Hydrologic Processes INCI  4138 Introduction to Water Resources Engineering Evaporation and Infiltration Processes Dr. Jor...
Evaporation <ul><li>The  process of water changing from its liquid phase to the vapor phase . </li></ul><ul><li>Water vapo...
Evaporation <ul><li>Rate of evaporation  depends on… </li></ul><ul><ul><li>*   Solar  Radiation </li></ul></ul><ul><ul><li...
Evaporation:  Radiation effect INCI 4138 Hydrologic Processes
Evaporation <ul><li>Latent Heat  is the heat that is given up or absorbed when a phase changes. </li></ul><ul><li>Latent h...
Evaporation Process INCI 4138 Hydrologic Processes Water molecules  are always moving around. This is caused by  solar rad...
Evaporation from  Water Bodies <ul><li>Four methods to determine evaporation. </li></ul><ul><li>Comparative method ( evapo...
INCI 4138 Hydrologic Processes Evaporation Evaporation  ( yr or monthly ) from water bodies are estimated by  measuring da...
Evaporation using  Pan near a Lake <ul><li>Consider the ability to transport water vapor away from the water surface. </li...
Evaporation using Pan near a Lake <ul><li>E L  and E p   has units of mm/day or in./day. </li></ul><ul><li>e sL  and  e sp...
Example 2.7  ( Gupta ) <ul><li>Pan constant = 0.7 </li></ul><ul><li>Pan Evaporation = 9 mm </li></ul><ul><li>a) E  L  = K*...
Evapotranspiration <ul><li>Considers  evaporation   from natural surfaces  whether the  water source is in the soil, plant...
Evapotranspiration <ul><li>Reference crop evapotranspiration, E to ,  is based on an idealized crop of a uniform height, c...
Infiltration process <ul><li>Figure 7.4.1  (p. 234) Subsurface water zones and processes (from Chow et al. (1988)). </li><...
Infiltration process <ul><li>Process of water penetrating into the soil . </li></ul><ul><li>Rate of infiltration  is influ...
Infiltration process <ul><li>Moisture zones during infiltration. </li></ul>INCI 4138 Hydrologic Processes Moisture profile...
Infiltration process:  Equations INCI 4138 Hydrologic Processes Φ  = Phi Index, SCS approach Horton Equation I ∑ (P i -Φ) ...
Infiltration -  Horton’s equation <ul><li>f p  is the infiltration rate  at time  t,  in./hr or mm/hr . </li></ul><ul><li>...
Infiltration -  Horton’s equation <ul><li>F t  = cumulative infiltration capacity  in  inches   (or mm)  at time  t   in h...
Rainfall Infiltration rate and Cumulative Infiltration <ul><li>The  rainfall hyetograph  illustrates the rainfall pattern ...
Infiltration -  Ponding time . <ul><li>This figure illustrates the concept of  ponding time  for a constant intensity rain...
Infiltration –  Ponding Process INCI 4138 Hydrologic Processes f o ’ = 5.24 in./hr Example Horton-RZL The standard f curve...
Infiltration –  Ponding Process <ul><li>( c)  Rainfall intensity is 1.5 in./hr for the first 40 minutes and then 6.0 in./h...
Infiltration:  Φ - Index (SCS) INCI 4138 Hydrologic Processes P total  =∑(i∆t) =∑(P i ∆t) R=∑R i  =∑(Q i ∆t)  ∑ (P i -Φ) ∆...
Infiltration:  Φ - Index (SCS) INCI 4138 Hydrologic Processes P total  =∑(i∆t) =∑(P i ∆t)  R=∑R i  =∑(Q i ∆t)  ∑ (P i -Φ) ...
Infiltration:  Φ - Index (SCS) INCI 4138 Hydrologic Processes P total  =∑(i∆t) =∑(P i ∆t)  R=∑R i  =∑(Q i ∆t)  ∑ (P i -Φ) ...
Extra slides for INCI4138 <ul><li>They will not be included as course material during the following term: </li></ul><ul><l...
Evaporation - Aerodynamic Method <ul><li>E a   has unit of mm/day. </li></ul><ul><li>e as  is vapor pressure at the water ...
Evaporation - Aerodynamic Method <ul><li>B  is the vapor transfer coefficient with units of mm/day-Pa. </li></ul><ul><li>u...
Evaporation - Aerodynamic Method <ul><li>e as  and  e a   have units of Pa (N/m 2 ). </li></ul><ul><li>T  is the air tempe...
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02 10 evaporation-and_infiltration_jrs-rzl

  1. 1. Hydrologic Processes INCI 4138 Introduction to Water Resources Engineering Evaporation and Infiltration Processes Dr. Jorge Rivera-Santos & Ra ú l E. Zapata-L ó pez INCI 4138 Hydrologic Processes
  2. 2. Evaporation <ul><li>The process of water changing from its liquid phase to the vapor phase . </li></ul><ul><li>Water vapor is the state of water in the atmosphere. </li></ul><ul><li>It is a two-phase process. </li></ul><ul><ul><li>Water molecules escape from the water surface to the atmosphere ( heat ? ). </li></ul></ul><ul><ul><li>Transport of water vapor molecules away from the evaporating surface ( wind ? ). </li></ul></ul>INCI 4138 Hydrologic Processes
  3. 3. Evaporation <ul><li>Rate of evaporation depends on… </li></ul><ul><ul><li>* Solar Radiation </li></ul></ul><ul><ul><li>================================================================================================================================================================== </li></ul></ul><ul><ul><li>* Atmospheric Pressure * Air Temperature </li></ul></ul><ul><ul><li>* Relative Humidity * Wind Speed </li></ul></ul><ul><ul><li>================================================================================================================================================================== </li></ul></ul><ul><ul><li>* Water Temperature * Quality of Water </li></ul></ul><ul><ul><li>* Geometry of the evaporating surface </li></ul></ul><ul><ul><li>=========================================================================================================================================== </li></ul></ul>INCI 4138 Hydrologic Processes
  4. 4. Evaporation: Radiation effect INCI 4138 Hydrologic Processes
  5. 5. Evaporation <ul><li>Latent Heat is the heat that is given up or absorbed when a phase changes. </li></ul><ul><li>Latent heat of vaporization is the heat given up during vaporization of liquid water to water vapor. </li></ul><ul><li>where T is the temperature in °C and l v is in joules per kilogram ( J/Kg ). </li></ul>INCI 4138 Hydrologic Processes
  6. 6. Evaporation Process INCI 4138 Hydrologic Processes 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.
  7. 7. Evaporation from Water Bodies <ul><li>Four methods to determine evaporation. </li></ul><ul><li>Comparative method ( evaporation pan ) </li></ul><ul><li>Energy balance method (energy budget) </li></ul><ul><li>Aerodynamic method (mass transfer) </li></ul><ul><li>Combined balance method (Penman Method) </li></ul>INCI 4138 Hydrologic Processes
  8. 8. INCI 4138 Hydrologic Processes Evaporation Evaporation ( 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). K Lp = 0.7 K lp = 1.5 at z=4m
  9. 9. Evaporation using Pan near a Lake <ul><li>Consider the ability to transport water vapor away from the water surface. </li></ul><ul><li>The transport is generated by the humidity gradient in the air near the surface and wind speed across the surface. </li></ul><ul><li>Saturation vapor pressure – pressure at which saturated vapor exists. </li></ul><ul><li>Saturated water vapor - the maximum moisture content the air can hold for a given temperature. </li></ul>INCI 4138 Hydrologic Processes
  10. 10. Evaporation using Pan near a Lake <ul><li>E L and E p has units of mm/day or in./day. </li></ul><ul><li>e sL and e sp are vapor pressure at the water surface of lake and pan, which is the saturation vapor pressure at maximum water temperature. </li></ul><ul><li>e z is the air vapor pressure at height z 2 above the water surface which is taken as the ambient vapor pressure in air considering its relative humidity, R h . </li></ul><ul><li>Vapor pressure data in Appendix C ( Gupta ) </li></ul>INCI 4138 Hydrologic Processes K lp = 1.5 at z=4m (See Ex.2.7, Problems 2.19 & 2.20 -Gupta ).
  11. 11. Example 2.7 ( Gupta ) <ul><li>Pan constant = 0.7 </li></ul><ul><li>Pan Evaporation = 9 mm </li></ul><ul><li>a) E L = K*E P = 0.7*9 = 6.3 mm </li></ul><ul><li>b) Lake Temperature Max. = 20°C & Min = 18 ° C </li></ul><ul><li>Pan Temperature Max. = 28 °C & Min = 25°C </li></ul><ul><li>Air Temperature @ 4m = 30°C </li></ul><ul><li>With Relative Humidity = 25% </li></ul><ul><li>Wind speed @ 4m =6 m/s </li></ul>INCI 4138 Hydrologic Processes E L = K’*(e sL – e z )/( e sp - e z )*E P = 1.5*(2.337- 1.061 )/( 3.781 - 1.061 )*9 = 6.33 mm From Table C.2: vapor pressure values are. e sL = 2.337 KPa e sp = 3.781 KPa by interpolation e sz = 4.243 KPa But with R h = 25% e z = 0.25*4.243 = 1.061 KPa
  12. 12. Evapotranspiration <ul><li>Considers evaporation from natural surfaces whether the water source is in the soil, plants or combination of both . </li></ul><ul><li>Plants extract water from soil and then is liberated to the air by the transpiration process. </li></ul><ul><li>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. </li></ul><ul><li>Thornthwaite (1948) introduced the term potential evapotranspiration to define evapotranspiration that will occur when the soil contains an adequate moisture supply at all times. </li></ul>INCI 4138 Hydrologic Processes
  13. 13. Evapotranspiration <ul><li>Reference crop evapotranspiration, E to , is based on an idealized crop of a uniform height, completely covering the ground, growing actively, and not experiencing any shortage of water. </li></ul><ul><li>Evapotranspirometers and lysimeters are used for these measurements but they are rare. The water balance budget is used to estimate its value. </li></ul><ul><li>Penman-Monteith Method is one of the equations used to estimate evapotranspiration. </li></ul><ul><li>Actual evapotranspiration, E t , from a surface depends on correction factors to account for the specified crop growth stage ( K c ) and available soil water (K a ). E t = K c K a E to ( Eq 2.34 –Gupta ) </li></ul>INCI 4138 Hydrologic Processes
  14. 14. Infiltration process <ul><li>Figure 7.4.1 (p. 234) Subsurface water zones and processes (from Chow et al. (1988)). </li></ul>INCI 4138 Hydrologic Processes Figure 7.4.1 (p. 234) Subsurface water zones and processes (from Chow et al. (1988)).
  15. 15. Infiltration process <ul><li>Process of water penetrating into the soil . </li></ul><ul><li>Rate of infiltration is influenced by: </li></ul><ul><li>soil surface condition </li></ul><ul><li>vegetative cover condition </li></ul><ul><li>soil properties </li></ul><ul><li>- Porosity [ n=V v /V t =e/(1+e) ] or void ratio [ e =V v /V s =n/(1-n)] </li></ul><ul><ul><li>- Hydraulic conductivity (K) </li></ul></ul><ul><ul><li>- Moisture content ( θ ) </li></ul></ul>INCI 4138 Hydrologic Processes
  16. 16. Infiltration process <ul><li>Moisture zones during infiltration. </li></ul>INCI 4138 Hydrologic Processes Moisture profile as a function of time for water added to the soil surface.
  17. 17. Infiltration process: Equations INCI 4138 Hydrologic Processes Φ = Phi Index, SCS approach Horton Equation I ∑ (P i -Φ) ∆t = R
  18. 18. Infiltration - Horton’s equation <ul><li>f p is the infiltration rate at time t, in./hr or mm/hr . </li></ul><ul><li>f 0 is initial infiltration rate , in./hr or mm/hr . </li></ul><ul><li>f c is ultimate infiltration rate , in./hr or mm/hr . </li></ul><ul><li>k is the decay constant , (time units) -1 . </li></ul>INCI 4138 Hydrologic Processes
  19. 19. Infiltration - Horton’s equation <ul><li>F t = cumulative infiltration capacity in inches (or mm) at time t in hours . </li></ul><ul><li>k = decay constant in (1/time units = 1/hr) </li></ul><ul><li>See example in file “ Example-Horton-RZL ” available in INCI4138 group at uprm.edu site. </li></ul>INCI 4138 Hydrologic Processes
  20. 20. Rainfall Infiltration rate and Cumulative Infiltration <ul><li>The rainfall hyetograph illustrates the rainfall pattern as a function of time. The cumulative infiltration at time t is F t or F ( t ) and at time t + Δ t is F t + Δ t or F ( t + Δ t ) is computed using equation 7.4.15. The increase in cumulative infiltration from time t to t + Δ t is F t + Δ t – F t or F ( t + Δ t ) – 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 . </li></ul>INCI 4138 Hydrologic Processes
  21. 21. Infiltration - Ponding time . <ul><li>This figure illustrates the concept of ponding time for a constant intensity rainfall. </li></ul><ul><li>Ponding time is the elapsed time between the time rainfall begins and the time water begins to pond on the soil surface. </li></ul>INCI 4138 Hydrologic Processes Review Example 2.14 (pgs 85-88, Gupta ) & Problems 2.34 & 2.35 (Pg 119) Also review Excel file “ Example Horton-RZL ”
  22. 22. Infiltration – Ponding Process INCI 4138 Hydrologic Processes f o ’ = 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. P 40 =1.5in./hr(40min)(hr/60min)= 1 in. f’ = 1.2 + (5.24 - 1.2) e -4.56t’ where t’ = t-40
  23. 23. Infiltration – Ponding Process <ul><li>( 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. </li></ul>INCI 4138 Hydrologic Processes 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* Δ t) = Σ (I* Δ t) up to F=1in.
  24. 24. Infiltration: Φ - Index (SCS) INCI 4138 Hydrologic Processes P total =∑(i∆t) =∑(P i ∆t) R=∑R i =∑(Q i ∆t) ∑ (P i -Φ) ∆t =∑R i =R Φ = (∑(P i ∆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 ” <ul><li>Φ -Index= Constant RATE of abstraction (in./hr or cm/hr). </li></ul><ul><li>Calculated by finding the loss difference between gross precipitation ( P total ) and observed surface runoff measured as a hydrograph ( R ). </li></ul><ul><li>Assumes uniform loss across the rainfall pattern. </li></ul>
  25. 25. Infiltration: Φ - Index (SCS) INCI 4138 Hydrologic Processes P total =∑(i∆t) =∑(P i ∆t) R=∑R i =∑(Q i ∆t) ∑ (P i -Φ) ∆t =∑R i =R or solving for Φ Φ = (∑(P i ∆t) – R)/(m∆t) 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 value T               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./hr Time Time   Time Precipitation Amount of   Increment Intensity Precipitation   (hr) (min) (hr) (in./hr) (in.) (in.)       δ t P (P* δ t) (P- Φ)δ t 0 0   0.5 4.5 2.25 (4.5-Φ)*0.5 0.5 30   0.5 3.0 1.5 (3-Φ)*0.5 1 60   0.5 1.0 0.5 (0)*0.5 1.5 90   0.5 3.5 1.75 (3.5-Φ)*0.5 2 120   0.5 2.0 1 (2.0-Φ)*0.5 2.5 150   0.5 0.0 0 (0)*0.5 3 180               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 = 2.52 Φ = (13 - 2.52*2) / 4 = 7.96/ 4 = 1.99 in./hr 1.99 OK.
  26. 26. Infiltration: Φ - Index (SCS) INCI 4138 Hydrologic Processes P total =∑(i∆t) =∑(P i ∆t) R=∑R i =∑(Q i ∆t) ∑ (P i -Φ) ∆t =∑R i =R or solving for Φ Φ = (∑(P i ∆t) – R)/(m∆t) 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 value T               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./hr Time Time   Time Precipitation Amount of   Increment Intensity Precipitation   (hr) (min) (hr) (in./hr) (in.) (in.)       δ t P (P* δ t) (P- Φ)δ t 0 0   0.5 4.5 2.25 (4.5-Φ)*0.5 0.5 30   0.5 3.0 1.5 (3-Φ)*0.5 1 60   0.5 1.0 0.5 (0)*0.5 1.5 90   0.5 3.5 1.75 (3.5-Φ)*0.5 2 120   0.5 2.0 1 (2.0-Φ)*0.5 2.5 150   0.5 0.0 0 (0)*0.5 3 180               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 = 2.52 Φ = (13 - 2.52*2) / 4 = 7.96/ 4 = 1.99 in./hr 1.99 OK.
  27. 27. Extra slides for INCI4138 <ul><li>They will not be included as course material during the following term: </li></ul><ul><li>First semester 2009-2010. </li></ul>INCI 4138 Hydrologic Processes
  28. 28. Evaporation - Aerodynamic Method <ul><li>E a has unit of mm/day. </li></ul><ul><li>e as is vapor pressure at the water surface which is the saturation vapor pressure at ambient air temperature. </li></ul><ul><li>e a is the vapor pressure at height z 2 above the water surface which is taken as the ambient vapor pressure in air. </li></ul>INCI 4138 Hydrologic Processes
  29. 29. Evaporation - Aerodynamic Method <ul><li>B is the vapor transfer coefficient with units of mm/day-Pa. </li></ul><ul><li>u 2 = wind speed (m/s) measured at height z 2 (cm). </li></ul><ul><li>z 0 is the roughness height (0.01 – 0.06 cm) of the water surface. </li></ul><ul><li>See example 7.3.2 (page 232) </li></ul>INCI 4138 Hydrologic Processes
  30. 30. Evaporation - Aerodynamic Method <ul><li>e as and e a have units of Pa (N/m 2 ). </li></ul><ul><li>T is the air temperature in °C. </li></ul><ul><li>R h is the relative humidity (0 ≤ R h ≤ 1). </li></ul><ul><li>See example 7.3.3 (page 233) </li></ul>INCI 4138 Hydrologic Processes

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