A Model to Describe the Inherent Spatial and Temporal Variability of Parameters in Lake Ontario 1974

El‐Shaarawi, A. H.; Kwiatkowski, R.E.

doi:10.1016/s0380-1330(77)72246-4

Cited by 29 publications

(9 citation statements)

References 4 publications

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“…The water quality of Lake Huron and Georgian Bay-North Channel continues to be characterized by a large offshore area of low concentrations of both the chemical and biological parameters measured. This is comparable to the findings on Lake Superior (Kwiatkowski 1980) and in contrast to analysis done on Lake Ontario by E1-Shaarawi & Kwiatkowski (1977) which indicated that large nearshore areas of significantly higher concentrations exist. Nearshore regions in the present study were spatially intermittent and localized around point sources as previously described by Kwiatkowski (1980).…”

Section: Discussionsupporting

confidence: 87%

“…Significant (p /> 0.01) temporal F(1) and spatial F(2) differences existed, with the temporal variability being much more pronounced (12 to 500 times) than the spatial variability. Similar findings were obtained by Kwiatkowski (1980) for Lake Superior, Lake Huron, and Georgian Bay-North Channel, and by E1-Shaarawi & Kwiatkowski (1977) for Lake Ontario. The zonations developed from the model, for each parameter studied, are given in Figs.…”

Section: Resultssupporting

confidence: 80%

“…A hierarchical classification procedure using estimates of spatial effects is then applied to divide the lake into statistically homogeneous zones. Application of the model on a variety of biological and chemical parameters was done by E1-Shaarawi & Kwiatkowski (1977) for Lake Ontario, and by Kwiatkowski (1980) for the Upper Great Lakes (Superior, Huron and Georgian Bay-North Channel). In the present study, as in the previous study done by Kwiatkowski (1980), the model was used to establish zones which were significantly different from one another at the 10% level (p ~> 0.10).…”

Section: Methodsmentioning

confidence: 99%

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Comparison of 1980 Lake Huron, Georgian Bay - North Channel surveillance data with historical data

Kwiatkowski¹

1984

Hydrobiologia

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A statistical regionalization procedure was used to delineate significantly (p t> 0.10) different areas, for a variety of surveillance parameters measured in 1980 in Lake Huron and Georgian Bay-North Channel. The analyses performed were compared with similar analyses done on 1971 (Lake Huron) and 1974 (Georgian Bay North Channel) data. The regions produced from the 1980 analyses compared favourably with the 1971 and 1974 analyses. Significant

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Section: Discussionsupporting

confidence: 87%

Section: Resultssupporting

confidence: 80%

Section: Methodsmentioning

confidence: 99%

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Comparison of 1980 Lake Huron, Georgian Bay - North Channel surveillance data with historical data

Kwiatkowski¹

1984

Hydrobiologia

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“…The diversity values were subjected to a regression model developed by El-Shaarawi & Kwiatkowski (1977) to study the spatial and temporal differences in the data . The model uses the family of transformations suggested by Cox & Box (1964) so that the transformated data approximately satisfy the assumptions required for the application of the analysis of variance : ie.…”

Section: Methodsmentioning

confidence: 99%

“…The model uses the family of transformations suggested by Cox & Box (1964) so that the transformated data approximately satisfy the assumptions required for the application of the analysis of variance : ie. the mean value can be expressed as a linear combination of the influencing factors ; constancy of variance; additivity of the error term ; and normality of distribution (El-Shaarawi & Kwiatkowski, 1977) . An additive linear model with seasonal and spatial components is then fitted to the transformed data .…”

Section: Methodsmentioning

confidence: 99%

The use of the Shannon-Wiener diversity index to delineate the horizontal distribution of crustacean zooplankton communities in Lake Superior, 1973

Kwiatkowski

1980

Hydrobiologia

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The Shannon-Wiener diversity index was calculated for the total zooplankton community found in Lake Superior in 1973, as well as for its components (ie . Calanoida, Cyclopoida, Cladocera and nauplii) . These values were then subjected to a model to develop statistically homogeneous zones, and to determine the temporal and spatial variability of the diversity values . A region roughly following the loo meter depth profile and having an average yearly temperature of 9 .8°C was found to exist along the south and southwestern shores of Lake Superior . In this region significantly (P > o .lo) higher diversity indices were found .

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Model clustering and its application to water quality monitoring

Zhu

El‐Shaarawi²

2008

Environmetrics

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SUMMARYThe classification of objects into groups where the objects within a group share a set of common traits is important in many areas of applications and particularly in environmental pollution studies. Consider the situation where variables are measured on different occasions for each of K objects, and the objective is to classify these objects into groups according to some common characteristics. The procedure introduced in this paper consists of two aspects: model fitting and clustering. The model fitting selects a family of models which is appropriate for the structure and nature of the available measurements, and then is performed for both individual and pooled datasets. The clustering starts with K models that represent the K objects and thus the similarity of the objects reduces to the similarity of their models. Since the models are members of the same family, the models similarity is defined as the equality of their parameters of interest. Here, we partition the parameter vector into two sub-vectors corresponding to the interested parameters and ancillary parameters. The clustering will group together objects that have common interested parameters while allowing the ancillary parameters to be object specifics. The p-value associated with the proposed model linking test is used as the similarity measure. Several grouping strategies are proposed like cluster peeling, pairwise combining, as well as a speeding technique called splitting-and-binding. A small simulation study is used to demonstrate the utility of the method. The paper concludes by presenting an environmental application where the interest is to classify E. coli bacteria according to their responses to antibiotic treatments. The data were collected bi-weekly at several locations within three Canadian watersheds during 2005. Metric closeness in parameter space used by conventional method and likelihood closeness in model space employed by model clustering are discussed in this application.

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A Model to Describe the Inherent Spatial and Temporal Variability of Parameters in Lake Ontario 1974

Cited by 29 publications

References 4 publications

Comparison of 1980 Lake Huron, Georgian Bay - North Channel surveillance data with historical data

Comparison of 1980 Lake Huron, Georgian Bay - North Channel surveillance data with historical data

The use of the Shannon-Wiener diversity index to delineate the horizontal distribution of crustacean zooplankton communities in Lake Superior, 1973

Model clustering and its application to water quality monitoring

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