{"id":61,"date":"2016-06-09T14:34:26","date_gmt":"2016-06-09T14:34:26","guid":{"rendered":"http:\/\/www.uncertain-future.org.uk\/?page_id=61"},"modified":"2016-06-09T20:16:32","modified_gmt":"2016-06-09T20:16:32","slug":"glossary","status":"publish","type":"page","link":"http:\/\/www.uncertain-future.org.uk\/?page_id=61","title":{"rendered":"Glossary"},"content":{"rendered":"

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\nfrom Beven, K J, Environmental Modelling: An Uncertain Future?<\/em> Routledge:London, 2009<\/p>\n

Aleatory Uncertainty<\/strong> The way in which a quantity varies in some random\u00a0stochastic way in a system. Often used in contrast to epistemic\u00a0uncertainty.<\/p>\n

Alpha(<\/strong>a<\/strong>)-cut<\/strong> Use in fuzzy set theory to define a level of uncertainty with\u00a0respect to the range of a degree of membership function (normally [0-1]).<\/p>\n

Autocorrelated Errors<\/strong> A time series of model residuals that exhibit\u00a0correlation at successive time steps. In distributed models, errors might\u00a0be correlated in both space and time.<\/p>\n

Auxiliary conditions<\/strong> The set of variables (and sometimes hypotheses) that\u00a0need to be specified to run a model for a particular case. Includes initial\u00a0conditions, boundary conditions and parameters representing system\u00a0characteristics.<\/p>\n

Axiom<\/strong> a proposition accepted as being fundamentally true on the basis of\u00a0principle, past research, or purely hypothetical speculation. Axioms\u00a0usually that specify something is or is not true and are the foundation for\u00a0deductive reasoning.<\/p>\n

Bayes Equation<\/strong> Equation for calculating a posterior probability given a prior\u00a0probability and a likelihood function. Used in the GLUE methodology to\u00a0calculate posterior model likelihood weights from subjective prior weights\u00a0and a likelihood measure chosen for model evaluation.<\/p>\n

Bayesianism \/ Bayes Explanation<\/strong> Approach in which subjective, empirical\u00a0(inductive) and theoretical (deductive) information can be combined. Fits\u00a0in well with current ideas about the sociological context of science and\u00a0the way it is done in practice.<\/p>\n

Behavioural Simulation<\/strong> A simulation that gives an acceptable reproduction\u00a0of any observations available for model evaluation. Simulations that are\u00a0not acceptable are non-behavioural .<\/p>\n

Blind Validation<\/strong> Evaluation of a model using parameter values estimated\u00a0before the modeller has seen any output data.<\/p>\n

Boundary Conditions<\/strong> Constraints and values of variables required to run a\u00a0model for a particular flow domain and time period. May include input\u00a0variables such as rainfalls and temperatures; or constraints such as\u00a0specifying a fixed head (Dirichlet boundary condition) or impermeable\u00a0boundary (Neumann boundary condition) or specified flux rate (Cauchy\u00a0boundary condition)<\/p>\n

Calibration<\/strong> The process of adjusting parameter values of a model to obtain a\u00a0better fit between observed and predicted variables. May be done\u00a0manually or using an automatic calibration algorithm<\/p>\n

Coherence<\/strong> A principle of probability theory that expresses that observations\u00a0should be used in the best possible way to condition probabilities of a\u00a0possible outcome. Can be applied most rigorously in ideal cases where\u00a0input errors and model structural errors are negligible. Where such\u00a0uncertainties are known to be significant it is not always obvious what is\u00a0the best possible way. A less formal, but more generally useful, definition\u00a0is that observations should not be used to condition probabilities of an\u00a0outcome in a way that is clearly worse than some other conditioning\u00a0process.<\/p>\n

Conditioning<\/strong> The process of refining a model structure, or a distribution of\u00a0parameter values of a model structure as more data become available\u00a0(see also data assimilation and real-time forecasting).<\/p>\n

Confirmation<\/strong> A process of evaluating model outputs to check that a model is\u00a0still providing acceptable simulations. Now preferred to the terms\u00a0validation or verification.<\/p>\n

Copula<\/strong> A method of transformation from a space of scaled unit axes to a\u00a0complex multivariate distribution with dependencies.<\/p>\n

Covariance Matrix<\/strong> A vary of expressing the statistical uncertainty for a set of\u00a0multiple parameters or variables as a square matrix of coefficients. The\u00a0diagonal elements in the matrix represent the variance of each individual\u00a0member of the set; the off-diagonal elements the covariation between\u00a0pairs of members. The higher the degree of covariance, the greater the\u00a0interaction between pairs of parameters or variables. The covariance\u00a0can be scaled to represent correlation between the members.<\/p>\n

Crisp set<\/strong> A set for which the boundaries of the set are defined such that any\u00a0potential member of the set will either be in the set or excluded.<\/p>\n

Data Assimilation <\/strong>The process of using observational data to update model\u00a0predictions (see Chapter 5, also Real-Time Forecasting and Updating)<\/p>\n

Deduction<\/strong> Inference from specific premises to some prediction. Theories\u00a0based on physical assumptions without resort to empirical\u00a0generalisations are examples of deductive reasoning. Examples\u00a0common in mathematics and logic but rare in environmental science.<\/p>\n

Degree of membership<\/strong> An expression of the strength with which a member\u00a0of a fuzzy set is associated with that set. Normally takes the range [0-1],\u00a0with zero values defining the range of support for the fuzzy set.<\/p>\n

Disaggregation \/ Downscaling<\/strong> The process of distributing variables\u00a0calculated at large scales to estimate appropriate values at smaller\u00a0scales. Required, for example, in modelling impacts of climate change\u00a0available at the grid scale of a GCM at scales of local interest.<\/p>\n

Entropy<\/strong> Used here as a measure of information due to Claude Shannon in\u00a01948 using an analogy with thermodynamic entropy.<\/p>\n

Epistemology<\/strong> Study of the possibility and theory of knowledge. Evolutionary\u00a0epistemology embodies the idea that knowledge will be revised and\u00a0improved over time.<\/p>\n

Epistemic Uncertainty<\/strong> The way in which the response of a system varies in\u00a0ways that cannot be simply described by random stochastic variation.\u00a0Often used in contrast to aleatory uncertainty. Also known as Knightian\u00a0<\/strong>uncertainties <\/strong>(after Frank Knight (1885-1872) who himself referred to\u00a0\u201ctrue uncertainties\u201d that could not be insured against, as opposed to risk\u00a0that could be assessed probabilistically, see Knight, 1921)<\/p>\n

Equifinality<\/strong> 1. The concept that there may be many models of a system that\u00a0are acceptably consistent with the observations available, derived from\u00a0the General Systems theory of Ludvig von Bertalanffy (1968) and\u00a0adopted in environmental modelling by Beven (1993, 2006).<\/p>\n

Equifinality<\/strong> 2. The adaption of the von Bertalanffy concept to\u00a0geomporphology by Culling (1957) that that similar landforms might arise\u00a0from different processes and histories.<\/p>\n

Equifinality<\/strong> 3. The nonlinear dynamical systems version later expressed by\u00a0Culling (1987, rejecting his earlier view). Culling distinguished between\u00a0strict equifinality where a perturbed system will return to its original form\u00a0after some transition time and weaker forms in which equifinality implies\u00a0only persistence or stability of some property of the system in its\u00a0trajectory in state space (as might be observed, for example, if there is\u00a0some attractor in state space).<\/p>\n

Extension Principle<\/strong> The extension principle is used in fuzzy theory and\u00a0allows the extrapolation of degrees of membership from members of a\u00a0fuzzy set to functions of the values of those members. Thus if the fuzzy\u00a0set A is defined by the membership values of a discrete set of points in\u00a0X, {x1, x2, x3, \u2026.xn} with membership values {\u03bc(x1), \u03bc(x2), \u03bc(x3), \u2026 \u03bc(xn)},\u00a0then for any other fuzzy set f(A) that is a function of A, membership will\u00a0be defined by the membership values{\u03bc(f(x1)), \u03bc(f(x2)), \u03bc(f(x3)), \u2026\u00a0\u03bc(f(xn))}.<\/p>\n

Falsification<\/strong> Answer to the problem of induction, primarily due to Karl\u00a0Popper. The idea that science proceeds by setting up theories and then\u00a0seeking evidence to falsify them. In a strong version, whereas no\u00a0amount of evidence can completely confirm a theory, one false\u00a0prediction might be sufficient to falsify it. This is the standard model of\u00a0the \u201cscientific method\u201d, which is now recognised to largely an ideal that is\u00a0rarely followed. To avoid falsification, it is more usual to neglect some\u00a0evidence as \u201coutliers\u201d or modify a theory to take account of the new\u00a0evidence, perhaps by changing auxiliary hypotheses or calibration\u00a0parameters.<\/p>\n

Formal likelihood<\/strong> A quantitative measure of the acceptability of a particular\u00a0model or parameter set in reproducing the system response being\u00a0modelled based on a formal parametric function to represent the\u00a0structure of the errors.<\/p>\n

Fuzzy Logic<\/strong> A system of logical rules involving variables associated with a\u00a0continuous fuzzy measure (normally in the range 0 to 1) rather than the\u00a0binary measure (right\/wrong, 0 or 1) of traditional logic. Rules are\u00a0available for operations such as addition and multiplication of fuzzy\u00a0measures and for variables grouped in fuzzy sets. Such rules can be\u00a0used to reflect imperfect knowledge of how a variable will respond in\u00a0different circumstances in terms of the possibilities of potential\u00a0outcomes.<\/p>\n

Fuzzy Measure<\/strong> A degree of membership of a quantity to a fuzzy set (see\u00a0fuzzy logic).<\/p>\n

Fuzzy Set<\/strong> A set of quantities, thought to have something in common, but for\u00a0which membership of the set cannot be described precisely but only\u00a0through a degree or grade of membership or fuzzy measure.<\/p>\n

Genetic algorithm<\/strong> A method of optimisation based on treating parameter\u00a0sets as \u201cgenes\u201d that then \u201cevolve\u201d by melding, mutation, and off-spring\u00a0processes.<\/p>\n

Global optimum<\/strong> A set of parameter values that gives the best fit possible to\u00a0a set of observations<\/p>\n

Heteroscedastic Errors<\/strong> A time series of model residuals that exhibit a\u00a0changing variance over a simulation period (see also Autocorrelated\u00a0Errors)<\/p>\n

Hypothesis<\/strong> A set of propositions about how a system works. Can be\u00a0expressed either qualitatively or as a theory or model.<\/p>\n

History Matching<\/strong> The calibration of a model by adjusting parameter values\u00a0to reduce the differences between observations and predicted variables<\/p>\n

Identifiability<\/strong> The ease with which particular parameter values in a model\u00a0might be calibrated or conditioned by comparing model outputs to\u00a0observed variables (see also calibration and conditioning)<\/p>\n

Incoherence<\/strong> The use of observations to condition probabilities in a way that\u00a0does not properly reflect the information content of the data (see\u00a0coherence).<\/p>\n

Incommensurate\/incommensurability<\/strong> Used here to refer to variables or\u00a0parameters with the same name that refer to different quantities because\u00a0of a change in scale<\/p>\n

Independence<\/strong> Two variables are independent if a change in the value of one\u00a0variable has no effect on the effect of the other.<\/p>\n

Induction<\/strong> The inference from experimental evidence to general theory. The\u00a0\u201cproblem of induction\u201d was originally identified by David Hume (1711-1776). This is that past evidence may not necessary be a good guide to\u00a0future experience (all swans are white\u2026; groundwater flow is\u00a0Darcian\u2026.) so that no theory can ever be verified by induction.<\/p>\n

Informal Likelihood<\/strong> A quantitative, but subjectively chosen, measure of the\u00a0acceptability of a particular model or parameter set in reproducing the\u00a0system response being modelled<\/p>\n

Initial Conditions<\/strong> The auxiliary conditions required at the start of a run of a\u00a0model to define all initial model states.<\/p>\n

Inverse Problem<\/strong> see History Matching<\/p>\n

Learning set<\/strong> A set of observed data used in the calibration of a Neural Net\u00a0model<\/p>\n

Likelihood Measure<\/strong> A quantitative measure of the acceptability of a\u00a0particular model or parameter set in reproducing the system response\u00a0being modelled<\/p>\n

Linearity<\/strong> A model (or model component) is linear if the outputs are in direct\u00a0proportion to the inputs.<\/p>\n

Linguistic uncertainties<\/strong> result from the fact that language, including the\u00a0scientific vocabulary, is often underspecific, ambiguous, vague, context\u00a0dependent, or exhibits theoretical indeterminacies. Linguistic\u00a0uncertainties often overlap with epistemic uncertainties.<\/p>\n

Local Optimum<\/strong> A local peak in the parameter response surface where a set\u00a0of parameter values gives a better fit to the observations than all\u00a0parameter sets around it, but not as good a fit as the global optimum<\/p>\n

Marginal distribution<\/strong> In a multivariate distribution, the marginal distribution\u00a0obtained by integrating over all but the dimension associated with the\u00a0particular variable for which the marginal distribution is required. It is\u00a0the distribution of that variable conditioned on the distributions of all the\u00a0other variables in the multivariate distribution function.<\/p>\n

Model <\/strong>A set of constructs, derived from explicit assumptions, about the how\u00a0a system responds to specified inputs. Quantitative models are normally\u00a0expressed as sets of assumptions and mathematical equations and\u00a0implemented as computer codes.<\/p>\n

Model Space<\/strong> A hyperspace defined by the ranges of feasible models and\u00a0parameter values, with dimensions for each parameter within each\u00a0model.<\/p>\n

Monte Carlo Simulation<\/strong> Simulation involving multiple runs of a model using\u00a0different randomly chosen sets of parameter values<\/p>\n

Multiple Working Hypotheses<\/strong> A scientific method, in the earth sciences\u00a0commonly assigned to T. Chamberlin (1896) and Gilbert (1897), that is\u00a0based on considering all possible explanations of a phenomenon and\u00a0then subjecting each hypothesis to test. Given the limitations of data\u00a0and measurement techniques it may not always be possible to reduce\u00a0the multiple hypotheses to a single explanation.<\/p>\n

Nomological System<\/strong> A formally defined system of theories and concepts in\u00a0science.<\/p>\n

Non-identifiability<\/strong> A expression of the problem of identifying parameter\u00a0values in a model, given limited observational data (see also equifinality)<\/p>\n

Nonlinear <\/strong>A model is nonlinear if the outputs are not in direct proportion to\u00a0the inputs but may vary with intensity or volume of the inputs or with\u00a0antecedent conditions<\/p>\n

Nonparametric Method<\/strong> A method of estimating distributions without making\u00a0any assumptions about the mathematical form of the distribution\u00a0<\/strong><\/p>\n

Nonstationarity<\/strong> A system in which the characteristics are expected to\u00a0change over time; a model in which the parameters are expected to\u00a0change over time.<\/p>\n

Non-uniqueness<\/strong> A expression of the problem of identifying parameter\u00a0values in a model, given limited observational data (see also equifinality)<\/p>\n

Normally Distributed<\/strong> A variable is normally distributed if its distribution can\u00a0be adequately fitted by the Normal or Gaussian distribution function that\u00a0is symmetrical about the mean, bell-shaped and with infinite tails.\u00a0<\/strong><\/p>\n

Objective Function<\/strong> (Performance measure, goodness-of-fit) A measure of\u00a0how well a simulation fits the available observations<\/p>\n

Open system<\/strong> A system defined by uncontrolled boundary conditions that\u00a0involve the exchanges of fluxes (of mass, energy, momentum etc.) with\u00a0the rest of the world. The boundaries of open systems are often defined\u00a0for convenience (for example where a measurement is being made),\u00a0rather because they can be physically well-defined (e.g. a lake).<\/p>\n

Optimisation<\/strong> The process of finding a parameter set that gives the best fit of\u00a0a model to the observations available. May be done manually or using\u00a0an automatic calibration algorithm.<\/p>\n

Over-parameterisation<\/strong> Problem induced by trying to calibrate the parameter\u00a0values of a model that has too many parameters than can be supported\u00a0by the information content of the calibration data<\/p>\n

Parameter<\/strong> A constant that must before defined before running a model\u00a0simulation.<\/p>\n

Parameter Space<\/strong> A space defined by the ranges of feasible model\u00a0parameters, with one dimension for each parameter\u00a0\u00a0<\/strong><\/p>\n

Pareto Optimal Set<\/strong> The set of models in a multi-objective evaluation that are\u00a0not dominated by any other model on at least on one evaluation\u00a0measure i.e. there is no model that performs better on that evaluation\u00a0measure and on another evaluation measure (named after Vilfredo\u00a0Pareto, 1848-1923, who originated the concept of Pareto efficiency in\u00a0economics).<\/p>\n

Pareto front<\/strong> The surface or manifold in the model space that joins all models\u00a0in the Pareto optimal set.<\/p>\n

Parsimony<\/strong> The concept, sometimes known as Occam’s razor, that a model\u00a0should be no more complex than necessary to predict the observations\u00a0sufficiently accurately to be useful<\/p>\n

Perceptual Model<\/strong> A qualitative description of the processes thought to be\u00a0controlling the hydrological response of an area<\/p>\n

Performance Measure<\/strong> (Objective function, goodness-of-fit) A measure of\u00a0how well a simulation fits the available observations<\/p>\n

Possibility <\/strong>A non-statistical measure of the potential for an outcome or\u00a0occurrence of an event as an alternative to probability theory. Used in\u00a0fuzzy set theory, but also has a more general usage (see George Klir,\u00a02006)<\/p>\n

Posterior distribution<\/strong> The statistical distribution of a model parameter or\u00a0output variable after conditioning on the basis of observed data, for\u00a0example, using a calculated likelihood in Bayes equation. In a Bayesian\u00a0learning process, the posterior distribution after one conditioning step\u00a0may become the prior distribution when new observational data are\u00a0made available.<\/p>\n

Prior distribution<\/strong> The statistical distribution of a model parameter or output\u00a0variable assumed or calculated on the basis of only knowledge about the\u00a0characteristics of the system before data are collected.<\/p>\n

Probability<\/strong> A statistical measure of the potential for an outcome or\u00a0occurrence of an event. Many statisticians, most notably Dennis Lindley\u00a0(2006), believe that probability is the only way of expressing uncertainty\u00a0in a potential outcome. There are a variety of foundations for the\u00a0estimation and interpretation of probabilities of which the main examples\u00a0are the Frequentist and the Bayesian views. Frequentists hold that\u00a0probabilities represent the likelihood of outcomes that would be found if it\u00a0possible to take a large number of samples over all potential\u00a0outcomes. Bayesians recognise that this can only ever be an ideal an\u00a0that prior (often subjective) estimates of probabilities might be useful as\u00a0an input to estimating probabilities based on limited amounts of\u00a0evidence.<\/p>\n

Random Sample<\/strong> A set of realisations of a model or variable generated by\u00a0making choices from a feasible range of possibilities drawn by selecting pseudo-random numbers from specified distributions.<\/p>\n

Real-time forecasting<\/strong> The use of a model to make predictions into the near\u00a0future (over some lead time), taking account of data becoming available\u00a0as the forecasting period progresses (see also data assimilation and\u00a0updating). Includes numerical weather prediction and models used for\u00a0flood forecasting (see Chapter 5).\u00a0\u00a0<\/strong><\/p>\n

Recursive estimation<\/strong> A form of model calibration and uncertainty estimation\u00a0based on updating time step by time step as new observations become available. Commonly used in data assimilation and real-time\u00a0forecasting.<\/p>\n

Response Surface<\/strong> The surface defined by the values of an objective function\u00a0as it changes with changes in parameter values. May be thought of\u00a0conceptually as a surface with ”peaks” and ”troughs” in the\u00a0multidimensional space defined by the parameter dimensions, where the\u00a0”peaks” represent good fits to the observations and the ”troughs”\u00a0represent poor fits to the observations (see also Parameter Space)<\/p>\n

Risk<\/strong> Uncertainty about responses of a real world system that can be\u00a0characterised in terms of probabilities. There is an ISO Standard on\u00a0Risk Management Terminology (ISO, 2002) that uses the definition that\u00a0risk is the combination of the probability of an event and its\u00a0consequence, but the term is often used more generally.\u00a0\u00a0<\/strong><\/p>\n

Risk Analysis<\/strong> The process of identifying sources of risk and assigning\u00a0values of risk.<\/p>\n

Risk Communication<\/strong> The process of exchanging and translating information\u00a0about risk between different stakeholder groups and decision-makers\u00a0<\/strong><\/p>\n

Robustness<\/strong> A decision is robust to future uncertainty if it leaves open the\u00a0possibility of alternative strategies as the future unfolds.<\/p>\n

Sensitivity<\/strong> The response of a model to a change in a parameter or input\u00a0variable. Can either be assessed locally in the model space (when it is\u00a0normally quantified as a gradient as a normalised rate of change of a\u00a0model output to the rate of change of the parameter or input variable) or\u00a0over a global sample of points in the model space.\u00a0\u00a0<\/strong><\/p>\n

Simulated annealing<\/strong> A method of optimisation based on an analogy with the \u00a0organisation of molecules in cooling liquid metal. Initially there is a\u00a0random scatter of parameter sets but as the \u201ctemperature\u201d cools, the\u00a0optimisation is becomes more and more structured. Useful when\u00a0searching for a global optimum when there may be many local optima.<\/p>\n

Stakeholder<\/strong> A individual, group or community who might be affected by the\u00a0outcome of a decision making process<\/p>\n

State Space<\/strong> The space of potential trajectories of a model (or, in a more\u00a0limited sense, of a particular variable in a model).<\/p>\n

Stochastic model<\/strong> A model that contains random elements as a way of\u00a0expressing uncertainty in inputs, system characteristics, or model\u00a0response. Often constructed by proposing a certain (simple) structure\u00a0for perturbations around some mean or control simulation. Introduces\u00a0additional parameters within the stochastic structure to define the\u00a0magnitude of the likely perturbations. Additive perturbations are often\u00a0assumed for simplicity (but multiplicative perturbations can be\u00a0transformed to an additive form by taking logs). If it is expected that the\u00a0nature of the perturbations will change (e.g. with heteroscedastic\u00a0variance) then more parameters will be required to represent such\u00a0changes.<\/p>\n

Support<\/strong> of a Fuzzy Set The range of possible values that will have degree of\u00a0membership greater than zero in a fuzzy set.<\/p>\n

System<\/strong> A part of the world that has been identified for study or for a\u00a0decision. Occupies some physical space, some time period, and is\u00a0separated from the rest of the world by the specification of certain\u00a0boundary conditions. Environmental systems are usually open systems.<\/p>\n

Theory<\/strong> A set of constructs, derived from explicit assumptions, about the\u00a0nature of the world. Formal theories are normally expressed as\u00a0mathematical axioms and equations.<\/p>\n

Trans-science<\/strong> The idea, proposed by Alvin Weinberg in 1972, that some\u00a0subjects, generally held to be within the realm of science, may not be\u00a0open to rigorous scientific study. Arguably, this applies to very many\u00a0environmental systems where boundary conditions cannot be controlled,\u00a0experiments are necessarily place and time specific (see uniqueness of\u00a0place), and details of processes are not fully known.<\/p>\n

Transfer Function<\/strong> A representation of the output from a system due to a unit\u00a0input<\/p>\n

Utility function<\/strong> An expression of the benefits arising from implementing\u00a0different levels of investment (costs) in formal decision making.<\/p>\n

Underdetermination thesis<\/strong> A theory (or model) is underdetermined if there\u00a0is at least one other theory (or model) that is equally compatible with the\u00a0available empirical evidence (observations with which a model can be\u00a0compared).<\/p>\n

Unknowabilty<\/strong> The concept that because of limitations of current\u00a0measurement techniques there is much about environmental systems\u00a0that cannot feasibly be known.<\/p>\n

Updating<\/strong> The process of using data available now to condition forecasts of a\u00a0variable into the future but changing values of parameters or state\u00a0variables in the model. A form of data assimilation, commonly used in\u00a0real-time forecasting. Includes different types of Kalman filter, and Variational data assimilation<\/p>\n

Validation <\/strong>1. A process of evaluation of models to confirm that they are\u00a0acceptable representations of a system. Philosphers of science have\u00a0some problems with the concept of validation and verification (e.g.\u00a0Oreskes et al., 1994) and it may be better to use ”evaluation” or\u00a0”confirmation” rather than validation or verification (which imply a degree\u00a0of truth in the model).<\/p>\n

Validation<\/strong> 2. Validation is sometimes used in the much more restrictive\u00a0sense of \u00a0validation of a computer code (mode) to show that it does\u00a0produce accurate solutions of the equations on which it is based. For\u00a0complex models this can also be difficult to show in practice.<\/p>\n

Variogram<\/strong> A spatial correlation function used in geostatistics, normally\u00a0plotted as the variance at different distances between points in a random\u00a0field. Normally increases with distance, up to the \u201crange\u201d where variance\u00a0becomes constant. If variance continues to increase with distance, the\u00a0field may be nonstationary (or fractal). Sometimes fitted by a functional\u00a0form that includes a random effect at zero distance, the \u201cnugget\u00a0variance\u201d. Underlies the Kriging method of spatial interpolation in\u00a0geostatistics. To estimate a variogram without a significant degree of\u00a0uncertainty requires a large number of measured values, more if the\u00a0measurements suggest that the correlation might vary with direction.<\/p>\n

Verification<\/strong> see Validation<\/p>\n

Verisimilitude<\/strong> A term used to express the concept of relative truthfulness of\u00a0false theories. The term was used by Karl Popper (1963), but his notion\u00a0of verisimilitude has since been criticised (e.g. by Tichy, 1974).<\/p>\n","protected":false},"excerpt":{"rendered":"

from Beven, K J, Environmental Modelling: An Uncertain Future? Routledge:London, 2009 Aleatory Uncertainty The way in which a quantity varies in some random\u00a0stochastic way in a system. Often used in contrast to epistemic\u00a0uncertainty. Alpha(a)-cut Use in fuzzy set theory to define a level of uncertainty with\u00a0respect to the range of a degree of membership function … Continue reading Glossary<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-61","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"http:\/\/www.uncertain-future.org.uk\/index.php?rest_route=\/wp\/v2\/pages\/61","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/www.uncertain-future.org.uk\/index.php?rest_route=\/wp\/v2\/pages"}],"about":[{"href":"http:\/\/www.uncertain-future.org.uk\/index.php?rest_route=\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"http:\/\/www.uncertain-future.org.uk\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/www.uncertain-future.org.uk\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=61"}],"version-history":[{"count":5,"href":"http:\/\/www.uncertain-future.org.uk\/index.php?rest_route=\/wp\/v2\/pages\/61\/revisions"}],"predecessor-version":[{"id":95,"href":"http:\/\/www.uncertain-future.org.uk\/index.php?rest_route=\/wp\/v2\/pages\/61\/revisions\/95"}],"wp:attachment":[{"href":"http:\/\/www.uncertain-future.org.uk\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=61"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}