Principal Investigator

At a Glance

Tropical forests represent a key terrestrial carbon sink, yet their levels of carbon storage have been challenging to estimate due to the multi-layered structure of tropical forest tree communities. The Pacala group has used data from Panama’s Barrow Colorado Island Rainforest to develop a model for investigating carbon storage in tropical forests with improved accuracy. Another challenge is understanding methane emissions from oil and gas infrastructure, due to the ephemeral nature of high-emitting sources. The Pacala group has created a new method for estimating methane emissions that combines systematic and biased sampling data with meteorological factors.


Research Highlight

Modeling Tropical Forest Carbon Storage

The terrestrial carbon sink is thought to be dominated by tropical forests. Tropical forests store roughly twice as much carbon in living trees as temperate forests per unit area. About half of this disparity stems from the rapid year-round growth of tropical trees, which creates a few extremely large individuals.

The other half is caused by a spectacular difference that temperate zone dwellers notice immediately when first walking into a tropical forest: if one drops a weighted line from a helicopter through the canopy of a temperate forest, the weight will, on average, pass through the crown of one canopy tree, and sometimes (i.e. a quarter of the time), the crown of one sapling before hitting the ground. Oldgrowth temperate forests are often compared to cathedrals because of this property.

If one drops the same line through a tropical forest, it will pass through three or four tree crowns on average before hitting the ground. In other words, tropical forests have a canopy, a sub-canopy, a subsub- canopy, and finally, a layer of saplings with some space between their crowns. This material in the middle (the sub-canopy and sub-sub-canopy) is the main reason why tropical forests appear so full, chaotic, and claustrophobic to temperate dwellers. Again, the material in the middle is important to the global carbon cycle because it accounts for half the difference between the living carbon in tropical and temperate forests. Although our Earth System models can predict the existence of very large trees in the tropics, they have not been able to predict the material in the middle.

The most amazing thing about the plant growth in the middle is that it is highly organized in every moist tropical forest, despite its tangled appearance. If one plots the logarithm of tree diameter on the horizontal axis against the logarithm of tree abundance on the vertical axis, one sees that the material in the middle—all but the smallest and largest size classes—follows a tight inverse-square power law: a tree with twice the stem diameter has one-fourth the abundance. (Figure 1.1.1 shows the plot for the Barrow Colorado Island Rainforest in Panama). In contrast, size distributions for the temperate zone and for the driest tropical forests do not follow a power law.

The Pacala group has shown that the power law is a consequence of competition for light following large disturbances, many of which are created by thunderstorm microbursts. They developed a simple model that accurately predicts the data (see Figure 1.1.1) and showed with an extensive data analysis that the mechanism in the model is also operating in an extensively studied Panamanian rainforest. The mechanism in the model has already been added to the Geophysical Fluid Dynamics Laboratory/Princeton Earth System Model. Other modeling centers will also add to this mechanism to predict the fate of rainforest carbon. The publication reporting this model won the CMI Best Paper Award this year.1

Figure 1.1.1. Size distribution of trees in a tropical forest. P(d) is the fraction of total stems with diameter d, blue bars indicate confidence limits, black line is an inverse-square (y = x-2) power law, red line is from a simple analytically tractable model, and gray bars are predictions of a slightly more complex simulation model. Parameters in both models were estimated from Barrow Colorado Island (BCI) Rainforest data.

Estimating Methane Emissions

Other recent work from the Pacala group focuses on methane emissions from the Barnett Shale region in Texas. Attempts to measure fugitive emissions are bedeviled by the fact that most of the emitted methane at any one time is due to a few sources (2-5% of the sources). High-emitting sources are also ephemeral, and typically last for hours to days, so that the high-emissions sources jump around in space.

Previous studies have systematically sampled methane emissions to achieve an unbiased sample, but this procedure cannot provide a large enough sample of the rare high-emitters to characterize them with any accuracy. Moreover, a systematic sample has a counter-intuitively high probability of underestimating total emissions when total emissions are dominated by ephemeral and rare high emitters. A recent study claims that all previous emissions estimates, except one by the Pacala group, underestimate fugitive emissions by a factor of two for this reason.2

In its study of the Barnett region, the Pacala group supplemented a systematic sample of emissions from oil and gas infrastructure with a sample deliberately biased toward high emitters (to achieve a sufficient sample size of the large sources). When a source emits methane, the gas spreads horizontally and vertically as it drifts downwind, until its concentration falls beneath the detection limit of an instrument. This means that a source has a detectable plume length that grows with the size of the source and depends on meteorological conditions. By driving a grid of roads with a methane detector, one can detect and identify upwind sources. By inverting a meteorological model, one can also estimate the size of the emission of methane from a given source. But this method is biased toward high emitters because the long plumes of high-emitting sources are more likely to be detected than the short plumes of low emitters. This bias is large; it artificially elevated the mean emissions level in the Barnett campaign by a factor of 80.

Figure 1.1.2. Former CMI postdoctoral fellow Caroline Farrior was presented with the 2016 CMI Best Paper Award by Gardiner Hill, Director of Carbon Solutions, during a ceremony this past February. Farrior, who worked in Stephen Pacala’s lab, was selected for her paper “Dominance of the suppressed: Power-law size structure in tropical forests” in recognition of the important finding that commonalities among tropical forests in their structure are due to simple and biologically intuitive mechanisms. The paper was published in the journal Science in early 2016.

To overcome this bias, the Pacala group developed a statistical method that correctly knits together systematic samples and biased samples obtained by searching a grid of roads. For the first time, this method successfully matched bottom-up estimates from on-the-ground samples with topdown estimates from aircraft, which greatly increased confidence in both types of estimates. This new method solved a long-standing problem, and has now greatly streamlined methane emissions estimates for other regions.

Other Work

In 2015, the Pacala group also produced a prototype of the terrestrial sink for a new Geophysical Fluid Dynamics Laboratory (GFDL)/Princeton carbon cycle model3 and addressed the interaction of the hydrological and carbon cycles, focusing on drought kill.4



  1. Farrior, C.E., S.A. Bohlman, S. Hubbell, and S.W. Pacala, 2016. Dominance of the suppressed: Power-law size structure in tropical forests. Science, 351(6269): 155-157. doi:10.1126/science.aad0592.
  2. Zavala-Araiza, D., D.R. Lyon, R.A. Alvarez, K.J. Davis, R. Harriss, S.C. Herndon, A. Karion, E.A. Kort, B.K. Lamb, X. Lan, A.J. Marchesei, S.W. Pacala, A.L. Robinson, P.B. Shepson, C. Sweeney, R. Talbot, A. Townsend-Small, T.I. Yacovitch, D. Zimmerle, and S.P. Hamburg, 2015. Reconciling divergent estimates of oil and gas methane emissions. Proc. Natl. Acad. Sci., 112(51): 15597-15602. doi:10.1073/pnas.1522126112.
  3. Weng, E.S., S. Malyshev, J.W. Lichstein, C.E. Farrior, R. Dybzinski, T. Zhang, E. Shevliakova, and S.W. Pacala, 2015. Scaling from individual trees to forests in an Earth system modeling framework using a mathematically tractable model of height-structured competition. Biogeosciences, 12(9): 2655-2694. doi:10.5194/bg-12-2655-2015.
  4. Anderegg, W.R.L., C. Schwalm, F. Biondi, J.J. Camarero, G. Koch, M. Litvak, K. Ogle, J.D. Shaw, E. Shevliakova, A.P. Williams, A. Wolf, E. Ziaco, and S. Pacala, 2015. Pervasive drought legacies in forest ecosystems and their implications for carbon cycle models. Science, 349(624): 528-532. doi:10.1126/science.aab1833.