Soil physicsMagnus Persson

Surface tensionDue to surface tension water can be held at negative pressure in capillary tubes. (P1

pF curveThe soil moisture potential, or soil water suction, is sometimes given in pF = log(-pressure in cm H2O).

The water retention curve, soil moisture characteristic, or pF curve, is the relationship between the water content, , and the soil water potential, . This curve is characteristic for different types of soil

(1 bar = 100 kPa = 1000 cm H2O)

Soil water potentialThe total potential consists of the moisture potential (synonyms; pore water tension, soil water suction) and the elevation potential, z. Normally the groundwater surface is used as a reference level (z = 0)

Water movementWater movement is driven by total potential gradients

Theory of one-dimensional unsaturated water flowUsing continuity (inflow outflow = change in storage over time) we get

where is the volumetric water content and t is time.(1)

Theory of one-dimensional unsaturated water flowThe Darcy law gives us thatwhere H is the total potential. The total potential consists of the moisture potential (synonyms; pore water tension, soil water suction) and the elevation potential, z. ThusCombining (1) and (3) we getThis is called the Richard equation. Remember that and K both are functions of . (2)(4)(3)

Theory of one-dimensional unsaturated water flowThere is a soil specific relationship between soil water content and moisture potential and hydraulic conductivity.

The soil moisture potential, or soil water suction, is sometimes given in pF = log(-pressure in cm H2O)

Theory of one-dimensional unsaturated water flowSeveral models exists for these relationships, today, the most commonly used were presented by van Genuchten (1980).(5)where n, m, and are soil specific parameters, r and s are residual and saturated water content, respectively. The term Ks is the saturated hydraulic conductivity. The parameter r is usually assumed to be equal to the water content at a suitable low pressure head, e.g., -150 m H2O, i.e., the wilting point (pF 4.2).(6)

InfiltrationA special case of one-dimensional unsaturated water flow is infiltrationInfiltration is of interest in hydrology (rainfall-runoff relationship) and Agriculture (irrigation).Infiltration parameters for different soil types are determined in infiltration experiments

InfiltrationTwo cases of wetting fronts, in the first, the infiltration rate i is lower than the saturated hydraulic conductivity Ks

Infiltration modelsGreen-Ampt

where I is the cumulative infiltration, Lf is the wetting front depth, is the change in potential between the soil surface and the wetting front (tabled values exists, see next slide)It can be assumed that I = Lf (t - i)

Infiltration modelsSoil parameters (Green-Ampt)

Infiltration modelsHortonwhere fo = infiltration capacity in dry soil (mm/h)fc = = infiltration capacity in wet soil (mm/h)k = time factor (h-1)

Solute transportSolute transport processes in unsaturated soiladvection

Solute transportThe dispersion coefficient includes effect of both molecular diffusion and mechanical dispersion.

Dispersivity = Dispersion coefficient/velocity

Solute transportThe solute transport in the saturated and unsaturated zones can be modeled using the advection-dispersion equation (ADE)

where D is the dispersion coefficient, R is the retardation coefficient (sorption), and vz is the (vertical) water velocity. In the groundwater, the water velocity is calculated by the Darcy law, in the unsaturated zone the water velocity is calculated using Richardss equation. Can also include source/sink terms, (chemical reactions, biodegredation)

Solute transportAnalythical solution of the CDE for a pulse input and constant v and Dwhere M is the applied mass and A is the cross sectional area.

Different conceptsIn the ADE concept described above, transport is governed by advection and dispersion. A different approach is the stochastic-advective concept. In this concept, solutes are transported in isolated stream tubes by advection only. The velocity distribution of the stream tubes can be described by a stochastic probability density function (pdf).

Different conceptsConvective-dispersive Stochastic-convectiveSolute transport concepts

Stochastic convective approachwhere l is the mean of the lognormal pdf and l2 is the corresponding variance for the reference depth l. Assuming that the solute is spread instantaneously at z=0 and that the average solute transport velocity is constant, the Crt*(z,t) can be described by

Stochastic convective approachThe l parameter of the CLT model is related to the variability of the velocity distribution. This can be considered to be a soil specific parameter, however, it will also be slightly dependent on the magnitude of the soil water flux. The where l can be used to calculate the average pore water velocity v using

ALT vs. ADEBoth models calibrated to measurements at 0.235 m depth.

Chart1

000

00.00000000480

0.004775720.0002453760.0001535623

0.0213206320.01299275690.0130984622

0.0794087630.07526369860.0783574849

0.1568323340.1604155450.1633406476

0.1897997290.20098617230.2018561867

0.1979747880.1846070810.1854768563

0.1448560.13983293480.1418253814

0.0875534820.09351506610.0960426218

0.0486621410.05758652860.0597791644

0.0292142360.03355086340.035012285

0.0205953120.01883221650.0195994965

0.0121318940.01031157410.0105994657

0.0063168390.00555619340.0055801843

0.004096710.00296468940.0028757642

0.0022731930.00157363420.0014567974

0.0010307880.00083367630.0007277058

0.0009211850.00044190430.000359321

0.000726820.00023479460.0001757159

0.0019918040.00012521770.000085232

210.0000670960.0000410573

220.00003614960.000019661

230.00001959370.0000093671

240.00001068830.0000044431

250.00000586930.0000020994

260.00000324510.0000009886

270.00000180670.0000004642

280.00000101290.0000002174

290.00000057190.0000001015

300.00000032510.0000000473

310.00000018610.000000022

320.00000010730.0000000102

330.00000006220.0000000047

340.00000003640.0000000022

350.00000002140.000000001

360.00000001260.0000000005

370.00000000750.0000000002

Measured

ALT

ADE

Days

Crt

ALT-model vs. measured data

Sheet1

ALT parametersADE parametersDepth

sigmamjulDazv

0.30673498981.81695086580.2350.00042356970.01162463690.235m0.0364372452[m/d]

ALTADE

tmeasuredCrterror^2

[days][-][-]

00000

100.0000000048000

20.004775720.0002453760.00015356230.0000205240.0000213643

30.0213206320.01299275690.01309846220.00006935350.0000676041

40.0794087630.07526369860.07835748490.00001718160.0000011052

50.1568323340.1604155450.16334064760.00001283940.0000423581

60.1897997290.20098617230.20185618670.00012513650.0001453582

70.1979747880.1846070810.18547685630.00017869560.0001561983

80.1448560.13983293480.14182538140.00002523120.0000091846

90.0875534820.09351506610.09604262180.00003554050.0000720655

100.0486621410.05758652860.05977916440.00007964470.0001235882

110.0292142360.03355086340.0350122850.00001880630.0000336174

120.0205953120.01883221650.01959949650.00000310850.0000009916

130.0121318940.01031157410.01059946570.00000331360.0000023483

140.0063168390.00555619340.00558018430.00000057860.0000005427

150.004096710.00296468940.00287576420.00000128150.0000014907

160.0022731930.00157363420.00145679740.00000048940.0000006665

170.0010307880.00083367630.00072770580.00000003890.0000000919

180.0009211850.00044190430.0003593210.00000022970.0000003157

190.000726820.00023479460.00017571590.00000024210.0000003037

200.0019918040.00012521770.0000852320.00000348410.000003635

210.0000670960.0000410573

220.00003614960.000019661RMSE0.00545765330.0058430732

230.00001959370.0000093671

240.00001068830.0000044431

250.00000586930.0000020994

260.00000324510.0000009886

270.00000180670.0000004642

280.00000101290.0000002174

290.00000057190.0000001015

300.00000032510.0000000473

310.00000018610.000000022

320.00000010730.0000000102

330.00000006220.0000000047

340.00000003640.0000000022

350.00000002140.000000001

360.00000001260.0000000005

370.00000000750.0000000002

Sheet1

Measured

ALT

ADE

Days

Crt

ALT-model vs. measured data

Sheet2

Sheet3

ALT vs. ADEPredicted BTCs at 0.6 m depth

Chart2

000

000

0.0047757200

0.0213206320.00000003720

0.0794087630.00000378770

0.1568323340.00007456130.0000000003

0.1897997290.00057449190.0000001267

0.1979747880.00245092370.000008434

0.1448560.00702168160.0001601594

0.0875534820.01518186250.0013191789

0.0486621410.02670715750.0060593006

0.0292142360.04021508430.0182096626

0.0205953120.05371045230.03982603

0.0121318940.06528344850.0682329778

0.0063168390.07360349040.0965174767

0.004096710.07809292330.1171452855

0.0022731930.07884516290.1255691833

0.0010307880.07641405390.1215224498

0.0009211850.07158322680.1080157427

0.000726820.06517842770.0893809961

0.0019918040.05794448720.0696022971

210.05048283160.0514538632

220.04323423760.0363690196

230.03648981690.0247244037

240.03041613850.0162455157

250.02508469370.0103596424

260.02049987020.0064338825

270.01662258320.0039030745

280.01338866950.0023187251

290.01072226370.0013519193

300.00854490980.0007750583

310.00678131830.0004376393

320.0053626490.0002437378

330.00422806250.0001340614

340.003325130.0000729027

350.00260953950.0000392349

360.00204440950.0000209156

370.0015994190.0000110529

Measured

ALT

ADE

Days

Crt

ALT-model vs. measured data

Sheet1

ALT parametersADE parametersDepth

sigmamjulDazv

0.30673498981.81695086580.2350.00042356970.01162463690.6m0.0364372452[m/d]

ALTADE

tmeasuredCrterror^2

[days][-][-]

00000

100000

20.00477572000.00002280750.0000228075

30.0213206320.000000037200.00045456780.0004545693

40.0794087630.000003787700.00630515010.0063057516

50.1568323340.00007456130.00000000030.02457299930.0245963809

60.1897997290.00057449190.00000012670.03580619030.036023889

70.1979747880.00245092370.0000084340.03822958150.0391906773

80.1448560.00702168160.00016015940.01899829930.0209368863

90.0875534820.01518186250.00131917890.00523765130.007436355

100.0486621410.02670715750.00605930060.00048202130.001815002

110.0292142360.04021508430.01820966260.00012101870.0001211006

120.0205953120.05371045230.039826030.00109661250.0003698205

130.0121318940.06528344850.06823297780.00282508770.0031473316

140.0063168390.07360349040.09651747670.00452749350.008136155

150.004096710.07809292330.11714528550.00547543960.0127799804

160.0022731930.07884516290.12556918330.00586326660.0152019012

170.0010307880.07641405390.12152244980.00568263680.0145182406

180.0009211850.07158322680.10801574270.00499312410.0114692443

190.000726820.06517842770.08938099610.00415400970.0078595629

200.0019918040.05794448720.06960229710.00313070280.0045711788

210.05048283160.0514538632

220.04323423760.0363690196RMSE0.09164569290.1036717983

230.03648981690.0247244037

240.03041613850.0162455157

250.02508469370.0103596424

260.02049987020.0064338825

270.01662258320.0039030745

280.01338866950.0023187251

290.01072226370.0013519193

300.00854490980.0007750583

310.00678131830.0004376393

320.0053626490.0002437378

330.00422806250.0001340614

340.003325130.0000729027

350.00260953950.0000392349

360.00204440950.0000209156

370.0015994190.0000110529

Sheet1

Measured

ALT

ADE

Days

Crt

ALT-model vs. measured data

Sheet2

Sheet3

QuestionsDiscuss one of these questions in small groups and present the answer to the others

Spatial variabilitySoil properties may change dramatically over short distances. Water will not flow uniformly in the soil profile, but may flow in so called macropores, i.e., along roots, desiccation cracks or worm holes. This is called preferential flow.Macropore flow is often triggered at a specific water content and may lead to that large amounts of solutes are transported directly to the groundwater.

MacroporesMacropores (desiccation cracks) in a clay soil in Egypt

Dye infiltration patterns

Water drop penetration testWater repellency can be determined with the water drop penetration test (WDPT)The procedure is as follows:5 30 g sample of dry soil is put on a horizontal surface.The samples are leveled and a small 2-3 mm drop of water is added to the surface of the soil.On non-wetting soils the water will form a ball and stay on the surface for a time.Record the time for the drop to infiltrate.The test should be repeated at least three times and the average time should be recorded.

Water drop penetration test

Time for water to infiltrate (s)Description0-5Not water repellent5-60Slightly water repellent60-600Moderately water repellent600-3600Severely water repellent>3600Extremely water repellent

How to account for variabilityDual porosity models (e.g., MACRO)Stream tube modelsStochastic modelsFractal models

Fractal modelsOne model capable of generating fractal clusters i the DLA model. Diffusion limited aggregation conceptually describes the growth of crystals.This model has been successfully applied to solute transport

DLA models

DLA cluster

DLA modeling

Literature and linkshttp://www.ars.usda.gov/Services/docs.htm?docid=15992 (models for download)http://wwwbrr.cr.usgs.gov/projects/GW_Unsat/Unsat_Zone_Book/index.html (online textbook)Persson and Berndtsson, 1999. Water application frequency effects on steady-state solute transport parameters J. Hydrol. 225:140-154http://www.pc-progress.cz/Default.htm (hydrus 1D code)http://bgf.mv.slu.se/ShowPage.cfm?OrgenhetSida_ID=5658 (MACRO model)