Hydrologic Losses

Introduction

Not all precipitation that falls becomes runoff. A significant portion is lost to Hydrologic Losses (or abstractions). The major components are evaporation, transpiration, interception, and infiltration.

Evaporation

Evaporation is the process by which water changes from liquid to vapor state. It occurs from water bodies, soil, and vegetation.

Factors Affecting Evaporation:

1. Solar Radiation: Primary energy source.
2. Temperature: Higher T increases saturation vapor pressure.
3. Wind: Removes saturated air layer, increasing rate.
4. Humidity: High humidity reduces the vapor pressure deficit, slowing evaporation.

Estimation Methods:

• Pan Evaporation: Using a standard US Weather Bureau Class A Pan.

  $$E_{lake} = C_p \cdot E_{pan}$$

  Where $C_p$ is the pan coefficient (typically 0.7).

• Empirical Equations (Meyer's Formula):

  $$E = C (e_s - e_a) (1 + 0.1 w)$$

  Where $e_s$ is saturation vapor pressure, $e_a$ is actual vapor pressure, and $w$ is wind speed.

Infiltration

Infiltration is the movement of water through the soil surface into the soil profile. It replenishes soil moisture and groundwater.

Infiltration Capacity ($f_p$)

The maximum rate at which soil can absorb water. It decreases over time during a storm as soil becomes saturated.

Horton's Equation

Horton modeled the decay of infiltration capacity over time:

Where:

• $f_p(t)$ = Infiltration capacity at time $t$ (mm/hr)
• $f_0$ = Initial infiltration capacity
• $f_c$ = Ultimate (constant) infiltration capacity
• $k$ = Decay constant ($hr^{-1}$)

Infiltration Indices

Used to estimate average infiltration over a storm duration.

1. $\Phi$ - Index (Phi Index): The average rainfall intensity above which the rainfall volume equals the runoff volume. It assumes a constant loss rate.

   $$\text{Total Runoff} = \sum (I - \Phi) \cdot \Delta t$$

   (Only for time intervals where $I > \Phi$)

2. W - Index: Average infiltration rate, excluding surface storage and retention.

   $$W = \frac{P - R - S}{t_r}$$