Soil water storage and mobility: Theoretical and Experimental Aspects

Dr. Greg ButtersSoil Physics

Department of Soil and Crop Sciences

A lecture for SOCR 571- Foundations of Soil Science

Soil water in a complex, multiple process domain

Outline• Fundamental relationships

– Conservation of Mass– From Darcy to Richards

• Major Experimental advances– Soil water pressure– Soil water content

• Current approaches - The blending of experimental and

numerical methods

• Solving a problem- An example water balance simulation

Conservation of mass

Consider a volume element of soil

Δ Storage = Inputs - Outputs

Δ Storage= (precipitation + irrigation+ run-on) - (evaporation. + transpiration +

deep drainage + run-off)

Ppt. + Irr.

Transpir.

Evap.

Deep drainage

Run-0nRun-off

Storage=(θv•L) where θv is the soil water content over depth L.

Capillary rise

Note- It is customary to express these flows on a volume per area basis, hence a length unit.

Conservation of mass continued…

Expressing as a rate

Rate of change of Storage = (flow rate in – flow rate out) – rate of extraction by sinks

Mathematically this may be written for 1D flow direction z as

= - - S

where q is the soil water flux (rate of flow per area).

Foundational equations for soil water flow

• Darcy’s Law (1856)

“It thus appears that for sand ofcomparable nature, one can conclude that flow volume is proportional to the head loss and inversely related to the thickness of the layer traversed.”

Buckingham (1907)Extended Darcy’s Law to unsaturated soil by recognizing that the hydraulic conductivity is a function of the degree of water saturation.

To this day, measuring K(h) (or K(θ)) remains a topic with evolving experimental methods

Richards (1931)Combined the Darcy-Buckingham equation with conservation of mass to derive the general flow equation for variably saturated soil.

The solution of Richards’ equation gives the predicted water content, water pressure, and water flow rate at any position and time within the soil in response to boundary conditions (precipitation, evaporation, etc.) and extraction by plant roots.

• Richards’ equation is the foundational model of water flow in variably saturated soil. To be useful, it requires the fundamental soil hydraulic properties (K(h) and θ(h)) and it needs to be solvable.

• In the 80 years since it’s introduction, research in soil water dynamics can be grouped into three main areas;1. Measurement and characterization of K(h) and θ(h) (including measurement and monitoring of θ and h).

2. Analytical and numerical solutions of Richards’ equation. Since the 1980’s, emphasis on numerical solutions.

3. Modifications/additions to Richards’ equation such as accounting for air phase interactions, swelling soils, and hysteresis in soil water properties.

Timeline of some key experimental approaches

• Measurement of soil water tension and characterization of the θ(h) relationship

Gardner (1922) proposed and Richards (1942) developed the tensiometer used to measure soil water pressure in unsaturated soil. This remains today as one of the fundamental tools of studies in unsaturated soil.

With the ability to measure soil h in the field and with the introduction of the laboratory pressure plate method (Richards (1947) and later standardized by Klute) to create know h in soils, characterization of the θ(h) became (and remains!) a common task. From this arose quantification of many concepts such as field capacity, plant available water, and wilting point.

“Elements of the Nature and Properties of Soils” by Brady and Weil (2002)

A marriage of the quantitative and the descriptive- In 1897, Briggs described soil water as comprised of three types; gravitational, capillary, and hygroscopic.

The pore-size distribution is a property of the particle size distribution

Timeline of key experimental approaches cont…

Timeline of key experimental approaches cont…

• Indirect measurement and monitoring of soil water contentGardner and Kirkham (1949) introduced neutron scattering for θ measurement. This remained the method of choice for 40 years.

Timeline of key experimental approaches cont…

• Late 1980s to present- Introduction of methods using the dielectric properties of soil water to estimate water content. This includes TDR (Time Domain Reflectometry and capacitance probes).

Timeline of key experimental approaches cont…

• 1990s to present- With the rise of the PC, advances in numerical methods and computational speed brings numerical solution of Richards’ equation to the common man.

• A spin off of the ease of computation of Richards equation is the rapidly expanding application of inverse methods to measure soil hydraulic properties.

Flowchart on inverse approach

0 5 10 15 20 25 30 35 40 45 500.15

0.2

0.25

0.3

0.35

0.4data it=2

time (min)

Wat

er co

nten

t at c

erta

in p

ositi

on

1. Experimental outcome

2. Guess K(h) and θ(h)3. Solve Richards equation to predict experimental outcome

4. Compare prediction to observation. Calc SSQ deviations

Repeat to minimum deviation

Keep best K(h) and θ(h)

End

90 cm (35 in.)

transpiration =? cm

evaporation= ?cm

drainage=? cm

0 cm 0 cm

Silty clay

200 cm

Loamy sand

ΔStorage= ? cm

90 cm (35 in.) evaporation= ? cm

transpiration= ? cm

0 cm 0 cm

drainage=? cm

Δ Storage= ? cm

Example simulation solving Richards’ equation- Single growing season water balance in irrigated corn (Greeley, Co). Compare expectation in silty clay versus loamy sand.

90 cm (35 in.)

transpiration =? cm

evaporation= ? cm

drainage=? cm

0 cm 0 cm

Silty clay

200 cm

Loamy sand

ΔStorage= ? cm

90 cm (35 in.) evaporation= ? cm

transpiration= ? cm

0 cm 0 cm

drainage=? cm

Δ Storage= ? cm

Example simulation solving Richards’ equation- Single growing season water balance in irrigated corn (Greeley, Co). Compare expectation in silty clay versus loamy sand.

Input weather data and irrigation schedule

Input K(h) and θ(h) for each soil. May have different functions for different depths. Input root water uptake properties.

90 cm (35 in.)

70 cm

25 cm

4 cm

0 cm 0 cm

Silty clay

200 cm

Loamy sand

ΔStorage= -10 cm

90 cm (35 in.) 13cm

66 cm

0 cm 0 cm

19 cm

ΔStorage= -8 cm

Predicted water balance

90 cm (35 in.)

70 cm

25 cm

4 cm

0 cm 0 cm

Silty clay

200 cm

Loamy sand

ΔStorage= -10 cm

26 Kg N/ha

90 cm (35 in.) 13cm

66 cm

0 cm 0 cm

19 cm

ΔStorage= -8 cm

308 Kg N/ha

Predicted water balance with nitrogen leaching

Summary- Foundational equations in soil water flow

• The basic water flow equation (Darcy-Buckingham)

• For transient conditions, mass balance

• General flow equation (Richards)

• Solve the general equation to find qw(x,t) and θ(x,t).

Sx

HhK

xt

])([

Sx

q

tW

x

HhKqW

)(

Developments-

• Added multidimensional flow analysis• Included additional features such as hysteresis

in K(h) and θ(h)• Advances in monitoring tools and

measurement methods (evolution of inverse approaches)

• Tremendous gains in computational methods and user friendly computer codes allowing laptop solution of complex flow systems

Modern times- Characterization , measurement, and analysis of coupled processes (Revenge of the reductionists! Simultaneous solution of multiple and interacting

flows)

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aqSbaq CCq

zz

CD

zt

CC

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CD

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aCggg

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g

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z

TCq

z

T

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TC Wws

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Sz

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Heat transport Gas transport

Solute transport