Soil physics

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Soil physics Magnus Persson

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Soil physics. Magnus Persson. 2·r. R. p-2q. 2·R·cos q. q. P 1. z. P 2. Surface tension. Due to surface tension water can be held at negative pressure in capillary tubes. (P 1

Transcript of Soil physics

  • 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)