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Isoline Retrieval
Isoline retrieval is a remote sensing inverse method that retrieves one or more isolines of a trace atmospheric constituent or variable. When used to validate another contour, it is the most accurate method possible for the task. When used to retrieve a whole field, it is a general, nonlinear inverse method and a robust estimator. For validating advected contours Rationale Suppose we have, as in contour advection, inferred knowledge of a single contour or isoline of an atmospheric constituent, ''q'' and we wish to validate this against satellite remote-sensing data. Since satellite instruments cannot measure the constituent directly, we need to perform some sort of inversion. In order to validate the contour, it is not necessary to know, at any given point, the exact value of the constituent. We only need to know whether it falls inside or outside, that is, is it greater than or less than the value of the contour, ''q0''. This is a classification problem. Let: : j = \begin 1 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Remote Sensing
Remote sensing is the acquisition of information about an object or phenomenon without making physical contact with the object, in contrast to in situ or on-site observation. The term is applied especially to acquiring information about Earth and other planets. Remote sensing is used in numerous fields, including geography, land surveying and most Earth science disciplines (e.g. hydrology, ecology, meteorology, oceanography, glaciology, geology); it also has military, intelligence, commercial, economic, planning, and humanitarian applications, among others. In current usage, the term ''remote sensing'' generally refers to the use of satellite- or aircraft-based sensor technologies to detect and classify objects on Earth. It includes the surface and the atmosphere and oceans, based on propagated signals (e.g. electromagnetic radiation). It may be split into "active" remote sensing (when a signal is emitted by a satellite or aircraft to the object and its reflection dete ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Robust Estimator
Robust statistics are statistics with good performance for data drawn from a wide range of probability distributions, especially for distributions that are not normal distribution, normal. Robust Statistics, statistical methods have been developed for many common problems, such as estimating location parameter, location, scale parameter, scale, and regression coefficient, regression parameters. One motivation is to produce statistical methods that are not unduly affected by outliers. Another motivation is to provide methods with good performance when there are small departures from a Parametric statistics, parametric distribution. For example, robust methods work well for mixtures of two normal distributions with different standard deviations; under this model, non-robust methods like a t-test work poorly. Introduction Robust statistics seek to provide methods that emulate popular statistical methods, but which are not unduly affected by outliers or other small departures from S ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Proxy (statistics)
In statistics, a proxy or proxy variable is a variable that is not in itself directly relevant, but that serves in place of an unobservable or immeasurable variable. In order for a variable to be a good proxy, it must have a close correlation, not necessarily linear, with the variable of interest. This correlation might be either positive or negative. Proxy variable must relate to an unobserved variable, must correlate with disturbance, and must not correlate with regressors once the disturbance is controlled for. Examples In social sciences, proxy measurements are often required to stand in for variables that cannot be directly measured. This process of standing in is also known as operationalization. Per-capita gross domestic product (GDP) is often used as a proxy for measures of standard of living or quality of life. Montgomery ''et al.'' examine several proxies used, and point out limitations with each, stating "In poor countries, no single empirical measure can be expected ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Interpolate
In the mathematical field of numerical analysis, interpolation is a type of estimation, a method of constructing (finding) new data points based on the range of a discrete set of known data points. In engineering and science, one often has a number of data points, obtained by sampling or experimentation, which represent the values of a function for a limited number of values of the independent variable. It is often required to interpolate; that is, estimate the value of that function for an intermediate value of the independent variable. A closely related problem is the approximation of a complicated function by a simple function. Suppose the formula for some given function is known, but too complicated to evaluate efficiently. A few data points from the original function can be interpolated to produce a simpler function which is still fairly close to the original. The resulting gain in simplicity may outweigh the loss from interpolation error and give better performance ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Local Minimum
In mathematical analysis, the maxima and minima (the respective plurals of maximum and minimum) of a function, known collectively as extrema (the plural of extremum), are the largest and smallest value of the function, either within a given range (the ''local'' or ''relative'' extrema), or on the entire domain (the ''global'' or ''absolute'' extrema). Pierre de Fermat was one of the first mathematicians to propose a general technique, adequality, for finding the maxima and minima of functions. As defined in set theory, the maximum and minimum of a set are the greatest and least elements in the set, respectively. Unbounded infinite sets, such as the set of real numbers, have no minimum or maximum. Definition A real-valued function ''f'' defined on a domain ''X'' has a global (or absolute) maximum point at ''x''∗, if for all ''x'' in ''X''. Similarly, the function has a global (or absolute) minimum point at ''x''∗, if for all ''x'' in ''X''. The value of the function a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Optimal Estimation
In applied statistics, optimal estimation is a regularized matrix inverse method based on Bayes' theorem. It is used very commonly in the geosciences, particularly for atmospheric sounding. A matrix inverse problem looks like this: : \mathbf \vec x = \vec y The essential concept is to transform the matrix, A, into a conditional probability and the variables, \vec x and \vec y into probability distributions by assuming Gaussian statistics and using empirically-determined covariance matrices. Derivation Typically, one expects the statistics of most measurements to be Gaussian. So for example for P(\vec y, \vec x), we can write: : P(\vec y, \vec x) = \frac \exp \left -\frac (\boldsymbol \vec - \vec)^T \boldsymbol ^ (\boldsymbol \vec - \vec) \right where ''m'' and ''n'' are the numbers of elements in \vec x and \vec y respectively \boldsymbol is the matrix to be solved (the linear or linearised forward model) and \boldsymbol is the covariance matrix of the vector \vec y. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Neural Network
A neural network is a network or circuit of biological neurons, or, in a modern sense, an artificial neural network, composed of artificial neurons or nodes. Thus, a neural network is either a biological neural network, made up of biological neurons, or an artificial neural network, used for solving artificial intelligence (AI) problems. The connections of the biological neuron are modeled in artificial neural networks as weights between nodes. A positive weight reflects an excitatory connection, while negative values mean inhibitory connections. All inputs are modified by a weight and summed. This activity is referred to as a linear combination. Finally, an activation function controls the amplitude of the output. For example, an acceptable range of output is usually between 0 and 1, or it could be −1 and 1. These artificial networks may be used for predictive modeling, adaptive control and applications where they can be trained via a dataset. Self-learning resulting fro ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Inverse Transform Sampling Method
Inverse transform sampling (also known as inversion sampling, the inverse probability integral transform, the inverse transformation method, Nikolai Smirnov (mathematician), Smirnov transform, or the golden ruleAalto University, N. Hyvönen, Computational methods in inverse problems. Twelfth lecture https://noppa.tkk.fi/noppa/kurssi/mat-1.3626/luennot/Mat-1_3626_lecture12.pdf) is a basic method for pseudo-random number sampling, i.e., for generating sample numbers at random from any probability distribution given its cumulative distribution function. Inverse transformation sampling takes Continuous uniform distribution, uniform samples of a number u between 0 and 1, interpreted as a probability, and then returns the largest number x from the domain of the distribution P(X) such that P(-\infty < X < x) \le u. For example, imagine that is the standard normal distribution with mean zero and standard deviation one. The table below shows samples taken from the u ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nonlinear
In mathematics and science, a nonlinear system is a system in which the change of the output is not proportional to the change of the input. Nonlinear problems are of interest to engineers, biologists, physicists, mathematicians, and many other scientists because most systems are inherently nonlinear in nature. Nonlinear dynamical systems, describing changes in variables over time, may appear chaotic, unpredictable, or counterintuitive, contrasting with much simpler linear systems. Typically, the behavior of a nonlinear system is described in mathematics by a nonlinear system of equations, which is a set of simultaneous equations in which the unknowns (or the unknown functions in the case of differential equations) appear as variables of a polynomial of degree higher than one or in the argument of a function which is not a polynomial of degree one. In other words, in a nonlinear system of equations, the equation(s) to be solved cannot be written as a linear combination of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Conditional Probability Proxy
Conditional (if then) may refer to: *Causal conditional, if X then Y, where X is a cause of Y *Conditional probability, the probability of an event A given that another event B has occurred *Conditional proof, in logic: a proof that asserts a conditional, and proves that the antecedent leads to the consequent *Strict conditional, in philosophy, logic, and mathematics *Material conditional, in propositional calculus, or logical calculus in mathematics * Relevance conditional, in relevance logic *Conditional (computer programming), a statement or expression in computer programming languages *A conditional expression in computer programming languages such as ?: *Conditions in a contract Grammar and linguistics *Conditional mood (or conditional tense), a verb form in many languages *Conditional sentence, a sentence type used to refer to hypothetical situations and their consequences **Indicative conditional, a conditional sentence expressing "if A then B" in a natural language **Cou ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
RTTOV (radiative Transfer Code)
RTTOV - the fast radiative transfer model for calculations of radiances for satellite infrared or microwave nadir scanning radiometers (see push broom scanner). Given an atmospheric profile of temperature, variable gas concentrations, cloud and surface properties RTTOV calculates radiances and brightness temperatures. The only mandatory input is water vapour. Optionally ozone, carbon dioxide, nitrous oxide, methane and carbon monoxide can be variable with all other constituents assumed to be constant. The range of temperatures and water vapour concentrations over which the optical depth computations are valid depends on the training datasets which were used. The spectral range of the RTTOV9.1 model is 3-20 micrometres (500 – 3000 cm-1) in the infrared. RTTOV contains forward, tangent linear, adjoint and K (full Jacobian matrices) versions of the model; the latter three modules for variational assimilation or retrieval applications. One of several applications of RTTOV a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
