Precipitation

Forms of Precipitation

Precipitation is the deposition of water from the atmosphere onto the Earth's surface. It occurs in various forms depending on atmospheric conditions:

• Rain: Liquid water droplets with diameter $> 0.5$ mm.
• Drizzle: Fine water droplets with diameter $< 0.5$ mm.
• Snow: Ice crystals formed by sublimation.
• Hail: Hard pellets of ice, usually formed in cumulonimbus clouds.
• Sleet: Frozen raindrops or refrozen melted snow water.

Measurement of Precipitation

Precipitation is typically measured as the vertical depth of water that would accumulate on a level surface if the precipitation remained where it fell.

Types of Rain Gauges:

1. Non-Recording Gauges: Symons' gauge (standard). Collects rain for manual measurement at fixed intervals (e.g., daily).
2. Recording Gauges: Provide a continuous record of rainfall over time (hyetograph).
   • Tipping Bucket: Tips after a specific volume (e.g., 0.25 mm) is collected. Good for intensity.
   • Weighing Type: Weighs the accumulated rain. Good for snow.
   • Float Type: Float rises as water level increases.

Areal Precipitation

Rain gauges provide point measurements. To estimate the average rainfall over a catchment area, statistical methods are used.

1. Arithmetic Mean Method

Simplest method. Suitable for flat terrain with uniformly distributed gauges.

$$P_{avg} = \frac{\sum P_i}{N}$$

Where $P_i$ is the rainfall at station $i$, and $N$ is the number of stations.

2. Thiessen Polygon Method

Weights station data based on the area closer to that station than to any other. Suitable for non-uniform gauge distribution.

$$P_{avg} = \frac{\sum (P_i \cdot A_i)}{\sum A_i}$$

Where $A_i$ is the area of the polygon associated with station $i$.

3. Isohyetal Method

Most accurate. Involves drawing isohyets (lines of equal rainfall) and calculating the weighted average based on areas between isohyets.

$$P_{avg} = \frac{\sum \left( \frac{P_j + P_{j+1}}{2} \cdot A_j \right)}{\sum A_j}$$

Where $P_j$ and $P_{j+1}$ are values of adjacent isohyets, and $A_j$ is the area between them.

Intensity-Duration-Frequency (IDF) Curves

IDF Curves relate rainfall intensity, duration, and return period (frequency). They are crucial for designing drainage systems.

• Intensity ($i$): Rate of rainfall (mm/hr).
• Duration ($t_d$): Time over which the rain falls.
• Frequency ($T$): Return period (e.g., 10-year storm).

Generally, intensity decreases as duration increases for a given return period.

$$i = \frac{K \cdot T^x}{(t_d + c)^n}$$

Where $K, x, c, n$ are location-specific constants.