Mathematics applied to the climate system: outstanding challenges and recent progress

The societal need for reliable climate predictions and a proper assessment of their uncertainties is pressing. Uncertainties arise not only from initial conditions and forcing scenarios, but also from model formulation. Here, we identify and document three broad classes of problems, each representing what we regard to be an outstanding challenge in the area of mathematics applied to the climate system. First, there is the problem of the development and evaluation of simple physically based models of the global climate. Second, there is the problem of the development and evaluation of the components of complex models such as general circulation models. Third, there is the problem of the development and evaluation of appropriate statistical frameworks. We discuss these problems in turn, emphasizing the recent progress made by the papers presented in this Theme Issue. Many pressing challenges in climate science require closer collaboration between climate scientists, mathematicians and statisticians. We hope the papers contained in this Theme Issue will act as inspiration for such collaborations and for setting future research directions.

Scenario and modelling uncertainty in global mean temperature change derived from emission-driven global climate models

We compare future changes in global mean temperature in response to different future scenarios which, for the first time, arise from emission-driven rather than concentration-driven perturbed parameter ensemble of a global climate model (GCM). These new GCM simulations sample uncertainties in atmospheric feedbacks, land carbon cycle, ocean physics and aerosol sulphur cycle processes. We find broader ranges of projected temperature responses arising when considering emission rather than concentration-driven simulations (with 10–90th percentile ranges of 1.7 K for the aggressive mitigation scenario, up to 3.9 K for the high-end, business as usual scenario). A small minority of simulations resulting from combinations of strong atmospheric feedbacks and carbon cycle responses show temperature increases in excess of 9 K (RCP8.5) and even under aggressive mitigation (RCP2.6) temperatures in excess of 4 K. While the simulations point to much larger temperature ranges for emission-driven experiments, they do not change existing expectations (based on previous concentration-driven experiments) on the timescales over which different sources of uncertainty are important. The new simulations sample a range of future atmospheric concentrations for each emission scenario. Both in the case of SRES A1B and the Representative Concentration Pathways (RCPs), the concentration scenarios used to drive GCM ensembles, lies towards the lower end of our simulated distribution. This design decision (a legacy of previous assessments) is likely to lead concentration-driven experiments to under-sample strong feedback responses in future projections. Our ensemble of emission-driven simulations span the global temperature response of the CMIP5 emission-driven simulations, except at the low end. Combinations of low climate sensitivity and low carbon cycle feedbacks lead to a number of CMIP5 responses to lie below our ensemble range. The ensemble simulates a number of high-end responses which lie above the CMIP5 carbon cycle range. These high-end simulations can be linked to sampling a number of stronger carbon cycle feedbacks and to sampling climate sensitivities above 4.5 K. This latter aspect highlights the priority in identifying real-world climate-sensitivity constraints which, if achieved, would lead to reductions on the upper bound of projected global mean temperature change. The ensembles of simulations presented here provides a framework to explore relationships between present-day observables and future changes, while the large spread of future-projected changes highlights the ongoing need for such work.

Multiscale geostatistical analysis of AVHRR, SPOT-VGT, and MODIS global NDVI products

Global NDVI data are routinely derived from the AVHRR, SPOT-VGT, and MODIS/Terra earth observation records for a range of applications from terrestrial vegetation monitoring to climate change modeling. This has led to a substantial interest in the harmonization of multisensor records. Most evaluations of the internal consistency and continuity of global multisensor NDVI products have focused on time-series harmonization in the spectral domain, often neglecting the spatial domain. We fill this void by applying variogram modeling (a) to evaluate the differences in spatial variability between 8-km AVHRR, 1-km SPOT-VGT, and 1-km, 500-m, and 250-m MODIS NDVI products over eight EOS (Earth Observing System) validation sites, and (b) to characterize the decay of spatial variability as a function of pixel size (i.e. data regularization) for spatially aggregated Landsat ETM+ NDVI products and a real multisensor dataset. First, we demonstrate that the conjunctive analysis of two variogram properties – the sill and the mean length scale metric – provides a robust assessment of the differences in spatial variability between multiscale NDVI products that are due to spatial (nominal pixel size, point spread function, and view angle) and non-spatial (sensor calibration, cloud clearing, atmospheric corrections, and length of multi-day compositing period) factors. Next, we show that as the nominal pixel size increases, the decay of spatial information content follows a logarithmic relationship with stronger fit value for the spatially aggregated NDVI products (R2 = 0.9321) than for the native-resolution AVHRR, SPOT-VGT, and MODIS NDVI products (R2 = 0.5064). This relationship serves as a reference for evaluation of the differences in spatial variability and length scales in multiscale datasets at native or aggregated spatial resolutions. The outcomes of this study suggest that multisensor NDVI records cannot be integrated into a long-term data record without proper consideration of all factors affecting their spatial consistency. Hence, we propose an approach for selecting the spatial resolution, at which differences in spatial variability between NDVI products from multiple sensors are minimized. This approach provides practical guidance for the harmonization of long-term multisensor datasets.

Optimising the FAMOUS climate model: inclusion of global carbon cycling

FAMOUS fills an important role in the hierarchy of climate models, both explicitly resolving atmospheric and oceanic dynamics yet being sufficiently computationally efficient that either very long simulations or large ensembles are possible. An improved set of carbon cycle parameters for this model has been found using a perturbed physics ensemble technique. This is an important step towards building the "Earth System" modelling capability of FAMOUS, which is a reduced resolution, and hence faster running, version of the Hadley Centre Climate model, HadCM3. Two separate 100 member perturbed parameter ensembles were performed; one for the land surface and one for the ocean. The land surface scheme was tested against present-day and past representations of vegetation and the ocean ensemble was tested against observations of nitrate. An advantage of using a relatively fast climate model is that a large number of simulations can be run and hence the model parameter space (a large source of climate model uncertainty) can be more thoroughly sampled. This has the associated benefit of being able to assess the sensitivity of model results to changes in each parameter. The climatologies of surface and tropospheric air temperature and precipitation are improved relative to previous versions of FAMOUS. The improved representation of upper atmosphere temperatures is driven by improved ozone concentrations near the tropopause and better upper level winds.

Historical and idealized climate model experiments: an intercomparison of Earth system models of intermediate complexity

Both historical and idealized climate model experiments are performed with a variety of Earth system models of intermediate complexity (EMICs) as part of a community contribution to the Intergovernmental Panel on Climate Change Fifth Assessment Report. Historical simulations start at 850 CE and continue through to 2005. The standard simulations include changes in forcing from solar luminosity, Earth's orbital configuration, CO2, additional greenhouse gases, land use, and sulphate and volcanic aerosols. In spite of very different modelled pre-industrial global surface air temperatures, overall 20th century trends in surface air temperature and carbon uptake are reasonably well simulated when compared to observed trends. Land carbon fluxes show much more variation between models than ocean carbon fluxes, and recent land fluxes appear to be slightly underestimated. It is possible that recent modelled climate trends or climate–carbon feedbacks are overestimated resulting in too much land carbon loss or that carbon uptake due to CO2 and/or nitrogen fertilization is underestimated. Several one thousand year long, idealized, 2 × and 4 × CO2 experiments are used to quantify standard model characteristics, including transient and equilibrium climate sensitivities, and climate–carbon feedbacks. The values from EMICs generally fall within the range given by general circulation models. Seven additional historical simulations, each including a single specified forcing, are used to assess the contributions of different climate forcings to the overall climate and carbon cycle response. The response of surface air temperature is the linear sum of the individual forcings, while the carbon cycle response shows a non-linear interaction between land-use change and CO2 forcings for some models. Finally, the preindustrial portions of the last millennium simulations are used to assess historical model carbon-climate feedbacks. Given the specified forcing, there is a tendency for the EMICs to underestimate the drop in surface air temperature and CO2 between the Medieval Climate Anomaly and the Little Ice Age estimated from palaeoclimate reconstructions. This in turn could be a result of unforced variability within the climate system, uncertainty in the reconstructions of temperature and CO2, errors in the reconstructions of forcing used to drive the models, or the incomplete representation of certain processes within the models. Given the forcing datasets used in this study, the models calculate significant land-use emissions over the pre-industrial period. This implies that land-use emissions might need to be taken into account, when making estimates of climate–carbon feedbacks from palaeoclimate reconstructions.

Evaluation of Earth system models using modern and palaeo-observations: the state-of-the-art

Earth system models are increasing in complexity and incorporating more processes than their predecessors, making them important tools for studying the global carbon cycle. However, their coupled behaviour has only recently been examined in any detail, and has yielded a very wide range of outcomes, with coupled climate-carbon cycle models that represent land-use change simulating total land carbon stores by 2100 that vary by as much as 600 Pg C given the same emissions scenario. This large uncertainty is associated with differences in how key processes are simulated in different models, and illustrates the necessity of determining which models are most realistic using rigorous model evaluation methodologies. Here we assess the state-of-the-art with respect to evaluation of Earth system models, with a particular emphasis on the simulation of the carbon cycle and associated biospheric processes. We examine some of the new advances and remaining uncertainties relating to (i) modern and palaeo data and (ii) metrics for evaluation, and discuss a range of strategies, such as the inclusion of pre-calibration, combined process- and system-level evaluation, and the use of emergent constraints, that can contribute towards the development of more robust evaluation schemes. An increasingly data-rich environment offers more opportunities for model evaluation, but it is also a challenge, as more knowledge about data uncertainties is required in order to determine robust evaluation methodologies that move the field of ESM evaluation from "beauty contest" toward the development of useful constraints on model behaviour.

TRY: a global database of plant traits

Plant traits – the morphological, anatomical, physiological, biochemical and phenological characteristics of plants and their organs – determine how primary producers respond to environmental factors, affect other trophic levels, influence ecosystem processes and services and provide a link from species richness to ecosystem functional diversity. Trait data thus represent the raw material for a wide range of research from evolutionary biology, community and functional ecology to biogeography. Here we present the global database initiative named TRY, which has united a wide range of the plant trait research community worldwide and gained an unprecedented buy-in of trait data: so far 93 trait databases have been contributed. The data repository currently contains almost three million trait entries for 69 000 out of the world's 300 000 plant species, with a focus on 52 groups of traits characterizing the vegetative and regeneration stages of the plant life cycle, including growth, dispersal, establishment and persistence. A first data analysis shows that most plant traits are approximately log-normally distributed, with widely differing ranges of variation across traits. Most trait variation is between species (interspecific), but significant intraspecific variation is also documented, up to 40% of the overall variation. Plant functional types (PFTs), as commonly used in vegetation models, capture a substantial fraction of the observed variation – but for several traits most variation occurs within PFTs, up to 75% of the overall variation. In the context of vegetation models these traits would better be represented by state variables rather than fixed parameter values. The improved availability of plant trait data in the unified global database is expected to support a paradigm shift from species to trait-based ecology, offer new opportunities for synthetic plant trait research and enable a more realistic and empirically grounded representation of terrestrial vegetation in Earth system models.

Priority research questions for the UK food system

The rise of food security up international political, societal and academic agendas has led to increasing interest in novel means of improving primary food production and reducing waste. There are however, also many ‘post-farm gate’ activities that are critical to food security, including processing, packaging, distributing, retailing, cooking and consuming. These activities all affect a range of important food security elements, notably availability, affordability and other aspects of access, nutrition and safety. Addressing the challenge of universal food security, in the context of a number of other policy goals (e.g. social, economic and environmental sustainability), is of keen interest to a range of UK stakeholders but requires an up-to-date evidence base and continuous innovation. An exercise was therefore conducted, under the auspices of the UK Global Food Security Programme, to identify priority research questions with a focus on the UK food system (though the outcomes may be broadly applicable to other developed nations). Emphasis was placed on incorporating a wide range of perspectives (‘world views’) from different stakeholder groups: policy, private sector, non-governmental organisations, advocacy groups and academia. A total of 456 individuals submitted 820 questions from which 100 were selected by a process of online voting and a three-stage workshop voting exercise. These 100 final questions were sorted into 10 themes and the ‘top’ question for each theme identified by a further voting exercise. This step also allowed four different stakeholder groups to select the top 7–8 questions from their perspectives. Results of these voting exercises are presented. It is clear from the wide range of questions prioritised in this exercise that the different stakeholder groups identified specific research needs on a range of post-farm gate activities and food security outcomes. Evidence needs related to food affordability, nutrition and food safety (all key elements of food security) featured highly in the exercise. While there were some questions relating to climate impacts on production, other important topics for food security (e.g. trade, transport, preference and cultural needs) were not viewed as strongly by the participants.

Climate change impacts on global food security

Climate change could potentially interrupt progress toward a world without hunger. A robust and coherent global pattern is discernible of the impacts of climate change on crop productivity that could have consequences for food availability. The stability of whole food systems may be at risk under climate change because of short-term variability in supply. However, the potential impact is less clear at regional scales, but it is likely that climate variability and change will exacerbate food insecurity in areas currently vulnerable to hunger and undernutrition. Likewise, it can be anticipated that food access and utilization will be affected indirectly via collateral effects on household and individual incomes, and food utilization could be impaired by loss of access to drinking water and damage to health. The evidence supports the need for considerable investment in adaptation and mitigation actions toward a “climate-smart food system” that is more resilient to climate change influences on food security.

Bounding the role of black carbon in the climate system: a scientific assessment

Black carbon aerosol plays a unique and important role in Earth’s climate system. Black carbon is a type of carbonaceous material with a unique combination of physical properties. This assessment provides an evaluation of black-carbon climate forcing that is comprehensive in its inclusion of all known and relevant processes and that is quantitative in providing best estimates and uncertainties of the main forcing terms: direct solar absorption; influence on liquid, mixed phase, and ice clouds; and deposition on snow and ice. These effects are calculated with climate models, but when possible, they are evaluated with both microphysical measurements and field observations. Predominant sources are combustion related, namely, fossil fuels for transportation, solid fuels for industrial and residential uses, and open burning of biomass. Total global emissions of black carbon using bottom-up inventory methods are 7500 Gg yr�-1 in the year 2000 with an uncertainty range of 2000 to 29000. However, global atmospheric absorption attributable to black carbon is too low in many models and should be increased by a factor of almost 3. After this scaling, the best estimate for the industrial-era (1750 to 2005) direct radiative forcing of atmospheric black carbon is +0.71 W m�-2 with 90% uncertainty bounds of (+0.08, +1.27)Wm�-2. Total direct forcing by all black carbon sources, without subtracting the preindustrial background, is estimated as +0.88 (+0.17, +1.48) W m�-2. Direct radiative forcing alone does not capture important rapid adjustment mechanisms. A framework is described and used for quantifying climate forcings, including rapid adjustments. The best estimate of industrial-era climate forcing of black carbon through all forcing mechanisms, including clouds and cryosphere forcing, is +1.1 W m�-2 with 90% uncertainty bounds of +0.17 to +2.1 W m�-2. Thus, there is a very high probability that black carbon emissions, independent of co-emitted species, have a positive forcing and warm the climate. We estimate that black carbon, with a total climate forcing of +1.1 W m�-2, is the second most important human emission in terms of its climate forcing in the present-day atmosphere; only carbon dioxide is estimated to have a greater forcing. Sources that emit black carbon also emit other short-lived species that may either cool or warm climate. Climate forcings from co-emitted species are estimated and used in the framework described herein. When the principal effects of short-lived co-emissions, including cooling agents such as sulfur dioxide, are included in net forcing, energy-related sources (fossil fuel and biofuel) have an industrial-era climate forcing of +0.22 (�-0.50 to +1.08) W m-�2 during the first year after emission. For a few of these sources, such as diesel engines and possibly residential biofuels, warming is strong enough that eliminating all short-lived emissions from these sources would reduce net climate forcing (i.e., produce cooling). When open burning emissions, which emit high levels of organic matter, are included in the total, the best estimate of net industrial-era climate forcing by all short-lived species from black-carbon-rich sources becomes slightly negative (�-0.06 W m�-2 with 90% uncertainty bounds of �-1.45 to +1.29 W m�-2). The uncertainties in net climate forcing from black-carbon-rich sources are substantial, largely due to lack of knowledge about cloud interactions with both black carbon and co-emitted organic carbon. In prioritizing potential black-carbon mitigation actions, non-science factors, such as technical feasibility, costs, policy design, and implementation feasibility play important roles. The major sources of black carbon are presently in different stages with regard to the feasibility for near-term mitigation. This assessment, by evaluating the large number and complexity of the associated physical and radiative processes in black-carbon climate forcing, sets a baseline from which to improve future climate forcing estimates.

An urban parameterization for a global climate model. Part I: Formulation and evaluation for two cities

Urbanization, the expansion of built-up areas, is an important yet less-studied aspect of land use/land cover change in climate science. To date, most global climate models used to evaluate effects of land use/land cover change on climate do not include an urban parameterization. Here, the authors describe the formulation and evaluation of a parameterization of urban areas that is incorporated into the Community Land Model, the land surface component of the Community Climate System Model. The model is designed to be simple enough to be compatible with structural and computational constraints of a land surface model coupled to a global climate model yet complex enough to explore physically based processes known to be important in determining urban climatology. The city representation is based upon the “urban canyon” concept, which consists of roofs, sunlit and shaded walls, and canyon floor. The canyon floor is divided into pervious (e.g., residential lawns, parks) and impervious (e.g., roads, parking lots, sidewalks) fractions. Trapping of longwave radiation by canyon surfaces and solar radiation absorption and reflection is determined by accounting for multiple reflections. Separate energy balances and surface temperatures are determined for each canyon facet. A one-dimensional heat conduction equation is solved numerically for a 10-layer column to determine conduction fluxes into and out of canyon surfaces. Model performance is evaluated against measured fluxes and temperatures from two urban sites. Results indicate the model does a reasonable job of simulating the energy balance of cities.

GridRM: an extensible resource monitoring system

GridRM is an open and extensible resource monitoring system, based on the Global Grid Forum's Grid Monitoring Architecture (GMA). GridRM is not intended to interact with applications; rather it is designed to monitor the resources that an application may use. This paper focuses on the dynamic driver infrastructure used by GridRM to interact with heterogeneous data sources, such as SNMP or Ganglia agents, and how it provides a homogeneous view of the underlying heterogeneous data. This paper discusses the local infrastructure and details work implementing and deploying a number of drivers.

Fire in the Earth system

Fire is a worldwide phenomenon that appears in the geological record soon after the appearance of terrestrial plants. Fire influences global ecosystem patterns and processes, including vegetation distribution and structure, the carbon cycle, and climate. Although humans and fire have always coexisted, our capacity to manage fire remains imperfect and may become more difficult in the future as climate change alters fire regimes. This risk is difficult to assess, however, because fires are still poorly represented in global models. Here, we discuss some of the most important issues involved in developing a better understanding of the role of fire in the Earth system.

Representation of model error in a convective-scale ensemble prediction system

In this paper ensembles of forecasts (of up to six hours) are studied from a convection-permitting model with a representation of model error due to unresolved processes. The ensemble prediction system (EPS) used is an experimental convection-permitting version of the UK Met Office’s 24- member Global and Regional Ensemble Prediction System (MOGREPS). The method of representing model error variability, which perturbs parameters within the model’s parameterisation schemes, has been modified and we investigate the impact of applying this scheme in different ways. These are: a control ensemble where all ensemble members have the same parameter values; an ensemble where the parameters are different between members, but fixed in time; and ensembles where the parameters are updated randomly every 30 or 60 min. The choice of parameters and their ranges of variability have been determined from expert opinion and parameter sensitivity tests. A case of frontal rain over the southern UK has been chosen, which has a multi-banded rainfall structure. The consequences of including model error variability in the case studied are mixed and are summarised as follows. The multiple banding, evident in the radar, is not captured for any single member. However, the single band is positioned in some members where a secondary band is present in the radar. This is found for all ensembles studied. Adding model error variability with fixed parameters in time does increase the ensemble spread for near-surface variables like wind and temperature, but can actually decrease the spread of the rainfall. Perturbing the parameters periodically throughout the forecast does not further increase the spread and exhibits “jumpiness” in the spread at times when the parameters are perturbed. Adding model error variability gives an improvement in forecast skill after the first 2–3 h of the forecast for near-surface temperature and relative humidity. For precipitation skill scores, adding model error variability has the effect of improving the skill in the first 1–2 h of the forecast, but then of reducing the skill after that. Complementary experiments were performed where the only difference between members was the set of parameter values (i.e. no initial condition variability). The resulting spread was found to be significantly less than the spread from initial condition variability alone.