CE 394K.2 Hydrology Infiltration Reading AH Sec 5.1 to 5.5 Some slides were prepared by Venkatesh Merwade Slides 2-6 come from http://biosystems.okstate.edu/Home/mkizer/C%20Soil %20Water%20Relationships.ppt Soil Water Measurement Neutron scattering (attenuation) Measures volumetric water content (v) Attenuation of high-energy neutrons by hydrogen nucleus Advantages: samples a relatively large soil sphere repeatedly sample same site and several depths accurate Disadvantages: high cost instrument radioactive licensing and safety

not reliable for shallow measurements near the soil surface Dielectric constant A soils dielectric constant is dependent on soil moisture Time domain reflectometry (TDR) Frequency domain reflectometry (FDR) Primarily used for research purposes at this time Soil Water Measurement Neutron Attenuation Soil Water Measurement Tensiometers Measure soil water potential (tension) Practical operating range is about 0 to 0.75 bar of tension (this can be a limitation on medium- and fine-textured soils) Electrical resistance blocks

Measure soil water potential (tension) Tend to work better at higher tensions (lower water contents) Thermal dissipation blocks Measure soil water potential (tension) Require individual calibration Tensiometer for Measuring Soil Water Potential Water Reservoir Variable Tube Length (12 in- 48 in) Based on Root Zone Depth Porous Ceramic Tip Vacuum Gauge (0-100 centibar) Electrical Resistance Blocks & Meters 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 Saturation Zone Transition Zone Transmission Zone Wetting Zone Saturated, transmission, wetting, and wetting front Wetting Front depth

Richards Equation Recall Darcys Law Total head So Darcy becomes D K q z K h z z z K K z D

K z q z K Soil water diffusivity Continuity becomes t q z K q D K z z z

K z Philips Equation Recall Richards Equation D K t z z Assume K and D are functions of , not z Solution Two terms represent effects of Suction head Gravity head

S Sorptivity Function of soil suction potential Found from experiment F (t ) St 1/ 2 Kt 1 1/ 2 f (t ) St K 2 Infiltration into a horizontal soil column Boundary conditions = o for x = 0, t > 0 = n for t = 0, x > 0 0 Equation:

x D t x z Measurement of Diffusivity by Evaporation from Soil Cores Air stream q x q = soil water flux = evaporation rate q D x Measurement of Diffusivity by Evaporation from Soil Cores http://www.regional.org.au/au/asa/2006/poster/water/4521_deeryd.htm Numerical Solution of Richards

Equation (Ernest To) http://www.ce.utexas.edu/prof/maidment/GradHydro2007/Ex4/Ex4Soln.doc Implicit Numerical Solution of Richards Equation t (j) j j -1 x (i) i-1 i i+1 Implicit Numerical Solution of Richards Equation Matrix solution of the equations f F

Definitions V gross volume of element Vv volume of pores Element of soil, V (Saturated) Pore with water solid Vs volume of solids Vw volume of water Vv n porosity V Vw S saturation; 0 S 1 Vv Vw nS moisture content; 0 n V Pore with

air Element of soil, V (Unsaturated) Infiltration Infiltration rate f (t ) Rate at which water enters the soil at the surface (in/hr or cm/hr) Cumulative infiltration Accumulated depth of water infiltrating during given time period t F (t ) f ( )d 0 f (t ) dF (t )

dt Infiltrometers Single Ring Double Ring http://en.wikipedia.org/wiki/Infiltrometer Infiltration Methods Horton and Phillips Infiltration models developed as approximate solutions of an exact theory (Richards Equation) Green Ampt Infiltration model developed from an approximate theory to an exact solution Hortonian Infiltration Recall Richards Equation Assume K and D are constants, not a function

of or z Solve for moisture diffusion at surface D K t z z 2 K D 2 t z z 2 D 2 t z 0

f (t ) f c ( f 0 f c )e kt f0 initial infiltration rate, fc is constant rate and k is decay constant Hortonian Infiltration 3.5 f0 3 Infiltration rate, f 2.5 k1 2 k1 < k2 < k3 1.5 k2 1

k3 fc 0.5 0 0 0.5 1 Time 1.5 2 Philips Equation Recall Richards Equation D K

t z z Assume K and D are functions of , not z Solution Two terms represent effects of Suction head Gravity head S Sorptivity Function of soil suction potential Found from experiment F (t ) St 1/ 2 Kt 1 1/ 2 f (t ) St K 2 Green Ampt Infiltration

L Depth to Wetting Front i Initial Soil Moisture Ponded Water h0 Ground Surface F (t ) L( i ) L Wetted Zone dF dL f dt dt Wetting Front h

q z K f z i n f K K z z Dry Soil L Green Ampt Infiltration (Cont.) f K

Ground Surface Wetted Zone K z Wetting Front Apply finite difference to the derivative, between Ground surface z 0, 0 Wetting front z L, f f 0 f K K K K K K z z

L 0 F (t ) L F L f K F f 1 i z

Dry Soil f K K z L Green Ampt Infiltration (Cont.) f K F f 1 f

Ground Surface Wetted Zone dL dt Wetting Front i F (t ) L f dL K 1 dt

L z f dL K dt dL f L Dry Soil Evaluate the constant of integration L 0 @ t 0 C f ln( f ) Integrate K t L f ln(

f L) C Kt L f ln( f f L ) L Green Ampt Infiltration (Cont.)

Kt L f ln( f f L Ground Surface Wetted Zone L Wetting Front ) i

F F Kt f ln(1 ) f f K F f 1 z Dry Soil Nonlinear equation, requiring iterative solution. See: http://www.ce.utexas.edu/prof/mckinney/ce311k/Lab/Lab8/Lab8.html

Soil Parameters Green-Ampt model requires Hydraulic conductivity, Porosity, Wetting Front Suction Head Brooks and Corey r se e e n r Effective saturation Soil Class Porosity Effective Porosity n e

0.437 0.463 0.475 0.417 0.434 0.385 Effective porosity (1 se ) e Sand Loam Clay Wetting Front Suction Head (cm) 4.95 9.89

31.63 Hydraulic Conductivity K (cm/h) 11.78 0.34 0.03 Ponding time Elapsed time between the time rainfall begins and the time water begins to pond on the soil surface (tp) Up to the time of ponding, all rainfall has infiltrated (i = rainfall rate) Infiltration rate, f Ponding Time Potential Infiltration

i Rainfall F i * t p f K F f 1 f i K 1 i *t p

t p K Actual Infiltration Cumulative Infiltration, F f i Accumulated Rainfall Time Infiltration F p i * t p f i (i K )

tp Time Example Silty-Loam soil, 30% effective saturation, rainfall 5 cm/hr intensity e 0.486 16.7 cm K 0.65 cm / hr se 0.30 (1 se ) e (1 0.3)(0.486) 0.340 16.7 * 0.340 t p K f i (i K ) 0.65

5.68 0.17 hr 5.0(5.0 0.65)(i K )