Stochastic perturbations to dynamical systems: a response theory approach

Using the formalism of the Ruelle response theory, we study how the invariant measure of an Axiom A dynamical system changes as a result of adding noise, and describe how the stochastic perturbation can be used to explore the properties of the underlying deterministic dynamics. We first find the expression for the change in the expectation value of a general observable when a white noise forcing is introduced in the system, both in the additive and in the multiplicative case. We also show that the difference between the expectation value of the power spectrum of an observable in the stochastically perturbed case and of the same observable in the unperturbed case is equal to the variance of the noise times the square of the modulus of the linear susceptibility describing the frequency-dependent response of the system to perturbations with the same spatial patterns as the considered stochastic forcing. This provides a conceptual bridge between the change in the fluctuation properties of the system due to the presence of noise and the response of the unperturbed system to deterministic forcings. Using Kramers-Kronig theory, it is then possible to derive the real and imaginary part of the susceptibility and thus deduce the Green function of the system for any desired observable. We then extend our results to rather general patterns of random forcing, from the case of several white noise forcings, to noise terms with memory, up to the case of a space-time random field. Explicit formulas are provided for each relevant case analysed. As a general result, we find, using an argument of positive-definiteness, that the power spectrum of the stochastically perturbed system is larger at all frequencies than the power spectrum of the unperturbed system. We provide an example of application of our results by considering the spatially extended chaotic Lorenz 96 model. These results clarify the property of stochastic stability of SRB measures in Axiom A flows, provide tools for analysing stochastic parameterisations and related closure ansatz to be implemented in modelling studies, and introduce new ways to study the response of a system to external perturbations. Taking into account the chaotic hypothesis, we expect that our results have practical relevance for a more general class of system than those belonging to Axiom A.

Attribution of climate change: a methodology to estimate the potential contribution to increases in potato yield in Scotland since 1960

Maincrop potato yields in Scotland have increased by 3035 similar to t similar to ha-1 since 1960 as a result of many changes, but has changing climate contributed anything to this? The purpose of this work was to answer this question. Daily weather data for the period 19602006 were analysed for five locations covering the zones of potato growing on the east coast of Scotland (between 55.213 and 57.646 similar to N) to determine trends in temperature, rainfall and solar radiation. A physiologically based potato yield model was validated using data obtained from a long-term field trial in eastern Scotland and then employed to simulate crop development and potential yield at each of the five sites. Over the 47 similar to years, there were significant increases in annual air and 30 similar to cm soil temperatures (0.27 and 0.30 similar to K similar to decade-1, respectively), but no significant changes in annual precipitation or in the timing of the last frost in spring and the first frost of autumn. There was no evidence of any north to south gradient of warming. Simulated emergence and canopy closure became earlier at all five sites over the period with the advance being greater in the north (3.7 and 3.6 similar to days similar to decade-1, respectively) than the south (0.5 and 0.8 similar to days similar to decade-1, respectively). Potential yield increased with time, generally reflecting the increased duration of the green canopy, at average rates of 2.8 similar to t similar to ha-1 decade-1 for chitted seed (sprouted prior to planting) and 2.5 similar to t similar to ha-1 decade-1 for unchitted seed. The measured warming could contribute potential yield increases of up to 13.2 similar to t similar to ha-1 for chitted potato (range 7.119.3 similar to t similar to ha-1) and 11.5 similar to t similar to ha-1 for unchitted potato (range 7.115.5 similar to t similar to ha-1) equivalent to 3439% of the increased potential yield over the period or 2326% of the increase in actual measured yields.

The development of a real-time PCR to detect pathogenic Leptospira species in kidney tissue

A LightCycler(R) real-time PCR hybridization probe-based assay that detects a conserved region of the 16S rRNA gene of pathogenic but not saprophytic Leptospira species was developed for the rapid detection of pathogenic leptospires directly from processed tissue samples. In addition, a differential PCR specific for saprophytic leptospires and a control PCR targeting the porcine beta-actin gene were developed. To assess the suitability of these PCR methods for diagnosis, a trial was performed on kidneys taken from adult pigs with evidence of leptospiral infection, primarily a history of reproductive disease and serological evidence of exposure to pathogenic leptospires (n = 180) and aborted pig foetuses (n = 24). Leptospire DNA was detected by the 'pathogenic' specific PCR in 25 tissues (14%) and the control beta-actin PCR was positive in all 204 samples confirming DNA was extracted from all samples. No leptospires were isolated from these samples by culture and no positives were detected with the 'saprophytic' PCR. In a subsidiary experiment, the 'pathogenic' PCR was used to analyse kidney samples from rodents (n = 7) collected as part of vermin control in a zoo, with show animals with high microagglutination titres to Leptospira species, and five were positive. Fifteen PCR amplicons from 1 mouse, 2 rat and 14 pig kidney samples, were selected at random from positive PCRs (n = 30) and sequenced. Sequence data indicated L. interrogans DNA in the pig and rat samples and L. inadai DNA, which is considered of intermediate pathogenicity, in the mouse sample. The only successful culture was from this mouse kidney and the isolate was confirmed to be L. inadai by classical serology. These data suggest this suite of PCRs is suitable for testing for the presence of pathogenic leptospires in pig herds where abortions and infertility occur and potentially in other animals such as rodents. Crown Copyright (C) 2007 Published by Elsevier Ltd. All rights reserved.

Separating the dynamical effects of climate change and ozone depletion. Part II: Southern Hemisphere troposphere

The separate effects of ozone depleting substances (ODSs) and greenhouse gases (GHGs) on forcing circulation changes in the Southern Hemisphere extratropical troposphere are investigated using a version of the Canadian Middle Atmosphere Model (CMAM) that is coupled to an ocean. Circulation-related diagnostics include zonal wind, tropopause pressure, Hadley cell width, jet location, annular mode index, precipitation, wave drag, and eddy fluxes of momentum and heat. As expected, the tropospheric response to the ODS forcing occurs primarily in austral summer, with past (1960-99) and future (2000-99) trends of opposite sign, while the GHG forcing produces more seasonally uniform trends with the same sign in the past and future. In summer the ODS forcing dominates past trends in all diagnostics, while the two forcings contribute nearly equally but oppositely to future trends. The ODS forcing produces a past surface temperature response consisting of cooling over eastern Antarctica, and is the dominant driver of past summertime surface temperature changes when the model is constrained by observed sea surface temperatures. For all diagnostics, the response to the ODS and GHG forcings is additive: that is, the linear trend computed from the simulations using the combined forcings equals (within statistical uncertainty) the sum of the linear trends from the simulations using the two separate forcings. Space time spectra of eddy fluxes and the spatial distribution of transient wave drag are examined to assess the viability of several recently proposed mechanisms for the observed poleward shift in the tropospheric jet.

Reconstruction of gusty wind speed time series from autonomous data logger records

The collection of wind speed time series by means of digital data loggers occurs in many domains, including civil engineering, environmental sciences and wind turbine technology. Since averaging intervals are often significantly larger than typical system time scales, the information lost has to be recovered in order to reconstruct the true dynamics of the system. In the present work we present a simple algorithm capable of generating a real-time wind speed time series from data logger records containing the average, maximum, and minimum values of the wind speed in a fixed interval, as well as the standard deviation. The signal is generated from a generalized random Fourier series. The spectrum can be matched to any desired theoretical or measured frequency distribution. Extreme values are specified through a postprocessing step based on the concept of constrained simulation. Applications of the algorithm to 10-min wind speed records logged at a test site at 60 m height above the ground show that the recorded 10-min values can be reproduced by the simulated time series to a high degree of accuracy.

Advances in sequential data assimilation and numerical weather forecasting: an Ensemble Transform Kalman-Bucy Filter, a study on clustering in deterministic Ensemble Square Root Filters, and a test of a new time stepping scheme in an atmospheric model

This dissertation deals with aspects of sequential data assimilation (in particular ensemble Kalman filtering) and numerical weather forecasting. In the first part, the recently formulated Ensemble Kalman-Bucy (EnKBF) filter is revisited. It is shown that the previously used numerical integration scheme fails when the magnitude of the background error covariance grows beyond that of the observational error covariance in the forecast window. Therefore, we present a suitable integration scheme that handles the stiffening of the differential equations involved and doesn’t represent further computational expense. Moreover, a transform-based alternative to the EnKBF is developed: under this scheme, the operations are performed in the ensemble space instead of in the state space. Advantages of this formulation are explained. For the first time, the EnKBF is implemented in an atmospheric model. The second part of this work deals with ensemble clustering, a phenomenon that arises when performing data assimilation using of deterministic ensemble square root filters in highly nonlinear forecast models. Namely, an M-member ensemble detaches into an outlier and a cluster of M-1 members. Previous works may suggest that this issue represents a failure of EnSRFs; this work dispels that notion. It is shown that ensemble clustering can be reverted also due to nonlinear processes, in particular the alternation between nonlinear expansion and compression of the ensemble for different regions of the attractor. Some EnSRFs that use random rotations have been developed to overcome this issue; these formulations are analyzed and their advantages and disadvantages with respect to common EnSRFs are discussed. The third and last part contains the implementation of the Robert-Asselin-Williams (RAW) filter in an atmospheric model. The RAW filter is an improvement to the widely popular Robert-Asselin filter that successfully suppresses spurious computational waves while avoiding any distortion in the mean value of the function. Using statistical significance tests both at the local and field level, it is shown that the climatology of the SPEEDY model is not modified by the changed time stepping scheme; hence, no retuning of the parameterizations is required. It is found the accuracy of the medium-term forecasts is increased by using the RAW filter.

A framework for agricultural adaptation to climate change in Southern Nigeria

The agricultural sector which contributes between 20-50% of gross domestic product in Africa and employs about 60% of the population is greatly affected by climate change impacts. Agricultural productivity and food prices are expected to rise due to this impact thereby worsening the food insecurity and poor nutritional health conditions in the continent. Incidentally, the capacity in the continent to adapt is very low. Addressing these challenges will therefore require a holistic and integrated adaptation framework hence this study. A total of 360 respondents selected through a multi-stage random sampling technique participated in the study that took place in Southern Nigeria from 2008-2011. Results showed that majority of respondents (84%) were aware that some climate change characteristics such as uncertainties at the onset of farming season, extreme weather events including flooding and droughts, pests, diseases, weed infestation, and land degradation have all been on the increase. The most significant effects of climate change that manifested in the area were declining soil fertility and weed infestation. Some of the adaptation strategies adopted by farmers include increased weeding, changing the timing of farm operations, and processing of crops to reduce post-harvest losses. Although majority of respondents were aware of government policies aimed at protecting the environment, most of them agreed that these policies were not being effectively implemented. A mutually inclusive framework comprising of both indigenous and modern techniques, processes, practices and technologies was then developed from the study in order to guide farmers in adapting to climate change effects/impacts.

Wildfire responses to abrupt climate change in North America

It is widely accepted, based on data from the last few decades and on model simulations, that anthropogenic climate change will cause increased fire activity. However, less attention has been paid to the relationship between abrupt climate changes and heightened fire activity in the paleorecord. We use 35 charcoal and pollen records to assess how fire regimes in North America changed during the last glacial–interglacial transition (15 to 10 ka), a time of large and rapid climate changes. We also test the hypothesis that a comet impact initiated continental-scale wildfires at 12.9 ka; the data do not support this idea, nor are continent-wide fires indicated at any time during deglaciation. There are, however, clear links between large climate changes and fire activity. Biomass burning gradually increased from the glacial period to the beginning of the Younger Dryas. Although there are changes in biomass burning during the Younger Dryas, there is no systematic trend. There is a further increase in biomass burning after the Younger Dryas. Intervals of rapid climate change at 13.9, 13.2, and 11.7 ka are marked by large increases in fire activity. The timing of changes in fire is not coincident with changes in human population density or the timing of the extinction of the megafauna. Although these factors could have contributed to fire-regime changes at individual sites or at specific times, the charcoal data indicate an important role for climate, and particularly rapid climate change, in determining broad-scale levels of fire activity.

The large-scale circulation change at the end of the Baiu season in Japan as seen in ERA40 data

The time evolution of the circulation change at the end of the Baiu season is investigated using ERA40 data. An end-day is defined for each of the 23 years based on the 850 hPa θe value at 40˚Nin the 130-140˚E sector exceeding 330 K. Daily time series of variables are composited with respect to this day. These composite time-series exhibit a clearer and more rapid change in the precipitation and the large-scale circulation over the whole East Asia region than those performed using calendar days. The precipitation change includes the abrupt end of the Baiu rain, the northward shift of tropical convection perhaps starting a few days before this, and the start of the heavier rain at higher latitudes. The northward migration of lower tropospheric warm, moist tropical air, a general feature of the seasonal march in the region, is fast over the continent and slow over the ocean. By mid to late July the cooler air over the Sea of Japan is surrounded on 3 sides by the tropical air. It is suggestive that the large-scale stage has been set for a jump to the post-Baiu state, i.e., for the end of the Baiu season. Two likely triggers for the actual change emerge from the analysis. The first is the northward movement of tropical convection into the Philippine region. The second is an equivalent barotropic Rossby wave-train, that over a 10-day period develops downstream across Eurasia. It appears likely that in most years one or both mechanisms can be important in triggering the actual end of the Baiu season.

Exploring the interplay between natural decadal variability and anthropogenic climate change in summer rainfall over China. Part I: Observational evidence

Summer rainfall over China has experienced substantial variability on longer time scales during the last century, and the question remains whether this is due to natural, internal variability or is part of the emerging signal of anthropogenic climate change. Using the best available observations over China, the decadal variability and recent trends in summer rainfall are investigated with the emphasis on changes in the seasonal evolution and on the temporal characteristics of daily rainfall. The possible relationships with global warming are reassessed. Substantial decadal variability in summer rainfall has been confirmed during the period 1958–2008; this is not unique to this period but is also seen in the earlier decades of the twentieth century. Two dominant patterns of decadal variability have been identified that contribute substantially to the recent trend of southern flooding and northern drought. Natural decadal variability appears to dominate in general but in the cases of rainfall intensity and the frequency of rainfall days, particularly light rain days, then the dominant EOFs have a rather different character, being of one sign over most of China, and having principal components (PCs) that appear more trendlike. The increasing intensity of rainfall throughout China and the decrease in light rainfall days, particularly in the north, could at least partially be of anthropogenic origin, both global and regional, linked to increased greenhouse gases and increased aerosols.

A framework for adapting survey design through time for wildlife population assessment

Sampling strategies for monitoring the status and trends in wildlife populations are often determined before the first survey is undertaken. However, there may be little information about the distribution of the population and so the sample design may be inefficient. Through time, as data are collected, more information about the distribution of animals in the survey region is obtained but it can be difficult to incorporate this information in the survey design. This paper introduces a framework for monitoring motile wildlife populations within which the design of future surveys can be adapted using data from past surveys whilst ensuring consistency in design-based estimates of status and trends through time. In each survey, part of the sample is selected from the previous survey sample using simple random sampling. The rest is selected with inclusion probability proportional to predicted abundance. Abundance is predicted using a model constructed from previous survey data and covariates for the whole survey region. Unbiased design-based estimators of status and trends and their variances are derived from two-phase sampling theory. Simulations over the short and long-term indicate that in general more precise estimates of status and trends are obtained using this mixed strategy than a strategy in which all of the sample is retained or all selected with probability proportional to predicted abundance. Furthermore the mixed strategy is robust to poor predictions of abundance. Estimates of status are more precise than those obtained from a rotating panel design.

Progressive palaeoenvironmental change during the Late Barremian-Early Aptian as prelude to Oceanic Anoxic Event 1a: Evidence from the Gorgo a Cerbara section (Umbria-Marche basin, central Italy)

During Oceanic Anoxic Event 1a (OAE 1a, 120 Ma; Li et al., 2008), organic carbon-rich layers were deposited in marine environments under anoxic conditions on a global scale. In this study, palaeoenvironmental conditions leading to this event are characterised by studying the Upper Barremian to the Lower Aptian succession of the Gorgo a Cerbara section (central Italy). For this, an integrated multi-proxy approach (δ13Ccarb; δ13Corg; δ18O; phosphorus; Total Organic Carbon, TOC; bulk-rock mineralogy, as well as redox-sensitive trace elements — RSTEs) has been applied. During the LateBarremian, thin organic-rich layers occur episodically, and associated Corg:Ptot ratios indicate the presence of intermittent dysoxic to anoxic conditions. Coarse correlations are observed between TOC, P and biogenic silica contents, indicating links between P availability, productivity, and TOC preservation. However, the corresponding δ13Ccarb and δ18O records remain quite stable, indicating that these brief periods of enhanced TOC preservation did not have sufficient impact on the marine carbon reservoir to deviate δ13C records. Around the Barremian–Aptian boundary, TOC-enriched layers become more frequent. These layers correlate with negative excursions in the δ13Ccarb and δ13Corg records, possibly due to a warming period as indicated by the δ18O record. During the earliest Aptian, this warming trend is reverted into a cooling trend, which is then followed by an important warming step near the onset of Oceanic Anoxic Event 1a (OAE 1a). During this time period, organic-rich intervals occur, which are characterised by the progressive increase in RSTE. The warming step prior the onset of OAE 1a is associated with the well-known negative spike in δ13Ccarb and δ13Corg records, an important peak in P accumulation, RSTE enrichments and Corg:Ptot ratios indicating the prevalence of anoxic conditions. The Selli Level itself may document a cooling phase. RSTE enrichments and Corg:Ptot ratios confirm the importance of anoxic conditions during OAE 1a at this site. The Gorgo a Cerbara section is interpreted to reflect the progressive impact of palaeoenvironmental change related to the formation of the Ontong-Java plate-basalt plateau, which started already around the Barremian–Aptian boundary and culminated into OAE 1a.

The role of transfer in language variation and change: Evidence from contact varieties of French

In this Special Issue, the focus is on contact-induced language variation and change in situations of societal bilingualism that involve long-term contact between French and another language. As is well known, when two or more languages are spoken by groups of speakers in the same geographical area, over time, features from one language can be transferred to the other language, especially when the languages in question are unequal in terms of prestige, institutional support and demographic factors. The process that leads to the adoption of such features in the contact languages is generally known as INTERFERENCE or TRANSFER, and these terms are also used to describe the features in question (i.e. the end product of the process of transfer). In this issue we prefer to use the term TRANSFER over the use of the notion INTERFERENCE, as the former has fewer negative connotations than the latter.

Global and regional temperature-change potentials for near-term climate forcers

We examine the climate effects of the emissions of near-term climate forcers (NTCFs) from 4 continental regions (East Asia, Europe, North America and South Asia) using radiative forcing from the task force on hemispheric transport of air pollution source-receptor global chemical transport model simulations. These simulations model the transport of 3 aerosol species (sulphate, particulate organic matter and black carbon) and 4 ozone precursors (methane, nitric oxides (NOx), volatile organic compounds and carbon monoxide). From the equilibrium radiative forcing results we calculate global climate metrics, global warming potentials (GWPs) and global temperature change potentials (GTPs) and show how these depend on emission region, and can vary as functions of time. For the aerosol species, the GWP(100) values are −37±12, −46±20, and 350±200 for SO2, POM and BC respectively for the direct effects only. The corresponding GTP(100) values are −5.2±2.4, −6.5±3.5, and 50±33. This analysis is further extended by examining the temperature-change impacts in 4 latitude bands. This shows that the latitudinal pattern of the temperature response to emissions of the NTCFs does not directly follow the pattern of the diagnosed radiative forcing. For instance temperatures in the Arctic latitudes are particularly sensitive to NTCF emissions in the northern mid-latitudes. At the 100-yr time horizon the ARTPs show NOx emissions can have a warming effect in the northern mid and high latitudes, but cooling in the tropics and Southern Hemisphere. The northern mid-latitude temperature response to northern mid-latitude emissions of most NTCFs is approximately twice as large as would be implied by the global average.

The benefits of a compute cluster approach to high spatial resolution biodiversity richness modelling: projecting the impact of climate change on Mediterranean flora

High spatial resolution environmental data gives us a better understanding of the environmental factors affecting plant distributions at fine spatial scales. However, large environmental datasets dramatically increase compute times and output species model size stimulating the need for an alternative computing solution. Cluster computing offers such a solution, by allowing both multiple plant species Environmental Niche Models (ENMs) and individual tiles of high spatial resolution models to be computed concurrently on the same compute cluster. We apply our methodology to a case study of 4,209 species of Mediterranean flora (around 17% of species believed present in the biome). We demonstrate a 16 times speed-up of ENM computation time when 16 CPUs were used on the compute cluster. Our custom Java ‘Merge’ and ‘Downsize’ programs reduce ENM output files sizes by 94%. The median 0.98 test AUC score of species ENMs is aided by various species occurrence data filtering techniques. Finally, by calculating the percentage change of individual grid cell values, we map the projected percentages of plant species vulnerable to climate change in the Mediterranean region between 1950–2000 and 2020.