Hydrologic plots and their interpretation: Which statements about hydrographs and mass curves are correct?
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AA hydrograph is a plot of discharge versus time at a specific location in a stream.
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BA mass curve plots accumulated flow (volume) versus time and therefore always rises.
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CThe slope of a mass curve at any instant equals the inflow (discharge) rate at that time.
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DAll of the above
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ENone of the above
Answer
Correct Answer: All of the above
Explanation
Introduction / Context:Hydrographs and mass curves are foundational tools in surface hydrology for analyzing stream response to rainfall, designing reservoirs, and determining storage requirements. Understanding what each plot represents is essential for correct design and operations.
Given Data / Assumptions:
- Hydrograph: time on x-axis, discharge on y-axis.
- Mass curve: cumulative volume on y-axis, time on x-axis.
- Steady datum and consistent units throughout plotting.
Concept / Approach:A hydrograph shows how discharge varies with time, capturing rising limbs, peaks, and recession. A mass curve integrates the hydrograph over time, so its slope equals instantaneous discharge; since accumulated volume cannot decrease (neglecting losses in the plotted record), the curve is non-decreasing.
Step-by-Step Solution:
Hydrograph definition → discharge vs time: statement true.Mass curve definition → accumulated volume vs time: curve rises monotonically: statement true.Derivative (slope) of mass curve = discharge: statement true.Verification / Alternative check:Integration-differentiation relationship: hydrograph is the time-derivative of the mass curve, reinforcing the slope interpretation.
Why Other Options Are Wrong:“None of the above” contradicts standard hydrologic definitions widely used in design manuals.
Common Pitfalls:Mixing cumulative rainfall with cumulative flow; misreading mass curves during periods of variable inflow and outflow when analyzing reservoirs (must include outflow and losses for storage calculations).
Final Answer:All of the above