Surface water balance

The incoming water balance components into the surface reservoir (S) are:

1. Rai – Vertically incoming water to the surface e.g.: precipitation (including snow), rainfall, sprinkler irrigation
2. Isu – Horizontally incoming surface water. This can consist of natural inundation or surface irrigation

The outgoing water balance components from the surface reservoir (S) are:

1. Eva – Evaporation from open water on the soil surface (see Penman equation)
2. Osu – Surface runoff (natural) or surface drainage (artificial)
3. Inf – Infiltration of water through the soil surface into the root zone

The surface water balance reads:

• Rai + Isu = Eva + Inf + Osu + Ws, where Ws is the change of water storage on top of the soil surface

Example of a surface water balance

An example is given of surface runoff according to the Curve number method.[3] The applicable equation is: Osu = (Rai – Ws)2 / (Pp – Ws + Rm) where Rm is the maximum retention of the area for which the method is used Normally one finds that Ws = 0.2 Rm and the value of Rm depends on the soil characteristics. The Curve Number method provides tables for these relations. The method yields cumulative runoff values. To obtain runoff intensity values or runoff velocity (volume per unit of time) the cumulative duration is to be divided into sequential time steps (for example in hours).

Root zone water balance

The incoming water balance components into the root zone (R) are:

1. Inf – Infiltration of water through the soil surface into the root zone
2. Cap – Capillary rise of water from the transition zone

The outgoing water balance components from the surface reservoir (R) are:

1. Era – Actual evaporation or evapotranspiration from the root zone
2. Per – Percolation of water from the unsaturated root zone into the transition zone

The root zone water balance reads:

• Inf + Cap = Era + Per + Wr, where Wr is the change of water storage in the root zone

Transition zone water balance

The incoming water balance components into the transition zone (T) are:

1. Per – Percolation of water from the unsaturated root zone into the transition zone
2. Lca – Infiltration of water from river, canal or drainage systems into the transition zone, often referred to as deep seepage losses
3. Ugw – Vertically upward seepage of water from the aquifer into the saturated transition zone

The outgoing water balance components from the transition zone (T) are:

1. Cap – Capillary rise of water into the root zone
2. Dtr – Artificial horizontal subsurface drainage, see also Drainage system (agriculture)
3. Dgw – Vertically downward drainage of water from the saturated transition zone into the aquifer

The water balance of the transition zone reads:

• Per + Lca + Ugw = Cap + Dtr + Dgw + Wt, where Wt is the change of water storage in the transition zone noticeable as a change of the level of the water table.

Aquifer water balance

The incoming water balance components into the aquifer (Q) are:

1. Dgw – Vertically downward drainage of water from the saturated transition zone into the aquifer
2. Iaq – Horizontally incoming groundwater into the aquifer

The outgoing water balance components from the aquifer (Q) are:

1. Ugw – Vertically upward seepage of water from the aquifer into the saturated transition zone
2. Oaq – Horizontally outgoing groundwater from the aquifer
3. Wel – Discharge from (tube)wells placed in the aquifer

The water balance of the aquifer reads:

• Dgw + Iaq = Ugw + Wel + Oaq + Wq

where Wq is the change of water storage in the aquifer noticeable as a change of the artesian pressure.

Combined balances

Water balances can be made for a combination of two bordering vertical soil zones discerned, whereby the components constituting the inflow and outflow from one zone to the other will disappear.
In long term water balances (month, season, year), the storage terms are often negligible small. Omitting these leads to steady state or equilibrium water balances.

Combination of surface reservoir (S)and root zone (R) in steady state yields the topsoil water balance :

• Rai + Isu + Cap = Eva + Era + Osu + Per, where the linkage factor Inf has disappeared.

Combination of root zone (R) and transition zone (T) in steady state yields the subsoil water balance :

• Inf + Lca + Ugw = Era + Dtr + Dgw, where Wr the linkage factors Per and Cap have disappeared.

Combination of transition zone (T) and aquifer (Q) in steady state yields the geohydrologic water balance :

• Per + Lca + Iaq = Cap + Dtr + Wel + Oaq, where Wr the linkage factors Ugw and Dgw have disappeared.

Combining the uppermost three water balances in steady state gives the agronomic water balance :

• Rai + Isu + Lca + Ugw = Eva + Era + Osu + Dtr + Dgw, where the linkage factors Inf, Per and Cap have disappeared.

Combining all four water balances in steady state gives the overall water balance :

• Rai + Isu + Lca + Iaq = Eva + Era + Osu + Dtr + Wel + Oaq, where the linkage factors Inf, Per, Cap, Ugw and Dgw have disappeared.

Example of an overall water balance

An example is given of the reuse of groundwater for irrigation by pumped wells. The total irrigation and the infiltration are: Inf = Irr + Wel, where Irr = surface irrigation from the canal system, and Wel = the irrigation from wells The field irrigation efficiency (Ff < 1) is: Ff = Era / Inf, where Era = the evapotranspiration of the crop (consumptive use) The value of Era is less than Inf, there is an excess of irrigation that percolates down to the subsoil (Per): Per = Irr + Wel – Era, or: Per = (1 − Ff) (Irr + Wel) The percolation Per is pumped up again by wells for irrigation (Wel), hence: Wel = Per, or: Wel = (1 − Ff) (Irr + Wel), and therefore: Wel / Irr = (1 − Ff) / Ff With this equation the following table can be prepared:   Ff   0.20     0.25     0.33     0.50     0.75     Well / Irr     4   3   2   1   0.33 It can be seen that with low irrigation efficiency the amount of water pumped by the wells (Wel) is several time greater than the amount of irrigation water brought in by the canal system (Irr). This is due to the fact that a drop of water must be recirculated on the average several times before it is used by the plants.

Water table outside transition zone

When the water table is above the soil surface, the balances containing the components Inf, Per, Cap are not appropriate as they do not exist. When the water table is inside the root zone, the balances containing the components Per, Cap are not appropriate as they do not exist. When the water table is below the transition zone, only the aquifer balance is appropriate.

Reduced number of zones

Under specific conditions it may be that no aquifer, transition zone or root zone is present. Water balances can be made omitting the absent zones.

Net and excess values

Vertical hydrological components along the boundary between two zones with arrows in the same direction can be combined into net values .
For example, : Npc = Per − Cap (net percolation), Ncp = Cap − Per (net capillary rise).
Horizontal hydrological components in the same zone with arrows in same direction can be combined into excess values .
For example, : Egio = Iaq − Oaq (excess groundwater inflow over outflow), Egoi = Oaq − Iaq (excess groundwater outflow over inflow).

Salt balances

Agricultural water balances are also used in the salt balances of irrigated lands.
Further, the salt and water balances are used in agro-hydro-salinity-drainage models like Saltmod.
Equally, they are used in groundwater salinity models like SahysMod which is a spatial variation of SaltMod using a polygonal network.