On instabilities in data assimilation algorithms

Data assimilation algorithms are a crucial part of operational systems in numerical weather prediction, hydrology and climate science, but are also important for dynamical reconstruction in medical applications and quality control for manufacturing processes. Usually, a variety of diverse measurement data are employed to determine the state of the atmosphere or to a wider system including land and oceans. Modern data assimilation systems use more and more remote sensing data, in particular radiances measured by satellites, radar data and integrated water vapor measurements via GPS/GNSS signals. The inversion of some of these measurements are ill-posed in the classical sense, i.e. the inverse of the operator H which maps the state onto the data is unbounded. In this case, the use of such data can lead to significant instabilities of data assimilation algorithms. The goal of this work is to provide a rigorous mathematical analysis of the instability of well-known data assimilation methods. Here, we will restrict our attention to particular linear systems, in which the instability can be explicitly analyzed. We investigate the three-dimensional variational assimilation and four-dimensional variational assimilation. A theory for the instability is developed using the classical theory of ill-posed problems in a Banach space framework. Further, we demonstrate by numerical examples that instabilities can and will occur, including an example from dynamic magnetic tomography.

Trypsin IV or mesotrypsin and p23 cleave protease-activated receptors 1 and 2 to induce inflammation and hyperalgesia

Although principally produced by the pancreas to degrade dietary proteins in the intestine, trypsins are also expressed in the nervous system and in epithelial tissues, where they have diverse actions that could be mediated by protease-activated receptors (PARs). We examined the biological actions of human trypsin IV (or mesotrypsin) and rat p23, inhibitor-resistant forms of trypsin. The zymogens trypsinogen IV and pro-p23 were expressed in Escherichia coli and purified to apparent homogeneity. Enteropeptidase cleaved both zymogens, liberating active trypsin IV and p23, which were resistant to soybean trypsin inhibitor and aprotinin. Trypsin IV cleaved N-terminal fragments of PAR(1), PAR(2), and PAR(4) at sites that would expose the tethered ligand (PAR(1) = PAR(4) > PAR(2)). Trypsin IV increased [Ca(2+)](i) in transfected cells expressing human PAR(1) and PAR(2) with similar potencies (PAR(1), 0.5 microm; PAR(2), 0.6 microm). p23 also cleaved fragments of PAR(1) and PAR(2) and signaled to cells expressing these receptors. Trypsin IV and p23 increased [Ca(2+)](i) in rat dorsal root ganglion neurons that responded to capsaicin and which thus mediate neurogenic inflammation and nociception. Intraplantar injection of trypsin IV and p23 in mice induced edema and granulocyte infiltration, which were not observed in PAR (-/-)(1)(trypsin IV) and PAR (-/-)(2) (trypsin IV and p23) mice. Trypsin IV and p23 caused thermal hyperalgesia and mechanical allodynia and hyperalgesia in mice, and these effects were absent in PAR (-/-)(2) mice but maintained in PAR (-/-)(1) mice. Thus, trypsin IV and p23 are inhibitor-resistant trypsins that can cleave and activate PARs, causing PAR(1)- and PAR(2)-dependent inflammation and PAR(2)-dependent hyperalgesia.

Pseudomonas aeruginosa elastase disables proteinase-activated receptor 2 in respiratory epithelial cells

Pseudomonas aeruginosa, a major lung pathogen in cystic fibrosis (CF) patients, secretes an elastolytic metalloproteinase (EPa) contributing to bacterial pathogenicity. Proteinase-activated receptor 2 (PAR2), implicated in the pulmonary innate defense, is activated by the cleavage of its extracellular N-terminal domain, unmasking a new N-terminal sequence starting with SLIGKV, which binds intramolecularly and activates PAR2. We show that EPa cleaves the N-terminal domain of PAR2 from the cell surface without triggering receptor endocytosis as trypsin does. As evaluated by measurements of cytosolic calcium as well as prostaglandin E(2) and interleukin-8 production, this cleavage does not activate PAR2, but rather disarms the receptor for subsequent activation by trypsin, but not by the synthetic receptor-activating peptide, SLIGKV-NH(2). Proteolysis by EPa of synthetic peptides representing the N-terminal cleavage/activation sequences of either human or rat PAR2 indicates that cleavages resulting from EPa activity would not produce receptor-activating tethered ligands, but would disarm PAR2 in regard to any further activating proteolysis by activating proteinases. Our data indicate that a pathogen-derived proteinase like EPa can potentially silence the function of PAR2 in the respiratory tract, thereby altering the host innate defense mechanisms and respiratory functions, and thus contributing to pathogenesis in the setting of a disease like CF.

Protease-activated receptor 2: activation, signalling and function

PARs (protease-activated receptors) are a family of four G-protein-coupled receptors for proteases from the circulation, inflammatory cells and epithelial tissues. This report focuses on PAR(2), which plays an important role in inflammation and pain. Pancreatic (trypsin I and II) and extrapancreatic (trypsin IV) trypsins, mast cell tryptase and coagulation factors VIIa and Xa cleave and activate PAR(2). Proteases cleave PAR(2) to expose a tethered ligand that binds to the cleaved receptor. Despite this irreversible activation, PAR(2) signalling is attenuated by beta-arrestin-mediated desensitization and endocytosis, and by lysosomal targeting and degradation, which requires ubiquitination of PAR(2). beta-Arrestins also act as scaffolds for the assembly of multi-protein signalling complexes that determine the location and function of activated mitogen-activated protein kinases. Observations of PAR(2)-deficient mice support a role for PAR(2) in inflammation, and many of the effects of PAR(2) activators promote inflammation. Inflammation is mediated in part by activation of PAR(2) in the peripheral nervous system, which results in neurogenic inflammation and hyperalgesia.

Protease-activated receptors: the role of cell-surface proteolysis in signalling

Certain extracellular proteases, derived from the circulation and inflammatory cells, can specifically cleave and trigger protease-activated receptors (PARs), a small, but important, sub-group of the G-protein-coupled receptor super-family. Four PARs have been cloned and they all share the same basic mechanism of activation: proteases cleave at a specific site within the extracellular N-terminus to expose a new N-terminal tethered ligand domain, which binds to and thereby activates the cleaved receptor. Thrombin activates PAR1, PAR3 and PAR4, trypsin activates PAR2 and PAR4, and mast cell tryptase activates PAR2 in this manner. Activated PARs couple to signalling cascades that affect cell shape, secretion, integrin activation, metabolic responses, transcriptional responses and cell motility. PARs are 'single-use' receptors: proteolytic activation is irreversible and the cleaved receptors are degraded in lysosomes. Thus, PARs play important roles in 'emergency situations', such as trauma and inflammation. The availability of selective agonists and antagonists of protease inhibitors and of genetic models has generated evidence to suggests that proteases and their receptors play important roles in coagulation, inflammation, pain, healing and protection. Therefore, selective antagonists or agonists of these receptors may be useful therapeutic agents for the treatment of human diseases.

‘NSC 68 and the Soviet Threat: A New Perspective on Western Threat Perception and Policy Making’

It has been argued that the US strategy paper NSC 68 of 1950 which ushered in the great Cold War rearmament process first in the US and then in NATO was a vast overreaction. This paper argues, by contrast, that given the intelligence about the Soviet Union's and its satellites' military buildup and the role of China in that period, this was a reasonable strategy to embrace.

Foreword: International Space Science Institute (ISSI) workshop on observing and predicting Earth’s energy flows

The Earth’s climate, as well as planetary climates in general, is broadly regulated by three fundamental parameters: the total solar irradiance, the planetary albedo and the planetary emissivity. Observations from series of different satellites during the last three decades indicate that these three quantities are generally very stable. The total solar irradiation of some 1,361 W/m2 at 1 A.U. varies within 1 W/m2 during the 11-year solar cycle (Fröhlich 2012). The albedo is close to 29 % with minute changes from year to year but with marked zonal differences (Stevens and Schwartz 2012). The only exception to the overall stability is a minor decrease in the planetary emissivity (the ratio between the radiation to space and the radiation from the surface of the Earth). This is a consequence of the increase in atmospheric greenhouse gas amounts making the atmosphere gradually more opaque to long-wave terrestrial radiation. As a consequence, radiation processes are slightly out of balance as less heat is leaving the Earth in the form of thermal radiation than the amount of heat from the incoming solar radiation. Present space-based systems cannot yet measure this imbalance, but the effect can be inferred from the increase in heat in the oceans where most of the heat accumulates. Minor amounts of heat are used to melt ice and to warm the atmosphere and the surface of the Earth.

Interpreting Differential Temperature Trends at the Surface and in the Lower Troposphere

Estimated global-scale temperature trends at Earth's surface (as recorded by thermometers) and in the lower troposphere (as monitored by satellites) diverge by up to 0.14°C per decade over the period 1979 to 1998. Accounting for differences in the spatial coverage of satellite and surface measurements reduces this differential, but still leaves a statistically significant residual of roughly 0.1°C per decade. Natural internal climate variability alone, as simulated in three state-of-the-art coupled atmosphere-ocean models, cannot completely explain this residual trend difference. A model forced by a combination of anthropogenic factors and volcanic aerosols yields surface-troposphere temperature trend differences closest to those observed.

Assessing levels of uncertainty in recent temperature time series

We examine to what degree we can expect to obtain accurate temperature trends for the last two decades near the surface and in the lower troposphere. We compare temperatures obtained from surface observations and radiosondes as well as satellite-based measurements from the Microwave Soundings Units (MSU), which have been adjusted for orbital decay and non-linear instrument-body effects, and reanalyses from the European Centre for Medium-Range Weather Forecasts (ERA) and the National Centre for Environmental Prediction (NCEP). In regions with abundant conventional data coverage, where the MSU has no major influence on the reanalysis, temperature anomalies obtained from microwave sounders, radiosondes and from both reanalyses agree reasonably. Where coverage is insufficient, in particular over the tropical oceans, large differences are found between the MSU and either reanalysis. These differences apparently relate to changes in the satellite data availability and to differing satellite retrieval methodologies, to which both reanalyses are quite sensitive over the oceans. For NCEP, this results from the use of raw radiances directly incorporated into the analysis, which make the reanalysis sensitive to changes in the underlying algorithms, e.g. those introduced in August 1992. For ERA, the bias-correction of the one-dimensional variational analysis may introduce an error when the satellite relative to which the correction is calculated is biased itself or when radiances change on a time scale longer than a couple of months, e.g. due to orbit decay. ERA inhomogeneities are apparent in April 1985, October/November 1986 and April 1989. These dates can be identified with the replacements of satellites. It is possible that a negative bias in the sea surface temperatures (SSTs) used in the reanalyses may have been introduced over the period of the satellite record. This could have resulted from a decrease in the number of ship measurements, a concomitant increase in the importance of satellite-derived SSTs, and a likely cold bias in the latter. Alternately, a warm bias in SSTs could have been caused by an increase in the percentage of buoy measurements (relative to deeper ship intake measurements) in the tropical Pacific. No indications for uncorrected inhomogeneities of land surface temperatures could be found. Near-surface temperatures have biases in the boundary layer in both reanalyses, presumably due to the incorrect treatment of snow cover. The increase of near-surface compared to lower tropospheric temperatures in the last two decades may be due to a combination of several factors, including high-latitude near-surface winter warming due to an enhanced NAO and upper-tropospheric cooling due to stratospheric ozone decrease.

Assimilation of non-synoptic observations

A system for continuous data assimilation described recently (Bengtsson & Gustavsson, 1971) has been further developed and tested under more realistic conditions. A balanced barotropic model is used and the integration is performed over an octagon covering the area to the north of 20° N. Comparisons have been made between using data from the actual aerological network and data from a satellite in a polar orbit. The result of the analyses has been studied in different subregions situated in data sparse as well as in data dense areas. The errors of the analysis have also been studied in the wave spectrum domain. Updating is performed using data generated by the model but also by model-independent data. Rather great differences are obtained between the two experiments especially with respect to the ultra-long waves. The more realistic approach gives much larger analysis error. In general the satellite updating yields somewhat better result than the updating from the conventional aerological network especially in the data sparse areas over the oceans. Most of the experiments are performed by a satellite making 200 observations/track, a sidescan capability of 40° and with a RMS-error of 20 m. It is found that the effect of increasing the number of satellite observations from 100 to 200 per orbit is almost negligible. Similarly the effect is small of improving the observations by diminishing the RMS-error below a certain value. An observing system using two satellites 90° out of phase has also been investigated. This is found to imply a substantial improvement. Finally an experiment has been performed using actual SIRS-soundings from NIMBUS IV. With respect to the very small number of soundings at 500 mb, 142 during 48 hours, the result can be regarded as quite satisfactory.

Numerical prediction of atmospheric blocking-A case study

A series of numerical models have been used to investigate the predictability of atmospheric blocking for an episode selected from FGGE Special Observing Period I. Level II-b FGGE data have been used in the experiment. The blocking took place over the North Atlantic region and is a very characteristic example of high winter blocking. It is found that the very high resolution models developed at ECMWF, in a remarkable way manage to predict the blocking event in great detail, even beyond 1 week. Although models with much less resolution manage to predict the blocking phenomenon as such, the actual evolution differs very much from the observed and consequently the practical value is substantially reduced. Wind observations from the geostationary satellites are shown to have a substantial impact on the forecast beyond 5 days, as well as an extension of the integration domain to the whole globe. Quasi-geostrophic baroclinic models and, even more, barotropic models, are totally inadequate to predict blocking except in its initial phase. The prediction experiment illustrates clearly that efforts which have gone into the improvement of numerical prediction models in the last decades have been worth while.

Scheduling satellite-based SAR acquisition for sequential assimilation of water level observations into flood modelling

Satellite-based Synthetic Aperture Radar (SAR) has proved useful for obtaining information on flood extent, which, when intersected with a Digital Elevation Model (DEM) of the floodplain, provides water level observations that can be assimilated into a hydrodynamic model to decrease forecast uncertainty. With an increasing number of operational satellites with SAR capability, information on the relationship between satellite first visit and revisit times and forecast performance is required to optimise the operational scheduling of satellite imagery. By using an Ensemble Transform Kalman Filter (ETKF) and a synthetic analysis with the 2D hydrodynamic model LISFLOOD-FP based on a real flooding case affecting an urban area (summer 2007,Tewkesbury, Southwest UK), we evaluate the sensitivity of the forecast performance to visit parameters. We emulate a generic hydrologic-hydrodynamic modelling cascade by imposing a bias and spatiotemporal correlations to the inflow error ensemble into the hydrodynamic domain. First, in agreement with previous research, estimation and correction for this bias leads to a clear improvement in keeping the forecast on track. Second, imagery obtained early in the flood is shown to have a large influence on forecast statistics. Revisit interval is most influential for early observations. The results are promising for the future of remote sensing-based water level observations for real-time flood forecasting in complex scenarios.

Response kinetics in the complex chemotaxis signalling pathway of Rhodobacter sphaeroides

Chemotaxis is one of the best characterised signalling systems in biology. It is the mechanism by which bacteria move towards optimal environments and is implicated in biofilm formation, pathogenesis and symbiosis. The properties of the bacterial chemosensory response have been described in detail for the single chemosensory pathway of Escherichia coli. We have characterised the properties of the chemosensory response of Rhodobacter sphaeroides, an -proteobacterium with multiple chemotaxis pathways, under two growth conditions allowing the effects of protein expression levels and cell architecture to be investigated. Using tethered cell assays we measured the responses of the system to step changes in concentration of the attractant propionate and show that, independently of the growth conditions, R. sphaeroides is chemotactic over at least five orders of magnitude and has a sensing profile following Weber’s law. Mathematical modelling also shows that, like E. coli, R. sphaeroides is capable of showing Fold-Change Detection (FCD). Our results indicate that general features of bacterial chemotaxis such as the range and sensitivity of detection, adaptation times, adherence to Weber’s law and the presence of FCD may be integral features of chemotaxis systems in general, regardless of network complexity, protein expression levels and cellular architecture across different species.

Intensification of winter transatlantic aviation turbulence in response to climate change

Atmospheric turbulence causes most weather-related aircraft incidents1. Commercial aircraft encounter moderate-or-greater turbulence tens of thousands of times each year worldwide, injuring probably hundreds of passengers (occasionally fatally), costing airlines tens of millions of dollars and causing structural damage to planes1, 2, 3. Clear-air turbulence is especially difficult to avoid, because it cannot be seen by pilots or detected by satellites or on-board radar4, 5. Clear-air turbulence is linked to atmospheric jet streams6, 7, which are projected to be strengthened by anthropogenic climate change8. However, the response of clear-air turbulence to projected climate change has not previously been studied. Here we show using climate model simulations that clear-air turbulence changes significantly within the transatlantic flight corridor when the concentration of carbon dioxide in the atmosphere is doubled. At cruise altitudes within 50–75° N and 10–60° W in winter, most clear-air turbulence measures show a 10–40% increase in the median strength of turbulence and a 40–170% increase in the frequency of occurrence of moderate-or-greater turbulence. Our results suggest that climate change will lead to bumpier transatlantic flights by the middle of this century. Journey times may lengthen and fuel consumption and emissions may increase. Aviation is partly responsible for changing the climate9, but our findings show for the first time how climate change could affect aviation.