Water budget equation and its role

The water budget (water balance) equation is an application of the law of conservation of mass to a hydrologic system: inflow minus outflow equals the change in storage over a time period.

$$I - O = \frac{dS}{dt} \quad\text{or}\quad I - O = \Delta S$$

For a catchment over a period $\Delta t$:

$$P + Q_{in} + G_{in} - E - T - Q_{out} - G_{out} = \Delta S$$

where $P$ = precipitation, $Q_{in}, Q_{out}$ = surface inflow and outflow, $G_{in}, G_{out}$ = groundwater inflow and outflow, $E$ = evaporation, $T$ = transpiration, and $\Delta S$ = change in storage (soil moisture, groundwater, surface water, snow). For a closed natural basin with no inflow, it reduces to

$$P - R - G - E_T = \Delta S$$

with $R$ = surface runoff, $G$ = net groundwater outflow and $E_T$ = evapotranspiration. Over a long period (many years) $\Delta S \approx 0$, so $P = R + G + E_T$.

Role of the water budget equation

• Estimating an unknown component: If P, R and ET are measured, the groundwater recharge or storage change can be found. Evaporation from lakes and reservoirs can be found in the same way.
• Water resources assessment: It gives the available yield of a basin for water supply, irrigation and hydropower.
• Reservoir planning: Inflow, outflow and storage are balanced to find the reservoir capacity and change in level.
• Checking data: A large non-closure of the budget shows errors in measured data.
• Impact studies: It helps to study the effect of land-use change, dams or climate change on a basin.