The absolutely continuous spectrum of one-dimensional Schr"odinger operators

This paper deals with general structural properties of one-dimensional Schr"odinger operators with some absolutely continuous spectrum. The basic result says that the omega limit points of the potential under the shift map are reflectionless on the support of the absolutely continuous part of the spectral measure. This implies an Oracle Theorem for such potentials and Denisov-Rakhmanov type theorems. In the discrete case, for Jacobi operators, these issues were discussed in my recent paper [19]. The treatment of the continuous case in the present paper depends on the same basic ideas.Comment: references added; a few very minor change

Comparison of the HadGEM2 climate-chemistry model against in situ and SCIAMACHY atmospheric methane data

Wetlands are a major emission source of methane (CH4) globally. In this study, we evaluate wetland emission estimates derived using the UK community land surface model (JULES, the Joint UK Land Earth Simulator) against atmospheric observations of methane, including, for the first time, total methane columns derived from the SCIAMACHY instrument on board the ENVISAT satellite. Two JULES wetland emission estimates are investigated: (a) from an offline run driven with Climatic Research Unit–National Centers for Environmental Prediction (CRU-NCEP) meteorological data and (b) from the same offline run in which the modelled wetland fractions are replaced with those derived from the Global Inundation Extent from Multi-Satellites (GIEMS) remote sensing product. The mean annual emission assumed for each inventory (181 Tg CH4 per annum over the period 1999–2007) is in line with other recently published estimates. There are regional differences as the unconstrained JULES inventory gives significantly higher emissions in the Amazon (by ~36 Tg CH4 yr−1) and lower emissions in other regions (by up to 10 Tg CH4 yr−1) compared to the JULES estimates constrained with the GIEMS product. Using the UK Hadley Centre's Earth System model with atmospheric chemistry (HadGEM2), we evaluate these JULES wetland emissions against atmospheric observations of methane. We obtain improved agreement with the surface concentration measurements, especially at high northern latitudes, compared to previous HadGEM2 runs using the wetland emission data set of Fung et al. (1991). Although the modelled monthly atmospheric methane columns reproduce the large-scale patterns in the SCIAMACHY observations, they are biased low by 50 part per billion by volume (ppb). Replacing the HadGEM2 modelled concentrations above 300 hPa with HALOE–ACE assimilated TOMCAT output results in a significantly better agreement with the SCIAMACHY observations. The use of the GIEMS product to constrain the JULES-derived wetland fraction improves the representation of the wetland emissions in JULES and gives a good description of the seasonality observed at surface sites influenced by wetlands, especially at high latitudes. We find that the annual cycles observed in the SCIAMACHY measurements and at many of the surface sites influenced by non-wetland sources cannot be reproduced in these HadGEM2 runs. This suggests that the emissions over certain regions (e.g. India and China) are possibly too high and/or the monthly emission patterns for specific sectors are incorrect. The comparisons presented in this paper show that the performance of the JULES wetland scheme is comparable to that of other process-based land surface models. We identify areas for improvement in this and the atmospheric chemistry components of the HadGEM Earth System model. The Earth Observation data sets used here will be of continued value in future evaluations of JULES and the HadGEM family of models

NGO Legitimacy: Four Models

The aim of this paper is to examine NGOs’ legitimacy in the context of global politics. In order to yield a better understanding of NGOs’ legitimacy at the international level it is important to examine how their legitimacy claims are evaluated. This paper proposes dividing the literature into four models based on the theoretical and analytical approaches to their legitimacy claims: the market model, social change model, new institutionalism model and the critical model. The legitimacy criteria generated by the models are significantly different in their analytical scope of how one is to assess the role of NGOs operating as political actors contributing to democracy. The paper argues that the models present incomplete, and sometimes conflicting, views of NGOs’ legitimacy and that this poses a legitimacy dilemma for those assessing the political agency of NGOs in world politics. The paper concludes that only by approaching their legitimacy holistically can the democratic role of NGOs be explored and analysed in the context of world politics

An integral method for solving nonlinear eigenvalue problems

We propose a numerical method for computing all eigenvalues (and the corresponding eigenvectors) of a nonlinear holomorphic eigenvalue problem that lie within a given contour in the complex plane. The method uses complex integrals of the resolvent operator, applied to at least $k$ column vectors, where $k$ is the number of eigenvalues inside the contour. The theorem of Keldysh is employed to show that the original nonlinear eigenvalue problem reduces to a linear eigenvalue problem of dimension $k$. No initial approximations of eigenvalues and eigenvectors are needed. The method is particularly suitable for moderately large eigenvalue problems where $k$ is much smaller than the matrix dimension. We also give an extension of the method to the case where $k$ is larger than the matrix dimension. The quadrature errors caused by the trapezoid sum are discussed for the case of analytic closed contours. Using well known techniques it is shown that the error decays exponentially with an exponent given by the product of the number of quadrature points and the minimal distance of the eigenvalues to the contour

Decomposing uncertainties in the future terrestrial carbon budget associated with emission scenarios, climate projections, and ecosystem simulations using the ISI-MIP results

We examined the changes to global net primary production (NPP), vegetation biomass carbon (VegC), and soil organic carbon (SOC) estimated by six global vegetation models (GVMs) obtained from the Inter-Sectoral Impact Model Intercomparison Project. Simulation results were obtained using five global climate models (GCMs) forced with four representative concentration pathway (RCP) scenarios. To clarify which component (i.e., emission scenarios, climate projections, or global vegetation models) contributes the most to uncertainties in projected global terrestrial C cycling by 2100, analysis of variance (ANOVA) and wavelet clustering were applied to 70 projected simulation sets. At the end of the simulation period, changes from the year 2000 in all three variables varied considerably from net negative to positive values. ANOVA revealed that the main sources of uncertainty are different among variables and depend on the projection period. We determined that in the global VegC and SOC projections, GVMs are the main influence on uncertainties (60 % and 90 %, respectively) rather than climate-driving scenarios (RCPs and GCMs). Moreover, the divergence of changes in vegetation carbon residence times is dominated by GVM uncertainty, particularly in the latter half of the 21st century. In addition, we found that the contribution of each uncertainty source is spatiotemporally heterogeneous and it differs among the GVM variables. The dominant uncertainty source for changes in NPP and VegC varies along the climatic gradient. The contribution of GVM to the uncertainty decreases as the climate division becomes cooler (from ca. 80 % in the equatorial division to 40 % in the snow division). Our results suggest that to assess climate change impacts on global ecosystem C cycling among each RCP scenario, the long-term C dynamics within the ecosystems (i.e., vegetation turnover and soil decomposition) are more critical factors than photosynthetic processes. The different trends in the contribution of uncertainty sources in each variable among climate divisions indicate that improvement of GVMs based on climate division or biome type will be effective. On the other hand, in dry regions, GCMs are the dominant uncertainty source in climate impact assessments of vegetation and soil C dynamics

Global multimodel analysis of drought in runoff for the second half of the twentieth century

During the past decades large-scale models have been developed to simulate global and continental terrestrial water cycles. It is an open question whether these models are suitable to capture hydrological drought, in terms of runoff, on global scale. A multi-model ensemble analysis was carried out to evaluate if ten of such large-scale models agree on major drought events during the second half of the 20th century. Time series of monthly precipitation, monthly total runoff from ten global hydrological models, and their ensemble median have been used to identify drought. Temporal development of area in drought for various regions across the globe was investigated. Model spread was largest in regions with low runoff and smallest in regions with high runoff. In vast regions, correlation between runoff drought derived from the models and meteorological drought was found to be low. This indicated that models add information to the signal derived from precipitation and that runoff drought cannot directly be determined from precipitation data alone in global drought analyses with a constant aggregation period. However, duration and spatial extent of major drought events differed between models. Some models showed a fast runoff response to rainfall, which led to deviations from reported drought events in slowly responding hydrological systems. By using an ensemble of models, this fast runoff response was partly overcome and delay in drought propagating from meteorological drought to drought in runoff was included. Finally, an ensemble of models also allows to consider uncertainty associated with individual model structures

Quantifying uncertainties in soil carbon responses to changes in global mean temperature and precipitation

Soil organic carbon (SOC) is the largest carbon pool in terrestrial ecosystems and may play a key role in biospheric feedbacks with elevated atmospheric carbon dioxide (CO2) in a warmer future world. We examined the simulation results of seven terrestrial biome models when forced with climate projections from four representative-concentration-pathways (RCPs)-based atmospheric concentration scenarios. The goal was to specify calculated uncertainty in global SOC stock projections from global and regional perspectives and give insight to the improvement of SOC-relevant processes in biome models. SOC stocks among the biome models varied from 1090 to 2650 Pg C even in historical periods (ca. 2000). In a higher forcing scenario (i.e., RCP8.5), inconsistent estimates of impact on the total SOC (2099–2000) were obtained from different biome model simulations, ranging from a net sink of 347 Pg C to a net source of 122 Pg C. In all models, the increasing atmospheric CO2 concentration in the RCP8.5 scenario considerably contributed to carbon accumulation in SOC. However, magnitudes varied from 93 to 264 Pg C by the end of the 21st century across biome models. Using the time-series data of total global SOC simulated by each biome model, we analyzed the sensitivity of the global SOC stock to global mean temperature and global precipitation anomalies (ΔT and ΔP respectively) in each biome model using a state-space model. This analysis suggests that ΔT explained global SOC stock changes in most models with a resolution of 1–2 °C, and the magnitude of global SOC decomposition from a 2 °C rise ranged from almost 0 to 3.53 Pg C yr−1 among the biome models. However, ΔP had a negligible impact on change in the global SOC changes. Spatial heterogeneity was evident and inconsistent among the biome models, especially in boreal to arctic regions. Our study reveals considerable climate uncertainty in SOC decomposition responses to climate and CO2 change among biome models. Further research is required to improve our ability to estimate biospheric feedbacks through both SOC-relevant and vegetation-relevant processes

Modelling the probability of microhabitat formation on trees using cross-sectional data

The rate of TreM formation per unit diameter growth was modelled as a function of tree diameter at breast height (DBH), and the model was calibrated considering cross-sectional observations TreMs on trees of different sizes. The model predicted realistic TreM formation rates at the tree and stand levels in forests dominated by Abies alba and Fagus sylvatica. This approach opens new perspectives to the analysis of forest biodiversity conservation strategies