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Instability in Environmental Modeling Kurt Fedra © K. Fedra 2000

Uncertainty ... Websters: the quality or condition of being indeterminate Handbook of Mathematics and Computational Science (Harris & Stocker, 1998) : ultrafuzzy unprejudiced underdeterminate uniqueness questions © K. Fedra 2000

Uncertainty ... Components of Mathematical Biology (A.J.Lotka, 1956 ): - A History of Western Philosophy (B.RusselI, 1945 ) - Objective Knowledge (K.R.Popper, 1972 ): Of Clouds and Clocks : sporadic, cluttered, erratic © K. Fedra 2000

Uncertainty ... The Logic of Scientific Discovery (1959): Uncertainty: see Hypothesis The issue of enlistment: from particular proclamations (perceptions) to general explanations (speculation, hypotheses, models) … troubles of inductive rationale … are difficult. © K. Fedra 2000

Uncertainty ... Reichenbach (Erkenntnis, 1930) … for it is not given to science to reach either truth or deception (cited in Popper, op.cit) Wittgenstein (Tractatus, 1918) 5.634 Alles was wir überhaupt beschreiben können, könnte auch anders sein. Xenophanes (6 th penny BC) … But with respect to certain truth, no man has known it. For all is yet a woven web of conjectures. © K. Fedra 2000

Uncertainty ... Bernoulli, Daniel: Mathematical activities (1724) incorporates dialog of vulnerability with regards to Faro; likelihood and political economy: moral estimation of pay, probabilistic salary: applications to protection. Euler, Paul: Calculus of varieties (1730), counselor on state lottery and protection (Berlin, 1740) Poisson, Simeon: Recherches sur la probabilite des jugements (1837) Poisson dissemination: likelihood of an arbitrary occasion in a period or space interim, when the likelihood is low yet the quantity of cases (trials) is extensive. © K. Fedra 2000

Uncertainty ... Hypothesis of Science (G.Gale, 1979) Correspondence hypothesis of truth: An announcement is valid if and just on the off chance that it compares to what it alludes to Reference to items, genuine or perfect (Plato) presents recognition (subjective), or estimation: Uncertainty Principle (Heisenberg, 1925) © K. Fedra 2000

Uncertainty ... instability connection: where x and p allude to position and energy and, h is Planck's quantum of activity, a consistent (Heisenberg, 1925). © K. Fedra 2000

Gödel's first inadequacy hypothesis For any formal framework S which is predictable (free from disagreements) and sufficiently rich (to contain number hypothesis) there are explanations which can be defined in S yet can't be demonstrated or negated in S however are valid and can be turned out to be valid by wealthier means. © K. Fedra 2000

Formal frameworks are triplets < L,A,R > comprising of a formal dialect L a set An of sayings (figured in L ) a set R of guidelines of induction (development, deducation, conceivable moves) with the end goal that there is no less than one saying or one run (i.e., A R 0) © K. Fedra 2000

Uncertainty ... In rundown: vast measure of writing, no attractive operational definition, however evident instinctive comprehension of the idea. Natural models, similar to some other formal technique depicting reality and depending on perceptions, contain vulnerability. © K. Fedra 2000

Uncertainty ... One can compose formally: for a dynamic framework with state vector X(t) and outside forcings U(t) © K. Fedra 2000

Uncertainty ... what's more, extend to: where is a blunder term, normally thought to be white or Gaussian commotion, © K. Fedra 2000

Uncertainty ... then again on the other hand extend to: where E is a vector speaking to beginning state instability, and G is a steady slanting dissemination network comparing to the vector Wiener prepare W(t) with free parts (from Filar and Haurie, 1998). © K. Fedra 2000

Uncertainty ... the dissemination network serves to energize the framework state practically equivalent to the irregular aggravation of particles in a Lagrangian display, i.e., an arbitrary segment is added to a deterministically figured state. © K. Fedra 2000

Uncertainty ... on the other hand, with regards to adjustment: where x speaks to the dynamic framework, and y its discrete perceptions at t k , with info unsettling influences and perception blunders , separately (Beck and van Straten, 1983) © K. Fedra 2000

Uncertainty ... then again, with regards to basic leadership: where signify controllable and wild forcings,and indicates every stochastic unsettling influence once more (Young,1983) © K. Fedra 2000

Uncertainty ... Questions: sources and impacts of vulnerability how to gauge levels of instability how to lessen instability how to join vulnerability into basic leadership forms. © K. Fedra 2000

Sources of Uncertainty ... Perceptions of nature can not be made without blunder - much of the time . Microscale (rudimentary vulnerability) Heisenberg (1925) , Monod (1970) Macroscale (Complex element frameworks) Eigen and Winkler (1975), Gleick (1987) © K. Fedra 2000

Uncertainty ... Macroscale: in light of tests examining mistakes: reasonable fleeting spatial at various scales and levels of accumulation. © K. Fedra 2000

Uncertainty ... In the event that perceptions (exact information) contain blunders, theory testing in an entirely Popperian sense (Popper, 1959, 1979) is no longer a double procedure however should be a measurable one: prompts to model vulnerability © K. Fedra 2000

Uncertainty ... In the event that a speculation (models are compound theories) can not unambiguously be distorted, we leave (in Poppers strict view) the domain of science. Taking after realistic instrumentalism (Feyerabend 1975), the question turns out to be: the manner by which valuable is the speculation (display) © K. Fedra 2000

Types of Uncertainty in Modeling... Vulnerability about the relationship among the factors (show structure) Uncertainty about the parameters (coefficients) in the model (alignment) Uncertainty related with the forecast of future state/conduct © K. Fedra 2000

Sources of Uncertainty ... Instability in Environmental Models: Dynamic Systems Perspective (Filar and Haurie, 1998) list wellsprings of vulnerability with regards to PC executed models of nature (IMAGE atmosphere affect demonstrate): © K. Fedra 2000

Sources of Uncertainty ... blunders in perceptions (which influence parameter estimation) mistakes in parameter estimation blunders in the arrangement calculations blunders in the PC execution mistakes in the demonstrating (show structure). (Filar and Haurie, 1998) © K. Fedra 2000

Uncertainty ... Blunder (Webster's): a demonstration or state of uninformed or unwise deviation from a code of conduct a demonstration including inadvertent deviation from truth or exactness. Suggests that a right, mistake free option exists ! © K. Fedra 2000

Sources of Uncertainty ... Information and perception vulnerability Model structure instability Parameter vulnerability Algorithmic instability/blunder Implementation mistakes © K. Fedra 2000

Sources of Uncertainty ... Information and perception instability Model structure vulnerability Parameter vulnerability Algorithmic vulnerability/blunder Implementation mistakes © K. Fedra 2000

Data Uncertainty ... rudimentary vulnerability inspecting mistakes scale and reasonable confound © K. Fedra 2000

Data Uncertainty ... Basic instability: naturally visible portrayal as fluctuation: hereditary inconstancy in a populace, conduct of turbulent frameworks Non-direct Systems (Lorenz, 1963) Fractal Geometry (Mandelbrot, 1977) Chaos Theory (Gleick 1987) © K. Fedra 2000

Data Uncertainty ... Examining mistakes: frameworks with an inalienable changeability or assorted qualities (parametric, spatial, transient) must be inspected (or homogenized), which prompts to testing blunders: the genuine populace measurements must be assessed with some vulnerability. © K. Fedra 2000

Data Uncertainty ... Ecological factors don't regularly take after ordinary appropriations: Patchiness Diversity: Shannon list (got from a data measure, Shannon and Weaver 1963) © K. Fedra 2000

Data Uncertainty ... Scale (spatial and worldly): due to spatial and fleeting non-typical inconstancy, scale influences examining gauges. Concise testing of various parameters: temperature (persistently) temperature slopes (twice per day) © K. Fedra 2000

Data Uncertainty ... Examination of testing sizes to: genuine articles: lake: test size 0.001 m 3 lake volume 1,000,000 m 3 show ideas: air quality example: 1 m 3 display cell: 10,000,000 m 3 © K. Fedra 2000

Data Uncertainty ... Calculated befuddle, alignment: research facility tests (restricted inconstancy of forcings, stress) estimation of intermediaries (remote detecting, ground truth) valuation techniques in ecological financial matters (unforeseen valuation, travel cost strategy) © K. Fedra 2000

Data Uncertainty ... A test program permitting US national parks … to raise their expenses has essentially helped incomes without influencing the quantity of guests … Four organizations revealed ... recreational expense incomes about multiplied from 93 M$ in 1996 to 179 M$ in 1998. In the meantime,… .number of guests to destinations with higher charges expanded by 5%. (IHT, December 5, 1998) © K. Fedra 2000

Data Uncertainty ... In rundown: (ecological) perception information can contain expansive mistakes; however they all the more dependably give ranges, appropriations semiquantitative connections imbalances, requirements examples and Gestalt © K. Fedra 2000

Sources of Uncertainty ... Information and perception vulnerability Model

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