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Kling–Gupta Efficiency
The Kling–Gupta efficiency (KGE) is a goodness-of-fit indicator widely used in the hydrologic sciences for comparing simulations to observations. It was created by hydrologic scientists Harald Kling and Hoshin Vijai Gupta. Its creators intended for it to improve upon widely used metrics such as the coefficient of determination and the Nash–Sutcliffe model efficiency coefficient. : \text =1-\sqrt where: * r is the Pearson correlation coefficient In statistics, the Pearson correlation coefficient (PCC) is a correlation coefficient that measures linear correlation between two sets of data. It is the ratio between the covariance of two variables and the product of their standard deviatio ..., * \alpha is a term representing the variability of prediction errors, * \beta is a bias term. The terms \alpha and \beta are defined as follows: : \beta=\frac where: * \mu_s is the mean of the simulated time series (e.g.: flows predicted by the model) * \mu_o is the mean of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Goodness-of-fit
The goodness of fit of a statistical model describes how well it fits a set of observations. Measures of goodness of fit typically summarize the discrepancy between observed values and the values expected under the model in question. Such measures can be used in statistical hypothesis testing, e.g. to test for normality of residuals, to test whether two samples are drawn from identical distributions (see Kolmogorov–Smirnov test), or whether outcome frequencies follow a specified distribution (see Pearson's chi-square test). In the analysis of variance, one of the components into which the variance is partitioned may be a lack-of-fit sum of squares. Fit of distributions In assessing whether a given distribution is suited to a data-set, the following tests and their underlying measures of fit can be used: *Bayesian information criterion *Kolmogorov–Smirnov test *Cramér–von Mises criterion *Anderson–Darling test * Berk-Jones tests *Shapiro–Wilk test *Chi-squared tes ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hydrologic Sciences
Hydrology () is the scientific study of the movement, distribution, and management of water on Earth and other planets, including the water cycle, water resources, and drainage basin sustainability. A practitioner of hydrology is called a hydrologist. Hydrologists are scientists studying earth or environmental science, civil or environmental engineering, and physical geography. Using various analytical methods and scientific techniques, they collect and analyze data to help solve water related problems such as environmental preservation, natural disasters, and water management. Hydrology subdivides into surface water hydrology, groundwater hydrology (hydrogeology), and marine hydrology. Domains of hydrology include hydrometeorology, surface hydrology, hydrogeology, drainage-basin management, and water quality. Oceanography and meteorology are not included because water is only one of many important aspects within those fields. Hydrological research can inform environment ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Coefficient Of Determination
In statistics, the coefficient of determination, denoted ''R''2 or ''r''2 and pronounced "R squared", is the proportion of the variation in the dependent variable that is predictable from the independent variable(s). It is a statistic used in the context of statistical models whose main purpose is either the prediction of future outcomes or the testing of hypotheses, on the basis of other related information. It provides a measure of how well observed outcomes are replicated by the model, based on the proportion of total variation of outcomes explained by the model. There are several definitions of ''R''2 that are only sometimes equivalent. In simple linear regression (which includes an intercept), ''r''2 is simply the square of the sample ''correlation coefficient'' (''r''), between the observed outcomes and the observed predictor values. If additional regressors are included, ''R''2 is the square of the '' coefficient of multiple correlation''. In both such cases, the coeffi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nash–Sutcliffe Model Efficiency Coefficient
The Nash–Sutcliffe model efficiency coefficient (NSE) is used to assess the predictive skill of hydrological models. It is defined as: : \text =1-\frac where \overline_o is the mean of observed discharges, Q_m^t is modeled discharge at time ''t'', and Q_o^t is observed discharge at time ''t''. The Nash–Sutcliffe efficiency is calculated as one minus the ratio of the error variance of the modeled time-series divided by the variance of the observed time-series. In the situation of a perfect model with an estimation error variance equal to zero, the resulting Nash–Sutcliffe Efficiency equals 1 (''NSE'' = 1). Conversely, a model that produces an estimation error variance equal to the variance of the observed time series results in a Nash–Sutcliffe efficiency of 0.0 (NSE = 0). In reality, NSE = 0 indicates that the model has the same predictive skill as the mean of the time-series in terms of the sum of the squared error. In the case of a m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pearson Correlation Coefficient
In statistics, the Pearson correlation coefficient (PCC) is a correlation coefficient that measures linear correlation between two sets of data. It is the ratio between the covariance of two variables and the product of their standard deviations; thus, it is essentially a normalized measurement of the covariance, such that the result always has a value between −1 and 1. As with covariance itself, the measure can only reflect a linear correlation of variables, and ignores many other types of relationships or correlations. As a simple example, one would expect the age and height of a sample of children from a school to have a Pearson correlation coefficient significantly greater than 0, but less than 1 (as 1 would represent an unrealistically perfect correlation). Naming and history It was developed by Karl Pearson from a related idea introduced by Francis Galton in the 1880s, and for which the mathematical formula was derived and published by Auguste Bravais in 1844. The nami ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
