Explanation of water-budget equation | Derivation of water-budget equation

Water- Budget Equation

The water- budget equation is nothing but the continuity equation of water in its various phase at time Δt. For the given problem area, there can be the various phases of water incoming and outgoing and the water-budget the equation simply balances the inflow and outflow of water in the equation.

For the given problem area at time Δt, continuity equation for water in various phase is given by:

Mass inflow – Mass outflow= change in Mass storage

This equation resembles with continuity equation because in the continuity equation we assumed that mass accumulated is zero. And because of that reason, the mass inflow was equal to mass outflow. But in this case, the mass inflow and mass outflow are different and that difference is the mass storage. However, the point is water-budget equation is the continuity equation and follows the principle of conservation of mass.

If the density of the water inflow, water outflow and the storage mass is the same, then the equation can be written as:

                                 Volume inflow- Volume outflow = change in Volume storage

                                                V_i-V_o= ΔS

Since the inflow and outflow occurs in different forms or phase so, more precisely water-budget equation can be written as:

                                                P-R-G-E-T= ΔS

Where,

P=Precipitation

R=Surface Runoff

G= groundwater flow

E= evaporation

T= transpiration

So, in different phases or forms of loss and gain of water, water budget equation is changed into

P-R-G-E-T= ΔS

Also, storage occurs in 3 forms they are stored as soil moisture, storage as groundwater and storage as surface water storage.

So, ΔS=ΔS_s+ΔS_g+ΔS_m

Where,

ΔS_s= storage as surface water storage

ΔS_g = storage as groundwater

ΔS_m= storage as soil moisture

In terms of the rainfall-runoff relationship, the water-budget equation can be written as

R=P-L

Where,

R= Runoff (storage)

P= Precipitation

L= All kind of losses due to evaporation, transpiration, groundwater flow, etc.

So, the required water-budget equation is R=P-L