4. Testing the LAI model

1
Testing current understanding of Amazon phenology
using a Monte Carlo Markov Chain algorithm Silvia
Caldararu (First year PhD) Paul Palmer, Drew
Purves
1. Introduction Forests play an important role
in the global carbon cycle through photosynthesis
and respiration, and through the emission of
hydrocarbons. To quantify forest carbon budgets
and understand how they will respond to changing
environmental conditions, we need to understand
the factors that determine the temporal
variations of vegetation. Ground-based data are
sparse in time and space, making it difficult to
relate these data to larger spatial and temporal
scales.
4. Testing the LAI model To accurately fit a
model to a large data set, as in the case of the
global-scale space-borne LAI data, there is a
need for an efficient algorithm. We use the
Metropolis algorithm, also known as simulated
annealing, which uses a Monte Carlo Markov Chain
(MCMC) approach to explore model parameter
space. How does it work?
Satellite observations of vegetation optical
properties allow us to observe vegetation cover
at global scales with sub-1km resolution. These
data are useful to fill in gaps left by
ground-based data, particularly over remote
tropical regions. Leaf area index (LAI), the
ratio of one-sided leaf area to the underlying
ground area, can be calculated using a radiative
algorithm based on the fraction of light at
different wavelengths absorbed and reflected by
vegetation.
Step 1 Choose a starting point
Step 2 Make the jump
Step 3 Calculate the likelihood L for both
points.
Step 4 Take the decision If L1gtL0 accept the
new parameters If L1ltL0
2. The Amazon Our initial focus is on the Amazon
rain forest, one of the largest tropical forests
in the world, where our knowledge of phenology is
incomplete due to its large biodiversity (see
Figure).
Accept the new parameters with probability P
Reject the new parameters with probability (1-P)
The Amazon exhibits two seasons 1) a dry season
(July to November) and 2) a wet season
(December-May) while May-June are transition
months. Longer dry seasons occur over Eastern
Amazonia. Satellite observations reveal large, as
yet unexplained, seasonal swings in LAI over the
Amazon rainforest (see Figure).
Step 5 Go back to step 2.
After convergence, the resulting posterior
distribution can be averaged to give the desired
parameter values.

• 5. Future work
• Can we accurately reproduce observed space-based
  LAI data over the Amazon using a relatively
  simple model description of driving environmental
  factors?
• How will vegetation respond to possible changes
  in climate such as the Amazon forest die-back as
  predicted by the Hadley Centre climate model?
• Does the phenology over other tropical
  rainforests behave in the same way, e.g., can the
  Amazon model reproduce phenology over African
  rainforests?
• What are the implications of our new phenology
  model for understanding the size and location of
  reactive and unreactive carbon fluxes?

Myneni et al, PNAS, 2006
3. Modelling approach The observed variation in
LAI can be described as the difference between
the number of leaf layers lost and the number
added
Leaf gain and loss for any vegetation type will
be limited by a number of environmental factors,
but mainly temperature, sunlight, water
availability and soil fertility. The deep root
system of the Amazonian rainforest gives plants
access to the deeper soil layers, which are not
water depleted during the dry season. We have
developed a simple phenology model that can be
fitted to available data to test hypotheses about
environmental factors.