First order k-th moment finite element analysis of nonlinear operator equations with stochastic data

We develop and analyze a class of efficient Galerkin approximation methods for uncertainty quantification of nonlinear operator equations. The algorithms are based on sparse Galerkin discretizations of tensorized linearizations at nominal parameters. Specifically, we consider abstract, nonlinear, parametric operator equations J(\alpha ,u)=0 for random input \alpha (\omega ) with almost sure realizations in a neighborhood of a nominal input parameter \alpha _0. Under some structural assumptions on the parameter dependence, we prove existence and uniqueness of a random solution, u(\omega ) = S(\alpha (\omega )). We derive a multilinear, tensorized operator equation for the deterministic computation of k-th order statistical moments of the random solution's fluctuations u(\omega ) - S(\alpha _0). We introduce and analyse sparse tensor Galerkin discretization schemes for the efficient, deterministic computation of the k-th statistical moment equation. We prove a shift theorem for the k-point correlation equation in anisotropic smoothness scales and deduce that sparse tensor Galerkin discretizations of this equation converge in accuracy vs. complexity which equals, up to logarithmic terms, that of the Galerkin discretization of a single instance of the mean field problem. We illustrate the abstract theory for nonstationary diffusion problems in random domains.

Evidence for changes in stratospheric transport and mixing over the past three decades based on multiple data sets and tropical leaky pipe analysis

Variability in the strength of the stratospheric Lagrangian mean meridional or Brewer-Dobson circulation and horizontal mixing into the tropics over the past three decades are examined using observations of stratospheric mean age of air and ozone. We use a simple representation of the stratosphere, the tropical leaky pipe (TLP) model, guided by mean meridional circulation and horizontal mixing changes in several reanalyses data sets and chemistry climate model (CCM) simulations, to help elucidate reasons for the observed changes in stratospheric mean age and ozone. We find that the TLP model is able to accurately simulate multiyear variability in ozone following recent major volcanic eruptions and the early 2000s sea surface temperature changes, as well as the lasting impact on mean age of relatively short-term circulation perturbations. We also find that the best quantitative agreement with the observed mean age and ozone trends over the past three decades is found assuming a small strengthening of the mean circulation in the lower stratosphere, a moderate weakening of the mean circulation in the middle and upper stratosphere, and a moderate increase in the horizontal mixing into the tropics. The mean age trends are strongly sensitive to trends in the horizontal mixing into the tropics, and the uncertainty in the mixing trends causes uncertainty in the mean circulation trends. Comparisons of the mean circulation and mixing changes suggested by the measurements with those from a recent suite of CCM runs reveal significant differences that may have important implications on the accurate simulation of future stratospheric climate.

Quantifying uncertainty in remotely sensed land cover maps

Remotely sensed land cover maps are increasingly used as inputs into environmental simulation models whose outputs inform decisions and policy-making. Risks associated with these decisions are dependent on model output uncertainty, which is in turn affected by the uncertainty of land cover inputs. This article presents a method of quantifying the uncertainty that results from potential mis-classification in remotely sensed land cover maps. In addition to quantifying uncertainty in the classification of individual pixels in the map, we also address the important case where land cover maps have been upscaled to a coarser grid to suit the users’ needs and are reported as proportions of land cover type. The approach is Bayesian and incorporates several layers of modelling but is straightforward to implement. First, we incorporate data in the confusion matrix derived from an independent field survey, and discuss the appropriate way to model such data. Second, we account for spatial correlation in the true land cover map, using the remotely sensed map as a prior. Third, spatial correlation in the mis-classification characteristics is induced by modelling their variance. The result is that we are able to simulate posterior means and variances for individual sites and the entire map using a simple Monte Carlo algorithm. The method is applied to the Land Cover Map 2000 for the region of England and Wales, a map used as an input into a current dynamic carbon flux model.

Simple uncertainty frameworks for selecting weighting schemes and interpreting multimodel ensemble climate change experiments

Future climate change projections are often derived from ensembles of simulations from multiple global circulation models using heuristic weighting schemes. This study provides a more rigorous justification for this by introducing a nested family of three simple analysis of variance frameworks. Statistical frameworks are essential in order to quantify the uncertainty associated with the estimate of the mean climate change response. The most general framework yields the “one model, one vote” weighting scheme often used in climate projection. However, a simpler additive framework is found to be preferable when the climate change response is not strongly model dependent. In such situations, the weighted multimodel mean may be interpreted as an estimate of the actual climate response, even in the presence of shared model biases. Statistical significance tests are derived to choose the most appropriate framework for specific multimodel ensemble data. The framework assumptions are explicit and can be checked using simple tests and graphical techniques. The frameworks can be used to test for evidence of nonzero climate response and to construct confidence intervals for the size of the response. The methodology is illustrated by application to North Atlantic storm track data from the Coupled Model Intercomparison Project phase 5 (CMIP5) multimodel ensemble. Despite large variations in the historical storm tracks, the cyclone frequency climate change response is not found to be model dependent over most of the region. This gives high confidence in the response estimates. Statistically significant decreases in cyclone frequency are found on the flanks of the North Atlantic storm track and in the Mediterranean basin.

An environmental uncertainty-based diagnostic reference tool for evaluating the performance of supply chain value streams

This research has responded to the need for diagnostic reference tools explicitly linking the influence of environmental uncertainty and performance within the supply chain. Uncertainty is a key factor influencing performance and an important measure of the operating environment. We develop and demonstrate a novel reference methodology based on data envelopment analysis (DEA) for examining the performance of value streams within the supply chain with specific reference to the level of environmental uncertainty they face. In this paper, using real industrial data, 20 product supply value streams within the European automotive industry sector are evaluated. Two are found to be efficient. The peer reference groups for the underperforming value streams are identified and numerical improvement targets are derived. The paper demonstrates how DEA can be used to guide supply chain improvement efforts through role-model identification and target setting, in a way that recognises the multiple dimensions/outcomes of the supply chain process and the influence of its environmental conditions. We have facilitated the contextualisation of environmental uncertainty and its incorporation into a specific diagnostic reference tool.

Direct soil moisture controls of future global soil carbon changes: An important source of uncertainty

The nature of the climate–carbon cycle feedback depends critically on the response of soil carbon to climate, including changes in moisture. However, soil moisture–carbon feedback responses have not been investigated thoroughly. Uncertainty in the response of soil carbon to soil moisture changes could arise from uncertainty in the relationship between soil moisture and heterotrophic respiration. We used twelve soil moisture–respiration functions (SMRFs) with a soil carbon model (RothC) and data from a coupled climate–carbon cycle general circulation model to investigate the impact of direct heterotrophic respiration dependence on soil moisture on the climate carbon cycle feedback. Global changes in soil moisture acted to oppose temperature‐driven decreases in soil carbon and hence tended to increase soil carbon storage. We found considerable uncertainty in soil carbon changes due to the response of soil respiration to soil moisture. The use of different SMRFs resulted in both large losses and small gains in future global soil carbon stocks, whether considering all climate forcings or only moisture changes. Regionally, the greatest range in soil carbon changes across SMRFs was found where the largest soil carbon changes occurred. Further research is needed to constrain the soil moisture–respiration relationship and thus reduce uncertainty in climate–carbon cycle feedbacks. There may also be considerable uncertainty in the regional responses of soil carbon to soil moisture changes since climate model predictions of regional soil moisture changes are less coherent than temperature changes.

Automated determination of auroral breakup during the substorm expansion phase using all sky imager data

This technique paper describes a novel method for quantitatively and routinely identifying auroral breakup following substorm onset using the Time History of Events and Macroscale Interactions During Substorms (THEMIS) all-sky imagers (ASIs). Substorm onset is characterised by a brightening of the aurora that is followed by auroral poleward expansion and auroral breakup. This breakup can be identified by a sharp increase in the auroral intensity i(t) and the time derivative of auroral intensity i'(t). Utilising both i(t) and i'(t) we have developed an algorithm for identifying the time interval and spatial location of auroral breakup during the substorm expansion phase within the field of view of ASI data based solely on quantifiable characteristics of the optical auroral emissions. We compare the time interval determined by the algorithm to independently identified auroral onset times from three previously published studies. In each case the time interval determined by the algorithm is within error of the onset independently identified by the prior studies. We further show the utility of the algorithm by comparing the breakup intervals determined using the automated algorithm to an independent list of substorm onset times. We demonstrate that up to 50% of the breakup intervals characterised by the algorithm are within the uncertainty of the times identified in the independent list. The quantitative description and routine identification of an interval of auroral brightening during the substorm expansion phase provides a foundation for unbiased statistical analysis of the aurora to probe the physics of the auroral substorm as a new scientific tool for aiding the identification of the processes leading to auroral substorm onset.

SPARC Data Initiative: Comparison of water vapor climatologies from international satellite limb sounders

Within the SPARC Data Initiative, the first comprehensive assessment of the quality of 13 water vapor products from 11 limb-viewing satellite instruments (LIMS, SAGE II, UARS-MLS, HALOE, POAM III, SMR, SAGE III, MIPAS, SCIAMACHY, ACE-FTS, and Aura-MLS) obtained within the time period 1978-2010 has been performed. Each instrument's water vapor profile measurements were compiled into monthly zonal mean time series on a common latitude-pressure grid. These time series serve as basis for the "climatological" validation approach used within the project. The evaluations include comparisons of monthly or annual zonal mean cross sections and seasonal cycles in the tropical and extratropical upper troposphere and lower stratosphere averaged over one or more years, comparisons of interannual variability, and a study of the time evolution of physical features in water vapor such as the tropical tape recorder and polar vortex dehydration. Our knowledge of the atmospheric mean state in water vapor is best in the lower and middle stratosphere of the tropics and midlatitudes, with a relative uncertainty of. 2-6% (as quantified by the standard deviation of the instruments' multiannual means). The uncertainty increases toward the polar regions (+/- 10-15%), the mesosphere (+/- 15%), and the upper troposphere/lower stratosphere below 100 hPa (+/- 30-50%), where sampling issues add uncertainty due to large gradients and high natural variability in water vapor. The minimum found in multiannual (1998-2008) mean water vapor in the tropical lower stratosphere is 3.5 ppmv (+/- 14%), with slightly larger uncertainties for monthly mean values. The frequently used HALOE water vapor data set shows consistently lower values than most other data sets throughout the atmosphere, with increasing deviations from the multi-instrument mean below 100 hPa in both the tropics and extratropics. The knowledge gained from these comparisons and regarding the quality of the individual data sets in different regions of the atmosphere will help to improve model-measurement comparisons (e.g., for diagnostics such as the tropical tape recorder or seasonal cycles), data merging activities, and studies of climate variability.

SPARC Data Initiative: A comparison of ozone climatologies from international satellite limb sounders

A comprehensive quality assessment of the ozone products from 18 limb-viewing satellite instruments is provided by means of a detailed intercomparison. The ozone climatologies in form of monthly zonal mean time series covering the upper troposphere to lower mesosphere are obtained from LIMS, SAGE I/II/III, UARS-MLS, HALOE, POAM II/III, SMR, OSIRIS, MIPAS, GOMOS, SCIAMACHY, ACE-FTS, ACE-MAESTRO, Aura-MLS, HIRDLS, and SMILES within 1978–2010. The intercomparisons focus on mean biases of annual zonal mean fields, interannual variability, and seasonal cycles. Additionally, the physical consistency of the data is tested through diagnostics of the quasi-biennial oscillation and Antarctic ozone hole. The comprehensive evaluations reveal that the uncertainty in our knowledge of the atmospheric ozone mean state is smallest in the tropical and midlatitude middle stratosphere with a 1σ multi-instrument spread of less than ±5%. While the overall agreement among the climatological data sets is very good for large parts of the stratosphere, individual discrepancies have been identified, including unrealistic month-to-month fluctuations, large biases in particular atmospheric regions, or inconsistencies in the seasonal cycle. Notable differences between the data sets exist in the tropical lower stratosphere (with a spread of ±30%) and at high latitudes (±15%). In particular, large relative differences are identified in the Antarctic during the time of the ozone hole, with a spread between the monthly zonal mean fields of ±50%. The evaluations provide guidance on what data sets are the most reliable for applications such as studies of ozone variability, model-measurement comparisons, detection of long-term trends, and data-merging activities.

Location and characteristics of the reconnection X line deduced from low-altitude satellite and ground-based observations: 2. Defense Meteorological Satellite Program and European Incoherent Scatter data

We present an analysis of a cusp ion step, observed by the Defense Meteorological Satellite Program (DMSP) F10 spacecraft, between two poleward moving events of enhanced ionospheric electron temperature, observed by the European Incoherent Scatter (EISCAT) radar. From the ions detected by the satellite, the variation of the reconnection rate is computed for assumed distances along the open-closed field line separatrix from the satellite to the X line, do. Comparison with the onset times of the associated ionospheric events allows this distance to be estimated, but with an uncertainty due to the determination of the low-energy cutoff of the ion velocity distribution function, ƒ(ν). Nevertheless, the reconnection site is shown to be on the dayside magnetopause, consistent with the reconnection model of the cusp during southward interplanetary magnetic field (IMF). Analysis of the time series of distribution function at constant energies, ƒ(ts), shows that the best estimate of the distance do is 14.5±2 RE. This is consistent with various magnetopause observations of the signatures of reconnection for southward IMF. The ion precipitation is used to reconstruct the field-parallel part of the Cowley D ion distribution function injected into the open low-latitude boundary layer in the vicinity of the X line. From this reconstruction, the field-aligned component of the magnetosheath flow is found to be only −55±65 km s−1 near the X line, which means either that the reconnection X line is near the stagnation region at the nose of the magnetosphere, or that it is closely aligned with the magnetosheath flow streamline which is orthogonal to the magnetosheath field, or both. In addition, the sheath Alfvén speed at the X line is found to be 220±45 km s−1, and the speed with which newly opened field lines are ejected from the X line is 165±30 km s−1. We show that the inferred magnetic field, plasma density, and temperature of the sheath near the X line are consistent with a near-subsolar reconnection site and confirm that the magnetosheath field makes a large angle (>58°) with the X line.

Model predictions of the occurrence of non-Maxwellian plasmas, and analysis of their effects on EISCAT data

The recent identification of non-thermal plasmas using EISCAT data has been made possible by their occurrence during large, short-lived flow bursts. For steady, yet rapid, ion convection the only available signature is the shape of the spectrum, which is unreliable because it is open to distortion by noise and sampling uncertainty and can be mimicked by other phenomena. Nevertheless, spectral shape does give an indication of the presence of non-thermal plasma, and the characteristic shape has been observed for long periods (of the order of an hour or more) in some experiments. To evaluate this type of event properly one needs to compare it to what would be expected theoretically. Predictions have been made using the coupled thermosphere-ionosphere model developed at University College London and the University of Sheffield to show where and when non-Maxwellian plasmas would be expected in the auroral zone. Geometrical and other factors then govern whether these are detectable by radar. The results are applicable to any incoherent scatter radar in this area, but the work presented here concentrates on predictions with regard to experiments on the EISCAT facility.

Efficient incorporation of channel cross-section geometry uncertainty into regional and global scale flood inundation models

This paper investigates the challenge of representing structural differences in river channel cross-section geometry for regional to global scale river hydraulic models and the effect this can have on simulations of wave dynamics. Classically, channel geometry is defined using data, yet at larger scales the necessary information and model structures do not exist to take this approach. We therefore propose a fundamentally different approach where the structural uncertainty in channel geometry is represented using a simple parameterization, which could then be estimated through calibration or data assimilation. This paper first outlines the development of a computationally efficient numerical scheme to represent generalised channel shapes using a single parameter, which is then validated using a simple straight channel test case and shown to predict wetted perimeter to within 2% for the channels tested. An application to the River Severn, UK is also presented, along with an analysis of model sensitivity to channel shape, depth and friction. The channel shape parameter was shown to improve model simulations of river level, particularly for more physically plausible channel roughness and depth parameter ranges. Calibrating channel Manning’s coefficient in a rectangular channel provided similar water level simulation accuracy in terms of Nash-Sutcliffe efficiency to a model where friction and shape or depth were calibrated. However, the calibrated Manning coefficient in the rectangular channel model was ~2/3 greater than the likely physically realistic value for this reach and this erroneously slowed wave propagation times through the reach by several hours. Therefore, for large scale models applied in data sparse areas, calibrating channel depth and/or shape may be preferable to assuming a rectangular geometry and calibrating friction alone.

Common components of risk and uncertainty attitudes across contexts and domains: Evidence from 30 countries

Attitudes towards risk and uncertainty have been indicated to be highly context-dependent, and to be sensitive to the measurement technique employed. We present data collected in controlled experiments with 2,939 subjects in 30 countries measuring risk and uncertainty attitudes through incentivized measures as well as survey questions. Our data show clearly that measures correlate not only within decision contexts or measurement methods, but also across contexts and methods. This points to the existence of one underlying “risk preference”, which influences attitudes independently of the measurement method or choice domain. We furthermore find that answers to a general and a financial survey question correlate with incentivized lottery choices in most countries. Incentivized and survey measures also correlate significantly between countries. This opens the possibility to conduct cultural comparisons on risk attitudes using survey instruments.

Joint data assimilation of satellite reflectance and net ecosystem exchange data constrains ecosystem carbon fluxes at a high-elevation subalpine forest

We utilized an ecosystem process model (SIPNET, simplified photosynthesis and evapotranspiration model) to estimate carbon fluxes of gross primary productivity and total ecosystem respiration of a high-elevation coniferous forest. The data assimilation routine incorporated aggregated twice-daily measurements of the net ecosystem exchange of CO2 (NEE) and satellite-based reflectance measurements of the fraction of absorbed photosynthetically active radiation (fAPAR) on an eight-day timescale. From these data we conducted a data assimilation experiment with fifteen different combinations of available data using twice-daily NEE, aggregated annual NEE, eight-day f AP AR, and average annual fAPAR. Model parameters were conditioned on three years of NEE and fAPAR data and results were evaluated to determine the information content from the different combinations of data streams. Across the data assimilation experiments conducted, model selection metrics such as the Bayesian Information Criterion and Deviance Information Criterion obtained minimum values when assimilating average annual fAPAR and twice-daily NEE data. Application of wavelet coherence analyses showed higher correlations between measured and modeled fAPAR on longer timescales ranging from 9 to 12 months. There were strong correlations between measured and modeled NEE (R2, coefficient of determination, 0.86), but correlations between measured and modeled eight-day fAPAR were quite poor (R2 = −0.94). We conclude that this inability to determine fAPAR on eight-day timescale would improve with the considerations of the radiative transfer through the plant canopy. Modeled fluxes when assimilating average annual fAPAR and annual NEE were comparable to corresponding results when assimilating twice-daily NEE, albeit at a greater uncertainty. Our results support the conclusion that for this coniferous forest twice-daily NEE data are a critical measurement stream for the data assimilation. The results from this modeling exercise indicate that for this coniferous forest, average annuals for satellite-based fAPAR measurements paired with annual NEE estimates may provide spatial detail to components of ecosystem carbon fluxes in proximity of eddy covariance towers. Inclusion of other independent data streams in the assimilation will also reduce uncertainty on modeled values.

One step forward, and two steps back: women and career progression in academia during times of uncertainty

While there is an extensive and still growing body of literature on women in academia and the challenges they encounter in career progression, there is little research on their experience specifically within a business school setting. In this study, we attempt to address this gap and examine the experiences and career development of female academics in a business school and how these are impacted by downsizing programmes. To this end, an exploratory case study is conducted. The findings of this study show that female business school academics experience numerous challenges in terms of promotion and development, networking, and the multiple and conflicting demands placed upon them. As a result, the lack of visibility seems to be a pertinent issue in terms of their career progression. Our data also demonstrates that that, paradoxically, during periods of downsizing women become more visible and thus vulnerable to layoffs as a consequence of the challenges and pressures created in their environment during this process. In this paper, we argue that this heightened visibility, and being subject to possible layoffs, further reproduces inequality regimes in academia.