1. The Hydrological Cycle and Water Balance6
Hillel, pp &
The Hydrological Cycle and Water Balance

2. The Hydrologic Cycle
The hydrologic cycle describes terrestrial pathways and transformation of water.
Evaporation, precipitation, and infiltration replenish soil water storage and recharge groundwater - key life supporting processes.
The hydrologic cycle is “driven” by solar radiation.
Reservoir
Volume (km3 x108)
% of Total
Oceans
1370
97.25
Ice Caps & Glaciers 29
2.05
Groundwater
9.5
0.68
Lakes
0.125
0.01
Soil Moisture
0.065
0.005
Atmosphere
0.013
0.001
Streams & Rivers
0.0017
0.0001
Biosphere
0.0006
More than 97% of earth’s water is found in oceans; soil water storage is less than 0.005% !
Residence times in various “hydrological compartments” vary considerably: >10,000yr ice caps; >1000yr deep ground water; <1 yr surface soil water.

3. The Water Balance Equation
The primary use of soil water content information is for evaluation of the water balance equation given as:
The concept is based on conservation of mass, balancing inputs and outputs from a soil profile (inputs are taken as positive, outputs negative sign).
Soil water storage W is defined as the equivalent depth of water stored in a certain soil depth.
Changes in storage are calculated for a given time interval (day, year): DW=Winitial-Wfinal.
Under typical conditions DW is fairly significant over short periods of time (weeks to months), but generally evens out to zero over one to several years.

4. The Water Balance Equation
Soil water measurements are coupled with other climatic information, such as evapotranspiration or precipitation.
The resulting information may be used for:
Irrigation Scheduling (time and amount of water)
Estimation of Evaporation or Drainage
Determination of Groundwater Recharge
Water balance calculations may be applied to different scales:
A single profile
A field
Watershed scale
Basin to continental scale
Global circulation models

5. Changes in Soil Water Storage
Soil Depth, Z 
Soil Depth, Z
W = Z *  i
Initial
Final
W = W

6. The Water Balance Equation: Example

7. The Water Balance Equation: Example

8. Equivalent Depth of Soil Water De
In the context of the water balance equation it is useful to recall the concept of equivalent depth of soil water De relating volumetric water content to water depth similar to climatic quantities (precipitation, irrigation, evapotranspiration) commonly expressed in equivalent units of water volume per unit soil surface area (or length).
Where D is the soil depth increment having uniform water content qv
De is the volumetric water content in a given depth increment expressed as soil water storage (Length)
De is very useful in water balance calculations. D De qv

9. The Water Balance Equation: Example

10. Plant Available Soil Water - Field Capacity
PLANT AVAILABLE SOIL WATER – The amount of soil water between “field capacity” and “wilting point”.
The concept of “field capacity” is based on observations that very wet soils tend to drain to a nearly constant value of water content within a day or two after irrigation or rainfall.
FIELD CAPACITY qvFC is defined as the water content at which internal drainage becomes negligible. The attainment of field capacity is not always assured. It is dependent on:
- Initial soil water content and depth of wetting
- The presence of impeding layers or a water table effect extent and rate of distribution
Silt Loam

11. Equivalent Depth of Soil Water De
Conceptual sketch illustrating internal drainage and redistribution as related to De

12. Plant Available Water - Permanent Wilting Point
qvWP (WILTING POINT) is the water content at which plants can no longer extract soil water at a rate sufficient to meet evaporative demand, hence irreversible wilt and die.
qvWP is dependent on soil texture (specific surface area), and on soil ability to transmit water, and to a lesser extent on plant’s ability to withstand drought. It is commonly considered as the water content at -15 bar matric potential.
FIELD CAPACITY and WILTING POINT enable determination of plant available soil water (more realistic than considering all soil water available to plants!) which varies with soil texture.
Rule of Thumb

13. The Energy State of Soil Water
Hillel, pp
The Energy State of Soil Water

14. The Energy State of Soil Water
The liquid phase content alone is insufficient to characterize soil water status.
Phenomena such as water exchange between two soils with identical water contents but different textures; or water accumulation at bottom of initially uniform vertical soil column – require examination of the energy state of the liquid phase.
Like all matter, soil water contains various amounts and forms of energy, the most important for hydrological applications are kinetic and potential energy.
Kinetic energy is acquired by virtue of motion – however, because water moves very slowly through soils we often neglect this form of energy.
Potential energy results from position within a force field or internal conditions is the primary form of energy that determines movement of soil water.

15. The Energy State of Soil Water
Like all other forms of matter, water flows from locations with high potential energy to locations of lower potential energy in pursuit of equilibrium state.
High potential energy
Low potential energy y1 y2 L
Dy1= y1- y2
The driving force for flow is a potential (energy) gradient, or the difference in potentials between different spatial locations.

16. Total Soil Water Potential
Soil water is subject to several forces. Their combined effects define the energy state of soil water often expressed relative to a predefined reference state. The Total Soil Water Potential yT is expressed as the sum of the following key components:
yT = yz + ym + yp + ys +....
yz gravitational potential
ym matric potential
yp pressure potential
ys solute or osmotic potential
DEFINITION - The amount of work that an infinitesimal unit quantity of water at equilibrium is capable of doing when it moves to a standard (reference) state.
As a conventional reference state we consider a hypothetical reservoir of pure water (no solutes and no external forces other than gravity) at a reference (atmospheric) pressure, temperature and elevation.

17. yw = ym + yp + ys Soil Water Potential
The difference in chemical and mechanical potentials between soil water and water at reference state is known as Soil Water Potential yw :
yw = ym + yp + ys
ym matric potential
yp pressure potential
ys solute or osmotic potential
Soil water potential is thus the result of inherent properties of soil water itself, and its physical and chemical interactions with its surroundings, while total potential includes the effects of gravity which is an external force.

18. yh = ym + yp + yg Hydraulic Potential ym matric potential
yp pressure potential
yg gravitational potential

19. Expressing Soil Water Potentials
The potential energy of soil water can be expressed in terms of chemical potential m (energy/mass), soil water potential y (energy/volume), or soil water head H (energy/ weight).
g acceleration of gravity
rw density of water

20. Water Potential Conversions - Example
Convert a soil water head of m to soil water potential in kPa and to chemical potential in J/kg
1. From m to kPa
g = 9.81 m/s2
rw= 1000 kg/m3

21. Water Potential Conversions - Example
Convert a soil water head of m to chemical potential in J/kg
2. From m to J/kg
g = 9.81 m/s2

22. The Gravitational Potential
yT = yz + ym + yp + ys +....
A body on the earth‘s surface is attracted towards the earth‘s center by a gravitational force that is equal to the weight of the body (w=mg).
To raise a body against the gravitational force work has to be expended, and this work is stored by the raised body in form of gravitational potential energy (conservation of energy).

23. The Gravitational Potential
When potentials are expressed as energy per unit weight, the gravitational potential is simply the vertical distance from a reference level to the point of interest.
The following examples illustrate that the reference level may be set at an arbitrary location.
CASE 1: Point A is 100 mm above the reference and point B 200 mm below.
CASE 2: Point A is 100 mm below the reference and point B 400 mm below.

24. The Gravitational Potential
When potentials are expressed as energy per unit weight, the gravitational potential is simply the vertical distance from a reference level to the point of interest.

25. The Matric Potential yT = yz + ym + yp + ys +....
The matric potential results from interactive capillary and adsorptive forces between the water and the soil matrix, which in effect binds water in the soil resulting in lower potential energy relative to that of bulk water.
The value of ym ranges from zero, when the soil is saturated to often very low negative numbers when the soil is dry.
Tensiometer
The matric potential per unit of weight is defined as the vertical distance between a porous cup in contact with the soil and the water level in a manometer connected to the cup [Hanks, 1992]

26. The Pressure Potential
yT = yz + ym + yp + ys +....
The pressure potential is the hydrostatic pressure exerted by unsupported water saturating the soil above a point of interest.
When expressed as energy per unit weight it is equal to the vertical distance from the point of interest to the free water surface, or unconfined water table elevation.
The pressure potential is always positive (superatmospheric) below the water table and zero if the point of interest is exactly at, or above the water table. yp and ym are “mutually exclusive“.

27. The Solute (Osmotic) Potential
yT = yz + ym + yp + ys +....
The presence of solutes in soil water lowers its potential energy and its vapor pressure.
The effect of ys is important when (1) there are appreciable amounts of solutes in the soil; and (2) in the presence of a selectively permeable membrane or a diffusion barrier which transmits water more readily than salts.
The solute potential, also called the osmotic pressure, is proportional to the solute concentration and temperature according to the van‘t Hoff relationship:
ys = -R T Cs [kPa]
where R is the universal gas constant [8,314x10-3 kPa m3/(mol K)], T is the absolute temperature in Kelvin, and Cs is the solute concentration [mol/m3].