We live in an information age, when computers and the software that drives them permeate every aspect of our society. There are two fundamentally important aspects of computation. - One concerns the resources needed to perform computational tasks: how many computational steps are needed, how much computer memory, etc. - The other concerns our ability to master the staggering complexity of the computer systems we create and use. The only way of managing this complexity is to use principles of modularity and abstraction, so that at each step of our design and construction of the system, we see only a very limited piece, whose complexity we can master. While the study of each of these aspects of computing has been greatly advanced as computer science has developed, currently we have a very limited understanding of how they relate to each other. Building on our previous work, this project aims to greatly enhance our common understanding of these issues, and to develop new mathematical tools and methods for studying computation based on this. This can lead in turn to new possibilities for fundamental advances in the field.

The dominant driver of anthropogenic global warming is the increasing amount of the greenhouse gas carbon dioxide in the atmosphere. This is increasing because it is being emitted by the burning of fossil fuel, deforestation and cement making, with only ~45% staying in the atmosphere. The rest is stored in other reservoirs at or near Earth's surface including the ocean, trees, soils, permafrost and methane ice, as well as sediments and rock. Carbon flows naturally between the atmosphere and these reservoirs by processes like photosynthesis, decay, weathering, burial and ocean circulation. Collectively, the exchange of carbon between these reservoirs is termed the carbon cycle. One of the biggest uncertainties about future climate change is how the carbon cycle will respond to (or 'feed back' on) our warming planet. It is possible, for example, that if global warming exceeds a threshold, permafrost and methane ice stored at the seafloor will melt rapidly, adding further greenhouse gases to the atmosphere and accelerating the warming. It is very difficult to predict whether 'tipping point' behaviour like this will occur in the global carbon cycle. C-FORCE will measure how the global carbon cycle responded from start to finish during a past period of global warming that was driven by emissions of carbon-based greenhouse gases to the atmosphere. The Paleocene-Eocene Thermal Maximum (PETM) is the largest natural climate change event of the last 65 million years, and the closest natural comparator to the modern rates of global warming and carbon greenhouse gas emissions. During the PETM, initial global warming of 4-5 degrees Celsius over a few thousand years was partially driven by carbon emissions from an unusually massive episode of volcanism, and the climate then gradually recovered to its pre-existing state over more than 100 thousand years. C-FORCE will use a novel model of the global carbon cycle to compare the carbon supplied by volcanism with the total PETM carbon budget; the difference between these two budgets can be attributed to carbon cycle feedbacks. We will make new high-resolution estimates of the rate at which volcanism supplied carbon to the atmosphere throughout the PETM by measuring the processes that generated the magma. We will calculate the total budget of carbon emissions to the atmosphere that caused the climate change by generating new high-resolution records of ocean acidification. Our carbon cycle modelling will allow the scientists who make these two sets of measurements to interface effectively to solve the net global carbon cycle feedback problem for the first time. Furthermore, because Earth's carbon reservoirs differ in isotopic composition, we can fingerprint which reservoirs most likely acted as carbon sources or sinks over the course of the PETM. Thus C-FORCE will determine how the global carbon cycle evolved throughout the PETM, and show whether or not tipping point behaviour occurred. Understanding how Earth's carbon reservoirs respond to global warming is crucial for predicting atmospheric carbon dioxide concentrations and climate change long into the future. Ultimately, an improved understanding of the carbon cycle affects future carbon budgets to limit global warming to 1.5 or 2 degrees Celcius and is therefore necessary for shaping mitigation targets and government policy. Beyond delivering a research product, C-FORCE challenges current understanding of the carbon cycle and we see our role as an empowering force in this space. The public discourse on climate change is a mixture of disaffection and anxiety, so C-FORCE will take a different direction to traditional public engagement, by partnering with community organisers and local government to train, mentor and co-develop our public engagement with young people.

Predictions of future climate, essential for safeguarding society and ecosystems, are underpinned by numerical models of the Earth system. These models are routinely tested against, and in many cases tuned towards, observations of the modern Earth system. However, the model predictions of the climate of the end of this century lie largely outside of this evaluation period, due to the projected future CO2 forcing being significantly greater than that seen in the observational record. Indeed, recent work reconstructing past CO2 has shown that the closest analogues to the 22nd century, in terms of CO2 concentration, are tens of millions of years ago, in 'Deep-Time'. The Palaeoclimate Modelling Intercomparison Project (PMIP) provides a framework (but no funding!) by which the palaeoclimate modelling community assesses state-of-the-art climate models relative to past climate data. Traditionally, PMIP has focussed on the relatively recent mid-Holocene (6,000 years ago) and Last Glacial Maximum (21,000 years ago), but these time periods have even lower CO2 than modern (~280 and ~180 ppmv respectively, c.f. ~400 ppmv for the modern). Recently, PMIP has expanded into other time periods, most notably the mid-Pliocene (3 million years ago), but even then, CO2 was most likely less than modern values (~380 ppmv). The modelling community would clearly benefit from an intercomparison of 'Deep-Time' climates, when CO2 levels were close to those predicted for the end of this century. We will organise and provide funding for 2 workshops, with the aim of producing papers describing the experimental design and outputs from a new climate Model Intercomparison Project - "DeepMIP", focussing on past climates in which atmospheric CO2 concentrations were similar to those projected for the end of this century. The papers will evaluate the models relative to past geological data, and aim to understand the reasons for the model-model differences and model-data (dis)agreements, providing information of relevance to the IPCC. A previous NERC grant, NE/K014757/1, is currently aiming to assess climate sensitivity (the response of surface air temperature to a doubling of atmospheric CO2), through geological time. That project is focussing on many time periods, but with only one model. This IOF will complement that project, and bring added-value, by focussing on one particular time period, but with many models. As such we will address the crucial issue of model-dependence.

Carbon dioxide, CO2, is a powerful greenhouse gas and its concentration in Earth's atmosphere has increased by around 35% since the start of the Industrial Revolution (in a ca. 250 yr time period) to a level that is higher than at any time in the past 800 thousand years as measured in air bubbles from ice cores. If man-made (anthropogenic) CO2 emissions to the atmosphere follow projected rates, then by 2100, concentrations will reach values not seen on Earth since the Palaeogene epoch (ca. 65-23 million years ago, Ma). These startling observations mean that we must improve our understanding of Palaeogene climate. Arguably, the pivotal Palaeogene climate event occurred around 34 Ma when, the first large Antarctic ice sheets were rapidly established across the Eocene/Oligocene transition, EOT. Results of ice-sheet-climate model experiments indicate that this event might represent a 'tipping point' response to slow decline in atmospheric CO2 levels (many orders of magnitude slower than the rate of anthropogenic increase). The results of our own previous research show that the growth of ice sheets on Antarctica across the EOT occurred in lock-step with a deepening (by more than a kilometer) in the calcite compensation depth (CCD) in the tropical Pacific Ocean. The CCD is the depth at which calcium carbonate sediments are dissolved in the ocean and can be thought of as 'an ocean acidity indicator'. Ocean de-acidification across the EOT demonstrates that the switch from a largely non-glaciated 'greenhouse' world to one with large ice sheets on Antarctica was closely associated with a big disruption in the global carbon cycle. What linked ice sheet growth on Antarctica to the acidity of the tropical deep Pacific Ocean? Previously we have suggested that growth of ice sheets on the Antarctic continent causes sea level to fall, killing off the large expanse of calcium carbonate (CaCO3)-secreting reefs that previously flourished on the continental shelves. This would have caused an imbalance between the inputs (from rivers) and outputs (sediment burial) of dissolved CaCO3 to the global ocean requiring a deepening in the CCD until balance was restored through increased CaCO3 sedimentation in the deep ocean. In numerical 'box model' tests, this 'shelf-to-basin CaCO3 switching' mechanism performed better than competing mechanisms proposed to explain EOT events. Yet shelf-basin-switching has been called into question on a number of grounds. For example, it has been suggested that the carbon cycle changes across the EOT were driven by changes in surface ocean productivity. In 2009, Integrated Ocean Drilling Program Expedition 320 drilled a series of holes across the Pacific Ocean on ocean crust of different age. The EOT was captured in four new sites at successively shallower depths. Our plan is to compare the chemistry of this EOT 'age-depth transect' of new sites with our existing records from a latitudinal transect of sites drilled previously in the region (ODP Leg 199). Hypotheses for the EOT that invoke CCD deepening in response to changes in global deep ocean carbonate chemistry (eg. shelf-basin-switching) should produce a pattern of sedimentation that is a simple function of depth whereas we predict the imprint of latitude from changes in surface productivity. One key to our work is the potential for unprecedented age-control in our target sediments. Other key aspects are the availability of two new sites that are richer in CaCO3 and calcareous microfossils across the EOT (specifically the latest Eocene) than the best previously available Pacific site (ODP 1218) and new geochemical techniques for determining changes in carbonate chemistry of the ancient oceans.

We propose to investigate the differences in the trophic ecology, distribution and foraging success of crabeater seals across a latitudinal gradient along the western Antarctica Peninsula (wAP). As a consequence of global climate change and local environmental processes, the atmosphere and oceans along the wAP are rapidly changing. Our study will enhance our ability to understand how the entire krill-dependent community of large predators will respond to the projected environmental changes. Furthermore, we have ecological baseline data from 20 years ago on movement patterns, diving behavior, feeding behavior, distribution and abundance for the species, as well as historical data and samples from the mid-1990s, providing us with a unique opportunity and advantageous position to detect changes in the ecology of this conspicuous Antarctic mesopredator and the extended predator community. The crabeater seal (Lobodon carcinophaga) is the most important predator of Antarctic krill Euphausia superba in Antarctic waters. This is due to its high degree of ecological specialization, large abundance and biomass, and high metabolic demand. Its high dependence on a single prey resource, combined with being an obligate inhabitant of the pack ice, makes the crabeater seal an excellent species to examine changes in krill distribution as well as potential changes in the structure of the entire ecosystem: the horizontal distribution of the seal is determined by the distribution of krill, and similarly the seals diving behavior provides insights into the vertical distribution of this euphausiid in the water column. Given the dichotomy in the daily habitat requirements of the crabeater seal, we aim to evaluate whether these previously-overlapping habitats are now separating in time and space along the western Antarctic Peninsula. Given the latitudinal differences in sea ice timing and extent. As well as the extreme dependence of crabeater seals on krill, we expect that individuals in the northern wAP have modified their foraging behavior and incur in elevated energetic costs as opposed to animals in the southern wAP. Alternatively, crabeater seals could have modified their habitat usage patterns and/or their diet in response to the changing climate along the wAP. We will use traditional aerial surveys combined with new technologies (UAS and satellite imagery) to census the population of seals in the wAP through a collaboration with BAS. The aerial surveys will provide a benchmark against which we can validate the new data obtained from these platforms, which are logistically easier and more cost-effective. The tracking studies will also provide concurrent data on haulout patterns of crabeater seals that will be used to correct the survey data for the proportion of individuals at sea1. The survey and tracking data will be utilized to first determine if the crabeater seal population has declined and or moved south in response to declining sea ice. Second, develop habitat models of the species distribution to define the variables that influence where the animals are eating versus where they are hauling out, determine how these habitats differ and predict the spatio-temporal co-occurrence of these environmental conditions.