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richards equation,green ampt model

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- 1. A presentation on Subsurface water K.Bhargav Kumar 154104063
- 2. Subsurface Water unit volume of subsurface consists of soil/rock, and pores which may be filled with water and/or air total porosity= volume voids/total volume water content=volume water/total volume saturation=volume water/volume voids degree of saturation delineates various zones of subsurface water
- 3. Definitions soil water - Ground surface to bottom of root zone depth depends on soil type and vegetation. May become saturated during periods of rainfall otherwise unsaturated (soil pores partially filled with air). Plants extract water from this zone. Evaporation occurs from this zone. intermediate vadose zone - Between soil water zone and capillary fringe. Unsaturated except during extreme precipitation events. Depth of zone may range from centimeters to 100s of meters.
- 4. Definitions Continued capillary zone - Above saturated zone. Water rises into this zone as a result of capillary force. Depth of this zone is a function of the soil type. Fractions of a meter for sands (mm) to meters for fine clays. All pores filled with H2O, p < 0. Effect seen if place bottom of dry porous media (soil or sponge) into water. Water will be drawn up into media to a height above water where soil suction and gravity forces are equal. saturated zone - All pores filled with water, p > 0. Formations in this zone with ability to transmit water are called aquifers.
- 5. Unsaturated Zone Water can exist in all its phases in the unsaturated zone. Liquid water occurs as: hygroscopic water - adsorbed from air by molecular interaction (H-bonds) capillary water - held by surface tension due to viscosity of liquid gravitational water-water in unsaturated zone in excess of field capacity which percolates downward due to gravity ultimately reaching saturated zone as recharge.
- 6. Unsaturated Zone Hygroscopic and capillary waters are held by molecular electrostatic forces (between polar bonds and particles -- surface tension) in thin films around soil particles drier soil, smaller pores hygroscopic and capillary forces Hygroscopic water - held at -31 to -10,000 bars. Water is unavailable to plants or for recharge to groundwater. Capillary water - Held at -0.33 to -31 bars. More water filling pores but discontinuous except in capillary fringe. This water can be used by plants.
- 7. Definitions Permanent wilting point: tension (suction, negative pressure) below which plant root system cannot extract water. Depends on soil and type of vegetation. Typically -15 bars (- 15x105 Pa, -15000cm Field capacity: tension (suction, negative pressure) below which water cannot be drained by gravity (due to capillary and hygroscopic forces) Depends on soil type. Typically about - 0.33 bars
- 8. Typical Moisture Profiles rain after a long dry period direction of moisture movement moisture content depth root zone hygroscopic wilting point field capacity saturation
- 9. Typical Moisture Profiles Drying process moisture depth field capacity saturation 1 - Drying in upper layers by ET. 2 - Bottom part of wetting front continues Upper part continues to dry. 3 - At some point and movement resu in no moisture gradient 4 - Dry front established. Lower zones ar being depleted to satisfy PET at surfa Drying continues until capillary forces are unable to move water to surface.
- 10. Dacry-Buckingham law Flow in unsaturated porous media governed by a modified Darcy’s law called Darcy-Buckingham law : - suction head (capillary head) or negative pressure head. Energy possessed by the fluid due to soil suction forces. Suction head varies with moisture content, n, 0, < n , is negative. K() - hydraulic conductivity is a function of water content , K() because more continuously connected pores, more space available for water to travel through, until at = n, K(n) = Ksat zh z h Kqz
- 11. Measuring Soil Suction Soil Suction () head measured with tensiometers, an airtight ceramic cup and tube containing water. Soil tension measured as vacuum in tubes created when water drawn out of tube into soil. Comes to equilibrium at soil tension value. Tensiometers often used to schedule irrigation.
- 12. Tensiometer
- 13. Why different flow equations? Steady-state Transient Saturated Unsaturated Darcy’s law Darcy’s law (with K(q)) N/A Richards’ equation Darcy’s law: L AKq q changes with time No K(q) No Dq No q(y)
- 14. Equation of Continuity (Conservation of Mass) Steady-state Transient Saturated Unsaturated Darcy’s law Darcy’s law (with K(q)) Richards’ equation Input – Output = Change in Storage x q = t tx q
- 15. Richards’ equation L Kq Given Darcy’s law: x K xx q Let things change from place to place (say, in the x-direction) tx q We also want conservation of mass x K xt So we substitute it in to the left-hand side
- 16. Richards’ equation x K xt Remember that the potential gradient, , combines elevation, osmotic, pressure, and matric components (among others). x Sometimes it’s convenient to separate out the elevation part: 1 x K xt Vertical 0 x K xt Horizontal Just remember that this y doesn’t include elevation!
- 17. depth Wetting Zone Transmission Zone Transition Zone Saturation Zone Wetting Front Infiltration General Process of water penetrating from ground into soil Factors affecting Condition of soil surface, vegetative cover, soil properties, hydraulic conductivity, antecedent soil moisture Four zones Saturated, transmission, wetting, and wetting front
- 18. Infiltration Infiltration rate, f(t) Rate at which water enters the soil at the surface (in/hr or cm/hr) Cumulative infiltration, F(t) Accumulated depth of water infiltrating during given time period t dftF 0 )()( dt tdF tf )( )( t f, F F f
- 19. Infiltrometers Single Ring Double Ring http://en.wikipedia.org/wiki/Infiltrometer
- 20. Infiltration Methods Horton and Phillips Infiltration models developed as approximate solutions of an exact theory (Richard’s Equation) Green – Ampt Infiltration model developed from an approximate theory to an exact solution
- 21. Horton Infiltration Model • one of earliest infiltration equations developed (1933) and the most common empirical equation used to predict infiltration if ponding occurs from above: • Instantaneous infiltration • Cumulative infiltration • fc, minimum infiltration capacity (approximately saturated hydraulic conductivity) • fo, maximum infiltration capacity (function of saturated conductivity and soil tension) • k constant representing exponential rate of decrease of infiltration kt cc ffftf exp)()( 0 t Ktco c K ff tfdftF 0 )exp1()()(
- 22. Horton’s Infiltration Model • All are empirical parameters which must be fit to each soil type using data from a ring infiltrometer experiment • Horton’s equations are only valid after ponding. Therefore all water the soil has potential to infiltrate is available at soil surface. Ponding will only occur if i > f(t). Should only be used during very high intensity precipitation events over small areas fc fo rate of decay governed by k, increase k, increase rate of decay (analogous to Ksat) t F(t) f(t) (time after ponding)
- 23. Green-Ampt Assumptions Wetted Zone Wetting Front Ground Surface Dry Soil L n i z = increase in moisture content as wetting front passes = Suction head at “sharp” wetting front Conductivity, K L = Wetted depth K = Conductivity in wetted zone Ponded Water 0h 0h = Depth of water ponding on surface (small)
- 24. Green-Ampt soil water variables Wetted Zone Wetting Front Ground Surface Dry Soil L n i z r e i = initial moisture content of dry soil before infiltration happens = increase in moisture content as wetting front passes = moisture content (volume of water/total volume of soil) r = residual water content of very dry soil e = effective porosity n = porosity
- 25. Green ampt equation: Infiltration rate: The cool thing is, though, that what we want (F or f) is a function of only things we can figure out (porosity, initial moisture content, soil conductivity, and soil capillary pressure). The problem is that you can’t easily put F on one side, and all the other stuff on the other. This inability to separate the equation means that the equation is nonlinear.
- 26. Ponding time Elapsed time between the time rainfall begins and the time water begins to pond on the soil surface (tp)
- 27. Ponding Time Up to the time of ponding, all rainfall has infiltrated (i = rainfall rate) if 1 F Kf ptiF * 1 * pti Ki Potential Infiltration Actual Infiltration Rainfall Accumulated Rainfall Infiltration Time Time Infiltrationrate,f Cumulative Infiltration,F i pt pp tiF * )( Kii K tp
- 28. References enchartedlearning.com tutor.com Huggett, J. (2005) Fundamentals of Geomorphology, Routeledge, Horton, Robert E (1933) "The role of infiltration in the hydrologic cycle" Transactions of the American Geophysics Union, 14th Annual Meeting, pp. 446–460. Horton, Robert E (1945) "Erosional development of streams and their drainage basins; Hydrophysical approach to quantitative morphology" Geological Society of America Bulletin, 56 (3): 275–370. doi:10.1130/0016-7606

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