Use of weighted least-squares method in evaluation of the relationship between dispersivity and field scale
- Kent State Univ., OH (United States). Dept. of Geology
Regression formulas relating dispersivity and field scale have been suggested in the literature by few researchers, among others: Arya (1986) and Neuman (1990). These studies employ conventional statistical techniques that cannot take into account the relative reliability level of a data point. Neuman (1990), using conventional statistics, discarded the low reliability data obtained by calibrating numerical grid models against solute concentrations of large-scale plumes. Although the numerical modeling data are of low reliability, they are important to consider because of the very limited overall availability of the data. Another problem is with the slope reduction of log{sub 10} {alpha}{sub L} versus log{sub 10} L for large values of L, where L is the field scale, and {alpha}{sub L} is the longitudinal dispersivity. Neuman (1990) used a different line of best fit with a reduced slope for L {ge} 100 m. Fitting two straight lines on a logarithmic scale, one for L {le} 100 m and another one for L {ge} 100 m, takes care of the slope change to some extent, but results in loss of data points for both statistical groups. In order to provide a better statistical model using the available data with varying reliabilities, a weighted least-squares data fitting method was used to define a relationship between dispersivity and field scale. By using this technique, less reliable data points were not simply ignored, but rather assigned a lower weight. The linear model is further improved by fitting a curve through the data drawn on a log{sub 10} {alpha}{sub L} versus log{sub 10} L diagram. The analysis shows a significant difference between the weighted and the unweighted curves. Further analysis indicated that the increase in longitudinal dispersivity is practically negligible when the scale of flow exceeds 1 km.
- Sponsoring Organization:
- USDOE
- OSTI ID:
- 128859
- Journal Information:
- Ground Water, Vol. 33, Issue 6; Other Information: PBD: Nov-Dec 1995
- Country of Publication:
- United States
- Language:
- English
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