Reduced relative entropy techniques for a posteriori analysis of multiphase problems in elastodynamics

We give an a posteriori analysis of a semidiscrete discontinuous Galerkin scheme approximating solutions to a model of multiphase elastodynamics, which involves an energy density depending not only on the strain but also the strain gradient. A key component in the analysis is the reduced relative entropy stability framework developed in Giesselmann (2014, SIAM J. Math. Anal., 46, 3518–3539). This framework allows energy-type arguments to be applied to continuous functions. Since we advocate the use of discontinuous Galerkin methods we make use of two families of reconstructions, one set of discrete reconstructions and a set of elliptic reconstructions to apply the reduced relative entropy framework in this setting.

Reduced relative entropy techniques for a priori analysis of multiphase problems in elastodynamics

We give an a priori analysis of a semi-discrete discontinuous Galerkin scheme approximating solutions to a model of multiphase elastodynamics which involves an energy density depending not only on the strain but also the strain gradient. A key component in the analysis is the reduced relative entropy stability framework developed in Giesselmann (SIAM J Math Anal 46(5):3518–3539, 2014). The estimate we derive is optimal in the L∞(0,T;dG) norm for the strain and the L2(0,T;dG) norm for the velocity, where dG is an appropriate mesh dependent H1-like space.

Measures of observation impact in non-Gaussian data assimilation

ABSTRACT Non-Gaussian/non-linear data assimilation is becoming an increasingly important area of research in the Geosciences as the resolution and non-linearity of models are increased and more and more non-linear observation operators are being used. In this study, we look at the effect of relaxing the assumption of a Gaussian prior on the impact of observations within the data assimilation system. Three different measures of observation impact are studied: the sensitivity of the posterior mean to the observations, mutual information and relative entropy. The sensitivity of the posterior mean is derived analytically when the prior is modelled by a simplified Gaussian mixture and the observation errors are Gaussian. It is found that the sensitivity is a strong function of the value of the observation and proportional to the posterior variance. Similarly, relative entropy is found to be a strong function of the value of the observation. However, the errors in estimating these two measures using a Gaussian approximation to the prior can differ significantly. This hampers conclusions about the effect of the non-Gaussian prior on observation impact. Mutual information does not depend on the value of the observation and is seen to be close to its Gaussian approximation. These findings are illustrated with the particle filter applied to the Lorenz ’63 system. This article is concluded with a discussion of the appropriateness of these measures of observation impact for different situations.

Observation impact in data assimilation: the effect of non-Gaussian observation error.

Data assimilation methods which avoid the assumption of Gaussian error statistics are being developed for geoscience applications. We investigate how the relaxation of the Gaussian assumption affects the impact observations have within the assimilation process. The effect of non-Gaussian observation error (described by the likelihood) is compared to previously published work studying the effect of a non-Gaussian prior. The observation impact is measured in three ways: the sensitivity of the analysis to the observations, the mutual information, and the relative entropy. These three measures have all been studied in the case of Gaussian data assimilation and, in this case, have a known analytical form. It is shown that the analysis sensitivity can also be derived analytically when at least one of the prior or likelihood is Gaussian. This derivation shows an interesting asymmetry in the relationship between analysis sensitivity and analysis error covariance when the two different sources of non-Gaussian structure are considered (likelihood vs. prior). This is illustrated for a simple scalar case and used to infer the effect of the non-Gaussian structure on mutual information and relative entropy, which are more natural choices of metric in non-Gaussian data assimilation. It is concluded that approximating non-Gaussian error distributions as Gaussian can give significantly erroneous estimates of observation impact. The degree of the error depends not only on the nature of the non-Gaussian structure, but also on the metric used to measure the observation impact and the source of the non-Gaussian structure.

A Posteriori analysis of discontinuous Galerkin schemes for systems of hyperbolic conservation laws

In this work we construct reliable a posteriori estimates for some semi- (spatially) discrete discontinuous Galerkin schemes applied to nonlinear systems of hyperbolic conservation laws. We make use of appropriate reconstructions of the discrete solution together with the relative entropy stability framework, which leads to error control in the case of smooth solutions. The methodology we use is quite general and allows for a posteriori control of discontinuous Galerkin schemes with standard flux choices which appear in the approximation of conservation laws. In addition to the analysis, we conduct some numerical benchmarking to test the robustness of the resultant estimator.

Farm income, population and farmland prices: a relative information approach

This paper uses an entropy-based information approach to determine if farmland values are more closely associated with urban pressure or farm income. The basic question is: how much information on changes in farm real estate values is contained in changes in population versus changes in returns to production agriculture? Results suggest population is informative, but changes in farmland values are more strongly associated with changes in the distribution of returns. However, this relationship is not true for every region nor does it hold over time, as for some regions and time periods changes in population are more informative. Results have policy implications for both equity and efficiency.

Transgenerational, dynamic methylation of stomata genes in response to low relative humidity

Transgenerational inheritance of abiotic stress-induced epigenetic modifications in plants has potential adaptive significance and might condition the offspring to improve the response to the same stress, but this is at least partly dependent on the potency, penetrance and persistence of the transmitted epigenetic marks. We examined transgenerational inheritance of low Relative Humidity-induced DNA methylation for two gene loci in the stomatal developmental pathway in Arabidopsis thaliana and the abundance of associated short-interfering RNAs (siRNAs). Heritability of low humidity-induced methylation was more predictable and penetrative at one locus (SPEECHLESS, entropy ≤ 0.02; χ2 < 0.001) than the other (FAMA, entropy ≤ 0.17; χ2 ns). Methylation at SPEECHLESS correlated positively with the continued presence of local siRNAs (r2 = 0.87; p = 0.013) which, however, could be disrupted globally in the progeny under repeated stress. Transgenerational methylation and a parental low humidity-induced stomatal phenotype were heritable, but this was reversed in the progeny under repeated treatment in a previously unsuspected manner.

Relative proportions of polycyclic aromatic hydrocarbons differ between accumulation bioassays and chemical methods to predict bioavailability

Chemical methods to predict the bioavailable fraction of organic contaminants are usually validated in the literature by comparison with established bioassays. A soil spiked with polycyclic aromatic hydrocarbons (PAHs) was aged over six months and subjected to butanol, cyclodextrin and tenax extractions as well as an exhaustive extraction to determine total PAH concentrations at several time points. Earthworm (Eisenia fetida) and rye grass root (Lolium multiflorum) accumulation bioassays were conducted in parallel. Butanol extractions gave the best relationship with earthworm accumulation (r2 ≤ 0.54, p ≤ 0.01); cyclodextrin, butanol and acetone–hexane extractions all gave good predictions of accumulation in rye grass roots (r2 ≤ 0.86, p ≤ 0.01). However, the profile of the PAHs extracted by the different chemical methods was significantly different (p < 0.01) to that accumulated in the organisms. Biota accumulated a higher proportion of the heavier 4-ringed PAHs. It is concluded that bioaccumulation is a complex process that cannot be predicted by measuring the bioavailable fraction alone. The ability of chemical methods to predict PAH accumulation in Eisenia fetida and Lolium multiflorum was hindered by the varied metabolic fate of the different PAHs within the organisms.

Climate entropy budget of the HadCM3 atmosphere-ocean general circulation model and of FAMOUS, its low resolution version

The entropy budget is calculated of the coupled atmosphere–ocean general circulation model HadCM3. Estimates of the different entropy sources and sinks of the climate system are obtained directly from the diabatic heating terms, and an approximate estimate of the planetary entropy production is also provided. The rate of material entropy production of the climate system is found to be ∼50 mW m−2 K−1, a value intermediate in the range 30–70 mW m−2 K−1 previously reported from different models. The largest part of this is due to sensible and latent heat transport (∼38 mW m−2 K−1). Another 13 mW m−2 K−1 is due to dissipation of kinetic energy in the atmosphere by friction and Reynolds stresses. Numerical entropy production in the atmosphere dynamical core is found to be about 0.7 mW m−2 K−1. The material entropy production within the ocean due to turbulent mixing is ∼1 mW m−2 K−1, a very small contribution to the material entropy production of the climate system. The rate of change of entropy of the model climate system is about 1 mW m−2 K−1 or less, which is comparable with the typical size of the fluctuations of the entropy sources due to interannual variability, and a more accurate closure of the budget than achieved by previous analyses. Results are similar for FAMOUS, which has a lower spatial resolution but similar formulation to HadCM3, while more substantial differences are found with respect to other models, suggesting that the formulation of the model has an important influence on the climate entropy budget. Since this is the first diagnosis of the entropy budget in a climate model of the type and complexity used for projection of twenty-first century climate change, it would be valuable if similar analyses were carried out for other such models.

Relative humidity changes in a warmer climate

Key climate feedbacks due to water vapor and clouds rest largely on how relative humidity R changes in a warmer climate, yet this has not been extensively analyzed in models. General circulation models (GCMs) from the CMIP3 archive and several higher resolution atmospheric GCMs examined here generally predict a characteristic pattern of R trend with global temperature that has been reported previously in individual models, including increase around the tropopause, decrease in the tropical upper troposphere, and decrease in midlatitudes. This pattern is very similar to that previously reported for cloud cover in the same GCMs, confirming the role of R in controlling changes in simulated cloud. Comparing different models, the trend in each part of the troposphere is approximately proportional to the upward and/or poleward gradient of R in the present climate. While this suggests that the changes simply reflect a shift of the R pattern upward with the tropopause and poleward with the zonal jets, the drying trend in the subtropics is roughly three times too large to be attributable to shifts of subtropical features, and the subtropical R minima deepen in most models. R trends are correlated with horizontal model resolution, especially outside the tropics, where they show signs of convergence and latitudinal gradients become close to available observations for GCM resolutions near T85 and higher. We argue that much of the systematic change in R can be explained by the local specific humidity having been set (by condensation) in remote regions with different temperature changes, hence the gradients and trends each depend on a model’s ability to resolve moisture transport. Finally, subtropical drying trends predicted from the warming alone fall well short of those observed in recent decades. While this discrepancy supports previous reports of GCMs underestimating Hadley Cell expansion, our results imply that shifts alone are not a sufficient interpretation of changes.

Evaluating explanations about drug prescriptions: effects of varying the nature of information about side effects and its relative position in explanations

This study evaluates computer-generated written explanations about drug prescriptions that are based on an analysis of both patient and doctor informational needs. Three experiments examine the effects of varying the type of information given about the possible side effects of the medication, and the order of information within the explanation. Experiment 1 investigated the effects of these two factors on people's ratings of how good they consider the explanations to be and of their perceived likelihood of taking the medication, as well as on their memory for the information in the explanation. Experiment 2 further examined the effects of varying information about side effects by separating out the contribution of number and severity of side effects. It was found that participants in this study did not “like” explanations that described severe side effects, and also judged that they would be less likely to take the medication if given such explanations. Experiment 3 therefore investigated whether information about severe side effects could be presented in such a way as to increase judgements of how good explanations are thought to be, as well as the perceived likelihood of adherence. The results showed some benefits of providing additional explanatory information.

Using a runway paradigm to assess the relative strength of rats' motivations for enrichment objects

Laboratory animals should be provided with enrichment objects in their cages; however, it is first necessary to test whether the proposed enrichment objects provide benefits that increase the animals’ welfare. The two main paradigms currently used to assess proposed enrichment objects are the choice test, which is limited to determining relative frequency of choice, and consumer demand studies, which can indicate the strength of a preference but are complex to design. Here, we propose a third methodology: a runway paradigm, which can be used to assess the strength of an animal’s motivation for enrichment objects, is simpler to use than consumer demand studies, and is faster to complete than typical choice tests. Time spent with objects in a standard choice test was used to rank several enrichment objects in order to compare with the ranking found in our runway paradigm. The rats ran significantly more times, ran faster, and interacted longer with objects with which they had previously spent the most time. It was concluded that this simple methodology is suitable for measuring rats’ motivation to reach enrichment objects. This can be used to assess the preference for different types of enrichment objects or to measure reward system processes.