Existence and stability of hole solutions to complex Ginzburg-Landau equations

We consider the existence and stability of the hole, or dark soliton, solution to a Ginzburg-Landau perturbation of the defocusing nonlinear Schroedinger equation (NLS), and to the nearly real complex Ginzburg-Landau equation (CGL). By using dynamical systems techniques, it is shown that the dark soliton can persist as either a regular perturbation or a singular perturbation of that which exists for the NLS. When considering the stability of the soliton, a major difficulty which must be overcome is that eigenvalues may bifurcate out of the continuous spectrum, i.e., an edge bifurcation may occur. Since the continuous spectrum for the NLS covers the imaginary axis, and since for the CGL it touches the origin, such a bifurcation may lead to an unstable wave. An additional important consideration is that an edge bifurcation can happen even if there are no eigenvalues embedded in the continuous spectrum. Building on and refining ideas first presented in Kapitula and Sandstede (Physica D, 1998) and Kapitula (SIAM J. Math. Anal., 1999), we show that when the wave persists as a regular perturbation, at most three eigenvalues will bifurcate out of the continuous spectrum. Furthermore, we precisely track these bifurcating eigenvalues, and thus are able to give conditions for which the perturbed wave will be stable. For the NLS the results are an improvement and refinement of previous work, while the results for the CGL are new. The techniques presented are very general and are therefore applicable to a much larger class of problems than those considered here.Comment: 41 pages, 4 figures, submitte

Modelling land-use futures in the context of climate change mitigation: The role of land use in global climate change mitigation and its connection to the water-land-energy-food-climate nexus

The land area of the Earth greatly influences climate dynamics through biogeophysical and biogeochemical processes. These processes concern, respectively, the exchange of energy and water, and the exchange of greenhouse gasses (GHGs) such as CO2, CH4 and N2O, between land systems and the atmosphere. By using the Earth’s land surface, humans have greatly altered it – leading to significant environmental impacts. Historically, climate change has mostly been caused by fossil fuel combustion. Land use, land-use change and forestry (LULUCF) have caused an estimated 34% of cumulative anthropogenic CO¬2 emissions since 1750. At the same time, agriculture is responsible for about 13% of global GHG emissions in the form of non-CO2 GHG emissions. The importance of land and land use in climate dynamics means that land has a role in preventing dangerous climate change. First, it is essential to significantly reduce the 23% of annual GHG emissions from the agriculture, forestry and other land use (AFOLU) sector to make ambitious climate targets feasible. Second, land is key to various techniques to remove carbon from the atmosphere (so-called negative emissions or carbon dioxide removal (CDR)). In this thesis, a large portfolio of land-based mitigation measures is assessed in the context of different land-use futures. In addition, detailed analysis are provided on two key land-based mitigation measures: afforestation, and peatland protection and restoration. In addition to climate, land is central to many other sustainable development issues and environmental challenges. For example, it is essential for the provision of resources such as food, energy and water, as well as to sustain terrestrial biodiversity, as also recognized in the Sustainable Development Goals and the planetary boundaries. A useful approach to study different dimensions of sustainable development and environmental change is the nexus concept which recognizes that components of a system are inherently interconnected and must be investigated and managed in an integrated, holistic manner. In this thesis, the water-land-energy-food-climate (WLEFC) nexus is addressed, taking into account trade-offs and synergies between these different systems in achieving multiple goals. Scenario analysis can be used to explore the role of land use in climate change and climate change mitigation, and for other societal goals related to the WLEFC nexus. An important ambition of the scientific community is to develop scenarios that achieve both climate and other environmental and sustainability goals such as the PBs and the SDGs. In this thesis, we use exploratory scenarios that investigate how the future might develop under pre-defined assumptions, as well as normative scenarios that aim for pre-defined targets and describe pathways that could achieve these goals. Examples of targets are stabilizing global warming, nature protection or limits to water extraction. These scenarios are developed using the IMAGE integrated assessment model framework

Challenges of Global Agriculture in a Climate Change Context by 2050 (AgCLIM50)

This report presents a global integrated assessment of the range of potential economic impacts of climate change and stringent mitigation measures in the agricultural sector. The analysis employs five global multi-region multi-commodity models and covers selected combinations of socioeconomic storylines and climate signals by mid-century. Model inputs are harmonised by using the same projections for population and GDP growth, as well as relative biophysical crop yield changes due to climate change. Model results can differ depending on model characteristics and the specific quantitative implementations of the socioeconomic storylines.JRC.D.4-Economics of Agricultur

Anthropogenic land use estimates for the Holocene – HYDE 3.2

Abstract. This paper presents an update and extension of HYDE, the History Database of the Global Environment (HYDE version 3.2). HYDE is an internally consistent combination of historical population estimates and allocation algorithms with time-dependent weighting maps for land use. Categories include cropland, with new distinctions for irrigated and rain-fed crops (other than rice) and irrigated and rain-fed rice. Grazing lands are also provided, divided into more intensively used pasture and less intensively used rangeland, and further specified with respect to conversion of natural vegetation to facilitate global change modellers. Population is represented by maps of total, urban, rural population, population density and built-up area. The period covered is 10 000 before Common Era (BCE) to 2015 Common Era (CE). All data can be downloaded from https://doi.org/10.17026/dans-25g-gez3. We estimate that global population increased from 4.4 million people (we also estimate a lower range  &lt;  0.01 and an upper range of 8.9 million) in 10 000 BCE to 7.257 billion in 2015 CE, resulting in a global population density increase from 0.03 persons (or capita, in short cap) km−2 (range 0–0.07) to almost 56 cap km−2 respectively. The urban built-up area evolved from almost zero to roughly 58 Mha in 2015 CE, still only less than 0.5 % of the total land surface of the globe. Cropland occupied approximately less than 1 % of the global land area (13 037 Mha, excluding Antarctica) for a long time period until 1 CE, quite similar to the grazing land area. In the following centuries the share of global cropland slowly grew to 2.2 % in 1700 CE (ca. 293 Mha, uncertainty range 220–367 Mha), 4.4 % in 1850 CE (578 Mha, range 522–637 Mha) and 12.2 % in 2015 CE (ca. 1591 Mha, range 1572–1604 Mha). Cropland can be further divided into rain-fed and irrigated land, and these categories can be further separated into rice and non-rice. Rain-fed croplands were much more common, with 2.2 % in 1700 CE (289 Mha, range 217–361 Mha), 4.2 % (549 Mha, range 496–606 Mha) in 1850 CE and 10.1 % (1316 Mha, range 1298–1325 Mha) in 2015 CE, while irrigated croplands used less than 0.05 % (4.3 Mha, range 3.1–5.5 Mha), 0.2 % (28 Mha, range 25–31 Mha) and 2.1 % (277 Mha, range 273–278 Mha) in 1700, 1850 and 2015 CE, respectively. We estimate the irrigated rice area (paddy) to be 0.1 % (13 Mha, range 9–16 Mha) in 1700 CE, 0.2 % (28 Mha, range 26–31 Mha) in 1850 CE and 0.9 % (118 Mha, range 117–120 Mha) in 2015 CE. The estimates for land used for grazing are much more uncertain. We estimate that the share of grazing land grew from 5.1 % in 1700 CE (667 Mha, range 507–820 Mha) to 9.6 % in 1850 CE (1192 Mha, range 1068–1304 Mha) and 24.9 % in 2015 CE (3241 Mha, range 3211–3270 Mha). To aid the modelling community we have divided land used for grazing into more intensively used pasture, less intensively used converted rangeland and less or unmanaged natural unconverted rangeland. Pasture occupied 1.1 % in 1700 CE (145 Mha, range 79–175 Mha), 1.9 % in 1850 CE (253 Mha, range 218–287 Mha) and 6.0 % (787 Mha, range 779–795 Mha) in 2015 CE, while rangelands usually occupied more space due to their occurrence in more arid regions and thus lower yields to sustain livestock. We estimate converted rangeland at 0.6 % in 1700 CE (82 Mha range 66–93 Mha), 1 % in 1850 CE (129 Mha range 118–136 Mha) and 2.4 % in 2015 CE (310 Mha range 306–312 Mha), while the unconverted natural rangelands occupied approximately 3.4 % in 1700 CE (437 Mha, range 334–533 Mha), 6.2 % in 1850 CE (810 Mha, range 733–881 Mha) and 16.5 % in 2015 CE (2145 Mha, range 2126–2164 Mha). </jats:p

Comparing the impact of future cropland expansion on global biodiversity and carbon storage across models and scenarios

Land-use change is a direct driver of biodiversity and carbon storage loss. Projections of future land use often include notable expansion of cropland areas in response to changes in climate and food demand, although there are large uncertainties in results between models and scenarios. This study examines these uncertainties by comparing three different socioeconomic scenarios (SSP1-3) across three models (IMAGE, GLOBIOM and PLUMv2). It assesses the impacts on biodiversity metrics and direct carbon loss from biomass and soil as a direct consequence of cropland expansion. Results show substantial variation between models and scenarios, with little overlap across all nine projections. Although SSP1 projects the least impact, there are still significant impacts projected. IMAGE and GLOBIOM project the greatest impact across carbon storage and biodiversity metrics due to both extent and location of cropland expansion. Furthermore, for all the biodiversity and carbon metrics used, there is a greater proportion of variance explained by the model used. This demonstrates the importance of improving the accuracy of land-based models. Incorporating effects of land-use change in biodiversity impact assessments would also help better prioritize future protection of biodiverse and carbon-rich areas.</p

Global Transition Rules for Translating Land-use Change (LUH2) To Land-cover Change for CMIP6 using GLM2

Information on historical land-cover change is important for understanding human impacts on the environment. Over the last decade, global models have characterized historical land-use changes, but few have been able to relate these changes with corresponding changes in land-cover. Utilizing the latest global land-use change data, we make several assumptions about the relationship between land-use and land-cover change, and evaluate each scenario with remote sensing data to identify optimal fit. The resulting transition rule can guide the incorporation of land-cover information within earth system models

Greenhouse gas emission curves for advanced biofuel supply chains

Most climate change mitigation scenarios that are consistent with the 1.5–2 °C target rely on a large-scale contribution from biomass, including advanced (second-generation) biofuels. However, land-based biofuel production has been associated with substantial land-use change emissions. Previous studies show a wide range of emission factors, often hiding the influence of spatial heterogeneity. Here we introduce a spatially explicit method for assessing the supply of advanced biofuels at different emission factors and present the results as emission curves. Dedicated crops grown on grasslands, savannahs and abandoned agricultural lands could provide 30 EJBiofuel yr−1 with emission factors less than 40 kg of CO2-equivalent (CO2e) emissions per GJBiofuel (for an 85-year time horizon). This increases to 100 EJBiofuel yr−1 for emission factors less than 60 kgCO2e GJBiofuel −1. While these results are uncertain and depend on model assumptions (including time horizon, spatial resolution, technology assumptions and so on), emission curves improve our understanding of the relationship between biofuel supply and its potential contribution to climate change mitigation while accounting for spatial heterogeneity

From future diets to dishes: communicating dietary shift associated with a 1.5°C scenario for Brazil, China, Sweden and the United Kingdom

Introduction: With the pressing need to mitigate greenhouse gas emissions, this study aims to simplify complex data from Integrated Assessment Models (IAMs). It focuses on identifying dietary shifts that align with the 1.5°C global warming limit as stipulated by the Paris Agreement. Methods: The research utilises the IMAGE Integrated Assessment Model and applies the Diets, Dishes, Dish Ingredients (DDDI) communication framework. This methodology enables the visualisation of potential dietary and dish composition changes, thereby making the data more comprehensible to a broader audience. Results: The study effectively translates traditional IAM outputs into accessible visualisations. These visual tools provide a nuanced understanding of a low greenhouse gas diet, extending its relevance beyond academia to include professionals in diet and nutrition. Discussion: This research stands as a significant advancement in the field, lowering the barrier to understanding sustainable diets for the future. It enriches the existing dialogue on dietary change and climate goals and serves as a catalyst for further research and practical applications in diverse contexts

Quantifying synergies and trade-offs in the global water-land-food-climate nexus using a multi-model scenario approach

The human-earth system is confronted with the challenge of providing a range of resources for a growing and more prosperous world population while simultaneously reducing environmental degradation. The sustainable development goals and the planetary boundaries define targets to manage this challenge. Many of these are linked to the land system, such as biodiversity, water, food, nutrients and climate, and are strongly interconnected. A key question is how measures can be designed in the context of multi-dimensional sustainability targets to exploit synergies. To address this, a nexus approach is adopted that acknowledges the interconnectedness between the important sub-systems water, land, food, and climate. This study quantifies synergies and trade-offs from ambitious interventions in different components of this water-land-fod-climate nexus at the global scale. For this purpose, a set of six harmonized scenarios is simulated with the model of agricultural production and its impact on the environment and Integrated model to assess the global environment models. The multi-model approach improves robustness of the results while shedding light on variations coming from different modelling approaches. Our results show that measures in the food component towards healthy diets with low meat consumption have synergies with all other nexus dimensions: Increased natural land improving terrestrial biodiversity (+4% to +8%), lower greenhouse gas emissions from land (−45% to −58%), reduced irrigation water withdrawals to protect or restore hydrological environmental flows (−3% to −24%), and reductions in nitrogen surpluses (−23% to −35%). Climate mitigation measures in line with the Paris Agreement have trade-offs with the water and food components of the nexus, as they adversely affect irrigation water withdrawals (+5% to +30% in 2050 compared to reference scenario) and food prices (+1% to +20%). The analysis of a scenario combining all measures reveals how certain measures are in conflict while others reinforce each other. This study provides an example of a nexus approach to scenario analysis providing input to the next generation of pathways aiming to achieve multiple dimensions of sustainable development.SHAPEHorizon 2020 Framework Programmehttp://dx.doi.org/10.13039/100010661Deutsche Bundesstiftung Umwelthttp://dx.doi.org/10.13039/100007636Peer Reviewe