Maximum principles for vectorial approximate minimisers on non-convex functionals

We establish Maximum Principles which apply to vectorial approximate minimizers of the general integral functional of Calculus of Variations. Our main result is a version of the Convex Hull Property. The primary advance compared to results already existing in the literature is that we have dropped the quasiconvexity assumption of the integrand in the gradient term. The lack of weak Lower semicontinuity is compensated by introducing a nonlinear convergence technique, based on the approximation of the projection onto a convex set by reflections and on the invariance of the integrand in the gradient term under the Orthogonal Group. Maximum Principles are implied for the relaxed solution in the case of non-existence of minimizers and for minimizing solutions of the Euler–Lagrange system of PDE.

Seasonal cycles and variability of O3 and H2O in the UT/LMS during SPURT

Airborne high resolution in situ measurements of a large set of trace gases including ozone (O3) and total water (H2O) in the upper troposphere and the lowermost stratosphere (UT/LMS) have been performed above Europe within the SPURT project. SPURT provides an extensive data coverage of the UT/LMS in each season within the time period between November 2001 and July 2003. In the LMS a distinct spring maximum and autumn minimum is observed in O3, whereas its annual cycle in the UT is shifted by 2–3 months later towards the end of the year. The more variable H2O measurements reveal a maximum during summer and a minimum during autumn/winter with no phase shift between the two atmospheric compartments. For a comprehensive insight into trace gas composition and variability in the UT/LMS several statistical methods are applied using chemical, thermal and dynamical vertical coordinates. In particular, 2-dimensional probability distribution functions serve as a tool to transform localised aircraft data to a more comprehensive view of the probed atmospheric region. It appears that both trace gases, O3 and H2O, reveal the most compact arrangement and are best correlated in the view of potential vorticity (PV) and distance to the local tropopause, indicating an advanced mixing state on these surfaces. Thus, strong gradients of PV seem to act as a transport barrier both in the vertical and the horizontal direction. The alignment of trace gas isopleths reflects the existence of a year-round extra-tropical tropopause transition layer. The SPURT measurements reveal that this layer is mainly affected by stratospheric air during winter/spring and by tropospheric air during autumn/summer. Normalised mixing entropy values for O3 and H2O in the LMS appear to be maximal during spring and summer, respectively, indicating highest variability of these trace gases during the respective seasons.

A nonparametric ensemble transform method for Bayesian inference

Many applications, such as intermittent data assimilation, lead to a recursive application of Bayesian inference within a Monte Carlo context. Popular data assimilation algorithms include sequential Monte Carlo methods and ensemble Kalman filters (EnKFs). These methods differ in the way Bayesian inference is implemented. Sequential Monte Carlo methods rely on importance sampling combined with a resampling step, while EnKFs utilize a linear transformation of Monte Carlo samples based on the classic Kalman filter. While EnKFs have proven to be quite robust even for small ensemble sizes, they are not consistent since their derivation relies on a linear regression ansatz. In this paper, we propose another transform method, which does not rely on any a priori assumptions on the underlying prior and posterior distributions. The new method is based on solving an optimal transportation problem for discrete random variables. © 2013, Society for Industrial and Applied Mathematics

Large inert carbon pool in the terrestrial biosphere at the Last Glacial Maximum

During each of the late Pleistocene glacial–interglacial transitions, atmospheric carbon dioxide concentrations rose by almost 100 ppm. The sources of this carbon are unclear, and efforts to identify them are hampered by uncertainties in the magnitude of carbon reservoirs and fluxes under glacial conditions. Here we use oxygen isotope measurements from air trapped in ice cores and ocean carbon-cycle modelling to estimate terrestrial and oceanic gross primary productivity during the Last Glacial Maximum. We find that the rate of gross terrestrial primary production during the Last Glacial Maximum was about 40±10 Pg C yr−1, half that of the pre-industrial Holocene. Despite the low levels of photosynthesis, we estimate that the late glacial terrestrial biosphere contained only 330 Pg less carbon than pre-industrial levels. We infer that the area covered by carbon-rich but unproductive biomes such as tundra and cold steppes was significantly larger during the Last Glacial Maximum, consistent with palaeoecological data. Our data also indicate the presence of an inert carbon pool of 2,300 Pg C, about 700 Pg larger than the inert carbon locked in permafrost today. We suggest that the disappearance of this carbon pool at the end of the Last Glacial Maximum may have contributed to the deglacial rise in atmospheric carbon dioxide concentrations.

Generalized Bayesian cloud detection for satellite imagery. part 1: technique and validation for night-time imagery over land and sea

Numerical Weather Prediction (NWP) fields are used to assist the detection of cloud in satellite imagery. Simulated observations based on NWP are used within a framework based on Bayes' theorem to calculate a physically-based probability of each pixel with an imaged scene being clear or cloudy. Different thresholds can be set on the probabilities to create application-specific cloud-masks. Here, this is done over both land and ocean using night-time (infrared) imagery. We use a validation dataset of difficult cloud detection targets for the Spinning Enhanced Visible and Infrared Imager (SEVIRI) achieving true skill scores of 87% and 48% for ocean and land, respectively using the Bayesian technique, compared to 74% and 39%, respectively for the threshold-based techniques associated with the validation dataset.

Generalised Bayesian cloud detection for satellite imagery. part 2: technique and validation for day-time imagery

Numerical Weather Prediction (NWP) fields are used to assist the detection of cloud in satellite imagery. Simulated observations based on NWP are used within a framework based on Bayes' theorem to calculate a physically-based probability of each pixel with an imaged scene being clear or cloudy. Different thresholds can be set on the probabilities to create application-specific cloud masks. Here, the technique is shown to be suitable for daytime applications over land and sea, using visible and near-infrared imagery, in addition to thermal infrared. We use a validation dataset of difficult cloud detection targets for the Spinning Enhanced Visible and Infrared Imager (SEVIRI) achieving true skill scores of 89% and 73% for ocean and land, respectively using the Bayesian technique, compared to 90% and 70%, respectively for the threshold-based techniques associated with the validation dataset.

Sea surface temperature estimation from the Geostationary Operational Environmental Satellite 12 (GOES-12)

This paper describes the techniques used to obtain sea surface temperature (SST) retrievals from the Geostationary Operational Environmental Satellite 12 (GOES-12) at the National Oceanic and Atmospheric Administration’s Office of Satellite Data Processing and Distribution. Previous SST retrieval techniques relying on channels at 11 and 12 μm are not applicable because GOES-12 lacks the latter channel. Cloud detection is performed using a Bayesian method exploiting fast-forward modeling of prior clear-sky radiances using numerical weather predictions. The basic retrieval algorithm used at nighttime is based on a linear combination of brightness temperatures at 3.9 and 11 μm. In comparison with traditional split window SSTs (using 11- and 12-μm channels), simulations show that this combination has maximum scatter when observing drier colder scenes, with a comparable overall performance. For daytime retrieval, the same algorithm is applied after estimating and removing the contribution to brightness temperature in the 3.9-μm channel from solar irradiance. The correction is based on radiative transfer simulations and comprises a parameterization for atmospheric scattering and a calculation of ocean surface reflected radiance. Potential use of the 13-μm channel for SST is shown in a simulation study: in conjunction with the 3.9-μm channel, it can reduce the retrieval error by 30%. Some validation results are shown while a companion paper by Maturi et al. shows a detailed analysis of the validation results for the operational algorithms described in this present article.

Online bayesian inference in some time-frequency representations of non-stationary processes

The use of Bayesian inference in the inference of time-frequency representations has, thus far, been limited to offline analysis of signals, using a smoothing spline based model of the time-frequency plane. In this paper we introduce a new framework that allows the routine use of Bayesian inference for online estimation of the time-varying spectral density of a locally stationary Gaussian process. The core of our approach is the use of a likelihood inspired by a local Whittle approximation. This choice, along with the use of a recursive algorithm for non-parametric estimation of the local spectral density, permits the use of a particle filter for estimating the time-varying spectral density online. We provide demonstrations of the algorithm through tracking chirps and the analysis of musical data.

Quantifying the roles of ocean circulation and biogeochemistry in governing ocean carbon-13 and atmospheric carbon dioxide at the last glacial maximum

We use a state-of-the-art ocean general circulation and biogeochemistry model to examine the impact of changes in ocean circulation and biogeochemistry in governing the change in ocean carbon-13 and atmospheric CO2 at the last glacial maximum (LGM). We examine 5 different realisations of the ocean's overturning circulation produced by a fully coupled atmosphere-ocean model under LGM forcing and suggested changes in the atmospheric deposition of iron and phytoplankton physiology at the LGM. Measured changes in carbon-13 and carbon-14, as well as a qualitative reconstruction of the change in ocean carbon export are used to evaluate the results. Overall, we find that while a reduction in ocean ventilation at the LGM is necessary to reproduce carbon-13 and carbon-14 observations, this circulation results in a low net sink for atmospheric CO2. In contrast, while biogeochemical processes contribute little to carbon isotopes, we propose that most of the change in atmospheric CO2 was due to such factors. However, the lesser role for circulation means that when all plausible factors are accounted for, most of the necessary CO2 change remains to be explained. This presents a serious challenge to our understanding of the mechanisms behind changes in the global carbon cycle during the geologic past.

Settlement patterns in the late Mesolithic of western Scotland: the implications of Bayesian analysis of radiocarbon dates and inter-site technological comparisons

The character of settlement patterns within the late Mesolithic communities of north-west Europe is a topic of substantial debate. An important case study concerns the five shell middens on the island of Oronsay, Inner Hebrides, western Scotland. Two conflicting interpretations have been proposed: the evidence from seasonality indicators and stable isotope analysis of human bones has been used to support a model of year-round settlement on this small island; alternatively, the middens have been interpreted as resulting from short-term intermittent visits to Oronsay within a regionally mobile settlement pattern. We contribute to this debate by describing Storakaig, a newly discovered site on the nearby island of Islay, undertaking a Bayesian chronological analysis and providing evidence for technological continuity between Oronsay and sites elsewhere in the region. While this new evidence remains open to alternative interpretation, we suggest that it makes regional mobility rather than year-round settlement on Oronsay a more viable interpretation for the Oronsay middens. Our analysis also confirms the likely overlap of the late Mesolithic with the earliest Neolithic within western Scotland.

Climatic impacts of fresh water hosing under Last Glacial Maximum conditions: a multi-model study

Fresh water hosing simulations, in which a fresh water flux is imposed in the North Atlantic to force fluctuations of the Atlantic Meridional Overturning Circulation, have been routinely performed, first to study the climatic signature of different states of this circulation, then, under present or future conditions, to investigate the potential impact of a partial melting of the Greenland ice sheet. The most compelling examples of climatic changes potentially related to AMOC abrupt variations, however, are found in high resolution palaeo-records from around the globe for the last glacial period. To study those more specifically, more and more fresh water hosing experiments have been performed under glacial conditions in the recent years. Here we compare an ensemble constituted by 11 such simulations run with 6 different climate models. All simulations follow a slightly different design, but are sufficiently close in their design to be compared. They all study the impact of a fresh water hosing imposed in the extra-tropical North Atlantic. Common features in the model responses to hosing are the cooling over the North Atlantic, extending along the sub-tropical gyre in the tropical North Atlantic, the southward shift of the Atlantic ITCZ and the weakening of the African and Indian monsoons. On the other hand, the expression of the bipolar see-saw, i.e., warming in the Southern Hemisphere, differs from model to model, with some restricting it to the South Atlantic and specific regions of the southern ocean while others simulate a widespread southern ocean warming. The relationships between the features common to most models, i.e., climate changes over the north and tropical Atlantic, African and Asian monsoon regions, are further quantified. These suggest a tight correlation between the temperature and precipitation changes over the extra-tropical North Atlantic, but different pathways for the teleconnections between the AMOC/North Atlantic region and the African and Indian monsoon regions.

A generalised Bayesian instrumental variable approach under student t-distributed errors with application

Bayesian analysis is given of an instrumental variable model that allows for heteroscedasticity in both the structural equation and the instrument equation. Specifically, the approach for dealing with heteroscedastic errors in Geweke (1993) is extended to the Bayesian instrumental variable estimator outlined in Rossi et al. (2005). Heteroscedasticity is treated by modelling the variance for each error using a hierarchical prior that is Gamma distributed. The computation is carried out by using a Markov chain Monte Carlo sampling algorithm with an augmented draw for the heteroscedastic case. An example using real data illustrates the approach and shows that ignoring heteroscedasticity in the instrument equation when it exists may lead to biased estimates.

How large is congressional dependence in agriculture. Bayesian inference about ‘scale’ and ‘scope’ in measuring a spatial externality

The political economy literature on agriculture emphasizes influence over political outcomes via lobbying conduits in general, political action committee contributions in particular and the pervasive view that political preferences with respect to agricultural issues are inherently geographic. In this context, ‘interdependence’ in Congressional vote behaviour manifests itself in two dimensions. One dimension is the intensity by which neighboring vote propensities influence one another and the second is the geographic extent of voter influence. We estimate these facets of dependence using data on a Congressional vote on the 2001 Farm Bill using routine Markov chain Monte Carlo procedures and Bayesian model averaging, in particular. In so doing, we develop a novel procedure to examine both the reliability and the consequences of different model representations for measuring both the ‘scale’ and the ‘scope’ of spatial (geographic) co-relations in voting behaviour.

Reducing inconsistencies in point observations of maximum flood inundation level

Flood simulation models and hazard maps are only as good as the underlying data against which they are calibrated and tested. However, extreme flood events are by definition rare, so the observational data of flood inundation extent are limited in both quality and quantity. The relative importance of these observational uncertainties has increased now that computing power and accurate lidar scans make it possible to run high-resolution 2D models to simulate floods in urban areas. However, the value of these simulations is limited by the uncertainty in the true extent of the flood. This paper addresses that challenge by analyzing a point dataset of maximum water extent from a flood event on the River Eden at Carlisle, United Kingdom, in January 2005. The observation dataset is based on a collection of wrack and water marks from two postevent surveys. A smoothing algorithm for identifying, quantifying, and reducing localized inconsistencies in the dataset is proposed and evaluated showing positive results. The proposed smoothing algorithm can be applied in order to improve flood inundation modeling assessment and the determination of risk zones on the floodplain.

Pollen, plant macrofossil and charcoal records for palaeovegetation reconstruction in the Mediterranean-Black Sea Corridor since the Last Glacial Maximum

New reconstructions of changing vegetation patterns in the Mediterranean-Black Sea Corridor since the Last Glacial Maximum are being produced by an improved biomisation scheme that uses both pollen and plant macrofossil data, in conjunction. Changes in fire regimes over the same interval will also be reconstructed using both microscopic and macroscopic charcoal remains. These reconstructions will allow a diagnosis of the interactions between climate, fire and vegetation on millennial timescales, and will also help to clarify the role of coastline and other geomorphic changes, salinity and impacts of human activities in this region. These new data sets are being produced as a result of collaboration between the Palynology Working Group (WG-2) within the IGCP-521 project and the international Palaeovegetation Mapping Project (BIOME 6000). The main objective of this paper is to present the goals of this cooperation, methodology, including limitations and planned improvements, and to show the initial results of some applications.