Spectral nonlocality, absolute equilibria and Kraichnan-Leith-Batchelor phenomenology in two-dimensional turbulent energy cascades

We study the degree to which Kraichnan–Leith–Batchelor (KLB) phenomenology describes two-dimensional energy cascades in α turbulence, governed by ∂θ/∂t+J(ψ,θ)=ν∇2θ+f, where θ=(−Δ)α/2ψ is generalized vorticity, and ψ^(k)=k−αθ^(k) in Fourier space. These models differ in spectral non-locality, and include surface quasigeostrophic flow (α=1), regular two-dimensional flow (α=2) and rotating shallow flow (α=3), which is the isotropic limit of a mantle convection model. We re-examine arguments for dual inverse energy and direct enstrophy cascades, including Fjørtoft analysis, which we extend to general α, and point out their limitations. Using an α-dependent eddy-damped quasinormal Markovian (EDQNM) closure, we seek self-similar inertial range solutions and study their characteristics. Our present focus is not on coherent structures, which the EDQNM filters out, but on any self-similar and approximately Gaussian turbulent component that may exist in the flow and be described by KLB phenomenology. For this, the EDQNM is an appropriate tool. Non-local triads contribute increasingly to the energy flux as α increases. More importantly, the energy cascade is downscale in the self-similar inertial range for 2.5<α<10. At α=2.5 and α=10, the KLB spectra correspond, respectively, to enstrophy and energy equipartition, and the triad energy transfers and flux vanish identically. Eddy turnover time and strain rate arguments suggest the inverse energy cascade should obey KLB phenomenology and be self-similar for α<4. However, downscale energy flux in the EDQNM self-similar inertial range for α>2.5 leads us to predict that any inverse cascade for α≥2.5 will not exhibit KLB phenomenology, and specifically the KLB energy spectrum. Numerical simulations confirm this: the inverse cascade energy spectrum for α≥2.5 is significantly steeper than the KLB prediction, while for α<2.5 we obtain the KLB spectrum.

High-latitude climate sensitivity to ice-sheet forcing over the last 120kyr

Interpretation of ice-core records is currently limited by paucity of modelling at adequate temporal and spatial resolutions. Several key questions relate to mechanisms of polar amplification and inter-hemispheric coupling on glacial/interglacial timescales. Here, we present the first results from a large set of global ocean–atmosphere climate model ‘snap-shot’ simulations covering the last 120 000 years using the Hadley Centre climate model (HadCM3) at up to 1 kyr temporal resolution. Two sets of simulations were performed in order to examine the roles of orbit and greenhouse gases versus ice-sheet forcing of orbital-scale climate change. A series of idealised Heinrich events were also simulated, but no changes to aerosols or vegetation were prescribed. This paper focuses on high latitudes and inter-hemispheric linkages. The simulations reproduce polar temperature trends well compared to ice-core reconstructions, although the magnitude is underestimated. Polar amplification varies with obliquity, but this variability is dampened by including variations in land ice coverage, while the overall amplification factor increases. The relatively constant amplification of Antarctic temperatures (with ice-sheet forcing included) suggests it is possible to use Antarctic temperature reconstructions to estimate global changes (which are roughly half the magnitude). Atlantic Ocean overturning circulation varies considerably only with the introduction of Northern Hemisphere ice sheets, but only weakens in the North Atlantic in the deep glacial, when ocean–sea-ice feedbacks result in the movement of the region of deep convection to lower latitudes and with the introduction of freshwater to the surface North Atlantic in order to simulate Heinrich events.

Sensitivity analysis of an ocean carbon cycle model in the North Atlantic: an investigation of parameters affecting the air-sea CO2 flux, primary production and export of detritus

The sensitivity of the biological parameters in a nutrient-phytoplankton-zooplankton-detritus (NPZD) model in the calculation of the air-sea CO2 flux, primary production and detrital export is analysed. We explore the effect on these outputs of variation in the values of the twenty parameters that control ocean ecosystem growth in a 1-D formulation of the UK Met Office HadOCC NPZD model used in GCMs. We use and compare the results from one-at-a-time and all-at-a-time perturbations performed at three sites in the EuroSITES European Ocean Observatory Network: the Central Irminger Sea (60° N 40° W), the Porcupine Abyssal Plain (49° N 16° W) and the European Station for Time series in the Ocean Canary Islands (29° N 15° W). Reasonable changes to the values of key parameters are shown to have a large effect on the calculation of the air-sea CO2 flux, primary production, and export of biological detritus to the deep ocean. Changes in the values of key parameters have a greater effect in more productive regions than in less productive areas. The most sensitive parameters are generally found to be those controlling well-established ocean ecosystem parameterisations widely used in many NPZD-type models. The air-sea CO2 flux is most influenced by variation in the parameters that control phytoplankton growth, detrital sinking and carbonate production by phytoplankton (the rain ratio). Primary production is most sensitive to the parameters that define the shape of the photosynthesis-irradiance curve. Export production is most sensitive to the parameters that control the rate of detrital sinking and the remineralisation of detritus.

Estimation of sea surface temperature from the Spinning Enhanced Visible and Infra Red Imager, improved using numerical weather prediction

Most of the operational Sea Surface Temperature (SST) products derived from satellite infrared radiometry use multi-spectral algorithms. They show, in general, reasonable performances with root mean square (RMS) residuals around 0.5 K when validated against buoy measurements, but have limitations, particularly a component of the retrieval error that relates to such algorithms' limited ability to cope with the full variability of atmospheric absorption and emission. We propose to use forecast atmospheric profiles and a radiative transfer model to simulate the algorithmic errors of multi-spectral algorithms. In the practical case of SST derived from the Spinning Enhanced Visible and Infrared Imager (SEVIRI) onboard Meteosat Second Generation (MSG), we demonstrate that simulated algorithmic errors do explain a significant component of the actual errors observed for the non linear (NL) split window algorithm in operational use at the Centre de Météorologie Spatiale (CMS). The simulated errors, used as correction terms, reduce significantly the regional biases of the NL algorithm as well as the standard deviation of the differences with drifting buoy measurements. The availability of atmospheric profiles associated with observed satellite-buoy differences allows us to analyze the origins of the main algorithmic errors observed in the SEVIRI field of view: a negative bias in the inter-tropical zone, and a mid-latitude positive bias. We demonstrate how these errors are explained by the sensitivity of observed brightness temperatures to the vertical distribution of water vapour, propagated through the SST retrieval algorithm.

Determination of a lower bound on Earth’s climate sensitivity

Transient and equilibrium sensitivity of Earth's climate has been calculated using global temperature, forcing and heating rate data for the period 1970–2010. We have assumed increased long-wave radiative forcing in the period due to the increase of the long-lived greenhouse gases. By assuming the change in aerosol forcing in the period to be zero, we calculate what we consider to be lower bounds to these sensitivities, as the magnitude of the negative aerosol forcing is unlikely to have diminished in this period. The radiation imbalance necessary to calculate equilibrium sensitivity is estimated from the rate of ocean heat accumulation as 0.37±0.03W m^−2 (all uncertainty estimates are 1−σ). With these data, we obtain best estimates for transient climate sensitivity 0.39±0.07K (W m^−2)^−1 and equilibrium climate sensitivity 0.54±0.14K (W m^−2)^−1, equivalent to 1.5±0.3 and 2.0±0.5K (3.7W m^−2)^−1, respectively. The latter quantity is equal to the lower bound of the ‘likely’ range for this quantity given by the 2007 IPCC Assessment Report. The uncertainty attached to the lower-bound equilibrium sensitivity permits us to state, within the assumptions of this analysis, that the equilibrium sensitivity is greater than 0.31K (W m^−2)^−1, equivalent to 1.16K(3.7W m^−2)^−1, at the 95% confidence level.

Error, reproducibility and sensitivity: a pipeline for data processing of Agilent oligonucleotide expression arrays

Background: Expression microarrays are increasingly used to obtain large scale transcriptomic information on a wide range of biological samples. Nevertheless, there is still much debate on the best ways to process data, to design experiments and analyse the output. Furthermore, many of the more sophisticated mathematical approaches to data analysis in the literature remain inaccessible to much of the biological research community. In this study we examine ways of extracting and analysing a large data set obtained using the Agilent long oligonucleotide transcriptomics platform, applied to a set of human macrophage and dendritic cell samples. Results: We describe and validate a series of data extraction, transformation and normalisation steps which are implemented via a new R function. Analysis of replicate normalised reference data demonstrate that intrarray variability is small (only around 2 of the mean log signal), while interarray variability from replicate array measurements has a standard deviation (SD) of around 0.5 log(2) units (6 of mean). The common practise of working with ratios of Cy5/Cy3 signal offers little further improvement in terms of reducing error. Comparison to expression data obtained using Arabidopsis samples demonstrates that the large number of genes in each sample showing a low level of transcription reflect the real complexity of the cellular transcriptome. Multidimensional scaling is used to show that the processed data identifies an underlying structure which reflect some of the key biological variables which define the data set. This structure is robust, allowing reliable comparison of samples collected over a number of years and collected by a variety of operators. Conclusions: This study outlines a robust and easily implemented pipeline for extracting, transforming normalising and visualising transcriptomic array data from Agilent expression platform. The analysis is used to obtain quantitative estimates of the SD arising from experimental (non biological) intra- and interarray variability, and for a lower threshold for determining whether an individual gene is expressed. The study provides a reliable basis for further more extensive studies of the systems biology of eukaryotic cells.

Using genomic DNA-based probe-selection to improve the sensitivity of high-density oligonucleotide arrays when applied to heterologous species

High-density oligonucleotide (oligo) arrays are a powerful tool for transcript profiling. Arrays based on GeneChip® technology are amongst the most widely used, although GeneChip® arrays are currently available for only a small number of plant and animal species. Thus, we have developed a method to improve the sensitivity of high-density oligonucleotide arrays when applied to heterologous species and tested the method by analysing the transcriptome of Brassica oleracea L., a species for which no GeneChip® array is available, using a GeneChip® array designed for Arabidopsis thaliana (L.) Heynh. Genomic DNA from B. oleracea was labelled and hybridised to the ATH1-121501 GeneChip® array. Arabidopsis thaliana probe-pairs that hybridised to the B. oleracea genomic DNA on the basis of the perfect-match (PM) probe signal were then selected for subsequent B. oleracea transcriptome analysis using a .cel file parser script to generate probe mask files. The transcriptional response of B. oleracea to a mineral nutrient (phosphorus; P) stress was quantified using probe mask files generated for a wide range of gDNA hybridisation intensity thresholds. An example probe mask file generated with a gDNA hybridisation intensity threshold of 400 removed > 68 % of the available PM probes from the analysis but retained >96 % of available A. thaliana probe-sets. Ninety-nine of these genes were then identified as significantly regulated under P stress in B. oleracea, including the homologues of P stress responsive genes in A. thaliana. Increasing the gDNA hybridisation intensity thresholds up to 500 for probe-selection increased the sensitivity of the GeneChip® array to detect regulation of gene expression in B. oleracea under P stress by up to 13-fold. Our open-source software to create probe mask files is freely available http://affymetrix.arabidopsis.info/xspecies/ webcite and may be used to facilitate transcriptomic analyses of a wide range of plant and animal species in the absence of custom arrays.

High sensitivity recording of afferent nerve activity using ultra-compliant microchannel electrodes: an acutein vivovalidation

Neuroprostheses interfaced with transected peripheral nerves are technological routes to control robotic limbs as well as convey sensory feedback to patients suffering from traumatic neural injuries or degenerative diseases. To maximize the wealth of data obtained in recordings, interfacing devices are required to have intrafascicular resolution and provide high signal-to-noise ratio (SNR) recordings. In this paper, we focus on a possible building block of a three-dimensional regenerative implant: a polydimethylsiloxane (PDMS) microchannel electrode capable of highly sensitive recordings in vivo. The PDMS 'micro-cuff' consists of a 3.5 mm long (100 µm × 70 µm cross section) microfluidic channel equipped with five evaporated Ti/Au/Ti electrodes of sub-100 nm thickness. Individual electrodes have average impedance of 640 ± 30 kΩ with a phase angle of −58 ± 1 degrees at 1 kHz and survive demanding mechanical handling such as twisting and bending. In proof-of-principle acute implantation experiments in rats, surgically teased afferent nerve strands from the L5 dorsal root were threaded through the microchannel. Tactile stimulation of the skin was reliably monitored with the three inner electrodes in the device, simultaneously recording signal amplitudes of up to 50 µV under saline immersion. The overall SNR was approximately 4. A small but consistent time lag between the signals arriving at the three electrodes was observed and yields a fibre conduction velocity of 30 m s−1. The fidelity of the recordings was verified by placing the same nerve strand in oil and recording activity with hook electrodes. Our results show that PDMS microchannel electrodes open a promising technological path to 3D regenerative interfaces.

Sensitivity of global sulphate aerosol production to changes in oxidant concentrations and climate

The oxidation of SO2 to sulphate aerosol is an important process to include in climate models, and uncertainties caused by ignoring feedback mechanisms affecting the oxidants concerned need to be investigated. Here we present the results of an investigation into the sensitivity of sulphate concentrations to oxidant changes (from changes in climate and in emissions of oxidant precursors) and to changes in climate, in a version of HadGAM1 (the atmosphere-only version of HadGEM1) with an improved sulphur cycle scheme. We find that, when oxidants alone are changed, the global total sulphate burden decreases by approximately 3%, due mainly to a reduction in the OH burden. When climate alone is changed, our results show that the global total sulphate burden increases by approximately 9%; we conclude that this is probably attributable to reduced precipitation in regions of high sulphate abundance. When both oxidants and climate are changed simultaneously, we find that the effects of the two changes combine approximately linearly.

Spectral asymmetry of the massless Dirac operator on a 3-torus

Consider the massless Dirac operator on a 3-torus equipped with Euclidean metric and standard spin structure. It is known that the eigenvalues can be calculated explicitly: the spectrum is symmetric about zero and zero itself is a double eigenvalue. The aim of the paper is to develop a perturbation theory for the eigenvalue with smallest modulus with respect to perturbations of the metric. Here the application of perturbation techniques is hindered by the fact that eigenvalues of the massless Dirac operator have even multiplicity, which is a consequence of this operator commuting with the antilinear operator of charge conjugation (a peculiar feature of dimension 3). We derive an asymptotic formula for the eigenvalue with smallest modulus for arbitrary perturbations of the metric and present two particular families of Riemannian metrics for which the eigenvalue with smallest modulus can be evaluated explicitly. We also establish a relation between our asymptotic formula and the eta invariant.

An examination of climate sensitivity for idealised climate change experiments in an intermediate general circulation model

Radiative forcing and climate sensitivity have been widely used as concepts to understand climate change. This work performs climate change experiments with an intermediate general circulation model (IGCM) to examine the robustness of the radiative forcing concept for carbon dioxide and solar constant changes. This IGCM has been specifically developed as a computationally fast model, but one that allows an interaction between physical processes and large-scale dynamics; the model allows many long integrations to be performed relatively quickly. It employs a fast and accurate radiative transfer scheme, as well as simple convection and surface schemes, and a slab ocean, to model the effects of climate change mechanisms on the atmospheric temperatures and dynamics with a reasonable degree of complexity. The climatology of the IGCM run at T-21 resolution with 22 levels is compared to European Centre for Medium Range Weather Forecasting Reanalysis data. The response of the model to changes in carbon dioxide and solar output are examined when these changes are applied globally and when constrained geographically (e.g. over land only). The CO2 experiments have a roughly 17% higher climate sensitivity than the solar experiments. It is also found that a forcing at high latitudes causes a 40% higher climate sensitivity than a forcing only applied at low latitudes. It is found that, despite differences in the model feedbacks, climate sensitivity is roughly constant over a range of distributions of CO2 and solar forcings. Hence, in the IGCM at least, the radiative forcing concept is capable of predicting global surface temperature changes to within 30%, for the perturbations described here. It is concluded that radiative forcing remains a useful tool for assessing the natural and anthropogenic impact of climate change mechanisms on surface temperature.

Radiative forcing of climate by hydrochlorofluorocarbons and hydrofluorocarbons

We measure infrared absorption spectra of 18 hydrochlorofluorocarbons and hydrofluorocarbons, seven of which do not yet appear in the literature. The spectra are used in a narrowband model of the terrestrial infrared radiation to calculate radiative forcing and global warming potentials. We investigate the sensitivity of the radiative forcing to the absorption spectrum temperature dependence, halocarbon vertical profile, stratospheric adjustment, cloudiness, spectral overlap, and latitude, and we make some recommendations for the reporting of radiative forcings that would help to resolve discrepancies between assessments. We investigate simple methods of estimating instantaneous radiative forcing directly from a molecule's absorption spectrum and we present a new method that agrees to within 0.3% with our narrowband model results.

The sensitivity of the tropical circulation and Maritime Continent precipitation to climate model resolution

The dependence of the annual mean tropical precipitation on horizontal resolution is investigated in the atmospheric version of the Hadley Centre General Environment Model (HadGEM1). Reducing the grid spacing from about 350 km to 110 km improves the precipitation distribution in most of the tropics. In particular, characteristic dry biases over South and Southeast Asia including the Maritime Continent as well as wet biases over the western tropical oceans are reduced. The annual-mean precipitation bias is reduced by about one third over the Maritime Continent and the neighbouring ocean basins associated with it via the Walker circulation. Sensitivity experiments show that much of the improvement with resolution in the Maritime Continent region is due to the specification of better resolved surface boundary conditions (land fraction, soil and vegetation parameters) at the higher resolution. It is shown that in particular the formulation of the coastal tiling scheme may cause resolution sensitivity of the mean simulated climate. The improvement in the tropical mean precipitation in this region is not primarily associated with the better representation of orography at the higher resolution, nor with changes in the eddy transport of moisture. Sizeable sensitivity to changes in the surface fields may be one of the reasons for the large variation of the mean tropical precipitation distribution seen across climate models.

Controls on inorganic nitrogen leaching from Finnish catchments assessed using a sensitivity and uncertainty analysis of the INCA-N model

The semi-distributed, dynamic INCA-N model was used to simulate the behaviour of dissolved inorganic nitrogen (DIN) in two Finnish research catchments. Parameter sensitivity and model structural uncertainty were analysed using generalized sensitivity analysis. The Mustajoki catchment is a forested upstream catchment, while the Savijoki catchment represents intensively cultivated lowlands. In general, there were more influential parameters in Savijoki than Mustajoki. Model results were sensitive to N-transformation rates, vegetation dynamics, and soil and river hydrology. Values of the sensitive parameters were based on long-term measurements covering both warm and cold years. The highest measured DIN concentrations fell between minimum and maximum values estimated during the uncertainty analysis. The lowest measured concentrations fell outside these bounds, suggesting that some retention processes may be missing from the current model structure. The lowest concentrations occurred mainly during low flow periods; so effects on total loads were small.