How to calculate Bowen ratio beta surface energy balance evapotranspiration

Calculate Bowen ratio beta = H/LE sensible vs latent heat flux surface energy balance dimensionless. beta<<1 humid ocean; beta>>1 desert. Ira Sprague Bowen USA 1898-1973 1926 Phys Rev 27:779. NOAA + USDA + AmeriFlux + FAO.

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How to calculate the Bowen ratio (beta or Bowen ratio) fundamental dimensionless ratio meteorology hydrology agronomy measuring sensible heat flux H vs latent heat flux LE at Earth surface in energy balance equation Rn = H + LE + G + S: beta = H / LE. H sensible heat flux W/m^2 (ocean 5-50; forest 50-200; irrigated cropland 50-100; desert 200-500; ice cap -50 to 50; urban heat island 100-300); LE latent heat flux of evapotranspiration W/m^2 (tropical ocean 100-300; humid forest 200-400; irrigated cropland 150-300; desert 5-30; lake 100-200).

Psychrometric Bowen 1926 method: beta = gamma * (dT/de) where gamma = c_p*p/(0.622*lambda) ~ 0.066 kPa/°C psychrometric constant + dT temperature difference two levels + de vapor pressure difference + Bowen Ratio Energy Balance method BREB.

Bowen Ratio Energy Balance BREB: LE = (Rn - G) / (1 + beta) + H = beta*(Rn - G)/(1 + beta) + Rn net radiation + G ground heat flux + derive fluxes from micrometeorological gradients.

Surface beta classification typical values: tropical ocean lake beta=0.1-0.3 + latent dominant 80-90% energy in evaporation; humid forests beta=0.2-0.5 + transpiration vegetation + evapotranspiration; cropland vegetation beta=0.5-2 + moderate balance; semi-arid beta=2-10 + sensible dominant + reduced evaporation; desert beta=10-100 + sensible nearly total + heat shimmer; oasis advection beta<0 + LE > Rn-G + horizontal energy transport + irrigated vegetation in desert.

Surface energy balance variables: Rn net radiation = (1-alpha)*Rs + Rl_in - Rl_out alpha albedo Rs solar Rl longwave; G ground heat flux typical 5-20% Rn + plate flux + soil temperature gradient; S canopy storage negligible short-term; P photosynthesis GPP negligible <1% energy.

Eddy covariance EC measurement: H = rho*c_p*; LE = rho*lambda* + sonic anemometer + IRGA infrared gas analyzer + 10-20 Hz sampling + Reynolds decomposition + closure problem typically 10-30% gap H+LE < Rn-G.

FLUXNET network: > 1500 global eddy covariance stations + ICOS Integrated Carbon Observation System Europe + AmeriFlux USA.

Penman-Monteith FAO 1998 equation: ET_0 = (0.408*Delta*(Rn-G) + gamma*(900/(T+273))*u_2*(e_s-e_a)) / (Delta + gamma*(1+0.34*u_2)) + ET_0 reference evapotranspiration grass + Delta slope vapor pressure curve + classical reference FAO-56 1998 Allen-Pereira-Raes-Smith.

Related numbers: Priestley-Taylor alpha = LE/LE_eq 1.26 humid ocean; evaporation fraction EF = LE/(Rn-G); Penman E_p potential evaporation; aerodynamic resistance r_a; surface stomatal resistance r_s. History: Ira Sprague Bowen (Seneca Falls New York 1898 - Pasadena California 1973) UC Berkeley + Caltech 1928-1948 + Mount Wilson Palomar Observatories Director 1948-1964; 1926 paper Phys Rev 27:779 'The ratio of heat losses by conduction and by evaporation from any water surface' classic Bowen ratio + classical reference surface energy balance + 1927 PNAS 13:212 + Bowen ratio eponym + classical reference micrometeorology hydrology; pioneer micrometeorology + Bowen lines spectroscopy planetary nebulae 1927 'forbidden lines' OIII NII + Henry Draper Medal 1942 + Bruce Medal 1957 + classical reference astronomy + Director Mount Wilson Palomar 200-inch Hale Telescope 1948 inauguration.

Howard Penman (UK 1909-1984) Rothamsted Experimental Station 1937-1974 + Royal Society 1953; 1948 Proc Roy Soc A 193:120 'Natural evaporation from open water bare soil and grass' classic Penman equation + Penman-Monteith 1965 + classical reference.

John Monteith (UK 1929-2012) Rothamsted + Edinburgh 1976-1992 + ICRISAT India 1991-1995; 1965 paper Symposia Soc Exp Biol 19:205 Penman-Monteith + 1973 'Principles of Environmental Physics' Edward Arnold 241 pages classical + ICRISAT crop water stress + Royal Society Edinburgh + Member US National Academy.

Charles Priestley (Australia 1915-1998) CSIRO Aspendale 1946-1977 director; 1972 Mon Weather Rev 100:81 with Taylor 'On the assessment of surface heat flux and evaporation using large-scale parameters' classic Priestley-Taylor alpha=1.26 + Australian Academy 1959 + Royal Society 1981.

Wilfried Brutsaert (Belgium-USA 1934-) Cornell University 1968-2004 emeritus; 1982 'Evaporation into the Atmosphere' Reidel 299 pages classic + 2005 'Hydrology An Introduction' Cambridge 605 pages + classical reference + International Hydrology Prize 2008 + Robert Horton Award AGU. Legacy: Brutsaert 1982 + Allen-Pereira-Raes-Smith 'Crop Evapotranspiration FAO-56' 1998 FAO 300 pages classical reference modern + Foken 'Micrometeorology' 2nd 2017 Springer 362 pages classic + Aubinet-Vesala-Papale 'Eddy Covariance' 2012 Springer 438 pages classical reference + Stull 'Boundary Layer Meteorology' 1988 Kluwer 666 pages classic + Garratt 1992 Cambridge 316 + Arya 2001 Academic 420 + Oke 'Boundary Layer Climates' 1987 Routledge 435 pages classic.

USA research evapotranspiration + agronomy + meteorology: NOAA Silver Spring Boulder 12000 + GFDL Princeton + NCEI; NCAR National Center Atmospheric Research Boulder 1500 world-leading + WRF + CLM Community Land Model; USDA United States Department Agriculture ARS 8400 + Beltsville + crop water requirements world-leading; NASA Goddard Marshall 17000 + MODIS land cover + GLDAS Global Land Data Assimilation System; NSF Geosciences 4500; EPA Environmental Protection Agency 14000; USGS Water Resources 8500; BLM Bureau Land Management 9500; NREL Boulder 3700 + renewable energy; National Atmospheric Deposition Program NADP 100.

USA universities micrometeorology + evapotranspiration: UC Berkeley Atmospheric Sciences 8500 + Dennis Baldocchi world-leading + AmeriFlux founder + classical reference; Stanford Earth System Science 11000; Cornell Civil Environmental 5200 + Wilfried Brutsaert legacy + Diane Pataki ecology; Univ Washington Seattle 47000; Penn State Meteorology 8500; Colorado State Atmospheric 31000 + David Randall climate modeling; Yale Forestry Environment 13000; Univ Wisconsin Madison 7000; UC Davis 35000 + Richard Snyder agroclimatology classical reference + grass reference ET; Texas A&M 70000 + crop water; Univ Florida 53000 + agriculture water; Iowa State 30000 + USDA.

USA industry agriculture + irrigation + agritech: John Deere Moline IL 80000 + automated irrigation precision + GreenStar; AGCO Duluth GA 24000 + Massey Ferguson + Fendt; CNH Industrial Burr Ridge 27000 + Case IH + New Holland; Trimble Sunnyvale CA 12000 + GPS GNSS precision agriculture; Lindsay Corporation Omaha NE 1500 + Zimmatic center pivot; Valley Irrigation Valmont 5500 + center pivot global leader; Netafim USA 1300 + drip irrigation Israel-USA; The Toro Company Bloomington 7500 + sprinkler; Hunter Industries San Marcos CA 2000; Rain Bird Azusa CA 2500.

USA industry HVAC dehumidifier evaporation cooling: Carrier Palm Beach 53000; Trane Davidson NC 36000; Lennox International Richardson TX 14000; Munters Corp 1500; Daikin USA 1500.

USA industry agritech sensors + drones: Climate Corporation Bayer 800; Granular Corteva 200; Farmers Edge 200; Onset Computer Bourne 200 + HOBO data loggers; Vaisala USA 200 + weather stations; Campbell Scientific Logan UT 800 + research weather stations world-leading.

Bowen ratio formula

Direct definition: beta = H / LE. H sensible heat flux W/m^2 + LE latent heat flux W/m^2 + dimensionless.

Psychrometric Bowen 1926 method: beta = gamma * (dT/de) + gamma psychrometric constant = 0.066 kPa/°C.

BREB Bowen Ratio Energy Balance: LE = (Rn - G)/(1 + beta) + H = beta*(Rn - G)/(1 + beta).

Evaporation fraction: EF = LE/(Rn-G) = 1/(1+beta).

Typical values: tropical ocean beta=0.1-0.3 latent 80-90%; forests beta=0.2-0.5; irrigated cropland beta=0.5-2; semi-arid beta=2-10; desert beta=10-100; oasis advection beta<0.

History and context

Ira Sprague Bowen (Seneca Falls 1898 - Pasadena 1973) UC Berkeley + Caltech 1928-1948 + Mount Wilson Palomar Observatories Director 1948-1964; 1926 paper Phys Rev 27:779 'The ratio of heat losses by conduction and by evaporation from any water surface' classic Bowen ratio + classical reference + 1927 PNAS 13:212 + Bowen ratio eponym + classical reference micrometeorology + Bowen lines spectroscopy planetary nebulae 1927 'forbidden lines' OIII NII + Henry Draper Medal 1942 + Bruce Medal 1957 + Member US National Academy + Director Mount Wilson Palomar 200-inch Hale Telescope 1948 inauguration.

Howard Penman (UK 1909-1984) Rothamsted 1937-1974 + Royal Society 1953; 1948 Proc Roy Soc A 193:120 classic Penman + Penman-Monteith 1965.

John Monteith (UK 1929-2012) Edinburgh + ICRISAT; 1965 Penman-Monteith + 1973 'Principles of Environmental Physics' Edward Arnold 241 + Royal Society Edinburgh + US National Academy.

Charles Priestley (Australia 1915-1998) CSIRO Aspendale; 1972 Priestley-Taylor alpha=1.26 + Australian Academy + Royal Society 1981.

Wilfried Brutsaert (1934-) Cornell 1968-2004; 1982 'Evaporation into Atmosphere' Reidel 299 + 2005 'Hydrology' Cambridge 605 + International Hydrology Prize 2008. Legacy: Brutsaert 1982 + Allen-Pereira-Raes-Smith FAO-56 1998 + Foken 2017 + Aubinet 2012 + Stull 1988 + Garratt 1992 + Arya 2001 + Oke 1987.

USA research: NOAA 12000 + GFDL; NCAR 1500 world-leading + WRF + CLM; USDA ARS 8400 world-leading; NASA 17000 + MODIS + GLDAS; USGS 8500; EPA 14000; NREL 3700.

Universities: UC Berkeley 8500 + Dennis Baldocchi world-leading + AmeriFlux founder; Stanford 11000; Cornell 5200 + Brutsaert legacy; UC Davis 35000 + Snyder agroclimatology classical; Penn State 8500; Colorado State 31000 + Randall climate; Yale 13000; Texas A&M 70000; Florida 53000; Iowa State 30000.

Agriculture: John Deere 80000; AGCO 24000; CNH Industrial 27000; Trimble 12000; Lindsay 1500; Valley 5500 world-leading; Netafim USA 1300; Toro 7500; Hunter 2000; Rain Bird 2500.

HVAC: Carrier 53000; Trane 36000; Lennox 14000; Munters 1500; Daikin USA 1500.

Agritech: Climate Corp Bayer 800; Onset 200; Vaisala USA 200; Campbell Scientific 800 world-leading.

Bowen values table

  • beta = H/LE: direct definition
  • beta = gamma*(dT/de): psychrometric
  • gamma = 0.066 kPa/°C: psychrometric constant
  • EF = 1/(1+beta): evaporation fraction
  • tropical ocean: beta=0.1-0.3
  • humid forest: beta=0.2-0.5
  • irrigated cropland: beta=0.5-2
  • semi-arid: beta=2-10
  • desert: beta=10-100
  • oasis advection: beta<0

5 numerical examples

  1. Tropical Atlantic ocean: H=30 + LE=150 + beta = 0.2 latent dominant 83% + ocean energy budget classical.
  2. Temperate forest Hubbard Brook USA: H=100 + LE=200 + beta = 0.5 transpiration 67% + AmeriFlux site Baldocchi.
  3. Irrigated cropland Iowa USDA: H=80 + LE=160 + beta = 0.5 + irrigation 67% + USDA ARS Beltsville.
  4. Sahara desert: H=400 + LE=30 + beta = 13.3 sensible 93% + heat shimmer + classical reference.
  5. Bowen 1926 psychrometric: dT=3 °C + de=0.5 kPa + beta = 0.066*3/0.5 = 0.4 + BREB station.

Limitations

Stationarity: BREB assumes stationary conditions + diurnal cycle distinct + Foken 2017 classical.

Closure problem eddy covariance: typically H+LE < Rn-G 10-30% gap + canopy storage P + horizontal advection + Aubinet 2012.

Reynolds analogy: K_h = K_v turbulent diffusion equal heat moisture + extension Webb-Pearman-Leuning 1980 WPL CO2 H2O vapor correction.

Surface heterogeneity: Bowen footprint + spatial variability + Foken 2017.

Common mistakes

  • Beta=-1 singularity: oasis advection LE > Rn-G + denominator 1+beta = 0 + numerical instability + Brutsaert 1982.
  • Sign convention H LE: positive upward away from surface micrometeorology convention + sign error common Foken 2017.
  • Rn vs Rs error: Rn net radiation = (1-alpha)*Rs + Rl_net + Rs solar shortwave incoming + albedo distinct Stull 1988.
  • G ground flux: 5-20% Rn diurnal + plate flux + soil temperature gradient + Brutsaert 2005.
  • Closure assumption: H + LE != Rn - G + storage + advection + 10-30% gap + Aubinet 2012.

Applications

  1. FLUXNET eddy covariance: AmeriFlux founder Dennis Baldocchi UC Berkeley world-leading + > 1500 stations global.
  2. Crop evapotranspiration FAO-56: Penman-Monteith + USDA ARS + irrigation scheduling + UC Davis Snyder.
  3. Climate modeling: NCAR + GFDL Princeton + scenarios + CLM Community Land Model.
  4. Hydrology water budget: Cornell Brutsaert legacy + UC Berkeley + watershed evaporation USGS.
  5. Urban heat island: cities + adaptation climate change + EPA.
  6. Forest carbon flux: Hubbard Brook + AmeriFlux + ICOS + carbon balance.
  7. Lake reservoir evaporation: hydropower + USGS + classical Penman.
  8. Greenhouse climate control: Carrier + Trane + Munters + dehumidification.
  9. Wildfire risk: drought indices + USFS + classical Bowen high beta.
  10. Precision agriculture irrigation: John Deere + AGCO + Trimble + Lindsay + Valley + Netafim USA.

Updated July 2026

Frequently Asked Questions

What does the Bowen ratio beta measure?

Bowen ratio beta = H/LE measures the dimensionless ratio between sensible heat flux H W/m^2 and latent heat flux LE W/m^2 at Earth surface in energy balance equation Rn = H + LE + G + S. beta<<1 tropical ocean lake latent dominant 80-90%; 0.2<beta>10 desert sensible dominant. Ira Sprague Bowen USA 1898-1973 1926 Phys Rev 27:779 classic.

What is the Bowen 1926 psychrometric method?

Psychrometric Bowen 1926 method: beta = gamma*(dT/de) where gamma psychrometric constant = c_p*p/(0.622*lambda) ~ 0.066 kPa/°C + dT temperature difference two levels + de vapor pressure difference two levels. BREB Bowen Ratio Energy Balance method derives LE = (Rn-G)/(1+beta) and H = beta*(Rn-G)/(1+beta) from micrometeorological gradients fixed station + pioneer Bowen 1926.

What is evapotranspiration fraction EF?

Evapotranspiration fraction EF = LE/(Rn-G) = 1/(1+beta) measures fraction of available energy at surface converted to latent heat of evapotranspiration. EF=1 Bowen=0 total latent; EF=0.5 Bowen=1 equilibrium H=LE; EF9 desert sensible dominant. Important for remote sensing modeling SEBAL METRIC + classical reference modern.

What is eddy covariance EC?

Eddy covariance EC direct measurement technique turbulent fluxes H = rho*c_p* and LE = rho*lambda* via 3D sonic anemometer + IRGA infrared gas analyzer + 10-20 Hz sampling + Reynolds decomposition w' T' fluctuations. FLUXNET > 1500 global stations + ICOS Europe + AmeriFlux + classical reference Aubinet-Vesala-Papale 'Eddy Covariance' 2012 Springer 438 pages.

What is Penman-Monteith FAO-56 1998 equation?

Penman-Monteith FAO-56 1998 standard reference evapotranspiration ET_0 grass: ET_0 = (0.408*Delta*(Rn-G) + gamma*(900/(T+273))*u_2*(e_s-e_a)) / (Delta + gamma*(1+0.34*u_2)) where Delta slope vapor pressure curve + gamma psychrometric + u_2 wind speed 2 m + e_s saturation vapor + e_a actual vapor. Penman 1948 + Monteith 1965 + Allen-Pereira-Raes-Smith FAO 1998 classical.

What are AmeriFlux stations?

AmeriFlux network of >120 long-term eddy covariance stations across Americas DOE-funded since 1996 + Hubbard Brook + Walker Branch + Harvard Forest + Niwot Ridge + Bondville + Vaira Ranch California Dennis Baldocchi UC Berkeley world-leading founder + classical reference + part of FLUXNET global network + ICOS Europe analog + Markus Reichstein MPI-BGC Jena classical.

Bowen ratio industrial applications?

Bowen ratio applications: precision agriculture FAO-56 ETO + John Deere AGCO Trimble Lindsay Valley; carbon flux FLUXNET AmeriFlux UC Berkeley Baldocchi world-leading; HVAC dehumidification Carrier Trane Munters; greenhouse climate control USDA; climate modeling NCAR; lake reservoir evaporation USGS hydropower; urban heat island EPA cities; wildfire risk drought indices USFS + classical Bowen high beta.

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