The Physics of Penguins: Recovering Spatial Information from Low-resolution Satellite Imagery

By Carole Hall

In an era of increasingly extreme weather events and natural disasters, the effects of human-driven climate change have become a focus of public discourse, policy formation, and academic research. Surprisingly, the remote environment of Antarctica is disproportionately afflicted by anthropogenic climate change—even though no permanent human populations reside there. Scientists, therefore, must establish reliable indicators to track Antarctica’s changing ecosystem.

Seabirds are particularly sensitive to shifts in their environments; their responses can manifest as changes in breeding success and behavior, alterations in diet, and variations in spatial distribution [6]. For Adélie penguins—colonial seabirds that live along the coast of Antarctica (see Figure 1 and Animation 1)—even subtle changes in nest position on the landscape impact breeding success and, ultimately, colony survival [7]. However, identifying colonies that are at risk of collapse with enough lead time to implement conservation measures remains a major challenge. The difficulty associated with data collection in Antarctica—which is expensive, time-consuming, and sometimes dangerous—exacerbates this already complicated problem. Remote sensing methods, such as the use of satellite imagery, offer a low-cost means of data collection over the necessary spatial scales to conserve penguin populations across this vast and inaccessible continent.

Figure 1. Adélie penguin colonies form complex shapes on the landscape. 1a. Adélie penguins and chicks at Madder Cliffs in Antarctica. 1b. Quadcopter aerial imagery of Adélie penguins nesting on Heroína Island in the Antarctic Danger Islands. Figure 1a courtesy of Michael Schrimpf; Figure 1b courtesy of Thomas Sayre-McCord, ©Woods Hole Oceanographic Institution/Massachusetts Institute of Technology.

Fortunately for researchers, Adélie penguins are prolific producers of waste; their pink-tinted guano (the accumulated excrement of bats and seabirds) is visible in satellite imagery. Because guano fills the area of nesting penguins, it allows scientists to directly measure the colony’s areal extent. In fact, previous studies have discovered formerly unknown colonies entirely from their guano stains in satellite imagery [1]. Since Adélies require dry nesting conditions on bare rock to successfully breed during the austral summer season—and since predatory skuas primarily target eggs and chicks on colony perimeters—the spatial configurations of these penguins are indicative of breeding success (see Figure 2) [5]. The availability of aerial colony imagery and trend information should make it easy for researchers to study the relationship between colony shape and colony health over time. However, the sub-meter resolution imagery that typically delineates colony boundaries has only been available for a few decades. When looking further into the past, scientists will have to utilize the abundant low-resolution imagery that is available through NASA’s Landsat satellite program, which originated in the early 1970s [2].

We aim to extract sufficient information from these low-resolution (30 m by 30 m per pixel) images in order to reconstruct colony shape over time. Since the process of identifying guano in Landsat images is well established [4], we can infer the percentage of guano coverage in a single pixel by considering the number of times that guano is detected in a pixel across repeated images within a single breeding season (see Figure 3). Given these coverage estimates, we must then reconstruct the colony’s true shape in a way that encompasses the aggregating behavior of penguins yet remains faithful to the coverage estimates from Landsat observations.

Figure 2. Sample Adélie penguin colony shapes. 2a. Beagle Island. 2b. Brash Island. Figure courtesy of Carole Hall.

The presence of predatory skuas that target isolated nests incentivizes Adélie penguins to nest near each other; at the same time, competition for nest-building materials prevents them from nesting so close to one another that a penguin sitting on one nest can steal stones from its neighbor [5]. The combination of repulsion between nests at short ranges and attraction at longer ranges is thus analogous to several physical systems with well-explored dynamics. In particular, we can use the pairwise Lennard-Jones interaction as a starting point to study the “physics” of penguins within the colony:

\[V_{LJ}(r) = 4 \varepsilon \left[\left(\frac{\sigma}{r} \right)^{12} - \left(\frac{\sigma}{r} \right)^6 \right].\]

This formula gives the Lennard-Jones expression for potential energy, which is a function of the distance between two particles \(r\). Here, \(\sigma\) is the distance at which the potential between these particles is zero and \(\varepsilon\) is the particles’ potential well depth. A previous study on king penguins—which do not build nests and instead tuck their eggs between a bulge of skin and their feet—argued that colonies displayed dynamics of a two-dimensional fluid under a Lennard-Jones-like interaction potential [3]. In our case, the particles are Adélie nests, which are static within a season but free to move between breeding seasons in response to local conditions. Using the aforementioned guano coverage model, we can estimate the number of nests that lie within each 30 m by 30 m pixel in the original Landsat imagery. If we assume that an Adélie parent’s decision to nest in a given location within the pixel is primarily affected by the presence of other nests, then we can employ a pair potential like Lennard-Jones to simulate this process until we reach an ideal configuration. In short, our goal is to use this fairly simple model of interactions to reconstruct high-resolution colony shapes based on the related physics, constrained by information found from low-resolution Landsat imagery.

Figure 3. While a single Landsat image provides a binary mask that indicates detected guano (3a), the use of repeated images over the course of the season allows us to estimate the percentage of each pixel that is covered in guano (3b). This estimation forms the input to our molecular dynamics model for shape reconstruction. Figure courtesy of Carole Hall.

Molecular dynamics (MD) is a sampling method that relies upon Newton’s laws of motion; researchers often utilize it to find minimum potential energy states in processes such as protein-ligand complex formation and protein folding. We employ MD to sample nest configurations until convergence to a minimum energy is attained (under the constraint that the discretized pixel areas maintain constant nest density). This process randomly generates nests according to our coverage model on a per-pixel area basis; the nests are simulated using MD, for which a Lennard-Jones potential dictates the pairwise interactions. We maintain the density constraint by enforcing hard boundaries at the edges of each pixel to ensure that nests always remain within their initial 30 m by 30 m block.

In our preliminary test of this method, we down-sampled an annotation of a colony shape from high-resolution aerial imagery and aligned it to the corresponding 30 m by 30 m resolution Landsat grid of the original colony site. We then performed an MD simulation to find an energetically favorable configuration of nests constrained by the coverage estimates in the Landsat grid. Next, we compared the configuration that we simulated from the down-sampled information with the original high-resolution annotated data; the initial tests yielded promising results (see Figure 4).

Figure 4. Comparison between the original binary map of guano (4a) and the high-resolution shape that is recovered using our molecular dynamics protocol (4b) for the Beagle Island Adélie penguin colony; each is overlaid with the original high-resolution colony annotation (in pink). The blue portions in 4b identify areas where the simulated configuration differs from the ground-truth colony annotation. Figure courtesy of Carole Hall.

Our upcoming steps include fitting Lennard-Jones simulation parameters to drone imagery—wherein individual nests are clearly visible—in order to more precisely estimate the parameters of the Lennard-Jones potential. In addition, we intend to validate the reconstruction over a range of colony conditions. Since landscape terrain plays such a critical role in the shapes of penguin colonies, we also plan to investigate possible methods to factor specific topographic features into our MD-inspired shape reconstruction.

References
[1] Borowicz, A., McDowall, P., Youngflesh, C., Sayre-McCord, T., Clucas, G., Herman, R., … Lynch, H.J. (2018). Multi-modal survey of Adélie penguin mega-colonies reveals the danger islands as a seabird hotspot. Sci. Rep., 8(1), 3926.
[2] Ferrigno, J.G., Williams Jr., R.S., Rosanova, C.E., Lucchitta, B.K., & Swithinbank, C. (1998). Analysis of coastal change in Marie Byrd Land and Ellsworth Land, West Antarctica, using Landsat imagery. Ann. Glaciol., 27, 33-40.
[3] Gerum, R., Richter, S., Fabry, B., Le Bohec, C., Bonadonna, F., Nesterova, A., & Zitterbart, D.P. (2018). Structural organisation and dynamics in king penguin colonies. J. Phys. D Appl. Phys., 51(16), 164004.
[4] Lynch, H.J., & Schwaller, M.R. (2014). Mapping the abundance and distribution of Adélie penguins using Landsat-7: First steps towards an integrated multi-sensor pipeline for tracking populations at the continental scale. PLoS One, 9(11), e113301.
[5] McDowall, P.S., & Lynch, H.J. (2019). When the “selfish herd” becomes the “frozen herd”: Spatial dynamics and population persistence in a colonial seabird. Ecology, 100(10), e02823.
[6] Sydeman, W.J., Thompson, S.A., & Kitaysky, A. (2012). Seabirds and climate change: Roadmap for the future. Mar. Ecol. Prog. Ser., 454, 107-117.
[7] Tenaza, R. (1971). Behavior and nesting success relative to nest location in Adelie penguins (Pygoscelis adeliae). Condor, 73(1), 81-92.

Carole Hall is a Ph.D. student in applied mathematics and statistics with a focus on computational biology at Stony Brook University. Her main research interests include image processing, geospatial analysis, and molecular modeling. Hall hopes to continue using quantitative methods to contribute to fields like ecology, earth systems, and medicine.