According to Professor Running in surface-water hydrology, which named technique is specifically recommended for extending a river discharge (rating) curve beyond measured stages?

Introduction / Context:
Hydrologists often need to extend a stage–discharge (rating) curve to high flows where direct discharge measurements are sparse or unsafe. Professor Running is associated with a specific named approach used for this extrapolation problem in river engineering and water-resources analysis.

Given Data / Assumptions:

• Objective: identify the method attributed to Professor Running for extending rating curves.
• Context: stage–discharge relation must be extrapolated to higher stages.
• Assume steady, gradually varied flow conditions typical for rating-curve development.

Concept / Approach:
Rating curves frequently show a near log-linear behavior when plotted suitably. The Running recommendation is the logarithmic method, which fits a logarithmic form to the measured portion and then extends beyond the observed range more conservatively than naive linear power-fit extrapolations. This helps avoid unrealistic high-flow estimates.

Step-by-Step Solution:

Verification / Alternative check:
Standard hydrology references list logarithmic extrapolation for rating curves; the other listed options are not established named methods associated with Running, supporting the choice.

Why Other Options Are Wrong:

• Y method: Not a standard named method for rating-curve extension.
• General method: Too vague; not attributed to Running.
• None of these: Incorrect because a specific method is known and listed.

Common Pitfalls:

• Using high-order polynomials that overshoot at flood stages.
• Forgetting to check backwater, controls, or overbank effects when extending curves.
• Assuming a single functional form applies across all stages without breakpoints.

Final Answer:
Logarithmic method