Statistical Prediction of Changes in Water Resources Trends Based on Set Pair Analysis
Antecedent physical factors are used in calculations, which endowed set pair analysis with predictive abilities. Set pair analysis can make predictions based on calculations using antecedent physical factors. In this study, the fitted value <InlineEquation ID="IEq1"> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <msub> <mover accent="true"> <mi mathvariant="italic">Y</mi> <mo stretchy="true">^</mo> </mover> <mn>1</mn> </msub> </math> </EquationSource> <EquationSource Format="TEX">$$ {\widehat{Y}}_1 $$</EquationSource> </InlineEquation> based on set pair analysis agreed with the actual value of the average annual discharge grade at Yamadu Station, which showed that the prediction was valid. It’s predicted that the average annual discharge at Yamadu Station in 1975 was a dry year, i.e. y > 385 m<Superscript>3</Superscript>/s, while the actual average annual discharge at Yamadu Station in 1975 was 301 m<Superscript>3</Superscript>/s, which confirmed the prediction that it was a dry year. Three physical factors were not processed using set pair analysis so they could be compared with the calculated results. These factors were used directly to establish a regression equation for the average annual discharge grade and obtained a fitted value of <InlineEquation ID="IEq2"> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <msub> <mover accent="true"> <mi mathvariant="italic">Y</mi> <mo stretchy="true">^</mo> </mover> <mn>3</mn> </msub> </math> </EquationSource> <EquationSource Format="TEX">$$ {\widehat{Y}}_3 $$</EquationSource> </InlineEquation> for the average annual discharge grade at Yamadu Station during 1953–1974. It’s known that the prediction of the average annual discharge grade for 1966 using a regression equation derived from the data differed from the actual situation, thereby indicating that set pair analysis can be used to improve the accuracy of predictions. Copyright Springer Science+Business Media Dordrecht 2014
