Lecture 4 Infiltration Elements of Hydrologic Cycle Precipitation

Lecture 4 Infiltration ﻧﻔﻮﺫ

Elements of Hydrologic Cycle: • Precipitation, P (Rain and snow) • Evaporation, E and Transpiration, T • Infiltration, I • Surface runoff, R • Groundwater flow, G Meteorology Precipitation Rain Runoff Deterministic Rainfall-runoff methods Snow? Evaporation Stochastic Rainfall-runoff methods Infiltration Groundwater Hydrology?

Elements of Hydrologic Cycle: • Precipitation, P (Rain and snow) • Evaporation, E and Transpiration, T • Infiltration, I • Surface runoff, R • Groundwater flow, G Meteorology Precipitation Rain Runoff Deterministic Rainfall-runoff methods Snow? Evaporation Stochastic Rainfall-runoff methods Infiltration Groundwater Hydrology?

Infiltration Definitions ﺗﻌﺎﺭیﻒ ﻧﻔﻮﺫ • Infiltration: is a process of water entry into a soil through surface ﻧﻔﻮﺫ • Infiltration Rate (capacity) : Rate at which water enters soil measured in L/T ﺳﺮﻋﺖ ﻧﻔﻮﺫ • Initial Infiltration Rate: Is the maximum rate of infiltration (L/T) ﺳﺮﻋﺖ ﻧﻔﻮﺫ ﺍﻭﻟﻴﻪ )ﻣﺎکﺰیﻤﻢ ( ﺳﺮﻋﺖ ﻧﻔﻮﺫ • Final Infiltration Rate: Is the minimum Infiltration rate (L/T) ( )ﻣیﻨیﻤﻢ ﺳﺮﻋﺖ ﻧﻔﻮﺫ • Cumulative Infiltration: Depth of infiltrated water at given time Rainfall Conditions: • Rainfall intensity • Rainfall duration ( L) Factors affecting Infiltration ﻓﺎکﺘﻮﺭﻫﺎی ﻣﻮﺛﺮ ﺑﺮ ﻧﻔﻮﺫ Underground Conditions: - Transmission characteristics of underlying soil • Evaporation • Transpiration ﺳﺮﻋﺖ ﻧﻔﻮﺫ ﻧﻬﺎﻳﻲ - Volume of storage available Soil Surface Conditions: - Vegetation Covers - Compaction /cracks

Infiltration Definitions ﺗﻌﺎﺭیﻒ ﻧﻔﻮﺫ • Infiltration rate, f(t) ﺳﺮﻋﺖ ﻧﻔﻮﺫ – Rate at which water enters the soil at the surface (in/hr or cm/hr) • Cumulative infiltration, F(t) ﻧﻔﻮﺫ ﺗﺠﻤﻌی – Accumulated depth of water infiltrating during given time period F • Initial Infiltration Rate • Final Infiltration Rate, f(t) (L/t) f t

is Infiltration a function of texture and vegetation? ﻧﻔﻮﺫ ﺗﺎﺑﻌی ﺍﺯ پﻮﺷﺶ ﻭ ﺑﺎﻓﺖ ﺯﻣیﻦ ﺍﺳﺖ؟ • The rate of infiltration depends on the soil type, slope, vegetation, soil moisture content, temperature, and the precipitation intensity.

is Infiltration a function of precipitation? ﻧﻔﻮﺫ ﺗﺎﺑﻌی ﺍﺯ ﺑﺎﺭﻧﺪگی ﺍﺳﺖ؟ • The actual infiltration rate is equal to the infiltration capacity (f) only when rain intensity, less the rate of retention, equals or exceeds the capacity (f). • The value of f is maximum ( = f 0 ) at the beginning of the storm. This becomes constant ( =f∞ ) as the soil becomes saturated.

is Infiltration a function of precipitation? ﻧﻔﻮﺫ ﺗﺎﺑﻌی ﺍﺯ ﺑﺎﺭﻧﺪگی ﺍﺳﺖ؟ • Surface Runoff occurs when surface water input exceeds infiltration capacity. (a) Infiltration rate = rainfall rate which is less than infiltration capacity. (b) Runoff rate = Rainfall intensity – Infiltration capacity. (from Dunne and Leopold, 1978)

is Infiltration a function of precipitation? ﻧﻔﻮﺫ ﺗﺎﺑﻌی ﺍﺯ ﺑﺎﺭﻧﺪگی ﺍﺳﺖ؟ • Where is runoff coming from?

Precipitation, Infiltration, and Runoff relationship ﻧﻔﻮﺫ ﻭ ﺭﻭﺍﻧﺎﺏ ، ﺭﺍﺑﻄﻪ ﺑﺎﺭﺵ

Final Infiltration Rate by Soil Group/ Texture ﺳﺮﻋﺖ ﻧﻔﻮﺫ ﻧﻬﺎیی ﺑﺎ ﺗﻮﺟﻪ ﺑﻪ ﺟﻨﺲ ﺧﺎک Source: Texas Council of Governments, 2003.

Infiltration tests آﺰﻣﺎیﺶ ﻧﻔﻮﺫ Infiltrometers ﻧﻔﻮﺫ ﺳﻨﺞ ﻫﺎ Single Ring Double Ring

Infiltration tests

Double Ring Infiltrometer Measure rate of fall in inner ring Infilration

Infiltration test

Infiltration Equations ﻣﻌﺎﺩﻻﺕ ﻧﻔﻮﺫ 1. Horton model 2. Green-Ampt model 3. Philip model 4. Kostiakov model

1 - Horton infiltration Equation • This is purely a mathematical function of the following form: fo fi = infiltration capacity at time, t fc = final infiltration capacity fo = initial infiltration capacity k = soil coefficient fc

1 - Horton infiltration Equation • Horton assumes that precipitation supply is greater than infiltration rate. 2 1 0

1 - Horton infiltration Equation

1 - Horton infiltration Equation • There are 3 parameters to estimate or calibrate for a watershed!! fo , fc & k

1 -Horton infiltration Equation (predefined coefficient) Example 1 Given initial infiltration capacity of 60 cm/hr and time constant, k of 0. 4 hr-1. Derive infiltration capacity vs. time curve if the final infiltration capacity is 10 cm/hr. 2. Estimate the total infiltrated water in m 3 for the first 10 hours for a 100 km 2 watershed using Horton model. Solution: Horton curve: f = f∞ + (f 0 – f∞) e-Kt Substituting: f = 10 + (50) e-0. 4 t Infiltration rate Integrating: F = ∫[10 + 50 e-0. 4 t] dt Cumulative Infiltration F = [10 t -(50/0. 4)e-0. 4 t│0 to 10 = [(10) –(50 / 0. 4)e-4] – (- 50/0. 4) = 141 cm Volume infiltrated = (141 cm x m/100 cm) x (100 km 2) (1000 m/km)2 = 1. 41 x 108 m 3

2 - Green-Ampt (Soil Water Variables) = moisture content (volume of water/total volume of soil) = initial moisture content of dry soil before infiltration happens Ground Surface Wetted Zone = increase in moisture content as wetting front passes = porosity Wetting Front = residual water content of very dry soil = effective porosity Dry Soil

2 - Green – Ampt (Infiltration) Ponded Water Ground Surface Wetted Zone Wetting Front Dry Soil

2 - Green – Ampt Infiltration Ground Surface Wetted Zone Wetting Front • Apply finite difference to the derivative, between – Ground surface Dry Soil – Wetting front

2 - Green – Ampt Infiltration f, F Use and integrate over time, gives F f t This is a Nonlinear equation, requiring iterative solution!!!

2 - Green – Ampt Infiltration Initial effective saturation 0 ≤ Se ≤ 1 Effective porosity

2 - Green-Ampt (Parameters)

2 - Green – Ampt Infiltration • Example 2 • Determine and plot the infiltration rate and the cumulative infiltration for an 8 hour precipitation on a clay loam soil with initial effective saturation of 30% Using Green-Ampt method. • Parameters: Texture Clay Loam Residual Porosity n Porosity ϴr 0. 464 0. 155 Effective Suction Head Porosity ϴe ψ (cm) 0. 309 20. 88 Conductivity K (cm/hr) 0. 10

2 - Green – Ampt Infiltration • Solution Use Excel Solver

Infiltration Methods (Parameter estimation)? ﺗﺨﻤیﻦ پﺎﺭﺍﻣﺘﺮﻫﺎ

Infiltration Methods (Parameter estimation)

Infiltration Equations Example 3 A clayey loam has exhibited the following values of infiltration capacity: Infiltration capacity, in. /h Time, min Infiltration Capacity, in. /h Time, min 0. 075 0. 0557 0. 045 0. 0353 0. 025 0. 020 0 2 4 6 8 10 15 0. 0145 0. 013 0. 0128 20 30 40 50 60 • Determine the value of soil constant for different models.