Isohyetal Method Rainfall Variation Assumption

The isohyetal method is a technique used in hydrology to calculate the average rainfall over a specific area. This method involves drawing lines, known as isohyets, which connect points having equal rainfall amounts. These lines are typically drawn on a map representing the area of interest.

Understanding Isohyets and Rainfall Calculation

To find the average rainfall over the entire area using the isohyetal method, the area between consecutive isohyetal lines is determined. For instance, if we have isohyets for 20 mm and 30 mm of rainfall, we calculate the area that received rainfall between 20 mm and 30 mm.

The core assumption made in the isohyetal method for calculating the average rainfall is about how rainfall varies *between* these drawn isohyetal lines. It is assumed that the rainfall intensity changes in a linear fashion between any two adjacent isohyets.

This means, for the area between the 20 mm and 30 mm isohyets, the rainfall is considered to increase (or decrease) steadily from 20 mm to 30 mm (or vice versa) as you move across that specific area. Mathematically, if $P_1$ and $P_2$ are rainfall depths corresponding to two consecutive isohyets, and $A_1$ and $A_2$ are the areas enclosed within these isohyets respectively, the average rainfall ($P_{avg}$) is calculated as:

$$ P_{avg} = \frac{\sum_{i=1}^{n} P_i A_i}{\sum_{i=1}^{n} A_i} $$

Where $P_i$ is the rainfall depth corresponding to the $i$-th isohyet and $A_i$ is the area between the $(i-1)$-th and $i$-th isohyet. The linear variation assumption simplifies the calculation of these contributing areas and the subsequent averaging.

Why Linear Variation?

• Simplicity: Assuming a linear variation is the simplest approach and makes the calculations manageable, especially when dealing with complex topographical data.
• Practicality: While the actual rainfall distribution might be more complex (parabolic, irregular, etc.), the linear assumption provides a reasonable approximation for practical engineering and hydrological purposes, especially when the isohyetals are relatively closely spaced.

Other options like parabolic, elliptical, or quadratic variations would imply a more complex, non-uniform change in rainfall between the isohyets, which is generally not assumed in the standard application of the isohyetal method due to the increased complexity in calculation and lack of precise data to support such assumptions.

Therefore, the variation of rainfall between two sections (or isohyets) in the isohyetal method is assumed as linear.