PENMAN EQUATION FOR POTENTIAL EVAPORATION

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PENMAN EQUATION FOR POTENTIAL EVAPORATION

• AE 520
• Carl E. Anderson

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PENMAN EQUATION FOR POTENTIAL EVAPORATIONNeed To
Know

• Location of the field (latitude in degrees)
• Elevation of the field (mean sea level)
• Day-of-the-year for the prediction
• Mean air temperature for this day

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PENMAN EQUATION FOR POTENTIAL EVAPORATIONNeed To
Know

• A measure of the average humidity for this day
  (Relative humidity or Dew Point Temperature or
  Vapor Pressure)
• Daily Solar Radiation
• Average wind speed for this day

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PENMAN EQUATION

• D ?is the slope of the vapor pressure-temperature
  curve at the mean air temperature.
• T is the mean air temperature in oC

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PSYCHROMETRIC CHART
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PENMAN EQUATION

• l the latent heat of vaporization of water at
  the mean air temperature in MJ / kg

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PENMAN EQUATION

• EL is the field elevation in meters above mean
  sea level.
• P the atmospheric pressure in kPa at this field
  elevation.

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PENMAN EQUATION

• g is the psychrometric constant for this
  temperature and pressure in kPa / oC.

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PENMAN EQUATION

• es is the saturation vapor pressure in kPa at the
  mean air temperature

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PENMAN EQUATION

• RH is the mean relative humidity for this site
  and this day
• ed is the actual vapor pressure for this
  temperature and relative humdity in kPa.

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PENMAN EQUATION

• Ta The mean daily air temperature expressed in
  oK.
• Ta T 273.16
• Rs the measured solar radiation for this field
  on this day in MJ/m2/day.
• a is the field surface albedo

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PENMAN EQUATION

• s is the Stefan-Boltzmann constant for radiant
  energy emission
• 4.903 x 10-9 MJ / m2 / day / 0k4
• n / N is the ratio of actual to possible sunshine
  for this day
• Rn is the estimated net radiation energy supply
  to this field on this day in MJ / m2 / day

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PENMAN EQUATION
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EQUATIONS FOR ESTIMATING CLEAR DAY SOLAR RADIATION

• d solar declination angle, degrees
• J Julian day-of-the-year (1-365)
• d 23.45 cos(2p/365(J-172))
• f Latitude angle for the location

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EQUATIONS FOR ESTIMATING CLEAR DAY SOLAR RADIATION

• DL The day length in hours for this location
  for day J (number of hours of daylight).
• DL 24/p cos-1(-tan f tan d)
• NOTE The angle in this equation must be in
  radians.

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EQUATIONS FOR ESTIMATING CLEAR DAY SOLAR RADIATION

• LD The length in hours of the longest day of
  the year at latitude f.
• This can be calculated from the day length
  equation given above for a solar declination
  angle of 23.45o 0.4093 rad.
• LD 24/p cos-1(-0.433775 tanf)

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EQUATIONS FOR ESTIMATING CLEAR DAY SOLAR RADIATION

• Now compute two parameters for the radiation
  equation
• A sinf (46.355 LD - 574.3885) 816.41 cosf
  sin(p LD / 24) (0.29 cosf 0.52)
• B sinf(574.3885 - 1.509 LD) - 26.59 cosf sin(p
  LD / 24) (0.29 cosf 0.52)

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EQUATIONS FOR ESTIMATING CLEAR DAY SOLAR RADIATION

• Now the maximum clear-day solar radiation at this
  location for any day can be estimated from the
  following equation.
• Rso A B cos ( 2p / 365 ( J-172 )) langleys
  / day

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PENMAN EQUATION
v (m / s)
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PENMAN EQUATION