What is water budget? Write mathematical equation of water balance and define its different terms.

A water budget, also known as a water balance, is a method used to quantify the movement of water into and out of a defined system or region over a specified period. It provides a comprehensive overview of the sources, uses, and changes in water storage within the system, helping to assess water availability, manage resources, and understand hydrological processes.

The mathematical equation of the water balance is:

[ \text{P} = \text{ET} + \text{R} + \text{ΔS} ]

Where:

• ( \text{P} ) = Precipitation (input)
• ( \text{ET} ) = Evapotranspiration (output)
• ( \text{R} ) = Runoff (output)
• ( \text{ΔS} ) = Change in storage (change in water stored within the system)

Each term in the equation represents a component of the water balance:

1. Precipitation (( \text{P} )): This refers to the amount of water that falls onto the system as rain, snow, or hail. Precipitation is the primary input into the water budget and can vary spatially and temporally within a region.

2. Evapotranspiration (( \text{ET} )): This represents the combined loss of water from the system through evaporation from surfaces such as soil, water bodies, and vegetation, as well as transpiration from plants. Evapotranspiration is influenced by factors such as temperature, humidity, wind speed, and vegetation cover.

3. Runoff (( \text{R} )): Runoff is the portion of precipitation that does not infiltrate into the soil or evaporate but instead flows over the land surface and eventually enters streams, rivers, lakes, or groundwater. Runoff can be influenced by factors such as soil type, land use, topography, and antecedent moisture conditions.

4. Change in storage (( \text{ΔS} )): This term accounts for any changes in water stored within the system over the specified period. Changes in storage can occur in surface water bodies, soil moisture, groundwater aquifers, and snowpack, among others.

By quantifying these components, the water balance equation provides valuable insights into the hydrological processes governing water movement within a system, helping to inform water resource management decisions, assess water availability, and understand the impacts of climate variability and land use changes.