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The '''Penman equation''' describes [[evaporation]] (''E'') from an open water surface, and was developed by [[Howard Penman]] in 1948. Penman's equation requires daily mean [[temperature]], [[wind speed]], [[relative humidity]], and [[solar radiation]] to predict E. Simpler [[Evapotranspiration#Hydrometeorological_equations|Hydrometeorological equations]] continue to be used where obtaining such data is impractical, to give comparable results within specific contexts, e.g. humid vs arid climates. | |||
==Details== | |||
Numerous variations of the Penman equation are used to estimate [[evaporation]] from water, and land. Specifically the [[Penman-Monteith]] equation refines weather based [[Evapotranspiration#Potential_evapotranspiration|potential evapotranspiration]] (PET) estimates of vegetated land areas.<ref>{{cite book |last=Allen |first=R.G. |coauthors=Pereira, L.S.; Raes, D.; Smith, M. |title=Crop Evapotranspiration—Guidelines for Computing Crop Water Requirements |url=http://www.fao.org/docrep/X0490E/x0490e00.HTM |accessdate=2007-10-08 |series=FAO Irrigation and drainage paper 56 |year=1998 |publisher=Food and Agriculture Organization of the United Nations |location=Rome, Italy |isbn=92-5-104219-5 }}</ref> It is widely regarded as one of the most accurate models, in terms of estimates.<!--.<ref>Rim Chang-Soo. A Study of the Evapotranspiration Estimation in the Semiarid Area.</ref><ref> http://www.cpc.ncep.noaa.gov/soilmst/paper.html</ref> these refs are incomplete, left in hidden comment for possible future expansion -->{{Citation needed|date=February 2007}} | |||
The original equation was developed by Howard Penman at the [[Rothamsted Experimental Station]], Harpenden, UK. | |||
The equation for evaporation given by Penman is: | |||
:<math>E_{mass}=\frac{m R_n + \rho_a c_p \left(\delta e \right) g_a }{\lambda_v \left(m + \gamma \right) } | |||
</math> | |||
where: | |||
:''m'' = Slope of the saturation [[vapor pressure]] curve (Pa K<sup>-1</sup>) | |||
:''R''<sub>n</sub> = Net [[irradiance]] (W m<sup>-2</sup>) | |||
:''ρ''<sub>a</sub> = [[density]] of air (kg m<sup>-3</sup>) | |||
:''c''<sub>p</sub> = [[heat capacity]] of air (J kg<sup>-1</sup> K<sup>-1</sup>) | |||
:''g''<sub>a</sub> = momentum surface aerodynamic conductance (m s<sup>-1</sup>) | |||
:δ''e'' = [[vapor pressure]] deficit (Pa) | |||
:''λ''<sub>v</sub> = [[latent heat of vaporization]] (J kg<sup>-1</sup>) | |||
:''γ'' = [[psychrometric constant]] (Pa K<sup>-1</sup>) | |||
which (if the SI units in parentheses are used) will give the evaporation ''E''<sub>mass</sub> in units of kg/(m²·s), kilograms of water evaporated every second for each square meter of area. | |||
Remove λ to obviate that this is fundamentally an energy balance. Replace ''λ''<sub>v</sub> with L to get familiar precipitation units ''ET''<sub>vol</sub>, where ''L''<sub>v</sub>=''λ''<sub>v</sub>''ρ''<sub>water</sub>. This has units of m/s, or more commonly mm/day, because it is flux m<sup>3</sup>/s per m<sup>2</sup>=m/s. | |||
This equation assumes a daily time step so that net heat exchange with the ground is insignificant, and a unit area surrounded by similar open water or vegetation so that net heat & vapor exchange with the surrounding area cancels out. Some times people replace ''R''<sub>n</sub> with and ''A'' for total net available energy when a situation warrants account of additional heat fluxes. | |||
[[temperature]], [[wind speed]], [[relative humidity]] impact the values of ''m'', ''g'', ''c''<sub>p</sub>, ''ρ'', and δ''e''. | |||
==Shuttleworth (1993)== | |||
In 1993, W.Jim Shuttleworth modified and adapted the Penman equation to use [[SI]], which made calculating evaporation simpler.<ref>Shuttleworth, J., Putting the vap' into evaporation http://www.hydrol-earth-syst-sci.net/11/210/2007/hess-11-210-2007.pdf</ref> The resultant equation is: | |||
:<math>E_{mass}=\frac{m R_n + \gamma * 6.43\left(1+0.536 * U_2 \right)\delta e}{\lambda_v \left(m + \gamma \right) } | |||
</math> | |||
where: | |||
:''E''<sub>mass</sub> = Evaporation rate (mm day<sup>-1</sup>) | |||
:''m'' = Slope of the saturation [[vapor pressure]] curve (kPa K<sup>-1</sup>) | |||
:''R''<sub>n</sub> = Net [[irradiance]] (MJ m<sup>-2</sup> day<sup>-1</sup>) | |||
:''γ'' = [[psychrometric constant]] = <math>\frac{0.0016286 * P_{kPa}} {\lambda_v}</math> (kPa K<sup>-1</sup>) | |||
:''U''<sub>2</sub> = wind speed (m s<sup>-1</sup>) | |||
:δ''e'' = [[vapor pressure]] deficit (kPa) | |||
:''λ''<sub>v</sub> = [[latent heat of vaporization]] (MJ kg<sup>-1</sup>) | |||
Note: this formula implicitly includes the division of the numerator by the density of water (1000 kg m<sup>-3</sup>) to obtain evaporation in units of mm d<sup>-1</sup> | |||
==Some useful relationships== | |||
:δ''e'' = (e<sub>s</sub> - e<sub>a</sub>) = (1-[[relative humidity]])e<sub>s</sub> | |||
:''e''<sub>s</sub> = saturated vapor pressure of air, as is found inside plant stoma. | |||
:''e''<sub>a</sub> = vapor pressure of free flowing air. | |||
:''e''<sub>s</sub>, mmHg = exp(21.07-5336/''T''<sub>a</sub>), approximation by Merva, 1975<ref>Merva, G.E. 1975. Physio-engineering Principles. AVI Publishing Company, Westport, CT.</ref> | |||
Therefore <math>m= \Delta =\frac{d e_s}{d T_a} = \frac{5336}{T_a^2} e^{\left(21.07 - \frac{5336}{T_a}\right)}</math>, mmHg/K | |||
:''T''<sub>a</sub> = air temperature in kelvins | |||
==See also== | |||
*[[Pan evaporation]] | |||
*[[Evapotranspiration]] | |||
*[[Thornthwaite model]] | |||
*[[Blaney-Criddle equation]] | |||
*[[Penman-Monteith]] | |||
==Notes== | |||
{{Reflist}} | |||
==References== | |||
{{refbegin}} | |||
* Jarvis, P.G. (1976) The interpretation of the variations in leaf water potential and stomatal conductance found in canopies in the field. Phil. Trans. R. Soc. Lond. B. 273, 593-610. | |||
* Neitsch, S.L.; J.G. Arnold; J.R. Kliniry; J.R. Wolliams. 2005. Soil and Water Assessment Tool Theoretical Document; Version 2005. Grassland, Soil and Water Research Laboratory; Agricultural Research Service. and Blackland Research Center; Texas Agricultural Experiment Station. Temple, Texas. http://www.brc.tamus.edu/swat/downloads/doc/swat2005/SWAT%202005%20theory%20final.pdf | |||
* Penman, H.L. (1948): ''Natural evaporation from open water, bare soil and grass.'' Proc. Roy. Soc. London A(194), S. 120-145. | |||
{{refend}} | |||
{{DEFAULTSORT:Penman Equation}} | |||
[[Category:Agronomy]] | |||
[[Category:Equations]] | |||
[[Category:Hydrology]] | |||
Revision as of 16:53, 21 October 2013
The Penman equation describes evaporation (E) from an open water surface, and was developed by Howard Penman in 1948. Penman's equation requires daily mean temperature, wind speed, relative humidity, and solar radiation to predict E. Simpler Hydrometeorological equations continue to be used where obtaining such data is impractical, to give comparable results within specific contexts, e.g. humid vs arid climates.
Details
Numerous variations of the Penman equation are used to estimate evaporation from water, and land. Specifically the Penman-Monteith equation refines weather based potential evapotranspiration (PET) estimates of vegetated land areas.[1] It is widely regarded as one of the most accurate models, in terms of estimates.Potter or Ceramic Artist Truman Bedell from Rexton, has interests which include ceramics, best property developers in singapore developers in singapore and scrabble. Was especially enthused after visiting Alejandro de Humboldt National Park.
The original equation was developed by Howard Penman at the Rothamsted Experimental Station, Harpenden, UK.
The equation for evaporation given by Penman is:
where:
- m = Slope of the saturation vapor pressure curve (Pa K-1)
- Rn = Net irradiance (W m-2)
- ρa = density of air (kg m-3)
- cp = heat capacity of air (J kg-1 K-1)
- ga = momentum surface aerodynamic conductance (m s-1)
- δe = vapor pressure deficit (Pa)
- λv = latent heat of vaporization (J kg-1)
- γ = psychrometric constant (Pa K-1)
which (if the SI units in parentheses are used) will give the evaporation Emass in units of kg/(m²·s), kilograms of water evaporated every second for each square meter of area.
Remove λ to obviate that this is fundamentally an energy balance. Replace λv with L to get familiar precipitation units ETvol, where Lv=λvρwater. This has units of m/s, or more commonly mm/day, because it is flux m3/s per m2=m/s.
This equation assumes a daily time step so that net heat exchange with the ground is insignificant, and a unit area surrounded by similar open water or vegetation so that net heat & vapor exchange with the surrounding area cancels out. Some times people replace Rn with and A for total net available energy when a situation warrants account of additional heat fluxes.
temperature, wind speed, relative humidity impact the values of m, g, cp, ρ, and δe.
Shuttleworth (1993)
In 1993, W.Jim Shuttleworth modified and adapted the Penman equation to use SI, which made calculating evaporation simpler.[2] The resultant equation is:
where:
- Emass = Evaporation rate (mm day-1)
- m = Slope of the saturation vapor pressure curve (kPa K-1)
- Rn = Net irradiance (MJ m-2 day-1)
- γ = psychrometric constant = (kPa K-1)
- U2 = wind speed (m s-1)
- δe = vapor pressure deficit (kPa)
- λv = latent heat of vaporization (MJ kg-1)
Note: this formula implicitly includes the division of the numerator by the density of water (1000 kg m-3) to obtain evaporation in units of mm d-1
Some useful relationships
- δe = (es - ea) = (1-relative humidity)es
- es = saturated vapor pressure of air, as is found inside plant stoma.
- ea = vapor pressure of free flowing air.
- es, mmHg = exp(21.07-5336/Ta), approximation by Merva, 1975[3]
- Ta = air temperature in kelvins
See also
Notes
43 year old Petroleum Engineer Harry from Deep River, usually spends time with hobbies and interests like renting movies, property developers in singapore new condominium and vehicle racing. Constantly enjoys going to destinations like Camino Real de Tierra Adentro.
References
- Jarvis, P.G. (1976) The interpretation of the variations in leaf water potential and stomatal conductance found in canopies in the field. Phil. Trans. R. Soc. Lond. B. 273, 593-610.
- Neitsch, S.L.; J.G. Arnold; J.R. Kliniry; J.R. Wolliams. 2005. Soil and Water Assessment Tool Theoretical Document; Version 2005. Grassland, Soil and Water Research Laboratory; Agricultural Research Service. and Blackland Research Center; Texas Agricultural Experiment Station. Temple, Texas. http://www.brc.tamus.edu/swat/downloads/doc/swat2005/SWAT%202005%20theory%20final.pdf
- Penman, H.L. (1948): Natural evaporation from open water, bare soil and grass. Proc. Roy. Soc. London A(194), S. 120-145.
- ↑ 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
My blog: http://www.primaboinca.com/view_profile.php?userid=5889534 - ↑ Shuttleworth, J., Putting the vap' into evaporation http://www.hydrol-earth-syst-sci.net/11/210/2007/hess-11-210-2007.pdf
- ↑ Merva, G.E. 1975. Physio-engineering Principles. AVI Publishing Company, Westport, CT.