02 10 evaporation-and_infiltration_jrs-rzl
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INCI 4138 Hydrologic Processes 1
Hydrologic Processes
INCI 4138
Introduction to Water Resources Engineering
Evaporation and Infiltration Processes
Dr. Jorge Rivera-Santos & Raúl E. Zapata-López
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INCI 4138 Hydrologic Processes 2
Evaporation
The process of water changing from its liquid phase to the vapor phase.
Water vapor is the state of water in the atmosphere.
It is a two-phase process. Water molecules escape
from the water surface to the atmosphere (heat?).
Transport of water vapor molecules away from the evaporating surface (wind?).
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INCI 4138 Hydrologic Processes 3
Evaporation Rate of evaporation depends on…
* Solar Radiation==================================================================================================================================================================
* Atmospheric Pressure * Air Temperature* Relative Humidity * Wind Speed==================================================================================================================================================================
* Water Temperature * Quality of Water* Geometry of the evaporating surface===========================================================================================================================================
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INCI 4138 Hydrologic Processes 4
Evaporation: Radiation effect
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INCI 4138 Hydrologic Processes 5
Evaporation Latent Heat is the heat that is given up or absorbed
when a phase changes.
Latent heat of vaporization is the heat given up during vaporization of liquid water to water vapor.
where T is the temperature in °C and lv is in joules per kilogram (J/Kg).
Tlv 237010501.2 6
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INCI 4138 Hydrologic Processes 6
Evaporation Process
Water molecules are always moving around.
This is caused by solar radiation.
When there is enough energy, water molecules are knocked away from the surface. Wind moves them out of the upper layer.
Water molecule transferred to the atmosphere become water vapor.
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INCI 4138 Hydrologic Processes 7
Evaporation from Water Bodies
Four methods to determine evaporation. Comparative method (evaporation pan)
Energy balance method (energy budget)
Aerodynamic method (mass transfer)
Combined balance method (Penman Method)
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INCI 4138 Hydrologic Processes 8
pLpL EKE
EvaporationEvaporation (yr or monthly) from water bodies are estimated by measuring daily evaporation from a pan and then corrected using a given factor based on local climatic conditions and measured daily rainfall (if present).
pzsp
zsLL E
ee
eeKE
Lp
'
KLp= 0.7
Klp = 1.5 at z=4m
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INCI 4138 Hydrologic Processes 9
Evaporation using Pan near a Lake
Consider the ability to transport water vapor away from the water surface.
The transport is generated by the humidity gradient in the air near the surface and wind speed across the surface.
Saturation vapor pressure – pressure at which saturated vapor exists.
Saturated water vapor - the maximum moisture content the air can hold for a given temperature.
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INCI 4138 Hydrologic Processes 10
Evaporation using Pan near a Lake
EL and Ep has units of mm/day or in./day.
esL and esp are vapor pressure at the water surface of lake and pan, which is the saturation vapor pressure at maximum water temperature.
ez is the air vapor pressure at height z2 above the water surface which is taken as the ambient vapor pressure in air considering its relative humidity, Rh.
Vapor pressure data in Appendix C (Gupta)
pzsp
zsLL E
ee
eeKE
Lp
'asha eRe Klp = 1.5 at z=4m
(See Ex.2.7, Problems 2.19 & 2.20 -Gupta).
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Example 2.7 (Gupta)
Pan constant = 0.7
Pan Evaporation = 9 mm
a) E L = K*EP = 0.7*9 = 6.3 mm
b) Lake Temperature Max. = 20°C & Min = 18 ° C
Pan Temperature Max. = 28 °C & Min = 25°C
Air Temperature @ 4m = 30°C
With Relative Humidity = 25%
Wind speed @ 4m =6 m/s
INCI 4138 Hydrologic Processes 11
E L = K’*(esL – ez)/(esp-ez)*EP = 1.5*(2.337-1.061)/(3.781-1.061)*9 = 6.33 mm
From Table C.2: vapor pressure values are.esL = 2.337 KPa esp = 3.781 KPa by interpolation esz = 4.243 KPa But with Rh = 25% ez = 0.25*4.243 = 1.061 KPa
pLpL EKE
pzsp
zsLL E
ee
eeKE
Lp
'
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INCI 4138 Hydrologic Processes 12
Evapotranspiration Considers evaporation from natural surfaces whether
the water source is in the soil, plants or combination of both.
Plants extract water from soil and then is liberated to the air by the transpiration process.
Consumptive use is the amount of water required to support the optimum growth of a particular crop under field conditions. It considers the water loss from soil and plants of the particular crop.
Thornthwaite (1948) introduced the term potential evapotranspiration to define evapotranspiration that will occur when the soil contains an adequate moisture supply at all times.
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INCI 4138 Hydrologic Processes 13
Evapotranspiration Reference crop evapotranspiration, Eto, is based on
an idealized crop of a uniform height, completely covering the ground, growing actively, and not experiencing any shortage of water.
Evapotranspirometers and lysimeters are used for these measurements but they are rare. The water balance budget is used to estimate its value.
Penman-Monteith Method is one of the equations used to estimate evapotranspiration.
Actual evapotranspiration, Et, from a surface depends on correction factors to account for the specified crop growth stage (Kc) and available soil water (Ka). Et = Kc Ka Eto (Eq 2.34 –Gupta)
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INCI 4138 Hydrologic Processes 14
Infiltration process
Figure 7.4.1 (p. 234)Subsurface water zones and processes (from Chow et al. (1988)).
Figure 7.4.1 (p. 234)Subsurface water zones and processes (from Chow et al. (1988)).
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INCI 4138 Hydrologic Processes 15
Infiltration process
Process of water penetrating into the soil.
Rate of infiltration is influenced by:
soil surface condition
vegetative cover condition
soil properties- Porosity [n=Vv/Vt =e/(1+e)] or void ratio [e =Vv/Vs =n/(1-n)]
- Hydraulic conductivity (K)
- Moisture content (θ)
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INCI 4138 Hydrologic Processes 16
Infiltration process
Moisture zones during infiltration. Moisture profile as a function of time for water added to the soil surface.
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INCI 4138 Hydrologic Processes 17
Infiltration process: EquationsΦ = Phi Index, SCS approach
Horton Equation
I
∑(Pi-Φ) ∆t = R
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INCI 4138 Hydrologic Processes 18
Infiltration - Horton’s equation
fp is the infiltration rate at time t, in./hr or mm/hr.
f0 is initial infiltration rate, in./hr or mm/hr.
fc is ultimate infiltration rate, in./hr or mm/hr.
k is the decay constant, (time units)-1.
ktccp effff 0
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INCI 4138 Hydrologic Processes 19
Infiltration - Horton’s equation
Ft = cumulative infiltration capacity in inches
(or mm) at time t in hours . k = decay constant in (1/time units = 1/hr) See example in file “Example-Horton-RZL”
available in INCI4138 group at uprm.edu site.
ktcct e
k
fftfF
10
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INCI 4138 Hydrologic Processes 20
Rainfall Infiltration rate and Cumulative Infiltration
The rainfall hyetograph illustrates the rainfall pattern as a function of time. The cumulative infiltration at time t is Ft or F(t) and at time t + Δt is Ft + Δt or F(t + Δt) is computed using equation 7.4.15. The increase in cumulative infiltration from time t to t + Δt is Ft + Δt – Ft or F(t + Δt) – F(t) as shown in the figure. Rainfall excess is defined in Chapter 8 as that rainfall that is neither retained on the land surface nor infiltrated into the soil.
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INCI 4138 Hydrologic Processes 21
Infiltration - Ponding time.
This figure illustrates the concept of ponding time for a constant intensity rainfall.
Ponding time is the elapsed time between the time rainfall begins and the time water begins to pond on the soil surface.
Review Example 2.14 (pgs 85-88, Gupta) & Problems 2.34 & 2.35 (Pg 119)Also review Excel file “Example Horton-RZL”
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Infiltration – Ponding Process
INCI 4138 Hydrologic Processes 22
ktccp effff 0
ktcct e
k
fftfF
10
fo’ = 5.24 in./hr
Example Horton-RZL
The standard f curve can be given by the equation f = 1.2 + (9 - 1.2) e-4.56t where f in in in./hr and t is in hr. (a & b) Develop and plot the standard infiltration and the cumulative infiltration curve. Rainfall intensity is 1.5 in./hr for the first 40 minutes and then 6.0 in./hr thereafter.
P40 =1.5in./hr(40min)(hr/60min)= 1 in.
f’ = 1.2 + (5.24 - 1.2) e-4.56t’ where t’ = t-40
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Infiltration – Ponding Process
( c) Rainfall intensity is 1.5 in./hr for the first 40 minutes and then 6.0 in./hr thereafter. For that event, draw the corresponding rainfall intensity curve as well as the actual infiltration and cumulative infiltration curve.
INCI 4138 Hydrologic Processes 23
ktccp effff 0
ktcct e
k
fftfF
10
After the 40 minutes the time value is adjusted to have t’ = t – 40 and the fo’ = 5.24 in./hr.
f = 1.2 + (5.24 - 1.2) e-4.56t’
and
F=1.0+1.2t’+(5.24-1.2)*(1- e-4.56t’)/4.56
For the first 40 minutes (f = I) and not
f = 1.2 + (9 - 1.2) e-4.56t.
Therefore, F=Σ(f*Δt) =Σ(I*Δt) up to F=1in.
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INCI 4138 Hydrologic Processes 24
Infiltration: Φ-Index (SCS)
Ptotal =∑(i∆t) =∑(Pi∆t)
R=∑Ri =∑(Qi∆t)
∑(Pi-Φ) ∆t =∑Ri=R
Φ = (∑(Pi∆t) – R)/(m∆t)
See Examples 2.19 & 2.20 (pg. 106-107, Gupta) & Problems 2.43, 2.44 & 2.45 (pg. 120, Gupta). Also review file “Example Phi-Index-RZL”
Φ-Index=Constant RATE of abstraction (in./hr or cm/hr).
Calculated by finding the loss difference between gross precipitation ( Ptotal) and observed surface runoff measured as a hydrograph (R).
Assumes uniform loss across the rainfall pattern.
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Infiltration: Φ-Index (SCS)EXAMPLE 2.19 (Gupta) Φ-INDEX EVALUATION
5
4.5 RunoffExcess=2.52in Infiltration
4
P 3.5 R E 3
C I 2.5
P I 2 Φ valueT
A 1.5 I O 1
N 0.5
(in./hr) 0
0 0.5 1 1.5 2 2.5 3 3.5
TIME (hr)
DATA:
Area (acre) = 500
Direct Runoff (acre-ft) 105 ‘=105/500*12 in. = 2.52 in.Assuming
Φ <2.0 in./hrTime Time Time Precipitation Amount of
Increment Intensity Precipitation (hr) (min) (hr) (in./hr) (in.) (in.)
δt P (P*δt) (P-Φ)δt0 0
0.5 4.5 2.25 (4.5-Φ)*0.50.5 30
0.5 3.0 1.5 (3-Φ)*0.51 60
0.5 1.0 0.5 (0)*0.51.5 90
0.5 3.5 1.75 (3.5-Φ)*0.52 120
0.5 2.0 1 (2.0-Φ)*0.52.5 150
0.5 0.0 0 (0)*0.53 180
Sumation 14 7 (13-4Φ)0.5
Total Precipitation (in.) = 7 Runoff (in.) = 105/500/12 = 2.52
Infiltration = P*t-R (in.) = 4.48
Therefore: (13-4Φ)*0.5 = 2.52Φ = (13 - 2.52*2) / 4 = 7.96/ 4 = 1.99 in./hr
1.99 OK.
INCI 4138 Hydrologic Processes25
Ptotal =∑(i∆t) =∑(Pi∆t) R=∑Ri =∑(Qi∆t)
∑(Pi-Φ) ∆t =∑Ri=R or solving for Φ
Φ = (∑(Pi∆t) – R)/(m∆t)
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Infiltration: Φ-Index (SCS)EXAMPLE 2.19 (Gupta) Φ-INDEX EVALUATION
5
4.5 RunoffExcess=2.52in Infiltration
4
P 3.5 R E 3
C I 2.5
P I 2 Φ valueT
A 1.5 I O 1
N 0.5
(in./hr) 0
0 0.5 1 1.5 2 2.5 3 3.5
TIME (hr)
DATA:
Area (acre) = 500
Direct Runoff (acre-ft) 105 ‘=105/500*12 in. = 2.52 in.Assuming
Φ <2.0 in./hrTime Time Time Precipitation Amount of
Increment Intensity Precipitation (hr) (min) (hr) (in./hr) (in.) (in.)
δt P (P*δt) (P-Φ)δt0 0
0.5 4.5 2.25 (4.5-Φ)*0.50.5 30
0.5 3.0 1.5 (3-Φ)*0.51 60
0.5 1.0 0.5 (0)*0.51.5 90
0.5 3.5 1.75 (3.5-Φ)*0.52 120
0.5 2.0 1 (2.0-Φ)*0.52.5 150
0.5 0.0 0 (0)*0.53 180
Sumation 14 7 (13-4Φ)0.5
Total Precipitation (in.) = 7 Runoff (in.) = 105/500/12 = 2.52
Infiltration = P*t-R (in.) = 4.48
Therefore: (13-4Φ)*0.5 = 2.52Φ = (13 - 2.52*2) / 4 = 7.96/ 4 = 1.99 in./hr
1.99 OK.
INCI 4138 Hydrologic Processes26
Ptotal =∑(i∆t) =∑(Pi∆t) R=∑Ri =∑(Qi∆t)
∑(Pi-Φ) ∆t =∑Ri=R or solving for Φ
Φ = (∑(Pi∆t) – R)/(m∆t)