The quantity of water going through various individual paths of the hydrological cycle in a given system can be described by the continuity principle known as Water Budget equation or Hydrologic Equations.
The conservation of Mass is the most useful physical principle in hydrologic analysis and is required in almost all applied problem.
For a given catchment area in an interval of time Δt, the continuity equation for water is
Mass of water inflow – mass of water outflow = change in mass of water storage
If the density of water inflow, outflow and storage water are same, then
Volume of inflow water – Volume of outflow water = Change in storage volume of water
i.e. Vi – V0 = ΔS
For solving the problem of water budget equation we should be clear in mind, what factor recharges the water discharged in the water body.
Water Budget Equation for a Catchment
For a particular time Δt
P – R – G – E – T = ΔS
Water Budget Equation for Water Bodies
I + P – G – E – O = ΔS
Water Budget Equation for Surface Flow
P + I + IG – O – E – T – In = ΔS
Water Budget Equation for Underground Flow
IG + In – OG – OS – T = ΔS
Where,
P = Precipitation
R = Surface Runoff
G = Net ground water flow out of the catchment
E = Evaporation
T = Transpiration
ΔS = Change in storage = SS + SSM + SG
SS = Surface water storage
SSM = Water storage as soil moisture
SG = Water in storage as ground water
I = Inflow
O = Outflow
IG = Ground water come to the surface
In = Infiltration
OG = Ground water outflow
OS = Ground water come to the surface
Water Budget Equation in terms of rainfall runoff relationship can be represented as
R = P – L, where, R = Runoff
P = Precipitation
L = Losses (infiltration, evaporation, transpiration and surface storage)
- For large catchment area, ground water inflow and outflow are almost equal.
- In general, after a long period the storage in catchment be same as prior.