Mathematics of Planet Earth

Workshop Announcement

The planet is constantly changing, but the pace of change has accelerated as a result of human activity. Construction and deforestation change habitats; fishing affects fish populations; fossil fuel combustion leads to atmospheric greenhouse gas buildup; commerce and transport introduce non-native species. We need to monitor global change to understand processes leading to change, learn how to mitigate and adapt to its effects, determine if we are meeting goals for our planet, and get early warning of dangerous trends.

Observation: This is the “age of observation,” with distributed and central repositories, sensor-driven, and diverse. The unprecedented volume of data poses immense challenges: Data sources can be inconsistent or uncertain; data arises at different scales; we need tools for detecting anomalies from the ´normal¡ pattern. We will explore different planetary observation processes and the mathematical sciences challenges they pose, focusing on modeling, data collection, and data assimilation.

Choosing what to watch and how often are key challenges. Climate data collected by agencies such as NOAA, the National Climate Data Center, and the Northeast Regional Climate Office are mostly physical, including precipitation, temperature and sea level rise. As climate modeling evolves, it becomes clear that more diverse data are needed, including greenhouse gas emissions, demographic projections, socioeconomic changes, and energy use or land use/urbanization. There is interplay between monitoring and modeling. The frequency, location, and spatial resolution of data collected are important and may depend on data use. For example, drainage engineers might need precipitation data more frequently than climate scientists. As a second example, the National Ecological Observatory Network is collecting data at 20 sites across the US to get a continent-wide picture of the impacts of climate change, land use change, and invasive species on natural resources and biodiversity. Since the 20 sites represent the entire continent, their selection was critical. We will explore how such sites are selected and what environmental variables drive selection.

Because many different variables, each with its own spatiotemporal spectrum, are necessary for characterizing planetary states, a wide array of sampling and monitoring designs with spatiotemporal attributes specific to the variable and application are needed. Illustrative examples are the effort to assess carbon pools, losses, and sequestration in hard-to-reach tropical forests, which faces challenges involving data requirements and acquisition methods for constructing remote sensing-based maps of sufficient quality to serve as the basis for assessing carbon trends. Similar issues arise in water monitoring, air pollution, assessment of ecological resources, and the monitoring of US forests. When samples are costly or difficult to obtain and there is large uncertainty, methods of optimal learning may be particularly relevant.

Metrics: Measuring global change and making better policy decisions requires metrics of planetary health. As noted in connection with climate change monitoring in New York City (NYC) “what cannot be measured cannot be managed” provides a variety of variables that might be used to develop a metric of impact of sea level rise for adaptation planning: brownfield cleanup acreage, flight delays, beach erosion, ferry service interruptions, salt water intrusion, water treatment plant operations, and emergency services demands. Combining these into useful metrics is a major challenge.

Biodiversity is another example. We are in the midst of one of the greatest mass extinctions in earth’s history; yet, we lack a good measure for biodiversity. The Convention on Biodiversity set a goal of achieving a significant reduction in biodiversity loss by 2010, but how can we measure progress? Biodiversity encompasses notions of species diversity, genetic diversity within species, ecosystem diversity, and ecosystem services, each needing to be made precise. Many biodiversity indices have been proposed over the years: richness or abundance of species; “evenness” in distribution of species as measured using Shannon entropy or the Simpson index; and combinations of richness and evenness. These approaches disregard spatial distribution, may count unwanted species, or miss the importance of indicator species that give early warning of environmental stress. We will consider various biodiversity indices; discuss the effect of sampling on diversity estimates; discuss axioms for biodiversity measures; consider approaches that depend on partial orders defined from vectors of species abundance; and study “consistent” families of biodiversity indices. We will look at similar issues for other metrics of global change, using biodiversity as a starting point.

Effects of Global Change: Global change affects urban services, disease, and natural habitats. A NYC Panel on Climate Change report highlights NYC infrastructure most vulnerable to climate change. It notes that rising temperatures accelerate degradation of materials, more intense precipitation may lead to inland flooding, and rising sea levels may result in increased saltwater inundation and river flooding. Sectors potentially affected by infrastructure damage include energy; construction; transportation; water supply; waste; and communications. Each of these potentially impacts other sectors, which calls for mathematical modeling and statistical analysis. We will review such impacts, outline mathematical approaches to modeling them, and discuss resulting modeling and statistical challenges. Traditional approaches to investment for adaptation and mitigation involve cost-benefit analysis; however, such approaches will not be adequate under global change because many benefits and costs cannot be readily “monetized.” This calls for new, risk-based approaches to evaluating adaptation and mitigation strategies.

Global change impacts infectious disease. Disease incidence is affected by changing climate and land use; migration of people, animals and disease vectors; and emergence of other diseases. For example, malaria incidence can significantly worsen with climate change. Temperature crucially impacts the population dynamics of its mosquito vector, and rainfall affects the carrying capacity for mosquito larvae, though models depending on average rainfall miss important spatial and temporal variation. Cholera, Lyme disease, and meningocccal meningitis may also be affected and abetted by global climate change. For instance, is the increasing incidence of Lyme disease in Canada due to climate change or to normal range expansion for ticks carrying the disease or to changing migration patterns of birds carrying it into Canada? We need to understand complex interactions among tick life cycles, bird migrations, climate, etc. We will address these eco-climatic complexities, exploring long-term ecological datasets and ecological niche modeling. Many existing landscape ecology, GIS and remote sensing models can be leveraged to assess the changes in vector populations. But models focusing on key predictive factors are needed. Risk of such vector-borne diseases as Lyme disease, West Nile virus, Rocky Mountain spotted fever, ehrlichiosis and many others depends on expected frequency of encounter with a competent vector and disease prevalence within that vector population. Locations that can harbor a given vector species are determined by many factors, e.g., temperature, habitat type, precipitation, or land use. We will seek key factors predictive of changes in existing vector populations as well as probabilities of new vector species invading that could be reasonably expected to take hold given global change.

Nonnative species are a common and often destructive embodiment of global change. Controlling or mitigating invasive species requires understanding of the resulting dynamics, which depend on species dispersal, growth, and habitat. Monitoring invasive species requires carefully-thought-out sampling strategies. For example, adaptive spatial sampling designs have been used to understand the rate of long distance dispersal of invasive species. Estimating the probability of establishment of the initial population (referred to as an “Allee effect”) is essential for controlling the invasive species, and temporal sampling of the population’s initial growth phase is critical for estimating the Allee effect. Such estimation is critically dependent on the size and proliferation rate of the initial, invading population, so successful sampling strategies targeting this period are a necessity.