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Optimal Rotation Age
In forestry, the optimal rotation age is the growth period required to derive maximum value from a stand of timber. The calculation of this period is specific to each stand and to the economic and sustainability goals of the harvester. Economically optimum rotation age In forestry rotation analysis, economically optimum rotation can be defined as “that age of rotation when the harvest of stumpage will generate the maximum revenue or economic yield”. In an economically optimum forest rotation analysis, the decision regarding optimum rotation age is undertake by calculating the maximum net present value. It can be shown as follows: *Revenue (R) = Volume × Price *Cost (C) = Cost of harvesting + handling. *Hence, Profit = Revenue − Cost. Since the benefit is generated over multiple years, it is necessary to calculate that particular age of harvesting which will generate the maximum revenue. The age of maximum revenue is calculated by discounting for future expected benefi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Forestry
Forestry is the science and craft of creating, managing, planting, using, conserving and repairing forests, woodlands, and associated resources for human and environmental benefits. Forestry is practiced in plantations and natural stands. The science of forestry has elements that belong to the biological, physical, social, political and managerial sciences. Forest management play essential role of creation and modification of habitats and affect ecosystem services provisioning. Modern forestry generally embraces a broad range of concerns, in what is known as multiple-use management, including: the provision of timber, fuel wood, wildlife habitat, natural water quality management, recreation, landscape and community protection, employment, aesthetically appealing landscapes, biodiversity management, watershed management, erosion control, and preserving forests as "sinks" for atmospheric carbon dioxide. Forest ecosystems have come to be seen as the most important comp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Modeling Population Growth
A model is an informative representation of an object, person or system. The term originally denoted the plans of a building in late 16th-century English, and derived via French and Italian ultimately from Latin ''modulus'', a measure. Models can be divided into physical models (e.g. a model plane) and abstract models (e.g. mathematical expressions describing behavioural patterns). Abstract or conceptual models are central to philosophy of science, as almost every scientific theory effectively embeds some kind of model of the physical or human sphere. In commerce, "model" can refer to a specific design of a product as displayed in a catalogue or show room (e.g. Ford Model T), and by extension to the sold product itself. Types of models include: Physical model A physical model (most commonly referred to simply as a model but in this context distinguished from a conceptual model) is a smaller or larger physical copy of an object. The object being modelled may be small (fo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Forest Modelling
A forest is an area of land dominated by trees. Hundreds of definitions of forest are used throughout the world, incorporating factors such as tree density, tree height, land use, legal standing, and ecological function. The United Nations' Food and Agriculture Organization (FAO) defines a forest as, "Land spanning more than 0.5 hectares with trees higher than 5 meters and a canopy cover of more than 10 percent, or trees able to reach these thresholds ''in situ''. It does not include land that is predominantly under agricultural or urban use." Using this definition, '' Global Forest Resources Assessment 2020'' (FRA 2020) found that forests covered , or approximately 31 percent of the world's land area in 2020. Forests are the predominant terrestrial ecosystem of Earth, and are found around the globe. More than half of the world's forests are found in only five countries (Brazil, Canada, China, Russia, and the United States). The largest share of forests (45 percent) are i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Forest Management
Forest management is a branch of forestry concerned with overall administrative, legal, economic, and social aspects, as well as scientific and technical aspects, such as silviculture, protection, and forest regulation. This includes management for timber, aesthetics, recreation, urban values, water, wildlife, inland and nearshore fisheries, wood products, plant genetic resources, and other forest resource values. Management objectives can be for conservation, utilisation, or a mixture of the two. Techniques include timber extraction, planting and replanting of different species, building and maintenance of roads and pathways through forests, and preventing fire. Definition The forest is a natural system that can supply different products and services. Forests supply water, mitigate climate change, provide habitats for wildlife including many pollinators which are essential for sustainable food production, provide timber and fuelwood, serve as a source of non-wood forest pr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Extended Rotation Forest
An extended rotation forest is a forest stand for which the harvest age is increased beyond the optimum economic harvest age to provide larger trees, wildlife habitat, and other non-timber values. Advantages of extended rotation forestry included enhanced carbon storage, better wood quality and the ability to create habitat for old growth dependent species. The main disadvantages of extended rotations is the lower present value of the stand and timber supply issues. These impacts can be mitigated by the application of commercial thinning. In the Pacific Northwest of the United States, commercially thinned stands have yet to reach cumulation age in spite of reaching ages of over 100 years on good to moderate sites. In managed for values other than timber, extended rotations are being considered. In Oregon, some environmental groups are calling for rotations as long as 250 years. The argument centres on the assertion that short-rotation management on either biological or financial ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pontryagin's Maximum Principle
Pontryagin's maximum principle is used in optimal control theory to find the best possible control for taking a dynamical system from one state to another, especially in the presence of constraints for the state or input controls. It states that it is necessary for any optimal control along with the optimal state trajectory to solve the so-called Hamiltonian system, which is a two-point boundary value problem, plus a maximum condition of the control Hamiltonian. These necessary conditions become sufficient under certain convexity conditions on the objective and constraint functions. The maximum principle was formulated in 1956 by the Russian mathematician Lev Pontryagin and his students, and its initial application was to the maximization of the terminal speed of a rocket. The result was derived using ideas from the classical calculus of variations. After a slight perturbation of the optimal control, one considers the first-order term of a Taylor expansion with respect to the per ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Singular Control
In optimal control, problems of singular control are problems that are difficult to solve because a straightforward application of Pontryagin's minimum principle fails to yield a complete solution. Only a few such problems have been solved, such as Merton's portfolio problem in financial economics or trajectory optimization in aeronautics. A more technical explanation follows. The most common difficulty in applying Pontryagin's principle arises when the Hamiltonian depends linearly on the control u, i.e., is of the form: H(u)=\phi(x,\lambda,t)u+\cdots and the control is restricted to being between an upper and a lower bound: a\le u(t)\le b. To minimize H(u), we need to make u as big or as small as possible, depending on the sign of \phi(x,\lambda,t), specifically: : u(t) = \begin b, & \phi(x,\lambda,t)0.\end If \phi is positive at some times, negative at others and is only zero instantaneously, then the solution is straightforward and is a bang-bang control that switches from b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hamiltonian (control Theory)
The Hamiltonian is a function used to solve a problem of optimal control for a dynamical system. It can be understood as an instantaneous increment of the Lagrangian expression of the problem that is to be optimized over a certain time period. Inspired by, but distinct from, the Hamiltonian of classical mechanics, the Hamiltonian of optimal control theory was developed by Lev Pontryagin as part of his maximum principle. Pontryagin proved that a necessary condition for solving the optimal control problem is that the control should be chosen so as to optimize the Hamiltonian. Problem statement and definition of the Hamiltonian Consider a dynamical system of n first-order differential equations :\dot(t) = \mathbf(\mathbf(t),\mathbf(t),t) where \mathbf(t) = \left x_(t), x_(t), \ldots, x_(t) \right denotes a vector of state variables, and \mathbf(t) = \left u_(t), u_(t), \ldots, u_(t) \right a vector of control variables. Once initial conditions \mathbf(t_) = \mathbf_ and controls ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Optimal Control
Optimal control theory is a branch of mathematical optimization that deals with finding a control for a dynamical system over a period of time such that an objective function is optimized. It has numerous applications in science, engineering and operations research. For example, the dynamical system might be a spacecraft with controls corresponding to rocket thrusters, and the objective might be to reach the moon with minimum fuel expenditure. Or the dynamical system could be a nation's economy, with the objective to minimize unemployment; the controls in this case could be fiscal and monetary policy. A dynamical system may also be introduced to embed operations research problems within the framework of optimal control theory. Optimal control is an extension of the calculus of variations, and is a mathematical optimization method for deriving control policies. The method is largely due to the work of Lev Pontryagin and Richard Bellman in the 1950s, after contributions to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Non-timber Forest Product
Non-timber forest products (NTFPs) are useful foods, substances, materials and/or commodities obtained from forests other than timber. Harvest ranges from wild collection to farming. They typically include game animals, fur-bearers, nuts, seeds, berries, mushrooms, oils, sap, foliage, pollarding, medicinal plants, peat, mast, fuelwood, fish, insects, spices, and forage. Overlapping concepts include non-wood forest products (NWFPs), wild forest products, minor forest produce, special, minor, alternative and secondary forest products – for further distinctions see the definition section below Research on NTFPs has focused on their ability to be produced as commodities for rural incomes and markets, as an expression of traditional knowledge or as a livelihood option for rural household needs, as a key component of sustainable forest management and conservation strategies, and for their important role in improving dietary diversity and providing nutritious food, particularly for ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stumpage
Stumpage is the price a private firm pays for the right to harvest timber from a given land base. It is paid to the current owner of the land. Historically, the price was determined on a basis of the number of trees harvested, or "per stump". Currently it is dictated by more standard measurements such as cubic metres, board feet, or tons. To determine stumpage, any stand that will be harvested by the firm is first assessed and appraised through processes aimed at finding the volume of timber that is to be harvested. A given stumpage rate, measured in $/volume, is then applied to the amount of timber to be harvested. The firm will then pay this price to the landowner. Stumpage in Canada Canadian forests exist mainly on what is considered to be crown land, under the provincial governments' control. On Canadian crown land, stumpage is known as the market value of standing trees that must be paid by firms for the right to harvest timber, currently measured in $/cubic meter. In Canada ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Periodic Annual Increment
In forestry, periodic annual increment (PAI) is the change in the size of a tree between the beginning and ending of a growth period, divided by the number of years that was designated as the growing period. For sigmoid growth, the graph of PAI increases rapidly and then quickly declines, approaching zero. PAI may go negative if a tree loses volume due to damage or disease. Periodic annual increment is commonly used instead of current annual increment as a basis for computing growth ''per cent''. Growth ''per cent'' indicates the rate of increase with relation to the wood capital required for its production, this is usually based on a single year's growth.Chapman, H.H.,1921, Forest Mensuration, second edition. p315 New York: Wiley & Sons, Inc. Equation PAI= \frac Where: Y is the yield (volume, height, DBH, etc.) at times 1 and 2 and T1 represents the year starting the growth period, and T2 is the end year. Example: Say that the growth period is from age 5 to age 10, and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
