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Crop & Evapotranspiration: FAO 56: Penman-Monteith, Thornthwaite

The Food and Agriculture Organization (FAO) Irrigation and Drainage paper 56 document provides the definitive standardized methodology for deriving estimates of reference evapotranspiration (aka, ET0) for a hypothetical "short" crop. Subsequently, the ASCE-ET (American Society of Civil Engineering) created additional parameters for a hypothetical "tall" crop (full-cover alfalfa). See Example 1a.

The primary purpose of the Penman-Monteith method is to calculate the loss of water from land surfaces due to evaporation.

NCL has implemented virtually all the FAO referenced equations into a library of functions which calculate many of the terms required to estimate evapotranspirtation. The "crop" category of functions is documented here.

The crop library is in beta mode. It will officially be released as part of NCL 6.4.0 The current version of the code may be downloaded from

The following [1]-[3] descriptions are quoted from WikiPedia:

  1. Evapotranspiration (ET) is the sum of evaporation and plant transpiration from the Earth's land and ocean surface to the atmosphere. Evaporation accounts for the movement of water to the air from sources such as the soil, canopy interception, and waterbodies. Transpiration accounts for the movement of water within a plant and the subsequent loss of water as vapor through stomata in its leaves. Evapotranspiration is an important part of the water cycle.

  2. Reference evapotranspiration (ET0), sometimes incorrectly referred to as potential ET, is a representation of the environmental demand for evapotranspiration and represents the evapotranspiration rate of a short green crop (grass), completely shading the ground, of uniform height and with adequate water status in the soil profile. It is a reflection of the energy available to evaporate water, and of the wind available to transport the water vapour from the ground up into the lower atmosphere. Actual evapotranspiration is said to equal reference evapotranspiration when there is ample water. Some US states utilize a full cover alfalfa reference crop that is 0.5 m in height, rather than the short green grass reference, due to the higher value of ET from the alfalfa reference.

  3. Potential evaporation or potential evapotranspiration (PET) is defined as the amount of evaporation that would occur if a sufficient water source were available. If the actual evapotranspiration is considered the net result of atmospheric demand for moisture from a surface and the ability of the surface to supply moisture, then PET is a measure of the demand side. Surface and air temperatures, insolation, and wind all affect this. A dryland is a place where annual potential evaporation exceeds annual precipitation.

  4. A brief description of the difference between potential evapotranspiration (PET) and reference evapotranspiration(ETo) is here.

References: Penman-Monteith

  Richard G. Allen, Luis S. Pereira, Dirk Raes, Martin Smith (1998) 
  Crop Evapotranspiration - Guidelines for Computing Crop Water Requirements 
       FAO Irrigation and drainage paper 56. Rome, Italy: 
  Food and Agriculture Organization of the United Nations. 
  In particular: Chapter 3 (Meteorological Data) & Chapter 4 (Determination of ET0)


  Zotarelli, L. et al (2013)
  Step by Step Calculation of the Penman-Monteith Evapotranspiration (FAO-56 Method)


  Tools for Agro-Meteorology and Biophysical Modelling
          Click Equations, Evapotranspirations Equations, Supporting Equations

References: Actual, Reference and Potential Evapotranspiration

  Pidwirny, M. (2006). 
  Actual and Potential Evapotranspiration 
  Fundamentals of Physical Geography, 2nd Edition.

  Irmak, S. and D.Z. Haman (2014; most recent)
  Evapotranspiration: Potential or Reference?

References: ASCE Standardized Reference Evapotranspiration Equation

  Jensen, M.E., R.D. Burman, and R.G. Allen. (1990) 
  Evapotranspiration and Irrigation Water Requirements 
  ASCE Manuals and Reports on Engineering Practice No. 70
  Am. Soc. Civil Engr., New York, NY. 332 pp.
fao56_1.ncl: Example 1: Using data generated by the CESM-CLM component, this example illustrates the standardized approach to computing the Penman-Monteith reference evapotranspiration via FAO-56 methodology: (refevt_penman_fao56).

This example uses the FAO-56 recommended:

  • albedo=0.23: This albedo is not the atmospheric or land surface albedo. Rather, the albedo refers to light reflected by the crop leaf surface ('leaf_albedo').

  • cnumer=900 and cdenom=0.34. These are the FAO-56 values appropriate for the hypothetical (short) reference crop. They are appropriate for day and month estimates. To apply to hourly data use (cnumer=37.5 [=900.0/24])

fao56_1a.ncl: Example 1a: Same as Example 1 but use the "tall" hypothetical reference crop coefficients specified by the ASCE-ET (American Society of Civil Engineering) for a hypothetical "tall" crop (cnumer=1600 and cdenom=0.38).

fao56_2.ncl: Example 2: Use the radext_fao56 and daylight_fao56 to calculate the extraterrestrial radiation and maximum number of daylight hours as described in FAO 56.

NOTE_1: The assumptions used to derive the 'simple' equations used by FAO-56 are less appropriate for latitudes poleward of (say) 55-60 degrees.

NOTE_2: Printed values (W/m2) at selected latitudes for each day of the year are here. These are from Example 3 at radext_fao56.

NOTE_3: If the user wishes all returned _FillValue to be set to zero (0.0), then after the radext_fao56 function use the where and ismissing functions to set all _FillValue to zero. Specifically:

  radext = radext_fao56(jday, lat, ounit)
  radext = where(ismissing(radext), 0, radext)  ; set all _FillValue = 0.0