Gaussian quadrature 4D-VAR

A new incremental four-dimensional variational (4D-Var) data assimilation algorithm is introduced. The algorithm does not require the computationally expensive integrations with the nonlinear model in the outer loops. Nonlinearity is accounted for by modifying the linearization trajectory of the observation operator based on integrations with the tangent linear (TL) model. This allows us to update the linearization trajectory of the observation operator in the inner loops at negligible computational cost. As a result the distinction between inner and outer loops is no longer necessary. The key idea on which the proposed 4D-Var method is based is that by using Gaussian quadrature it is possible to get an exact correspondence between the nonlinear time evolution of perturbations and the time evolution in the TL model. It is shown that J-point Gaussian quadrature can be used to derive the exact adjoint-based observation impact equations and furthermore that it is straightforward to account for the effect of multiple outer loops in these equations if the proposed 4D-Var method is used. The method is illustrated using a three-level quasi-geostrophic model and the Lorenz (1996) model.

On discrimination algorithms for ill-posed problems with an application to magnetic tomography

In this paper we explore classification techniques for ill-posed problems. Two classes are linearly separable in some Hilbert space X if they can be separated by a hyperplane. We investigate stable separability, i.e. the case where we have a positive distance between two separating hyperplanes. When the data in the space Y is generated by a compact operator A applied to the system states ∈ X, we will show that in general we do not obtain stable separability in Y even if the problem in X is stably separable. In particular, we show this for the case where a nonlinear classification is generated from a non-convergent family of linear classes in X. We apply our results to the problem of quality control of fuel cells where we classify fuel cells according to their efficiency. We can potentially classify a fuel cell using either some external measured magnetic field or some internal current. However we cannot measure the current directly since we cannot access the fuel cell in operation. The first possibility is to apply discrimination techniques directly to the measured magnetic fields. The second approach first reconstructs currents and then carries out the classification on the current distributions. We show that both approaches need regularization and that the regularized classifications are not equivalent in general. Finally, we investigate a widely used linear classification algorithm Fisher's linear discriminant with respect to its ill-posedness when applied to data generated via a compact integral operator. We show that the method cannot stay stable when the number of measurement points becomes large.

Optimal linearization trajectories for tangent linear models

We examine differential equations where nonlinearity is a result of the advection part of the total derivative or the use of quadratic algebraic constraints between state variables (such as the ideal gas law). We show that these types of nonlinearity can be accounted for in the tangent linear model by a suitable choice of the linearization trajectory. Using this optimal linearization trajectory, we show that the tangent linear model can be used to reproduce the exact nonlinear error growth of perturbations for more than 200 days in a quasi-geostrophic model and more than (the equivalent of) 150 days in the Lorenz 96 model. We introduce an iterative method, purely based on tangent linear integrations, that converges to this optimal linearization trajectory. The main conclusion from this article is that this iterative method can be used to account for nonlinearity in estimation problems without using the nonlinear model. We demonstrate this by performing forecast sensitivity experiments in the Lorenz 96 model and show that we are able to estimate analysis increments that improve the two-day forecast using only four backward integrations with the tangent linear model. Copyright © 2011 Royal Meteorological Society

The link between the Barents Sea and ENSO events simulated by NEMO model

An analysis of observational data in the Barents Sea along a meridian at 33°30' E between 70°30' and 72°30' N has reported a negative correlation between El Niño/La Niña Southern Oscillation (ENSO) events and water temperature in the top 200 m: the temperature drops about 0.5 °C during warm ENSO events while during cold ENSO events the top 200 m layer of the Barents Sea is warmer. Results from 1 and 1/4-degree global NEMO models show a similar response for the whole Barents Sea. During the strong warm ENSO event in 1997–1998 an anomalous anticyclonic atmospheric circulation over the Barents Sea enhances heat loses, as well as substantially influencing the Barents Sea inflow from the North Atlantic, via changes in ocean currents. Under normal conditions along the Scandinavian peninsula there is a warm current entering the Barents Sea from the North Atlantic, however after the 1997–1998 event this current is weakened. During 1997–1998 the model annual mean temperature in the Barents Sea is decreased by about 0.8 °C, also resulting in a higher sea ice volume. In contrast during the cold ENSO events in 1999–2000 and 2007–2008, the model shows a lower sea ice volume, and higher annual mean temperatures in the upper layer of the Barents Sea of about 0.7 °C. An analysis of model data shows that the strength of the Atlantic inflow in the Barents Sea is the main cause of heat content variability, and is forced by changing pressure and winds in the North Atlantic. However, surface heat-exchange with the atmosphere provides the means by which the Barents sea heat budget relaxes to normal in the subsequent year after the ENSO events.

Protease-activated receptor 2 sensitizes the transient receptor potential vanilloid 4 ion channel to cause mechanical hyperalgesia in mice

Exacerbated sensitivity to mechanical stimuli that are normally innocuous or mildly painful (mechanical allodynia and hyperalgesia) occurs during inflammation and underlies painful diseases. Proteases that are generated during inflammation and disease cleave protease-activated receptor 2 (PAR2) on afferent nerves to cause mechanical hyperalgesia in the skin and intestine by unknown mechanisms. We hypothesized that PAR2-mediated mechanical hyperalgesia requires sensitization of the ion channel transient receptor potential vanilloid 4 (TRPV4). Immunoreactive TRPV4 was coexpressed by rat dorsal root ganglia (DRG) neurons with PAR2, substance P (SP) and calcitonin gene-related peptide (CGRP), mediators of pain transmission. In PAR2-expressing cell lines that either naturally expressed TRPV4 (bronchial epithelial cells) or that were transfected to express TRPV4 (HEK cells), pretreatment with a PAR2 agonist enhanced Ca2+ and current responses to the TRPV4 agonists phorbol ester 4alpha-phorbol 12,13-didecanoate (4alphaPDD) and hypotonic solutions. PAR2-agonist similarly sensitized TRPV4 Ca2+ signals and currents in DRG neurons. Antagonists of phospholipase Cbeta and protein kinases A, C and D inhibited PAR2-induced sensitization of TRPV4 Ca2+ signals and currents. 4alphaPDD and hypotonic solutions stimulated SP and CGRP release from dorsal horn of rat spinal cord, and pretreatment with PAR2 agonist sensitized TRPV4-dependent peptide release. Intraplantar injection of PAR2 agonist caused mechanical hyperalgesia in mice and sensitized pain responses to the TRPV4 agonists 4alphaPDD and hypotonic solutions. Deletion of TRPV4 prevented PAR2 agonist-induced mechanical hyperalgesia and sensitization. This novel mechanism, by which PAR2 activates a second messenger to sensitize TRPV4-dependent release of nociceptive peptides and induce mechanical hyperalgesia, may underlie inflammatory hyperalgesia in diseases where proteases are activated and released.

Protease-activated receptor 2 sensitizes TRPV1 by protein kinase Cepsilon- and A-dependent mechanisms in rats and mice

Proteases that are released during inflammation and injury cleave protease-activated receptor 2 (PAR2) on primary afferent neurons to cause neurogenic inflammation and hyperalgesia. PAR2-induced thermal hyperalgesia depends on sensitization of transient receptor potential vanilloid receptor 1 (TRPV1), which is gated by capsaicin, protons and noxious heat. However, the signalling mechanisms by which PAR2 sensitizes TRPV1 are not fully characterized. Using immunofluorescence and confocal microscopy, we observed that PAR2 was colocalized with protein kinase (PK) Cepsilon and PKA in a subset of dorsal root ganglia neurons in rats, and that PAR2 agonists promoted translocation of PKCepsilon and PKA catalytic subunits from the cytosol to the plasma membrane of cultured neurons and HEK 293 cells. Subcellular fractionation and Western blotting confirmed this redistribution of kinases, which is indicative of activation. Although PAR2 couples to phospholipase Cbeta, leading to stimulation of PKC, we also observed that PAR2 agonists increased cAMP generation in neurons and HEK 293 cells, which would activate PKA. PAR2 agonists enhanced capsaicin-stimulated increases in [Ca2+]i and whole-cell currents in HEK 293 cells, indicating TRPV1 sensitization. The combined intraplantar injection of non-algesic doses of PAR2 agonist and capsaicin decreased the latency of paw withdrawal to radiant heat in mice, indicative of thermal hyperalgesia. Antagonists of PKCepsilon and PKA prevented sensitization of TRPV1 Ca2+ signals and currents in HEK 293 cells, and suppressed thermal hyperalgesia in mice. Thus, PAR2 activates PKCepsilon and PKA in sensory neurons, and thereby sensitizes TRPV1 to cause thermal hyperalgesia. These mechanisms may underlie inflammatory pain, where multiple proteases are generated and released.

Protease-activated receptor 2 sensitizes the capsaicin receptor transient receptor potential vanilloid receptor 1 to induce hyperalgesia

Inflammatory proteases (mast cell tryptase and trypsins) cleave protease-activated receptor 2 (PAR2) on spinal afferent neurons and cause persistent inflammation and hyperalgesia by unknown mechanisms. We determined whether transient receptor potential vanilloid receptor 1 (TRPV1), a cation channel activated by capsaicin, protons, and noxious heat, mediates PAR2-induced hyperalgesia. PAR2 was coexpressed with TRPV1 in small- to medium-diameter neurons of the dorsal root ganglia (DRG), as determined by immunofluorescence. PAR2 agonists increased intracellular [Ca2+] ([Ca2+]i) in these neurons in culture, and PAR2-responsive neurons also responded to the TRPV1 agonist capsaicin, confirming coexpression of PAR2 and TRPV1. PAR2 agonists potentiated capsaicin-induced increases in [Ca2+]i in TRPV1-transfected human embryonic kidney (HEK) cells and DRG neurons and potentiated capsaicin-induced currents in DRG neurons. Inhibitors of phospholipase C and protein kinase C (PKC) suppressed PAR2-induced sensitization of TRPV1-mediated changes in [Ca2+]i and TRPV1 currents. Activation of PAR2 or PKC induced phosphorylation of TRPV1 in HEK cells, suggesting a direct regulation of the channel. Intraplantar injection of a PAR2 agonist caused persistent thermal hyperalgesia that was prevented by antagonism or deletion of TRPV1. Coinjection of nonhyperalgesic doses of PAR2 agonist and capsaicin induced hyperalgesia that was inhibited by deletion of TRPV1 or antagonism of PKC. PAR2 activation also potentiated capsaicin-induced release of substance P and calcitonin gene-related peptide from superfused segments of the dorsal horn of the spinal cord, where they mediate hyperalgesia. We have identified a novel mechanism by which proteases that activate PAR2 sensitize TRPV1 through PKC. Antagonism of PAR2, TRPV1, or PKC may abrogate protease-induced thermal hyperalgesia.

Carbon monoxide mediates the anti-apoptotic effects of heme oxygenase-1 in medulloblastoma DAOY cells via K+ channel inhibition

Tumor cell survival and proliferation is attributable in part to suppression of apoptotic pathways, yet the mechanisms by which cancer cells resist apoptosis are not fully understood. Many cancer cells constitutively express heme oxygenase-1 (HO-1), which catabolizes heme to generate biliverdin, Fe(2+), and carbon monoxide (CO). These breakdown products may play a role in the ability of cancer cells to suppress apoptotic signals. K(+) channels also play a crucial role in apoptosis, permitting K(+) efflux which is required to initiate caspase activation. Here, we demonstrate that HO-1 is constitutively expressed in human medulloblastoma tissue, and can be induced in the medulloblastoma cell line DAOY either chemically or by hypoxia. Induction of HO-1 markedly increases the resistance of DAOY cells to oxidant-induced apoptosis. This effect was mimicked by exogenous application of the heme degradation product CO. Furthermore we demonstrate the presence of the pro-apoptotic K(+) channel, Kv2.1, in both human medulloblastoma tissue and DAOY cells. CO inhibited the voltage-gated K(+) currents in DAOY cells, and largely reversed the oxidant-induced increase in K(+) channel activity. p38 MAPK inhibition prevented the oxidant-induced increase of K(+) channel activity in DAOY cells, and enhanced their resistance to apoptosis. Our findings suggest that CO-mediated inhibition of K(+) channels represents an important mechanism by which HO-1 can increase the resistance to apoptosis of medulloblastoma cells, and support the idea that HO-1 inhibition may enhance the effectiveness of current chemo- and radiotherapies.

Gap junction-mediated spontaneous Ca(2+) waves in differentiated cholinergic SN56 cells

Neuronal gap junctions are receiving increasing attention as a physiological means of intercellular communication, yet our understanding of them is poorly developed when compared to synaptic communication. Using microfluorimetry, we demonstrate that differentiation of SN56 cells (hybridoma cells derived from murine septal neurones) leads to the spontaneous generation of Ca(2+) waves. These waves were unaffected by tetrodotoxin (1microM), but blocked by removal of extracellular Ca(2+), or addition of non-specific Ca(2+) channel inhibitors (Cd(2+) (0.1mM) or Ni(2+) (1mM)). Combined application of antagonists of NMDA receptors (AP5; 100microM), AMPA/kainate receptors (NBQX; 20microM), nicotinic AChR receptors (hexamethonium; 100microM) or inotropic purinoceptors (brilliant blue; 100nM) was also without effect. However, Ca(2+) waves were fully prevented by carbenoxolone (200microM), halothane (3mM) or niflumic acid (100microM), three structurally diverse inhibitors of gap junctions, and mRNA for connexin 36 was detected by PCR. Whole-cell patch-clamp recordings revealed spontaneous inward currents in voltage-clamped cells which we inhibited by Cd(2+), Ni(2+) or niflumic acid. Our data suggest that differentiated SN56 cells generated spontaneous Ca(2+) waves which are propagated by intercellular gap junctions. We propose that this system can be exploited conveniently for the development of neuronal gap junction modulators.

Carbon monoxide inhibits L-type Ca2+ channels via redox modulation of key cysteine residues by mitochondrial reactive oxygen species

Conditions of stress, such as myocardial infarction, stimulate up-regulation of heme oxygenase (HO-1) to provide cardioprotection. Here, we show that CO, a product of heme catabolism by HO-1, directly inhibits native rat cardiomyocyte L-type Ca2+ currents and the recombinant alpha1C subunit of the human cardiac L-type Ca2+ channel. CO (applied via a recognized CO donor molecule or as the dissolved gas) caused reversible, voltage-independent channel inhibition, which was dependent on the presence of a spliced insert in the cytoplasmic C-terminal region of the channel. Sequential molecular dissection and point mutagenesis identified three key cysteine residues within the proximal 31 amino acids of the splice insert required for CO sensitivity. CO-mediated inhibition was independent of nitric oxide and protein kinase G but was prevented by antioxidants and the reducing agent, dithiothreitol. Inhibition of NADPH oxidase and xanthine oxidase did not affect the inhibitory actions of CO. Instead, inhibitors of complex III (but not complex I) of the mitochondrial electron transport chain and a mitochondrially targeted antioxidant (Mito Q) fully prevented the effects of CO. Our data indicate that the cardioprotective effects of HO-1 activity may be attributable to an inhibitory action of CO on cardiac L-type Ca2+ channels. Inhibition arises from the ability of CO to promote generation of reactive oxygen species from complex III of mitochondria. This in turn leads to redox modulation of any or all of three critical cysteine residues in the channel's cytoplasmic C-terminal tail, resulting in channel inhibition.

Molecular requirements for L-type Ca2+ channel blockade by testosterone

Despite being generally perceived as detrimental to the cardiovascular system, testosterone has marked beneficial vascular effects; most notably it acutely and directly causes vasodilatation. Indeed, men with hypotestosteronaemia can present with myocardial ischemia and angina which can be rapidly alleviated by infusion of testosterone. To date, however, in vitro studies have failed to provide a convincing mechanism to account for this clinically important effect. Here, using whole-cell patch-clamp recordings to measure current flow through recombinant human L-type Ca2+ channel alpha(1C) subunits (Ca(v)1.2), we demonstrate that testosterone inhibits such currents in a concentration-dependent manner. Importantly, this occurs over the physiological range of testosterone concentrations (IC50 34 nM), and is not mimicked by the metabolite 5alpha-androstan-17beta-ol-3-one (DHT), nor by progesterone or estradiol, even at high (10 microM) concentration. L-type Ca2+ channels in the vasculature are also important clinical targets for vasodilatory dihydropyridines. A single point mutation (T1007Y) almost completely abolishes nifedipine sensitivity in our recombinant expression system. Crucially, the same mutation renders the channels insensitive to testosterone. Our data strongly suggest, for the first time, the molecular requirements for testosterone binding to L-type Ca2+ channels, thereby supporting its beneficial role as an endogenous Ca2+ channel antagonist in the treatment of cardiovascular disease.

Atlantic meridional heat transports in two ocean reanalyes evaluated against the RAPID array

The Atlantic meridional overturning circulation in two versions of the NEMO ¼° global ocean model has been compared with the RAPID transport array at 26oN. Both model versions reproduce the mean MOC strength well although the Florida Straits flows differ because the pathway of the Gulf Stream is not strongly constrained at this resolution. Both models however have a mean meridional heat transport of 1.07PW, much lower than the 1.35PW from RAPID observations in Apr04-Oct07. Much of the heat transport discrepancy is due to lower transports in summer across the MidOcean (Bahamas-Africa) section, due to stronger southward geostrophic flows in the top 100m where the water is warmest. Seasonal thermocline changes increase temperature differences across the basin driving stronger geostrophic shear, but this effect is much weaker in the top 100m of the RAPID velocity data. The effect accounts for a reduction of 1.1Sv in MOC and 0.1PW in heat transports. The rest of the discrepancy comes from lower Ekman transports from using ERAInterim winds instead of QuikSCAT, a smaller zonally-varying “Eddy” heat transport component, estimated from repeat XBT sections in the observations, and the southward throughflow in the model. Other differences in depth structure of the model MOC and RAPID observations are described but have much less impact on heat transports.

Impact of stratospheric ozone on Southern Hemisphere circulation change: A multimodel assessment

The impact of stratospheric ozone on the tropospheric general circulation of the Southern Hemisphere (SH) is examined with a set of chemistry‐climate models participating in the Stratospheric Processes and their Role in Climate (SPARC)/Chemistry‐Climate Model Validation project phase 2 (CCMVal‐2). Model integrations of both the past and future climates reveal the crucial role of stratospheric ozone in driving SH circulation change: stronger ozone depletion in late spring generally leads to greater poleward displacement and intensification of the tropospheric midlatitude jet, and greater expansion of the SH Hadley cell in the summer. These circulation changes are systematic as poleward displacement of the jet is typically accompanied by intensification of the jet and expansion of the Hadley cell. Overall results are compared with coupled models participating in the Intergovernmental Panel on Climate Change Fourth Assessment Report (IPCC AR4), and possible mechanisms are discussed. While the tropospheric circulation response appears quasi‐linearly related to stratospheric ozone changes, the quantitative response to a given forcing varies considerably from one model to another. This scatter partly results from differences in model climatology. It is shown that poleward intensification of the westerly jet is generally stronger in models whose climatological jet is biased toward lower latitudes. This result is discussed in the context of quasi‐geostrophic zonal mean dynamics.

Foreword: International Space Science Institute (ISSI) workshop on the Earth’s cryosphere and sea level change

Rising sea level is perhaps the most severe consequence of climate warming, as much of the world’s population and infrastructure is located near current sea level (Lemke et al. 2007). A major rise of a metre or more would cause serious problems. Such possibilities have been suggested by Hansen and Sato (2011) who pointed out that sea level was several metres higher than now during the Holsteinian and Eemian interglacials (about 250,000 and 120,000 years ago, respectively), even though the global temperature was then only slightly higher than it is nowadays. It is consequently of the utmost importance to determine whether such a sea level rise could occur and, if so, how fast it might happen. Sea level undergoes considerable changes due to natural processes such as the wind, ocean currents and tidal motions. On longer time scales, the sea level is influenced by steric effects (sea water expansion caused by temperature and salinity changes of the ocean) and by eustatic effects caused by changes in ocean mass. Changes in the Earth’s cryosphere, such as the retreat or expansion of glaciers and land ice areas, have been the dominant cause of sea level change during the Earth’s recent history. During the glacial cycles of the last million years, the sea level varied by a large amount, of the order of 100 m. If the Earth’s cryosphere were to disappear completely, the sea level would rise by some 65 m. The scientific papers in the present volume address the different aspects of the Earth’s cryosphere and how the different changes in the cryosphere affect sea level change. It represents the outcome of the first workshop held within the new ISSI Earth Science Programme. The workshop took place from 22 to 26 March, 2010, in Bern, Switzerland, with the objective of providing an in-depth insight into the future of mountain glaciers and the large land ice areas of Antarctica and Greenland, which are exposed to natural and anthropogenic climate influences, and their effects on sea level change. The participants of the workshop are experts in different fields including meteorology, climatology, oceanography, glaciology and geodesy; they use advanced space-based observational studies and state-of-the-art numerical modelling.

On the use of a time sequence of surface pressures in four-dimensional data assimilation

The possibility of using a time sequence of surface pressure observations in four-dimensional data assimilation is being investigated. It is shown that a linear multilevel quasi-geostrophic model can be updated successfully with surface data alone, provided the number of time levels are at least as many as the number of vertical levels. It is further demonstrated that current statistical analysis procedures are very inefficient to assimilate surface observations, and it is shown by numerical experiments that the vertical interpolation must be carried out using the structure of the most dominating baroclinic mode in order to obtain a satisfactory updating. Different possible ways towards finding a practical solution are being discussed.