Come calcolare il rapporto di Bowen (beta o Bowen ratio) rapporto adimensionale fondamentale meteorologia idrologia agronomia che misura il rapporto tra flusso di calore sensibile H e flusso di calore latente LE alla superficie terrestre nell'equazione del bilancio energetico Rn = H + LE + G + S: beta = H / LE. H flusso di calore sensibile W/m^2 (oceano 5-50; foresta 50-200; coltivi irrigati 50-100; deserto 200-500; cap glaciale -50 a 50; città heat island 100-300); LE flusso di calore latente di evapotraspirazione W/m^2 (oceano tropicale 100-300; foresta umida 200-400; coltivi irrigati 150-300; deserto 5-30; lago 100-200).

Metodo psychrometric Bowen 1926: beta = gamma * (dT/de) dove gamma = c_p*p/(0.622*lambda) ~ 0.066 kPa/°C costante psicrometrica + dT differenza temperatura due livelli + de differenza pressione vapore due livelli + Bowen ratio energy balance method BREB.

Bowen Ratio Energy Balance BREB: LE = (Rn - G) / (1 + beta) + H = beta*(Rn - G)/(1 + beta) + Rn radiazione netta + G flusso suolo + ricavare flussi da gradienti micrometeorologici.

Classificazione superfici beta tipici: oceano lago tropicale beta=0.1-0.3 + latente dominante 80-90% energia in evaporazione; foreste umide beta=0.2-0.5 + transpirazione vegetazione + evapotraspirazione; vegetazione coltivi beta=0.5-2 + balance moderato; semi-arido beta=2-10 + sensibile dominante + ridotta evaporazione; deserto beta=10-100 + sensibile quasi totale + heat shimmer; oasi advection beta<0 + LE > Rn-G + transport orizzontale energia + vegetazione irrigata in deserto.

Variabili surface energy balance: Rn radiazione netta = (1-alpha)*Rs + Rl_in - Rl_out alpha albedo Rs solare Rl longwave; G ground heat flux tipico 5-20% Rn + plate flux + soil temperature gradient; S storage canopy heat trascurabile breve termine; P fotosintesi GPP trascurabile <1% energia.

Misurazione eddy covariance EC: 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 stazioni eddy covariance globali + ICOS Integrated Carbon Observation System Europe + AmeriFlux USA + Italy 12 sites La Thuile San Rossore Lavarone Bonis Roccarespampani Castelporziano.

Equazione Penman-Monteith FAO 1998: 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 + gamma psychrometric + u_2 wind speed 2 m FAO-56 1998 Allen-Pereira-Raes-Smith.

Numeri correlati: numero Priestley-Taylor alpha = LE/LE_eq 1.26 oceano humid; evaporation fraction EF = LE/(Rn-G); Penman E_p potential evaporation; aerodynamic resistance r_a; surface stomatal resistance r_s. Storia: Ira Sprague Bowen (Seneca Falls New York USA 1898 - Pasadena California 1973) Univ California Berkeley + Caltech 1928-1948 + Mount Wilson Palomar Observatories Director 1948-1964 + UC Berkeley physics 1948-1964; 1926 paper Phys Rev 27:779 'The ratio of heat losses by conduction and by evaporation from any water surface' classico Bowen ratio surface energy balance + 1927 paper PNAS 13:212 + Bowen ratio eponym micrometeorologia idrologia; pioneer micrometeorologia + Bowen lines spectroscopy nebule planetarie 1927 + Henry Draper Medal 1942 + Bruce Medal 1957 Astronomical Society Pacific astronomy.

Howard Latimer Penman (UK 1909-1984) Rothamsted Experimental Station 1937-1974; 1948 paper Proc Roy Soc A 193:120 'Natural evaporation from open water bare soil and grass' classico Penman equation + 1949 'Drainage and Salinity in the Sutton-on-Trent Project' + Penman-Monteith 1965 con Monteith evapotranspiration.

John L Monteith (UK 1929-2012) Rothamsted + Univ Edinburgh 1976-1992 + ICRISAT India 1991-1995; 1965 paper Symposia Soc Exp Biol 19:205 'Evaporation and environment' Penman-Monteith + 1973 textbook 'Principles of Environmental Physics' Edward Arnold 241 pages classico micrometeorologia + ICRISAT crop water stress + International Bicentenary Medal Royal Society Edinburgh + Ramsay Memorial Medal.

Charles Henry Brian Priestley (Australia 1915-1998) CSIRO Aspendale 1946-1977 founding member; 1972 paper Mon Weather Rev 100:81 con Taylor 'On the assessment of surface heat flux and evaporation using large-scale parameters' classico Priestley-Taylor + Australian Academy of Science micrometeorologia.

Charles HB Priestley + R J Taylor; 1972 Priestley-Taylor alpha=1.26 evapotranspiration constant for humid surface;.

Wilfried Brutsaert (Belgio-USA 1934-) Cornell University Civil Engineering 1968-2004 emeritus; 1982 textbook 'Evaporation into the Atmosphere' Reidel 299 pages classico + 2005 'Hydrology An Introduction' Cambridge 605 pages classico hydrology evaporation + International Hydrology Prize 2008 + Robert Horton Award AGU. Eredita: Brutsaert 'Evaporation into the Atmosphere' 1982 Reidel 299 pages classic + Allen-Pereira-Raes-Smith 'Crop Evapotranspiration FAO-56' 1998 FAO 300 pages Foken 'Micrometeorology' 2nd 2017 Springer 362 pages classic + Aubinet-Vesala-Papale 'Eddy Covariance' 2012 Springer 438 pages Stull 'An Introduction to Boundary Layer Meteorology' 1988 Kluwer 666 pages classico + Garratt 'The Atmospheric Boundary Layer' 1992 Cambridge 316 pages + Arya 'Introduction to Micrometeorology' 2nd 2001 Academic Press 420 pages.

Italia ricerca Bowen + evapotraspirazione + idrologia + agronomia: CNR-IBE Istituto BioEconomia Firenze + Bologna + Sassari + Roma + 7 sedi 250 + FLUXNET Italia stations La Thuile + San Rossore + Lavarone + Bonis + Roccarespampani + Castelporziano + Castelloni di Mezzo + Brasimone + Renon + Tarvisio + Capo Caccia + Vicenza world-leading + Giorgio Matteucci; CNR-ISAC Istituto Scienze Atmosfera Clima Roma + Bologna + Lecce + Padova + Torino 350 + atmosfera + clima + meteorologia; CREA Consiglio Ricerca Agricoltura Roma 1500 + agroecosistemi + crop water; CNR-IRSA Istituto Ricerca Acque Roma + Bari + Brugherio 200; CNR-IIA Istituto Inquinamento Atmosferico Roma 200; OGS Trieste 250; CNR-ISP Polari 80; CMCC Lecce + Bologna + Capua + Sassari + Venezia 280 climate Mediterraneo; ENEA Casaccia + Frascati + Brindisi + 11 centri 2700; FBK Trento 480.

Italia università evapotraspirazione + idrologia + agronomia: Padova DAFNAE TESAF 3000 + Vincenzo Fabbroni evapotraspirazione + Marco Borga idrologia world-leading; Bologna DISTAL DICAM 4000 + Marco Bittelli soil physics + Andrea Buzzi atmosphere; Sapienza Roma DICEA 4000; Federico II Napoli DiSTAR DIA 5000 + Fabio Terribile soil; Politecnico Milano DICA 7500 + Marco Mancini hydrology + Renzo Rosso; Politecnico Torino DENERG DIATI 5000 + Pierluigi Claps; Pisa DAF DST 2500 + Marco Doveri hydrology; Genova DICCA 2000; Catania DAF 2000; Firenze DiCEA DAGRI 1321 + Simone Orlandini agrometeorologia; Bari DAF 1080; Tuscia Viterbo DIBAF 800 + Riccardo Valentini eddy covariance world-leading + Dario Papale FLUXNET; Sassari DAGRI 1500; L'Aquila DSFC CETEMPS 1500; Camerino MARS 1000.

Italia industria agricoltura + irrigazione + agritech: Coldiretti 1.6M associati; CIA-Agricoltori Italiani 900000; Bonifiche Italiane 100; CER Romagna 200 + irrigazione; ARPA regionali 8000 + monitoraggio agrometeorologia; Aeronautica Militare CNMCA 800 + meteo agricoltura; Coordinamento Idrografica Roma 200.

Italia industria irrigazione tecnologica: Lattanzi Roma 100 + irrigazione drip; Netafim Italia Verona 200 + drip irrigation Israele Italia; Rivulis Italia 100 + drip; Toro Company Italia 50; Casa Mondo Verona 200.

Italia industria agritech sensors precision agriculture: xFarm Lugano-Milano 100 + precision agriculture; Agricolus Perugia 80; FieldClimate Pessl Italy 50; Agroptima Spain-Italy 80; Trimble Italia 200 + GPS GNSS precision; John Deere Italia 800 + automated irrigation; Massey Ferguson AGCO Italia 200.

Italia industria HVAC dehumidifier evaporation cooling: Daikin Italia 500; Mitsubishi Electric Italia 400; Carrier Italia 300; Climaveneta 800; Aermec 1100; Galletti 600; Sabiana 700; Munters Italia 200 + dehumidification + evaporation cooling.

Formula Bowen ratio

Definizione diretta: beta = H / LE. H flusso calore sensibile W/m^2 + LE flusso calore latente W/m^2 + adimensionale.

Metodo psicrometrico Bowen 1926: beta = gamma * (dT/de) + gamma costante psicrometrica = 0.066 kPa/°C + dT differenza temperatura + de differenza pressione vapore.

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

Frazione evapotraspirazione: EF = LE/(Rn-G) = 1/(1+beta) + frazione energia disponibile in evaporazione.

Coefficienti tipici: oceano tropicale beta=0.1-0.3 latente 80-90%; foreste beta=0.2-0.5; coltivi irrigati beta=0.5-2; semi-arido beta=2-10; deserto beta=10-100; oasi advection beta<0.

Storia e contesto

Ira Sprague Bowen (Seneca Falls New York USA 1898 - Pasadena California 1973) Univ California Berkeley + Caltech 1928-1948 + Mount Wilson Palomar Observatories Director 1948-1964 + UC Berkeley physics 1948-1964; 1926 paper Phys Rev 27:779 'The ratio of heat losses by conduction and by evaporation from any water surface' classico Bowen ratio surface energy balance + 1927 paper PNAS 13:212 + Bowen ratio eponym micrometeorologia idrologia; pioneer micrometeorologia + Bowen lines spectroscopy nebule planetarie 1927 'forbidden lines' OIII NII + spectroscopy astronomy + Henry Draper Medal 1942 National Academy Sciences USA + Bruce Medal 1957 Astronomical Society Pacific + Member US National Academy astronomy + Director Mount Wilson Palomar 200-inch Hale Telescope inauguration 1948.

Howard Latimer Penman (UK 1909-1984) Rothamsted Experimental Station 1937-1974 + Royal Society fellow 1953; 1948 paper Proc Roy Soc A 193:120 'Natural evaporation from open water bare soil and grass' classico Penman equation evaporation + 1949 'Drainage and Salinity Sutton-on-Trent' + Penman-Monteith 1965 con Monteith + International Glory Symposium 1989 evapotranspiration.

John Lennox Monteith (UK 1929-2012) Rothamsted Experimental Station 1957-1976 + Univ Edinburgh 1976-1992 + ICRISAT International Crops Research Institute Semi-Arid Tropics India 1991-1995 director; 1965 paper Symposia Soc Exp Biol 19:205 'Evaporation and environment' Penman-Monteith + 1973 textbook 'Principles of Environmental Physics' Edward Arnold 241 pages 4th 2013 Academic Press 401 pages micrometeorologia agronomia + ICRISAT crop water stress + International Bicentenary Medal Royal Society Edinburgh 1976 + Ramsay Memorial Medal + Member US National Academy.

Charles Henry Brian Priestley (Australia 1915-1998) CSIRO Aspendale Atmospheric Research 1946-1977 founding member 1949 director; 1972 paper Mon Weather Rev 100:81 con Taylor R J 'On the assessment of surface heat flux and evaporation using large-scale parameters' classico Priestley-Taylor alpha=1.26 micrometeorologia + Australian Academy of Science 1959 + David Rivett Medal 1956 + Royal Society fellow 1981.

Wilfried Brutsaert (Belgio-USA 1934-) Cornell University Civil and Environmental Engineering 1968-2004 emeritus; 1982 textbook 'Evaporation into the Atmosphere' Reidel 299 pages classico + 2005 'Hydrology An Introduction' Cambridge 605 pages classico hydrology evaporation + International Hydrology Prize 2008 + Robert Horton Award AGU 1987 + Member US National Academy. Eredita: Brutsaert 'Evaporation into the Atmosphere' 1982 Reidel 299 pages classic + Allen-Pereira-Raes-Smith 'Crop Evapotranspiration FAO-56' 1998 FAO 300 pages modern + Foken 'Micrometeorology' 2nd 2017 Springer 362 pages classic + Aubinet-Vesala-Papale 'Eddy Covariance' 2012 Springer 438 pages Stull 'An Introduction to Boundary Layer Meteorology' 1988 Kluwer 666 pages classico + Garratt 'The Atmospheric Boundary Layer' 1992 Cambridge 316 pages + Arya 'Introduction to Micrometeorology' 2nd 2001 Academic 420 pages + Oke 'Boundary Layer Climates' 1987 Routledge 435 pages classico.

Italia ricerca: CNR-IBE Firenze + Bologna + Sassari 250 FLUXNET Italia stations world-leading + Giorgio Matteucci; CNR-ISAC 350 atmosphere; CREA 1500 agroecosistemi; CNR-IRSA 200; CNR-IIA 200; OGS 250; CNR-ISP 80; CMCC 280 climate Mediterraneo; ENEA 2700; FBK 480.

Universita: Padova DAFNAE 3000 + Vincenzo Fabbroni + Marco Borga idrologia world-leading; Bologna 4000 + Marco Bittelli + Andrea Buzzi; Sapienza 4000; Federico II Napoli 5000 + Fabio Terribile; Politecnico Milano 7500 + Marco Mancini + Renzo Rosso; Politecnico Torino 5000; Pisa 2500; Genova 2000; Catania 2000; Firenze DAGRI 1321 + Simone Orlandini agrometeo; Bari 1080; Tuscia Viterbo 800 + Riccardo Valentini eddy covariance world-leading + Dario Papale FLUXNET; Sassari 1500; L'Aquila CETEMPS 1500; Camerino 1000.

Industria agricoltura: Coldiretti 1.6M; CIA 900000; Bonifiche 100; CER Romagna 200; ARPA regionali 8000; Aeronautica CNMCA 800.

Irrigazione: Netafim 200; Rivulis 100; Toro 50; Casa Mondo 200.

Agritech: xFarm 100; Agricolus 80; FieldClimate Pessl 50; Trimble 200; John Deere 800; AGCO 200.

HVAC: Daikin 500; Climaveneta 800; Aermec 1100; Munters 200.

Tabella valori Bowen ratio

• beta = H/LE: definizione diretta
• beta = gamma*(dT/de): psicrometrica
• gamma = 0.066 kPa/°C: psicrometrica costante
• EF = 1/(1+beta): frazione evaporazione
• oceano tropicale: beta=0.1-0.3
• foresta umida: beta=0.2-0.5
• coltivi irrigati: beta=0.5-2
• semi-arido: beta=2-10
• deserto: beta=10-100
• oasi advection: beta<0

5 esempi numerici

1. Oceano tropicale Atlantico: H=30 + LE=150 + beta = 30/150 = 0.2 latente dominante 83% + ocean energy budget classical.
2. Foresta temperata Vallombrosa Toscana: H=100 + LE=200 + beta = 100/200 = 0.5 transpirazione 67% + Tuscia FLUXNET site.
3. Coltivi irrigati Pianura Padana: H=80 + LE=160 + beta = 0.5 + irrigazione 67% + CER Romagna + Coldiretti.
4. Deserto Sahara: H=400 + LE=30 + beta = 13.3 sensibile 93% + heat shimmer + Sahara.
5. Metodo psicrometrico Bowen 1926: dT=3 °C + de=0.5 kPa + beta = 0.066*3/0.5 = 0.4 + BREB station ARPA.

Limiti e ipotesi

Stationarity: BREB assume condizioni stazionarie + diurnal cycle distinct + Foken 2017 classical.

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

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

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

Errori comuni Bowen ratio

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

Applicazioni Bowen ratio

1. FLUXNET eddy covariance: > 1500 station globali + ICOS Europe + Italia 12 sites + CNR-IBE + Tuscia Riccardo Valentini world-leading.
2. Crop evapotranspiration FAO-56: Penman-Monteith + irrigation scheduling + CER Romagna + Coldiretti + Acque CER.
3. Climate modeling Mediterranean: CMCC Lecce + RegCM ECHAM ICON + scenarios climate change.
4. Hydrology water budget: Politecnico Milano + Padova world-leading + watershed evaporation.
5. Urban heat island: ARPA città + Politecnico + adaptation climate change.
6. Forest carbon flux: Tuscia Viterbo Riccardo Valentini world-leading FLUXNET + ICOS Italia + carbon balance.
7. Lake reservoir evaporation: hydropower + Acea + Iren + classical Penman.
8. Greenhouse climate control: Daikin + Climaveneta + Munters + dehumidification.
9. Wildfire risk modeling: ARPA + drought indices + classical Bowen high beta.
10. Precision agriculture irrigation: xFarm + Agricolus + Trimble + John Deere + drip Netafim.

Aggiornato a luglio 2026