CIVE 445 - ENGINEERING HYDROLOGY

CHAPTER 2B: BASIC HYDROLOGIC PRINCIPLES, HYDROLOGIC ABSTRACTIONS

  • Hydrologic abstractions important in Engineering Hydrology are the following:

    • Interception

    • Infiltration

    • Surface or depression storage

    • Evaporation

    • Evapotranspiration

 

Interception

  • Interception is the process by which precipitation is abstracted by vegetation or other forms of surface cover.

  • Throughfall is that part of precipitation which reaches the ground after passing through the vegetative cover.

  • Interception losses are a function of

    1. storm character, including intensity, depth and duration;

    2. type, extent and density of vegetative cover,

    3. time of the year (season).

  • Annual interception losses, primarily from light storms, can amount to 25% of rainfall.

  • For heavy storms, interception losses usually amount to a small fraction of total rainfall.

  • For flood studies, the neglect of interception is generally justified on practical grounds.

 

Infiltration

  • Infiltration is the process by which precipitation is abstracted by seeping into the soil below the land surface.

  • The infiltrated water moves mostly vertically until it reaches the groundwater table (saturation).

  • Groundwater flows laterally (along a piezometric gradient) toward zones of lower elevation, and eventually reaches streams or rivers (baseflow).

  • Infiltration is measured in in/hr or mm/hr.

  • Rate of infiltration is integrated over the storm duration to obtain the total infiltration (mm or in).

  • Average rate is obtained by dividing total infiltration amount by the storm duration.

  • Infiltration rates vary as function of the following:

    • The condition of the land surface (crust)

    • The type, extent, and density of vegetative cover

    • The physical properties of the soil, including grain size and gradation

    • The storm character. i.e., intensity, depth, and duration

    • The water temperature

    • The water quality, including chemical constituents and other impurities

    • In general, as a function of physical, chemical, and biological properties of the soil mass.

 

Infiltration formulas

  • Infiltration rates have a tendency to decrease with time.

  • This fact led Horton to develop his decay formula for infiltration:

    f= fc + (fo - fc) e-kt

  • in which f = instantaneous infiltration rate; fo = initial infiltration rate; fc = final infiltration rate; k = a decay constant; t = time.

  • This equation has three parameters: initial rate fo, final rate fc, and decay constant k.

  • With a knowledge of the final rate, two sets of measurements can be solved to give initial rate and constant k.

Fig. 2-13

  • Typical infiltration rates at the end of 1 hr are shown in Table 2-3.

Table 2-3

 

Infiltration Index

  • Practical evaluations of infltration rate have been hampered by its spatial and temporal variability.

  • This has led to the concept of infiltration index.

  • Infiltration index assumes that the rate is constant throughout the storm.

  • It underestimates the initial rate and may overestimate the final rate.

  • Best suited for long-duration storms.

  • In this case, the neglect of variation with time is justified in practice.

  • φ-index is defined as the constant infiltration rate to be substracted from the prevailing rainfall rate in order to obtain the runoff volume that actually occurred.

  • Calculation is by trial and error.

Fig. 2-14

 

Surface or depression storage

  • Surface or depresion storage is the process by which precipitation is abstracted by being retained in puddles, ditches, and other natural or artificial depressions of the land surface.

  • Spatial variability of storage in surface depressions precludes its precise calculation.

  • Depression storage is inversely related to catchment slope.

  • NRCS's TR-55 model uses a surface storage correction factor F to account for depression storage (small ponds occupying less than 5 percent of the catchment area).

  • Conceptual model of depression storage:

    Vs = Sd (1- e-kPe)

    in which:

  • Vs = equivalent depth of depression storage (mm).

  • Pe = precipitation excess; i.e., precipitation minus interception minus infiltration

  • Sd = depression storage capacity (mm)

  • k = a constant.

  • For very small values of Pe, essentially all the precipitation goes into depression storage (dVs/dPe = 1).

  • Therefore, value of k is estimated as 1/Sd.

 

Evaporation

  • Evaporation is the process by which water accumulated on the land surface is converted into vapor state and returned to the atmosphere.

  • Evaporation occurs at the evaporation surface, the contact between water body and overlying air.

  • Evaporation refers to the net rate of water loss from the body of water to the atmosphere.

  • Evaporation is expressed in mm/day, cm/day, or in/day.

  • Evaporation rate is a function of meteorological and environmental factors.

  • Those factors important from engineering standpoint are:

    • Net solar radiation

    • Saturation vapor pressure

    • Vapor pressure of the air

    • Air and water temperatures

    • Wind velocity

    • Atmospheric pressure

  • Evaporation rates depend on the climate.

  • In the U.S., evaporation rates can vary from 20 inches in Maine to 86 inches in Arizona.

  • Methods for determining evaporation:

    • Water budget

    • Energy budget

    • Mass-transfer techniques

 

Water budget method

  • Assumes that all relevant water-transport phases can be evaluated for a period of time Δt, and expressed in terms of volumes.

  • Reservoir or lake evaporation can be evaluated as follows:

    E = P + Q - O - I - ΔS

    in which

    E= volume evaporated from the reservoir

    P = precipitation falling directly into the reservoir

    Q = surface runoff inflow into the reservoir

    O = outflow from the reservoir

    I = net volume infiltrated from the reservoir into the ground

    ΔS = change in stored volume.  

  • Precipitation is readily measured.

  • Inflow and outflow can be obtained by integrating flow records.

  • Net infiltration can be evaluated only indirectly, either by measuring soil permeability or monitoring changes in groundwater level in nearby wells.

  • Change in stored volume is determined by means of water stage recorders.

 

Energy budget method

  • During evaporation, significant energy exchanges occur at the evaporating surface.

  • A balance of these energy exchanges leads to the energy budget method.

  • The amount of heat required to convert one gram of water into vapor, i.e., the heat of vaporization, varies with the temperature.

  • At 20oC, the heat of vaporization is 568 calories.

  • Heat must be supplied for evaporation to take place.

     

  • Radiation is the emission of energy in the form of electromagnetic waves.

  • Solar radiation received at the Earth's surface is a major component of the energy balance.

  • Solar radiation reaches the outer surface of the atmosphere at a nearly constant flux of 1.94 cal/cm2/min, of 1.94 langleys/min.

  • 1 langley = 1 cal/cm2.

  • Nearly all of this radiation is of wavelengths in the range 0.3-3.0 μm, with about half in the visible range (0.4-0.7 μm).

  • The Earth also emits radiation, but since its surface temperature is about 300oK, this terrestrial radiation is of much lower intensity and greater wavelength (3-50 μm) than solar radiation.

  • It is customary to refer to solar radiation as short-wave radiation, and to terrestrial radiation as long-wave radiation.

     

  • The fraction of original solar radiation that reaches the Earth's surface is called direct solar radiation.

  • The fraction that is reaches the ground after reflection and scattering is called sky radiation.

  • The sum of these two is global radiation.

  • Albedo is the reflectivity coefficient of a surface toward shortwave radiation.

  • This coefficient varies with color, roughness, and inclination of the surface.

  • It is 0.1 for water, 0.1-0.3 for vegetated areas, 0.15-0.4 for bare soil, and 0.7-0.9 for snow-covered areas.

     

  • In addition to short wave radiation, there is also a long-wave radiation balance (Figure).

  • The Earth also emits radiation, part of which is absorbed and reflected back by the atmosphere.

  • The difference between outgoing and incoming fluxes is called long-wave radiation loss.

  • At night, long-wave radiation predominates.

  • Net radiation is equal to the net short-wave (solar) radiation minus the long-wave (terrestrial) radiation loss.

  • Incoming energy:

Qi = Qs (1 - A) - Qb + Qa

    in which

      Qi= incoming energy

      Qs = global radiation

      A = albedo

      Qb= long-wave radiation loss

      Qa = net energy advected into the waterbody by streams, rain, snow, etc.  

       

  • Outgoing energy:

    Qo = Qh + Qe + Qt

    in which

      Qo = energy expenditure

      Qh = sensible heat transfer from waterbody to atmosphere by convection and conduction

      Qe = energy used in the evaporation process

      Qt = increase in energy stored

  • The energy used in the evaporation process is:  

    Qe = ρ Υ E

    in which

      Qe= energy used in evaporation process (cal/cm2/day)

      ρ = density of water (gr/cm3)

      Υ = heat of vaporization (cal/gr)

      E = evaporation rate (cm/day)

     

    B = Qh / Qe = γ [(Ts - Ta)/(es -ea)] (p/1000)

    in which

      B = Bowen's ratio

      γ = a psychrometric constant equal to 0.66 mb/oC

      Ts = water surface temperature, oC

      Ta = overlying air temperature, oC

      es= saturation vapor pressure at the water surface temperature, mb

      ea= vapor pressure at the overlying air temperature, mb

      p = atmospheric pressure, mb  

      E = [Qs (1 - A) - Qb + Qa - Qt] / [ρ Υ (1 + B)]

  • The quantities Qs (1 - A) and Qb can be measured with radiometers.

  • The quantity Qa can be determined by measuring volumes and temperatures of the water flowing into and out of the body.

  • The quantity Qt is evaluated by periodic measurements of water temperature.

 

Mass-transfer approach

  • Evaporation rates are dependent on the temperature of the water surface and the prevailing atmospheric pressure.

  • Higher water temperatures result in higher evaporation rates.

  • Higher atmospheric pressure results in lower evaporation rates.

  • Temperature has a larger effect than atmospheric pressure on evaporation.

  • Evaporation rates are a function of the difference between the saturation vapor pressure at the water surface temperature es and the vapor pressure of the overlying air ea (partial vapor pressure).

  • The saturation vapor pressure is a function of temperature (Table A-1 and Table A-2).

  • The partial vapor pressure can be obtained by multiplying the saturation vapor pressure at the air temperature eo by the relative humidity of the air (%) and dividing by 100.

     

  • As the process of mass-transfer continues, the lowest layer of the atmosphere eventually becomes saturated, and net evaporation reduces to zero and can become negative (condensation).

  • Wind carries away water molecules and helps continuous evaporation.

  • The Dalton formula considers both vapor pressure gradient and wind effects.

    E = f(u) (es -ea)

  • The Meyer formula is an example of mass-transfer evaporation (daily and monthly formulas):

    E = Cd (es -ea) [1 + (W/10)]

    E = Cm (eo -ea) [1 + (W/10)]

 

Penman method (Combination energy budget-mass transfer method)

  • Assume p = 1000 mb (close to atmospheric pressure 1013.2 mb).

  • Bowen's ratio reduces to:  

    B = γ [(Ts - Ta)/(es -ea)]

  • A gradient of vapor pressure and temperature is defined as follows:  

    Δ = (es - eo)/(Ts - Ta)

  • Penman in 1945 assumed that the temperatures of water surface and overlying air are equal, and the following statement:  

    Ea / E = (eo - ea)/(es - ea)

    in which:

  • Ea = evaporation due only to mass-transfer.

  • E = total evaporation.

  • Combination of these equations led Penman to:  

    E = (Δ En + γ Ea) / (Δ + γ)

    in which:

    E = total evaporation.

    En = evaporation due only to net radiation.

    Ea = evaporation due only to mass-transfer.  

  • The radiation part of evaporation is evaluated with Qn.

  • The mass-transfer part of evaporation is evaluated with a mass-transfer equation.  

    E = (α En + Ea) / (α + 1)

  • α = Δ/γ is a function of temperature (Table 2-4).

     

  • Penman-Monteith 1966 equation is a modification of the Penman equation.  


    Table 2-4

  • Monteith explained the physical basis of the mass-transfer formulas such as Dalton's.

  • This enabled a better calculation of the mass-transfer evaporation rate and improved the combination model of Penman's.

 

Evaporation determinations using pans

  • Evaporation pan is a device to measure evaporation by monitoring the loss of water in a pan during one day.

  • It provides an integrated effect of net radiation, wind, temperature, and humidity on evaporation from an open surface.

  • The measurement is likely to be somewhat greater than the actual evaporation.

  • The ratio of lake-to-pan evaporation is an empirical constant referred to as pan coefficient.

 

Evapotranspiration

  • Evapotranspiration is the process by which water in the land surface, soil, and vegetation is converted into vapor state and returned to the atmosphere.

  • Evaporation refers to bodies of water; evapotranspiration refers to evaporation from an ecosystem, comprising water, soil, and vegetation.

  • Transpiration is the process by which plants transfer water from the root zone to the leaf, providing turgor (the capability of remaining erect).

  • Osmotic pressures at root level move water into the roots.

  • Water is transported through stem to proximity of leaf surface.

  • Air enters leaf surface through small openings called stomata.

  • Chloroplasts within the leaves use carbon dioxide from the air and small amounts of the available water to manufacture biomass.

  • Water escapes through the stomata as air enters.

  • Ratio of water evapotranspired to that used in biomass production is very large (about 800 or more).

  • Transpiration occurs continuously, but it is limited by the rate at which moisture becomes available to plants.

  • Some authorities believe that transpiration is independent of soil moisture as long as the latter is above the permanent wilting point.

  • Others believe that transpiration is proportional to soil moisture.

  • Transpiration amounts are a function of the same meteorological and climatic factors that control evaporation rates.

  • Evapotranspiration includes all the water returned to the atmosphere from an ecosystem.

     

  • Potential evapotranspiration (PET) is the amount that would take place under the assumption of an ample supply of moisture at all times.

  • PET is an indication of optimum crop water requirements.

  • Reference crop evapotranspiration (ETo) is the rate from an extended surface of 8-15 mm tall green grass cover of uniform height, actively growing, completely shading the ground, and not short of water.

  • Potential evapotranspiration is equivalent to the evaporation of a body of water with negligible heat storage capacity.

  • Methods to calculate one overlap the other.

  • Penman method is used for both evaporation and evapotranspiration.

  • Evapotranspiration models are of several types:

    • Temperature models

    • Radiation models

    • Combination models

    • Pan-evaporation models.
 

Temperature models to estimate evapotranspiration

  • The Blaney-Criddle formula has been used to estimate crop water requirements.

    f = p (0.46 t + 8.13)

  • in which

    • f = daily consumptive use factor (mm)

    • p = ratio of mean daily daytime hours for a given month to total daytime hours in the year (%), a function of latitude (Table A-3) [average monthly value = (100%)/12 = 8.33%; daily value at 0o latitude, 8.33/30.4 days/mo= 0.27]

    • t = mean daily temperature (oC)

  • Consumptive water requirement is the consumptive use factor f times a crop coefficient kc. (Table 2-5)

     

  • Doorenbos and Pruitt have proposed a modification of the Blaney-Criddle formula:

    ETo = a + bf

    in which

  • ETo = reference crop evapotranspiration

  • a and b = constants that vary with actual insolation time (ratio n/N between actual and maximum possible bright sunshine hours), minimum relative humidity (%), and daytime wind speed (m/s).

Fig. 2-16

     

  • The consumptive water requirement for a given crop is:

    ETc = kc (ETo)

  • kc varies with each crop, from 0.15 to 1.1 (Table 2-5).  

  • The Thornthwaite method is also widely used to estimate potential evapotranspiration.

  • The method is popular because it is based only on temperature, which is widely available.

  • The method is based on an annual temperature efficiency index J, defined as the sum of 12 monthly values of heat index I.

  • Each monthly index I is a function of mean monthy temperature T, in oC:

    I = (T/5)1.514

  • Evapotranspiration at zero latitude PET(0) in cm/month is calculated by the following formula:

    PET(0) = 1.6 (10T/J)c

    c = 0.000000675 J3 - 0.0000771 J2 + 0.01792 J + 0.49239

  • At other latitudes, evapotranspiration PET (in cm/month) is calculated by the following formula:

    PET = K [PET(0)]

  • K is a constant for each month of the year, varying as a function of latitude (Table A-4).
 

Radiation models

  • Priestley and Taylor proposed that potential evapotranspiration be taken as the radiation part of the Penman equation, affected with an empirical constant.

    PET = 1.26 Δ [Qn/(ρ Υ)] / ( Δ + γ)

    PET = 1.26 α [Qn/(ρ Υ)] / ( α + 1)

  • However, the constant 1.26 may vary with climatic conditions (it has been reported to be 1.7 in arid regions).
 

Combination models to estimate evapotranspiration

  • The original Penman model provided an estimate of evaporation from a free surface.

  • Experimental crop coefficients were suggested to convert to evapotranspiration.

  • These coefficients (0.6 in the winter and 0.8 in the summer) were intended to multiply the evaporation to get evapotranspiration.

  • Other studies have suggested that free-water-surface evaporation and evapotranspiration are nearly the same.

  • It seems that energy-budget and mass-transfer components compensate themselves to make evaporation and evapotranspiration nearly equal.

  • Potential evapotranspiration correlates well with combination data such as solar radiation and wind velocity.

  • Pan evaporation models are also used in evapotranspiration studies.

Table 2-6

  • NWS Class A pan is generally used for estimating potential evapotranspiration.

Fig. 3-3

 

Go to Chapter 2C.

 
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