Revision History for Scientific Investigations Report 2015–5019–F
Roy Sando, Steven K. Sando, Peter M. McCarthy, and DeAnn M. Dutton
Methods for Estimating Peak-Flow Frequencies at Ungaged Sites in Montana Based on Data through Water Year 2011: Chapter F in Montana StreamStats
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Posted online April 6, 2016
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Revised and reposted February 6, 2018, version 1.1
The text version was modified. Text was changed in the abstract on page 1 to include weighted least squares as part of the methods used. Text was added on page two to indicate the weighted least squares method was used and to provide a reference for the method. The section heading on page 10 was changed from "Generalized Least Squares Regression Analysis" to "Regional Regression Analysis." The first paragraph in this section was changed to indicate the weighted least squares method was used in the Northwest hydrologic region and to provide context for this analysis. A new level 4 section heading titled "Generalized Least Squares Regression Analysis" was added on page 10. A new paragraph that explains why weighted least squares were used in the Northwest hydrologic region was added on page 10. A new level 4 section titled "Weighted Least Squares Regression Analysis" was added on page 10 to describe the weighted least squares analysis used in the Northwest hydrologic region. The section heading "Regional Regression Equations" was removed on page 10. The reference to Helsel and Hirsch (2002) was removed on page 11. Text was added to the covariance matrix definition to indicate the same variable combination is used to represent the covariance matrices for the regression equations developed using weighted least squares regression. Text on page 16 was changed to incorporate changes in the results compared to previous studies because of the change in methods from generalized least squares regression to weighted least squares regression. Text was added on page 16 to indicate weighted least squares regression and generalized least squares regression were used. Text was modified on page 23 to indicate the example basin had a SLP30 value of 0.05 percent, instead of 5 percent. The equation number for equation 7 was moved to be aligned with the equation. Text was added on page 25 to indicate weighted least squares regression and generalized least squares regression were used. Reference to weighted least squares regression method was added to page 27. Text was added to appendix 1 to include weighted least squares regression.
Changes were made to figure 3 to show updated standard errors of prediction for the Northwest hydrologic region from this study.
Changes were made to table 3 to indicate that mean annual precipitation ("P") was removed as an explanatory variable in the Northwest hydrologic region.
The following changes were made to table 4:
Under the heading "SEP of regression equation for 1-percent annual exceedance probability," the subheading "Omang (1992)" was added and values were included for each of the hydrologic regions.
For the Northwest hydrologic region:
o Changed the explanatory variables to “A” for “this report,”
o Changed the “mean SEP of regression equations” for “this report” to 36.7, and
o Changed the “SEP of regression equation for 1-percent annual exceedance probability” for “this report” to 13.6.
In appendix table 1–3, all values for P in the Northwest hydrologic region were changed to "--" to indicate that precipitation was not used as an explanatory variable.
The following changes were made to appendix table 1–4:
· The title was changed to “Table 1–4. Final generalized least squares (GLS) and weighted least squares (WLS) regression equations for estimating peak-flow frequencies at ungaged sites in Montana.”
· In the definitions of abbreviations in the headnote, “Pseudo R2, pseudo coefficient of determination;” was changed to “Pseudo R2, pseudo coefficient of determination presented for generalized least squares regression analysis; Adjusted R2, adjusted coefficient of determination presented for weighted least squares regression analysis.”
· The heading for column G was changed from “Pseudo R2, in percent” to “Pseudo or adjusted R2, in percent.”
· In appendix table 1–4, the 4th equation under the "Southwest hydrologic region" spanner, the exponent at the end was changed from positive (0.088) to negative (-0.088), which affected values in appendix table 1–2 of chapter D.
· Footnote 2 was added behind “West hydrologic region,” “Northwest Foothills hydrologic region,” “Northeast Plains hydrologic region,” “East-Central Plains hydrologic region,” “Southeast Plains hydrologic region,” “Upper Yellowstone-Central Mountain hydrologic region,” and “Southwest hydrologic region” in the hydrologic region headings.
· Footnote 3 was added behind “Northwest hydrologic region” in the hydrologic region headings.
· Footnote 2 was added to the footnotes and defined as “Regression equations were developed using generalized least squares regression analyses.”
· Footnote 3 was added to the footnotes and defined as “Regression equations were developed using weighted least squares regression analyses.”
· All values for each recurrence interval equation were changed in the Northwest hydrologic region except the “Number of streamflow-gaging stations.”
The following changes were made to appendix table 1–5:
· Footnote 1 was added behind “West hydrologic region,” “Northwest Foothills hydrologic region,” “Northeast Plains hydrologic region,” “East-Central Plains hydrologic region,” “Southeast Plains hydrologic region,” “Upper Yellowstone-Central Mountain hydrologic region,” and “Southwest hydrologic region” in the hydrologic region headings.
· Footnote 2 was added behind “Northwest hydrologic region” in the hydrologic region headings.
· Footnote 1 was added to the footnotes and defined as “Covariance matrices were calculated using generalized least squares regression analysis.”
· Footnote 2 was added to the footnotes and defined as “Covariance matrices were calculated using weighted least squares regression analysis.”
· All values for the Northwest hydrologic region were updated.