Climate determinism revisited: multiple equilibria in a complex climate model

Multiple equilibria in a coupled ocean–atmosphere–sea ice general circulation model (GCM) of an aquaplanet with many degrees of freedom are studied. Three different stable states are found for exactly the same set of parameters and external forcings: a cold state in which a polar sea ice cap extends into the midlatitudes; a warm state, which is ice free; and a completely sea ice–covered “snowball” state. Although low-order energy balance models of the climate are known to exhibit intransitivity (i.e., more than one climate state for a given set of governing equations), the results reported here are the first to demonstrate that this is a property of a complex coupled climate model with a consistent set of equations representing the 3D dynamics of the ocean and atmosphere. The coupled model notably includes atmospheric synoptic systems, large-scale circulation of the ocean, a fully active hydrological cycle, sea ice, and a seasonal cycle. There are no flux adjustments, with the system being solely forced by incoming solar radiation at the top of the atmosphere. It is demonstrated that the multiple equilibria owe their existence to the presence of meridional structure in ocean heat transport: namely, a large heat transport out of the tropics and a relatively weak high-latitude transport. The associated large midlatitude convergence of ocean heat transport leads to a preferred latitude at which the sea ice edge can rest. The mechanism operates in two very different ocean circulation regimes, suggesting that the stabilization of the large ice cap could be a robust feature of the climate system. Finally, the role of ocean heat convergence in permitting multiple equilibria is further explored in simpler models: an atmospheric GCM coupled to a slab mixed layer ocean and an energy balance model

Balance model for equatorial long waves

Geophysical fluid models often support both fast and slow motions. As the dynamics are often dominated by the slow motions, it is desirable to filter out the fast motions by constructing balance models. An example is the quasi geostrophic (QG) model, which is used widely in meteorology and oceanography for theoretical studies, in addition to practical applications such as model initialization and data assimilation. Although the QG model works quite well in the mid-latitudes, its usefulness diminishes as one approaches the equator. Thus far, attempts to derive similar balance models for the tropics have not been entirely successful as the models generally filter out Kelvin waves, which contribute significantly to tropical low-frequency variability. There is much theoretical interest in the dynamics of planetary-scale Kelvin waves, especially for atmospheric and oceanic data assimilation where observations are generally only of the mass field and thus do not constrain the wind field without some kind of diagnostic balance relation. As a result, estimates of Kelvin wave amplitudes can be poor. Our goal is to find a balance model that includes Kelvin waves for planetary-scale motions. Using asymptotic methods, we derive a balance model for the weakly nonlinear equatorial shallow-water equations. Specifically we adopt the ‘slaving’ method proposed by Warn et al. (Q. J. R. Meteorol. Soc., vol. 121, 1995, pp. 723–739), which avoids secular terms in the expansion and thus can in principle be carried out to any order. Different from previous approaches, our expansion is based on a long-wave scaling and the slow dynamics is described using the height field instead of potential vorticity. The leading-order model is equivalent to the truncated long-wave model considered previously (e.g. Heckley & Gill, Q. J. R. Meteorol. Soc., vol. 110, 1984, pp. 203–217), which retains Kelvin waves in addition to equatorial Rossby waves. Our method allows for the derivation of higher-order models which significantly improve the representation of Rossby waves in the isotropic limit. In addition, the ‘slaving’ method is applicable even when the weakly nonlinear assumption is relaxed, and the resulting nonlinear model encompasses the weakly nonlinear model. We also demonstrate that the method can be applied to more realistic stratified models, such as the Boussinesq model.

The Greenland Ice Sheet's surface mass balance in a seasonally sea-ice free Arctic

General circulation models predict a rapid decrease in sea ice extent with concurrent increases in near surface air temperature and precipitation in the Arctic over the 21st century. This has led to suggestions that some Arctic land ice masses may experience an increase in accumulation due to enhanced evaporation from a seasonally sea ice free Arctic Ocean. To investigate the impact of this phenomenon on Greenland ice sheet climate and surface mass balance (SMB) a regional climate model, HadRM3, was used to force an insolation-temperature melt SMB model. A set of experiments designed to investigate the role of sea ice independently from sea surface temperature (SST) forcing are described. In the warmer and wetter SI + SST simulation Greenland experiences a 23% increase in winter SMB but 65% reduced summer SMB, resulting in a net decrease in the annual value. This study shows that sea ice decline contributes to the increased winter balance, causing 25% of the increase in winter accumulation; this is largest in eastern Greenland as the result of increased evaporation in the Greenland Sea. These results indicate that the seasonal cycle of Greenland's SMB will increase dramatically as global temperatures increase, with the largest changes in temperature and precipitation occurring in winter. This demonstrates that the accurate prediction of changes in sea ice cover is important for predicting Greenland SMB and ice sheet evolution.

Nutrient-limited toxin production and the dynamics of two phytoplankton in culture media: a mathematical model

In this paper we have proposed and analyzed a simple mathematical model consisting of four variables, viz., nutrient concentration, toxin producing phytoplankton (TPP), non-toxic phytoplankton (NTP), and toxin concentration. Limitation in the concentration of the extracellular nutrient has been incorporated as an environmental stress condition for the plankton population, and the liberation of toxic chemicals has been described by a monotonic function of extracellular nutrient. The model is analyzed and simulated to reproduce the experimental findings of Graneli and Johansson [Graneli, E., Johansson, N., 2003. Increase in the production of allelopathic Prymnesium parvum cells grown under N- or P-deficient conditions. Harmful Algae 2, 135–145]. The robustness of the numerical experiments are tested by a formal parameter sensitivity analysis. As the first theoretical model consistent with the experiment of Graneli and Johansson (2003), our results demonstrate that, when nutrient-deficient conditions are favorable for the TPP population to release toxic chemicals, the TPP species control the bloom of other phytoplankton species which are non-toxic. Consistent with the observations made by Graneli and Johansson (2003), our model overcomes the limitation of not incorporating the effect of nutrient-limited toxic production in several other models developed on plankton dynamics.

Distribution of calcium (Ca) and magnesium (Mg) in the leaves of Brassica rapa under varying exogenous Ca and Mg supply

Background and Aims Leafy vegetable Brassica crops are an important source of dietary calcium (Ca) and magnesium (Mg) and represent potential targets for increasing leaf Ca and Mg concentrations through agronomy or breeding. Although the internal distribution of Ca and Mg within leaves affects the accumulation of these elements, such data are not available for Brassica. The aim of this study was to characterize the internal distribution of Ca and Mg in the leaves of a vegetable Brassica and to determine the effects of altered exogenous Ca and Mg supply on this distribution. Methods Brassica rapa ssp. trilocularis ‘R-o-18’ was grown at four different Ca:Mg treatments for 21 d in a controlled environment. Concentrations of Ca and Mg were determined in fully expanded leaves using inductively coupled plasma-mass spectrometry (ICP-MS). Internal distributions of Ca and Mg were determined in transverse leaf sections at the base and apex of leaves using energy-dispersive X-ray spectroscopy (EDS) with cryo-scanning electron microscopy (cryo-SEM). Key Results Leaf Ca and Mg concentrations were greatest in palisade and spongy mesophyll cells, respectively, although this was dependent on exogenous supply. Calcium accumulation in palisade mesophyll cells was enhanced slightly under high Mg supply; in contrast, Mg accumulation in spongy mesophyll cells was not affected by Ca supply. Conclusions The results are consistent with Arabidopsis thaliana and other Brassicaceae, providing phenotypic evidence that conserved mechanisms regulate leaf Ca and Mg distribution at a cellular scale. The future study of Arabidopsis gene orthologues in mutants of this reference B. rapa genotype will improve our understanding of Ca and Mg homeostasis in plants and may provide a model-to-crop translation pathway for targeted breeding.

Updated empirical model of genetically-modified maize grain production practices to achieve European Union labeling thresholds

An updated empirical approach is proposed for specifying coexistence requirements for genetically modified (GM) maize (Zea mays L.) production to ensure compliance with the 0.9% labeling threshold for food and feed in the European Union. The model improves on a previously published (Gustafson et al., 2006) empirical model by adding recent data sources to supplement the original database and including the following additional cases: (i) more than one GM maize source field adjacent to the conventional or organic field, (ii) the possibility of so-called “stacked” varieties with more than one GM trait, and (iii) lower pollen shed in the non-GM receptor field. These additional factors lead to the possibility for somewhat wider combinations of isolation distance and border rows than required in the original version of the empirical model. For instance, in the very conservative case of a 1-ha square non-GM maize field surrounded on all four sides by homozygous GM maize with 12 m isolation (the effective isolation distance for a single GM field), non-GM border rows of 12 m are required to be 95% confident of gene flow less than 0.9% in the non-GM field (with adventitious presence of 0.3%). Stacked traits of higher GM mass fraction and receptor fields of lower pollen shed would require a greater number of border rows to comply with the 0.9% threshold, and an updated extension to the model is provided to quantify these effects.

Atmospheric blocking in a high resolution climate model: influences of mean state, orography and eddy forcing

An underestimate of atmospheric blocking occurrence is a well-known limitation of many climate models. This article presents an analysis of Northern Hemisphere winter blocking in an atmospheric model with increased horizontal resolution. European blocking frequency increases with model resolution, and this results from an improvement in the atmospheric patterns of variability as well as a simple improvement in the mean state. There is some evidence that the transient eddy momentum forcing of European blocks is increased at high resolution, which could account for this. However, it is also shown that the increase in resolution of the orography is needed to realise the improvement in blocking, consistent with the increase in height of the Rocky Mountains acting to increase the tilt of the Atlantic jet stream and giving higher mean geopotential heights over northern Europe. Blocking frequencies in the Pacific sector are also increased with atmospheric resolution, but in this case the improvement in orography actually leads to a decrease in blocking

Proactive R&D management and firm growth: a punctuated equilibrium model

The external environment is characterized by periods of relative stability interspersed with periods of extreme change, implying that high performing firms must practice exploration and exploitation in order to survive and thrive. In this paper, we posit that R&D expenditure volatility indicates the presence of proactive R&D management, and is evidence of a firm moving from exploitation to exploration over time. This is consistent with a punctuated equilibrium model of R&D investment where shocks are induced by reactions to external turbulence. Using an unbalanced panel of almost 11,000 firm-years from 1997 to 2006, we show that greater fluctuations in the firm's R&D expenditure over time are associated with higher firm growth. Developing a contextual view of the relationship between R&D expenditure volatility and firm growth, we find that this relationship is weaker among firms with higher levels of corporate diversification and negative among smaller firms and those in slow clockspeed industries.

A self-similar expansion model for use in solar wind transient propogation studies

Since the advent of wide-angle imaging of the inner heliosphere, a plethora of techniques have been developed to investigate the three-dimensional structure and kinematics of solar wind transients, such as coronal mass ejections, from their signatures in single- and multi-spacecraft imaging observations. These techniques, which range from the highly complex and computationally intensive to methods based on simple curve fitting, all have their inherent advantages and limitations. In the analysis of single-spacecraft imaging observations, much use has been made of the fixed φ fitting (FPF) and harmonic mean fitting (HMF) techniques, in which the solar wind transient is considered to be a radially propagating point source (fixed φ, FP, model) and a radially expanding circle anchored at Sun centre (harmonic mean, HM, model), respectively. Initially, we compare the radial speeds and propagation directions derived from application of the FPF and HMF techniques to a large set of STEREO/Heliospheric Imager (HI) observations. As the geometries on which these two techniques are founded constitute extreme descriptions of solar wind transients in terms of their extent along the line of sight, we describe a single-spacecraft fitting technique based on a more generalized model for which the FP and HM geometries form the limiting cases. In addition to providing estimates of a transient’s speed and propagation direction, the self-similar expansion fitting (SSEF) technique provides, in theory, the capability to estimate the transient’s angular extent in the plane orthogonal to the field of view. Using the HI observations, and also by performing a Monte Carlo simulation, we assess the potential of the SSEF technique.

Multiwavelength Observations of EXO 0748-676. I. Reprocessing of X-Ray Bursts

We present high time-resolution multiwavelength observations of X-ray bursts in the low-mass X-ray binary UY Vol. Strong reprocessed signals are present in the ultraviolet and optical, lagged and smeared with respect to the X-rays. The addition of far-ultraviolet coverage for one burst allows much tighter constraints on the temperature and geometry of the reprocessing region than previously possible. A blackbody reprocessing model for this burst suggests a rise in temperatures during the burst from 18,000 to 35,000 K and an emitting area comparable to that expected for the disk and/or irradiated companion star. The lags are consistent with those expected. The single-zone blackbody model cannot reproduce the ratio of optical to ultraviolet flux during the burst, however. The discrepancy seems too large to explain with deviations from a local blackbody spectrum and more likely indicates that a range of reprocessing temperatures are required. Comparable results are derived from other bursts, and in particular the lag and smearing both appear shorter when the companion star is on the near side of the disk as predicted. The burst observed by HST also yielded a spectrum of the reprocessed light. It is dominated by continuum, with a spectral shape consistent with the temperatures derived from lightcurve modeling. Taken as a whole, our observations confirm the standard paradigm of prompt reprocessing distributed across the disk and companion star, with the response dominated by a thermalized continuum rather than by emission lines.

Present state of global wetland extent and wetland methane modelling: conclusions from a model inter-comparison project (WETCHIMP)

Global wetlands are believed to be climate sensitive, and are the largest natural emitters of methane (CH4). Increased wetland CH4 emissions could act as a positive feedback to future warming. The Wetland and Wetland CH4 Inter-comparison of Models Project (WETCHIMP) investigated our present ability to simulate large-scale wetland characteristics and corresponding CH4 emissions. To ensure inter-comparability, we used a common experimental protocol driving all models with the same climate and carbon dioxide (CO2) forcing datasets. The WETCHIMP experiments were conducted for model equilibrium states as well as transient simulations covering the last century. Sensitivity experiments investigated model response to changes in selected forcing inputs (precipitation, temperature, and atmospheric CO2 concentration). Ten models participated, covering the spectrum from simple to relatively complex, including models tailored either for regional or global simulations. The models also varied in methods to calculate wetland size and location, with some models simulating wetland area prognostically, while other models relied on remotely sensed inundation datasets, or an approach intermediate between the two. Four major conclusions emerged from the project. First, the suite of models demonstrate extensive disagreement in their simulations of wetland areal extent and CH4 emissions, in both space and time. Simple metrics of wetland area, such as the latitudinal gradient, show large variability, principally between models that use inundation dataset information and those that independently determine wetland area. Agreement between the models improves for zonally summed CH4 emissions, but large variation between the models remains. For annual global CH4 emissions, the models vary by ±40% of the all-model mean (190 Tg CH4 yr−1). Second, all models show a strong positive response to increased atmospheric CO2 concentrations (857 ppm) in both CH4 emissions and wetland area. In response to increasing global temperatures (+3.4 °C globally spatially uniform), on average, the models decreased wetland area and CH4 fluxes, primarily in the tropics, but the magnitude and sign of the response varied greatly. Models were least sensitive to increased global precipitation (+3.9 % globally spatially uniform) with a consistent small positive response in CH4 fluxes and wetland area. Results from the 20th century transient simulation show that interactions between climate forcings could have strong non-linear effects. Third, we presently do not have sufficient wetland methane observation datasets adequate to evaluate model fluxes at a spatial scale comparable to model grid cells (commonly 0.5°). This limitation severely restricts our ability to model global wetland CH4 emissions with confidence. Our simulated wetland extents are also difficult to evaluate due to extensive disagreements between wetland mapping and remotely sensed inundation datasets. Fourth, the large range in predicted CH4 emission rates leads to the conclusion that there is both substantial parameter and structural uncertainty in large-scale CH4 emission models, even after uncertainties in wetland areas are accounted for.

Present state of global wetland extent and wetland methane modelling: methodology of a model inter-comparison project (WETCHIMP)

The Wetland and Wetland CH4 Intercomparison of Models Project (WETCHIMP) was created to evaluate our present ability to simulate large-scale wetland characteristics and corresponding methane (CH4) emissions. A multi-model comparison is essential to evaluate the key uncertainties in the mechanisms and parameters leading to methane emissions. Ten modelling groups joined WETCHIMP to run eight global and two regional models with a common experimental protocol using the same climate and atmospheric carbon dioxide (CO2) forcing datasets. We reported the main conclusions from the intercomparison effort in a companion paper (Melton et al., 2013). Here we provide technical details for the six experiments, which included an equilibrium, a transient, and an optimized run plus three sensitivity experiments (temperature, precipitation, and atmospheric CO2 concentration). The diversity of approaches used by the models is summarized through a series of conceptual figures, and is used to evaluate the wide range of wetland extent and CH4 fluxes predicted by the models in the equilibrium run. We discuss relationships among the various approaches and patterns in consistencies of these model predictions. Within this group of models, there are three broad classes of methods used to estimate wetland extent: prescribed based on wetland distribution maps, prognostic relationships between hydrological states based on satellite observations, and explicit hydrological mass balances. A larger variety of approaches was used to estimate the net CH4 fluxes from wetland systems. Even though modelling of wetland extent and CH4 emissions has progressed significantly over recent decades, large uncertainties still exist when estimating CH4 emissions: there is little consensus on model structure or complexity due to knowledge gaps, different aims of the models, and the range of temporal and spatial resolutions of the models.

Impact of the modal aerosol scheme GLOMAP-mode on aerosol forcing in the Hadley Centre Global Environmental Model

The Hadley Centre Global Environmental Model (HadGEM) includes two aerosol schemes: the Coupled Large-scale Aerosol Simulator for Studies in Climate (CLASSIC), and the new Global Model of Aerosol Processes (GLOMAP-mode). GLOMAP-mode is a modal aerosol microphysics scheme that simulates not only aerosol mass but also aerosol number, represents internally-mixed particles, and includes aerosol microphysical processes such as nucleation. In this study, both schemes provide hindcast simulations of natural and anthropogenic aerosol species for the period 2000–2006. HadGEM simulations of the aerosol optical depth using GLOMAP-mode compare better than CLASSIC against a data-assimilated aerosol re-analysis and aerosol ground-based observations. Because of differences in wet deposition rates, GLOMAP-mode sulphate aerosol residence time is two days longer than CLASSIC sulphate aerosols, whereas black carbon residence time is much shorter. As a result, CLASSIC underestimates aerosol optical depths in continental regions of the Northern Hemisphere and likely overestimates absorption in remote regions. Aerosol direct and first indirect radiative forcings are computed from simulations of aerosols with emissions for the year 1850 and 2000. In 1850, GLOMAP-mode predicts lower aerosol optical depths and higher cloud droplet number concentrations than CLASSIC. Consequently, simulated clouds are much less susceptible to natural and anthropogenic aerosol changes when the microphysical scheme is used. In particular, the response of cloud condensation nuclei to an increase in dimethyl sulphide emissions becomes a factor of four smaller. The combined effect of different 1850 baselines, residence times, and abilities to affect cloud droplet number, leads to substantial differences in the aerosol forcings simulated by the two schemes. GLOMAP-mode finds a presentday direct aerosol forcing of −0.49Wm−2 on a global average, 72% stronger than the corresponding forcing from CLASSIC. This difference is compensated by changes in first indirect aerosol forcing: the forcing of −1.17Wm−2 obtained with GLOMAP-mode is 20% weaker than with CLASSIC. Results suggest that mass-based schemes such as CLASSIC lack the necessary sophistication to provide realistic input to aerosol-cloud interaction schemes. Furthermore, the importance of the 1850 baseline highlights how model skill in predicting present-day aerosol does not guarantee reliable forcing estimates. Those findings suggest that the more complex representation of aerosol processes in microphysical schemes improves the fidelity of simulated aerosol forcings.

Aerosol indirect effects – general circulation model intercomparison and evaluation with satellite data

Aerosol indirect effects continue to constitute one of the most important uncertainties for anthropogenic climate perturbations. Within the international AEROCOM initiative, the representation of aerosol-cloud-radiation interactions in ten different general circulation models (GCMs) is evaluated using three satellite datasets. The focus is on stratiform liquid water clouds since most GCMs do not include ice nucleation effects, and none of the model explicitly parameterises aerosol effects on convective clouds. We compute statistical relationships between aerosol optical depth (τa) and various cloud and radiation quantities in a manner that is consistent between the models and the satellite data. It is found that the model-simulated influence of aerosols on cloud droplet number concentration (Nd ) compares relatively well to the satellite data at least over the ocean. The relationship between �a and liquid water path is simulated much too strongly by the models. This suggests that the implementation of the second aerosol indirect effect mainly in terms of an autoconversion parameterisation has to be revisited in the GCMs. A positive relationship between total cloud fraction (fcld) and �a as found in the satellite data is simulated by the majority of the models, albeit less strongly than that in the satellite data in most of them. In a discussion of the hypotheses proposed in the literature to explain the satellite-derived strong fcld–�a relationship, our results indicate that none can be identified as a unique explanation. Relationships similar to the ones found in satellite data between �a and cloud top temperature or outgoing long-wave radiation (OLR) are simulated by only a few GCMs. The GCMs that simulate a negative OLR - �a relationship show a strong positive correlation between �a and fcld. The short-wave total aerosol radiative forcing as simulated by the GCMs is strongly influenced by the simulated anthropogenic fraction of �a, and parameterisation assumptions such as a lower bound on Nd . Nevertheless, the strengths of the statistical relationships are good predictors for the aerosol forcings in the models. An estimate of the total short-wave aerosol forcing inferred from the combination of these predictors for the modelled forcings with the satellite-derived statistical relationships yields a global annual mean value of −1.5±0.5Wm−2. In an alternative approach, the radiative flux perturbation due to anthropogenic aerosols can be broken down into a component over the cloud-free portion of the globe (approximately the aerosol direct effect) and a component over the cloudy portion of the globe (approximately the aerosol indirect effect). An estimate obtained by scaling these simulated clearand cloudy-sky forcings with estimates of anthropogenic �a and satellite-retrieved Nd–�a regression slopes, respectively, yields a global, annual-mean aerosol direct effect estimate of −0.4±0.2Wm−2 and a cloudy-sky (aerosol indirect effect) estimate of −0.7±0.5Wm−2, with a total estimate of −1.2±0.4Wm−2.

General circulation model estimates of aerosol transport and radiative forcing during the Indian Ocean Experiment

Aerosol sources, transport, and sinks are simulated, and aerosol direct radiative effects are assessed over the Indian Ocean for the Indian Ocean Experiment (INDOEX) Intensive Field Phase during January to March 1999 using the Laboratoire de Me´te´orologie Dynamique (LMDZT) general circulation model. The model reproduces the latitudinal gradient in aerosol mass concentration and optical depth (AOD). The model-predicted aerosol concentrations and AODs agree reasonably well with measurements but are systematically underestimated during high-pollution episodes, especially in the month of March. The largest aerosol loads are found over southwestern China, the Bay of Bengal, and the Indian subcontinent. Aerosol emissions from the Indian subcontinent are transported into the Indian Ocean through either the west coast or the east coast of India. Over the INDOEX region, carbonaceous aerosols are the largest contributor to the estimated AOD, followed by sulfate, dust, sea salt, and fly ash. During the northeast winter monsoon, natural and anthropogenic aerosols reduce the solar flux reaching the surface by 25 W m�2, leading to 10–15% less insolation at the surface. A doubling of black carbon (BC) emissions from Asia results in an aerosol single-scattering albedo that is much smaller than in situ measurements, reflecting the fact that BC emissions are not underestimated in proportion to other (mostly scattering) aerosol types. South Asia is the dominant contributor to sulfate aerosols over the INDOEX region and accounts for 60–70% of the AOD by sulfate. It is also an important but not the dominant contributor to carbonaceous aerosols over the INDOEX region with a contribution of less than 40% to the AOD by this aerosol species. The presence of elevated plumes brings significant quantities of aerosols to the Indian Ocean that are generated over Africa and Southeast and east Asia.