Adapting the International System of Units to the twenty-first century

We review the proposal of the International Committee for Weights and Measures (Comité International des Poids et Mesures, CIPM), currently being considered by the General Conference on Weights and Measures (Conférences Générales des Poids et Mesures, CGPM), to revise the International System of Units (Le Système International d’Unitès, SI). The proposal includes new definitions for four of the seven base units of the SI, and a new form of words to present the definitions of all the units. The objective of the proposed changes is to adopt definitions referenced to constants of nature, taken in the widest sense, so that the definitions may be based on what are believed to be true invariants. In particular, whereas in the current SI the kilogram, ampere, kelvin and mole are linked to exact numerical values of the mass of the international prototype of the kilogram, the magnetic constant (permeability of vacuum), the triple-point temperature of water and the molar mass of carbon-12, respectively, in the new SI these units are linked to exact numerical values of the Planck constant, the elementary charge, the Boltzmann constant and the Avogadro constant, respectively. The new wording used expresses the definitions in a simple and unambiguous manner without the need for the distinction between base and derived units. The importance of relations among the fundamental constants to the definitions, and the importance of establishing a mise en pratique for the realization of each definition, are also discussed.

Symmetry breaking, mixing, instability, and low frequency variability in a minimal Lorenz-like system

Starting from the classical Saltzman two-dimensional convection equations, we derive via a severe spectral truncation a minimal 10 ODE system which includes the thermal effect of viscous dissipation. Neglecting this process leads to a dynamical system which includes a decoupled generalized Lorenz system. The consideration of this process breaks an important symmetry and couples the dynamics of fast and slow variables, with the ensuing modifications to the structural properties of the attractor and of the spectral features. When the relevant nondimensional number (Eckert number Ec) is different from zero, an additional time scale of O(Ec−1) is introduced in the system, as shown with standard multiscale analysis and made clear by several numerical evidences. Moreover, the system is ergodic and hyperbolic, the slow variables feature long-term memory with 1/f3/2 power spectra, and the fast variables feature amplitude modulation. Increasing the strength of the thermal-viscous feedback has a stabilizing effect, as both the metric entropy and the Kaplan-Yorke attractor dimension decrease monotonically with Ec. The analyzed system features very rich dynamics: it overcomes some of the limitations of the Lorenz system and might have prototypical value in relevant processes in complex systems dynamics, such as the interaction between slow and fast variables, the presence of long-term memory, and the associated extreme value statistics. This analysis shows how neglecting the coupling of slow and fast variables only on the basis of scale analysis can be catastrophic. In fact, this leads to spurious invariances that affect essential dynamical properties (ergodicity, hyperbolicity) and that cause the model losing ability in describing intrinsically multiscale processes.

Thermodynamic efficiency and entropy production in the climate system

We present an outlook on the climate system thermodynamics. First, we construct an equivalent Carnot engine with efficiency and frame the Lorenz energy cycle in a macroscale thermodynamic context. Then, by exploiting the second law, we prove that the lower bound to the entropy production is times the integrated absolute value of the internal entropy fluctuations. An exergetic interpretation is also proposed. Finally, the controversial maximum entropy production principle is reinterpreted as requiring the joint optimization of heat transport and mechanical work production. These results provide tools for climate change analysis and for climate models’ validation.

Terrestrial biogeochemical feedbacks in the climate system

The terrestrial biosphere is a key regulator of atmospheric chemistry and climate. During past periods of climate change, vegetation cover and interactions between the terrestrial biosphere and atmosphere changed within decades. Modern observations show a similar responsiveness of terrestrial biogeochemistry to anthropogenically forced climate change and air pollution. Although interactions between the carbon cycle and climate have been a central focus, other biogeochemical feedbacks could be as important in modulating future climate change. Total positive radiative forcings resulting from feedbacks between the terrestrial biosphere and the atmosphere are estimated to reach up to 0.9 or 1.5 W m−2 K−1 towards the end of the twenty-first century, depending on the extent to which interactions with the nitrogen cycle stimulate or limit carbon sequestration. This substantially reduces and potentially even eliminates the cooling effect owing to carbon dioxide fertilization of the terrestrial biota. The overall magnitude of the biogeochemical feedbacks could potentially be similar to that of feedbacks in the physical climate system, but there are large uncertainties in the magnitude of individual estimates and in accounting for synergies between these effects.

Mixed copper, silver, and gold cyanides, (MxM′1–x)CN: tailoring chain structures to influence physical properties

Binary mixed-metal variants of the one-dimensional MCN compounds (M = Cu, Ag, and Au) have been prepared and characterized using powder X-ray diffraction, vibrational spectroscopy, and total neutron diffraction. A solid solution with the AgCN structure exists in the (CuxAg1–x)CN system over the range (0 ≤ x ≤ 1). Line phases with compositions (Cu1/2Au1/2)CN, (Cu7/12Au5/12)CN, (Cu2/3Au1/3)CN, and (Ag1/2Au1/2)CN, all of which have the AuCN structure, are found in the gold-containing systems. Infrared and Raman spectroscopies show that complete ordering of the type [M–C≡N–M′–N≡C−]n occurs only in (Cu1/2Au1/2)CN and (Ag1/2Au1/2)CN. The sense of the cyanide bonding was determined by total neutron diffraction to be [Ag–NC–Au–CN−]n in (Ag1/2Au1/2)CN and [Cu–NC–Au–CN−]n in (Cu1/2Au1/2)CN. In contrast, in (Cu0.50Ag0.50)CN, metal ordering is incomplete, and strict alternation of metals does not occur. However, there is a distinct preference (85%) for the N end of the cyanide ligand to be bonded to copper and for Ag–CN–Cu links to predominate. Contrary to expectation, aurophilic bonding does not appear to be the controlling factor which leads to (Cu1/2Au1/2)CN and (Ag1/2Au1/2)CN adopting the AuCN structure. The diffuse reflectance, photoluminescence, and 1-D negative thermal expansion (NTE) behaviors of all three systems are reported and compared with those of the parent cyanide compounds. The photophysical properties are strongly influenced both by the composition of the individual chains and by how such chains pack together. The NTE behavior is also controlled by structure type: the gold-containing mixed-metal cyanides with the AuCN structure show the smallest contraction along the chain length on heating.

Deriving global flood hazard maps of fluvial floods through a physical model cascade

Global flood hazard maps can be used in the assessment of flood risk in a number of different applications, including (re)insurance and large scale flood preparedness. Such global hazard maps can be generated using large scale physically based models of rainfall-runoff and river routing, when used in conjunction with a number of post-processing methods. In this study, the European Centre for Medium Range Weather Forecasts (ECMWF) land surface model is coupled to ERA-Interim reanalysis meteorological forcing data, and resultant runoff is passed to a river routing algorithm which simulates floodplains and flood flow across the global land area. The global hazard map is based on a 30 yr (1979–2010) simulation period. A Gumbel distribution is fitted to the annual maxima flows to derive a number of flood return periods. The return periods are calculated initially for a 25×25 km grid, which is then reprojected onto a 1×1 km grid to derive maps of higher resolution and estimate flooded fractional area for the individual 25×25 km cells. Several global and regional maps of flood return periods ranging from 2 to 500 yr are presented. The results compare reasonably to a benchmark data set of global flood hazard. The developed methodology can be applied to other datasets on a global or regional scale.

Design of a forecasting system for ECMWF

As laid out in its convention there are 8 different objectives for ECMWF. One of the major objectives will consist of the preparation, on a regular basis, of the data necessary for the preparation of medium-range weather forecasts. The interpretation of this item is that the Centre will make forecasts once a day for a prediction period of up to 10 days. It is also evident that the Centre should not carry out any real weather forecasting but merely disseminate to the member countries the basic forecasting parameters with an appropriate resolution in space and time. It follows from this that the forecasting system at the Centre must from the operational point of view be functionally integrated with the Weather Services of the Member Countries. The operational interface between ECMWF and the Member Countries must be properly specified in order to get a reasonable flexibility for both systems. The problem of making numerical atmospheric predictions for periods beyond 4-5 days differs substantially from 2-3 days forecasting. From the physical point we can define a medium range forecast as a forecast where the initial disturbances have lost their individual structure. However we are still interested to predict the atmosphere in a similar way as in short range forecasting which means that the model must be able to predict the dissipation and decay of the initial phenomena and the creation of new ones. With this definition, medium range forecasting is indeed very difficult and generally regarded as more difficult than extended forecasts, where we usually only predict time and space mean values. The predictability of atmospheric flow has been extensively studied during the last years in theoretical investigations and by numerical experiments. As has been discussed elsewhere in this publication (see pp 338 and 431) a 10-day forecast is apparently on the fringe of predictability.

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.

The physical pendulum in an advanced undergraduate course in mechanics

The physical pendulum treated with a Hamiltonian formulation is a natural topic for study in a course in advanced classical mechanics. For the past three years, we have been offering a series of problem sets studying this system numerically in our third-year undergraduate courses in mechanics. The problem sets investigate the physics of the pendulum in ways not easily accessible without computer technology and explore various algorithms for solving mechanics problems. Our computational physics is based on Mathematica with some C communicating with Mathematica, although nothing in this paper is dependent on that choice. We have nonetheless found this system, and particularly its graphics, to be a good one for use with undergraduates.

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.

Sustainable urban metabolism as a link between bio-physical sciences and urban planning: the BRIDGE project

Urban metabolism considers a city as a system with flows of energy and material between it and the environment. Recent advances in bio-physical sciences provide methods and models to estimate local scale energy, water, carbon and pollutant fluxes. However, good communication is required to provide this new knowledge and its implications to endusers (such as urban planners, architects and engineers). The FP7 project BRIDGE (sustainaBle uRban plannIng Decision support accountinG for urban mEtabolism) aimed to address this gap by illustrating the advantages of considering these issues in urban planning. The BRIDGE Decision Support System (DSS) aids the evaluation of the sustainability of urban planning interventions. The Multi Criteria Analysis approach adopted provides a method to cope with the complexity of urban metabolism. In consultation with targeted end-users, objectives were defined in relation to the interactions between the environmental elements (fluxes of energy, water, carbon and pollutants) and socioeconomic components (investment costs, housing, employment, etc.) of urban sustainability. The tool was tested in five case study cities: Helsinki, Athens, London, Florence and Gliwice; and sub-models were evaluated using flux data selected. This overview of the BRIDGE project covers the methods and tools used to measure and model the physical flows, the selected set of sustainability indicators, the methodological framework for evaluating urban planning alternatives and the resulting DSS prototype.

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.

Development and evaluation of an Earth-System model – HadGEM2

We describe here the development and evaluation of an Earth system model suitable for centennial-scale climate prediction. The principal new components added to the physical climate model are the terrestrial and ocean ecosystems and gas-phase tropospheric chemistry, along with their coupled interactions. The individual Earth system components are described briefly and the relevant interactions between the components are explained. Because the multiple interactions could lead to unstable feedbacks, we go through a careful process of model spin up to ensure that all components are stable and the interactions balanced. This spun-up configuration is evaluated against observed data for the Earth system components and is generally found to perform very satisfactorily. The reason for the evaluation phase is that the model is to be used for the core climate simulations carried out by the Met Office Hadley Centre for the Coupled Model Intercomparison Project (CMIP5), so it is essential that addition of the extra complexity does not detract substantially from its climate performance. Localised changes in some specific meteorological variables can be identified, but the impacts on the overall simulation of present day climate are slight. This model is proving valuable both for climate predictions, and for investigating the strengths of biogeochemical feedbacks.

Solutions of the fully compressible semi-geostrophic system

The fully compressible semi-geostrophic system is widely used in the modelling of large-scale atmospheric flows. In this paper, we prove rigorously the existence of weak Lagrangian solutions of this system, formulated in the original physical coordinates. In addition, we provide an alternative proof of the earlier result on the existence of weak solutions of this system expressed in the so-called geostrophic, or dual, coordinates. The proofs are based on the optimal transport formulation of the problem and on recent general results concerning transport problems posed in the Wasserstein space of probability measures.

High density lipoprotein: guardian of the vascular system?

The role of low-density lipoprotein in the development of coronary heart disease (CHD) is well recognised. There is also growing evidence that high-density lipoprotein cholesterol (HDL-C) is a powerful inverse predictor for premature CHD and that maintaining a high HDL-C level may guard against atherosclerosis. Patients with low HDL-C levels often also have central obesity, insulin resistance and other features of the metabolic syndrome. This syndrome is both increasingly common and strongly implicated in the growing worldwide epidemic of type 2 diabetes. HDL-C may be increased by lifestyle changes, e.g. weight loss, physical activity and smoking cessation. Pharmacological agents such as fibrates, niacin and statins have also been shown significantly to elevate HDL-C. Although current guidelines are beginning to recognise the protective role of HDL-C level in preventing coronary events, HDL-C should be adopted soon as a target for intervention in its own right.