Amos Zemel

Accounting for global warming risks: Resource management under event uncertainty

Abstract Optimal management of atmospheric pollution is discussed with a special emphasis on the uncertainty concerning the occurrence of undesirable events associated with the greenhouse effect. The uncertainty considered here stems from our ignorance of the exact pollution level required to trigger the event rather than from the genuinely stochastic nature of the processes involved. Taking atmospheric pollution level as the state variable, it is found that uncertainty implies the existence of an equilibrium interval, within which the emission rate of the greenhouse gases should be kept equal to the natural removal rate of these gases. Processes initiated outside the equilibrium interval must converge monotonically to its nearest endpoint. The determination of the interval requires no knowledge of the optimal policy. In contrast, ignoring event occurrence risk implies a single equilibrium level, attracting the optimal process from any initial level.

Optimal transition to backstop substitutes for nonrenewable resources

Abstract We analyze the optimal transition from a primary, nonrenewable resource to a backstop substitute for a class of problems characterized by the property that the backstop cost decreases continuously as learning from R&D efforts accumulates to increase the knowledge base. The transition policy consists of the R&D process and of the time profiles of the primary and backstop resource supply rates. We find that the optimal R&D process follows a most rapid approach path (MRAP): the knowledge process associated with R&D should approach some (endogenously derived) target process as rapidly as possible and proceed along it thereafter. Thus, if the initial knowledge level is sufficiently low and the cost structure justifies R&D activities, the R&D efforts should be initiated without delay at the highest affordable rate and slow down later on. This pattern contrasts previous findings that typically recommend a single-humped R&D process with a possible initial delay.

Validation of models for global irradiance on inclined planes

Abstract The accuracy of models to estimate irradiance on inclined planes is tested by comparing the predictions to measurements taken with four instruments of various tilt and azimuth angles in Sede Boqer, Israel. The three models investigated are: the Perez model, Hays anisotropic model, and the isotropic model. The Perez model is found to perform significantly better than the other two, with residual errors that are comparable to the accuracy of the measuring instruments themselves. The same data are also used to evaluate the precision of empirical correlations to estimate the direct component from global horizontal radiation, and to assess the sensitivity of the predicted irradiance on tilted surfaces to the errors associated with these correlations.

The infinite horizon dynamic optimization problem revisited: A simple method to determine equilibrium states

Abstract This work addresses intertemporal decision problems in which the policy adopted at any given time affects the state of the system during later periods. The standard treatment of such problems employs dynamic optimization methods. When the planning period extends over an infinite time horizon, the identification of the optimal equilibrium states is of prime importance. In this work we introduce a method to reduce the identification task to the algebraic problem of solving for the roots of a simple function of the state variable, denoted the evolution function. An explicit expression for the evolution function is derived for a general setup that covers a large variety of economic and management models. When the evolution function possesses a unique feasible root, the steady state is readily identified and a characterization of the dynamic behavior is possible. The application of the proposed method is illustrated by considering several resource exploitation problems.

LONG-TERM PERSPECTIVE ON THE DEVELOPMENT OF SOLAR ENERGY

We use dynamic optimization methods to analyze the development of solar technologies in light of the increasing scarcity and environmental pollution associated with fossil fuel combustion. Learning from solar R&D efforts accumulates in the form of knowledge to gradually reduce the cost of solar energy, while the scarcity and pollution externalities associated with fossil fuel combustion come into effect through shadow prices that must be included in the effective cost of fossil energy. Accounting for these processes, we characterize the optimal time profiles of fossil and solar energy supply rates and the optimal investment in solar R&D. We find that the optimal rate of fossil energy supply should decrease over time and vanish continuously upon depletion of the fossil fuel reserves, while the optimal supply of solar energy should gradually increase and eventually take over the entire energy demand. The optimal solar R&D investment should initially be set at the highest feasible rate, calling for early engagement in solar R&D programs, long before large scale solar energy production becomes competitive.

Inter-group competition and stable group sizes

The stability of the sizes of foraging groups of animals is reviewed with a special emphasis on the effect of inter-group competition. A simple model, in which cooperation, within-group and inter-group competition are explicitly accounted for, shows that when resources are scarce and patchy, inter-group competition tends to keep animals within their groups, even when these groups are overpopulated. The models conclusions are in accord with empirical observations indicating that animals tend to forage in groups that are larger than the expected optimal size.

On the dynamics of competing energy sources

We characterize the dynamics of energy markets in which energy is derived from polluting (fossil) and clean (solar) resources. The analysis is based on geometric optimal control considerations. An important feature of solar energy technologies is that their cost of supply is predominantly due to upfront investment in capital infrastructure (rather than to actual supply rate) and this feature has important implications for the market allocation outcome. In particular, it gives rise to a threshold behavior in that solar energy is adopted only when the price of fossil energy exceeds a certain threshold. Under this condition solar technologies will (eventually) dominate energy supply by driving fossil energy altogether out of the energy sector. A tax on fossil energy can have a substantial impact since it changes the threshold price. A quantity restriction (e.g., a cap on fossil energy) allows for the coexistence of clean and polluting energy technologies also in the long run, and its effect on the use of fossil energy is more moderate.

Thermodynamic Analysis of Latent Heat Storage in a Shell-and-Tube Heat Exchanger

This work addresses the entropy generation aspects of a latent heat storage in which the energy delivered by a hot gas flowing through a cylindrical tube induces melting of the material surrounding the tube. The heat transfer for conduction-dominated melting is analyzed, taking into account the two-dimensional effects. The storage process irreversibilities associated with both the gas flow and the heat transfer (including entropy generation in the melted layer) are considered. The number of entropy generation units, which is a measure of the thermodynamic imperfection of the energy storage process, is expressed as a function of the main design parameters of the system. Analytic bounds and simplified asymptotic expressions for this quantity are derived. The results are compared with earlier one-dimensional studies.

A method for monitoring insolation in remote regions

Abstract A method is proposed for measuring the beam and diffuse components of solar radiation via the use of a set of fixed pyranometers tilted in various orientations. A detailed error analysis is performed for the two cases of three and four pyranometers, and it is shown how orientations may be found such that the resultant errors on the derived beam and diffuse components may be expected to be of a magnitude comparable to the errors associated with the pyranometers themselves. Attention is drawn to the fact that certain anisotropic models for the diffuse component may be recast—via the definition of “effective” beam and diffuse components—in such a manner that they take on the mathematical simplicity of an isotropic model.

R&D policies for desalination technologies

In many arid and semi-arid regions whether or not to desalinate seawater has long been a non-issue and policy debates are focused on the timing and extent of the desalination activities. We analyze how water scarcity and demand structure, on the one hand, and cost reduction via R&D programs, on the other hand, affect the desirable development of desalination technologies and the time profiles of fresh and desalinated water supplies. We show that the optimal R&D policy is of a non-standard most rapid approach path (NSMRAP) type, under which the state of desalination technology - the accumulated learning from R&D efforts - should approach a pre-specified target process as rapidly as possible and proceed along it thereafter. The NSMRAP property enables a complete characterization of the optimal water policy. The renewable nature of the fresh water stock permits a non-monotonic behavior of the optimal stock process: under certain conditions, the stock is depleted, to be (fully or partly) refilled at a later date.