A.A. Krasovskii

Modeling biomass burning and related carbon emissions during the 21st century in Europe

In this study we present an assessment of the impact of future climate change on total fire probability, burned area, and carbon (C) emissions from fires in Europe. The analysis was performed with the Community Land Model (CLM) extended with a prognostic treatment of fires that was specifically refined and optimized for application over Europe. Simulations over the 21st century are forced by five different high-resolution Regional Climate Models under the Special Report on Emissions Scenarios A1B. Both original and bias-corrected meteorological forcings is used. Results show that the simulated C emissions over the present period are improved by using bias corrected meteorological forcing, with a reduction of the intermodel variability. In the course of the 21st century, burned area and C emissions from fires are shown to increase in Europe, in particular in the Mediterranean basins, in the Balkan regions and in Eastern Europe. However, the projected increase is lower than in other studies that did not fully account for the effect of climate on ecosystem functioning. We demonstrate that the lower sensitivity of burned area and C emissions to climate change is related to the predicted reduction of the net primary productivity, which is identified as the most important determinant of fire activity in the Mediterranean region after anthropogenic interaction. This behavior, consistent with the intermediate fire-productivity hypothesis, limits the sensitivity of future burned area and C emissions from fires on climate change, providing more conservative estimates of future fire patterns, and demonstrates the importance of coupling fire simulation with a climate driven ecosystem productivity model.

Properties of Hamiltonian Systems in the Pontryagin Maximum Principle for Economic Growth Problems

We consider an optimal control problem with a functional defined by an improper integral. We study the concavity properties of the maximized Hamiltonian and analyze the Hamiltonian systems in the Pontryagin maximum principle. On the basis of this analysis, we propose an algorithm for constructing an optimal trajectory by gluing the dynamics of the Hamiltonian systems. The algorithm is illustrated by calculating an optimal economic growth trajectory for macroeconomic data.

Conjugation of Hamiltonian Systems in Optimal Control Problems

Abstract The optimal control problem with a functional given by an improper integral is considered for models of economic growth. Properties of concavity of the maximized Hamiltonian are examined and analysis of Hamiltonian systems in the Pontryagin maximum principle is implemented including estimation of steady states and conjugation of domains with different Hamiltonian dynamics. On the basis of this analysis an algorithm is proposed for construction of optimal trajectories by sewing dynamics of Hamiltonian systems. The proposed algorithm is illustrated by computer simulations of optimal trajectories in models of economic growth for real macroeconomic data.

Dynamic optimization of investments in the economic growth models

Consideration was given to the optimal control of investments in the economic growth model. The basic construction of the model is the production function relating the growth of production with the dynamics of production factors, and the investments in the production factors are the control parameters. The integral indicator of the discounted consumption index is the optimization functional. The Pontryagin principle of maximum for problems on infinite horizon was used to construct the optimal investment control. For the corresponding Hamiltonian system, considered were its qualitative properties such as existence and uniqueness of the steady state, properties of the eigenvalues and eigenvectors of the linearized system, and characteristics of the saddle point. This analysis allows one to obtain an algorithm to construct the optimal growth trajectories. The model was calibrated for the USA macroeconomic indicators.

Regional aspects of modelling burned areas in Europe

This paper presents a series of improvements to the quantitative modelling of burned areas in Europe under historical climate. The Standalone Fire Model (SFM) based on a state-of-the-art large scale mechanistic fire modelling algorithm is used to reproduce historical burned areas reported in the two publicly available datasets – European Forest Fire Information System (EFFIS) and Global Fire Emissions Database (GFED). The most recent versions of these sources allow a broader validation of SFM’s modelled burned areas at a country level. Our analysis is carried out for the years 2000–2008 for 17 European countries utilising both EFFIS and GFED datasets for model benchmarking. We suggest improving the original model by modifying the fire probability function reflecting fuel moisture. This modification allows for a dramatic improvement of accuracy in modelled burned areas for a range of European countries. We also explore in detail a pixel-level parametrisation of firefighting efficiency in SFM along with modifications of the biomass map. In comparison with the aggregated country-level approach, the advantages of the finer calibration are quite minor for the most recent version of the GFED dataset. Overall, the annual burned areas modelled by this improved SFM version are in good agreement with historical observations.

Nonlinear stabilizers of economic growth under exhausting energy resources

The paper is devoted to the model of the optimal economic growth with the exogenous dynamics of the energy factor. The research is based on the real data representing main macroeconomic indicators of the US economy. These indicators are GDP and three production factors: capital, labor and useful work. The specific production function is implemented in the model to express the relationship between factors of production and the quantity of output produced. The trends of the economys growth are analyzed by means of the dynamic model which formalizes the process in the mathematical optimal control problem. This problem is solved using the version of the Pontryagin maximum principle, elements of the qualitative theory of differential equations and methods of differential games. A nonlinear stabilizer is proposed for constructing synthetic trajectories of economic growth. Numerical experiments are fulfilled via elaborated software. The comparison of optimal trajectories and real trends are presented. Based on the model simulations the scenarios of future growth are discussed.

Impacts of the fairly priced REDD-based Co 2 offset options on the electricity producers and consumers

This paper deals with the modeling of two sectors of a regional economy: electricity and forestry. We show that CO2 price will impact not only the profits of the CO2 emitting electricity producer (decrease), but also the electricity prices for the consumer (increase), and, hence, some financial instruments might be implemented today in order to be prepared for the uncertain CO2 prices in the future. We elaborate financial instrument based on the Reduced Emissions from Deforestation and Degradation (REDD+) mechanism. We model optimal behavior of forest owner and electricity producer under uncertainty and determine equilibrium fair prices of REDD-based-options.

Optimization of functionality development

The problem of regulation of logistic growth trends is examined in the framework of control theory for problems with infinite horizon. The problem statement is related to microeconomic models of dynamic optimization of a companys indicator of functionality development. Various control regimes of functionality development are studied for identification of plausible production trends. Optimal control problem is posed to optimize the utility function of logarithmic consumption index of the system entropy type. Solution of the problem is constructed in analysis of the Hamiltonian system and its algebraic properties. Based on this analysis nonlinear stabilizers are elaborated which lead the system to the steady state with the same growth rates as the optimal control regime. The model is tested on the real time series of dynamic trends of functionality development for two generations of mobile phones in Japan.

Construction of nonlinear regulators in economic growth models

An infinite-horizon optimal control problem is considered which arises in an economic growthmodel with exhaustible energy resources. The Hamiltonian system in the Pontryagin maximum principle is analyzed and nonlinear regulators are constructed for the dynamical system under consideration. The presented results of synthetic economic growth trajectories generated by nonlinear regulators of the system are based on real-life data.

High-Precision Algorithms for Constructing Optimal Trajectories via Solving Hamiltonian Systems

The paper deals with analysis of optimal control problems arising in models of economic growth. The Pontryagin maximum principle is applied for analysis of the optimal investment problem. Specifically, the research is based on existence results and necessary conditions of optimality in problems with infinite horizon. Properties of Hamiltonian systems are examined for different regimes of optimal control. The existence and uniqueness result is proved for a steady state of the Hamiltonian system. Analysis of properties of eigenvalues and eigenvectors is completed for the linearized system in a neighborhood of the steady state. Description of behavior of the nonlinear Hamiltonian system is provided on the basis of results of the qualitative theory of differential equations. This analysis allows us to outline proportions of the main economic factors and trends of optimal growth in the model. A numerical algorithm for construction of optimal trajectories of economic growth is elaborated on the basis of constructions of backward procedures and conjugation of an approximation linear dynamics with the nonlinear Hamiltonian dynamics. High order precision estimates are obtained for the proposed algorithm. These estimates establish connection between precision parameters in the phase space and precision parameters for functional indices.