Agricultural hydrology


Agricultural hydrology is the study of water balance components intervening in agricultural water management, especially in irrigation and drainage.

Water balance components

The water balance components can be grouped into components corresponding to zones in a vertical cross-section in the soil forming reservoirs with inflow, outflow and storage of water:
  1. the surface reservoir
  2. the root zone or unsaturated with mainly vertical flows
  3. the aquifer with mainly horizontal flows
  4. a transition zone in which vertical and horizontal flows are converted
The general water balance reads:
  • inflow = outflow + change of storage
and it is applicable to each of the reservoirs or a combination thereof.
In the following balances it is assumed that the water table is inside the transition zone.

Surface water balance

The incoming water balance components into the surface reservoir are:
  1. Rai – Vertically incoming water to the surface e.g.: precipitation, 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 are:
  1. Eva – Evaporation from open water on the soil surface
  2. Osu – Surface runoff or surface drainage
  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
  • Osu = 2 /
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 the cumulative duration is to be divided into sequential time steps.

Root zone water balance

The incoming water balance components into the root zone 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 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 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 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 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 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.

Specific water balances

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, the storage terms are often negligible small. Omitting these leads to steady state or equilibrium water balances.
Combination of surface reservoir and root zone 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 and transition zone 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 and aquifer 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.
The total irrigation and the infiltration are:
The field irrigation efficiency is:
The value of Era is less than Inf, there is an excess of irrigation that percolates down to the subsoil :
  • Per = Irr + Wel – Era, or:
  • Per =
The percolation Per is pumped up again by wells for irrigation, hence:
  • Wel = Per, or:
  • Wel =, and therefore:
  • Wel / Irr = / Ff
With this equation the following table can be prepared:

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, Ncp = Cap − Per.
Horizontal hydrological components in the same zone with arrows in same direction can be combined into excess values.
For example, : Egio = Iaq − Oaq, Egoi = Oaq − Iaq.

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.

Irrigation and drainage requirements

The irrigation requirement can be calculated from the topsoil water balance, the agronomic water balance or the overall water balance, as defined in the section "Combined balances", depending on the availability of data on the water balance components.
Considering surface irrigation, assuming the evaporation of surface water is negligibly small, setting the actual evapotranspiration Era equal to the potential evapotranspiration so that Era = Epo and setting the surface inflow Isu equal to Irr so that Isu = Irr, the balances give respectively:
  • Irr = Epo + Osu + Per − Rai − Cap
  • Irr = Epo + Osu + Dtr + Dgw − Rai − Lca − Ugw
  • Irr = Epo + Osu + Dtr + Oaq − Rai − Lca − Iaq
Defining the irrigation efficiency as IEFF = Epo/Irr, i.e. the fraction of the irrigation water that is consumed by the crop, it is found respectively that :
  • IEFF = 1 − / Irr
  • IEFF = 1 − / Irr
  • IEFF = 1 − / Irr
Likewise the safe yield of wells, extracting water from the aquifer without overexploitation, can be determined using the geohydrologic water balance or the overall water balance, as defined in the section "Combined balances", depending on the availability of data on the water balance components.
Similarly, the subsurface drainage requirement can be found from the drain discharge in the subsoil water balance, the agronomic water balance, the geohydrologic water balance or the overall water balance.
In the same fashion, the well drainage requirement can be found from well discharge in the geohydrologic water balance or the overall water balance.
The subsurface drainage requirement and well drainage requirement play an important role in the design of agricultural drainage systems.