}{\displaystyle \sum_{t_{\mathrm{def}}=1970}^t{\left(1-{\lambda}_{\mathrm{res}}\right)}^{t-{t}_{\mathrm{def}}}}\left\{\left(1-\alpha \right)\cdot {r}_{C:M}\cdot {B}_{\mathrm{trees}}+{f}_{\mathrm{rels}}\cdot {C}_{\mathrm{soil}}\right\}\cdot \Delta A\left({t}_{\mathrm{def}}\right)}}\hfill \end{array} $$

(6.11)

with symbols explained in the main text and/or Table 6.1.

1.2 Carbon Uptake from the Atmosphere by Re-establishing land Vegetation

For the assumed time course of carbon uptake by regrowth after deforestation in year t _def (Eq. 6.3) the flux from atmosphere to land vegetation in year t is

$$ \begin{array}{l}{F}_{\mathrm{at}\to \mathrm{l}\mathrm{d}}^{\mathrm{rgrwth}}\left(t,{t}_{\mathrm{def}}\right)=C\left(t+\Delta t,{t}_{\mathrm{def}}\right)-C\left(t,{t}_{\mathrm{def}}\right)=\dots =\\ {}=\left(1-{e}^{-{\lambda}_{\mathrm{rgrwth}}\cdot \varDelta t}\right)\cdot {e}^{-{\lambda}_{\mathrm{rgrwth}}\left(t-{t}_{\mathrm{def}}\right)}\cdot {C}_{\mathrm{steady}}\end{array} $$

(6.12)

with Δt = 1 (in units of years, the time step we are using for summing contributions because satellite data of deforested area from Brazil are annual). The total flux of carbon at time t from the atmosphere to land due to regrowth in the wake of all deforestation events in the past is then

$$ {F}_{\mathrm{at}\to \mathrm{l}\mathrm{d}}^{\mathrm{rgrwth},\mathrm{tot}}(t)={r}_{C:M}\cdot {B}_{\mathrm{veg}}\cdot \left(1-{e}^{-{\lambda}_{\mathrm{rgrwth}}\cdot \Delta t}\right)\cdot {\displaystyle \sum_{t_{\mathrm{def}}=1970}^{t-1}{e}^{-{\lambda}_{\mathrm{rgrwth}}\cdot \left(t-{t}_{\mathrm{def}}\right)}\Delta A\left({t}_{\mathrm{def}}\right)}. $$

(6.13)

B _veg is the mass per area of the new vegetation type once fully established and as above Δt = 1.