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.

Inhalation exposure to particulate matter in rooms with underfloor air distribution

This work investigated the personal exposure to indoor particulate matters using the intake fraction metric and provided a possible way to trace the particle inhaled from an indoor particle source. A turbulence model validated by the particle measurements in a room with underfloor air distribution (UFAD) system was used to predict the indoor particle concentrations. Inhalation intake fraction of indoor particles was defined and evaluated in two rooms equipped with the UFAD, i.e., the experimental room and a small office. According to the exposure characteristics and a typical respiratory rate, the intake fraction was determined in two rooms with a continuous and episodic (human cough) source of particles, respectively. The findings showed that the well-mixing assumption of indoor air failed to give an accurate estimation of inhalation exposure and the average concentration at return outlet or within the overall room could not relate well the intake fraction to the amount of particle emitted from an indoor source.

The national food safety control system of China: a systematic review

In recent years, there have been increasing concerns over the safety of the Chinese food supply. Although many of these have only raised concern internally within China, several major food safety issues have had international repercussions. In response, China has implemented new food safety laws and management systems to improve its national food safety control system and reduce public and international concerns. This paper has describes and discusses the components of the Chinese system using the five key elements of a national food control system identified by the World Health Organization (WHO) and the Food and Agriculture Organization (FAO) as essential for an effective system. The latest Chinese national food safety control has made significantly improvement on its regulation framework, however, more work need to be done on standards, law enforcement, and information exchange.

Restricting microbial exposure in early life negates the immune benefits associated with gut colonization in environments of high microbial diversity

Background: Acquisition of the intestinal microbiota in early life corresponds with the development of the mucosal immune system. Recent work on caesarean-delivered infants revealed that early microbial composition is influenced by birthing method and environment. Furthermore, we have confirmed that early-life environment strongly influences both the adult gut microbiota and development of the gut immune system. Here, we address the impact of limiting microbial exposure after initial colonization on the development of adult gut immunity. Methodology/Principal Findings: Piglets were born in indoor or outdoor rearing units, allowing natural colonization in the immediate period after birth, prior to transfer to high-health status isolators. Strikingly, gut closure and morphological development were strongly affected by isolator-rearing, independent of indoor or outdoor origins of piglets. Isolator-reared animals showed extensive vacuolation and disorganization of the gut epithelium, inferring that normal gut closure requires maturation factors present in maternal milk. Although morphological maturation and gut closure were delayed in isolatorreared animals, these hard-wired events occurred later in development. Type I IFN, IL-22, IL-23 and Th17 pathways were increased in indoor-isolator compared to outdoor-isolator animals during early life, indicating greater immune activation in pigs originating from indoor environments reflecting differences in the early microbiota. This difference was less apparent later in development due to enhanced immune activation and convergence of the microbiota in all isolator-reared animals. This correlated with elevation of Type I IFN pathways in both groups, although T cell pathways were still more affected in indoor-reared animals. Conclusions/Significance: Environmental factors, in particular microbial exposure, influence expression of a large number of immune-related genes. However, the homeostatic effects of microbial colonization in outdoor environments require sustained microbial exposure throughout development. Gut development in high-hygiene environments negatively impacts on normal succession of the gut microbiota and promotes innate immune activation which may impair immune homeostasis.

Tracing troposphere-to-stratosphere transport above a mid-latitude deep convective system

Within the project SPURT (trace gas measurements in the tropopause region) a variety of trace gases have been measured in situ in order to investigate the role of dynamical and chemical processes in the extra-tropical tropopause region. In this paper we report on a flight on 10 November 2001 leading from Hohn, Germany (52�N) to Faro, Portugal (37�N) through a strongly developed deep stratospheric intrusion. This streamer was associated with a large convective system over the western Mediterranean with potentially significant troposphere-to-stratosphere transport. Along major parts of the flight we measured unexpectedly high NOy mixing ratios. Also H2O mixing ratios were significantly higher than stratospheric background levels confirming the extraordinary chemical signature of the probed air masses in the interior of the streamer. Backward trajectories encompassing the streamer enable to analyze the origin and physical characteristics of the air masses and to trace troposphere-to-stratosphere transport. Near the western flank of the streamer features caused by long range transport, such as tropospheric filaments characterized by sudden drops in the O3 and NOy mixing ratios and enhanced CO and H2O can be reconstructed in great detail using the reverse domain filling technique. These filaments indicate a high potential for subsequent mixing with the stratospheric air. At the south-western edge of the streamer a strong gradient in the NOy and the O3 mixing ratios coincides very well with a sharp gradient in potential vorticity in the ECMWF fields. In contrast, in the interior of the streamer the observed highly elevated NOy and H2O mixing ratios up to a potential temperature level of 365K and potential vorticity values of maximum 10 PVU cannot be explained in terms of resolved troposphere-to-stratosphere transport along the backward trajectories. Also mesoscale simulations with a High Resolution Model reveal no direct evidence for convective H2O injection up to this level. Elevated H2O mixing ratios in the ECMWF and HRM are seen only up to about tropopause height at 340 hPa and 270 hPa, respectively, well below flight altitude of about 200 hPa. However, forward tracing of the convective influence as identified by satellite brightness temperature measurements and counts of lightning strokes shows that during this part of the flight the aircraft was closely following the border of an air mass which was heavily impacted by convective activity over Spain and Algeria. This is evidence that deep convection at mid-latitudes may have a large impact on the tracer distribution of the lowermost stratosphere reaching well above the thunderstorms anvils as claimed by recent studies using cloud-resolving models.

Perceived helplessness is associated with individual differences in the central motor output system

Learned helplessness is a maladaptive response to uncontrollable stress characterized by impaired motor escape responses, reduced motivation and learning deficits. There are important individual differences in the likelihood of becoming helpless following exposure to uncontrollable stress but little is known about the neural mechanisms underlying these individual differences. Here we used structural MRI to measure gray and white matter in individuals with chronic pain, a population at high risk for helplessness due to prolonged exposure to a poorly controlled stressor (pain). Given that self-reported helplessness is predictive of treatment outcomes in chronic pain, understanding such differences might provide valuable clinical insight. We found that the magnitude of self-reported helplessness correlated with cortical thickness in the supplementary motor area (SMA) and midcingulate cortex, regions implicated in cognitive aspects of motor behavior. We then examined the white matter connectivity of these regions and found that fractional anisotropy of connected white matter tracts along the corticospinal tract was associated with helplessness and mediated the relationship between SMA cortical thickness and helplessness. These data provide novel evidence that links individual differences in the motor output pathway with perceived helplessness over a chronic and poorly controlled stressor.

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.

A universal agro-hydrological model for water and nitrogen cycles in the soil-crop system SMCR_N: critical update and further validation

Agro-hydrological models have widely been used for optimizing resources use and minimizing environmental consequences in agriculture. SMCRN is a recently developed sophisticated model which simulates crop response to nitrogen fertilizer for a wide range of crops, and the associated leaching of nitrate from arable soils. In this paper, we describe the improvements of this model by replacing the existing approximate hydrological cascade algorithm with a new simple and explicit algorithm for the basic soil water flow equation, which not only enhanced the model performance in hydrological simulation, but also was essential to extend the model application to the situations where the capillary flow is important. As a result, the updated SMCRN model could be used for more accurate study of water dynamics in the soil-crop system. The success of the model update was demonstrated by the simulated results that the updated model consistently out-performed the original model in drainage simulations and in predicting time course soil water content in different layers in the soil-wheat system. Tests of the updated SMCRN model against data from 4 field crop experiments showed that crop nitrogen offtakes and soil mineral nitrogen in the top 90 cm were in a good agreement with the measured values, indicating that the model could make more reliable predictions of nitrogen fate in the crop-soil system, and thus provides a useful platform to assess the impacts of nitrogen fertilizer on crop yield and nitrogen leaching from different production systems. (C) 2010 Elsevier B.V. All rights reserved.

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.

Use of batch culture and a two-stage continuous culture system to study the effect of supplemental a-lactalbumin and glycomacropeptide on mixed populations of human gut bacteria

Certain milk factors can promote the growth of a host-friendly gastrointestinal microflora. This may explain why breast-fed infants experience fewer intestinal infections than their formula-fed counterparts. The effect of formula supplementation with two such factors was investigated in this study. Infant faecal specimens were used to ferment formulas supplemented with glycomacropeptide and α-lactalbumin in a two-stage compound continuous culture model. Bacteriology was determined by fluorescence in situ hybridisation. Vessels that contained breast milk as well as α-lactalbumin and glycomacropeptide had stable counts of bifidobacteria while lactobacilli increased significantly only in vessels with breast milk. Bacteroides, clostridia and Escherichia coli decreased significantly in all runs. Acetate was the principal acid found along with high amounts of propionate and lactate. Supplementation of infant formulas with appropriate milk proteins may be useful in simulating the beneficial bacteriological effects of breast milk.

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.

The water quality of the River Enborne, UK: observations from high-frequency Monitoring in a rural, lowland river system

This paper reports the results of a 2-year study of water quality in the River Enborne, a rural river in lowland England. Concentrations of nitrogen and phosphorus species and other chemical determinands were monitored both at high-frequency (hourly), using automated in situ instrumentation, and by manual weekly sampling and laboratory analysis. The catchment land use is largely agricultural, with a population density of 123 persons km−2. The river water is largely derived from calcareous groundwater, and there are high nitrogen and phosphorus concentrations. Agricultural fertiliser is the dominant source of annual loads of both nitrogen and phosphorus. However, the data show that sewage effluent discharges have a disproportionate effect on the river nitrogen and phosphorus dynamics. At least 38% of the catchment population use septic tank systems, but the effects are hard to quantify as only 6% are officially registered, and the characteristics of the others are unknown. Only 4% of the phosphorus input and 9% of the nitrogen input is exported from the catchment by the river, highlighting the importance of catchment process understanding in predicting nutrient concentrations. High-frequency monitoring will be a key to developing this vital process understanding.

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

Earth system models (ESMs) are increasing in complexity by incorporating more processes than their predecessors, making them potentially important tools for studying the evolution of climate and associated biogeochemical cycles. However, their coupled behaviour has only recently been examined in any detail, and has yielded a very wide range of outcomes. For example, coupled climate–carbon cycle models that represent land-use change simulate total land carbon stores at 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 methods of model evaluation. Here we assess the state-of-the-art in evaluation of ESMs, 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 palaeodata and (ii) metrics for evaluation. We note that the practice of averaging results from many models is unreliable and no substitute for proper evaluation of individual models. We 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 to the development of more robust evaluation schemes. An increasingly data-rich environment offers more opportunities for model evaluation, but also presents a challenge. Improved knowledge of data uncertainties is still necessary to move the field of ESM evaluation away from a "beauty contest" towards the development of useful constraints on model outcomes.

The impact of sea ice dynamics on the Arctic climate system

Five paired global climate model experiments, one with an ice pack that only responds thermodynamically (TI) and one including sea-ice dynamics (DI), were used to investigate the sensitivity of Arctic climates to sea-ice motion. The sequence of experiments includes situations in which the Arctic was both considerably colder (Glacial Inception, ca 115,000 years ago) and considerably warmer (3 × CO2) than today. Sea-ice motion produces cooler anomalies year-round than simulations without ice dynamics, resulting in reduced Arctic warming in warm scenarios and increased Arctic cooling in cold scenarios. These changes reflect changes in atmospheric circulation patterns: the DI simulations favor outflow of Arctic air and sea ice into the North Atlantic by promoting cyclonic circulation centered over northern Eurasia, whereas the TI simulations favor southerly inflow of much warmer air from the North Atlantic by promoting cyclonic circulation centered over Greenland. The differences between the paired simulations are sufficiently large to produce different vegetation cover over >19% of the land area north of 55°N, resulting in changes in land-surface characteristics large enough to have an additional impact on climate. Comparison of the DI and TI experiments for the mid-Holocene (6000 years ago) with paleovegetation reconstructions suggests the incorporation of sea-ice dynamics yields a more realistic simulation of high-latitude climates. The spatial pattern of sea-ice anomalies in the warmer-than-modern DI experiments strongly resembles the observed Arctic Ocean sea-ice dipole structure in recent decades, consistent with the idea that greenhouse warming is already impacting the high-northern latitudes.

The influence of system designer intention over collaborative tagging. an analysis of tagging behaviour in CiteULike and Delicious

Tagging provides support for retrieval and categorization of online content depending on users' tag choice. A number of models of tagging behaviour have been proposed to identify factors that are considered to affect taggers, such as users' tagging history. In this paper, we use Semiotics Analysis and Activity theory, to study the effect the system designer has over tagging behaviour. The framework we use shows the components that comprise the tagging system and how they interact together to direct tagging behaviour. We analysed two collaborative tagging systems: CiteULike and Delicious by studying their components by applying our framework. Using datasets from both systems, we found that 35% of CiteULike users did not provide tags compared to only 0.1% of Delicious users. This was directly linked to the type of tools used by the system designer to support tagging.