Level of Analysis and Methods

Examples

References

Design of Experiments

Factor analysis

Raw Data Criticism

Double mass analysis

Parametric tests (Anderson test)

Nonparametric tests Variance ratio test, Bartlett's test, et al. Wilcoxon, Mann-Whitney, Kruskal-Wallis, Wilks tests

Statistical parameters Arithmetic mean (or geometric mean for data lognormally distributed) Variance or standard deviation Ranges

Pearson's and Fisher's coefficients

Point-Frequency Analysis

Empirical frequency plotting

Probability papers Plotting formulae

Theoretical probability (distributions discrete and continuous)

Method of moments Method of maximum likelihood Hypothesis testing and confidence intervals

Tests of means and variances Goodness-of-fit tests

Multivariate Analysis

Simple Regression Analysis best fit procedure choice tests of fit spurious correlations

Choosing experimental catchments or measuring sites for a given experimental program: land uses catchments parameters water quality sampling

Choosing number of experiments using physical models

Testing for systematic errors in time data series such as cumulative rainfall or runoff depths at various points in the same climatic areas

Testing the random aspect of a data series such as rainfall and runoff

Testing of the hypothesis on equal variance of two populations: rainfall runoff, runoff quality data

Testing of the hypothesis on equal means and identical location of population: rainfall or runoff, runoff quality data from several catchments

Comparison of samples and homogeneity testing

Parameters can be time and/or flow weighted for runoff quality data

Preliminary statistical analysis

Analysis of a separate variable considered as a random variable:

rainfall depths for various time intervals

(I.D.F. curves) peak runoff risk analysis Choice of a theoretical probability distribution Almost all hydrological variables (rainfall, runoff, quantity, quality) considered as a random variable

Testing the adequacy of a given probability distribution to a given sample

Applied to a pair of hydrological variables rainfall and runoff volumes runoff coefficients and imperviousness rainfall depths at two sites overland flow detention storage and discharge pollutants loads and peak runoff etc.

Cochran & Cox, 1957; Kendall & Stuart, 1973; Snedecor & Cochran, 1957

Bennet & Franklin, 1967; Dagnelie, 1970; Haan, 1977; Pearson & Hartley, 1969 Dagnelie, 1970; Kendall & Stuart, 1973; Kite, 1976; Pettitt, 1979

Adamowski, 1981; Bennet & Franklin, 1967; Cunnane, 1973; Dagnelie, 1970; Haan, 1977; Kendall & Stuart, 1977a; Kite, 1976; Snedecor & Cochran, 1957; Yevjevich, 1972b

Chow, 1964; Dagnelie, 1970; Gumbel, 1960; Haan, 1977; Kendall & Stuart, 1977a; Kite, 1976; Linsley et al., 1975; Snedecor & Cochran, 1957; Viessman et al., 1977; Yevjevich, 1972b Chow, 1964; Dagnelie, 1970; Haan, 1977; Kendall & Stuart, 1977a; Kendall & Stuart, 1973; Kite, 1976; Snedecor & Cochran, 1957; Yevjevich, 1972b

Chatfield & Collins, 1980; Haan, 1977; Morrison, 1976; Draper & Smith, 1966; Haan, 1977; Viessman et al., 1977

Continued

Level of Analysis and Methods

Examples

References

Multivariate probability distributions

Simple matrix procedure of best fit Stepwise regression procedure Orthogonal regression procedure Ridge regression procedure Cross validation procedure Better results when Xi variables are correlated

Interdependence analysis

Correlation analysis Principal components analysis (P.C.A.)

Factor analysis

Cluster analysis Discriminant analysis

Time Series Analysis

Trend analysis Tests of randomness Least squares procedures Moving average methods Periodic analysis

Spectral analysis on the time domain (Autocorrelation function) Spectral analysis on the frequency domain (Spectral density function)

Applied to several independent variables considered to be purely random variables risk analysis in urban water management spatial rainfall depths distribution hydrological stochastic processes (discrete and continuous)

Applied to one explained variable Y and to several explanatory variables Xi:

interpolation between a set of raingauges generation of data for incomplete data series rainfall-runoff modeling at a given location versus rainfall and/or runoff at other locations runoff coefficients versus urban catchment parameters and rainfall characteristics lag times and times of concentration versus catchments and rainfall parameters Urban runoff pollutant loads versus rainfall and runoff parameters, catchment characteristics such as land uses, imperviousness, slopes, etc. Mostly for qualitative analysis. Not frequently applied in urban hydrology Just two variables

More than two variables: reduction of dimensionality, preliminary analysis for regression procedures. Sometimes quantitative spatial distribution of rainfall urban runoff pollutants loads Similar aims as P.C.A. but with assumption of a proper statistical model. Covariance analysis Grouping tests of individuals Separation of individuals in two populations.

Preliminary analysis for regression procedures Testing the random aspect of a given variable for preliminary statistical analysis

Stochastic modelling of hydrological processes (not very frequent in urban hydrology due to time and space intervals to be considered) Testing gradual natural or man-induced changes in data series

Changes in urban hydrological data due to continuous urbanization Testing the existence of cycles:

Seasonal aspects of rainfall, runoff, quality, quantity data Short cycles due to some industrial or domestic water uses

Testing the random aspect of a given process

Identifying Instantaneous Unit Hydrographs (IHU) for small urbanized catchments

Adamowski, 1981; Dagnelie, 1970; Kendall & Stuart, 1977a; Kite, 1976; Yevjevich, 1972a; Yevjevich, 1972b

Chatfield & Collins, 1980; Draper & Smith, 1966; Haan, 1977; Pearson & Hartley, 1969; Robitaille and Bobbee, 1975; Stone, 1974; Yevjevich, 1972a

Chatfield & Collins, 1980; Haan, 1977; Morrison, 1976

Bartlett, 1966; Box & Jenkins, 1970; Cox & Miller, 1968; Jenkins & Watts, 1968; Kendall & Stuart, 1977b; Yevjevich, 1972a orifice. The static pressure may be measured either by the inclined manometer or pressure tranducer devices. Some devices are available with internal PROMs for flow data reduction. In fast flowing water, the dip tube may be protected by a simple still well: a concentrically placed perforated tube. Shortcomings include contaminant build-up on the dip tube in the vicinity of the measuring tube, and relatively low accuracy in the total part of the total pressure range.

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