Ryve's Formula Explained

Ryve's formula is a method used in hydrology to estimate the peak discharge of a flood based on the characteristics of the catchment basin.

Peak Discharge Proportionality

According to Ryve's empirical formula, the peak discharge ($Q_p$) of a flood is directly proportional to a specific power of the catchment basin area ($A$). The formula establishes a relationship between these two key hydrological parameters.

The relationship is expressed as:

$$Q_p \propto A^{2/3}$$

Where:

• $Q_p$ represents the peak discharge (the maximum flow rate during a flood).
• $A$ represents the area of the catchment basin (the total area that contributes water to a river or stream at a specific point).

This means that as the catchment area increases, the peak discharge also increases, but not linearly. The exponent $ \frac{2}{3} $ indicates the specific rate of this increase according to Ryve's empirical observations.

Understanding the Options

Let's look at why $A^{2/3}$ is the correct relationship:

• Option 1 ($A$): This would imply peak discharge increases linearly with area, which is generally not the case for flood estimations.
• Option 2 ($A^{2/3}$): This matches Ryve's formula, indicating a specific non-linear relationship observed empirically.
• Option 3 ($A^{3/4}$): This represents a different empirical relationship, not Ryve's formula.
• Option 4 ($A^{1/2}$): This suggests peak discharge is proportional to the square root of the area, also differing from Ryve's formula.

Therefore, the peak discharge in Ryve's formula is proportional to $A^{2/3}$.