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Earth's Systems / Biological processes / Terrestrial ecosystem functioning / Living soil system / Water infiltration, retention and movement / Unsaturated hydraulic conductivity and Richards flow

Unsaturated hydraulic conductivity and Richards flow

How the flux of liquid water in soil follows the Buckingham-Darcy law, with hydraulic conductivity falling by orders of magnitude as pores drain, controlling infiltration, redistribution and the supply of water to roots.

Boundary: where this process starts

Starts with: Flux follows Buckingham-Darcy, q = -K(h) times the gradient of total potential, and combined with mass balance gives the Richards equation

Boundary: where it ends

Ends after: Roots move water at night by hydraulic lift from moist deep layers to dry shallow layers

PARTICIPANTSRESOURCESSoil waterSoil poresPlant rootsGravitySoil textureOtherparticipantsWaterPore spaceClay mineralsImpact +3 of 5. Click for details and evidence.Impact +3 of 5. Click for details and evidence.Impact +3 of 5. Click for details and evidence.Impact -3 of 5. Click for details and evidence.Impact -3 of 5. Click for details and evidence.Impact +3 of 5. Click for details and evidence.Impact +3 of 5. Click for details and evidence.Impact +3 of 5. Click for details and evidence.Impact +2 of 5. Click for details and evidence.Impact +3 of 5. Click for details and evidence.Impact -4 of 5. Click for details and evidence.↻ balances · strong · 0.4 Uptake dries the sImpact +2 of 5. Click for details and evidence.↻ balances · weak · 0.15 Lifted water moisteFlux follows Buckingham-Darcy, q = -K(h) times the gradient of total potential, and combined with mass balance gives the Richards equation: uses WaterFlow through a pore scales with radius to the fourth power, so doubling radius gives 16 times the flow and large pores dominate conductivity: uses WaterFlow through a pore scales with radius to the fourth power, so doubling radius gives 16 times the flow and large pores dominate conductivity: uses Pore spaceSaturated conductivity spans about three orders of magnitude by texture: sand about 20 cm/h, silt loam about 0.7 cm/h, clay about 0.03-0.1 cm/h: uses WaterSaturated conductivity spans about three orders of magnitude by texture: sand about 20 cm/h, silt loam about 0.7 cm/h, clay about 0.03-0.1 cm/h: uses Pore spaceSurface seals, compaction or water repellency throttle the top boundary, so rain exceeding the seal conductivity runs off: uses WaterSurface seals, compaction or water repellency throttle the top boundary, so rain exceeding the seal conductivity runs off: uses Pore spaceHydraulic conductivity drops steeply as suction rises because the largest pores drain first: uses WaterHydraulic conductivity drops steeply as suction rises because the largest pores drain first: uses Pore spaceWith Carsel & Parrish parameters in the van Genuchten-Mualem model, K at -10 kPa is about 1e-8 of Ks for sand but about 4e-3 of Ks for clay, so at that suction clay conducts more than sand: uses WaterWith Carsel & Parrish parameters in the van Genuchten-Mualem model, K at -10 kPa is about 1e-8 of Ks for sand but about 4e-3 of Ks for clay, so at that suction clay conducts more than sand: uses Clay mineralsInfiltration rate starts high and declines toward the saturated conductivity as the wetted zone deepens: uses WaterInfiltration rate starts high and declines toward the saturated conductivity as the wetted zone deepens: uses Pore spaceIn dry soil conductivity is so low that supply to roots, not root uptake capacity, limits transpiration, so plants wilt with some water still in the soil: uses WaterRoots move water at night by hydraulic lift from moist deep layers to dry shallow layers: uses Waterflux driven by potentialgradientWater: flux driven by potential gradientflow scales with poreradiusWater: flow scales with pore radiuslarge pores carry mostflowPore space: large pores carry most flowconducts according totextureWater: conducts according to texturesize controls saturatedconductivityPore space: size controls saturated conductivityruns off above sealconductivityWater: runs off above seal conductivityreduced by surface sealsPore space: reduced by surface sealsconduction falls assuction risesWater: conduction falls as suction riseslargest pores drainfirstPore space: largest pores drain firstconducted differently bytextureWater: conducted differently by textureconduct more at highsuctionClay minerals: conduct more at high suctioninfiltrates faster atfirstWater: infiltrates faster at firstwetted zone deepens overtimePore space: wetted zone deepens over timesupply to roots limitstranspirationWater: supply to roots limits transpirationmoved from deep moistlayersWater: moved from deep moist layersStart: Unsaturatedhydraulic conductivityand Richards flowSTARTStart: Unsaturated hydraulic conductivity and Richards flowEnd: Unsaturatedhydraulic conductivityand Richards flowENDEnd: Unsaturated hydraulic conductivity and Richards flowFlux followsBuckingham-Darcy, q =-K(h) times t…📄1Flux follows Buckingham-Darcy, q = -K(h) times the gradient of total potential, and combined with mass balance gives the Richards equationFlow through a porescales with radius tothe fourth power, …📄1Flow through a pore scales with radius to the fourth power, so doubling radius gives 16 times the flow and large pores dominate conductivitySaturated conductivityspans about threeorders of magnitude …📄1Saturated conductivity spans about three orders of magnitude by texture: sand about 20 cm/h, silt loam about 0.7 cm/h, clay about 0.03-0.1 cm/hSurface seals,compaction or waterrepellency throttle t…📄1Surface seals, compaction or water repellency throttle the top boundary, so rain exceeding the seal conductivity runs offHydraulic conductivitydrops steeply assuction rises becau…📄1Hydraulic conductivity drops steeply as suction rises because the largest pores drain firstWith Carsel & Parrishparameters in the vanGenuchten-Mualem mode…📄1With Carsel & Parrish parameters in the van Genuchten-Mualem model, K at -10 kPa is about 1e-8 of Ks for sand but about 4e-3 of Ks for clay, so at that suction clay conducts more than sandInfiltration ratestarts high anddeclines toward t…📄1Infiltration rate starts high and declines toward the saturated conductivity as the wetted zone deepensIn dry soilconductivity is so lowthat supply to root…📄1In dry soil conductivity is so low that supply to roots, not root uptake capacity, limits transpiration, so plants wilt with some water still in the soilRoots move water atnight by hydraulic liftfrom moist deep laye…📄1Roots move water at night by hydraulic lift from moist deep layers to dry shallow layers
Line thickness = size of impact (1 to 5)% on a line = chance a fork takes that branch📄 = pieces of evidence on a stepNegative effectLoops backHypothesisResource used up (arrow into the step)Resource used, not used upResource made or released (arrow out of the step)
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Flux follows Buckingham-Darcy, q = -K(h) times the gradient of total potential, and combined with mass balance gives the Richards equation
Soil waterGravityWater
Evidence (1) · added by Fern-C
  • Richards 1931, Physics 1:318-333, Capillary conduction of liquids through porous mediums: Extended Darcy law to unsaturated media with water-content dependent conductivity; basis of the Richards equation. (confidence 0.85)
Flow through a pore scales with radius to the fourth power, so doubling radius gives 16 times the flow and large pores dominate conductivity
Soil poresPore spaceWater
Evidence (1) · added by Fern-C
  • Hillel 1998, Environmental Soil Physics (Poiseuille law): Poiseuille flow in a capillary is proportional to r^4, so conductivity is governed by the widest water-filled pores. (confidence 0.85)
Saturated conductivity spans about three orders of magnitude by texture: sand about 20 cm/h, silt loam about 0.7 cm/h, clay about 0.03-0.1 cm/h
Soil textureWaterPore space
Evidence (1) · added by Fern-C
  • Rawls, Brakensiek & Saxton 1982, Transactions of the ASAE 25:1316-1320: Mean saturated hydraulic conductivity by USDA texture class, from about 21 cm/h in sand to below 0.1 cm/h in clays. (confidence 0.6)
Surface seals, compaction or water repellency throttle the top boundary, so rain exceeding the seal conductivity runs off
RaindropsSoil surfaceWaterPore space
Evidence (1) · added by Fern-C
  • Assouline 2004, Vadose Zone Journal 3:570-591, Rainfall-induced soil surface sealing: Seal saturated conductivity is one to three orders of magnitude below that of the underlying soil, controlling infiltration and runoff. (confidence 0.6)
Hydraulic conductivity drops steeply as suction rises because the largest pores drain first
Soil poresSoil waterWaterPore space
Evidence (1) · added by Fern-C
  • van Genuchten 1980, Soil Science Society of America Journal 44:892-898; Mualem 1976, Water Resources Research 12:513-522: Closed-form K(h) from the retention curve predicts K falling by many orders of magnitude between saturation and dry soil. (confidence 0.85)
With Carsel & Parrish parameters in the van Genuchten-Mualem model, K at -10 kPa is about 1e-8 of Ks for sand but about 4e-3 of Ks for clay, so at that suction clay conducts more than sand
SandClay mineralsWaterClay minerals
Evidence (1) · added by Fern-C
  • Carsel & Parrish 1988, Water Resources Research 24:755-769: Sand: alpha 0.145 per cm, n 2.68, Ks 713 cm/d; clay: alpha 0.008 per cm, n 1.09, Ks 4.8 cm/d; substituting at h = 100 cm gives the quoted ratios (derived estimate). (confidence 0.65)
Infiltration rate starts high and declines toward the saturated conductivity as the wetted zone deepens
Rain and irrigationWetting frontWaterPore space
Evidence (1) · added by Fern-C
  • Green & Ampt 1911, Journal of Agricultural Science 4:1-24: Infiltration rate falls as 1/depth of the wetting front, approaching Ks at long times. (confidence 0.85)
In dry soil conductivity is so low that supply to roots, not root uptake capacity, limits transpiration, so plants wilt with some water still in the soil
Plant rootsSoil waterWater
Evidence (1) · added by Fern-C
  • Gardner 1960, Soil Science 89:63-73, Dynamic aspects of water availability to plants: At low soil water content the soil conductivity becomes limiting for root water uptake. (confidence 0.7)
Roots move water at night by hydraulic lift from moist deep layers to dry shallow layers
Plant rootsDeep soilWater
Evidence (1) · added by Fern-C
  • Richards & Caldwell 1987, Oecologia 73:486-489; Neumann & Cardon 2012, New Phytologist 194:337-352: Sagebrush roots lifted water from deep moist soil into dry upper soil overnight, raising its water potential. (confidence 0.85)