The FEST Model for Testing the Importance of Hysteresis in Hydrology J. Philip OâKane Department of Civil & Environmental Engineering, Environmental Research Institute UCC Int. Workshop on HYSTERESIS & MULTI-SCALE ASYMPTOTICS, University College Cork, Ireland, March 17-21, 2004Slide 2
Content 1. Presentation soil material science 2. The BASE model bare soil with dissipation and waste 3. The FEST model fully vegetated soil chunk with transpiration 4. The structure of FEST feedback structure bifurcationSlide 3
1. Presentation 1. Hysteresis in hydrology, climatology, ecohydrology Is it noteworthy? For what questions? 2. Hysteresis in open channel stream Rate subordinate 3. Hysteresis in soil material science Rate free 4. Strategy Build âtest rigsâ to answer the inquiries BASE model - pde - soil material science FEST model - tribute - conceivable soil bio-physical scienceSlide 6
Some dirt physical scienceSlide 7
Soil: a multi-stage material Each stage has mass M and volume V The REV â agent rudimentary volume 1 cm Air M a , V a Water M w , V w Soil-solids M s , V s 1 cm 1 cmSlide 8
Ratios depict the multi-stage material Total porosity f = (V a + V w )/(V a + V w + V s ) Void ratio e = (V a + V w )/V s [m 3 m - 3 ] Particle thickness r s = M s/V s Dry mass thickness r b = M s/(V a + V w + V s ) Water thickness r w = M w/V w [Mg m - 3 ] Air M a , V a Water M w , V w Soil-solids M s , V sSlide 9
Moisture content Volumetric wetness q = V w/(V a +V w +V s ) In mud soils the dirt lattice swells , V s = f(V w ), q has no very much characterized most extreme worth In rock, sand and residue, the dirt network is ârigidâ q has a greatest at immersion 0 < q < q s < 1, at immersion V a = 0 Mass wetness w = M w/M s q = w r b/r w in inflexible soilsSlide 10
Potential vitality of soil water A mass m of soil water of volume V and thickness ï² w = m/V is proceeded onward a self-assertive way through a vertical separation z by a power mg = ï² w Vg The dissipationless work done against the power of gravity is mgz = ( ï² w Vg)z There are three option methods for speaking to the potential vitality of this water as dissipationless work (a) per unit mass, (b) per unit volume, and (c) per unit weightSlide 11
Potential vitality per unit mass, volume and weightSlide 12
Total potential is a total of fractional possibilities y = y g + y m + y o + y p + y a + y W y g gravitational potential y m matric potential y o osmotic potential y p hydrostatic potential y an environmental y W overburden potentialSlide 13
Partial possibilities with regular reference state - free water at z=0Slide 14
Soil-dampness trademark - matric potential, soil suction or drying ï¹ m = ï¹ m ( ï± ), ï¹ m ï£ ï¹ e < 0, 0 < ï± ï£ ï± s , ï¹ e air-passage potential, ï± = ï± s ï± = ï± ( ï¹ m ) inverse capacity Specific water limit C( ï± ) = d ï±/d ï¹ m Drying and wetting are diverse - hysteresis - normally disregarded !Slide 15
Y m (z) allotments q( z ) into fluid and vapor parts h(z) relative mugginess of soil-air M w is the molar mass of water (0.018 kg/mol) , R the molar gas consistent (8.314 J/mol K) T the steady temperature in degrees Kelvin (293 K at 20 0 C) .Slide 16
The BASE model - exposed soil with vanishing and wasteSlide 17
T E P Water stream in a section of soil Vertical direction starting from the earliest stage positive downwards to the watertable (no air) 0 Soil 1 I Soil 2 10 m z Soil 3 1 m 1 m C DSlide 18
Conservation of water mass in one measurement f l is the flux thickness of fluid water ( kg m - 2 s - 1 ) f v is the flux thickness of water vapor ( kg m - 2 s - 1 ), in the bearing of positive z i.e. downwards,Slide 19
Generalized Darcyâs Law Philip, 1955 Buckingham, 1907Slide 20
Philip-Richards mathematical statement â Ï structure Solutions looked for in the space of persistent capacities y m (z,t) Discontinuities permitted in q (z,t) to coordinate spasmodic soil skylines Philip 1955, Richards, 1931Slide 21
Boundary conditions & driving Flux Boundary conditions Precipitation Evaporation Overland stream - overlook at first Interflow - disregard in one measurement Potential Boundary condition Ponded invasion Fixed water table Mixed Boundary condition Evaporation Drainage to a moving water table Forcing capacity TranspirationSlide 22
Standard hydrological inquiries Infiltration & surface spillover Evaporation Transpiration Redistribution Capillary ascent DrainageSlide 23
Two sets of exchanged limit conditions -air or soil control of fluxes? External pair - fluxes at potential rates Raining or drying atmosphere control Inner pair - fluxes at littler real rates Surface ponding or stage 2 drying soil controlSlide 24
The sprinkling and drying cycle t d Potential vanishing Actual dissipation Soil drying starts Ea<Ep Ea=Ep t E t Q Soil wetting starts q 0 <q R q 0 =q R Actual invasion Potential penetration t pSlide 25
Alternating control t d Potential vanishing Actual dissipation Atmosphere control! Ea=Ep Soil control ? Ea<Ep Soil drying starts t E t Q Soil wetting starts Soil control ? q 0 <q R Atmosphere control! q 0 =q R Actual invasion Potential penetration t pSlide 26
Richards mathematical statement â Î¸ structureSlide 27
Infiltration - environment control D \ K constant K linear K non-straight K delta capacity D Mein & Larson (1973) consistent D Breaster Breaster Clothier et al (1973) (1973) (1981) âFujita Dâ Knight & Rogers et al. Sander et al. Philip (1983) (1988) (1974)Slide 28
Infiltration - soil control D \ K constant K linear K non-direct K delta capacity D Green & Ampt (1911) steady D Carslaw & Philip Philip Jaeger (1969) (1974) (1946) âFujita Dâ Fujita not solved not comprehended (1952)Slide 29
Evaporation - climate control D \ K constant K linear K non-straight K delta capacity D not relevant consistent D Breaster* Breaster* KÃ¼hnel (1973) (1973) (1989 [C]) âFujita Dâ Knight & Sander & Sander & Philip* KÃ¼hnel KÃ¼hnel (1974) (19**) (19**) *complementary to penetration arrangementSlide 30
Evaporation - soil control D \ K constant K linear K non-straight K delta capacity D not pertinent steady D Carslaw & KÃ¼hnel Jaeger* Sander (1989 [C]) (1946) (19**) âFujita Dâ Fujita* not solved not illuminated (1952) *complementary to invasion arrangementSlide 31
The FEST model - completely vegetated soil piece with transpiration Goal: from conceivable biophysics a tribute - for testing hysteresis administratorsSlide 32
FEST common differential comparison Uniform dampness in the root zone Gradients in potential get to be contrasts Brooks-Corey-Campbell parametric expressions for the matric potential and pressure driven conductivities of soils Square wave barometrical constrainingSlide 33
Transpiration Roots totally enter the uniform root zone A 3-D wick sucks water from the uniform roots to a uniform shelter Leaf potential is matric capability of soil water in addition to change in gravitational potential between the roots and covering Potential transpiration ( given ) drives genuine transpirationSlide 34
Potential transpiration - given The Philip limit condition Leaf vanishing is corresponding to the distinction in stickiness between (a) the air, and (b) the stomatal air in âthermodynamicâ balance with its plant water in the overhangSlide 35
Actual transpiration drops beneath the potential rate when stomates close at leaf possibilities between some higher worth (e.g. - 5,000cm) and the shriveling potential (e.g. - 10,000cm)Slide 36
Feedback circles for transpirationSlide 37
Transpiration circles with soil material science parametersSlide 38
Infiltration Actual invasion is the precipitation\'s base rate and the potential penetration rate Infiltration is accepted to happen all through the dirt section through particular ways because of worm openings, creature tunnels and dead roots showing the invading water consistently to the dirt framework .Slide 39
Potential penetration rate is equivalent to the pressure driven conductivity at the dirt water potential times the contrast between that potential and the air passage capability of the downpour separated by a self-assertive pore dispersingSlide 40
Infiltration input circlesSlide 41
Infiltration with parametersSlide 42
Feedback circles for seepage/fine ascent with soil material science parametersSlide 43
Feedback circles for waste, slim ascentSlide 44
Cut the criticism circles Multiple equilibria BifurcationSlide 45
Bifurcation to leaveSlide 46
Titles Bifurcation on e over p = 1.2, 1, 0.8; period 10 Bifurcation on e over p = 1.2, 1, 0.8; period 20 Bifurcation on e over p = 1.2, 1, 0.8; period 40 Bifurcation on theta(0)Slide 53
Insertion of Preisach administrator One insertion makes everything hysteretic Extension in space horizontally with
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