Hydrologic plots and their interpretation: Which statements about hydrographs and mass curves are correct?

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:

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