Model Comparison Study Research Articles

Thou shalt identify! The identifiability of two high-threshold models in confidence-rating recognition (and super-recognition) paradigms

Model identifiability i.e., the possibility to determine the ’true’ parameters of a model in a unique manner based on an empirical dataset, is a vital property of any scientific model. Indeed, the absence of this property undermines the model’s use qua measurement and inference tool. Here, I examined the identifiability of different variants of the successful two-high threshold model (2HTM) in the confidence-rating recognition paradigm. Traditionally, 2HTM has adopted the certainty assumption according to which, detected test-probes receive only the highest correct confidence rating. Modern variants, however, allow responses for detected items to distribute across all correct confidence levels (Detect–Correct; DC) or even across erroneous confidence levels (Free Response Mapping, FRM). Here, I present identifiability proofs for the certainty variant and, when there are multiple target conditions, for DC. Additionally, I present non-identifiability proofs for DC when there is a single target condition and for FRM. One important advantage of identifiability proofs over fitting-based methods for testing identifiability is that they highlight the mathematical principles that are instrumental for a deeper understanding of models. Based on these principles, I present a novel extended super-confidence paradigm, which includes super-strong targets and lures and that identifies FRM. I illustrate the perils of non-identifiability by reanalyzing a recent model comparison study of Chen et al. (2015). Finally, solutions for non-identifiability problems are discussed. While the current study focuses on identifiability in the context of recognition-memory, it should serve as a universal reminder for the importance of identifying models in any domain of research.

A Model Comparison Study of Fragment Production in 140 A MeV 58,64Ni+9Be Reactions**Supported by the Program for Science and Technology Innovation Talents in Universities of Henan Province under Grant No 13HASTIT046.

The cross sections of fragments produced in the 140 A MeV58,64Ni+9 Be projectile fragmentation reactions are calculated by using the antisymmetrized molecular dynamics (AMD) model, the modified statistical abrasion-ablation (SAA) model, and the empirical EPAX2/EPAX3 formulae. The Gogny-g0 interaction is taken as the effective nucleon-nucleon interaction in the AMD calculation, and the decays of fragments obtained from the AMD results are calculated by using the GEMINI code. The calculated cross sections of fragments are compared.

A model comparison study of the flowering time regulatory network in Arabidopsis

BackgroundSeveral dynamic models of a gene regulatory network of the light-induced floral transition process in Arabidopsis have been developed to capture the behavior of gene transcription and infer predictions based on experimental observations. It has been proven that the models can make accurate and novel predictions, which generate testable hypotheses.Two major issues were addressed in this study. First, construction of dynamic models for gene regulatory networks requires the use of mathematic modeling that comprises equations of a large number of parameters. Second, the binding mechanism of the transcription factor with DNA is another factor that requires detailed modeling. The first issue was tackled by adopting an optimization algorithm, and the second was addressed by comparing the performance of three alternative modeling approaches, namely the S-system, the Michaelis-Menten model and the Mass-action model. The efficiencies of parameter estimation and modeling performance were calculated based on least square error (O(p)), mean relative error (MRE) and Akaike Information Criterion (AIC).ResultsWe compared three models to describe gene regulation of the flowering transition process in Arabidopsis. The Mass-action model is the simplest and has the least parameters. It is therefore less computation-intensive with the smallest AIC value. The disadvantage, however, is that it assumes the system is simply a second order reaction which is not the case in our study. The Michaelis-Menten model also assumes the system is homogeneous and ignores the intracellular protein transport process. The S-system model has the best performance and it does describe the diffusion effects. A disadvantage of the S-system is that it involves the most parameters. The largest AIC value also implies an over-fitting may occur in parameter estimation.ConclusionsThree dynamic models were adopted to describe the dynamics of the gene regulatory network of the flowering transition process in Arabidopsis. Based on MRE, the least square error and global sensitivity analysis, the S-system has the best performance. However, the fact that it has the highest AIC suggests an over-fitting may occur in parameter estimation. The result of this study may need to be applied carefully when modeling complex gene regulatory networks.

Comparing supply-side specifications in models of global agriculture and the food system

This article compares the theoretical and functional specification of production in partial equilibrium (PE) and computable general equilibrium (CGE) models of the global agricultural and food system included in the AgMIP model comparison study. The two model families differ in their scope—partial versus economy-wide—and in how they represent technology and the behavior of supply and demand in markets. The CGE models are “deep” structural models in that they explicitly solve the maximization problem of consumers and producers, assuming utility maximization and profit maximization with production/cost functions that include all factor inputs. The PE models divide into two groups on the supply side: (1) “shallow” structural models, which essentially specify area/yield supply functions with no explicit maximization behavior, and (2) “deep” structural models that provide a detailed activity-analysis specification of technology and explicit optimizing behavior by producers. While the models vary in their specifications of technology, both within and between the PE and CGE families, we consider two stylized theoretical models to compare the behavior of crop yields and supply functions in CGE models with their behavior in shallow structural PE models. We find that the theoretical responsiveness of supply to changes in prices can be similar, depending on parameter choices that define the behavior of implicit supply functions over the domain of applicability defined by the common scenarios used in the AgMIP comparisons. In practice, however, the applied models are more complex and differ in their empirical sensitivity to variations in specification—comparability of results given parameter choices is an empirical question. To illustrate the issues, sensitivity analysis is done with one global CGE model, MAGNET, to indicate how the results vary with different specification of technical change, and how they compare with the results from PE models.

The impact of near-term climate policy choices on technology and emission transition pathways

Abstract This paper explores the implications of delays (to 2030) in implementing optimal policies for long-term transition pathways to limit climate forcing to 450 ppm CO2e on the basis of the AMPERE Work Package 2 model comparison study. The paper highlights the critical importance of the period 2030–2050 for ambitious mitigation strategies. In this period, the most rapid shift to low greenhouse gas emitting technology occurs. In the delayed response emission mitigation scenarios, an even faster transition rate in this period is required to compensate for the additional emissions before 2030. Our physical deployment measures indicate that the availability of CCS technology could play a critical role in facilitating the attainment of ambitious mitigation goals. Without CCS, deployment of other mitigation technologies would become extremely high in the 2030–2050 period. Yet the presence of CCS greatly alleviates the challenges to the transition particularly after the delayed climate policies, lowering the risk that the long-term goal becomes unattainable. The results also highlight the important role of bioenergy with CO2 capture and storage (BECCS), which facilitates energy production with negative carbon emissions. If BECCS is available, transition pathways exceed the emission budget in the mid-term, removing the excess with BECCS in the long term. Excluding either BE or CCS from the technology portfolio implies that emission reductions need to take place much earlier.

EUROPEAN-LED CLIMATE POLICY VERSUS GLOBAL MITIGATION ACTION: IMPLICATIONS ON TRADE, TECHNOLOGY, AND ENERGY

This paper examines how changes in an international climate regime would affect the European decarbonization strategy and costs through the mechanisms of trade, technology, and innovation. We present the results from the Energy Modeling Forum (EMF) model comparison study on European climate policy to 2050. Moving from a no-policy scenario to an existing-policies case reduces all energy imports, on average. Introducing a more stringent climate policy target for the EU only leads to slightly greater global emission reductions. Consumers and producers in Europe bear most of the additional burden and inevitably face some economic losses. More ambitious mitigation action outside Europe, especially when paired with a well-operating global carbon market, could reduce the burden for Europe significantly. Because of global learning, the costs of wind and especially solar-PV in Europe would decline below the levels observed in the existing-policy case and increased R&D spending outside the EU would leverage EU R&D investments as well.

Elimination of HIV in South Africa through Expanded Access to Antiretroviral Therapy: A Model Comparison Study

Expanded access to antiretroviral therapy (ART) using universal test and treat (UTT) has been suggested as a strategy to eliminate HIV in South Africa within 7 y based on an influential mathematical modeling study. However, the underlying deterministic model was criticized widely, and other modeling studies did not always confirm the study's finding. The objective of our study is to better understand the implications of different model structures and assumptions, so as to arrive at the best possible predictions of the long-term impact of UTT and the possibility of elimination of HIV. We developed nine structurally different mathematical models of the South African HIV epidemic in a stepwise approach of increasing complexity and realism. The simplest model resembles the initial deterministic model, while the most comprehensive model is the stochastic microsimulation model STDSIM, which includes sexual networks and HIV stages with different degrees of infectiousness. We defined UTT as annual screening and immediate ART for all HIV-infected adults, starting at 13% in January 2012 and scaled up to 90% coverage by January 2019. All models predict elimination, yet those that capture more processes underlying the HIV transmission dynamics predict elimination at a later point in time, after 20 to 25 y. Importantly, the most comprehensive model predicts that the current strategy of ART at CD4 count ≤350 cells/µl will also lead to elimination, albeit 10 y later compared to UTT. Still, UTT remains cost-effective, as many additional life-years would be saved. The study's major limitations are that elimination was defined as incidence below 1/1,000 person-years rather than 0% prevalence, and drug resistance was not modeled. Our results confirm previous predictions that the HIV epidemic in South Africa can be eliminated through universal testing and immediate treatment at 90% coverage. However, more realistic models show that elimination is likely to occur at a much later point in time than the initial model suggested. Also, UTT is a cost-effective intervention, but less cost-effective than previously predicted because the current South African ART treatment policy alone could already drive HIV into elimination. Please see later in the article for the Editors' Summary.

Environmental change impacts on the C- and N-cycle of European forests: a model comparison study

Abstract. Forests are important components of the greenhouse gas balance of Europe. There is considerable uncertainty about how predicted changes to climate and nitrogen deposition will perturb the carbon and nitrogen cycles of European forests and thereby alter forest growth, carbon sequestration and N2O emission. The present study aimed to quantify the carbon and nitrogen balance, including the exchange of greenhouse gases, of European forests over the period 2010–2030, with a particular emphasis on the spatial variability of change. The analysis was carried out for two tree species: European beech and Scots pine. For this purpose, four different dynamic models were used: BASFOR, DailyDayCent, INTEGRATOR and Landscape-DNDC. These models span a range from semi-empirical to complex mechanistic. Comparison of these models allowed assessment of the extent to which model predictions depended on differences in model inputs and structure. We found a European average carbon sink of 0.160 ± 0.020 kgC m−2 yr−1 (pine) and 0.138 ± 0.062 kgC m−2 yr−1 (beech) and N2O source of 0.285 ± 0.125 kgN ha−1 yr−1 (pine) and 0.575 ± 0.105 kgN ha−1 yr−1 (beech). The European average greenhouse gas potential of the carbon sink was 18 (pine) and 8 (beech) times that of the N2O source. Carbon sequestration was larger in the trees than in the soil. Carbon sequestration and forest growth were largest in central Europe and lowest in northern Sweden and Finland, N. Poland and S. Spain. No single driver was found to dominate change across Europe. Forests were found to be most sensitive to change in environmental drivers where the drivers were limiting growth, where changes were particularly large or where changes acted in concert. The models disagreed as to which environmental changes were most significant for the geographical variation in forest growth and as to which tree species showed the largest rate of carbon sequestration. Pine and beech forests were found to have differing sensitivities to environmental change, in particular the response to changes in nitrogen and precipitation, with beech forest more vulnerable to drought. There was considerable uncertainty about the geographical location of N2O emissions. Two of the models BASFOR and LandscapeDNDC had largest emissions in central Europe where nitrogen deposition and soil nitrogen were largest, whereas the two other models identified different regions with large N2O emission. N2O emissions were found to be larger from beech than pine forests and were found to be particularly sensitive to forest growth.

Multi-step-ahead prediction of NOx emissions for a coal-based boiler

Until 2016 power plants within the EU will have to meet new limits on emissions as dictated by EU regulations. One of the major challenges is to reduce emissions of nitrogen oxides (NOx) due to health and ozone-formation concerns. Combustion optimisation is one of the primary measures for reducing NOx emissions from boilers burning coal, oil, or natural gas. The optimisation can be achieved by excess air control, boiler fine tuning and balancing the fuel and air flow to the various burners in order to reach minimum NOx formation.In this paper, a multi-step-ahead prediction of NOx emissions that can provide a basis for on-line control is presented. About 9days’ worth of real data were acquired from an operator of a coal-based power plant for this study. It begins with a presentation of measured variables, pre-processing of the data and a definition of performance measures. Feature selection analysis follows, identifying the variables important for multi-step NOx prediction. In this respect, the impact of primary variables that are directly related to the combustion process is compared against that of other variables important in boiler operation and some transformed variables. Based on optimal features, a model comparison study including linear (ARX and ARMAX) and nonlinear (NN and SVR) modelling approaches is presented. Results of the model comparison study reveal that for the analysed boiler, nonlinear models do not improve the robust prediction performance of a linear ARX model. In the last part of the paper, an adaptive modelling approach further investigates the potential improvements in NOx prediction. A comparison of static and adaptive versions of the linear ARX model reveals that the adaptive approach does not improve prediction performance significantly. Hence the static ARX model in combination with an optimally selected set of input variables and extracted features is recommended for the multi-step NOx prediction of the coal-based boiler.

Implementations of a Flexible Framework for Managing Geologic Sequestration Modeling Projects

Numerical simulation is a standard practice used to support designing, operating, and monitoring CO2 injection projects. Although a variety of computational tools have been developed that support the numerical simulation process, many are single-purpose or platform specific and have a prescribed workflow that may or may not be suitable for a particular project. We are developing an open-source, flexible framework named Velo that provides a knowledge management infrastructure and tools to support modeling and simulation for various types of projects in a number of scientific domains. The Geologic Sequestration Software Suite (GS3) is a version of this framework with features and tools specifically tailored for geologic sequestration studies. Because of its general nature, GS3 is being employed in a variety of ways on projects with differing goals. GS3 is being used to support the Sim-SEQ international model comparison study, by providing a collaborative framework for the modeling teams and providing tools for model comparison. Another customized deployment of GS3 has been made to support the Class VI Well geologic sequestration permit application process. In this case, GS3 is being used to manage data in support of conceptual model development and provide documentation and provenance for numerical simulations. An additional customized deployment of GS3 is being created for use by the United States Environmental Protection Agency (US EPA) Underground Injection Control (UIC) Program to aid in the Class VI Well geologic sequestration permit application review process. These use cases demonstrate GS3's flexibility. utility, and broad applicability.

Long-term simulations of the sulfur concentrations over the China, Japan and Korea: A model comparison study

Three comprehensive acid deposition models were used to simulate the sulfur concentrations over northeast Asia over the period covering entire year of 2002, and discussed the aggregated uncertainties and discrepancies of the three models. The participating models are from the countries participating in the project of Longrange Transboundary Air Pollutants in Northeast Asia (LTP): China, Japan and Korea. The Eulerian Model-3/CMAQ (by China), Regional Air Quality Model (RAQM, by Japan), and Comprehensive Acid Deposition Model (CADM, by Korea) were employed by each country with common emissions data established by the administrative agencies of China, Japan and Korea. The episodic simulation results between 1 to 15, March 2002 are also presented, during which aircraft measurements were carried out over the Yellow sea. The episodic results show both a wide short-term variability in simulations against measurements, and maximum concentration differences of 3∼5 times among the three models, requiring that further attention before confidence among the three models can be claimed for short-term simulations. However, the year-long cumulative simulations showed almost the same general features, with lower aggregated uncertainties between the three models, produced by the long term integration over northeast Asia.

Modelling tide–surge interaction effects using finite volume and finite element models of the Irish Sea

An unstructured mesh model of the west coast of Britain, covering the same domain and using topography and open boundary forcing that are identical to a previous validated uniform grid finite difference model of the region, is used to compare the performance of a finite volume (FV) and a finite element (FE) model of the area in determining tide–surge interaction in the region. Initial calculations show that although qualitatively both models give comparable tidal solutions in the region, comparison with observations shows that the FV model tends to under-estimate tidal amplitudes and hence background tidal friction in the eastern Irish Sea. Storm surge elevations in the eastern Irish Sea due to westerly, northerly and southerly uniform wind stresses computed with the FV model tend to be slightly higher than those computed with the FE model, due to differences in background tidal friction. However, both models showed comparable non-linear tide–surge interaction effects for all wind directions, suggesting that they can reproduce the extensive tide–surge interaction processes that occur in the eastern Irish Sea. Following on from this model comparison study, the physical processes contributing to surge generation and tide–surge interaction in the region are examined. Calculations are performed with uniform wind stresses from a range of directions, and the balance of various terms in the hydrodynamic equations is examined. A detailed comparison of the spatial variability of time series of non-linear bottom friction and non-linear momentum advection terms at six adjacent nodes at two locations in water depths of 20 and 6 m showed some spatial variability from one node to another. This suggests that even in the near coastal region, where water depths are of the order of 6 m and the mesh is fine (of order 0.5 km), there is significant spatial variability in the non-linear terms. In addition, distributions of maximum bed stress due to tides and wind forcing in nearshore regions show appreciable spatial variability. This suggests that intensive measurement campaigns and very high-resolution mesh models are required to validate and reproduce the non-linear processes that occur in these regions and to predict extreme bed stresses that can give rise to sediment movement. High-resolution meshes will also be required in pollution transport problems.

Modelling drainage fluxes in managed and natural forests in the Dinaric karst: a model comparison study

Two models for calculating the forest water balance were applied to different development stages of managed and non-managed forests in the Dinaric Karst for two hydrologically contrasting growing seasons. A simple model WATBAL, which calculates water balance on a monthly basis, and the BROOK90 model, which calculates water balance on daily basis, were used. Differences between calculated drainage fluxes between the models were less pronounced in the drier growing season and were lower in the forest stands compared to forest gaps. Average calculated drainage fluxes of the two growing seasons were highest in the gaps and lowest in the stand in the virgin forest remnant, followed by the mature stand in the managed forest. According to model fitting, testing the calibration robustness and sensitivity analysis the BROOK90 model was considered best at simulating the water balance of the various research sites. The difference in model behaviour is considered to be mainly the result of the difference in model time step and the inclusion of macropore flow in BROOK90. The greater complexity of the BROOK90 model meant it could be parameterized to describe more fully the complexity of the horizontal and vertical structure of forest stand and soil properties. A disadvantage of the BROOK90 model is the greater need of input data. WATBAL, however, was useful for obtaining rougher estimates of the water balance components and can be applied to areas where there is less data available. Choice of model is therefore determined by data availability.

Modelling and estimating heterogeneous variances in threshold models for ordinal discrete data via Winbugs/Openbugs

Analysis of discrete repeated outcomes is an important issue in biomedical studies. The aim of this paper is to propose a flexible and parsimonious model to account for heterogeneous variances for discrete outcomes. The proposed method is based on the use of a linear mixed model on the log of the standard deviation parameters. It is also shown how parameter estimation in this model can be performed with an exact procedure based on a Gibbs sampling algorithm implemented with the Winbugs/Openbugs software. A model comparison study is presented to illustrate the efficiency of this procedure using a well known example from the clinical trial literature. It was found that the proposed methodology considerably improved the predictive ability of the model while remaining very parsimonious. In particular, it was found that adding a random subject effect in the variance model significantly improved the posterior predictive p-value criterion of the model.

A model comparison study of large-scale mantle–lithosphere dynamics driven by subduction

Modelling subduction involves solving the dynamic interaction between a rigid (solid yet deformable) plate and the fluid (easily deformable) mantle. Previous approaches neglected the solid-like behavior of the lithosphere by only considering a purely fluid description. However, over the past 5 years, a more self-consistent description of a mechanically differentiated subducting plate has emerged. The key feature in this mechanical description is incorporation of a strong core which provides small resistance to plate bending at subduction zones while simultaneously providing adequate stretching resistance such that slab pull drives forward plate motion. Additionally, the accompanying numerical approaches for simulating large-scale lithospheric deformation processes coupled to the underlying viscous mantle flow, have been become available. Here we put forward three fundamentally different numerical strategies, each of which is capabable of treating the advection of mechanically distinct materials that describe the subducting plate. We demonstrate their robustness by calculating the numerically challenging problem of subduction of a 6000 km wide slab at high-resolution in three-dimensions, the successfuly achievement of which only a few codes in the world can presently even attempt. In spite of the differences of the approaches, all three codes pass the simple qualitative test of developing an “S-bend” trench curvature previously observed in similar models. While reproducing this emergent feature validates that the lithosphere–mantle interaction has been correctly modelled, this is not a numerical benchmark in the traditional sense where the objective is for all codes to achieve exact agreement on a unique numerical solution. However, we do provide some quantitative comparisons such as trench and plate kinematics in addition to discussing the strength and weaknesses of the individual approaches. Consequently, we believe these developed algorithms can now be applied to study the parameters involved in the dynamics of subduction and offer a toolbox to be used by the entire geoscience community.

Soil Suspension/Dispersion Modeling Methods for Estimating Health-Based Soil Cleanup Levels of Hexavalent Chromium at Chromite Ore Processing Residue Sites

The primary health concern associated with exposures to chromite ore processing residue (COPR)-affected soils is inhalation of hexavalent chromium [Cr(VI)] particulates. Site-specific soil alternative remediation standards (ARSs) are set using soil suspension and dispersion models to be protective of the theoretical excess cancer risk associated with inhalation of soil suspended by vehicle traffic and wind. The purpose of this study was to update a previous model comparison study that identified the 1995 AP-42 particulate emission model for vehicle traffic over un-paved roads and the Fugitive Dust Model (FDM) as the most appropriate model combination for estimating site-specific ARSs. Because the AP-42 model has been revised, we have updated our past evaluation. Specifically, the 2006 AP-42 particulate emissions model; the Industrial Source Complex–Short Term model, version 3 (ISCST3); and the American Meteorological Society/Environmental Protection Agency Regulatory Model (AERMOD) air dispersion models were evaluated, and the results were compared with those from the previously used modeling approaches. Two sites with and two sites without vehicle traffic were evaluated to determine if wind erosion is a significant source of emissions. For the two sites with vehicle traffic, both FDM and ISCST3 produced total suspended particulate (TSP) estimates that were, on average, within a factor of 2 of measured; whereas AERMOD produced estimates that were as much as 5-fold higher than measured. In general, the estimated TSP concentrations for FDM were higher than those for ISCST3. For airborne Cr(VI), the ISCST3 model produced estimates that were only 2- to 8-fold of the measured concentrations, and both FDM and AERMOD estimated airborne Cr(VI) concentrations that were approximately 4- to 14-fold higher than measured. Results using the 1995 AP-42 model were closer to measured than those from the 2006 AP-42 model. Wind erosion was an insignificant contributor to particulate emissions at COPR sites.

Analysing the effects of soil properties changes associated with land use changes on the simulated water balance: A comparison of three hydrological catchment models for scenario analysis

This paper presents results of a model comparison study within the LUCHEM framework (‘assessing the impact of Land Use Change on Hydrology by Ensemble Modelling’) where the effects of land use change on catchment water balances were assessed with various hydrological catchment models. The motivation for this part of LUCHEM is that it is well known that land use changes may induce changes in soil chemical and soil physical properties (e.g. bulk density). Unfortunately the effects of land use change on soil hydraulic properties are seldom investigated directly, but some information on changes in bulk density is available. Changes in bulk density can be used as input for pedotransfer functions to derive changes in soil hydraulic model parameters. In this study, three different catchment models (SWAT, TOPLATS, WASIM) are compared with respect to their sensitivity to land use change with and without consideration of associated changes in soil parameterisation. The results reveal that different models show a different sensitivity to the change in soil parameterisation while the magnitude of absolute changes in simulated evapotranspiration and discharge is similar. SWAT calculates largest changes in the water balance in a German mesoscale catchment. TOPLATS also shows significant changes in the calculated catchment water balances as well as in the runoff generation while WASIM reacts least sensitive. While TOPLATS and WASIM show similar patterns with respect to changes in the water flows for all subcatchments and land use scenarios, SWAT results are similar for the different catchments, but show scenario specific patterns. In relation to the magnitude of the effects on simulated water flows induced by land use change, the significance of considering soil change effects depends on both, the scenario definition and on the model sensitivity to soil parameterisation. For two of the three land use scenarios representing an intensified land use, SWAT and TOPLATS simulate water balance changes in the same order of magnitude due to both, land use and soil property changes. Therefore, a consideration of changes in soil properties as part of land use change scenario analysis is recommended. Future field work needs to aim at the validation of the assumed dependency of soil hydrologic properties on land use change.

Multi-gas scenarios to stabilize radiative forcing

Using the results of a recent model comparison study performed by the Energy Modeling Forum, we have shown in this paper that including non-CO 2 gases in mitigation analysis is crucial in the formulation of a cost-effective response. In the absence of climate policies, the emissions of non-CO 2 greenhouse increase from 2.7 GtC-eq/year in 2000 to 5.1 GtC-eq/year in 2100 (averaged across all the models). A multi-gas reduction strategy stabilizing radiative forcing at 4.5 W/m 2 (compared to pre-industrial) reduces the emissions (on average) to 2.5 GtC-eq. Such an approach leads to a cost reduction of 30–40% compared to a CO 2 only reduction strategy for the same target. The choices of a target and how the gases are valued form an essential part of developing multi-gas strategies. Model results show that using IPCC global warming potentials (GWPs) as basis for substitution has large consequences for the timing of methane reductions. In this context, further research and assessment on multi-gas metrics, going beyond the mere physical aspects, are important for both research and policy-making.

What controls the uptake of transient tracers in the Southern Ocean?

We apply “residual mean” theory of tracer transport, in which eddy transfer plays a fundamental role, to develop scalings and idealized numerical models of the Southern Ocean uptake of transient tracers. The streamline‐averaged numerical model, which represents transport in the meridional plane, captures the observed distributions of CFC‐11, bomb‐Δ14C, and anthropogenic CO2. The model reproduces the observed relationship between CFC‐11 and bomb‐Δ14C and suggests that the upper branch of the residual overturning flow in the Southern Ocean is about 14 Sv, supporting previous inferences based on the observed buoyancy distribution and air‐sea buoyancy fluxes. Scale analysis suggests that the limit of fast air‐sea gas exchange is applicable to CFC‐11, for which the surface concentration is close to equilibrium and cumulative ocean uptake is largely determined by physical transport processes. In the slow gas exchange limit, applicable to bomb‐Δ14C, the surface concentration is far from equilibrium and the cumulative uptake is most sensitive to the parameterization of the gas transfer coefficient. Anthropogenic CO2 falls between those two limit cases and is sensitive to both transport processes and the gas transfer coefficient. Sensitivity studies using the streamline‐averaged model suggest that uncertainties in air‐sea buoyancy fluxes in current climatologies result in significant uncertainty in estimates of Southern Ocean uptake of anthropogenic CO2 based on circulation and biogeochemistry models driven by, or brought into consistency with, the climatological fluxes. This uncertainty is sufficient to explain a significant amount of the spread in a recent model comparison study.

Model studies of near‐inertial motion on the continental shelf off northeast Spain: A three‐dimensional/two‐dimensional/one‐dimensional model comparison study

A three‐dimensional nonlinear model of the Balearic Sea region is used to examine the spatial distribution of wind‐induced near‐inertial internal waves. Results from the model are compared with those from two‐dimensional cross‐section and single‐point models. In the case of motion induced by a wind pulse, there is no significant along‐shelf flow, and comparable solutions are obtained from the three‐and two‐dimensional models. However, when forced with a realistic wind, a significant along‐shelf flow is produced that is larger in the cross‐section model than in the three‐dimensional model because of the absence of an along‐shelf pressure gradient. Associated with this change in flow are important differences in across‐shelf currents and temperature fields that influence the distribution of near‐inertial motion. Since the point model cannot take account of internal pressure gradients, near‐inertial internal waves are absent. However, when some account of barotropic pressure gradients related to local wind stress are included, currents and inertial oscillations were in better agreement with the three‐dimensional model than with the cross‐section model. Although the major features of the wind‐induced deepening of the thermocline could be reproduced by the single‐point model, the absence of internal waves and mixing associated with them lead to a sharper thermocline than in the three‐dimensional model. Comparison of two‐ and one‐dimensional models with the full three‐dimensional model shows some severe limitations in the simpler models.