Statistical inference of OH concentrations and air mass dilution rates from successive observations of non-methane hydrocarbons in single air masses

Bayesian inference has been used to determine rigorous estimates of hydroxyl radical concentrations () and air mass dilution rates (K) averaged following air masses between linked observations of nonmethane hydrocarbons (NMHCs) spanning the North Atlantic during the Intercontinental Transport and Chemical Transformation (ITCT)-Lagrangian-2K4 experiment. The Bayesian technique obtains a refined (posterior) distribution of a parameter given data related to the parameter through a model and prior beliefs about the parameter distribution. Here, the model describes hydrocarbon loss through OH reaction and mixing with a background concentration at rate K. The Lagrangian experiment provides direct observations of hydrocarbons at two time points, removing assumptions regarding composition or sources upstream of a single observation. The estimates are sharpened by using many hydrocarbons with different reactivities and accounting for their variability and measurement uncertainty. A novel technique is used to construct prior background distributions of many species, described by variation of a single parameter . This exploits the high correlation of species, related by the first principal component of many NMHC samples. The Bayesian method obtains posterior estimates of , K and following each air mass. Median values are typically between 0.5 and 2.0 × 106 molecules cm−3, but are elevated to between 2.5 and 3.5 × 106 molecules cm−3, in low-level pollution. A comparison of estimates from absolute NMHC concentrations and NMHC ratios assuming zero background (the “photochemical clock” method) shows similar distributions but reveals systematic high bias in the estimates from ratios. Estimates of K are ∼0.1 day−1 but show more sensitivity to the prior distribution assumed.

Diagnosis of variability and trends in a global precipitation dataset using a physically motivated statistical model

A physically motivated statistical model is used to diagnose variability and trends in wintertime ( October - March) Global Precipitation Climatology Project (GPCP) pentad (5-day mean) precipitation. Quasi-geostrophic theory suggests that extratropical precipitation amounts should depend multiplicatively on the pressure gradient, saturation specific humidity, and the meridional temperature gradient. This physical insight has been used to guide the development of a suitable statistical model for precipitation using a mixture of generalized linear models: a logistic model for the binary occurrence of precipitation and a Gamma distribution model for the wet day precipitation amount. The statistical model allows for the investigation of the role of each factor in determining variations and long-term trends. Saturation specific humidity q(s) has a generally negative effect on global precipitation occurrence and with the tropical wet pentad precipitation amount, but has a positive relationship with the pentad precipitation amount at mid- and high latitudes. The North Atlantic Oscillation, a proxy for the meridional temperature gradient, is also found to have a statistically significant positive effect on precipitation over much of the Atlantic region. Residual time trends in wet pentad precipitation are extremely sensitive to the choice of the wet pentad threshold because of increasing trends in low-amplitude precipitation pentads; too low a choice of threshold can lead to a spurious decreasing trend in wet pentad precipitation amounts. However, for not too small thresholds, it is found that the meridional temperature gradient is an important factor for explaining part of the long-term trend in Atlantic precipitation.

Statistical inferences in phylogeography

In conventional phylogeographic studies, historical demographic processes are elucidated from the geographical distribution of individuals represented on an inferred gene tree. However, the interpretation of gene trees in this context can be difficult as the same demographic/geographical process can randomly lead to multiple different genealogies. Likewise, the same gene trees can arise under different demographic models. This problem has led to the emergence of many statistical methods for making phylogeographic inferences. A popular phylogeographic approach based on nested clade analysis is challenged by the fact that a certain amount of the interpretation of the data is left to the subjective choices of the user, and it has been argued that the method performs poorly in simulation studies. More rigorous statistical methods based on coalescence theory have been developed. However, these methods may also be challenged by computational problems or poor model choice. In this review, we will describe the development of statistical methods in phylogeographic analysis, and discuss some of the challenges facing these methods.

Assembly rules for protein networks derived from phylogenetic-statistical analysis of whole genomes

Background: We report an analysis of a protein network of functionally linked proteins, identified from a phylogenetic statistical analysis of complete eukaryotic genomes. Phylogenetic methods identify pairs of proteins that co-evolve on a phylogenetic tree, and have been shown to have a high probability of correctly identifying known functional links. Results: The eukaryotic correlated evolution network we derive displays the familiar power law scaling of connectivity. We introduce the use of explicit phylogenetic methods to reconstruct the ancestral presence or absence of proteins at the interior nodes of a phylogeny of eukaryote species. We find that the connectivity distribution of proteins at the point they arise on the tree and join the network follows a power law, as does the connectivity distribution of proteins at the time they are lost from the network. Proteins resident in the network acquire connections over time, but we find no evidence that 'preferential attachment' - the phenomenon of newly acquired connections in the network being more likely to be made to proteins with large numbers of connections - influences the network structure. We derive a 'variable rate of attachment' model in which proteins vary in their propensity to form network interactions independently of how many connections they have or of the total number of connections in the network, and show how this model can produce apparent power-law scaling without preferential attachment. Conclusion: A few simple rules can explain the topological structure and evolutionary changes to protein-interaction networks: most change is concentrated in satellite proteins of low connectivity and small phenotypic effect, and proteins differ in their propensity to form attachments. Given these rules of assembly, power law scaled networks naturally emerge from simple principles of selection, yielding protein interaction networks that retain a high-degree of robustness on short time scales and evolvability on longer evolutionary time scales.

Diagnosis of variability and trends in a global precipitation dataset using a physically motivated statistical model

A physically motivated statistical model is used to diagnose variability and trends in wintertime ( October - March) Global Precipitation Climatology Project (GPCP) pentad (5-day mean) precipitation. Quasi-geostrophic theory suggests that extratropical precipitation amounts should depend multiplicatively on the pressure gradient, saturation specific humidity, and the meridional temperature gradient. This physical insight has been used to guide the development of a suitable statistical model for precipitation using a mixture of generalized linear models: a logistic model for the binary occurrence of precipitation and a Gamma distribution model for the wet day precipitation amount. The statistical model allows for the investigation of the role of each factor in determining variations and long-term trends. Saturation specific humidity q(s) has a generally negative effect on global precipitation occurrence and with the tropical wet pentad precipitation amount, but has a positive relationship with the pentad precipitation amount at mid- and high latitudes. The North Atlantic Oscillation, a proxy for the meridional temperature gradient, is also found to have a statistically significant positive effect on precipitation over much of the Atlantic region. Residual time trends in wet pentad precipitation are extremely sensitive to the choice of the wet pentad threshold because of increasing trends in low-amplitude precipitation pentads; too low a choice of threshold can lead to a spurious decreasing trend in wet pentad precipitation amounts. However, for not too small thresholds, it is found that the meridional temperature gradient is an important factor for explaining part of the long-term trend in Atlantic precipitation.

The distribution of species diversity across a flora's component lineages: dating the Cape's 'relicts'

The Cape Floristic Region is exceptionally species-rich both for its area and latitude, and this diversity is highly unevenly distributed among genera. The modern flora is hypothesized to result largely from recent (post-Oligocene) speciation, and it has long been speculated that particular species-poor lineages pre-date this burst of speciation. Here, we employ molecular phylogenetic data in combination with fossil calibrations to estimate the minimum duration of Cape occupation by 14 unrelated putative relicts. Estimates vary widely between lineages (7-101 Myr ago), and when compared with the estimated timing of onset of the modern flora's radiation, it is clear that many, but possibly not all, of these lineages pre-date its establishment. Statistical comparisons of diversities with lineage age show that low species diversity of many of the putative relicts results from a lower rate of diversification than in dated Cape radiations. In other putative relicts, however, we cannot reject the possibility that they diversify at the same underlying rate as the radiations, but have been present in the Cape for insufficient time to accumulate higher diversity. Although the extremes in diversity of currently dated Cape lineages fall outside expectations under a underlying diversification rate, sampling of all Cape lineages would be required to reject this null hypothesis.

Habitat correlates of distribution and local population decline of the endemic Sardinian newt Euproctus platycephalus

Habitat-based statistical models relating patterns of presence and absence of species to habitat variables could be useful to resolve conservation-related problems and highlight the causes of population declines. In this paper, we apply such a modelling approach to an endemic amphibian, the Sardinian mountain newt Euproctus platycephalus, considered by IUCN a critically endangered species. Sardinian newts inhabit freshwater habitat in streams, small lakes and pools on the island of Sardinia (Italy). Reported declines of newt populations are not yet supported by quantitative data, however, they are perceived or suspected across the species' historical range. This study represents a first attempt trying to statistically relate habitat characteristics to Sardinian newt occurrence and persistence. Linear regression analysis revealed that newts are more likely to be found in sites with colder water temperature, less riparian vegetation and, marginally, absence of fish. The implications of the results for the conservation of the species are discussed, and suggestions for the short-term management of newt inhabited sites suggested. (C) 2003 Elsevier Ltd. All rights reserved.

Hitting emissions targets with (statistical) confidence in multi-instrument Emissions Trading Schemes

A means of assessing, monitoring and controlling aggregate emissions from multi-instrument Emissions Trading Schemes is proposed. The approach allows contributions from different instruments with different forms of emissions targets to be integrated. Where Emissions Trading Schemes are helping meet specific national targets, the approach allows the entry requirements of new participants to be calculated and set at a level that will achieve these targets. The approach is multi-levelled, and may be extended downwards to support pooling of participants within instruments, or upwards to embed Emissions Trading Schemes within a wider suite of policies and measures with hard and soft targets. Aggregate emissions from each instrument are treated stochastically. Emissions from the scheme as a whole are then the joint probability distribution formed by integrating the emissions from its instruments. Because a Bayesian approach is adopted, qualitative and semi-qualitative data from expert opinion can be used where quantitative data is not currently available, or is incomplete. This approach helps government retain sufficient control over emissions trading scheme targets to allow them to meet their emissions reduction obligations, while minimising the need for retrospectively adjusting existing participants’ conditions of entry. This maintains participant confidence, while providing the necessary policy levers for good governance.

Assessing the vulnerability of blanket peat to climate change using an ensemble of statistical bioclimatic envelope models

We assessed the vulnerability of blanket peat to climate change in Great Britain using an ensemble of 8 bioclimatic envelope models. We used 4 published models that ranged from simple threshold models, based on total annual precipitation, to Generalised Linear Models (GLMs, based on mean annual temperature). In addition, 4 new models were developed which included measures of water deficit as threshold, classification tree, GLM and generalised additive models (GAM). Models that included measures of both hydrological conditions and maximum temperature provided a better fit to the mapped peat area than models based on hydrological variables alone. Under UKCIP02 projections for high (A1F1) and low (B1) greenhouse gas emission scenarios, 7 out of the 8 models showed a decline in the bioclimatic space associated with blanket peat. Eastern regions (Northumbria, North York Moors, Orkney) were shown to be more vulnerable than higher-altitude, western areas (Highlands, Western Isles and Argyle, Bute and The Trossachs). These results suggest a long-term decline in the distribution of actively growing blanket peat, especially under the high emissions scenario, although it is emphasised that existing peatlands may well persist for decades under a changing climate. Observational data from long-term monitoring and manipulation experiments in combination with process-based models are required to explore the nature and magnitude of climate change impacts on these vulnerable areas more fully.

Numerical convergence of the Block-Maxima approach to the generalized extreme value distribution

In this paper we perform an analytical and numerical study of Extreme Value distributions in discrete dynamical systems. In this setting, recent works have shown how to get a statistics of extremes in agreement with the classical Extreme Value Theory. We pursue these investigations by giving analytical expressions of Extreme Value distribution parameters for maps that have an absolutely continuous invariant measure. We compare these analytical results with numerical experiments in which we study the convergence to limiting distributions using the so called block-maxima approach, pointing out in which cases we obtain robust estimation of parameters. In regular maps for which mixing properties do not hold, we show that the fitting procedure to the classical Extreme Value Distribution fails, as expected. However, we obtain an empirical distribution that can be explained starting from a different observable function for which Nicolis et al. (Phys. Rev. Lett. 97(21): 210602, 2006) have found analytical results.

Strengthening the link between climate, hydrological and species distribution modeling to assess the impacts of climate change on freshwater biodiversity

To understand the resilience of aquatic ecosystems to environmental change, it is important to determine how multiple, related environmental factors, such as near-surface air temperature and river flow, will change during the next century. This study develops a novel methodology that combines statistical downscaling and fish species distribution modeling, to enhance the understanding of how global climate changes (modeled by global climate models at coarse-resolution) may affect local riverine fish diversity. The novelty of this work is the downscaling framework developed to provide suitable future projections of fish habitat descriptors, focusing particularly on the hydrology which has been rarely considered in previous studies. The proposed modeling framework was developed and tested in a major European system, the Adour-Garonne river basin (SW France, 116,000 km(2)), which covers distinct hydrological and thermal regions from the Pyrenees to the Atlantic coast. The simulations suggest that, by 2100, the mean annual stream flow is projected to decrease by approximately 15% and temperature to increase by approximately 1.2 °C, on average. As consequence, the majority of cool- and warm-water fish species is projected to expand their geographical range within the basin while the few cold-water species will experience a reduction in their distribution. The limitations and potential benefits of the proposed modeling approach are discussed. Copyright © 2012 Elsevier B.V. All rights reserved.

Downscaling from GCM precipitation: a benchmark for dynamical and statistical downscaling methods

A precipitation downscaling method is presented using precipitation from a general circulation model (GCM) as predictor. The method extends a previous method from monthly to daily temporal resolution. The simplest form of the method corrects for biases in wet-day frequency and intensity. A more sophisticated variant also takes account of flow-dependent biases in the GCM. The method is flexible and simple to implement. It is proposed here as a correction of GCM output for applications where sophisticated methods are not available, or as a benchmark for the evaluation of other downscaling methods. Applied to output from reanalyses (ECMWF, NCEP) in the region of the European Alps, the method is capable of reducing large biases in the precipitation frequency distribution, even for high quantiles. The two variants exhibit similar performances, but the ideal choice of method can depend on the GCM/reanalysis and it is recommended to test the methods in each case. Limitations of the method are found in small areas with unresolved topographic detail that influence higher-order statistics (e.g. high quantiles). When used as benchmark for three regional climate models (RCMs), the corrected reanalysis and the RCMs perform similarly in many regions, but the added value of the latter is evident for high quantiles in some small regions.

From ensemble forecasts to predictive distribution functions

The translation of an ensemble of model runs into a probability distribution is a common task in model-based prediction. Common methods for such ensemble interpretations proceed as if verification and ensemble were draws from the same underlying distribution, an assumption not viable for most, if any, real world ensembles. An alternative is to consider an ensemble as merely a source of information rather than the possible scenarios of reality. This approach, which looks for maps between ensembles and probabilistic distributions, is investigated and extended. Common methods are revisited, and an improvement to standard kernel dressing, called ‘affine kernel dressing’ (AKD), is introduced. AKD assumes an affine mapping between ensemble and verification, typically not acting on individual ensemble members but on the entire ensemble as a whole, the parameters of this mapping are determined in parallel with the other dressing parameters, including a weight assigned to the unconditioned (climatological) distribution. These amendments to standard kernel dressing, albeit simple, can improve performance significantly and are shown to be appropriate for both overdispersive and underdispersive ensembles, unlike standard kernel dressing which exacerbates over dispersion. Studies are presented using operational numerical weather predictions for two locations and data from the Lorenz63 system, demonstrating both effectiveness given operational constraints and statistical significance given a large sample.

The statistical cusp: a flux transfer event model

Traditionally, the cusp has been described in terms of a time-stationary feature of the magnetosphere which allows access of magnetosheath-like plasma to low altitudes. Statistical surveys of data from low-altitude spacecraft have shown the average characteristics and position of the cusp. Recently, however, it has been suggested that the ionospheric footprint of flux transfer events (FTEs) may be identified as variations of the “cusp” on timescales of a few minutes. In this model, the cusp can vary in form between a steady-state feature in one limit and a series of discrete ionospheric FTE signatures in the other limit. If this time-dependent cusp scenario is correct, then the signatures of the transient reconnection events must be able, on average, to reproduce the statistical cusp occurrence previously determined from the satellite observations. In this paper, we predict the precipitation signatures which are associated with transient magnetopause reconnection, following recent observations of the dependence of dayside ionospheric convection on the orientation of the IMF. We then employ a simple model of the longitudinal motion of FTE signatures to show how such events can easily reproduce the local time distribution of cusp occurrence probabilities, as observed by low-altitude satellites. This is true even in the limit where the cusp is a series of discrete events. Furthermore, we investigate the existence of double cusp patches predicted by the simple model and show how these events may be identified in the data.