[Acoustics] Developing Rating Equations via Multiple Linear Regression

[Daniel Nowacki]

To answer your first request, the two reports are available at:

http://pubs.er.usgs.gov/usgspubs/ofr/ofr97220
http://fl.water.usgs.gov/publications/Abstracts/wri01_4164_hittle.html 
(PDF download at top of page)

Both were accessed via the USGS pubs gateway at http://pubs.usgs.gov

Dan

Daniel J. Nowacki, Hydrologist
U.S. Geological Survey, 430 National Center, Reston, VA 20192
703.648.5467  |  http://water.usgs.gov/nrp/sheetflow/



"Huston, Dave" <dwhuston at water.ca.gov> 
Sent by: acoustics-bounces at simon.er.usgs.gov
04/16/2008 04:47 PM

To
<acoustics at simon.er.usgs.gov>
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Subject
[Acoustics] Developing Rating Equations via Multiple Linear     Regression






Hey All,
 
First off, I'm wondering if anyone out there can send me electronic copies 
of the following USGS reports:
 
1) Patino and Ockerman, 1997, Computations of mean velocity in open 
channels using acoustic velocity meters:  USGS Open-File Report 97-220
2) Hittle, Patino, and Zucker, 2001, Freshwater flow from estuarine creeks 
into north-eastern Florida bay: USGS Water-Resources Investigations Report 
01-4164
 
I've read a couple of papers that discuss the use of multiple linear 
regression for sites where mean channel velocity may not be only function 
of index velocity but also of stage.  This might happen particularly when 
water level changes are large relative to the mean cross-sectional depth. 
Morlock et al. 2002 - USGS Report 01-4157 and Sloat & Hull, 2004, 
Sontek/YSI both reference the above papers.  We have a couple sites that 
seem to fit into this category.  Both of these papers express a common 
form of a regression model for these conditions as:
 
    Vmean = a*Vindex + b*Vindex*Stage + c,
        where a, b, and c are coefficients determined via regression.
 
We have a particular site that doesn't fit the basic regression models 
(linear or quadratic equations) nor does it fit the above model.  However, 
in a discussion with a reputable water resources statistician, he 
mentioned that if one uses "higher order" terms (e.g. Vindex*Stage) within 
a multiple linear regression, that the basic term of the higher order form 
should also be used.  So, for our troublesome site, I ran a multiple 
linear regression of the form:
 
    Vmean = a*Vindex + b*Vindex*Stage + c*Stage + d,
        where a, b, c, and d are coefficients determined via regression.
 
This provided a much better regression model for this site based on 
several measures of quality: adjusted R2, p-statistics, SSE, VIF's, the 
PRESS, Mallow's Cp, and the data are normal based on a probability plot of 
the residuals.  My last question is then, has anyone ever used this form 
of regression equation?  I've never seen it in the literature.  That's 
partly why I'm hoping to read the two papers I'm requesting.
 
Thanks All,
Dave 
 
************************************************
Dave Huston
Water Resources Engineer, P.E.
CA Dept. of Water Resources
Division of Planning and Local Assistance
Central District
901 P Street, Room 313A
Sacramento, CA. 95814
(916) 651-0762 (W)
(916) 651-0766 (Fax)
************************************************
 
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