Bayesian Learning for a Class of Priors with Prescribed Marginals

We present Bayesian updating of an imprecise probability measure, represented by a class of precise multidimensional probability measures. Choice and analysis of our class are motivated by expert interviews that we conducted with modelers in the context of climatic change. From the interviews we deduce that generically, experts hold a much more informed opinion on the marginals of uncertain parameters rather than on their correlations. Accordingly, we specify the class by prescribing precise measures for the marginals while letting the correlation structure subject to complete ignorance. For sake of transparency, our discussion focuses on the tutorial example of a linear two-dimensional Gaussian model. We operationalize Bayesian learning for that class by various updating rules, starting with (a modified version of) the generalized Bayes' rule and the maximum likelihood update rule (after Gilboa and Schmeidler). Over a large range of potential observations, the generalized Bayes' rule would provide non-informative results. We restrict this counter-intuitive and unnecessary growth of uncertainty by two means, the discussion of which refers to any kind of imprecise model, not only to our class. First, we find our class of priors too inclusive and, hence, require certain additional properties of prior measures in terms of smoothness of probability density functions. Second, we argue that both updating rules are dissatisfying, the generalized Bayes' rule being too conservative, i.e., too inclusive, the maximum likelihood rule being too exclusive. Instead, we introduce two new ways of Bayesian updating of imprecise probabilities: a ``weighted maximum likelihood method'' and a ``semi-classical method.'' The former bases Bayesian updating on the whole set of priors, however, with weighted influence of its members. By referring to the whole set, the weighted maximum likelihood method allows for more robust inferences than the standard maximum likelihood method and, hence, is better to justify than the latter.Furthermore, the semi-classical method is more objective than the weighted maximum likelihood method as it does not require the subjective definition of a weighting function. Both new methods reveal much more informative results than the generalized Bayes' rule, what we demonstrate for the example of a stylized insurance model

Future growth patterns of world regions – A GDP scenario approach

Global GDP projections for the 21st century are needed for the exploration of long-term global environmental problems, in particular climate change. Greenhouse gas emissions as well as climate change mitigation and adaption capacities strongly depend on growth of per capita income. However, long-term economic projections are highly uncertain. This paper provides five new long-term economic scenarios as part of the newly developed shared socio-economic pathways (SSPs) which represent a set of widely diverging narratives. A method of GDP scenario building is presented that is based on assumptions about technological progress, and human and physical capital formation as major drivers of long-term GDP per capita growth. The impact of these drivers differs significantly between different shared socio-economic pathways and is traced back to the underlying narratives and the associated population and education scenarios. In a highly fragmented world, technological and knowledge spillovers are low. Hence, the growth impact of technological progress and human capital is comparatively low, and per capita income diverges between world regions. These factors play a much larger role in globalization scenarios, leading to higher economic growth and stronger convergence between world regions. At the global average, per capita GDP is projected to grow annually in a range between 1.0% (SSP3) and 2.8% (SSP5) from 2010 to 2100. While this covers a large portion of variety in future global economic growth projections, plausible lower and higher growth projections may still be conceivable. The GDP projections are put into the context of historic patterns of economic growth (stylized facts), and their sensitivity to key assumptions is explored

Potential and costs of carbon dioxide removal by enhanced weathering of rocks

The chemical weathering of rocks currently absorbs about 1.1 Gt CO2 a−1 being mainly stored as bicarbonate in the ocean. An enhancement of this slow natural process could remove substantial amounts of CO2 from the atmosphere, aiming to offset some unavoidable anthropogenic emissions in order to comply with the Paris Agreement, while at the same time it may decrease ocean acidification. We provide the first comprehensive assessment of economic costs, energy requirements, technical parameterization, and global and regional carbon removal potential. The crucial parameters defining this potential are the grain size and weathering rates. The main uncertainties about the potential relate to weathering rates and rock mass that can be integrated into the soil. The discussed results do not specifically address the enhancement of weathering through microbial processes, feedback of geogenic nutrient release, and bioturbation. We do not only assess dunite rock, predominantly bearing olivine (in the form of forsterite) as the mineral that has been previously proposed to be best suited for carbon removal, but focus also on basaltic rock to minimize potential negative side effects. Our results show that enhanced weathering is an option for carbon dioxide removal that could be competitive already at 60 US $t−1 CO2 removed for dunite, but only at 200 US$ t−1 CO2 removed for basalt. The potential carbon removal on cropland areas could be as large as 95 Gt CO2 a−1 for dunite and 4.9 Gt CO2 a−1 for basalt. The best suited locations are warm and humid areas, particularly in India, Brazil, South-East Asia and China, where almost 75% of the global potential can be realized. This work presents a techno-economic assessment framework, which also allows for the incorporation of further processes

Is atmospheric carbon dioxide removal a game changer for climate change mitigation?

The ability to directly remove carbon dioxide from the atmosphere allows the decoupling of emissions and emissions control in space and time. We ask the question whether this unique feature of carbon dioxide removal technologies fundamentally alters the dynamics of climate mitigation pathways. The analysis is performed in the coupled energy-economy-climate model ReMIND using the bioenergy with CCS route as an application of CDR technology. BECCS is arguably the least cost CDR option if biomass availability is not a strongly limiting factor. We compare mitigation pathways with and without BECCS to explore the impact of CDR technologies on the mitigation portfolio. Effects are most pronounced for stringent climate policies where BECCS is a key technology for the effectiveness of carbon pricing policies. The decoupling of emissions and emissions control allows prolonging the use of fossil fuels in sectors that are difficult to decarbonize, particularly in the transport sector. It also balances the distribution of mitigation costs across future generations. CDR is not a silver bullet technology. The largest part of emissions reductions continues to be provided by direct mitigation measures at the emissions source. The value of CDR lies in its flexibility to alleviate the most costly constraints on mitigating emissions

Carbon dioxide removal technologies are not born equal

Technologies for carbon dioxide removal (CDR) from the atmosphere have been recognized as an important part of limiting warming to well below 2 °C called for in the Paris Agreement. However, many scenarios so far rely on bioenergy in combination with carbon capture and storage as the only CDR technology. Various other options have been proposed, but have scarcely been taken up in an integrated assessment of mitigation pathways. In this study we analyze a comprehensive portfolio of CDR options in terms of their regional and temporal deployment patterns in climate change mitigation pathways and the resulting challenges. We show that any CDR option with sufficient potential can reduce the economic costs of achieving the 1.5 °C target substantially without increasing the temperature overshoot. CDR helps to reduce net CO2 emissions faster and achieve carbon neutrality earlier. The regional distribution of CDR deployment in cost-effective mitigation pathways depends on which options are available. If only enhanced weathering of rocks on croplands or re- and afforestation are available, Latin America and Asia cover nearly all of global CDR deployment. Besides fairness and sustainability concerns, such a regional concentration would require large international transfers and thus strong international institutions. In our study, the full portfolio scenario is the most balanced from a regional perspective. This indicates that different CDR options should be developed such that all regions can contribute according to their regional potentials

Between Scylla and Charybdis: Delayed mitigation narrows the passage between large-scale CDR and high costs

There are major concerns about the sustainability of large-scale deployment of carbon dioxide removal (CDR) technologies. It is therefore an urgent question to what extent CDR will be needed to implement the long term ambition of the Paris Agreement. Here we show that ambitious near term mitigation significantly decreases CDR requirements to keep the Paris climate targets within reach. Following the nationally determined contributions (NDCs) until 2030 makes 2 °C unachievable without CDR. Reducing 2030 emissions by 20% below NDC levels alleviates the trade-off between high transitional challenges and high CDR deployment. Nevertheless, transitional challenges increase significantly if CDR is constrained to less than 5 Gt CO2 a−1 in any year. At least 8 Gt CO2 a−1 CDR are necessary in the long term to achieve 1.5 °C and more than 15 Gt CO2 a−1 to keep transitional challenges in bounds

Mid- and long-term climate projections for fragmented and delayed-action scenarios

This paper explores the climate consequences of “delayed near-term action” and “staged accession” scenarios for limiting warming below 2 °C. The stabilization of greenhouse gas concentrations at low levels requires a large-scale transformation of the energy system. Depending on policy choices, there are alternative pathways to reach this objective. An “optimal” path, as emerging from energy-economic modeling, implies immediate action with stringent emission reductions, while the currently proposed international policies translate into reduction delays and higher near-term emissions. In our delayed action scenarios, low stabilization levels need thus to be reached from comparatively high 2030 emission levels. Negative consequences are higher economic cost as explored in accompanying papers and significantly higher mid-term warming, as indicated by a rate of warming 50% higher by the 2040s. By contrast, both mid- and long-term warming are significantly higher in another class of scenarios of staged accession that lets some regions embark on emission reductions, while others follow later, with conservation of carbon-price pathways comparable to the optimal scenarios. Not only is mid-term warming higher in staged accession cases, but the probability to exceed 2 °C in the 21st century increases by a factor of 1.5

Combining ambitious climate policies with efforts to eradicate poverty

Climate change threatens to undermine efforts to eradicate extreme poverty. However, climate policies could impose a financial burden on the global poor through increased energy and food prices. Here, we project poverty rates until 2050 and assess how they are influenced by mitigation policies consistent with the 1.5 °C target. A continuation of historical trends will leave 350 million people globally in extreme poverty by 2030. Without progressive redistribution, climate policies would push an additional 50 million people into poverty. However, redistributing the national carbon pricing revenues domestically as an equal-per-capita climate dividend compensates this policy side effect, even leading to a small net reduction of the global poverty headcount (−6 million). An additional international climate finance scheme enables a substantial poverty reduction globally and also in Sub-Saharan Africa. Combining national redistribution with international climate finance thus provides an important entry point to climate policy in developing countries

Bio-energy and CO2 emission reductions: an integrated land-use and energy sector perspective

Biomass feedstocks can be used to substitute fossil fuels and effectively remove carbon from the atmosphere to offset residual CO2 emissions from fossil fuel combustion and other sectors. Both features make biomass valuable for climate change mitigation; therefore, CO2 emission mitigation leads to complex and dynamic interactions between the energy and the land-use sector via emission pricing policies and bioenergy markets. Projected bioenergy deployment depends on climate target stringency as well as assumptions about context variables such as technology development, energy and land markets as well as policies. This study investigates the intra- and intersectorial effects on physical quantities and prices by coupling models of the energy (REMIND) and land-use sector (MAgPIE) using an iterative soft-link approach. The model framework is used to investigate variations of a broad set of context variables, including the harmonized variations on bioenergy technologies of the 33rd model comparison study of the Stanford Energy Modeling Forum (EMF-33) on climate change mitigation and large scale bioenergy deployment. Results indicate that CO2 emission mitigation triggers strong decline of fossil fuel use and rapid growth of bioenergy deployment around midcentury (~ 150 EJ/year) reaching saturation towards end-of-century. Varying context variables leads to diverse changes on mid-century bioenergy markets and carbon pricing. For example, reducing the ability to exploit the carbon value of bioenergy increases bioenergy use to substitute fossil fuels, whereas limitations on bioenergy supply shift bioenergy use to conversion alternatives featuring higher carbon capture rates. Radical variations, like fully excluding all technologies that combine bioenergy use with carbon removal, lead to substantial intersectorial effects by increasing bioenergy demand and increased economic pressure on both sectors. More gradual variations like selective exclusion of advanced bioliquid technologies in the energy sector or changes in diets mostly lead to substantial intrasectorial reallocation effects. The results deepen our understanding of the land-energy nexus, and we discuss the importance of carefully choosing variations in sensitivity analyses to provide a balanced assessment. © 2020, The Author(s)