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The "Hotelling rule" (HR) called to be "the fundamental principle of the economics of exhaustible resources" has a logical deficiency which was never paid a sufficient attention to. This deficiency should be taken into account before attempting to explain discrepancies between the price prediction provided by the HR and historically observed prices. Our analysis is focused on the HR in its original form, we do not touch upon other aspects such as varying extraction costs and other ways of upgrading the original model underlying the Hotelling rule. We conclude that HR can not be derived from the simple models as it was claimed, therefore it should be understood as an assumption on its own, and not as a rule derived from other more basic assumptions.

This paper investigates the role of a transmission system operator within a carbon footprint reduction strategy incorporating carbon taxes and renewable energy generation subsidies in the decentralised energy market. This is achieved via an optimisation bi-level model in which a welfare-maximizing transmission system operator makes investments in transmission lines at the upper level while considering power market dynamics at the lower level. To account for the deregulated energy market structure, this paper assumes that the generation companies at the lower level make capacity investments as price-takers in perfect competition. Considering alternative transmission infrastructure expansion budgets, carbon emission taxes and monetary incentives for renewable energy generation capacity expansion, the impact of alternative compositions of these factors is analysed against three output factors: the share of renewable energy in the generation mix, total generation amount, and social welfare. The proposed modelling assessment is applied to an illustrative three-node instance and a case study considering a simplified representation of the energy system of the Nordic and Baltic countries. The results highlight that, under certain circumstances, renewable energy generation subsidies may lead to an increase of renewable energy in the generation mix followed by a simultaneous fall in the total generation amount. Nevertheless, when applied together, these three measures demonstrated a positive impact on all output factors within Nordics' and Baltics' energy systems. The experiments additionally suggest that considering the high value of the carbon tax does not have an impact on the output factors while the composition of high values of renewable energy generation subsidies and budget for transmission infrastructure expansion has the strongest effect., Comment: 33 pages, 20 Figures, 12 Tables

Shadow prices are well understood and are widely used in economic applications. However, there are limits to where shadow prices can be applied assuming their natural interpretation and the fact that they reflect the first order optimality conditions (FOC). In this paper, we present a simple ad-hoc example demonstrating that marginal cost associated with exercising an optimal control may exceed the respective cost estimated from a ratio of shadow prices. Moreover, such cost estimation through shadow prices is arbitrary and depends on a particular (mathematically equivalent) formulation of the optimization problem. These facts render a ratio of shadow prices irrelevant to estimation of optimal marginal cost. The provided illustrative optimization problem links to a similar approach of calculating social cost of carbon (SCC) in the widely used dynamic integrated model of climate and the economy (DICE).

Social cost of carbon (SCC) is estimated by integrated assessment models (IAM) and is widely used by government agencies to value climate policy impacts. While there is an ongoing debate about obtained numerical estimates and related uncertainties, little attention has been paid so far to the SCC calculation method itself. This work attempts to fill the gap by providing theoretical background and economic interpretation of the SCC calculation approach implemented in the open-source IAM DICE (Dynamic Integrated model of Climate and the Economy). Our analysis indicates that the present calculation method provides an approximation that might work pretty well in some cases, while in the other cases the estimated value substantially (by the factor of four) deviates from the "true" value. This deviation stems from the inability of the present calculation method to catch the linkages between two key IAM's components -- complex interconnected systems -- climate and economy, both influenced by emission abatement policies. Within the modeling framework of DICE, the presently estimated SCC valuates policy-uncontrolled emissions against economically unjustified consumption, which makes it irrelevant for application in climate-economic policies and, therefore, calls for a replacement by a more appropriate indicator. An apparent SCC alternative, which can be employed for policy formulation is the direct output of the DICE model -- the socially optimal marginal abatement cost (SMAC), which corresponds to technological possibilities at optimal level of carbon emissions abatement. In policy making, because of the previously employed implicit approximation, great attention needs to be paid to the use of SCC estimates obtained earlier.

A limited nuclear war between India and Pakistan could ignite fires large enough to emit more than 5 Tg of soot into the stratosphere. Climate model simulations have shown severe resulting climate perturbations with declines in global mean temperature by 1.8 ◦C and precipitation by 8%, for at least 5 y. Here we evaluate impacts for the global food system. Six harmonized state-of-the-art crop models show that global caloric production from maize, wheat, rice, and soybean falls by 13 (±1)%, 11 (±8)%, 3 (±5)%, and 17 (±2)% over 5 y. Total single-year losses of 12 (±4)% quadruple the largest observed historical anomaly and exceed impacts caused by historic droughts and volcanic eruptions. Colder temperatures drive losses more than changes in precipitation and solar radiation, leading to strongest impacts in temperate regions poleward of 30◦N, including the United States, Europe, and China for 10 to 15 y. Integrated food trade network analyses show that domestic reserves and global trade can largely buffer the production anomaly in the first year. Persistent multiyear losses, however, would constrain domestic food availability and propagate to the Global South, especially to food-insecure countries. By year 5, maize and wheat availability would decrease by 13% globally and by more than 20% in 71 countries with a cumulative population of 1.3 billion people. In view of increasing instability in South Asia, this study shows that a regional conflict using <1% of the worldwide nuclear arsenal could have adverse consequences for global food security unmatched in modern history.

Global gridded crop models (GGCMs) combine agronomic or plant growth models with gridded spatial input data to estimate spatially explicit crop yields and agricultural externalities at the global scale. Differences in GGCM outputs arise from the use of different biophysical models, setups, and input data. GGCM ensembles are frequently employed to bracket uncertainties in impact studies without investigating the causes of divergence in outputs. This study explores differences in maize yield estimates from five GGCMs based on the public domain field-scale model Environmental Policy Integrated Climate (EPIC) that participate in the AgMIP Global Gridded Crop Model Intercomparison initiative. Albeit using the same crop model, the GGCMs differ in model version, input data, management assumptions, parameterization, and selection of subroutines affecting crop yield estimates via cultivar distributions, soil attributes, and hydrology among others. The analyses reveal inter-annual yield variability and absolute yield levels in the EPIC-based GGCMs to be highly sensitive to soil parameterization and crop management. All GGCMs show an intermediate performance in reproducing reported yields with a higher skill if a static soil profile is assumed or sufficient plant nutrients are supplied. An in-depth comparison of setup domains for two EPIC-based GGCMs shows that GGCM performance and plant stress responses depend substantially on soil parameters and soil process parameterization, i.e. hydrology and nutrient turnover, indicating that these often neglected domains deserve more scrutiny. For agricultural impact assessments, employing a GGCM ensemble with its widely varying assumptions in setups appears the best solution for coping with uncertainties from lack of comprehensive global data on crop management, cultivar distributions and coefficients for agro-environmental processes. However, the underlying assumptions require systematic specifications to cover representative agricultural systems and environmental conditions. Furthermore, the interlinkage of parameter sensitivity from various domains such as soil parameters, nutrient turnover coefficients, and cultivar specifications highlights that global sensitivity analyses and calibration need to be performed in an integrated manner to avoid bias resulting from disregarded core model domains. Finally, relating evaluations of the EPIC-based GGCMs to a wider ensemble based on individual core models shows that structural differences outweigh in general differences in configurations of GGCMs based on the same model, and that the ensemble mean gains higher skill from the inclusion of structurally different GGCMs. Although the members of the wider ensemble herein do not consider crop-soil-management interactions, their sensitivity to nutrient supply indicates that findings for the EPIC-based sub-ensemble will likely become relevant for other GGCMs with the progressing inclusion of such processes.

Agricultural production must increase to feed a growing and wealthier population, as well as to satisfy increasing demands for biomaterials and biomass-based energy. At the same time, deforestation and land-use change need to be minimized in order to preserve biodiversity and maintain carbon stores in vegetation and soils. Consequently, agricultural land use needs to be intensified in order to increase food production per unit area of land. Here we use simulations of AgMIP's Global Gridded Crop Model Intercomparison (GGCMI) phase 1 to assess implications of input-driven intensification (water, nutrients) on crop yield and yield stability, which is an important aspect in food security. We find region- and crop-specific responses for the simulated period 1980+/-2009 with broadly increasing yield variability under additional nitrogen inputs and stabilizing yields under additional water inputs (irrigation), reflecting current patterns of water and nutrient limitation. The different models of the GGCMI ensemble show similar response patterns, but model differences warrant further research on management assumptions, such as variety selection and soil management, and inputs as well as on model implementation of different soil and plant processes, such as on heat stress, and parameters. Higher variability in crop productivity under higher fertilizer input will require adequate buffer mechanisms in trade and distribution/storage networks to avoid food price volatility.

Humans are increasing the amount of carbon dioxide (CO2) in the air through CO2 emissions. This is changing the climate, making life harder for many plants in areas that suffer from heat and drought. However, plants need CO2 to grow, and more CO2 can make them grow better. So will plants overall benefit from increased CO2 level or suffer from it? We wanted to test if the positive effect would offset the negative ones. To do so, we used scientific models to calculate future crop production and water use of four important crops all over the world under different scenarios of CO2 emissions and climate change. Our calculations show that although there will be large reductions in crop yield due to climate change over the next century, some crops will still be able to grow well. This is also because crops can grow with less water when CO2 levels are raised.

Crop models are increasingly used to simulate crop yields at the global scale, but so far there is no general framework on how to assess model performance. Here we evaluate the simulation results of 14 global gridded crop modeling groups that have contributed historic crop yield simulations for maize, wheat, rice and soybean to the Global Gridded Crop Model Intercomparison (GGCMI) of the Agricultural Model Intercomparison and Improvement Project (AgMIP). Simulation results are compared to reference data at global, national and grid cell scales and we evaluate model performance with respect to time series correlation, spatial correlation and mean bias. We find that global gridded crop models (GGCMs) show mixed skill in reproducing time series correlations or spatial patterns at the different spatial scales. Generally, maize, wheat and soybean simulations of many GGCMs are capable of reproducing larger parts of observed temporal variability (time series correlation coefficients (r) of up to 0.888 for maize, 0.673 for wheat and 0.643 for soybean at the global scale) but rice yield variability cannot be well reproduced by most models. Yield variability can be well reproduced for most major producing countries by many GGCMs and for all countries by at least some. A comparison with gridded yield data and a statistical analysis of the effects of weather variability on yield variability shows that the ensemble of GGCMs can explain more of the yield variability than an ensemble of regression models for maize and soybean, but not for wheat and rice. We identify future research needs in global gridded crop modeling and for all individual crop modeling groups. In the absence of a purely observation-based benchmark for model evaluation, we propose that the best performing crop model per crop and region establishes the benchmark for all others, and modelers are encouraged to investigate how crop model performance can be increased. We make our evaluation system accessible to all crop modelers so that other modeling groups can also test their model performance against the reference data and the GGCMI benchmark.

The aggregation of simulated gridded crop yields to national or regional scale requires information on temporal and spatial patterns of crop-specific harvested areas. This analysis estimates the uncertainty of simulated gridded yield time series related to the aggregation with four different harvested area data sets. We compare aggregated yield time series from the Global Gridded Crop Model Inter-comparison project for four crop types from 14 models at global, national, and regional scale to determine aggregation-driven differences in mean yields and temporal patterns as measures of uncertainty. The quantity and spatial patterns of harvested areas differ for individual crops among the four datasets applied for the aggregation. Also simulated spatial yield patterns differ among the 14 models. These differences in harvested areas and simulated yield patterns lead to differences in aggregated productivity estimates, both in mean yield and in the temporal dynamics. Among the four investigated crops, wheat yield (17% relative difference) is most affected by the uncertainty introduced by the aggregation at the global scale. The correlation of temporal patterns of global aggregated yield time series can be as low as for soybean (r = 0.28).For the majority of countries, mean relative differences of nationally aggregated yields account for10% or less. The spatial and temporal difference can be substantial higher for individual countries. Of the top-10 crop producers, aggregated national multi-annual mean relative difference of yields can be up to 67% (maize, South Africa), 43% (wheat, Pakistan), 51% (rice, Japan), and 427% (soybean, Bolivia).Correlations of differently aggregated yield time series can be as low as r = 0.56 (maize, India), r = 0.05∗Corresponding (wheat, Russia), r = 0.13 (rice, Vietnam), and r = −0.01 (soybean, Uruguay). The aggregation to sub-national scale in comparison to country scale shows that spatial uncertainties can cancel out in countries with large harvested areas per crop type. We conclude that the aggregation uncertainty can be substantial for crop productivity and production estimations in the context of food security, impact assessment, and model evaluation exercises.

Rising atmospheric carbon dioxide concentrations are expected to enhance photosynthesis and reduce crop water use. However, there is high uncertainty about the global implications of these effects for future crop production and agricultural water requirements under climate change. Here we combine results from networks of field experiments and global crop models to present a spatially explicit global perspective on crop water productivity (CWP, the ratio of crop yield to evapotranspiration) for wheat, maize, rice and soybean under elevated carbon dioxide and associated climate change projected for a high-end greenhouse gas emissions scenario. We find carbon dioxide effects increase global CWP by 10[0;47]%-27[7;37]% (median[interquartile range] across the model ensemble) by the 2080s depending on crop types, with particularly large increases in arid regions (by up to 48[25;56]% for rain fed wheat). If realized in the fields, the effects of elevated carbon dioxide could considerably mitigate global yield losses whilst reducing agricultural consumptive water use (4-17%). We identify regional disparities driven by differences in growing conditions across agro-ecosystems that could have implications for increasing food production without compromising water security. Finally, our results demonstrate the need to expand field experiments and encourage greater consistency in modeling the effects of rising carbon dioxide across crop and hydrological modeling communities.