Power properties if invariant tests for spatial autocorrelation in linear regression

This paper derives some exact power properties of tests for spatial autocorrelation in the context of a linear regression model. In particular, we characterize the circumstances in which the power vanishes as the autocorrelation increases, thus extending the work of Krämer (2005). More generally, the analysis in the paper sheds new light on how the power of tests for spatial autocorrelation is affected by the matrix of regressors and by the spatial structure. We mainly focus on the problem of residual spatial autocorrelation, in which case it is appropriate to restrict attention to the class of invariant tests, but we also consider the case when the autocorrelation is due to the presence of a spatially lagged dependent variable among the regressors. A numerical study aimed at assessing the practical relevance of the theoretical results is included

Non-intrusive monitoring of atmospheric CO2 in analogue models of terrestrial carbon cycle

1. Closed Ecological Systems (CES) are small manmade ecosystems which do not have any material exchange with the surrounding environment. Recent ecological and technological advances enable successful establishment and maintenance of CES, making them a suitable tool for detecting and measuring subtle feedbacks and mechanisms. 2. As a part of an analogue (physical) C cycle modelling experiment, we developed a non-intrusive methodology to control the internal environment and to monitor atmospheric CO2 concentration inside 16 replicated CES. Whilst maintaining an air-tight seal of all CES, this approach allowed for access to the CO2 measuring equipment for periodic re-calibration and repairs. 3. To ensure reliable cross-comparison of CO2 observations between individual CES units and to minimise the cost of the system, only one CO2 sampling unit was used. An ADC BioScientific OP-2 (open-path) analyser mounted on a swinging arm was passing over a set of 16 measuring cells. Each cell was connected to an individual CES with air continuously circulating between them. 4. Using this setup, we were able to continuously measure several environmental variables and CO2 concentration within each closed system, allowing us to study minute effects of changing temperature on C fluxes within each CES. The CES and the measuring cells showed minimal air leakage during an experimental run lasting, on average, 3 months. The CO2 analyser assembly performed reliably for over 2 years, however an early iteration of the present design proved to be sensitive to positioning errors. 5. We indicate how the methodology can be further improved and suggest possible avenues where future CES based research could be applied.

An LMS style variable tap-length algorithm for structure adaptation

Searching for the optimum tap-length that best balances the complexity and steady-state performance of an adaptive filter has attracted attention recently. Among existing algorithms that can be found in the literature, two of which, namely the segmented filter (SF) and gradient descent (GD) algorithms, are of particular interest as they can search for the optimum tap-length quickly. In this paper, at first, we carefully compare the SF and GD algorithms and show that the two algorithms are equivalent in performance under some constraints, but each has advantages/disadvantages relative to the other. Then, we propose an improved variable tap-length algorithm using the concept of the pseudo fractional tap-length (FT). Updating the tap-length with instantaneous errors in a style similar to that used in the stochastic gradient [or least mean squares (LMS)] algorithm, the proposed FT algorithm not only retains the advantages from both the SF and the GD algorithms but also has significantly less complexity than existing algorithms. Both performance analysis and numerical simulations are given to verify the new proposed algorithm.

Large-scale length and time scales for use with stochastic convective parameterization

Many numerical models for weather prediction and climate studies are run at resolutions that are too coarse to resolve convection explicitly, but too fine to justify the local equilibrium assumed by conventional convective parameterizations. The Plant-Craig (PC) stochastic convective parameterization scheme, developed in this paper, solves this problem by removing the assumption that a given grid-scale situation must always produce the same sub-grid-scale convective response. Instead, for each timestep and gridpoint, one of the many possible convective responses consistent with the large-scale situation is randomly selected. The scheme requires as input the large-scale state as opposed to the instantaneous grid-scale state, but must nonetheless be able to account for genuine variations in the largescale situation. Here we investigate the behaviour of the PC scheme in three-dimensional simulations of radiative-convective equilibrium, demonstrating in particular that the necessary space-time averaging required to produce a good representation of the input large-scale state is not in conflict with the requirement to capture large-scale variations. The resulting equilibrium profiles agree well with those obtained from established deterministic schemes, and with corresponding cloud-resolving model simulations. Unlike the conventional schemes the statistics for mass flux and rainfall variability from the PC scheme also agree well with relevant theory and vary appropriately with spatial scale. The scheme is further shown to adapt automatically to changes in grid length and in forcing strength.

Forest soil carbon cycle under elevated CO2 – a case of increased throughput?

Forest soils account for a large part of the stable carbon pool held in terrestrial ecosystems. Future levels of atmospheric CO2 are likely to increase C input into the soils through increased above- and below-ground production of forests. This increased input will result in greater sequestration of C only if the additional C enters stable pools. In this review, we compare current observations from four large-scale Free Air FACE Enrichment (FACE) experiments on forest ecosystems (EuroFACE, Aspen-FACE, Duke FACE and ORNL-FACE) and consider their predictive power for long-term C sequestration. At all sites, FACE increased fine root biomass, and in most cases higher fine root turnover resulted in higher C input into soil via root necromass. However, at all sites, soil CO2 efflux also increased in excess of the increased root necromass inputs. A mass balance calculation suggests that a large part of the stimulation of soil CO2 efflux may be due to increased root respiration. Given the duration of these experiments compared with the life cycle of a forest and the complexity of processes involved, it is not yet possible to predict whether elevated CO2 will result in increased C storage in forest soil.

Modelling of the natural chlorine cycling in a coniferous stand: implications for chlorine-36 behaviour in a contaminated forest environment

Considered as one of the most available radionuclide in soileplant system, 36Cl is of potential concern for long-term management of radioactive wastes, due to its high mobility and its long half-life. To evaluate the risk of dispersion and accumulation of 36Cl in the biosphere as a consequence of a potential contamination, there is a need for an appropriate understanding of the chlorine cycling dynamics in the ecosystems. To date, a small number of studies have investigated the chlorine transfer in the ecosystem including the transformation of chloride to organic chlorine but, to our knowledge, none have modelled this cycle. In this study, a model involving inorganic as well as organic pools in soils has been developed and parameterised to describe the biogeochemical fate of chlorine in a pine forest. The model has been evaluated for stable chlorine by performing a range of sensitivity analyses and by comparing the simulated to the observed values. Finally a range of contamination scenarios, which differ in terms of external supply, exposure time and source, has been simulated to estimate the possible accumulation of 36Cl within the different compartments of the coniferous stand. The sensitivity study supports the relevancy of the model and its compartments, and has highlighted the chlorine transfers affecting the most the residence time of chlorine in the stand. Compared to observations, the model simulates realistic values for the chlorine content within the different forest compartments. For both atmospheric and underground contamination scenarios most of the chlorine can be found in its organic form in the soil. However, in case of an underground source, about two times less chlorine accumulates in the system and proportionally more chlorine leaves the system through drainage than through volatilisation.

The last glacial cycle: transient simulations with an AOGCM

A number of transient climate runs simulating the last 120kyr have been carried out using FAMOUS, a fast atmosphere-ocean general circulation model (AOGCM). This is the first time such experiments have been done with a full AOGCM, providing a three-dimensional simulation of both atmosphere and ocean over this period. Our simulation thus includes internally generated temporal variability over periods from days to millennia, and physical, detailed representations of important processes such as clouds and precipitation. Although the model is fast, computational restrictions mean that the rate of change of the forcings has been increased by a factor of 10, making each experiment 12kyr long. Atmospheric greenhouse gases (GHGs), northern hemisphere ice sheets and variations in solar radiation arising from changes in the Earth's orbit are treated as forcing factors, and are applied either separately or combined in different experiments. The long-term temperature changes on Antarctica match well with reconstructions derived from ice-core data, as does variability on timescales longer than 10 kyr. Last Glacial Maximum (LGM) cooling on Greenland is reasonably well simulated, although our simulations, which lack ice-sheet meltwater forcing, do not reproduce the abrupt, millennial scale climate shifts seen in northern hemisphere climate proxies or their slower southern hemisphere counterparts. The spatial pattern of sea surface cooling at the LGM matches proxy reconstructions reasonably well. There is significant anti-correlated variability in the strengths of the Atlantic Meridional Overturning Circulation (AMOC) and the Antarctic Circumpolar Current (ACC) on timescales greater than 10kyr in our experiments. We find that GHG forcing weakens the AMOC and strengthens the ACC, whilst the presence of northern hemisphere ice-sheets strengthens the AMOC and weakens the ACC. The structure of the AMOC at the LGM is found to be sensitive to the details of the ice-sheet reconstruction used. The precessional component of the orbital forcing induces ~20kyr oscillations in the AMOC and ACC, whose amplitude is mediated by changes in the eccentricity of the Earth's orbit. These forcing influences combine, to first order, in a linear fashion to produce the mean climate and ocean variability seen in the run with all forcings.

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.

Bistable systems with stochastic noise: virtues and limits of effective one-dimensional Langevin equations

The understanding of the statistical properties and of the dynamics of multistable systems is gaining more and more importance in a vast variety of scientific fields. This is especially relevant for the investigation of the tipping points of complex systems. Sometimes, in order to understand the time series of given observables exhibiting bimodal distributions, simple one-dimensional Langevin models are fitted to reproduce the observed statistical properties, and used to investing-ate the projected dynamics of the observable. This is of great relevance for studying potential catastrophic changes in the properties of the underlying system or resonant behaviours like those related to stochastic resonance-like mechanisms. In this paper, we propose a framework for encasing this kind of studies, using simple box models of the oceanic circulation and choosing as observable the strength of the thermohaline circulation. We study the statistical properties of the transitions between the two modes of operation of the thermohaline circulation under symmetric boundary forcings and test their agreement with simplified one-dimensional phenomenological theories. We extend our analysis to include stochastic resonance-like amplification processes. We conclude that fitted one-dimensional Langevin models, when closely scrutinised, may result to be more ad-hoc than they seem, lacking robustness and/or well-posedness. They should be treated with care, more as an empiric descriptive tool than as methodology with predictive power.

An investigation of QBO signals in the east Asian and Indian monsoon in GCM experiments

Observations have shown that the monsoon is a highly variable phenomenon of the tropical troposphere, which exhibits significant variance in the temporal range of two to three years. The reason for this specific interannual variability has not yet been identified unequivocally. Observational analyses have also shown that EI Niño indices or western Pacific SSTs exhibit some power in the two to three year period range and therefore it was suggested that an ocean-atmosphere interaction could excite and support such a cycle. Similar mechanisms include land-surface-atmosphere interaction as a possible driving mechanism. A rather different explanation could be provided by a forcing mechanism based on the quasi-biennial oscillation of the zonal wind in the lower equatorial stratosphere (QBO). The QBO is a phenomenon driven by equatorial waves with periods of some days which are excited in the troposphere. Provided that the monsoon circulation reacts to the modulation of tropopause conditions as forced by the QBO, this could explain monsoon variability in the quasi-biennial window. The possibility of a QBO-driven monsoon variability is investigated in this study in a number of general circulation model experiments where the QBO is assimilated to externally controlled phase states. These experiments show that the boreal summer monsoon is significantly influenced by the QBO. A QBO westerly phase implies less precipitation in the western Pacific, but more in India, in agreement with observations. The austral summer monsoon is exposed to similar but weaker mechanisms and the precipitation does not change significantly.

Global biomass burning: a synthesis and review of Holocene paleofire records and their controls.

We synthesize existing sedimentary charcoal records to reconstruct Holocene fire history at regional, continental and global scales. The reconstructions are compared with the two potential controls of burning at these broad scales – changes in climate and human activities – to assess their relative importance on trends in biomass burning. Here we consider several hypotheses that have been advanced to explain the Holocene record of fire, including climate, human activities and synergies between the two. Our results suggest that 1) episodes of high fire activity were relatively common in the early Holocene and were consistent with climate changes despite low global temperatures and low levels of biomass burning globally; 2) there is little evidence from the paleofire record to support the Early Anthropocene Hypothesis of human modification of the global carbon cycle; 3) there was a nearly-global increase in fire activity from 3 to 2 ka that is difficult to explain with either climate or humans, but the widespread and synchronous nature of the increase suggests at least a partial climate forcing; and 4) burning during the past century generally decreased but was spatially variable; it declined sharply in many areas, but there were also large increases (e.g., Australia and parts of Europe). Our analysis does not exclude an important role for human activities on global biomass burning during the Holocene, but instead provides evidence for a pervasive influence of climate across multiple spatial and temporal scales.

Generation of nonvernal-obligate, faster-cycling Noccaea caerulescens lines through fast neutron mutagenesis

Noccaea caerulescens (formerly Thlaspi caerulescens) is a widely studied metal hyperaccumulator. However, molecular genetic studies are challenging in this species because of its vernal-obligate biennial life cycle of 7-9 months. Here, we describe the development of genetically stable, faster cycling lines of N. caerulescens which are nonvernal-obligate. A total of 5500 M(0) seeds from Saint Laurent Le Minier (France) were subjected to fast neutron mutagenesis. Following vernalization of young plants, 79 of plants survived to maturity. In all, 80 000 M(2) lines were screened for flowering in the absence of vernalization. Floral initials were observed in 35 lines, with nine flowering in < 12 wk. Two lines (A2 and A7) were selfed to the M(4) generation. Floral initials were observed 66 and 87 d after sowing (DAS) in A2 and A7, respectively. Silicle development occurred for all A2 and for most A7 at 92 and 123 DAS, respectively. Floral or silicle development was not observed in wild-type (WT) plants. Leaf zinc (Zn) concentration was similar in WT, A2 and A7 lines. These lines should facilitate future genetic studies of this remarkable species. Seed is publicly available through the European Arabidopsis Stock Centre (NASC).

Impact of oceanic processes on the carbon cycle during the last termination

During the last termination (from ~18 000 years ago to ~9000 years ago), the climate significantly warmed and the ice sheets melted. Simultaneously, atmospheric CO2 increased from ~190 ppm to ~260 ppm. Although this CO2 rise plays an important role in the deglacial warming, the reasons for its evolution are difficult to explain. Only box models have been used to run transient simulations of this carbon cycle transition, but by forcing the model with data constrained scenarios of the evolution of temperature, sea level, sea ice, NADW formation, Southern Ocean vertical mixing and biological carbon pump. More complex models (including GCMs) have investigated some of these mechanisms but they have only been used to try and explain LGM versus present day steady-state climates. In this study we use a coupled climate-carbon model of intermediate complexity to explore the role of three oceanic processes in transient simulations: the sinking of brines, stratification-dependent diffusion and iron fertilization. Carbonate compensation is accounted for in these simulations. We show that neither iron fertilization nor the sinking of brines alone can account for the evolution of CO2, and that only the combination of the sinking of brines and interactive diffusion can simultaneously simulate the increase in deep Southern Ocean δ13C. The scenario that agrees best with the data takes into account all mechanisms and favours a rapid cessation of the sinking of brines around 18 000 years ago, when the Antarctic ice sheet extent was at its maximum. In this scenario, we make the hypothesis that sea ice formation was then shifted to the open ocean where the salty water is quickly mixed with fresher water, which prevents deep sinking of salty water and therefore breaks down the deep stratification and releases carbon from the abyss. Based on this scenario, it is possible to simulate both the amplitude and timing of the long-term CO2 increase during the last termination in agreement with ice core data. The atmospheric δ13C appears to be highly sensitive to changes in the terrestrial biosphere, underlining the need to better constrain the vegetation evolution during the termination.

Further evidence for variable synchrotron emission in XTE J1118+480 in outburst

We present simultaneous multicolor infrared and optical photometry of the black hole X-ray transient XTE J1118+480 during its short 2005 January outburst, supported by simultaneous X-ray observations. The variability is dominated by short timescales, ~10 s, although a weak superhump also appears to be present in the optical. The optical rapid variations, at least, are well correlated with those in X-rays. Infrared JHKs photometry, as in the previous outburst, exhibits especially large-amplitude variability. The spectral energy distribution (SED) of the variable infrared component can be fitted with a power law of slope α=-0.78+/-0.07, where F_ν~ν^α. There is no compelling evidence for evolution in the slope over five nights, during which time the source brightness decayed along almost the same track as seen in variations within the nights. We conclude that both short-term variability and longer timescale fading are dominated by a single component of constant spectral shape. We cannot fit the SED of the IR variability with a credible thermal component, either optically thick or thin. This IR SED is, however, approximately consistent with optically thin synchrotron emission from a jet. These observations therefore provide indirect evidence to support jet-dominated models for XTE J1118+480 and also provide a direct measurement of the slope of the optically thin emission, which is impossible, based on the average spectral energy distribution alone.

Upland streamwater nitrate dynamics across decadal to sub-daily timescales: a case study of Plynlimon, Wales

Streamwater nitrate dynamics in the River Hafren, Plynlimon, mid-Wales were investigated over decadal to sub-daily timescales using a range of statistical techniques. Long-term data were derived from weekly grab samples (1984–2010) and high-frequency data from 7-hourly samples (2007–2009) both measured at two sites: a headwater stream draining moorland and a downstream site below plantation forest. This study is one of the first to analyse upland streamwater nitrate dynamics across such a wide range of timescales and report on the principal mechanisms identified. The data analysis provided no clear evidence that the long-term decline in streamwater nitrate concentrations was related to a decline in atmospheric deposition alone, because nitrogen deposition first increased and then decreased during the study period. Increased streamwater temperature and denitrification may also have contributed to the decline in stream nitrate concentrations, the former through increased N uptake rates and the latter resultant from increased dissolved organic carbon concentrations. Strong seasonal cycles, with concentration minimums in the summer, were driven by seasonal flow minimums and seasonal biological activity enhancing nitrate uptake. Complex diurnal dynamics were observed, with seasonal changes in phase and amplitude of the cycling, and the diurnal dynamics were variable along the river. At the moorland site, a regular daily cycle, with minimum concentrations in the early afternoon, corresponding with peak air temperatures, indicated the importance of instream biological processing. At the downstream site, the diurnal dynamics were a composite signal, resultant from advection, dispersion and nitrate processing in the soils of the lower catchment. The diurnal streamwater nitrate dynamics were also affected by drought conditions. Enhanced diurnal cycling in Spring 2007 was attributed to increased nitrate availability in the post-drought period as well as low flow rates and high temperatures over this period. The combination of high-frequency short-term measurements and long-term monitoring provides a powerful tool for increasing understanding of the controls of element fluxes and concentrations in surface waters.